Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [650,6,Mod(599,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.599");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.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: | \(104.249482878\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.2 | ||
Root | \(1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.599 |
Dual form | 650.6.b.g.599.3 |
$q$-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 \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 17.8114i | 1.14260i | 0.820741 | + | 0.571301i | \(0.193561\pi\) | ||||
−0.820741 | + | 0.571301i | \(0.806439\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 71.2456 | 0.807941 | ||||||||
\(7\) | 86.7544i | 0.669186i | 0.942363 | + | 0.334593i | \(0.108599\pi\) | ||||
−0.942363 | + | 0.334593i | \(0.891401\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −74.2456 | −0.305537 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −203.285 | −0.506551 | −0.253275 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253275 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(12\) | − 284.982i | − 0.571301i | ||||||||
\(13\) | 169.000i | 0.277350i | ||||||||
\(14\) | 347.018 | 0.473186 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 406.605i | − 0.341233i | −0.985338 | − | 0.170616i | \(-0.945424\pi\) | ||||
0.985338 | − | 0.170616i | \(-0.0545758\pi\) | |||||||
\(18\) | 296.982i | 0.216047i | ||||||||
\(19\) | 2326.61 | 1.47856 | 0.739281 | − | 0.673397i | \(-0.235166\pi\) | ||||
0.739281 | + | 0.673397i | \(0.235166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1545.22 | −0.764612 | ||||||||
\(22\) | 813.139i | 0.358185i | ||||||||
\(23\) | − 3280.84i | − 1.29320i | −0.762829 | − | 0.646600i | \(-0.776190\pi\) | ||||
0.762829 | − | 0.646600i | \(-0.223810\pi\) | |||||||
\(24\) | −1139.93 | −0.403970 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 676.000 | 0.196116 | ||||||||
\(27\) | 3005.75i | 0.793494i | ||||||||
\(28\) | − 1388.07i | − 0.334593i | ||||||||
\(29\) | 2726.43 | 0.602005 | 0.301002 | − | 0.953623i | \(-0.402679\pi\) | ||||
0.301002 | + | 0.953623i | \(0.402679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4914.62 | 0.918514 | 0.459257 | − | 0.888303i | \(-0.348116\pi\) | ||||
0.459257 | + | 0.888303i | \(0.348116\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | − 3620.78i | − 0.578785i | ||||||||
\(34\) | −1626.42 | −0.241288 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1187.93 | 0.152769 | ||||||||
\(37\) | 3126.78i | 0.375486i | 0.982218 | + | 0.187743i | \(0.0601172\pi\) | ||||
−0.982218 | + | 0.187743i | \(0.939883\pi\) | |||||||
\(38\) | − 9306.43i | − 1.04550i | ||||||||
\(39\) | −3010.12 | −0.316901 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15061.9 | 1.39933 | 0.699664 | − | 0.714472i | \(-0.253333\pi\) | ||||
0.699664 | + | 0.714472i | \(0.253333\pi\) | |||||||
\(42\) | 6180.87i | 0.540663i | ||||||||
\(43\) | − 2794.35i | − 0.230467i | −0.993338 | − | 0.115234i | \(-0.963238\pi\) | ||||
0.993338 | − | 0.115234i | \(-0.0367616\pi\) | |||||||
\(44\) | 3252.56 | 0.253275 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13123.4 | −0.914431 | ||||||||
\(47\) | 16679.4i | 1.10138i | 0.834711 | + | 0.550689i | \(0.185635\pi\) | ||||
−0.834711 | + | 0.550689i | \(0.814365\pi\) | |||||||
\(48\) | 4559.72i | 0.285650i | ||||||||
\(49\) | 9280.67 | 0.552191 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7242.20 | 0.389893 | ||||||||
\(52\) | − 2704.00i | − 0.138675i | ||||||||
\(53\) | − 17262.9i | − 0.844158i | −0.906559 | − | 0.422079i | \(-0.861300\pi\) | ||||
0.906559 | − | 0.422079i | \(-0.138700\pi\) | |||||||
\(54\) | 12023.0 | 0.561085 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5552.28 | −0.236593 | ||||||||
\(57\) | 41440.1i | 1.68941i | ||||||||
\(58\) | − 10905.7i | − 0.425682i | ||||||||
\(59\) | −2762.75 | −0.103326 | −0.0516632 | − | 0.998665i | \(-0.516452\pi\) | ||||
−0.0516632 | + | 0.998665i | \(0.516452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16849.0 | −0.579761 | −0.289881 | − | 0.957063i | \(-0.593616\pi\) | ||||
−0.289881 | + | 0.957063i | \(0.593616\pi\) | |||||||
\(62\) | − 19658.5i | − 0.649488i | ||||||||
\(63\) | − 6441.13i | − 0.204461i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14483.1 | −0.409263 | ||||||||
\(67\) | 19057.9i | 0.518665i | 0.965788 | + | 0.259332i | \(0.0835025\pi\) | ||||
−0.965788 | + | 0.259332i | \(0.916497\pi\) | |||||||
\(68\) | 6505.68i | 0.170616i | ||||||||
\(69\) | 58436.4 | 1.47761 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8326.03 | 0.196016 | 0.0980082 | − | 0.995186i | \(-0.468753\pi\) | ||||
0.0980082 | + | 0.995186i | \(0.468753\pi\) | |||||||
\(72\) | − 4751.72i | − 0.108024i | ||||||||
\(73\) | − 49498.2i | − 1.08713i | −0.839366 | − | 0.543566i | \(-0.817074\pi\) | ||||
0.839366 | − | 0.543566i | \(-0.182926\pi\) | |||||||
\(74\) | 12507.1 | 0.265508 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37225.7 | −0.739281 | ||||||||
\(77\) | − 17635.9i | − 0.338977i | ||||||||
\(78\) | 12040.5i | 0.224083i | ||||||||
\(79\) | −95807.1 | −1.72715 | −0.863575 | − | 0.504220i | \(-0.831780\pi\) | ||||
−0.863575 | + | 0.504220i | \(0.831780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71578.3 | −1.21218 | ||||||||
\(82\) | − 60247.5i | − 0.989474i | ||||||||
\(83\) | − 34154.5i | − 0.544192i | −0.962270 | − | 0.272096i | \(-0.912283\pi\) | ||||
0.962270 | − | 0.272096i | \(-0.0877168\pi\) | |||||||
\(84\) | 24723.5 | 0.382306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11177.4 | −0.162965 | ||||||||
\(87\) | 48561.6i | 0.687851i | ||||||||
\(88\) | − 13010.2i | − 0.179093i | ||||||||
\(89\) | 26681.8 | 0.357059 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14661.5 | −0.185599 | ||||||||
\(92\) | 52493.5i | 0.646600i | ||||||||
\(93\) | 87536.3i | 1.04950i | ||||||||
\(94\) | 66717.7 | 0.778792 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 18238.9 | 0.201985 | ||||||||
\(97\) | 24960.0i | 0.269349i | 0.990890 | + | 0.134674i | \(0.0429988\pi\) | ||||
−0.990890 | + | 0.134674i | \(0.957001\pi\) | |||||||
\(98\) | − 37122.7i | − 0.390458i | ||||||||
\(99\) | 15093.0 | 0.154770 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 99719.9 | 0.972698 | 0.486349 | − | 0.873765i | \(-0.338328\pi\) | ||||
0.486349 | + | 0.873765i | \(0.338328\pi\) | |||||||
\(102\) | − 28968.8i | − 0.275696i | ||||||||
\(103\) | 68985.8i | 0.640718i | 0.947296 | + | 0.320359i | \(0.103803\pi\) | ||||
−0.947296 | + | 0.320359i | \(0.896197\pi\) | |||||||
\(104\) | −10816.0 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −69051.6 | −0.596910 | ||||||||
\(107\) | 120316.i | 1.01593i | 0.861378 | + | 0.507964i | \(0.169602\pi\) | ||||
−0.861378 | + | 0.507964i | \(0.830398\pi\) | |||||||
\(108\) | − 48092.0i | − 0.396747i | ||||||||
\(109\) | 173293. | 1.39706 | 0.698529 | − | 0.715582i | \(-0.253838\pi\) | ||||
0.698529 | + | 0.715582i | \(0.253838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −55692.3 | −0.429030 | ||||||||
\(112\) | 22209.1i | 0.167296i | ||||||||
\(113\) | 95289.3i | 0.702018i | 0.936372 | + | 0.351009i | \(0.114161\pi\) | ||||
−0.936372 | + | 0.351009i | \(0.885839\pi\) | |||||||
\(114\) | 165761. | 1.19459 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −43622.9 | −0.301002 | ||||||||
\(117\) | − 12547.5i | − 0.0847408i | ||||||||
\(118\) | 11051.0i | 0.0730629i | ||||||||
\(119\) | 35274.8 | 0.228348 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119726. | −0.743406 | ||||||||
\(122\) | 67395.9i | 0.409953i | ||||||||
\(123\) | 268273.i | 1.59887i | ||||||||
\(124\) | −78634.0 | −0.459257 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −25764.5 | −0.144576 | ||||||||
\(127\) | 70746.9i | 0.389223i | 0.980880 | + | 0.194611i | \(0.0623446\pi\) | ||||
−0.980880 | + | 0.194611i | \(0.937655\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 49771.2 | 0.263332 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192442. | 0.979764 | 0.489882 | − | 0.871789i | \(-0.337040\pi\) | ||||
0.489882 | + | 0.871789i | \(0.337040\pi\) | |||||||
\(132\) | 57932.5i | 0.289393i | ||||||||
\(133\) | 201844.i | 0.989432i | ||||||||
\(134\) | 76231.4 | 0.366752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 26022.7 | 0.120644 | ||||||||
\(137\) | 280120.i | 1.27509i | 0.770411 | + | 0.637547i | \(0.220051\pi\) | ||||
−0.770411 | + | 0.637547i | \(0.779949\pi\) | |||||||
\(138\) | − 233746.i | − 1.04483i | ||||||||
\(139\) | −331722. | −1.45626 | −0.728128 | − | 0.685441i | \(-0.759609\pi\) | ||||
−0.728128 | + | 0.685441i | \(0.759609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −297084. | −1.25844 | ||||||||
\(142\) | − 33304.1i | − 0.138604i | ||||||||
\(143\) | − 34355.1i | − 0.140492i | ||||||||
\(144\) | −19006.9 | −0.0763843 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −197993. | −0.768718 | ||||||||
\(147\) | 165302.i | 0.630933i | ||||||||
\(148\) | − 50028.5i | − 0.187743i | ||||||||
\(149\) | −205133. | −0.756956 | −0.378478 | − | 0.925610i | \(-0.623553\pi\) | ||||
−0.378478 | + | 0.925610i | \(0.623553\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 493417. | 1.76105 | 0.880525 | − | 0.474000i | \(-0.157190\pi\) | ||||
0.880525 | + | 0.474000i | \(0.157190\pi\) | |||||||
\(152\) | 148903.i | 0.522750i | ||||||||
\(153\) | 30188.6i | 0.104259i | ||||||||
\(154\) | −70543.4 | −0.239693 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 48162.0 | 0.158450 | ||||||||
\(157\) | 299589.i | 0.970011i | 0.874511 | + | 0.485006i | \(0.161182\pi\) | ||||
−0.874511 | + | 0.485006i | \(0.838818\pi\) | |||||||
\(158\) | 383229.i | 1.22128i | ||||||||
\(159\) | 307476. | 0.964536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 284628. | 0.865391 | ||||||||
\(162\) | 286313.i | 0.857144i | ||||||||
\(163\) | 479059.i | 1.41228i | 0.708073 | + | 0.706139i | \(0.249565\pi\) | ||||
−0.708073 | + | 0.706139i | \(0.750435\pi\) | |||||||
\(164\) | −240990. | −0.699664 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −136618. | −0.384802 | ||||||||
\(167\) | 388300.i | 1.07740i | 0.842498 | + | 0.538699i | \(0.181084\pi\) | ||||
−0.842498 | + | 0.538699i | \(0.818916\pi\) | |||||||
\(168\) | − 98893.9i | − 0.270331i | ||||||||
\(169\) | −28561.0 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −172740. | −0.451756 | ||||||||
\(172\) | 44709.5i | 0.115234i | ||||||||
\(173\) | − 20482.9i | − 0.0520327i | −0.999662 | − | 0.0260163i | \(-0.991718\pi\) | ||||
0.999662 | − | 0.0260163i | \(-0.00828219\pi\) | |||||||
\(174\) | 194246. | 0.486384 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −52040.9 | −0.126638 | ||||||||
\(177\) | − 49208.4i | − 0.118061i | ||||||||
\(178\) | − 106727.i | − 0.252479i | ||||||||
\(179\) | −320609. | −0.747898 | −0.373949 | − | 0.927449i | \(-0.621997\pi\) | ||||
−0.373949 | + | 0.927449i | \(0.621997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −685416. | −1.55510 | −0.777549 | − | 0.628822i | \(-0.783537\pi\) | ||||
−0.777549 | + | 0.628822i | \(0.783537\pi\) | |||||||
\(182\) | 58646.0i | 0.131238i | ||||||||
\(183\) | − 300104.i | − 0.662436i | ||||||||
\(184\) | 209974. | 0.457215 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 350145. | 0.742105 | ||||||||
\(187\) | 82656.6i | 0.172852i | ||||||||
\(188\) | − 266871.i | − 0.550689i | ||||||||
\(189\) | −260762. | −0.530995 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −139964. | −0.277609 | −0.138804 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138804 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(192\) | − 72955.4i | − 0.142825i | ||||||||
\(193\) | 520732.i | 1.00628i | 0.864203 | + | 0.503142i | \(0.167823\pi\) | ||||
−0.864203 | + | 0.503142i | \(0.832177\pi\) | |||||||
\(194\) | 99839.9 | 0.190458 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −148491. | −0.276095 | ||||||||
\(197\) | − 408213.i | − 0.749414i | −0.927143 | − | 0.374707i | \(-0.877743\pi\) | ||||
0.927143 | − | 0.374707i | \(-0.122257\pi\) | |||||||
\(198\) | − 60371.9i | − 0.109439i | ||||||||
\(199\) | 853536. | 1.52788 | 0.763940 | − | 0.645288i | \(-0.223262\pi\) | ||||
0.763940 | + | 0.645288i | \(0.223262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −339447. | −0.592627 | ||||||||
\(202\) | − 398879.i | − 0.687802i | ||||||||
\(203\) | 236530.i | 0.402853i | ||||||||
\(204\) | −115875. | −0.194946 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 275943. | 0.453056 | ||||||||
\(207\) | 243588.i | 0.395121i | ||||||||
\(208\) | 43264.0i | 0.0693375i | ||||||||
\(209\) | −472964. | −0.748966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −277058. | −0.428415 | −0.214207 | − | 0.976788i | \(-0.568717\pi\) | ||||
−0.214207 | + | 0.976788i | \(0.568717\pi\) | |||||||
\(212\) | 276206.i | 0.422079i | ||||||||
\(213\) | 148298.i | 0.223968i | ||||||||
\(214\) | 481263. | 0.718370 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −192368. | −0.280542 | ||||||||
\(217\) | 426365.i | 0.614657i | ||||||||
\(218\) | − 693171.i | − 0.987869i | ||||||||
\(219\) | 881632. | 1.24216 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 68716.2 | 0.0946409 | ||||||||
\(222\) | 222769.i | 0.303370i | ||||||||
\(223\) | 1.40025e6i | 1.88557i | 0.333403 | + | 0.942784i | \(0.391803\pi\) | ||||
−0.333403 | + | 0.942784i | \(0.608197\pi\) | |||||||
\(224\) | 88836.6 | 0.118296 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 381157. | 0.496402 | ||||||||
\(227\) | − 114539.i | − 0.147533i | −0.997276 | − | 0.0737666i | \(-0.976498\pi\) | ||||
0.997276 | − | 0.0737666i | \(-0.0235020\pi\) | |||||||
\(228\) | − 663042.i | − 0.844703i | ||||||||
\(229\) | 501586. | 0.632057 | 0.316029 | − | 0.948750i | \(-0.397650\pi\) | ||||
0.316029 | + | 0.948750i | \(0.397650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 314119. | 0.387315 | ||||||||
\(232\) | 174492.i | 0.212841i | ||||||||
\(233\) | − 147822.i | − 0.178381i | −0.996015 | − | 0.0891904i | \(-0.971572\pi\) | ||||
0.996015 | − | 0.0891904i | \(-0.0284280\pi\) | |||||||
\(234\) | −50190.0 | −0.0599208 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 44204.0 | 0.0516632 | ||||||||
\(237\) | − 1.70646e6i | − 1.97344i | ||||||||
\(238\) | − 141099.i | − 0.161466i | ||||||||
\(239\) | 442991. | 0.501649 | 0.250824 | − | 0.968033i | \(-0.419298\pi\) | ||||
0.250824 | + | 0.968033i | \(0.419298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 807221. | 0.895262 | 0.447631 | − | 0.894218i | \(-0.352268\pi\) | ||||
0.447631 | + | 0.894218i | \(0.352268\pi\) | |||||||
\(242\) | 478905.i | 0.525668i | ||||||||
\(243\) | − 544511.i | − 0.591549i | ||||||||
\(244\) | 269584. | 0.289881 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.07309e6 | 1.13057 | ||||||||
\(247\) | 393197.i | 0.410079i | ||||||||
\(248\) | 314536.i | 0.324744i | ||||||||
\(249\) | 608338. | 0.621794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.21143e6 | 1.21371 | 0.606853 | − | 0.794814i | \(-0.292432\pi\) | ||||
0.606853 | + | 0.794814i | \(0.292432\pi\) | |||||||
\(252\) | 103058.i | 0.102231i | ||||||||
\(253\) | 666945.i | 0.655072i | ||||||||
\(254\) | 282988. | 0.275222 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.15116e6i | 1.08718i | 0.839350 | + | 0.543592i | \(0.182936\pi\) | ||||
−0.839350 | + | 0.543592i | \(0.817064\pi\) | |||||||
\(258\) | − 199085.i | − 0.186204i | ||||||||
\(259\) | −271262. | −0.251270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −202426. | −0.183935 | ||||||||
\(262\) | − 769768.i | − 0.692798i | ||||||||
\(263\) | − 930449.i | − 0.829475i | −0.909941 | − | 0.414737i | \(-0.863873\pi\) | ||||
0.909941 | − | 0.414737i | \(-0.136127\pi\) | |||||||
\(264\) | 231730. | 0.204632 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 807375. | 0.699634 | ||||||||
\(267\) | 475239.i | 0.407976i | ||||||||
\(268\) | − 304926.i | − 0.259332i | ||||||||
\(269\) | 2.08547e6 | 1.75721 | 0.878605 | − | 0.477549i | \(-0.158475\pi\) | ||||
0.878605 | + | 0.477549i | \(0.158475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.48375e6 | −1.22726 | −0.613632 | − | 0.789592i | \(-0.710292\pi\) | ||||
−0.613632 | + | 0.789592i | \(0.710292\pi\) | |||||||
\(272\) | − 104091.i | − 0.0853081i | ||||||||
\(273\) | − 261142.i | − 0.212065i | ||||||||
\(274\) | 1.12048e6 | 0.901628 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −934982. | −0.738806 | ||||||||
\(277\) | − 753280.i | − 0.589871i | −0.955517 | − | 0.294935i | \(-0.904702\pi\) | ||||
0.955517 | − | 0.294935i | \(-0.0952982\pi\) | |||||||
\(278\) | 1.32689e6i | 1.02973i | ||||||||
\(279\) | −364889. | −0.280640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −771041. | −0.582521 | −0.291261 | − | 0.956644i | \(-0.594075\pi\) | ||||
−0.291261 | + | 0.956644i | \(0.594075\pi\) | |||||||
\(282\) | 1.18833e6i | 0.889848i | ||||||||
\(283\) | − 132716.i | − 0.0985047i | −0.998786 | − | 0.0492523i | \(-0.984316\pi\) | ||||
0.998786 | − | 0.0492523i | \(-0.0156839\pi\) | |||||||
\(284\) | −133217. | −0.0980082 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −137420. | −0.0993428 | ||||||||
\(287\) | 1.30668e6i | 0.936410i | ||||||||
\(288\) | 76027.4i | 0.0540119i | ||||||||
\(289\) | 1.25453e6 | 0.883560 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −444572. | −0.307758 | ||||||||
\(292\) | 791971.i | 0.543566i | ||||||||
\(293\) | 435111.i | 0.296095i | 0.988980 | + | 0.148047i | \(0.0472988\pi\) | ||||
−0.988980 | + | 0.148047i | \(0.952701\pi\) | |||||||
\(294\) | 661206. | 0.446137 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −200114. | −0.132754 | ||||||||
\(297\) | − 611023.i | − 0.401945i | ||||||||
\(298\) | 820534.i | 0.535249i | ||||||||
\(299\) | 554463. | 0.358669 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 242422. | 0.154225 | ||||||||
\(302\) | − 1.97367e6i | − 1.24525i | ||||||||
\(303\) | 1.77615e6i | 1.11141i | ||||||||
\(304\) | 595612. | 0.369640 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 120754. | 0.0737224 | ||||||||
\(307\) | − 707726.i | − 0.428567i | −0.976771 | − | 0.214284i | \(-0.931258\pi\) | ||||
0.976771 | − | 0.214284i | \(-0.0687417\pi\) | |||||||
\(308\) | 282174.i | 0.169488i | ||||||||
\(309\) | −1.22873e6 | −0.732085 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.19086e6 | 1.28444 | 0.642221 | − | 0.766519i | \(-0.278013\pi\) | ||||
0.642221 | + | 0.766519i | \(0.278013\pi\) | |||||||
\(312\) | − 192648.i | − 0.112041i | ||||||||
\(313\) | − 1.16467e6i | − 0.671960i | −0.941869 | − | 0.335980i | \(-0.890933\pi\) | ||||
0.941869 | − | 0.335980i | \(-0.109067\pi\) | |||||||
\(314\) | 1.19836e6 | 0.685902 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.53291e6 | 0.863575 | ||||||||
\(317\) | − 2.33420e6i | − 1.30464i | −0.757946 | − | 0.652318i | \(-0.773797\pi\) | ||||
0.757946 | − | 0.652318i | \(-0.226203\pi\) | |||||||
\(318\) | − 1.22990e6i | − 0.682030i | ||||||||
\(319\) | −554242. | −0.304946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.14299e6 | −1.16080 | ||||||||
\(322\) | − 1.13851e6i | − 0.611924i | ||||||||
\(323\) | − 946011.i | − 0.504533i | ||||||||
\(324\) | 1.14525e6 | 0.606092 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.91624e6 | 0.998631 | ||||||||
\(327\) | 3.08659e6i | 1.59628i | ||||||||
\(328\) | 963960.i | 0.494737i | ||||||||
\(329\) | −1.44701e6 | −0.737026 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 755890. | 0.379218 | 0.189609 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(332\) | 546471.i | 0.272096i | ||||||||
\(333\) | − 232150.i | − 0.114725i | ||||||||
\(334\) | 1.55320e6 | 0.761835 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −395576. | −0.191153 | ||||||||
\(337\) | 2.81171e6i | 1.34864i | 0.738441 | + | 0.674319i | \(0.235563\pi\) | ||||
−0.738441 | + | 0.674319i | \(0.764437\pi\) | |||||||
\(338\) | 114244.i | 0.0543928i | ||||||||
\(339\) | −1.69723e6 | −0.802126 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −999068. | −0.465274 | ||||||||
\(342\) | 690961.i | 0.319439i | ||||||||
\(343\) | 2.26322e6i | 1.03870i | ||||||||
\(344\) | 178838. | 0.0814824 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −81931.6 | −0.0367927 | ||||||||
\(347\) | 1.36358e6i | 0.607935i | 0.952682 | + | 0.303967i | \(0.0983114\pi\) | ||||
−0.952682 | + | 0.303967i | \(0.901689\pi\) | |||||||
\(348\) | − 776985.i | − 0.343926i | ||||||||
\(349\) | −488343. | −0.214616 | −0.107308 | − | 0.994226i | \(-0.534223\pi\) | ||||
−0.107308 | + | 0.994226i | \(0.534223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −507972. | −0.220076 | ||||||||
\(352\) | 208164.i | 0.0895464i | ||||||||
\(353\) | − 1.45693e6i | − 0.622301i | −0.950361 | − | 0.311151i | \(-0.899286\pi\) | ||||
0.950361 | − | 0.311151i | \(-0.100714\pi\) | |||||||
\(354\) | −196834. | −0.0834817 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −426908. | −0.178529 | ||||||||
\(357\) | 628293.i | 0.260911i | ||||||||
\(358\) | 1.28243e6i | 0.528844i | ||||||||
\(359\) | −675187. | −0.276495 | −0.138248 | − | 0.990398i | \(-0.544147\pi\) | ||||
−0.138248 | + | 0.990398i | \(0.544147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.93701e6 | 1.18614 | ||||||||
\(362\) | 2.74166e6i | 1.09962i | ||||||||
\(363\) | − 2.13249e6i | − 0.849417i | ||||||||
\(364\) | 234584. | 0.0927994 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.20042e6 | −0.468413 | ||||||||
\(367\) | − 623601.i | − 0.241680i | −0.992672 | − | 0.120840i | \(-0.961441\pi\) | ||||
0.992672 | − | 0.120840i | \(-0.0385589\pi\) | |||||||
\(368\) | − 839896.i | − 0.323300i | ||||||||
\(369\) | −1.11828e6 | −0.427547 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.49763e6 | 0.564899 | ||||||||
\(372\) | − 1.40058e6i | − 0.524748i | ||||||||
\(373\) | − 2.83653e6i | − 1.05564i | −0.849357 | − | 0.527819i | \(-0.823010\pi\) | ||||
0.849357 | − | 0.527819i | \(-0.176990\pi\) | |||||||
\(374\) | 330626. | 0.122225 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.06748e6 | −0.389396 | ||||||||
\(377\) | 460767.i | 0.166966i | ||||||||
\(378\) | 1.04305e6i | 0.375470i | ||||||||
\(379\) | −5.54522e6 | −1.98299 | −0.991495 | − | 0.130147i | \(-0.958455\pi\) | ||||
−0.991495 | + | 0.130147i | \(0.958455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.26010e6 | −0.444726 | ||||||||
\(382\) | 559856.i | 0.196299i | ||||||||
\(383\) | − 3.71036e6i | − 1.29247i | −0.763140 | − | 0.646234i | \(-0.776343\pi\) | ||||
0.763140 | − | 0.646234i | \(-0.223657\pi\) | |||||||
\(384\) | −291822. | −0.100993 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.08293e6 | 0.711551 | ||||||||
\(387\) | 207468.i | 0.0704163i | ||||||||
\(388\) | − 399360.i | − 0.134674i | ||||||||
\(389\) | −4.96384e6 | −1.66320 | −0.831599 | − | 0.555377i | \(-0.812574\pi\) | ||||
−0.831599 | + | 0.555377i | \(0.812574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.33401e6 | −0.441282 | ||||||||
\(392\) | 593963.i | 0.195229i | ||||||||
\(393\) | 3.42766e6i | 1.11948i | ||||||||
\(394\) | −1.63285e6 | −0.529916 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −241488. | −0.0773851 | ||||||||
\(397\) | − 3.75615e6i | − 1.19610i | −0.801459 | − | 0.598049i | \(-0.795943\pi\) | ||||
0.801459 | − | 0.598049i | \(-0.204057\pi\) | |||||||
\(398\) | − 3.41414e6i | − 1.08037i | ||||||||
\(399\) | −3.59512e6 | −1.13053 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.20829e6 | −0.996352 | −0.498176 | − | 0.867076i | \(-0.665997\pi\) | ||||
−0.498176 | + | 0.867076i | \(0.665997\pi\) | |||||||
\(402\) | 1.35779e6i | 0.419051i | ||||||||
\(403\) | 830571.i | 0.254750i | ||||||||
\(404\) | −1.59552e6 | −0.486349 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 946121. | 0.284860 | ||||||||
\(407\) | − 635627.i | − 0.190203i | ||||||||
\(408\) | 463501.i | 0.137848i | ||||||||
\(409\) | −4.11220e6 | −1.21553 | −0.607765 | − | 0.794117i | \(-0.707934\pi\) | ||||
−0.607765 | + | 0.794117i | \(0.707934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.98932e6 | −1.45692 | ||||||||
\(412\) | − 1.10377e6i | − 0.320359i | ||||||||
\(413\) | − 239681.i | − 0.0691446i | ||||||||
\(414\) | 974352. | 0.279393 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 173056. | 0.0490290 | ||||||||
\(417\) | − 5.90844e6i | − 1.66392i | ||||||||
\(418\) | 1.89186e6i | 0.529599i | ||||||||
\(419\) | 1.21350e6 | 0.337680 | 0.168840 | − | 0.985643i | \(-0.445998\pi\) | ||||
0.168840 | + | 0.985643i | \(0.445998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 500559. | 0.137642 | 0.0688208 | − | 0.997629i | \(-0.478076\pi\) | ||||
0.0688208 | + | 0.997629i | \(0.478076\pi\) | |||||||
\(422\) | 1.10823e6i | 0.302935i | ||||||||
\(423\) | − 1.23837e6i | − 0.336512i | ||||||||
\(424\) | 1.10482e6 | 0.298455 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 593193. | 0.158370 | ||||||||
\(427\) | − 1.46172e6i | − 0.387968i | ||||||||
\(428\) | − 1.92505e6i | − 0.507964i | ||||||||
\(429\) | 611912. | 0.160526 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18753.3 | −0.00486279 | −0.00243139 | − | 0.999997i | \(-0.500774\pi\) | ||||
−0.00243139 | + | 0.999997i | \(0.500774\pi\) | |||||||
\(432\) | 769472.i | 0.198373i | ||||||||
\(433\) | 1.10350e6i | 0.282849i | 0.989949 | + | 0.141424i | \(0.0451682\pi\) | ||||
−0.989949 | + | 0.141424i | \(0.954832\pi\) | |||||||
\(434\) | 1.70546e6 | 0.434628 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.77269e6 | −0.698529 | ||||||||
\(437\) | − 7.63324e6i | − 1.91208i | ||||||||
\(438\) | − 3.52653e6i | − 0.878338i | ||||||||
\(439\) | −3.67024e6 | −0.908935 | −0.454467 | − | 0.890763i | \(-0.650170\pi\) | ||||
−0.454467 | + | 0.890763i | \(0.650170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −689048. | −0.168715 | ||||||||
\(442\) | − 274865.i | − 0.0669212i | ||||||||
\(443\) | 4.19972e6i | 1.01674i | 0.861138 | + | 0.508371i | \(0.169752\pi\) | ||||
−0.861138 | + | 0.508371i | \(0.830248\pi\) | |||||||
\(444\) | 891077. | 0.214515 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.60099e6 | 1.33330 | ||||||||
\(447\) | − 3.65371e6i | − 0.864899i | ||||||||
\(448\) | − 355346.i | − 0.0836482i | ||||||||
\(449\) | −2.61245e6 | −0.611551 | −0.305775 | − | 0.952104i | \(-0.598916\pi\) | ||||
−0.305775 | + | 0.952104i | \(0.598916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.06185e6 | −0.708831 | ||||||||
\(452\) | − 1.52463e6i | − 0.351009i | ||||||||
\(453\) | 8.78844e6i | 2.01218i | ||||||||
\(454\) | −458157. | −0.104322 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.65217e6 | −0.597295 | ||||||||
\(457\) | − 5.86700e6i | − 1.31409i | −0.753851 | − | 0.657046i | \(-0.771806\pi\) | ||||
0.753851 | − | 0.657046i | \(-0.228194\pi\) | |||||||
\(458\) | − 2.00634e6i | − 0.446932i | ||||||||
\(459\) | 1.22215e6 | 0.270766 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −95542.2 | −0.0209384 | −0.0104692 | − | 0.999945i | \(-0.503333\pi\) | ||||
−0.0104692 | + | 0.999945i | \(0.503333\pi\) | |||||||
\(462\) | − 1.25648e6i | − 0.273873i | ||||||||
\(463\) | 3.43498e6i | 0.744682i | 0.928096 | + | 0.372341i | \(0.121445\pi\) | ||||
−0.928096 | + | 0.372341i | \(0.878555\pi\) | |||||||
\(464\) | 697967. | 0.150501 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −591286. | −0.126134 | ||||||||
\(467\) | 4.27512e6i | 0.907102i | 0.891230 | + | 0.453551i | \(0.149843\pi\) | ||||
−0.891230 | + | 0.453551i | \(0.850157\pi\) | |||||||
\(468\) | 200760.i | 0.0423704i | ||||||||
\(469\) | −1.65335e6 | −0.347083 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.33610e6 | −1.10834 | ||||||||
\(472\) | − 176816.i | − 0.0365314i | ||||||||
\(473\) | 568048.i | 0.116743i | ||||||||
\(474\) | −6.82583e6 | −1.39544 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −564397. | −0.114174 | ||||||||
\(477\) | 1.28169e6i | 0.257922i | ||||||||
\(478\) | − 1.77196e6i | − 0.354719i | ||||||||
\(479\) | 331105. | 0.0659367 | 0.0329683 | − | 0.999456i | \(-0.489504\pi\) | ||||
0.0329683 | + | 0.999456i | \(0.489504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −528426. | −0.104141 | ||||||||
\(482\) | − 3.22888e6i | − 0.633046i | ||||||||
\(483\) | 5.06962e6i | 0.988797i | ||||||||
\(484\) | 1.91562e6 | 0.371703 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.17804e6 | −0.418288 | ||||||||
\(487\) | 9.33331e6i | 1.78326i | 0.452769 | + | 0.891628i | \(0.350436\pi\) | ||||
−0.452769 | + | 0.891628i | \(0.649564\pi\) | |||||||
\(488\) | − 1.07833e6i | − 0.204977i | ||||||||
\(489\) | −8.53271e6 | −1.61367 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.20484e6 | 0.974325 | 0.487162 | − | 0.873311i | \(-0.338032\pi\) | ||||
0.487162 | + | 0.873311i | \(0.338032\pi\) | |||||||
\(492\) | − 4.29237e6i | − 0.799437i | ||||||||
\(493\) | − 1.10858e6i | − 0.205424i | ||||||||
\(494\) | 1.57279e6 | 0.289970 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.25814e6 | 0.229629 | ||||||||
\(497\) | 722320.i | 0.131171i | ||||||||
\(498\) | − 2.43335e6i | − 0.439675i | ||||||||
\(499\) | 9.51149e6 | 1.71000 | 0.855002 | − | 0.518624i | \(-0.173556\pi\) | ||||
0.855002 | + | 0.518624i | \(0.173556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.91616e6 | −1.23104 | ||||||||
\(502\) | − 4.84572e6i | − 0.858220i | ||||||||
\(503\) | − 2.34504e6i | − 0.413267i | −0.978418 | − | 0.206633i | \(-0.933749\pi\) | ||||
0.978418 | − | 0.206633i | \(-0.0662507\pi\) | |||||||
\(504\) | 412232. | 0.0722879 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.66778e6 | 0.463206 | ||||||||
\(507\) | − 508711.i | − 0.0878924i | ||||||||
\(508\) | − 1.13195e6i | − 0.194611i | ||||||||
\(509\) | −1.04128e6 | −0.178144 | −0.0890720 | − | 0.996025i | \(-0.528390\pi\) | ||||
−0.0890720 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29419e6 | 0.727493 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 6.99321e6i | 1.17323i | ||||||||
\(514\) | 4.60464e6 | 0.768755 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −796339. | −0.131666 | ||||||||
\(517\) | − 3.39067e6i | − 0.557904i | ||||||||
\(518\) | 1.08505e6i | 0.177674i | ||||||||
\(519\) | 364829. | 0.0594526 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.07451e6 | −0.173427 | −0.0867135 | − | 0.996233i | \(-0.527636\pi\) | ||||
−0.0867135 | + | 0.996233i | \(0.527636\pi\) | |||||||
\(522\) | 809702.i | 0.130062i | ||||||||
\(523\) | − 2.30085e6i | − 0.367819i | −0.982943 | − | 0.183910i | \(-0.941125\pi\) | ||||
0.982943 | − | 0.183910i | \(-0.0588754\pi\) | |||||||
\(524\) | −3.07907e6 | −0.489882 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.72180e6 | −0.586527 | ||||||||
\(527\) | − 1.99831e6i | − 0.313427i | ||||||||
\(528\) | − 926920.i | − 0.144696i | ||||||||
\(529\) | −4.32759e6 | −0.672368 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 205122. | 0.0315701 | ||||||||
\(532\) | − 3.22950e6i | − 0.494716i | ||||||||
\(533\) | 2.54546e6i | 0.388104i | ||||||||
\(534\) | 1.90096e6 | 0.288482 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.21970e6 | −0.183376 | ||||||||
\(537\) | − 5.71048e6i | − 0.854549i | ||||||||
\(538\) | − 8.34189e6i | − 1.24254i | ||||||||
\(539\) | −1.88662e6 | −0.279713 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.85493e6 | −1.44764 | −0.723819 | − | 0.689989i | \(-0.757615\pi\) | ||||
−0.723819 | + | 0.689989i | \(0.757615\pi\) | |||||||
\(542\) | 5.93501e6i | 0.867807i | ||||||||
\(543\) | − 1.22082e7i | − 1.77686i | ||||||||
\(544\) | −416364. | −0.0603220 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.04457e6 | −0.149953 | ||||||||
\(547\) | 4.90591e6i | 0.701054i | 0.936553 | + | 0.350527i | \(0.113998\pi\) | ||||
−0.936553 | + | 0.350527i | \(0.886002\pi\) | |||||||
\(548\) | − 4.48192e6i | − 0.637547i | ||||||||
\(549\) | 1.25096e6 | 0.177139 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34335e6 | 0.890101 | ||||||||
\(552\) | 3.73993e6i | 0.522415i | ||||||||
\(553\) | − 8.31169e6i | − 1.15578i | ||||||||
\(554\) | −3.01312e6 | −0.417102 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.30756e6 | 0.728128 | ||||||||
\(557\) | − 1.82826e6i | − 0.249689i | −0.992176 | − | 0.124845i | \(-0.960157\pi\) | ||||
0.992176 | − | 0.124845i | \(-0.0398432\pi\) | |||||||
\(558\) | 1.45956e6i | 0.198443i | ||||||||
\(559\) | 472244. | 0.0639201 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.47223e6 | −0.197500 | ||||||||
\(562\) | 3.08417e6i | 0.411905i | ||||||||
\(563\) | 8.05618e6i | 1.07117i | 0.844481 | + | 0.535585i | \(0.179909\pi\) | ||||
−0.844481 | + | 0.535585i | \(0.820091\pi\) | |||||||
\(564\) | 4.75334e6 | 0.629218 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −530864. | −0.0696533 | ||||||||
\(567\) | − 6.20973e6i | − 0.811176i | ||||||||
\(568\) | 532866.i | 0.0693022i | ||||||||
\(569\) | −8.62680e6 | −1.11704 | −0.558521 | − | 0.829491i | \(-0.688631\pi\) | ||||
−0.558521 | + | 0.829491i | \(0.688631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.14626e6 | 1.04561 | 0.522803 | − | 0.852454i | \(-0.324886\pi\) | ||||
0.522803 | + | 0.852454i | \(0.324886\pi\) | |||||||
\(572\) | 549682.i | 0.0702460i | ||||||||
\(573\) | − 2.49295e6i | − 0.317196i | ||||||||
\(574\) | 5.22674e6 | 0.662142 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 304110. | 0.0381922 | ||||||||
\(577\) | 6.35136e6i | 0.794195i | 0.917777 | + | 0.397097i | \(0.129982\pi\) | ||||
−0.917777 | + | 0.397097i | \(0.870018\pi\) | |||||||
\(578\) | − 5.01812e6i | − 0.624772i | ||||||||
\(579\) | −9.27496e6 | −1.14978 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.96305e6 | 0.364165 | ||||||||
\(582\) | 1.77829e6i | 0.217618i | ||||||||
\(583\) | 3.50928e6i | 0.427609i | ||||||||
\(584\) | 3.16788e6 | 0.384359 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.74044e6 | 0.209371 | ||||||||
\(587\) | − 1.42583e7i | − 1.70794i | −0.520324 | − | 0.853969i | \(-0.674189\pi\) | ||||
0.520324 | − | 0.853969i | \(-0.325811\pi\) | |||||||
\(588\) | − 2.64482e6i | − 0.315467i | ||||||||
\(589\) | 1.14344e7 | 1.35808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.27085e6 | 0.856281 | ||||||||
\(592\) | 800456.i | 0.0938714i | ||||||||
\(593\) | − 5.76780e6i | − 0.673556i | −0.941584 | − | 0.336778i | \(-0.890663\pi\) | ||||
0.941584 | − | 0.336778i | \(-0.109337\pi\) | |||||||
\(594\) | −2.44409e6 | −0.284218 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.28214e6 | 0.378478 | ||||||||
\(597\) | 1.52027e7i | 1.74576i | ||||||||
\(598\) | − 2.21785e6i | − 0.253618i | ||||||||
\(599\) | 1.08344e7 | 1.23378 | 0.616891 | − | 0.787049i | \(-0.288392\pi\) | ||||
0.616891 | + | 0.787049i | \(0.288392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.23326e7 | 1.39273 | 0.696366 | − | 0.717687i | \(-0.254799\pi\) | ||||
0.696366 | + | 0.717687i | \(0.254799\pi\) | |||||||
\(602\) | − 969687.i | − 0.109054i | ||||||||
\(603\) | − 1.41496e6i | − 0.158471i | ||||||||
\(604\) | −7.89467e6 | −0.880525 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.10460e6 | 0.785883 | ||||||||
\(607\) | 4.32462e6i | 0.476405i | 0.971215 | + | 0.238203i | \(0.0765582\pi\) | ||||
−0.971215 | + | 0.238203i | \(0.923442\pi\) | |||||||
\(608\) | − 2.38245e6i | − 0.261375i | ||||||||
\(609\) | −4.21293e6 | −0.460300 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.81882e6 | −0.305467 | ||||||||
\(612\) | − 483018.i | − 0.0521296i | ||||||||
\(613\) | 1.19846e7i | 1.28816i | 0.764957 | + | 0.644082i | \(0.222760\pi\) | ||||
−0.764957 | + | 0.644082i | \(0.777240\pi\) | |||||||
\(614\) | −2.83090e6 | −0.303043 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.12869e6 | 0.119846 | ||||||||
\(617\) | − 8.12346e6i | − 0.859069i | −0.903050 | − | 0.429535i | \(-0.858678\pi\) | ||||
0.903050 | − | 0.429535i | \(-0.141322\pi\) | |||||||
\(618\) | 4.91493e6i | 0.517662i | ||||||||
\(619\) | 6.07174e6 | 0.636923 | 0.318461 | − | 0.947936i | \(-0.396834\pi\) | ||||
0.318461 | + | 0.947936i | \(0.396834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.86140e6 | 1.02615 | ||||||||
\(622\) | − 8.76346e6i | − 0.908238i | ||||||||
\(623\) | 2.31476e6i | 0.238939i | ||||||||
\(624\) | −770592. | −0.0792251 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.65869e6 | −0.475147 | ||||||||
\(627\) | − 8.42414e6i | − 0.855770i | ||||||||
\(628\) | − 4.79343e6i | − 0.485006i | ||||||||
\(629\) | 1.27137e6 | 0.128128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.56443e6 | 0.756315 | 0.378158 | − | 0.925741i | \(-0.376558\pi\) | ||||
0.378158 | + | 0.925741i | \(0.376558\pi\) | |||||||
\(632\) | − 6.13166e6i | − 0.610640i | ||||||||
\(633\) | − 4.93479e6i | − 0.489507i | ||||||||
\(634\) | −9.33679e6 | −0.922517 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.91962e6 | −0.482268 | ||||||||
\(637\) | 1.56843e6i | 0.153150i | ||||||||
\(638\) | 2.21697e6i | 0.215629i | ||||||||
\(639\) | −618171. | −0.0598903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04819e7 | 1.00761 | 0.503806 | − | 0.863817i | \(-0.331933\pi\) | ||||
0.503806 | + | 0.863817i | \(0.331933\pi\) | |||||||
\(642\) | 8.57196e6i | 0.820810i | ||||||||
\(643\) | − 52467.4i | − 0.00500452i | −0.999997 | − | 0.00250226i | \(-0.999204\pi\) | ||||
0.999997 | − | 0.00250226i | \(-0.000796494\pi\) | |||||||
\(644\) | −4.55404e6 | −0.432696 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.78404e6 | −0.356759 | ||||||||
\(647\) | − 1.90086e7i | − 1.78521i | −0.450839 | − | 0.892605i | \(-0.648875\pi\) | ||||
0.450839 | − | 0.892605i | \(-0.351125\pi\) | |||||||
\(648\) | − 4.58101e6i | − 0.428572i | ||||||||
\(649\) | 561625. | 0.0523401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.59416e6 | −0.702307 | ||||||||
\(652\) | − 7.66495e6i | − 0.706139i | ||||||||
\(653\) | 1.41889e7i | 1.30216i | 0.759007 | + | 0.651082i | \(0.225685\pi\) | ||||
−0.759007 | + | 0.651082i | \(0.774315\pi\) | |||||||
\(654\) | 1.23463e7 | 1.12874 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.85584e6 | 0.349832 | ||||||||
\(657\) | 3.67502e6i | 0.332159i | ||||||||
\(658\) | 5.78806e6i | 0.521156i | ||||||||
\(659\) | 1.56797e7 | 1.40645 | 0.703226 | − | 0.710966i | \(-0.251742\pi\) | ||||
0.703226 | + | 0.710966i | \(0.251742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.59619e7 | 1.42095 | 0.710477 | − | 0.703721i | \(-0.248479\pi\) | ||||
0.710477 | + | 0.703721i | \(0.248479\pi\) | |||||||
\(662\) | − 3.02356e6i | − 0.268148i | ||||||||
\(663\) | 1.22393e6i | 0.108137i | ||||||||
\(664\) | 2.18589e6 | 0.192401 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −928599. | −0.0811227 | ||||||||
\(667\) | − 8.94500e6i | − 0.778513i | ||||||||
\(668\) | − 6.21280e6i | − 0.538699i | ||||||||
\(669\) | −2.49403e7 | −2.15445 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.42514e6 | 0.293678 | ||||||||
\(672\) | 1.58230e6i | 0.135166i | ||||||||
\(673\) | − 2.19109e7i | − 1.86475i | −0.361487 | − | 0.932377i | \(-0.617731\pi\) | ||||
0.361487 | − | 0.932377i | \(-0.382269\pi\) | |||||||
\(674\) | 1.12468e7 | 0.953631 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 456976. | 0.0384615 | ||||||||
\(677\) | 9.11801e6i | 0.764590i | 0.924040 | + | 0.382295i | \(0.124866\pi\) | ||||
−0.924040 | + | 0.382295i | \(0.875134\pi\) | |||||||
\(678\) | 6.78894e6i | 0.567189i | ||||||||
\(679\) | −2.16539e6 | −0.180244 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.04010e6 | 0.168572 | ||||||||
\(682\) | 3.99627e6i | 0.328999i | ||||||||
\(683\) | − 1.57797e7i | − 1.29434i | −0.762346 | − | 0.647170i | \(-0.775953\pi\) | ||||
0.762346 | − | 0.647170i | \(-0.224047\pi\) | |||||||
\(684\) | 2.76385e6 | 0.225878 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.05288e6 | 0.734474 | ||||||||
\(687\) | 8.93394e6i | 0.722189i | ||||||||
\(688\) | − 715352.i | − 0.0576168i | ||||||||
\(689\) | 2.91743e6 | 0.234127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32527e7 | −1.05587 | −0.527935 | − | 0.849285i | \(-0.677033\pi\) | ||||
−0.527935 | + | 0.849285i | \(0.677033\pi\) | |||||||
\(692\) | 327726.i | 0.0260163i | ||||||||
\(693\) | 1.30938e6i | 0.103570i | ||||||||
\(694\) | 5.45432e6 | 0.429875 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.10794e6 | −0.243192 | ||||||||
\(697\) | − 6.12424e6i | − 0.477496i | ||||||||
\(698\) | 1.95337e6i | 0.151756i | ||||||||
\(699\) | 2.63291e6 | 0.203818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.84764e6 | 0.449455 | 0.224727 | − | 0.974422i | \(-0.427851\pi\) | ||||
0.224727 | + | 0.974422i | \(0.427851\pi\) | |||||||
\(702\) | 2.03189e6i | 0.155617i | ||||||||
\(703\) | 7.27480e6i | 0.555179i | ||||||||
\(704\) | 832654. | 0.0633188 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.82770e6 | −0.440033 | ||||||||
\(707\) | 8.65114e6i | 0.650916i | ||||||||
\(708\) | 787335.i | 0.0590305i | ||||||||
\(709\) | 8.45478e6 | 0.631665 | 0.315833 | − | 0.948815i | \(-0.397716\pi\) | ||||
0.315833 | + | 0.948815i | \(0.397716\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.11325e6 | 0.527709 | ||||||||
\(712\) | 1.70763e6i | 0.126239i | ||||||||
\(713\) | − 1.61241e7i | − 1.18782i | ||||||||
\(714\) | 2.51317e6 | 0.184492 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.12974e6 | 0.373949 | ||||||||
\(717\) | 7.89028e6i | 0.573184i | ||||||||
\(718\) | 2.70075e6i | 0.195512i | ||||||||
\(719\) | 9.16187e6 | 0.660940 | 0.330470 | − | 0.943817i | \(-0.392793\pi\) | ||||
0.330470 | + | 0.943817i | \(0.392793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.98482e6 | −0.428759 | ||||||||
\(722\) | − 1.17480e7i | − 0.838730i | ||||||||
\(723\) | 1.43777e7i | 1.02293i | ||||||||
\(724\) | 1.09667e7 | 0.777549 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.52997e6 | −0.600628 | ||||||||
\(727\) | 2.08394e7i | 1.46234i | 0.682195 | + | 0.731170i | \(0.261026\pi\) | ||||
−0.682195 | + | 0.731170i | \(0.738974\pi\) | |||||||
\(728\) | − 938336.i | − 0.0656191i | ||||||||
\(729\) | −7.69503e6 | −0.536280 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.13619e6 | −0.0786429 | ||||||||
\(732\) | 4.80166e6i | 0.331218i | ||||||||
\(733\) | − 1.13361e7i | − 0.779298i | −0.920964 | − | 0.389649i | \(-0.872596\pi\) | ||||
0.920964 | − | 0.389649i | \(-0.127404\pi\) | |||||||
\(734\) | −2.49440e6 | −0.170894 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.35958e6 | −0.228608 | ||||||||
\(737\) | − 3.87417e6i | − 0.262730i | ||||||||
\(738\) | 4.47311e6i | 0.302321i | ||||||||
\(739\) | −6.74529e6 | −0.454349 | −0.227174 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227174 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00338e6 | −0.468557 | ||||||||
\(742\) | − 5.99053e6i | − 0.399444i | ||||||||
\(743\) | 1.63250e7i | 1.08488i | 0.840094 | + | 0.542440i | \(0.182499\pi\) | ||||
−0.840094 | + | 0.542440i | \(0.817501\pi\) | |||||||
\(744\) | −5.60232e6 | −0.371053 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.13461e7 | −0.746449 | ||||||||
\(747\) | 2.53582e6i | 0.166271i | ||||||||
\(748\) | − 1.32251e6i | − 0.0864258i | ||||||||
\(749\) | −1.04379e7 | −0.679845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.54751e7 | −1.64822 | −0.824110 | − | 0.566430i | \(-0.808324\pi\) | ||||
−0.824110 | + | 0.566430i | \(0.808324\pi\) | |||||||
\(752\) | 4.26993e6i | 0.275344i | ||||||||
\(753\) | 2.15772e7i | 1.38678i | ||||||||
\(754\) | 1.84307e6 | 0.118063 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.17220e6 | 0.265497 | ||||||||
\(757\) | − 2.49077e6i | − 0.157977i | −0.996876 | − | 0.0789886i | \(-0.974831\pi\) | ||||
0.996876 | − | 0.0789886i | \(-0.0251691\pi\) | |||||||
\(758\) | 2.21809e7i | 1.40219i | ||||||||
\(759\) | −1.18792e7 | −0.748486 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.96708e6 | 0.436103 | 0.218052 | − | 0.975937i | \(-0.430030\pi\) | ||||
0.218052 | + | 0.975937i | \(0.430030\pi\) | |||||||
\(762\) | 5.04040e6i | 0.314469i | ||||||||
\(763\) | 1.50339e7i | 0.934891i | ||||||||
\(764\) | 2.23942e6 | 0.138804 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.48415e7 | −0.913913 | ||||||||
\(767\) | − 466905.i | − 0.0286576i | ||||||||
\(768\) | 1.16729e6i | 0.0714126i | ||||||||
\(769\) | −6.80390e6 | −0.414899 | −0.207449 | − | 0.978246i | \(-0.566516\pi\) | ||||
−0.207449 | + | 0.978246i | \(0.566516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.05038e7 | −1.24222 | ||||||||
\(772\) | − 8.33171e6i | − 0.503142i | ||||||||
\(773\) | − 2.04878e7i | − 1.23324i | −0.787262 | − | 0.616619i | \(-0.788502\pi\) | ||||
0.787262 | − | 0.616619i | \(-0.211498\pi\) | |||||||
\(774\) | 829871. | 0.0497918 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.59744e6 | −0.0952291 | ||||||||
\(777\) | − 4.83156e6i | − 0.287101i | ||||||||
\(778\) | 1.98554e7i | 1.17606i | ||||||||
\(779\) | 3.50431e7 | 2.06899 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.69256e6 | −0.0992922 | ||||||||
\(782\) | 5.33603e6i | 0.312034i | ||||||||
\(783\) | 8.19498e6i | 0.477687i | ||||||||
\(784\) | 2.37585e6 | 0.138048 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.37106e7 | 0.791591 | ||||||||
\(787\) | − 1.89888e7i | − 1.09285i | −0.837508 | − | 0.546425i | \(-0.815988\pi\) | ||||
0.837508 | − | 0.546425i | \(-0.184012\pi\) | |||||||
\(788\) | 6.53142e6i | 0.374707i | ||||||||
\(789\) | 1.65726e7 | 0.947759 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.26677e6 | −0.469780 | ||||||||
\(792\) | 965951.i | 0.0547195i | ||||||||
\(793\) | − 2.84748e6i | − 0.160797i | ||||||||
\(794\) | −1.50246e7 | −0.845769 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.36566e7 | −0.763940 | ||||||||
\(797\) | 2.20925e7i | 1.23197i | 0.787759 | + | 0.615983i | \(0.211241\pi\) | ||||
−0.787759 | + | 0.615983i | \(0.788759\pi\) | |||||||
\(798\) | 1.43805e7i | 0.799403i | ||||||||
\(799\) | 6.78194e6 | 0.375826 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.98100e6 | −0.109095 | ||||||||
\(802\) | 1.28332e7i | 0.704527i | ||||||||
\(803\) | 1.00622e7i | 0.550688i | ||||||||
\(804\) | 5.43115e6 | 0.296314 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.32229e6 | 0.180135 | ||||||||
\(807\) | 3.71452e7i | 2.00779i | ||||||||
\(808\) | 6.38207e6i | 0.343901i | ||||||||
\(809\) | 3.46398e7 | 1.86082 | 0.930410 | − | 0.366521i | \(-0.119451\pi\) | ||||
0.930410 | + | 0.366521i | \(0.119451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.39750e6 | 0.448330 | 0.224165 | − | 0.974551i | \(-0.428035\pi\) | ||||
0.224165 | + | 0.974551i | \(0.428035\pi\) | |||||||
\(812\) | − 3.78448e6i | − 0.201427i | ||||||||
\(813\) | − 2.64277e7i | − 1.40227i | ||||||||
\(814\) | −2.54251e6 | −0.134494 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.85400e6 | 0.0974732 | ||||||||
\(817\) | − 6.50135e6i | − 0.340760i | ||||||||
\(818\) | 1.64488e7i | 0.859509i | ||||||||
\(819\) | 1.08855e6 | 0.0567073 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.98105e7 | −1.02574 | −0.512869 | − | 0.858467i | \(-0.671418\pi\) | ||||
−0.512869 | + | 0.858467i | \(0.671418\pi\) | |||||||
\(822\) | 1.99573e7i | 1.03020i | ||||||||
\(823\) | − 336504.i | − 0.0173177i | −0.999963 | − | 0.00865886i | \(-0.997244\pi\) | ||||
0.999963 | − | 0.00865886i | \(-0.00275624\pi\) | |||||||
\(824\) | −4.41509e6 | −0.226528 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −958724. | −0.0488926 | ||||||||
\(827\) | − 1.02845e7i | − 0.522903i | −0.965217 | − | 0.261451i | \(-0.915799\pi\) | ||||
0.965217 | − | 0.261451i | \(-0.0842011\pi\) | |||||||
\(828\) | − 3.89741e6i | − 0.197560i | ||||||||
\(829\) | −3.43440e7 | −1.73566 | −0.867829 | − | 0.496863i | \(-0.834485\pi\) | ||||
−0.867829 | + | 0.496863i | \(0.834485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.34170e7 | 0.673987 | ||||||||
\(832\) | − 692224.i | − 0.0346688i | ||||||||
\(833\) | − 3.77357e6i | − 0.188425i | ||||||||
\(834\) | −2.36337e7 | −1.17657 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.56742e6 | 0.374483 | ||||||||
\(837\) | 1.47721e7i | 0.728836i | ||||||||
\(838\) | − 4.85401e6i | − 0.238776i | ||||||||
\(839\) | 1.00761e7 | 0.494185 | 0.247092 | − | 0.968992i | \(-0.420525\pi\) | ||||
0.247092 | + | 0.968992i | \(0.420525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.30777e7 | −0.637590 | ||||||||
\(842\) | − 2.00224e6i | − 0.0973273i | ||||||||
\(843\) | − 1.37333e7i | − 0.665590i | ||||||||
\(844\) | 4.43293e6 | 0.214207 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.95349e6 | −0.237950 | ||||||||
\(847\) | − 1.03868e7i | − 0.497477i | ||||||||
\(848\) | − 4.41930e6i | − 0.211040i | ||||||||
\(849\) | 2.36385e6 | 0.112552 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.02585e7 | 0.485578 | ||||||||
\(852\) | − 2.37277e6i | − 0.111984i | ||||||||
\(853\) | − 3.71613e7i | − 1.74871i | −0.485286 | − | 0.874355i | \(-0.661285\pi\) | ||||
0.485286 | − | 0.874355i | \(-0.338715\pi\) | |||||||
\(854\) | −5.84690e6 | −0.274335 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.70021e6 | −0.359185 | ||||||||
\(857\) | 3.89491e7i | 1.81153i | 0.423783 | + | 0.905764i | \(0.360702\pi\) | ||||
−0.423783 | + | 0.905764i | \(0.639298\pi\) | |||||||
\(858\) | − 2.44765e6i | − 0.113509i | ||||||||
\(859\) | 2.13532e7 | 0.987371 | 0.493685 | − | 0.869641i | \(-0.335649\pi\) | ||||
0.493685 | + | 0.869641i | \(0.335649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.32739e7 | −1.06994 | ||||||||
\(862\) | 75013.4i | 0.00343851i | ||||||||
\(863\) | 6.49502e6i | 0.296861i | 0.988923 | + | 0.148431i | \(0.0474222\pi\) | ||||
−0.988923 | + | 0.148431i | \(0.952578\pi\) | |||||||
\(864\) | 3.07789e6 | 0.140271 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.41402e6 | 0.200004 | ||||||||
\(867\) | 2.23449e7i | 1.00956i | ||||||||
\(868\) | − 6.82185e6i | − 0.307328i | ||||||||
\(869\) | 1.94761e7 | 0.874889 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.22078e6 | −0.143852 | ||||||||
\(872\) | 1.10907e7i | 0.493934i | ||||||||
\(873\) | − 1.85317e6i | − 0.0822961i | ||||||||
\(874\) | −3.05330e7 | −1.35204 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.41061e7 | −0.621079 | ||||||||
\(877\) | − 8.33527e6i | − 0.365949i | −0.983118 | − | 0.182975i | \(-0.941427\pi\) | ||||
0.983118 | − | 0.182975i | \(-0.0585726\pi\) | |||||||
\(878\) | 1.46809e7i | 0.642714i | ||||||||
\(879\) | −7.74993e6 | −0.338318 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.91817e6 | −0.213483 | −0.106742 | − | 0.994287i | \(-0.534042\pi\) | ||||
−0.106742 | + | 0.994287i | \(0.534042\pi\) | |||||||
\(882\) | 2.75619e6i | 0.119299i | ||||||||
\(883\) | 1.93128e7i | 0.833571i | 0.909005 | + | 0.416786i | \(0.136843\pi\) | ||||
−0.909005 | + | 0.416786i | \(0.863157\pi\) | |||||||
\(884\) | −1.09946e6 | −0.0473204 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.67989e7 | 0.718945 | ||||||||
\(887\) | 1.36071e7i | 0.580708i | 0.956919 | + | 0.290354i | \(0.0937731\pi\) | ||||
−0.956919 | + | 0.290354i | \(0.906227\pi\) | |||||||
\(888\) | − 3.56431e6i | − 0.151685i | ||||||||
\(889\) | −6.13761e6 | −0.260462 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45508e7 | 0.614033 | ||||||||
\(892\) | − 2.24039e7i | − 0.942784i | ||||||||
\(893\) | 3.88065e7i | 1.62845i | ||||||||
\(894\) | −1.46148e7 | −0.611576 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.42138e6 | −0.0591482 | ||||||||
\(897\) | 9.87575e6i | 0.409816i | ||||||||
\(898\) | 1.04498e7i | 0.432432i | ||||||||
\(899\) | 1.33994e7 | 0.552950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.01918e6 | −0.288054 | ||||||||
\(902\) | 1.22474e7i | 0.501219i | ||||||||
\(903\) | 4.31787e6i | 0.176218i | ||||||||
\(904\) | −6.09852e6 | −0.248201 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.51538e7 | 1.42282 | ||||||||
\(907\) | − 6.88886e6i | − 0.278054i | −0.990289 | − | 0.139027i | \(-0.955603\pi\) | ||||
0.990289 | − | 0.139027i | \(-0.0443975\pi\) | |||||||
\(908\) | 1.83263e6i | 0.0737666i | ||||||||
\(909\) | −7.40376e6 | −0.297196 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.68632e7 | −1.87084 | −0.935418 | − | 0.353544i | \(-0.884976\pi\) | ||||
−0.935418 | + | 0.353544i | \(0.884976\pi\) | |||||||
\(912\) | 1.06087e7i | 0.422351i | ||||||||
\(913\) | 6.94308e6i | 0.275661i | ||||||||
\(914\) | −2.34680e7 | −0.929203 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.02537e6 | −0.316029 | ||||||||
\(917\) | 1.66952e7i | 0.655644i | ||||||||
\(918\) | − 4.88861e6i | − 0.191460i | ||||||||
\(919\) | 1.51786e7 | 0.592849 | 0.296425 | − | 0.955056i | \(-0.404206\pi\) | ||||
0.296425 | + | 0.955056i | \(0.404206\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.26056e7 | 0.489681 | ||||||||
\(922\) | 382169.i | 0.0148057i | ||||||||
\(923\) | 1.40710e6i | 0.0543651i | ||||||||
\(924\) | −5.02590e6 | −0.193657 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.37399e7 | 0.526570 | ||||||||
\(927\) | − 5.12189e6i | − 0.195763i | ||||||||
\(928\) | − 2.79187e6i | − 0.106420i | ||||||||
\(929\) | 4.61722e7 | 1.75526 | 0.877629 | − | 0.479341i | \(-0.159124\pi\) | ||||
0.877629 | + | 0.479341i | \(0.159124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.15925e7 | 0.816447 | ||||||||
\(932\) | 2.36515e6i | 0.0891904i | ||||||||
\(933\) | 3.90223e7i | 1.46761i | ||||||||
\(934\) | 1.71005e7 | 0.641418 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 803040. | 0.0299604 | ||||||||
\(937\) | − 9.28215e6i | − 0.345382i | −0.984976 | − | 0.172691i | \(-0.944754\pi\) | ||||
0.984976 | − | 0.172691i | \(-0.0552462\pi\) | |||||||
\(938\) | 6.61341e6i | 0.245425i | ||||||||
\(939\) | 2.07445e7 | 0.767782 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.88066e7 | −1.79682 | −0.898410 | − | 0.439157i | \(-0.855277\pi\) | ||||
−0.898410 | + | 0.439157i | \(0.855277\pi\) | |||||||
\(942\) | 2.13444e7i | 0.783712i | ||||||||
\(943\) | − 4.94157e7i | − 1.80961i | ||||||||
\(944\) | −707264. | −0.0258316 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.27219e6 | 0.0825500 | ||||||||
\(947\) | − 4.19678e6i | − 0.152069i | −0.997105 | − | 0.0760347i | \(-0.975774\pi\) | ||||
0.997105 | − | 0.0760347i | \(-0.0242260\pi\) | |||||||
\(948\) | 2.73033e7i | 0.986722i | ||||||||
\(949\) | 8.36520e6 | 0.301516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.15753e7 | 1.49068 | ||||||||
\(952\) | 2.25759e6i | 0.0807332i | ||||||||
\(953\) | − 2.79666e7i | − 0.997487i | −0.866750 | − | 0.498743i | \(-0.833795\pi\) | ||||
0.866750 | − | 0.498743i | \(-0.166205\pi\) | |||||||
\(954\) | 5.12677e6 | 0.182378 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.08785e6 | −0.250824 | ||||||||
\(957\) | − 9.87183e6i | − 0.348432i | ||||||||
\(958\) | − 1.32442e6i | − 0.0466243i | ||||||||
\(959\) | −2.43016e7 | −0.853275 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.47563e6 | −0.156331 | ||||||||
\(962\) | 2.11371e6i | 0.0736388i | ||||||||
\(963\) | − 8.93291e6i | − 0.310404i | ||||||||
\(964\) | −1.29155e7 | −0.447631 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.02785e7 | 0.699185 | ||||||||
\(967\) | 5.45774e7i | 1.87692i | 0.345383 | + | 0.938462i | \(0.387749\pi\) | ||||
−0.345383 | + | 0.938462i | \(0.612251\pi\) | |||||||
\(968\) | − 7.66248e6i | − 0.262834i | ||||||||
\(969\) | 1.68498e7 | 0.576480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.64787e7 | 0.901258 | 0.450629 | − | 0.892711i | \(-0.351200\pi\) | ||||
0.450629 | + | 0.892711i | \(0.351200\pi\) | |||||||
\(972\) | 8.71217e6i | 0.295775i | ||||||||
\(973\) | − 2.87784e7i | − 0.974506i | ||||||||
\(974\) | 3.73333e7 | 1.26095 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.31334e6 | −0.144940 | ||||||||
\(977\) | 1.85214e7i | 0.620780i | 0.950609 | + | 0.310390i | \(0.100460\pi\) | ||||
−0.950609 | + | 0.310390i | \(0.899540\pi\) | |||||||
\(978\) | 3.41308e7i | 1.14104i | ||||||||
\(979\) | −5.42400e6 | −0.180868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.28662e7 | −0.426853 | ||||||||
\(982\) | − 2.08194e7i | − 0.688952i | ||||||||
\(983\) | − 2.22953e7i | − 0.735919i | −0.929842 | − | 0.367959i | \(-0.880057\pi\) | ||||
0.929842 | − | 0.367959i | \(-0.119943\pi\) | |||||||
\(984\) | −1.71695e7 | −0.565287 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.43433e6 | −0.145256 | ||||||||
\(987\) | − 2.57733e7i | − 0.842127i | ||||||||
\(988\) | − 6.29115e6i | − 0.205040i | ||||||||
\(989\) | −9.16781e6 | −0.298040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.55658e7 | 1.47385 | 0.736927 | − | 0.675972i | \(-0.236276\pi\) | ||||
0.736927 | + | 0.675972i | \(0.236276\pi\) | |||||||
\(992\) | − 5.03257e6i | − 0.162372i | ||||||||
\(993\) | 1.34635e7i | 0.433295i | ||||||||
\(994\) | 2.88928e6 | 0.0927521 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.73341e6 | −0.310897 | ||||||||
\(997\) | 3.81521e7i | 1.21557i | 0.794101 | + | 0.607786i | \(0.207942\pi\) | ||||
−0.794101 | + | 0.607786i | \(0.792058\pi\) | |||||||
\(998\) | − 3.80460e7i | − 1.20916i | ||||||||
\(999\) | −9.39833e6 | −0.297946 |
(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 | 650.6.b.g.599.2 | 4 | ||
5.2 | odd | 4 | 650.6.a.h.1.2 | 2 | |||
5.3 | odd | 4 | 130.6.a.a.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 650.6.b.g.599.3 | 4 | ||
20.3 | even | 4 | 1040.6.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.6.a.a.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
650.6.a.h.1.2 | 2 | 5.2 | odd | 4 | |||
650.6.b.g.599.2 | 4 | 1.1 | even | 1 | trivial | ||
650.6.b.g.599.3 | 4 | 5.4 | even | 2 | inner | ||
1040.6.a.e.1.2 | 2 | 20.3 | even | 4 |