Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,5,Mod(80,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.80");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.37296700979\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.39400128.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{9} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Root | \(-1.28901 + 2.23263i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.80 |
Dual form | 81.5.b.a.80.5 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.46526i | − 1.11632i | −0.829735 | − | 0.558158i | \(-0.811508\pi\) | ||||
0.829735 | − | 0.558158i | \(-0.188492\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.93857 | −0.246161 | ||||||||
\(5\) | 16.0226i | 0.640904i | 0.947265 | + | 0.320452i | \(0.103835\pi\) | ||||
−0.947265 | + | 0.320452i | \(0.896165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 72.4837 | 1.47926 | 0.739630 | − | 0.673014i | \(-0.235001\pi\) | ||||
0.739630 | + | 0.673014i | \(0.235001\pi\) | |||||||
\(8\) | − 53.8574i | − 0.841523i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 71.5451 | 0.715451 | ||||||||
\(11\) | − 96.1576i | − 0.794691i | −0.917669 | − | 0.397345i | \(-0.869932\pi\) | ||||
0.917669 | − | 0.397345i | \(-0.130068\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 153.906 | 0.910686 | 0.455343 | − | 0.890316i | \(-0.349517\pi\) | ||||
0.455343 | + | 0.890316i | \(0.349517\pi\) | |||||||
\(14\) | − 323.659i | − 1.65132i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −303.505 | −1.18557 | ||||||||
\(17\) | − 72.7905i | − 0.251870i | −0.992038 | − | 0.125935i | \(-0.959807\pi\) | ||||
0.992038 | − | 0.125935i | \(-0.0401931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −190.660 | −0.528145 | −0.264072 | − | 0.964503i | \(-0.585066\pi\) | ||||
−0.264072 | + | 0.964503i | \(0.585066\pi\) | |||||||
\(20\) | − 63.1062i | − 0.157765i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −429.369 | −0.887126 | ||||||||
\(23\) | − 14.4552i | − 0.0273256i | −0.999907 | − | 0.0136628i | \(-0.995651\pi\) | ||||
0.999907 | − | 0.0136628i | \(-0.00434914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 368.276 | 0.589242 | ||||||||
\(26\) | − 687.231i | − 1.01661i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −285.482 | −0.364135 | ||||||||
\(29\) | − 716.262i | − 0.851679i | −0.904799 | − | 0.425839i | \(-0.859979\pi\) | ||||
0.904799 | − | 0.425839i | \(-0.140021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −302.568 | −0.314847 | −0.157423 | − | 0.987531i | \(-0.550319\pi\) | ||||
−0.157423 | + | 0.987531i | \(0.550319\pi\) | |||||||
\(32\) | 493.509i | 0.481943i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −325.029 | −0.281167 | ||||||||
\(35\) | 1161.38i | 0.948063i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 826.277 | 0.603562 | 0.301781 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(38\) | 851.348i | 0.589576i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 862.936 | 0.539335 | ||||||||
\(41\) | 556.119i | 0.330826i | 0.986224 | + | 0.165413i | \(0.0528958\pi\) | ||||
−0.986224 | + | 0.165413i | \(0.947104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 892.680 | 0.482791 | 0.241395 | − | 0.970427i | \(-0.422395\pi\) | ||||
0.241395 | + | 0.970427i | \(0.422395\pi\) | |||||||
\(44\) | 378.723i | 0.195622i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −64.5464 | −0.0305040 | ||||||||
\(47\) | 3955.43i | 1.79060i | 0.445465 | + | 0.895299i | \(0.353038\pi\) | ||||
−0.445465 | + | 0.895299i | \(0.646962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2852.89 | 1.18821 | ||||||||
\(50\) | − 1644.45i | − 0.657780i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −606.170 | −0.224175 | ||||||||
\(53\) | 1966.96i | 0.700234i | 0.936706 | + | 0.350117i | \(0.113858\pi\) | ||||
−0.936706 | + | 0.350117i | \(0.886142\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1540.69 | 0.509320 | ||||||||
\(56\) | − 3903.79i | − 1.24483i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3198.30 | −0.950742 | ||||||||
\(59\) | 5414.94i | 1.55557i | 0.628530 | + | 0.777785i | \(0.283657\pi\) | ||||
−0.628530 | + | 0.777785i | \(0.716343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1712.42 | −0.460204 | −0.230102 | − | 0.973166i | \(-0.573906\pi\) | ||||
−0.230102 | + | 0.973166i | \(0.573906\pi\) | |||||||
\(62\) | 1351.04i | 0.351468i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2652.43 | −0.647565 | ||||||||
\(65\) | 2465.97i | 0.583663i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4634.49 | −1.03241 | −0.516205 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516205 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(68\) | 286.691i | 0.0620006i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5185.86 | 1.05834 | ||||||||
\(71\) | − 6697.12i | − 1.32853i | −0.747497 | − | 0.664265i | \(-0.768744\pi\) | ||||
0.747497 | − | 0.664265i | \(-0.231256\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4823.86 | −0.905208 | −0.452604 | − | 0.891712i | \(-0.649505\pi\) | ||||
−0.452604 | + | 0.891712i | \(0.649505\pi\) | |||||||
\(74\) | − 3689.54i | − 0.673766i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 750.929 | 0.130008 | ||||||||
\(77\) | − 6969.86i | − 1.17555i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5728.79 | −0.917929 | −0.458964 | − | 0.888455i | \(-0.651779\pi\) | ||||
−0.458964 | + | 0.888455i | \(0.651779\pi\) | |||||||
\(80\) | − 4862.94i | − 0.759834i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2483.22 | 0.369307 | ||||||||
\(83\) | − 2832.23i | − 0.411124i | −0.978644 | − | 0.205562i | \(-0.934098\pi\) | ||||
0.978644 | − | 0.205562i | \(-0.0659022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1166.29 | 0.161425 | ||||||||
\(86\) | − 3986.05i | − 0.538947i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5178.80 | −0.668750 | ||||||||
\(89\) | 14277.7i | 1.80251i | 0.433290 | + | 0.901255i | \(0.357353\pi\) | ||||
−0.433290 | + | 0.901255i | \(0.642647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11155.7 | 1.34714 | ||||||||
\(92\) | 56.9330i | 0.00672649i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17662.0 | 1.99887 | ||||||||
\(95\) | − 3054.87i | − 0.338490i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7165.31 | 0.761538 | 0.380769 | − | 0.924670i | \(-0.375659\pi\) | ||||
0.380769 | + | 0.924670i | \(0.375659\pi\) | |||||||
\(98\) | − 12738.9i | − 1.32641i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1450.48 | −0.145048 | ||||||||
\(101\) | 1959.20i | 0.192060i | 0.995378 | + | 0.0960298i | \(0.0306144\pi\) | ||||
−0.995378 | + | 0.0960298i | \(0.969386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5155.48 | −0.485953 | −0.242976 | − | 0.970032i | \(-0.578124\pi\) | ||||
−0.242976 | + | 0.970032i | \(0.578124\pi\) | |||||||
\(104\) | − 8288.98i | − 0.766363i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8782.98 | 0.781682 | ||||||||
\(107\) | − 9117.08i | − 0.796321i | −0.917316 | − | 0.398161i | \(-0.869649\pi\) | ||||
0.917316 | − | 0.398161i | \(-0.130351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16161.1 | −1.36024 | −0.680122 | − | 0.733099i | \(-0.738073\pi\) | ||||
−0.680122 | + | 0.733099i | \(0.738073\pi\) | |||||||
\(110\) | − 6879.60i | − 0.568562i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21999.2 | −1.75376 | ||||||||
\(113\) | 21099.2i | 1.65238i | 0.563393 | + | 0.826189i | \(0.309496\pi\) | ||||
−0.563393 | + | 0.826189i | \(0.690504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 231.611 | 0.0175131 | ||||||||
\(116\) | 2821.05i | 0.209650i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24179.1 | 1.73651 | ||||||||
\(119\) | − 5276.13i | − 0.372582i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5394.72 | 0.368467 | ||||||||
\(122\) | 7646.41i | 0.513733i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1191.68 | 0.0775029 | ||||||||
\(125\) | 15914.9i | 1.01855i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20660.9 | −1.28098 | −0.640489 | − | 0.767968i | \(-0.721268\pi\) | ||||
−0.640489 | + | 0.767968i | \(0.721268\pi\) | |||||||
\(128\) | 19739.9i | 1.20483i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11011.2 | 0.651552 | ||||||||
\(131\) | 3201.45i | 0.186554i | 0.995640 | + | 0.0932768i | \(0.0297342\pi\) | ||||
−0.995640 | + | 0.0932768i | \(0.970266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13819.8 | −0.781263 | ||||||||
\(134\) | 20694.2i | 1.15250i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3920.31 | −0.211955 | ||||||||
\(137\) | 3871.92i | 0.206293i | 0.994666 | + | 0.103147i | \(0.0328911\pi\) | ||||
−0.994666 | + | 0.103147i | \(0.967109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11679.2 | −0.604484 | −0.302242 | − | 0.953231i | \(-0.597735\pi\) | ||||
−0.302242 | + | 0.953231i | \(0.597735\pi\) | |||||||
\(140\) | − 4574.17i | − 0.233376i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −29904.4 | −1.48306 | ||||||||
\(143\) | − 14799.2i | − 0.723714i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11476.4 | 0.545844 | ||||||||
\(146\) | 21539.8i | 1.01050i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3254.35 | −0.148573 | ||||||||
\(149\) | − 15091.8i | − 0.679778i | −0.940466 | − | 0.339889i | \(-0.889610\pi\) | ||||
0.940466 | − | 0.339889i | \(-0.110390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30255.3 | 1.32693 | 0.663465 | − | 0.748207i | \(-0.269085\pi\) | ||||
0.663465 | + | 0.748207i | \(0.269085\pi\) | |||||||
\(152\) | 10268.5i | 0.444446i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −31122.2 | −1.31229 | ||||||||
\(155\) | − 4847.92i | − 0.201787i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20622.7 | 0.836656 | 0.418328 | − | 0.908296i | \(-0.362616\pi\) | ||||
0.418328 | + | 0.908296i | \(0.362616\pi\) | |||||||
\(158\) | 25580.6i | 1.02470i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7907.31 | −0.308879 | ||||||||
\(161\) | − 1047.77i | − 0.0404216i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 39790.7 | 1.49764 | 0.748818 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748818 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(164\) | − 2190.31i | − 0.0814364i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12646.7 | −0.458944 | ||||||||
\(167\) | − 27450.7i | − 0.984283i | −0.870515 | − | 0.492141i | \(-0.836214\pi\) | ||||
0.870515 | − | 0.492141i | \(-0.163786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4873.95 | −0.170651 | ||||||||
\(170\) | − 5207.81i | − 0.180201i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3515.89 | −0.118844 | ||||||||
\(173\) | − 10079.7i | − 0.336787i | −0.985720 | − | 0.168393i | \(-0.946142\pi\) | ||||
0.985720 | − | 0.168393i | \(-0.0538578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26694.0 | 0.871642 | ||||||||
\(176\) | 29184.3i | 0.942158i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 63753.6 | 2.01217 | ||||||||
\(179\) | − 1215.45i | − 0.0379343i | −0.999820 | − | 0.0189672i | \(-0.993962\pi\) | ||||
0.999820 | − | 0.0189672i | \(-0.00603779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28359.9 | 0.865661 | 0.432831 | − | 0.901475i | \(-0.357515\pi\) | ||||
0.432831 | + | 0.901475i | \(0.357515\pi\) | |||||||
\(182\) | − 49813.0i | − 1.50383i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −778.522 | −0.0229951 | ||||||||
\(185\) | 13239.1i | 0.386826i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6999.36 | −0.200159 | ||||||||
\(188\) | − 15578.8i | − 0.440775i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13640.8 | −0.377862 | ||||||||
\(191\) | 9751.84i | 0.267313i | 0.991028 | + | 0.133656i | \(0.0426719\pi\) | ||||
−0.991028 | + | 0.133656i | \(0.957328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −53402.8 | −1.43367 | −0.716836 | − | 0.697242i | \(-0.754410\pi\) | ||||
−0.716836 | + | 0.697242i | \(0.754410\pi\) | |||||||
\(194\) | − 31995.0i | − 0.850117i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11236.3 | −0.292490 | ||||||||
\(197\) | − 68537.7i | − 1.76603i | −0.469349 | − | 0.883013i | \(-0.655511\pi\) | ||||
0.469349 | − | 0.883013i | \(-0.344489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8237.42 | −0.208010 | −0.104005 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104005 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(200\) | − 19834.4i | − 0.495860i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8748.34 | 0.214399 | ||||||||
\(203\) | − 51917.3i | − 1.25985i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8910.47 | −0.212028 | ||||||||
\(206\) | 23020.6i | 0.542477i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −46711.2 | −1.07968 | ||||||||
\(209\) | 18333.4i | 0.419712i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40787.4 | 0.916138 | 0.458069 | − | 0.888917i | \(-0.348541\pi\) | ||||
0.458069 | + | 0.888917i | \(0.348541\pi\) | |||||||
\(212\) | − 7747.00i | − 0.172370i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −40710.2 | −0.888946 | ||||||||
\(215\) | 14303.1i | 0.309423i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21931.2 | −0.465740 | ||||||||
\(218\) | 72163.4i | 1.51846i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6068.13 | −0.125375 | ||||||||
\(221\) | − 11202.9i | − 0.229375i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −59919.6 | −1.20492 | −0.602461 | − | 0.798148i | \(-0.705813\pi\) | ||||
−0.602461 | + | 0.798148i | \(0.705813\pi\) | |||||||
\(224\) | 35771.4i | 0.712918i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 94213.5 | 1.84458 | ||||||||
\(227\) | − 98810.4i | − 1.91757i | −0.284134 | − | 0.958785i | \(-0.591706\pi\) | ||||
0.284134 | − | 0.958785i | \(-0.408294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5317.94 | −0.101408 | −0.0507040 | − | 0.998714i | \(-0.516147\pi\) | ||||
−0.0507040 | + | 0.998714i | \(0.516147\pi\) | |||||||
\(230\) | − 1034.20i | − 0.0195501i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −38576.0 | −0.716707 | ||||||||
\(233\) | 18467.8i | 0.340176i | 0.985429 | + | 0.170088i | \(0.0544052\pi\) | ||||
−0.985429 | + | 0.170088i | \(0.945595\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −63376.3 | −1.14760 | ||||||||
\(236\) | − 21327.1i | − 0.382920i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23559.3 | −0.415919 | ||||||||
\(239\) | 25846.2i | 0.452482i | 0.974071 | + | 0.226241i | \(0.0726437\pi\) | ||||
−0.974071 | + | 0.226241i | \(0.927356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 83072.3 | 1.43028 | 0.715142 | − | 0.698979i | \(-0.246362\pi\) | ||||
0.715142 | + | 0.698979i | \(0.246362\pi\) | |||||||
\(242\) | − 24088.9i | − 0.411325i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6744.49 | 0.113284 | ||||||||
\(245\) | 45710.7i | 0.761527i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29343.8 | −0.480974 | ||||||||
\(248\) | 16295.5i | 0.264951i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 71064.1 | 1.13703 | ||||||||
\(251\) | − 49051.6i | − 0.778585i | −0.921114 | − | 0.389292i | \(-0.872720\pi\) | ||||
0.921114 | − | 0.389292i | \(-0.127280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1389.98 | −0.0217154 | ||||||||
\(254\) | 92256.3i | 1.42998i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 45705.2 | 0.697405 | ||||||||
\(257\) | 97105.7i | 1.47021i | 0.677955 | + | 0.735104i | \(0.262867\pi\) | ||||
−0.677955 | + | 0.735104i | \(0.737133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 59891.6 | 0.892825 | ||||||||
\(260\) | − 9712.41i | − 0.143675i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14295.3 | 0.208253 | ||||||||
\(263\) | − 41478.0i | − 0.599662i | −0.953992 | − | 0.299831i | \(-0.903070\pi\) | ||||
0.953992 | − | 0.299831i | \(-0.0969303\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31515.8 | −0.448783 | ||||||||
\(266\) | 61708.9i | 0.872136i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18253.3 | 0.254139 | ||||||||
\(269\) | 115737.i | 1.59944i | 0.600370 | + | 0.799722i | \(0.295020\pi\) | ||||
−0.600370 | + | 0.799722i | \(0.704980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5077.71 | −0.0691400 | −0.0345700 | − | 0.999402i | \(-0.511006\pi\) | ||||
−0.0345700 | + | 0.999402i | \(0.511006\pi\) | |||||||
\(272\) | 22092.3i | 0.298609i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17289.1 | 0.230289 | ||||||||
\(275\) | − 35412.5i | − 0.468265i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −42385.8 | −0.552409 | −0.276205 | − | 0.961099i | \(-0.589077\pi\) | ||||
−0.276205 | + | 0.961099i | \(0.589077\pi\) | |||||||
\(278\) | 52150.9i | 0.674795i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 62548.8 | 0.797817 | ||||||||
\(281\) | 41456.6i | 0.525027i | 0.964928 | + | 0.262513i | \(0.0845514\pi\) | ||||
−0.964928 | + | 0.262513i | \(0.915449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 38388.0 | 0.479316 | 0.239658 | − | 0.970857i | \(-0.422965\pi\) | ||||
0.239658 | + | 0.970857i | \(0.422965\pi\) | |||||||
\(284\) | 26377.1i | 0.327032i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −66082.4 | −0.807893 | ||||||||
\(287\) | 40309.6i | 0.489378i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 78222.5 | 0.936561 | ||||||||
\(290\) | − 51245.0i | − 0.609335i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18999.1 | 0.222827 | ||||||||
\(293\) | − 12978.2i | − 0.151175i | −0.997139 | − | 0.0755876i | \(-0.975917\pi\) | ||||
0.997139 | − | 0.0755876i | \(-0.0240833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −86761.4 | −0.996971 | ||||||||
\(296\) | − 44501.2i | − 0.507911i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −67388.7 | −0.758847 | ||||||||
\(299\) | − 2224.75i | − 0.0248850i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 64704.8 | 0.714173 | ||||||||
\(302\) | − 135098.i | − 1.48127i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 57866.3 | 0.626150 | ||||||||
\(305\) | − 27437.4i | − 0.294947i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −126105. | −1.33799 | −0.668997 | − | 0.743265i | \(-0.733276\pi\) | ||||
−0.668997 | + | 0.743265i | \(0.733276\pi\) | |||||||
\(308\) | 27451.3i | 0.289375i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21647.2 | −0.225258 | ||||||||
\(311\) | − 99803.5i | − 1.03187i | −0.856628 | − | 0.515935i | \(-0.827445\pi\) | ||||
0.856628 | − | 0.515935i | \(-0.172555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2225.35 | −0.0227148 | −0.0113574 | − | 0.999936i | \(-0.503615\pi\) | ||||
−0.0113574 | + | 0.999936i | \(0.503615\pi\) | |||||||
\(314\) | − 92085.9i | − 0.933972i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22563.3 | 0.225958 | ||||||||
\(317\) | 168069.i | 1.67251i | 0.548342 | + | 0.836254i | \(0.315259\pi\) | ||||
−0.548342 | + | 0.836254i | \(0.684741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −68874.0 | −0.676821 | ||||||||
\(320\) | − 42498.8i | − 0.415027i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4678.56 | −0.0451233 | ||||||||
\(323\) | 13878.3i | 0.133024i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 56679.9 | 0.536615 | ||||||||
\(326\) | − 177676.i | − 1.67183i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29951.1 | 0.278398 | ||||||||
\(329\) | 286704.i | 2.64876i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6758.86 | 0.0616904 | 0.0308452 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308452 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(332\) | 11154.9i | 0.101202i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −122574. | −1.09877 | ||||||||
\(335\) | − 74256.6i | − 0.661676i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −222093. | −1.95557 | −0.977787 | − | 0.209600i | \(-0.932784\pi\) | ||||
−0.977787 | + | 0.209600i | \(0.932784\pi\) | |||||||
\(338\) | 21763.5i | 0.190500i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4593.53 | −0.0397364 | ||||||||
\(341\) | 29094.2i | 0.250206i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 32754.4 | 0.278408 | ||||||||
\(344\) | − 48077.5i | − 0.406280i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −45008.4 | −0.375960 | ||||||||
\(347\) | − 162548.i | − 1.34996i | −0.737835 | − | 0.674981i | \(-0.764152\pi\) | ||||
0.737835 | − | 0.674981i | \(-0.235848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −72696.9 | −0.596850 | −0.298425 | − | 0.954433i | \(-0.596461\pi\) | ||||
−0.298425 | + | 0.954433i | \(0.596461\pi\) | |||||||
\(350\) | − 119196.i | − 0.973027i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 47454.7 | 0.382995 | ||||||||
\(353\) | − 128629.i | − 1.03226i | −0.856509 | − | 0.516131i | \(-0.827372\pi\) | ||||
0.856509 | − | 0.516131i | \(-0.172628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 107305. | 0.851461 | ||||||||
\(356\) | − 56233.6i | − 0.443707i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5427.32 | −0.0423467 | ||||||||
\(359\) | − 95302.8i | − 0.739463i | −0.929139 | − | 0.369732i | \(-0.879450\pi\) | ||||
0.929139 | − | 0.369732i | \(-0.120550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −93969.7 | −0.721063 | ||||||||
\(362\) | − 126635.i | − 0.966351i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −43937.4 | −0.331613 | ||||||||
\(365\) | − 77290.7i | − 0.580152i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 104146. | 0.773233 | 0.386616 | − | 0.922241i | \(-0.373644\pi\) | ||||
0.386616 | + | 0.922241i | \(0.373644\pi\) | |||||||
\(368\) | 4387.23i | 0.0323963i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 59116.1 | 0.431820 | ||||||||
\(371\) | 142572.i | 1.03583i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 245831. | 1.76693 | 0.883463 | − | 0.468501i | \(-0.155206\pi\) | ||||
0.883463 | + | 0.468501i | \(0.155206\pi\) | |||||||
\(374\) | 31254.0i | 0.223441i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 213029. | 1.50683 | ||||||||
\(377\) | − 110237.i | − 0.775612i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 200830. | 1.39814 | 0.699070 | − | 0.715053i | \(-0.253597\pi\) | ||||
0.699070 | + | 0.715053i | \(0.253597\pi\) | |||||||
\(380\) | 12031.8i | 0.0833230i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 43544.5 | 0.298406 | ||||||||
\(383\) | 135338.i | 0.922615i | 0.887240 | + | 0.461308i | \(0.152620\pi\) | ||||
−0.887240 | + | 0.461308i | \(0.847380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 111675. | 0.753417 | ||||||||
\(386\) | 238458.i | 1.60043i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28221.1 | −0.187461 | ||||||||
\(389\) | 202177.i | 1.33608i | 0.744126 | + | 0.668039i | \(0.232866\pi\) | ||||
−0.744126 | + | 0.668039i | \(0.767134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1052.20 | −0.00688251 | ||||||||
\(392\) | − 153649.i | − 0.999904i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −306039. | −1.97144 | ||||||||
\(395\) | − 91790.2i | − 0.588304i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 102384. | 0.649608 | 0.324804 | − | 0.945781i | \(-0.394702\pi\) | ||||
0.324804 | + | 0.945781i | \(0.394702\pi\) | |||||||
\(398\) | 36782.2i | 0.232205i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −111774. | −0.698585 | ||||||||
\(401\) | − 90097.2i | − 0.560302i | −0.959956 | − | 0.280151i | \(-0.909615\pi\) | ||||
0.959956 | − | 0.280151i | \(-0.0903846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46567.0 | −0.286727 | ||||||||
\(404\) | − 7716.45i | − 0.0472775i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −231824. | −1.40639 | ||||||||
\(407\) | − 79452.8i | − 0.479645i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 149722. | 0.895033 | 0.447517 | − | 0.894276i | \(-0.352309\pi\) | ||||
0.447517 | + | 0.894276i | \(0.352309\pi\) | |||||||
\(410\) | 39787.6i | 0.236690i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20305.2 | 0.119623 | ||||||||
\(413\) | 392495.i | 2.30109i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45379.7 | 0.263491 | ||||||||
\(416\) | 75954.1i | 0.438899i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 81863.6 | 0.468531 | ||||||||
\(419\) | 126351.i | 0.719697i | 0.933011 | + | 0.359848i | \(0.117172\pi\) | ||||
−0.933011 | + | 0.359848i | \(0.882828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −215289. | −1.21467 | −0.607335 | − | 0.794446i | \(-0.707762\pi\) | ||||
−0.607335 | + | 0.794446i | \(0.707762\pi\) | |||||||
\(422\) | − 182126.i | − 1.02270i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 105935. | 0.589263 | ||||||||
\(425\) | − 26807.0i | − 0.148413i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −124123. | −0.680762 | ||||||||
\(428\) | 35908.3i | 0.196023i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 63866.9 | 0.345413 | ||||||||
\(431\) | 121972.i | 0.656607i | 0.944572 | + | 0.328304i | \(0.106477\pi\) | ||||
−0.944572 | + | 0.328304i | \(0.893523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −152419. | −0.812951 | −0.406475 | − | 0.913662i | \(-0.633242\pi\) | ||||
−0.406475 | + | 0.913662i | \(0.633242\pi\) | |||||||
\(434\) | 97928.7i | 0.519913i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63651.5 | 0.334839 | ||||||||
\(437\) | 2756.04i | 0.0144319i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 231128. | 1.19929 | 0.599643 | − | 0.800267i | \(-0.295309\pi\) | ||||
0.599643 | + | 0.800267i | \(0.295309\pi\) | |||||||
\(440\) | − 82977.9i | − 0.428605i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −50023.9 | −0.256055 | ||||||||
\(443\) | 20185.7i | 0.102858i | 0.998677 | + | 0.0514289i | \(0.0163775\pi\) | ||||
−0.998677 | + | 0.0514289i | \(0.983622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −228766. | −1.15524 | ||||||||
\(446\) | 267557.i | 1.34507i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −192258. | −0.957917 | ||||||||
\(449\) | 92962.8i | 0.461123i | 0.973058 | + | 0.230561i | \(0.0740562\pi\) | ||||
−0.973058 | + | 0.230561i | \(0.925944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53475.0 | 0.262905 | ||||||||
\(452\) | − 83100.7i | − 0.406750i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −441215. | −2.14061 | ||||||||
\(455\) | 178743.i | 0.863388i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 220887. | 1.05764 | 0.528819 | − | 0.848735i | \(-0.322635\pi\) | ||||
0.528819 | + | 0.848735i | \(0.322635\pi\) | |||||||
\(458\) | 23746.0i | 0.113203i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −912.215 | −0.00431103 | ||||||||
\(461\) | − 106195.i | − 0.499690i | −0.968286 | − | 0.249845i | \(-0.919620\pi\) | ||||
0.968286 | − | 0.249845i | \(-0.0803797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −68179.9 | −0.318049 | −0.159025 | − | 0.987275i | \(-0.550835\pi\) | ||||
−0.159025 | + | 0.987275i | \(0.550835\pi\) | |||||||
\(464\) | 217389.i | 1.00972i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 82463.6 | 0.379744 | ||||||||
\(467\) | − 224350.i | − 1.02871i | −0.857578 | − | 0.514353i | \(-0.828032\pi\) | ||||
0.857578 | − | 0.514353i | \(-0.171968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −335925. | −1.52720 | ||||||||
\(470\) | 282992.i | 1.28109i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 291635. | 1.30905 | ||||||||
\(473\) | − 85838.0i | − 0.383669i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −70215.6 | −0.311205 | ||||||||
\(476\) | 20780.4i | 0.0917149i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 115410. | 0.505113 | ||||||||
\(479\) | 109169.i | 0.475802i | 0.971289 | + | 0.237901i | \(0.0764594\pi\) | ||||
−0.971289 | + | 0.237901i | \(0.923541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 127169. | 0.549656 | ||||||||
\(482\) | − 370940.i | − 1.59665i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21247.5 | −0.0907021 | ||||||||
\(485\) | 114807.i | 0.488073i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 106309. | 0.448240 | 0.224120 | − | 0.974562i | \(-0.428049\pi\) | ||||
0.224120 | + | 0.974562i | \(0.428049\pi\) | |||||||
\(488\) | 92226.6i | 0.387272i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 204110. | 0.850105 | ||||||||
\(491\) | − 74446.6i | − 0.308803i | −0.988008 | − | 0.154402i | \(-0.950655\pi\) | ||||
0.988008 | − | 0.154402i | \(-0.0493450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −52137.1 | −0.214513 | ||||||||
\(494\) | 131028.i | 0.536919i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 91830.8 | 0.373271 | ||||||||
\(497\) | − 485432.i | − 1.96524i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −111207. | −0.446612 | −0.223306 | − | 0.974748i | \(-0.571685\pi\) | ||||
−0.223306 | + | 0.974748i | \(0.571685\pi\) | |||||||
\(500\) | − 62681.8i | − 0.250727i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −219028. | −0.869146 | ||||||||
\(503\) | − 115897.i | − 0.458077i | −0.973417 | − | 0.229038i | \(-0.926442\pi\) | ||||
0.973417 | − | 0.229038i | \(-0.0735581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31391.5 | −0.123092 | ||||||||
\(506\) | 6206.63i | 0.0242412i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 81374.4 | 0.315326 | ||||||||
\(509\) | − 196644.i | − 0.759007i | −0.925190 | − | 0.379503i | \(-0.876095\pi\) | ||||
0.925190 | − | 0.379503i | \(-0.123905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −349651. | −1.33904 | ||||||||
\(512\) | 111753.i | 0.426305i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 433603. | 1.64122 | ||||||||
\(515\) | − 82604.1i | − 0.311449i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 380345. | 1.42297 | ||||||||
\(518\) | − 267432.i | − 0.996675i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 132811. | 0.491165 | ||||||||
\(521\) | − 299306.i | − 1.10266i | −0.834289 | − | 0.551328i | \(-0.814121\pi\) | ||||
0.834289 | − | 0.551328i | \(-0.185879\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −162892. | −0.595520 | −0.297760 | − | 0.954641i | \(-0.596240\pi\) | ||||
−0.297760 | + | 0.954641i | \(0.596240\pi\) | |||||||
\(524\) | − 12609.1i | − 0.0459222i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −185210. | −0.669412 | ||||||||
\(527\) | 22024.1i | 0.0793006i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279632. | 0.999253 | ||||||||
\(530\) | 140726.i | 0.500983i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 54430.1 | 0.192316 | ||||||||
\(533\) | 85590.0i | 0.301279i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 146079. | 0.510365 | ||||||||
\(536\) | 249602.i | 0.868796i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 516798. | 1.78548 | ||||||||
\(539\) | − 274327.i | − 0.944257i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −62918.7 | −0.214974 | −0.107487 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107487 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(542\) | 22673.3i | 0.0771820i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 35922.8 | 0.121387 | ||||||||
\(545\) | − 258942.i | − 0.871786i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14807.1 | −0.0494876 | −0.0247438 | − | 0.999694i | \(-0.507877\pi\) | ||||
−0.0247438 | + | 0.999694i | \(0.507877\pi\) | |||||||
\(548\) | − 15249.8i | − 0.0507813i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −158126. | −0.522732 | ||||||||
\(551\) | 136563.i | 0.449810i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −415244. | −1.35785 | ||||||||
\(554\) | 189264.i | 0.616663i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 45999.5 | 0.148800 | ||||||||
\(557\) | − 254392.i | − 0.819962i | −0.912094 | − | 0.409981i | \(-0.865535\pi\) | ||||
0.912094 | − | 0.409981i | \(-0.134465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 137389. | 0.439671 | ||||||||
\(560\) | − 352484.i | − 1.12399i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 185115. | 0.586096 | ||||||||
\(563\) | 93307.5i | 0.294374i | 0.989109 | + | 0.147187i | \(0.0470220\pi\) | ||||
−0.989109 | + | 0.147187i | \(0.952978\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −338064. | −1.05902 | ||||||||
\(566\) | − 171412.i | − 0.535068i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −360690. | −1.11799 | ||||||||
\(569\) | 158024.i | 0.488089i | 0.969764 | + | 0.244045i | \(0.0784744\pi\) | ||||
−0.969764 | + | 0.244045i | \(0.921526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −438375. | −1.34454 | −0.672270 | − | 0.740306i | \(-0.734681\pi\) | ||||
−0.672270 | + | 0.740306i | \(0.734681\pi\) | |||||||
\(572\) | 58287.8i | 0.178150i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 179993. | 0.546300 | ||||||||
\(575\) | − 5323.52i | − 0.0161014i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 214770. | 0.645094 | 0.322547 | − | 0.946554i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946554i | \(0.395461\pi\) | |||||||
\(578\) | − 349284.i | − 1.04550i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −45200.5 | −0.134365 | ||||||||
\(581\) | − 205291.i | − 0.608158i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 189138. | 0.556469 | ||||||||
\(584\) | 259801.i | 0.761753i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −57951.3 | −0.168759 | ||||||||
\(587\) | − 656412.i | − 1.90502i | −0.304502 | − | 0.952512i | \(-0.598490\pi\) | ||||
0.304502 | − | 0.952512i | \(-0.401510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57687.6 | 0.166285 | ||||||||
\(590\) | 387413.i | 1.11293i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −250779. | −0.715563 | ||||||||
\(593\) | 118369.i | 0.336612i | 0.985735 | + | 0.168306i | \(0.0538296\pi\) | ||||
−0.985735 | + | 0.168306i | \(0.946170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 84537.3 | 0.238789 | ||||||||
\(596\) | 59440.0i | 0.167335i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9934.08 | −0.0277796 | ||||||||
\(599\) | − 354139.i | − 0.987006i | −0.869744 | − | 0.493503i | \(-0.835716\pi\) | ||||
0.869744 | − | 0.493503i | \(-0.164284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −595639. | −1.64905 | −0.824526 | − | 0.565824i | \(-0.808558\pi\) | ||||
−0.824526 | + | 0.565824i | \(0.808558\pi\) | |||||||
\(602\) | − 288924.i | − 0.797242i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −119163. | −0.326638 | ||||||||
\(605\) | 86437.5i | 0.236152i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9721.62 | 0.0263853 | 0.0131926 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131926 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(608\) | − 94092.6i | − 0.254536i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −122515. | −0.329254 | ||||||||
\(611\) | 608765.i | 1.63067i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 194450. | 0.517473 | 0.258736 | − | 0.965948i | \(-0.416694\pi\) | ||||
0.258736 | + | 0.965948i | \(0.416694\pi\) | |||||||
\(614\) | 563090.i | 1.49362i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −375379. | −0.989255 | ||||||||
\(617\) | 487639.i | 1.28094i | 0.767984 | + | 0.640469i | \(0.221260\pi\) | ||||
−0.767984 | + | 0.640469i | \(0.778740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17256.5 | 0.0450371 | 0.0225185 | − | 0.999746i | \(-0.492832\pi\) | ||||
0.0225185 | + | 0.999746i | \(0.492832\pi\) | |||||||
\(620\) | 19093.9i | 0.0496719i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −445649. | −1.15189 | ||||||||
\(623\) | 1.03490e6i | 2.66638i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24825.0 | −0.0635520 | ||||||||
\(626\) | 9936.78i | 0.0253569i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −81224.1 | −0.205952 | ||||||||
\(629\) | − 60145.1i | − 0.152019i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −429836. | −1.07955 | −0.539777 | − | 0.841808i | \(-0.681491\pi\) | ||||
−0.539777 | + | 0.841808i | \(0.681491\pi\) | |||||||
\(632\) | 308538.i | 0.772458i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 750471. | 1.86705 | ||||||||
\(635\) | − 331041.i | − 0.820984i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 439076. | 1.08208 | ||||||||
\(638\) | 307540.i | 0.755546i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −316285. | −0.772181 | ||||||||
\(641\) | 32308.0i | 0.0786310i | 0.999227 | + | 0.0393155i | \(0.0125177\pi\) | ||||
−0.999227 | + | 0.0393155i | \(0.987482\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 277048. | 0.670091 | 0.335045 | − | 0.942202i | \(-0.391248\pi\) | ||||
0.335045 | + | 0.942202i | \(0.391248\pi\) | |||||||
\(644\) | 4126.71i | 0.00995022i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 61970.1 | 0.148497 | ||||||||
\(647\) | 125452.i | 0.299689i | 0.988710 | + | 0.149844i | \(0.0478773\pi\) | ||||
−0.988710 | + | 0.149844i | \(0.952123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 520687. | 1.23620 | ||||||||
\(650\) | − 253091.i | − 0.599031i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −156718. | −0.368659 | ||||||||
\(653\) | 283982.i | 0.665985i | 0.942930 | + | 0.332992i | \(0.108058\pi\) | ||||
−0.942930 | + | 0.332992i | \(0.891942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51295.5 | −0.119563 | ||||||||
\(656\) | − 168785.i | − 0.392216i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.28021e6 | 2.95685 | ||||||||
\(659\) | − 359272.i | − 0.827280i | −0.910440 | − | 0.413640i | \(-0.864257\pi\) | ||||
0.910440 | − | 0.413640i | \(-0.135743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 197804. | 0.452723 | 0.226362 | − | 0.974043i | \(-0.427317\pi\) | ||||
0.226362 | + | 0.974043i | \(0.427317\pi\) | |||||||
\(662\) | − 30180.1i | − 0.0688659i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −152537. | −0.345970 | ||||||||
\(665\) | − 221429.i | − 0.500715i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10353.7 | −0.0232726 | ||||||||
\(668\) | 108116.i | 0.242292i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −331575. | −0.738639 | ||||||||
\(671\) | 164662.i | 0.365720i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 238072. | 0.525628 | 0.262814 | − | 0.964847i | \(-0.415349\pi\) | ||||
0.262814 | + | 0.964847i | \(0.415349\pi\) | |||||||
\(674\) | 991702.i | 2.18304i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19196.4 | 0.0420075 | ||||||||
\(677\) | − 250150.i | − 0.545787i | −0.962044 | − | 0.272894i | \(-0.912019\pi\) | ||||
0.962044 | − | 0.272894i | \(-0.0879807\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 519368. | 1.12651 | ||||||||
\(680\) | − 62813.6i | − 0.135843i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 129913. | 0.279309 | ||||||||
\(683\) | − 267358.i | − 0.573129i | −0.958061 | − | 0.286564i | \(-0.907487\pi\) | ||||
0.958061 | − | 0.286564i | \(-0.0925132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62038.2 | −0.132214 | ||||||||
\(686\) | − 146257.i | − 0.310791i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −270933. | −0.572380 | ||||||||
\(689\) | 302727.i | 0.637694i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 336686. | 0.705129 | 0.352565 | − | 0.935787i | \(-0.385310\pi\) | ||||
0.352565 | + | 0.935787i | \(0.385310\pi\) | |||||||
\(692\) | 39699.5i | 0.0829036i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −725817. | −1.50698 | ||||||||
\(695\) | − 187132.i | − 0.387417i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40480.2 | 0.0833253 | ||||||||
\(698\) | 324611.i | 0.666273i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −105136. | −0.214564 | ||||||||
\(701\) | − 635795.i | − 1.29384i | −0.762557 | − | 0.646921i | \(-0.776056\pi\) | ||||
0.762557 | − | 0.646921i | \(-0.223944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −157538. | −0.318768 | ||||||||
\(704\) | 255051.i | 0.514614i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −574363. | −1.15233 | ||||||||
\(707\) | 142010.i | 0.284106i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 431026. | 0.857455 | 0.428728 | − | 0.903434i | \(-0.358962\pi\) | ||||
0.428728 | + | 0.903434i | \(0.358962\pi\) | |||||||
\(710\) | − 479147.i | − 0.950499i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 768959. | 1.51685 | ||||||||
\(713\) | 4373.69i | 0.00860337i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 237122. | 0.463831 | ||||||||
\(716\) | 4787.15i | 0.00933793i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −425552. | −0.825475 | ||||||||
\(719\) | 798370.i | 1.54435i | 0.635409 | + | 0.772176i | \(0.280832\pi\) | ||||
−0.635409 | + | 0.772176i | \(0.719168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −373688. | −0.718850 | ||||||||
\(722\) | 419599.i | 0.804934i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −111698. | −0.213092 | ||||||||
\(725\) | − 263782.i | − 0.501845i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 317113. | 0.599992 | 0.299996 | − | 0.953940i | \(-0.403015\pi\) | ||||
0.299996 | + | 0.953940i | \(0.403015\pi\) | |||||||
\(728\) | − 600816.i | − 1.13365i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −345123. | −0.647632 | ||||||||
\(731\) | − 64978.7i | − 0.121601i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −977843. | −1.81996 | −0.909979 | − | 0.414654i | \(-0.863902\pi\) | ||||
−0.909979 | + | 0.414654i | \(0.863902\pi\) | |||||||
\(734\) | − 465039.i | − 0.863172i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7133.80 | 0.0131694 | ||||||||
\(737\) | 445641.i | 0.820446i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −392565. | −0.718825 | −0.359412 | − | 0.933179i | \(-0.617023\pi\) | ||||
−0.359412 | + | 0.933179i | \(0.617023\pi\) | |||||||
\(740\) | − 52143.2i | − 0.0952213i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 636623. | 1.15631 | ||||||||
\(743\) | 1.03860e6i | 1.88135i | 0.339314 | + | 0.940673i | \(0.389805\pi\) | ||||
−0.339314 | + | 0.940673i | \(0.610195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 241809. | 0.435673 | ||||||||
\(746\) | − 1.09770e6i | − 1.97245i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27567.5 | 0.0492713 | ||||||||
\(749\) | − 660840.i | − 1.17797i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 319565. | 0.566604 | 0.283302 | − | 0.959031i | \(-0.408570\pi\) | ||||
0.283302 | + | 0.959031i | \(0.408570\pi\) | |||||||
\(752\) | − 1.20049e6i | − 2.12287i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −492237. | −0.865828 | ||||||||
\(755\) | 484769.i | 0.850435i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 500321. | 0.873085 | 0.436543 | − | 0.899684i | \(-0.356203\pi\) | ||||
0.436543 | + | 0.899684i | \(0.356203\pi\) | |||||||
\(758\) | − 896760.i | − 1.56077i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −164528. | −0.284847 | ||||||||
\(761\) | − 904875.i | − 1.56250i | −0.624220 | − | 0.781249i | \(-0.714583\pi\) | ||||
0.624220 | − | 0.781249i | \(-0.285417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.17141e6 | −2.01215 | ||||||||
\(764\) | − 38408.3i | − 0.0658019i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 604318. | 1.02993 | ||||||||
\(767\) | 833392.i | 1.41664i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 143377. | 0.242453 | 0.121227 | − | 0.992625i | \(-0.461317\pi\) | ||||
0.121227 | + | 0.992625i | \(0.461317\pi\) | |||||||
\(770\) | − 498659.i | − 0.841051i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 210331. | 0.352914 | ||||||||
\(773\) | − 710063.i | − 1.18833i | −0.804342 | − | 0.594166i | \(-0.797482\pi\) | ||||
0.804342 | − | 0.594166i | \(-0.202518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −111428. | −0.185521 | ||||||||
\(776\) | − 385905.i | − 0.640851i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 902772. | 1.49148 | ||||||||
\(779\) | − 106030.i | − 0.174724i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −643979. | −1.05577 | ||||||||
\(782\) | 4698.37i | 0.00768305i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −865865. | −1.40870 | ||||||||
\(785\) | 330430.i | 0.536216i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −601711. | −0.971490 | −0.485745 | − | 0.874101i | \(-0.661452\pi\) | ||||
−0.485745 | + | 0.874101i | \(0.661452\pi\) | |||||||
\(788\) | 269941.i | 0.434726i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −409867. | −0.656733 | ||||||||
\(791\) | 1.52935e6i | 2.44429i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −263552. | −0.419102 | ||||||||
\(794\) | − 457172.i | − 0.725168i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32443.7 | 0.0512040 | ||||||||
\(797\) | − 429811.i | − 0.676645i | −0.941030 | − | 0.338322i | \(-0.890141\pi\) | ||||
0.941030 | − | 0.338322i | \(-0.109859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 287918. | 0.450999 | ||||||||
\(800\) | 181748.i | 0.283981i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −402308. | −0.625474 | ||||||||
\(803\) | 463850.i | 0.719361i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16788.0 | 0.0259064 | ||||||||
\(806\) | 207934.i | 0.320077i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 105517. | 0.161622 | ||||||||
\(809\) | − 629639.i | − 0.962042i | −0.876709 | − | 0.481021i | \(-0.840266\pi\) | ||||
0.876709 | − | 0.481021i | \(-0.159734\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 577760. | 0.878428 | 0.439214 | − | 0.898383i | \(-0.355257\pi\) | ||||
0.439214 | + | 0.898383i | \(0.355257\pi\) | |||||||
\(812\) | 204480.i | 0.310126i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −354778. | −0.535436 | ||||||||
\(815\) | 637550.i | 0.959841i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −170199. | −0.254984 | ||||||||
\(818\) | − 668548.i | − 0.999140i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35094.5 | 0.0521929 | ||||||||
\(821\) | − 44719.6i | − 0.0663455i | −0.999450 | − | 0.0331727i | \(-0.989439\pi\) | ||||
0.999450 | − | 0.0331727i | \(-0.0105612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −292578. | −0.431958 | −0.215979 | − | 0.976398i | \(-0.569294\pi\) | ||||
−0.215979 | + | 0.976398i | \(0.569294\pi\) | |||||||
\(824\) | 277661.i | 0.408940i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.75259e6 | 2.56874 | ||||||||
\(827\) | − 806491.i | − 1.17920i | −0.807694 | − | 0.589601i | \(-0.799285\pi\) | ||||
0.807694 | − | 0.589601i | \(-0.200715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 204904. | 0.298154 | 0.149077 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149077 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(830\) | − 202632.i | − 0.294139i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −408224. | −0.589729 | ||||||||
\(833\) | − 207663.i | − 0.299274i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 439831. | 0.630831 | ||||||||
\(836\) | − 72207.5i | − 0.103317i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 564189. | 0.803409 | ||||||||
\(839\) | − 771105.i | − 1.09544i | −0.836661 | − | 0.547721i | \(-0.815495\pi\) | ||||
0.836661 | − | 0.547721i | \(-0.184505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 194250. | 0.274643 | ||||||||
\(842\) | 961324.i | 1.35596i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −160644. | −0.225517 | ||||||||
\(845\) | − 78093.4i | − 0.109371i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 391030. | 0.545058 | ||||||||
\(848\) | − 596981.i | − 0.830173i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −119700. | −0.165675 | ||||||||
\(851\) | − 11944.0i | − 0.0164927i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.08237e6 | 1.48757 | 0.743784 | − | 0.668420i | \(-0.233029\pi\) | ||||
0.743784 | + | 0.668420i | \(0.233029\pi\) | |||||||
\(854\) | 554240.i | 0.759945i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −491023. | −0.670122 | ||||||||
\(857\) | 533345.i | 0.726183i | 0.931753 | + | 0.363092i | \(0.118279\pi\) | ||||
−0.931753 | + | 0.363092i | \(0.881721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.13105e6 | 1.53283 | 0.766417 | − | 0.642343i | \(-0.222038\pi\) | ||||
0.766417 | + | 0.642343i | \(0.222038\pi\) | |||||||
\(860\) | − 56333.6i | − 0.0761677i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 544637. | 0.732981 | ||||||||
\(863\) | 110025.i | 0.147730i | 0.997268 | + | 0.0738649i | \(0.0235334\pi\) | ||||
−0.997268 | + | 0.0738649i | \(0.976467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 161503. | 0.215848 | ||||||||
\(866\) | 680592.i | 0.907510i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 86377.7 | 0.114647 | ||||||||
\(869\) | 550867.i | 0.729470i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −713275. | −0.940202 | ||||||||
\(872\) | 870394.i | 1.14468i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12306.4 | 0.0161105 | ||||||||
\(875\) | 1.15357e6i | 1.50670i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −408753. | −0.531450 | −0.265725 | − | 0.964049i | \(-0.585611\pi\) | ||||
−0.265725 | + | 0.964049i | \(0.585611\pi\) | |||||||
\(878\) | − 1.03205e6i | − 1.33878i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −467608. | −0.603833 | ||||||||
\(881\) | − 235809.i | − 0.303815i | −0.988395 | − | 0.151907i | \(-0.951458\pi\) | ||||
0.988395 | − | 0.151907i | \(-0.0485416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −273719. | −0.351061 | −0.175531 | − | 0.984474i | \(-0.556164\pi\) | ||||
−0.175531 | + | 0.984474i | \(0.556164\pi\) | |||||||
\(884\) | 44123.4i | 0.0564631i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 90134.6 | 0.114822 | ||||||||
\(887\) | 371896.i | 0.472687i | 0.971670 | + | 0.236344i | \(0.0759491\pi\) | ||||
−0.971670 | + | 0.236344i | \(0.924051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.49758e6 | −1.89490 | ||||||||
\(890\) | 1.02150e6i | 1.28961i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 235997. | 0.296604 | ||||||||
\(893\) | − 754144.i | − 0.945695i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19474.7 | 0.0243122 | ||||||||
\(896\) | 1.43082e6i | 1.78226i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 415103. | 0.514758 | ||||||||
\(899\) | 216718.i | 0.268148i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 143176. | 0.176368 | ||||||||
\(902\) | − 238780.i | − 0.293484i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.13635e6 | 1.39051 | ||||||||
\(905\) | 454400.i | 0.554806i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −143931. | −0.174960 | −0.0874801 | − | 0.996166i | \(-0.527881\pi\) | ||||
−0.0874801 | + | 0.996166i | \(0.527881\pi\) | |||||||
\(908\) | 389172.i | 0.472030i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 798134. | 0.963814 | ||||||||
\(911\) | 891661.i | 1.07439i | 0.843457 | + | 0.537196i | \(0.180517\pi\) | ||||
−0.843457 | + | 0.537196i | \(0.819483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −272340. | −0.326716 | ||||||||
\(914\) | − 986317.i | − 1.18066i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20945.1 | 0.0249627 | ||||||||
\(917\) | 232053.i | 0.275961i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −582156. | −0.689300 | −0.344650 | − | 0.938731i | \(-0.612002\pi\) | ||||
−0.344650 | + | 0.938731i | \(0.612002\pi\) | |||||||
\(920\) | − 12474.0i | − 0.0147377i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −474187. | −0.557812 | ||||||||
\(923\) | − 1.03073e6i | − 1.20987i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 304298. | 0.355644 | ||||||||
\(926\) | 304441.i | 0.355043i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 353482. | 0.410460 | ||||||||
\(929\) | 771371.i | 0.893782i | 0.894588 | + | 0.446891i | \(0.147469\pi\) | ||||
−0.894588 | + | 0.446891i | \(0.852531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −543932. | −0.627546 | ||||||||
\(932\) | − 72736.8i | − 0.0837380i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.00178e6 | −1.14836 | ||||||||
\(935\) | − 112148.i | − 0.128283i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46097e6 | −1.66403 | −0.832015 | − | 0.554753i | \(-0.812813\pi\) | ||||
−0.832015 | + | 0.554753i | \(0.812813\pi\) | |||||||
\(938\) | 1.49999e6i | 1.70484i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 249612. | 0.282494 | ||||||||
\(941\) | 169346.i | 0.191248i | 0.995418 | + | 0.0956240i | \(0.0304846\pi\) | ||||
−0.995418 | + | 0.0956240i | \(0.969515\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8038.83 | 0.00904002 | ||||||||
\(944\) | − 1.64346e6i | − 1.84423i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −383289. | −0.428296 | ||||||||
\(947\) | − 593888.i | − 0.662224i | −0.943591 | − | 0.331112i | \(-0.892576\pi\) | ||||
0.943591 | − | 0.331112i | \(-0.107424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −742420. | −0.824361 | ||||||||
\(950\) | 313531.i | 0.347403i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −284159. | −0.313536 | ||||||||
\(953\) | 1.25477e6i | 1.38159i | 0.723050 | + | 0.690796i | \(0.242740\pi\) | ||||
−0.723050 | + | 0.690796i | \(0.757260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −156250. | −0.171322 | ||||||||
\(956\) | − 101797.i | − 0.111383i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 487466. | 0.531145 | ||||||||
\(959\) | 280651.i | 0.305161i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −831974. | −0.900872 | ||||||||
\(962\) | − 567843.i | − 0.613590i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −327186. | −0.352080 | ||||||||
\(965\) | − 855652.i | − 0.918846i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.05786e6 | −1.13129 | −0.565645 | − | 0.824649i | \(-0.691373\pi\) | ||||
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(968\) | − 290546.i | − 0.310073i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 512643. | 0.544843 | ||||||||
\(971\) | − 775745.i | − 0.822774i | −0.911461 | − | 0.411387i | \(-0.865044\pi\) | ||||
0.911461 | − | 0.411387i | \(-0.134956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −846555. | −0.894189 | ||||||||
\(974\) | − 474696.i | − 0.500377i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 519728. | 0.545603 | ||||||||
\(977\) | − 496516.i | − 0.520168i | −0.965586 | − | 0.260084i | \(-0.916250\pi\) | ||||
0.965586 | − | 0.260084i | \(-0.0837503\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.37291e6 | 1.43244 | ||||||||
\(980\) | − 180035.i | − 0.187458i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −332424. | −0.344722 | ||||||||
\(983\) | − 300964.i | − 0.311464i | −0.987799 | − | 0.155732i | \(-0.950226\pi\) | ||||
0.987799 | − | 0.155732i | \(-0.0497736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.09815e6 | 1.13185 | ||||||||
\(986\) | 232806.i | 0.239464i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 115572. | 0.118397 | ||||||||
\(989\) | − 12903.9i | − 0.0131925i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.70094e6 | 1.73197 | 0.865987 | − | 0.500067i | \(-0.166691\pi\) | ||||
0.865987 | + | 0.500067i | \(0.166691\pi\) | |||||||
\(992\) | − 149320.i | − 0.151738i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.16758e6 | −2.19383 | ||||||||
\(995\) | − 131985.i | − 0.133315i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −625837. | −0.629609 | −0.314805 | − | 0.949156i | \(-0.601939\pi\) | ||||
−0.314805 | + | 0.949156i | \(0.601939\pi\) | |||||||
\(998\) | 496568.i | 0.498560i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 81.5.b.a.80.2 | 6 | ||
3.2 | odd | 2 | inner | 81.5.b.a.80.5 | 6 | ||
4.3 | odd | 2 | 1296.5.e.c.161.5 | 6 | |||
9.2 | odd | 6 | 9.5.d.a.5.3 | yes | 6 | ||
9.4 | even | 3 | 9.5.d.a.2.3 | ✓ | 6 | ||
9.5 | odd | 6 | 27.5.d.a.8.1 | 6 | |||
9.7 | even | 3 | 27.5.d.a.17.1 | 6 | |||
12.11 | even | 2 | 1296.5.e.c.161.2 | 6 | |||
36.7 | odd | 6 | 432.5.q.a.17.1 | 6 | |||
36.11 | even | 6 | 144.5.q.a.113.3 | 6 | |||
36.23 | even | 6 | 432.5.q.a.305.1 | 6 | |||
36.31 | odd | 6 | 144.5.q.a.65.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.3 | ✓ | 6 | 9.4 | even | 3 | ||
9.5.d.a.5.3 | yes | 6 | 9.2 | odd | 6 | ||
27.5.d.a.8.1 | 6 | 9.5 | odd | 6 | |||
27.5.d.a.17.1 | 6 | 9.7 | even | 3 | |||
81.5.b.a.80.2 | 6 | 1.1 | even | 1 | trivial | ||
81.5.b.a.80.5 | 6 | 3.2 | odd | 2 | inner | ||
144.5.q.a.65.3 | 6 | 36.31 | odd | 6 | |||
144.5.q.a.113.3 | 6 | 36.11 | even | 6 | |||
432.5.q.a.17.1 | 6 | 36.7 | odd | 6 | |||
432.5.q.a.305.1 | 6 | 36.23 | even | 6 | |||
1296.5.e.c.161.2 | 6 | 12.11 | even | 2 | |||
1296.5.e.c.161.5 | 6 | 4.3 | odd | 2 |