Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(4049,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4400.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.96668224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 15x^{4} + 61x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.4 | ||
Root | \(0.841083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.4049 |
Dual form | 4400.2.b.bb.4049.3 |
$q$-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 \(\left(\mathbb{Z}/4400\mathbb{Z}\right)^\times\).
\(n\) | \(177\) | \(1201\) | \(2751\) | \(3301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.841083i | 0.485599i | 0.970076 | + | 0.242800i | \(0.0780658\pi\) | ||||
−0.970076 | + | 0.242800i | \(0.921934\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.29258i | 1.24448i | 0.782827 | + | 0.622239i | \(0.213777\pi\) | ||||
−0.782827 | + | 0.622239i | \(0.786223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.29258 | 0.764193 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.15892i | − 0.281079i | −0.990075 | − | 0.140539i | \(-0.955116\pi\) | ||||
0.990075 | − | 0.140539i | \(-0.0448837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.31783 | 0.302332 | 0.151166 | − | 0.988508i | \(-0.451697\pi\) | ||||
0.151166 | + | 0.988508i | \(0.451697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.76933 | −0.604318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.84108i | 0.800921i | 0.916314 | + | 0.400461i | \(0.131150\pi\) | ||||
−0.916314 | + | 0.400461i | \(0.868850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.45150i | 0.856691i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.61041 | −1.22752 | −0.613762 | − | 0.789491i | \(-0.710344\pi\) | ||||
−0.613762 | + | 0.789491i | \(0.710344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.58516 | −1.36233 | −0.681167 | − | 0.732128i | \(-0.738527\pi\) | ||||
−0.681167 | + | 0.732128i | \(0.738527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.841083i | − 0.146414i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.13366i | 0.350772i | 0.984500 | + | 0.175386i | \(0.0561173\pi\) | ||||
−0.984500 | + | 0.175386i | \(0.943883\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.841083 | 0.134681 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.13366 | 0.957917 | 0.478959 | − | 0.877838i | \(-0.341014\pi\) | ||||
0.478959 | + | 0.877838i | \(0.341014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.81583i | 1.34440i | 0.740369 | + | 0.672201i | \(0.234651\pi\) | ||||
−0.740369 | + | 0.672201i | \(0.765349\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.76933i | − 0.403949i | −0.979391 | − | 0.201974i | \(-0.935264\pi\) | ||||
0.979391 | − | 0.201974i | \(-0.0647357\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.84108 | −0.548726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.974745 | 0.136492 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1956i | 1.40047i | 0.713912 | + | 0.700235i | \(0.246921\pi\) | ||||
−0.713912 | + | 0.700235i | \(0.753079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.10841i | 0.146812i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76933 | 0.360536 | 0.180268 | − | 0.983618i | \(-0.442303\pi\) | ||||
0.180268 | + | 0.983618i | \(0.442303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.61041 | −0.462266 | −0.231133 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231133 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.54850i | 0.951022i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.90299i | − 0.354657i | −0.984152 | − | 0.177329i | \(-0.943254\pi\) | ||||
0.984152 | − | 0.177329i | \(-0.0567455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.23067 | −0.388927 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.866337 | −0.102815 | −0.0514077 | − | 0.998678i | \(-0.516371\pi\) | ||||
−0.0514077 | + | 0.998678i | \(0.516371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.87774i | − 0.687937i | −0.938981 | − | 0.343969i | \(-0.888229\pi\) | ||||
0.938981 | − | 0.343969i | \(-0.111771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.29258i | − 0.375224i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7441 | 1.32131 | 0.660656 | − | 0.750689i | \(-0.270278\pi\) | ||||
0.660656 | + | 0.750689i | \(0.270278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.13366 | 0.348185 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.92825i | 0.980003i | 0.871722 | + | 0.490001i | \(0.163004\pi\) | ||||
−0.871722 | + | 0.490001i | \(0.836996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 5.55991i | − 0.596084i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.2926 | −1.51501 | −0.757505 | − | 0.652829i | \(-0.773582\pi\) | ||||
−0.757505 | + | 0.652829i | \(0.773582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.29258 | 0.345156 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.37975i | − 0.661549i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 12.4262i | − 1.26169i | −0.775907 | − | 0.630847i | \(-0.782708\pi\) | ||||
0.775907 | − | 0.630847i | \(-0.217292\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.29258 | −0.230413 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.15892 | 0.214820 | 0.107410 | − | 0.994215i | \(-0.465744\pi\) | ||||
0.107410 | + | 0.994215i | \(0.465744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.07175i | 0.302669i | 0.988483 | + | 0.151334i | \(0.0483570\pi\) | ||||
−0.988483 | + | 0.151334i | \(0.951643\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4882i | 1.59397i | 0.603999 | + | 0.796985i | \(0.293573\pi\) | ||||
−0.603999 | + | 0.796985i | \(0.706427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2926 | −0.985850 | −0.492925 | − | 0.870072i | \(-0.664072\pi\) | ||||
−0.492925 | + | 0.870072i | \(0.664072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.79459 | −0.170335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4980i | 1.08164i | 0.841138 | + | 0.540820i | \(0.181886\pi\) | ||||
−0.841138 | + | 0.540820i | \(0.818114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.29258i | − 0.211949i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.81583 | 0.349796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.15892i | 0.465164i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.37975i | − 0.388640i | −0.980938 | − | 0.194320i | \(-0.937750\pi\) | ||||
0.980938 | − | 0.194320i | \(-0.0622500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.41484 | −0.652840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.01140 | 0.437848 | 0.218924 | − | 0.975742i | \(-0.429745\pi\) | ||||
0.218924 | + | 0.975742i | \(0.429745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.33908i | 0.376246i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 16.2421i | − 1.38765i | −0.720142 | − | 0.693827i | \(-0.755923\pi\) | ||||
0.720142 | − | 0.693827i | \(-0.244077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.7555 | −1.93009 | −0.965047 | − | 0.262076i | \(-0.915593\pi\) | ||||
−0.965047 | + | 0.262076i | \(0.915593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.32924 | 0.196157 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000i | 0.0836242i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 3.23067i | − 0.266461i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.2673 | −1.49652 | −0.748259 | − | 0.663407i | \(-0.769110\pi\) | ||||
−0.748259 | + | 0.663407i | \(0.769110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0832 | −1.30883 | −0.654414 | − | 0.756136i | \(-0.727085\pi\) | ||||
−0.654414 | + | 0.756136i | \(0.727085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.65691i | − 0.214798i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 15.1703i | − 1.21072i | −0.795951 | − | 0.605362i | \(-0.793028\pi\) | ||||
0.795951 | − | 0.605362i | \(-0.206972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.57532 | −0.680067 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.6471 | −0.996729 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.24608i | 0.489231i | 0.969620 | + | 0.244616i | \(0.0786617\pi\) | ||||
−0.969620 | + | 0.244616i | \(0.921338\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.594999i | 0.0460424i | 0.999735 | + | 0.0230212i | \(0.00732852\pi\) | ||||
−0.999735 | + | 0.0230212i | \(0.992671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.02124 | 0.231040 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.31783i | 0.100193i | 0.998744 | + | 0.0500966i | \(0.0159529\pi\) | ||||
−0.998744 | + | 0.0500966i | \(0.984047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.32924i | 0.175076i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.70742 | −0.351849 | −0.175925 | − | 0.984404i | \(-0.556291\pi\) | ||||
−0.175925 | + | 0.984404i | \(0.556291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0212 | −0.744873 | −0.372437 | − | 0.928058i | \(-0.621478\pi\) | ||||
−0.372437 | + | 0.928058i | \(0.621478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.03666i | − 0.224476i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.15892i | 0.0847484i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.6569 | −1.06613 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2421 | −1.17523 | −0.587617 | − | 0.809139i | \(-0.699934\pi\) | ||||
−0.587617 | + | 0.809139i | \(0.699934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3643i | 1.10595i | 0.833198 | + | 0.552974i | \(0.186507\pi\) | ||||
−0.833198 | + | 0.552974i | \(0.813493\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.52325i | 0.536009i | 0.963418 | + | 0.268005i | \(0.0863642\pi\) | ||||
−0.963418 | + | 0.268005i | \(0.913636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.5094 | 1.73742 | 0.868712 | − | 0.495317i | \(-0.164948\pi\) | ||||
0.868712 | + | 0.495317i | \(0.164948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.44166 | 0.172221 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 21.7653i | − 1.52763i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.80599i | 0.612059i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.31783 | −0.0911565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.35449 | −0.368618 | −0.184309 | − | 0.982868i | \(-0.559005\pi\) | ||||
−0.184309 | + | 0.982868i | \(0.559005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 0.728661i | − 0.0499271i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 24.9747i | − 1.69540i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.94367 | 0.334062 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.15892 | −0.0779572 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.40500i | 0.495876i | 0.968776 | + | 0.247938i | \(0.0797529\pi\) | ||||
−0.968776 | + | 0.247938i | \(0.920247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 16.2926i | − 1.08138i | −0.841223 | − | 0.540688i | \(-0.818164\pi\) | ||||
0.841223 | − | 0.540688i | \(-0.181836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0579 | 1.25938 | 0.629691 | − | 0.776846i | \(-0.283182\pi\) | ||||
0.629691 | + | 0.776846i | \(0.283182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.76933 | 0.182209 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.97475i | 0.456931i | 0.973552 | + | 0.228465i | \(0.0733708\pi\) | ||||
−0.973552 | + | 0.228465i | \(0.926629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.87774i | 0.641628i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.513409 | −0.0332097 | −0.0166048 | − | 0.999862i | \(-0.505286\pi\) | ||||
−0.0166048 | + | 0.999862i | \(0.505286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4727 | 0.803440 | 0.401720 | − | 0.915763i | \(-0.368413\pi\) | ||||
0.401720 | + | 0.915763i | \(0.368413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.9902i | 1.02577i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.31783i | − 0.0838518i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50940 | −0.475889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.4727 | −0.913511 | −0.456756 | − | 0.889592i | \(-0.650989\pi\) | ||||
−0.456756 | + | 0.889592i | \(0.650989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.84108i | − 0.241487i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.6218i | 1.41111i | 0.708655 | + | 0.705555i | \(0.249302\pi\) | ||||
−0.708655 | + | 0.705555i | \(0.750698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.02525 | −0.436528 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.1549 | −0.938065 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.5445i | 0.896852i | 0.893820 | + | 0.448426i | \(0.148015\pi\) | ||||
−0.893820 | + | 0.448426i | \(0.851985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 12.0212i | − 0.735688i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.42624 | −0.452786 | −0.226393 | − | 0.974036i | \(-0.572693\pi\) | ||||
−0.226393 | + | 0.974036i | \(0.572693\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.40500 | 0.0853477 | 0.0426739 | − | 0.999089i | \(-0.486412\pi\) | ||||
0.0426739 | + | 0.999089i | \(0.486412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.76933i | 0.167608i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9397i | 1.07789i | 0.842341 | + | 0.538945i | \(0.181177\pi\) | ||||
−0.842341 | + | 0.538945i | \(0.818823\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3896 | −1.04109 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.49799 | −0.327983 | −0.163991 | − | 0.986462i | \(-0.552437\pi\) | ||||
−0.163991 | + | 0.986462i | \(0.552437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.25592i | 0.490764i | 0.969427 | + | 0.245382i | \(0.0789133\pi\) | ||||
−0.969427 | + | 0.245382i | \(0.921087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.1956i | 1.19211i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6569 | 0.920995 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4515 | 0.612678 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6357i | 0.855025i | 0.904009 | + | 0.427512i | \(0.140610\pi\) | ||||
−0.904009 | + | 0.427512i | \(0.859390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.45150i | − 0.258302i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.84108 | 0.222136 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.0268 | −1.67308 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.81583i | 0.104317i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.3292i | − 1.04610i | −0.852301 | − | 0.523052i | \(-0.824793\pi\) | ||||
0.852301 | − | 0.523052i | \(-0.175207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.58360 | −0.146976 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.09701 | −0.345729 | −0.172865 | − | 0.984946i | \(-0.555302\pi\) | ||||
−0.172865 | + | 0.984946i | \(0.555302\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 0.317835i | − 0.0179651i | −0.999960 | − | 0.00898254i | \(-0.997141\pi\) | ||||
0.999960 | − | 0.00898254i | \(-0.00285927\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.3797i | 1.36930i | 0.728871 | + | 0.684651i | \(0.240046\pi\) | ||||
−0.728871 | + | 0.684651i | \(0.759954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.61041 | 0.370112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.8679 | −0.774031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.52726i | − 0.0849791i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 8.65691i | − 0.478728i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.11825 | 0.502705 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.54850 | 0.195043 | 0.0975217 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975217 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.89159i | 0.268058i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 10.0000i | − 0.544735i | −0.962193 | − | 0.272367i | \(-0.912193\pi\) | ||||
0.962193 | − | 0.272367i | \(-0.0878066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.67076 | −0.525244 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.58516 | 0.410759 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4010i | 0.561601i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.70742i | − 0.467439i | −0.972304 | − | 0.233719i | \(-0.924910\pi\) | ||||
0.972304 | − | 0.233719i | \(-0.0750897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8565 | −0.902308 | −0.451154 | − | 0.892446i | \(-0.648987\pi\) | ||||
−0.451154 | + | 0.892446i | \(0.648987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.45150 | 0.237603 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3643i | 0.551638i | 0.961210 | + | 0.275819i | \(0.0889490\pi\) | ||||
−0.961210 | + | 0.275819i | \(0.911051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.20943i | 0.169861i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.9030 | −1.31433 | −0.657165 | − | 0.753747i | \(-0.728244\pi\) | ||||
−0.657165 | + | 0.753747i | \(0.728244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2633 | −0.908595 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.841083i | 0.0441454i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.98860i | − 0.156004i | −0.996953 | − | 0.0780018i | \(-0.975146\pi\) | ||||
0.996953 | − | 0.0780018i | \(-0.0248540\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0619 | 0.732034 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.5697 | −1.74285 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.4475i | − 1.11051i | −0.831681 | − | 0.555254i | \(-0.812621\pi\) | ||||
0.831681 | − | 0.555254i | \(-0.187379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.61041i | 0.340454i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.45150 | 0.331391 | 0.165696 | − | 0.986177i | \(-0.447013\pi\) | ||||
0.165696 | + | 0.986177i | \(0.447013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.68373 | 0.188723 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 22.0872i | − 1.12860i | −0.825569 | − | 0.564301i | \(-0.809146\pi\) | ||||
0.825569 | − | 0.564301i | \(-0.190854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.2110i | 1.02738i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.2633 | 1.58511 | 0.792556 | − | 0.609799i | \(-0.208750\pi\) | ||||
0.792556 | + | 0.609799i | \(0.208750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.45150 | 0.225122 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.21500i | 0.212619i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.74408i | − 0.288287i | −0.989557 | − | 0.144143i | \(-0.953957\pi\) | ||||
0.989557 | − | 0.144143i | \(-0.0460427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.64952 | −0.182705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.1605 | 1.70589 | 0.852947 | − | 0.521998i | \(-0.174813\pi\) | ||||
0.852947 | + | 0.521998i | \(0.174813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.58516i | 0.377844i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.13366i | − 0.105762i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.7188 | 1.02448 | 0.512240 | − | 0.858842i | \(-0.328816\pi\) | ||||
0.512240 | + | 0.858842i | \(0.328816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6609 | 0.673844 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.11825i | 0.448680i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 19.1392i | − 0.937253i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.81984 | 0.333171 | 0.166586 | − | 0.986027i | \(-0.446726\pi\) | ||||
0.166586 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.5134 | −1.77955 | −0.889777 | − | 0.456395i | \(-0.849140\pi\) | ||||
−0.889777 | + | 0.456395i | \(0.849140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 6.34891i | − 0.308695i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11.8876i | − 0.575280i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.841083 | −0.0406079 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4010 | 0.500998 | 0.250499 | − | 0.968117i | \(-0.419405\pi\) | ||||
0.250499 | + | 0.968117i | \(0.419405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.7090i | 1.42772i | 0.700287 | + | 0.713861i | \(0.253055\pi\) | ||||
−0.700287 | + | 0.713861i | \(0.746945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.06191i | 0.242144i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.3292 | −1.44754 | −0.723768 | − | 0.690044i | \(-0.757591\pi\) | ||||
−0.723768 | + | 0.690044i | \(0.757591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.80599 | −0.419333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 25.0465i | − 1.18999i | −0.803728 | − | 0.594997i | \(-0.797153\pi\) | ||||
0.803728 | − | 0.594997i | \(-0.202847\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 15.3643i | − 0.726708i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.2322 | 1.80429 | 0.902145 | − | 0.431432i | \(-0.141992\pi\) | ||||
0.902145 | + | 0.431432i | \(0.141992\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.13366 | −0.288823 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 13.5273i | − 0.635566i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 32.7302i | − 1.53106i | −0.643403 | − | 0.765528i | \(-0.722478\pi\) | ||||
0.643403 | − | 0.765528i | \(-0.277522\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.15892 | 0.240798 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8118 | 0.969303 | 0.484651 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484651 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.51185i | 0.0702614i | 0.999383 | + | 0.0351307i | \(0.0111848\pi\) | ||||
−0.999383 | + | 0.0351307i | \(0.988815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 23.4783i | − 1.08645i | −0.839588 | − | 0.543223i | \(-0.817204\pi\) | ||||
0.839588 | − | 0.543223i | \(-0.182796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.55834 | 0.441363 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7595 | 0.587926 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8.81583i | − 0.405352i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.3742i | 1.07023i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7188 | −0.672520 | −0.336260 | − | 0.941769i | \(-0.609162\pi\) | ||||
−0.336260 | + | 0.941769i | \(0.609162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.13366 | 0.0972866 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 10.6372i | − 0.484011i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.7595i | − 1.07665i | −0.842739 | − | 0.538323i | \(-0.819058\pi\) | ||||
0.842739 | − | 0.538323i | \(-0.180942\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.25347 | −0.237570 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7555 | −0.846423 | −0.423211 | − | 0.906031i | \(-0.639097\pi\) | ||||
−0.423211 | + | 0.906031i | \(0.639097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.66092i | 0.345031i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.85249i | − 0.127951i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.9747 | −1.20756 | −0.603778 | − | 0.797153i | \(-0.706339\pi\) | ||||
−0.603778 | + | 0.797153i | \(0.706339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.500443 | −0.0223582 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.2941i | 1.93039i | 0.261530 | + | 0.965195i | \(0.415773\pi\) | ||||
−0.261530 | + | 0.965195i | \(0.584227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0930i | 0.448246i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.8312 | 0.480086 | 0.240043 | − | 0.970762i | \(-0.422838\pi\) | ||||
0.240043 | + | 0.970762i | \(0.422838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.3529 | 0.856123 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.86634i | 0.259005i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.76933i | 0.121795i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.10841 | −0.0486537 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.1337 | 0.925883 | 0.462941 | − | 0.886389i | \(-0.346794\pi\) | ||||
0.462941 | + | 0.886389i | \(0.346794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.7921i | − 1.39017i | −0.718926 | − | 0.695087i | \(-0.755366\pi\) | ||||
0.718926 | − | 0.695087i | \(-0.244634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.79057i | 0.382923i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.24608 | 0.358525 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.34891 | 0.275519 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 6.13366i | − 0.265678i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 3.95933i | − 0.170858i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.84108 | 0.165447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.3757 | 1.30595 | 0.652977 | − | 0.757377i | \(-0.273520\pi\) | ||||
0.652977 | + | 0.757377i | \(0.273520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.42869i | − 0.361710i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.83707i | − 0.206818i | −0.994639 | − | 0.103409i | \(-0.967025\pi\) | ||||
0.994639 | − | 0.103409i | \(-0.0329751\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.27716 | −0.353261 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.71143 | −0.371120 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.6683i | 1.64434i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.6317i | 1.29790i | 0.760829 | + | 0.648952i | \(0.224793\pi\) | ||||
−0.760829 | + | 0.648952i | \(0.775207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.81583 | 0.372870 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.974745 | −0.0411538 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 14.2461i | − 0.600401i | −0.953876 | − | 0.300200i | \(-0.902946\pi\) | ||||
0.953876 | − | 0.300200i | \(-0.0970536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.3178i | 0.433308i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.3194 | −1.69028 | −0.845139 | − | 0.534547i | \(-0.820482\pi\) | ||||
−0.845139 | + | 0.534547i | \(0.820482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.98860 | 0.376161 | 0.188081 | − | 0.982154i | \(-0.439773\pi\) | ||||
0.188081 | + | 0.982154i | \(0.439773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 13.6609i | − 0.570693i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2787i | 0.427909i | 0.976844 | + | 0.213955i | \(0.0686344\pi\) | ||||
−0.976844 | + | 0.213955i | \(0.931366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9227 | −0.537048 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.3970 | −1.21959 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10.1956i | − 0.422258i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4.52325i | − 0.186694i | −0.995634 | − | 0.0933472i | \(-0.970243\pi\) | ||||
0.995634 | − | 0.0933472i | \(-0.0297567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.99599 | −0.411877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.32767 | −0.260286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.0326i | 1.15116i | 0.817745 | + | 0.575581i | \(0.195224\pi\) | ||||
−0.817745 | + | 0.575581i | \(0.804776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.6144i | 0.843692i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8876 | 0.649149 | 0.324574 | − | 0.945860i | \(-0.394779\pi\) | ||||
0.324574 | + | 0.945860i | \(0.394779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.83124 | 0.197071 | 0.0985353 | − | 0.995134i | \(-0.468584\pi\) | ||||
0.0985353 | + | 0.995134i | \(0.468584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6.65535i | − 0.271027i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2633i | 1.51247i | 0.654299 | + | 0.756236i | \(0.272964\pi\) | ||||
−0.654299 | + | 0.756236i | \(0.727036\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.3064 | 0.741814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.76933 | −0.112035 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 44.1857i | − 1.78465i | −0.451398 | − | 0.892323i | \(-0.649075\pi\) | ||||
0.451398 | − | 0.892323i | \(-0.350925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 13.3080i | − 0.535760i | −0.963452 | − | 0.267880i | \(-0.913677\pi\) | ||||
0.963452 | − | 0.267880i | \(-0.0863230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.4783 | −1.34561 | −0.672804 | − | 0.739821i | \(-0.734910\pi\) | ||||
−0.672804 | + | 0.739821i | \(0.734910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.0986 | −0.686142 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 47.0595i | − 1.88540i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.10841i | − 0.0442655i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.47274 | 0.0985945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.1411 | 1.95627 | 0.978137 | − | 0.207961i | \(-0.0666826\pi\) | ||||
0.978137 | + | 0.207961i | \(0.0666826\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.50357i | − 0.179001i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.84108i | 0.152189i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.98615 | −0.0785708 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.36433 | 0.330371 | 0.165186 | − | 0.986262i | \(-0.447178\pi\) | ||||
0.165186 | + | 0.986262i | \(0.447178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 40.8020i | − 1.60907i | −0.593903 | − | 0.804536i | \(-0.702414\pi\) | ||||
0.593903 | − | 0.804536i | \(-0.297586\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 40.0832i | − 1.57583i | −0.615783 | − | 0.787916i | \(-0.711160\pi\) | ||||
0.615783 | − | 0.787916i | \(-0.288840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.76933 | −0.108706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0058 | 0.823283 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.1352i | − 0.553154i | −0.960992 | − | 0.276577i | \(-0.910800\pi\) | ||||
0.960992 | − | 0.276577i | \(-0.0892001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 13.4752i | − 0.525717i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.51341 | −0.0589541 | −0.0294770 | − | 0.999565i | \(-0.509384\pi\) | ||||
−0.0294770 | + | 0.999565i | \(0.509384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4050 | 0.599185 | 0.299593 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299593 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.974745i | − 0.0378560i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 25.3911i | − 0.983149i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.22822 | −0.240797 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.61041 | 0.139379 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 36.8426i | − 1.42018i | −0.704111 | − | 0.710090i | \(-0.748654\pi\) | ||||
0.704111 | − | 0.710090i | \(-0.251346\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.0367i | 1.07754i | 0.842454 | + | 0.538768i | \(0.181110\pi\) | ||||
−0.842454 | + | 0.538768i | \(0.818890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.9144 | 1.57015 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.7034 | 0.525116 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.7416i | 1.09977i | 0.835241 | + | 0.549884i | \(0.185328\pi\) | ||||
−0.835241 | + | 0.549884i | \(0.814672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0293i | 0.611555i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.1956 | 0.388420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.2729 | 0.885343 | 0.442671 | − | 0.896684i | \(-0.354031\pi\) | ||||
0.442671 | + | 0.896684i | \(0.354031\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.54850i | − 0.286744i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7.10841i | − 0.269250i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.86634 | −0.221885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.8891 | −1.01559 | −0.507794 | − | 0.861478i | \(-0.669539\pi\) | ||||
−0.507794 | + | 0.861478i | \(0.669539\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.81181i | 0.106050i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.10841i | 0.267339i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6357 | 0.624766 | 0.312383 | − | 0.949956i | \(-0.398873\pi\) | ||||
0.312383 | + | 0.949956i | \(0.398873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.9242 | 1.00974 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 29.1352i | − 1.09112i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 0.431820i | − 0.0161266i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.8158 | −0.440656 | −0.220328 | − | 0.975426i | \(-0.570713\pi\) | ||||
−0.220328 | + | 0.975426i | \(0.570713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.1140 | −0.376664 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.4906i | 0.390150i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7767i | 1.14145i | 0.821143 | + | 0.570723i | \(0.193337\pi\) | ||||
−0.821143 | + | 0.570723i | \(0.806663\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.04806 | −0.149928 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2168 | 0.377883 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6782i | 0.874572i | 0.899322 | + | 0.437286i | \(0.144060\pi\) | ||||
−0.899322 | + | 0.437286i | \(0.855940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.90299i | 0.106933i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.6569 | 1.12773 | 0.563866 | − | 0.825866i | \(-0.309313\pi\) | ||||
0.563866 | + | 0.825866i | \(0.309313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.10841 | 0.0407184 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.4164i | 0.638946i | 0.947595 | + | 0.319473i | \(0.103506\pi\) | ||||
−0.947595 | + | 0.319473i | \(0.896494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.4687i | 0.748911i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.2886 | −1.98366 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2926 | 0.886449 | 0.443224 | − | 0.896411i | \(-0.353834\pi\) | ||||
0.443224 | + | 0.896411i | \(0.353834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 12.1728i | − 0.443600i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1565i | 1.24144i | 0.784033 | + | 0.620719i | \(0.213159\pi\) | ||||
−0.784033 | + | 0.620719i | \(0.786841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.23067 | 0.117266 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.5347 | 1.90438 | 0.952190 | − | 0.305507i | \(-0.0988260\pi\) | ||||
0.952190 | + | 0.305507i | \(0.0988260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 33.8891i | − 1.22687i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.76933i | − 0.0999948i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4010 | 0.879922 | 0.439961 | − | 0.898017i | \(-0.354992\pi\) | ||||
0.439961 | + | 0.898017i | \(0.354992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.0268 | −0.685234 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2966i | 0.442278i | 0.975242 | + | 0.221139i | \(0.0709774\pi\) | ||||
−0.975242 | + | 0.221139i | \(0.929023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 5.90882i | − 0.211978i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.08315 | 0.289609 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.866337 | 0.0310000 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 29.4262i | − 1.05161i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.66831i | 0.0951151i | 0.998868 | + | 0.0475575i | \(0.0151437\pi\) | ||||
−0.998868 | + | 0.0475575i | \(0.984856\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.2331 | −0.435511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.8581 | −1.34608 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.61041i | 0.128210i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2054i | 0.928243i | 0.885771 | + | 0.464122i | \(0.153630\pi\) | ||||
−0.885771 | + | 0.464122i | \(0.846370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.20943 | −0.113541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.7669 | −1.15776 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.87774i | 0.207421i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6.24608i | − 0.219873i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.0733 | 0.705740 | 0.352870 | − | 0.935672i | \(-0.385206\pi\) | ||||
0.352870 | + | 0.935672i | \(0.385206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2575 | 0.500648 | 0.250324 | − | 0.968162i | \(-0.419463\pi\) | ||||
0.250324 | + | 0.968162i | \(0.419463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.18172i | 0.0414448i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6178i | 0.406455i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.54850 | 0.263766 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0872 | −0.561446 | −0.280723 | − | 0.959789i | \(-0.590574\pi\) | ||||
−0.280723 | + | 0.959789i | \(0.590574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6120i | 0.962493i | 0.876585 | + | 0.481247i | \(0.159816\pi\) | ||||
−0.876585 | + | 0.481247i | \(0.840184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.4980i | 0.712785i | 0.934336 | + | 0.356393i | \(0.115993\pi\) | ||||
−0.934336 | + | 0.356393i | \(0.884007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.5232 | 1.06012 | 0.530058 | − | 0.847961i | \(-0.322170\pi\) | ||||
0.530058 | + | 0.847961i | \(0.322170\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0887 | −0.523422 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.45150i | 0.154235i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 33.7653i | − 1.16710i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.8737 | −0.996832 | −0.498416 | − | 0.866938i | \(-0.666085\pi\) | ||||
−0.498416 | + | 0.866938i | \(0.666085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.6976 | 0.506813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.62427i | − 0.159268i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.29258i | 0.113134i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.94391 | −0.238314 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.19557 | −0.280941 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.5729i | 1.62886i | 0.580259 | + | 0.814432i | \(0.302951\pi\) | ||||
−0.580259 | + | 0.814432i | \(0.697049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.7148i | 0.673445i | 0.941604 | + | 0.336723i | \(0.109318\pi\) | ||||
−0.941604 | + | 0.336723i | \(0.890682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.6822 | 1.62689 | 0.813447 | − | 0.581639i | \(-0.197588\pi\) | ||||
0.813447 | + | 0.581639i | \(0.197588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.9861 | −0.578886 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 15.8297i | − 0.538849i | −0.963022 | − | 0.269424i | \(-0.913167\pi\) | ||||
0.963022 | − | 0.269424i | \(-0.0868334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.1688i | 0.447234i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7441 | −0.398391 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.90299 | −0.0983642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 28.4882i | − 0.964178i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 43.5248i | − 1.46973i | −0.678214 | − | 0.734864i | \(-0.737246\pi\) | ||||
0.678214 | − | 0.734864i | \(-0.262754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.3098 | −0.415200 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.5461 | 1.80401 | 0.902006 | − | 0.431723i | \(-0.142094\pi\) | ||||
0.902006 | + | 0.431723i | \(0.142094\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.2535i | 1.52290i | 0.648223 | + | 0.761450i | \(0.275512\pi\) | ||||
−0.648223 | + | 0.761450i | \(0.724488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.54850i | 0.0519936i | 0.999662 | + | 0.0259968i | \(0.00827598\pi\) | ||||
−0.999662 | + | 0.0259968i | \(0.991724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4207 | 0.483654 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.13366 | −0.104982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.64952i | − 0.122127i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.23067i | 0.107869i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.1411 | 1.67230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8158 | 0.393642 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 24.4140i | − 0.812446i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.7090i | 1.35172i | 0.737030 | + | 0.675860i | \(0.236228\pi\) | ||||
−0.737030 | + | 0.675860i | \(0.763772\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.94949 | 0.164164 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9030 | 0.825073 | 0.412537 | − | 0.910941i | \(-0.364643\pi\) | ||||
0.412537 | + | 0.910941i | \(0.364643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 8.92825i | − 0.295482i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.5004i | 0.544893i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.09299 | −0.0690414 | −0.0345207 | − | 0.999404i | \(-0.510990\pi\) | ||||
−0.0345207 | + | 0.999404i | \(0.510990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4164 | 0.507988 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.866337i | 0.0285158i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.04223i | 0.231297i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.7555 | 1.20591 | 0.602954 | − | 0.797776i | \(-0.293990\pi\) | ||||
0.602954 | + | 0.797776i | \(0.293990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.06191 | −0.165897 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.12809i | − 0.167886i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 50.2673i | − 1.64216i | −0.570812 | − | 0.821081i | \(-0.693371\pi\) | ||||
0.570812 | − | 0.821081i | \(-0.306629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.267325 | 0.00872383 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.3000 | 1.31374 | 0.656871 | − | 0.754003i | \(-0.271880\pi\) | ||||
0.656871 | + | 0.754003i | \(0.271880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.5599i | 0.767216i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 0.133663i | − 0.00434345i | −0.999998 | − | 0.00217173i | \(-0.999309\pi\) | ||||
0.999998 | − | 0.00217173i | \(-0.000691282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.87774 | −0.190800 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5054 | −0.664933 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 0.728661i | − 0.0236037i | −0.999930 | − | 0.0118018i | \(-0.996243\pi\) | ||||
0.999930 | − | 0.0118018i | \(-0.00375673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.55991i | 0.179726i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.4783 | 1.72690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.5347 | 0.855956 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.8004i | 1.21810i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.5769i | 1.81939i | 0.415277 | + | 0.909695i | \(0.363685\pi\) | ||||
−0.415277 | + | 0.909695i | \(0.636315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28455 | 0.0412658 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.8232 | −1.56681 | −0.783406 | − | 0.621511i | \(-0.786519\pi\) | ||||
−0.783406 | + | 0.621511i | \(0.786519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 74.9242i | − 2.40196i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.21099i | − 0.230700i | −0.993325 | − | 0.115350i | \(-0.963201\pi\) | ||||
0.993325 | − | 0.115350i | \(-0.0367990\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2926 | 0.456793 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.5966 | −0.753380 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 58.4278i | − 1.86356i | −0.363027 | − | 0.931779i | \(-0.618257\pi\) | ||||
0.363027 | − | 0.931779i | \(-0.381743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.66920i | 0.244113i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.8623 | −1.07676 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0114 | 0.762747 | 0.381374 | − | 0.924421i | \(-0.375451\pi\) | ||||
0.381374 | + | 0.924421i | \(0.375451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.98458i | 0.0947129i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.4222i | 1.21684i | 0.793614 | + | 0.608422i | \(0.208197\pi\) | ||||
−0.793614 | + | 0.608422i | \(0.791803\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.49799 | −0.300503 |
(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 | 4400.2.b.bb.4049.4 | 6 | ||
4.3 | odd | 2 | 2200.2.b.m.1849.3 | 6 | |||
5.2 | odd | 4 | 4400.2.a.bz.1.2 | 3 | |||
5.3 | odd | 4 | 4400.2.a.by.1.2 | 3 | |||
5.4 | even | 2 | inner | 4400.2.b.bb.4049.3 | 6 | ||
20.3 | even | 4 | 2200.2.a.v.1.2 | yes | 3 | ||
20.7 | even | 4 | 2200.2.a.u.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 2200.2.b.m.1849.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.u.1.2 | ✓ | 3 | 20.7 | even | 4 | ||
2200.2.a.v.1.2 | yes | 3 | 20.3 | even | 4 | ||
2200.2.b.m.1849.3 | 6 | 4.3 | odd | 2 | |||
2200.2.b.m.1849.4 | 6 | 20.19 | odd | 2 | |||
4400.2.a.by.1.2 | 3 | 5.3 | odd | 4 | |||
4400.2.a.bz.1.2 | 3 | 5.2 | odd | 4 | |||
4400.2.b.bb.4049.3 | 6 | 5.4 | even | 2 | inner | ||
4400.2.b.bb.4049.4 | 6 | 1.1 | even | 1 | trivial |