Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(4.65113077458\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 278x^{10} + 28285x^{8} + 1260472x^{6} + 22944832x^{4} + 140087936x^{2} + 966400 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{14}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.12 | ||
Root | \(9.47123i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.6.b.a.28.1 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.47123i | 1.67429i | 0.546979 | + | 0.837146i | \(0.315778\pi\) | ||||
−0.546979 | + | 0.837146i | \(0.684222\pi\) | |||||||
\(3\) | 19.9099i | 1.27722i | 0.769531 | + | 0.638609i | \(0.220490\pi\) | ||||
−0.769531 | + | 0.638609i | \(0.779510\pi\) | |||||||
\(4\) | −57.7042 | −1.80326 | ||||||||
\(5\) | −4.84615 | −0.0866906 | −0.0433453 | − | 0.999060i | \(-0.513802\pi\) | ||||
−0.0433453 | + | 0.999060i | \(0.513802\pi\) | |||||||
\(6\) | −188.571 | −2.13844 | ||||||||
\(7\) | 219.131 | 1.69028 | 0.845138 | − | 0.534548i | \(-0.179518\pi\) | ||||
0.845138 | + | 0.534548i | \(0.179518\pi\) | |||||||
\(8\) | − | 243.450i | − | 1.34489i | ||||||
\(9\) | −153.403 | −0.631288 | ||||||||
\(10\) | − | 45.8990i | − | 0.145145i | ||||||
\(11\) | − | 12.7646i | − | 0.0318072i | −0.999874 | − | 0.0159036i | \(-0.994938\pi\) | ||
0.999874 | − | 0.0159036i | \(-0.00506249\pi\) | |||||||
\(12\) | − | 1148.88i | − | 2.30315i | ||||||
\(13\) | −566.970 | −0.930469 | −0.465234 | − | 0.885187i | \(-0.654030\pi\) | ||||
−0.465234 | + | 0.885187i | \(0.654030\pi\) | |||||||
\(14\) | 2075.44i | 2.83002i | ||||||||
\(15\) | − | 96.4863i | − | 0.110723i | ||||||
\(16\) | 459.241 | 0.448477 | ||||||||
\(17\) | − | 1156.19i | − | 0.970302i | −0.874430 | − | 0.485151i | \(-0.838765\pi\) | ||
0.874430 | − | 0.485151i | \(-0.161235\pi\) | |||||||
\(18\) | − | 1452.92i | − | 1.05696i | ||||||
\(19\) | 2227.86i | 1.41580i | 0.706310 | + | 0.707902i | \(0.250358\pi\) | ||||
−0.706310 | + | 0.707902i | \(0.749642\pi\) | |||||||
\(20\) | 279.643 | 0.156325 | ||||||||
\(21\) | 4362.86i | 2.15885i | ||||||||
\(22\) | 120.897 | 0.0532546 | ||||||||
\(23\) | 4382.29 | 1.72736 | 0.863678 | − | 0.504044i | \(-0.168155\pi\) | ||||
0.863678 | + | 0.504044i | \(0.168155\pi\) | |||||||
\(24\) | 4847.07 | 1.71771 | ||||||||
\(25\) | −3101.51 | −0.992485 | ||||||||
\(26\) | − | 5369.91i | − | 1.55788i | ||||||
\(27\) | 1783.86i | 0.470926i | ||||||||
\(28\) | −12644.8 | −3.04800 | ||||||||
\(29\) | 4035.37 | − | 2055.94i | 0.891023 | − | 0.453959i | ||||
\(30\) | 913.844 | 0.185383 | ||||||||
\(31\) | − | 2588.50i | − | 0.483775i | −0.970304 | − | 0.241887i | \(-0.922234\pi\) | ||
0.970304 | − | 0.241887i | \(-0.0777665\pi\) | |||||||
\(32\) | − | 3440.84i | − | 0.594004i | ||||||
\(33\) | 254.142 | 0.0406248 | ||||||||
\(34\) | 10950.5 | 1.62457 | ||||||||
\(35\) | −1061.94 | −0.146531 | ||||||||
\(36\) | 8852.00 | 1.13837 | ||||||||
\(37\) | 12430.1i | 1.49269i | 0.665558 | + | 0.746346i | \(0.268194\pi\) | ||||
−0.665558 | + | 0.746346i | \(0.731806\pi\) | |||||||
\(38\) | −21100.6 | −2.37047 | ||||||||
\(39\) | − | 11288.3i | − | 1.18841i | ||||||
\(40\) | 1179.80i | 0.116589i | ||||||||
\(41\) | 3689.31i | 0.342756i | 0.985205 | + | 0.171378i | \(0.0548220\pi\) | ||||
−0.985205 | + | 0.171378i | \(0.945178\pi\) | |||||||
\(42\) | −41321.7 | −3.61455 | ||||||||
\(43\) | − | 12839.1i | − | 1.05892i | −0.848336 | − | 0.529459i | \(-0.822395\pi\) | ||
0.848336 | − | 0.529459i | \(-0.177605\pi\) | |||||||
\(44\) | 736.572i | 0.0573566i | ||||||||
\(45\) | 743.415 | 0.0547268 | ||||||||
\(46\) | 41505.7i | 2.89210i | ||||||||
\(47\) | − | 6917.34i | − | 0.456767i | −0.973571 | − | 0.228383i | \(-0.926656\pi\) | ||
0.973571 | − | 0.228383i | \(-0.0733439\pi\) | |||||||
\(48\) | 9143.42i | 0.572804i | ||||||||
\(49\) | 31211.2 | 1.85704 | ||||||||
\(50\) | − | 29375.2i | − | 1.66171i | ||||||
\(51\) | 23019.6 | 1.23929 | ||||||||
\(52\) | 32716.6 | 1.67787 | ||||||||
\(53\) | 21951.5 | 1.07343 | 0.536716 | − | 0.843763i | \(-0.319665\pi\) | ||||
0.536716 | + | 0.843763i | \(0.319665\pi\) | |||||||
\(54\) | −16895.4 | −0.788468 | ||||||||
\(55\) | 61.8593i | 0.00275739i | ||||||||
\(56\) | − | 53347.4i | − | 2.27323i | ||||||
\(57\) | −44356.4 | −1.80829 | ||||||||
\(58\) | 19472.3 | + | 38220.0i | 0.760060 | + | 1.49183i | ||||
\(59\) | 6943.35 | 0.259680 | 0.129840 | − | 0.991535i | \(-0.458554\pi\) | ||||
0.129840 | + | 0.991535i | \(0.458554\pi\) | |||||||
\(60\) | 5567.67i | 0.199662i | ||||||||
\(61\) | − | 24856.9i | − | 0.855306i | −0.903943 | − | 0.427653i | \(-0.859340\pi\) | ||
0.903943 | − | 0.427653i | \(-0.140660\pi\) | |||||||
\(62\) | 24516.2 | 0.809981 | ||||||||
\(63\) | −33615.3 | −1.06705 | ||||||||
\(64\) | 47284.7 | 1.44301 | ||||||||
\(65\) | 2747.62 | 0.0806629 | ||||||||
\(66\) | 2407.04i | 0.0680178i | ||||||||
\(67\) | −43952.6 | −1.19618 | −0.598091 | − | 0.801428i | \(-0.704074\pi\) | ||||
−0.598091 | + | 0.801428i | \(0.704074\pi\) | |||||||
\(68\) | 66717.1i | 1.74970i | ||||||||
\(69\) | 87250.9i | 2.20621i | ||||||||
\(70\) | − | 10057.9i | − | 0.245336i | ||||||
\(71\) | −12059.2 | −0.283905 | −0.141952 | − | 0.989874i | \(-0.545338\pi\) | ||||
−0.141952 | + | 0.989874i | \(0.545338\pi\) | |||||||
\(72\) | 37346.0i | 0.849011i | ||||||||
\(73\) | 39425.0i | 0.865893i | 0.901420 | + | 0.432947i | \(0.142526\pi\) | ||||
−0.901420 | + | 0.432947i | \(0.857474\pi\) | |||||||
\(74\) | −117728. | −2.49921 | ||||||||
\(75\) | − | 61750.8i | − | 1.26762i | ||||||
\(76\) | − | 128557.i | − | 2.55306i | ||||||
\(77\) | − | 2797.12i | − | 0.0537630i | ||||||
\(78\) | 106914. | 1.98975 | ||||||||
\(79\) | 34619.6i | 0.624101i | 0.950066 | + | 0.312050i | \(0.101016\pi\) | ||||
−0.950066 | + | 0.312050i | \(0.898984\pi\) | |||||||
\(80\) | −2225.55 | −0.0388788 | ||||||||
\(81\) | −72793.4 | −1.23276 | ||||||||
\(82\) | −34942.3 | −0.573875 | ||||||||
\(83\) | 21990.2 | 0.350376 | 0.175188 | − | 0.984535i | \(-0.443947\pi\) | ||||
0.175188 | + | 0.984535i | \(0.443947\pi\) | |||||||
\(84\) | − | 251755.i | − | 3.89297i | ||||||
\(85\) | 5603.08i | 0.0841161i | ||||||||
\(86\) | 121602. | 1.77294 | ||||||||
\(87\) | 40933.6 | + | 80343.8i | 0.579805 | + | 1.13803i | ||||
\(88\) | −3107.55 | −0.0427771 | ||||||||
\(89\) | − | 64375.4i | − | 0.861480i | −0.902476 | − | 0.430740i | \(-0.858253\pi\) | ||
0.902476 | − | 0.430740i | \(-0.141747\pi\) | |||||||
\(90\) | 7041.05i | 0.0916286i | ||||||||
\(91\) | −124240. | −1.57275 | ||||||||
\(92\) | −252877. | −3.11487 | ||||||||
\(93\) | 51536.6 | 0.617887 | ||||||||
\(94\) | 65515.7 | 0.764761 | ||||||||
\(95\) | − | 10796.5i | − | 0.122737i | ||||||
\(96\) | 68506.7 | 0.758673 | ||||||||
\(97\) | − | 143461.i | − | 1.54812i | −0.633110 | − | 0.774062i | \(-0.718222\pi\) | ||
0.633110 | − | 0.774062i | \(-0.281778\pi\) | |||||||
\(98\) | 295608.i | 3.10922i | ||||||||
\(99\) | 1958.13i | 0.0200795i | ||||||||
\(100\) | 178970. | 1.78970 | ||||||||
\(101\) | 4588.83i | 0.0447609i | 0.999750 | + | 0.0223804i | \(0.00712451\pi\) | ||||
−0.999750 | + | 0.0223804i | \(0.992875\pi\) | |||||||
\(102\) | 218024.i | 2.07493i | ||||||||
\(103\) | 63906.9 | 0.593546 | 0.296773 | − | 0.954948i | \(-0.404090\pi\) | ||||
0.296773 | + | 0.954948i | \(0.404090\pi\) | |||||||
\(104\) | 138029.i | 1.25137i | ||||||||
\(105\) | − | 21143.1i | − | 0.187152i | ||||||
\(106\) | 207908.i | 1.79724i | ||||||||
\(107\) | −38764.2 | −0.327319 | −0.163660 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163660 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(108\) | − | 102936.i | − | 0.849200i | ||||||
\(109\) | 159706. | 1.28752 | 0.643761 | − | 0.765227i | \(-0.277373\pi\) | ||||
0.643761 | + | 0.765227i | \(0.277373\pi\) | |||||||
\(110\) | −585.883 | −0.00461668 | ||||||||
\(111\) | −247482. | −1.90650 | ||||||||
\(112\) | 100634. | 0.758051 | ||||||||
\(113\) | − | 56711.6i | − | 0.417807i | −0.977936 | − | 0.208904i | \(-0.933011\pi\) | ||
0.977936 | − | 0.208904i | \(-0.0669895\pi\) | |||||||
\(114\) | − | 420109.i | − | 3.02761i | ||||||
\(115\) | −21237.3 | −0.149746 | ||||||||
\(116\) | −232858. | + | 118637.i | −1.60674 | + | 0.818604i | ||||
\(117\) | 86974.9 | 0.587394 | ||||||||
\(118\) | 65762.1i | 0.434781i | ||||||||
\(119\) | − | 253357.i | − | 1.64008i | ||||||
\(120\) | −23489.6 | −0.148910 | ||||||||
\(121\) | 160888. | 0.998988 | ||||||||
\(122\) | 235425. | 1.43203 | ||||||||
\(123\) | −73453.7 | −0.437775 | ||||||||
\(124\) | 149367.i | 0.872370i | ||||||||
\(125\) | 30174.6 | 0.172730 | ||||||||
\(126\) | − | 318378.i | − | 1.78656i | ||||||
\(127\) | − | 158805.i | − | 0.873682i | −0.899539 | − | 0.436841i | \(-0.856097\pi\) | ||
0.899539 | − | 0.436841i | \(-0.143903\pi\) | |||||||
\(128\) | 337737.i | 1.82202i | ||||||||
\(129\) | 255624. | 1.35247 | ||||||||
\(130\) | 26023.4i | 0.135053i | ||||||||
\(131\) | 90328.1i | 0.459880i | 0.973205 | + | 0.229940i | \(0.0738530\pi\) | ||||
−0.973205 | + | 0.229940i | \(0.926147\pi\) | |||||||
\(132\) | −14665.0 | −0.0732569 | ||||||||
\(133\) | 488192.i | 2.39310i | ||||||||
\(134\) | − | 416285.i | − | 2.00276i | ||||||
\(135\) | − | 8644.88i | − | 0.0408248i | ||||||
\(136\) | −281475. | −1.30495 | ||||||||
\(137\) | − | 221885.i | − | 1.01001i | −0.863116 | − | 0.505006i | \(-0.831490\pi\) | ||
0.863116 | − | 0.505006i | \(-0.168510\pi\) | |||||||
\(138\) | −826373. | −3.69384 | ||||||||
\(139\) | −72649.2 | −0.318929 | −0.159465 | − | 0.987204i | \(-0.550977\pi\) | ||||
−0.159465 | + | 0.987204i | \(0.550977\pi\) | |||||||
\(140\) | 61278.4 | 0.264233 | ||||||||
\(141\) | 137723. | 0.583391 | ||||||||
\(142\) | − | 114215.i | − | 0.475339i | ||||||
\(143\) | 7237.15i | 0.0295956i | ||||||||
\(144\) | −70448.9 | −0.283118 | ||||||||
\(145\) | −19556.0 | + | 9963.42i | −0.0772433 | + | 0.0393540i | ||||
\(146\) | −373403. | −1.44976 | ||||||||
\(147\) | 621411.i | 2.37184i | ||||||||
\(148\) | − | 717269.i | − | 2.69171i | ||||||
\(149\) | −284587. | −1.05014 | −0.525072 | − | 0.851058i | \(-0.675962\pi\) | ||||
−0.525072 | + | 0.851058i | \(0.675962\pi\) | |||||||
\(150\) | 584856. | 2.12237 | ||||||||
\(151\) | −345064. | −1.23157 | −0.615783 | − | 0.787916i | \(-0.711160\pi\) | ||||
−0.615783 | + | 0.787916i | \(0.711160\pi\) | |||||||
\(152\) | 542373. | 1.90410 | ||||||||
\(153\) | 177363.i | 0.612540i | ||||||||
\(154\) | 26492.1 | 0.0900150 | ||||||||
\(155\) | 12544.3i | 0.0419388i | ||||||||
\(156\) | 651383.i | 2.14301i | ||||||||
\(157\) | 111826.i | 0.362071i | 0.983477 | + | 0.181035i | \(0.0579449\pi\) | ||||
−0.983477 | + | 0.181035i | \(0.942055\pi\) | |||||||
\(158\) | −327891. | −1.04493 | ||||||||
\(159\) | 437052.i | 1.37101i | ||||||||
\(160\) | 16674.8i | 0.0514946i | ||||||||
\(161\) | 960294. | 2.91971 | ||||||||
\(162\) | − | 689444.i | − | 2.06401i | ||||||
\(163\) | − | 563756.i | − | 1.66197i | −0.556297 | − | 0.830984i | \(-0.687778\pi\) | ||
0.556297 | − | 0.830984i | \(-0.312222\pi\) | |||||||
\(164\) | − | 212889.i | − | 0.618078i | ||||||
\(165\) | −1231.61 | −0.00352179 | ||||||||
\(166\) | 208275.i | 0.586632i | ||||||||
\(167\) | 100531. | 0.278938 | 0.139469 | − | 0.990226i | \(-0.455460\pi\) | ||||
0.139469 | + | 0.990226i | \(0.455460\pi\) | |||||||
\(168\) | 1.06214e6 | 2.90341 | ||||||||
\(169\) | −49837.8 | −0.134228 | ||||||||
\(170\) | −53068.0 | −0.140835 | ||||||||
\(171\) | − | 341760.i | − | 0.893781i | ||||||
\(172\) | 740868.i | 1.90950i | ||||||||
\(173\) | −522238. | −1.32664 | −0.663321 | − | 0.748335i | \(-0.730853\pi\) | ||||
−0.663321 | + | 0.748335i | \(0.730853\pi\) | |||||||
\(174\) | −760954. | + | 387692.i | −1.90540 | + | 0.970763i | ||||
\(175\) | −679637. | −1.67757 | ||||||||
\(176\) | − | 5862.03i | − | 0.0142648i | ||||||
\(177\) | 138241.i | 0.331669i | ||||||||
\(178\) | 609715. | 1.44237 | ||||||||
\(179\) | 700959. | 1.63516 | 0.817579 | − | 0.575816i | \(-0.195316\pi\) | ||||
0.817579 | + | 0.575816i | \(0.195316\pi\) | |||||||
\(180\) | −42898.1 | −0.0986864 | ||||||||
\(181\) | −228696. | −0.518873 | −0.259437 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259437 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(182\) | − | 1.17671e6i | − | 2.63324i | ||||||
\(183\) | 494897. | 1.09241 | ||||||||
\(184\) | − | 1.06687e6i | − | 2.32310i | ||||||
\(185\) | − | 60238.2i | − | 0.129402i | ||||||
\(186\) | 488115.i | 1.03452i | ||||||||
\(187\) | −14758.3 | −0.0308626 | ||||||||
\(188\) | 399160.i | 0.823667i | ||||||||
\(189\) | 390899.i | 0.795995i | ||||||||
\(190\) | 102257. | 0.205498 | ||||||||
\(191\) | − | 824840.i | − | 1.63601i | −0.575211 | − | 0.818005i | \(-0.695080\pi\) | ||
0.575211 | − | 0.818005i | \(-0.304920\pi\) | |||||||
\(192\) | 941432.i | 1.84305i | ||||||||
\(193\) | 937075.i | 1.81084i | 0.424512 | + | 0.905422i | \(0.360446\pi\) | ||||
−0.424512 | + | 0.905422i | \(0.639554\pi\) | |||||||
\(194\) | 1.35876e6 | 2.59201 | ||||||||
\(195\) | 54704.9i | 0.103024i | ||||||||
\(196\) | −1.80102e6 | −3.34871 | ||||||||
\(197\) | 44740.0 | 0.0821354 | 0.0410677 | − | 0.999156i | \(-0.486924\pi\) | ||||
0.0410677 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(198\) | −18545.9 | −0.0336190 | ||||||||
\(199\) | −237978. | −0.425996 | −0.212998 | − | 0.977053i | \(-0.568323\pi\) | ||||
−0.212998 | + | 0.977053i | \(0.568323\pi\) | |||||||
\(200\) | 755065.i | 1.33478i | ||||||||
\(201\) | − | 875091.i | − | 1.52779i | ||||||
\(202\) | −43461.9 | −0.0749428 | ||||||||
\(203\) | 884274. | − | 450520.i | 1.50607 | − | 0.767316i | ||||
\(204\) | −1.32833e6 | −2.23475 | ||||||||
\(205\) | − | 17879.0i | − | 0.0297138i | ||||||
\(206\) | 605277.i | 0.993770i | ||||||||
\(207\) | −672257. | −1.09046 | ||||||||
\(208\) | −260376. | −0.417294 | ||||||||
\(209\) | 28437.7 | 0.0450328 | ||||||||
\(210\) | 200251. | 0.313348 | ||||||||
\(211\) | − | 194564.i | − | 0.300855i | −0.988621 | − | 0.150427i | \(-0.951935\pi\) | ||
0.988621 | − | 0.150427i | \(-0.0480649\pi\) | |||||||
\(212\) | −1.26669e6 | −1.93567 | ||||||||
\(213\) | − | 240097.i | − | 0.362608i | ||||||
\(214\) | − | 367145.i | − | 0.548029i | ||||||
\(215\) | 62220.1i | 0.0917982i | ||||||||
\(216\) | 434283. | 0.633342 | ||||||||
\(217\) | − | 567219.i | − | 0.817714i | ||||||
\(218\) | 1.51261e6i | 2.15569i | ||||||||
\(219\) | −784947. | −1.10594 | ||||||||
\(220\) | − | 3569.54i | − | 0.00497228i | ||||||
\(221\) | 655526.i | 0.902836i | ||||||||
\(222\) | − | 2.34396e6i | − | 3.19203i | ||||||
\(223\) | 242137. | 0.326061 | 0.163031 | − | 0.986621i | \(-0.447873\pi\) | ||||
0.163031 | + | 0.986621i | \(0.447873\pi\) | |||||||
\(224\) | − | 753993.i | − | 1.00403i | ||||||
\(225\) | 475782. | 0.626544 | ||||||||
\(226\) | 537129. | 0.699532 | ||||||||
\(227\) | −1.27196e6 | −1.63835 | −0.819177 | − | 0.573540i | \(-0.805570\pi\) | ||||
−0.819177 | + | 0.573540i | \(0.805570\pi\) | |||||||
\(228\) | 2.55955e6 | 3.26082 | ||||||||
\(229\) | − | 48917.8i | − | 0.0616422i | −0.999525 | − | 0.0308211i | \(-0.990188\pi\) | ||
0.999525 | − | 0.0308211i | \(-0.00981222\pi\) | |||||||
\(230\) | − | 201143.i | − | 0.250718i | ||||||
\(231\) | 55690.2 | 0.0686672 | ||||||||
\(232\) | −500521. | − | 982413.i | −0.610523 | − | 1.19832i | ||||
\(233\) | 467458. | 0.564095 | 0.282048 | − | 0.959400i | \(-0.408986\pi\) | ||||
0.282048 | + | 0.959400i | \(0.408986\pi\) | |||||||
\(234\) | 823760.i | 0.983470i | ||||||||
\(235\) | 33522.5i | 0.0395974i | ||||||||
\(236\) | −400660. | −0.468270 | ||||||||
\(237\) | −689273. | −0.797113 | ||||||||
\(238\) | 2.39960e6 | 2.74597 | ||||||||
\(239\) | 297093. | 0.336432 | 0.168216 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168216 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(240\) | − | 44310.4i | − | 0.0496567i | ||||||
\(241\) | −212345. | −0.235504 | −0.117752 | − | 0.993043i | \(-0.537569\pi\) | ||||
−0.117752 | + | 0.993043i | \(0.537569\pi\) | |||||||
\(242\) | 1.52381e6i | 1.67260i | ||||||||
\(243\) | − | 1.01583e6i | − | 1.10358i | ||||||
\(244\) | 1.43435e6i | 1.54234i | ||||||||
\(245\) | −151254. | −0.160988 | ||||||||
\(246\) | − | 695697.i | − | 0.732963i | ||||||
\(247\) | − | 1.26313e6i | − | 1.31736i | ||||||
\(248\) | −630171. | −0.650622 | ||||||||
\(249\) | 437823.i | 0.447507i | ||||||||
\(250\) | 285791.i | 0.289200i | ||||||||
\(251\) | 531502.i | 0.532502i | 0.963904 | + | 0.266251i | \(0.0857849\pi\) | ||||
−0.963904 | + | 0.266251i | \(0.914215\pi\) | |||||||
\(252\) | 1.93974e6 | 1.92417 | ||||||||
\(253\) | − | 55938.3i | − | 0.0549424i | ||||||
\(254\) | 1.50407e6 | 1.46280 | ||||||||
\(255\) | −111557. | −0.107435 | ||||||||
\(256\) | −1.68568e6 | −1.60759 | ||||||||
\(257\) | −796939. | −0.752649 | −0.376324 | − | 0.926488i | \(-0.622812\pi\) | ||||
−0.376324 | + | 0.926488i | \(0.622812\pi\) | |||||||
\(258\) | 2.42107e6i | 2.26443i | ||||||||
\(259\) | 2.72382e6i | 2.52306i | ||||||||
\(260\) | −158549. | −0.145456 | ||||||||
\(261\) | −619039. | + | 315388.i | −0.562492 | + | 0.286579i | ||||
\(262\) | −855518. | −0.769974 | ||||||||
\(263\) | 96852.0i | 0.0863414i | 0.999068 | + | 0.0431707i | \(0.0137459\pi\) | ||||
−0.999068 | + | 0.0431707i | \(0.986254\pi\) | |||||||
\(264\) | − | 61870.9i | − | 0.0546357i | ||||||
\(265\) | −106380. | −0.0930565 | ||||||||
\(266\) | −4.62378e6 | −4.00675 | ||||||||
\(267\) | 1.28171e6 | 1.10030 | ||||||||
\(268\) | 2.53625e6 | 2.15702 | ||||||||
\(269\) | 1.97762e6i | 1.66634i | 0.553020 | + | 0.833168i | \(0.313475\pi\) | ||||
−0.553020 | + | 0.833168i | \(0.686525\pi\) | |||||||
\(270\) | 81877.7 | 0.0683527 | ||||||||
\(271\) | − | 441551.i | − | 0.365223i | −0.983185 | − | 0.182611i | \(-0.941545\pi\) | ||
0.983185 | − | 0.182611i | \(-0.0584550\pi\) | |||||||
\(272\) | − | 530970.i | − | 0.435158i | ||||||
\(273\) | − | 2.47361e6i | − | 2.00875i | ||||||
\(274\) | 2.10152e6 | 1.69106 | ||||||||
\(275\) | 39589.6i | 0.0315682i | ||||||||
\(276\) | − | 5.03474e6i | − | 3.97837i | ||||||
\(277\) | −443173. | −0.347035 | −0.173518 | − | 0.984831i | \(-0.555513\pi\) | ||||
−0.173518 | + | 0.984831i | \(0.555513\pi\) | |||||||
\(278\) | − | 688078.i | − | 0.533981i | ||||||
\(279\) | 397083.i | 0.305401i | ||||||||
\(280\) | 258530.i | 0.197068i | ||||||||
\(281\) | 1.37176e6 | 1.03637 | 0.518183 | − | 0.855270i | \(-0.326609\pi\) | ||||
0.518183 | + | 0.855270i | \(0.326609\pi\) | |||||||
\(282\) | 1.30441e6i | 0.976767i | ||||||||
\(283\) | −736175. | −0.546405 | −0.273203 | − | 0.961956i | \(-0.588083\pi\) | ||||
−0.273203 | + | 0.961956i | \(0.588083\pi\) | |||||||
\(284\) | 695866. | 0.511953 | ||||||||
\(285\) | 214958. | 0.156762 | ||||||||
\(286\) | −68544.8 | −0.0495518 | ||||||||
\(287\) | 808441.i | 0.579353i | ||||||||
\(288\) | 527835.i | 0.374988i | ||||||||
\(289\) | 83080.5 | 0.0585133 | ||||||||
\(290\) | −94365.9 | − | 185220.i | −0.0658901 | − | 0.129328i | ||||
\(291\) | 2.85630e6 | 1.97729 | ||||||||
\(292\) | − | 2.27499e6i | − | 1.56143i | ||||||
\(293\) | − | 1.61860e6i | − | 1.10147i | −0.834681 | − | 0.550734i | \(-0.814348\pi\) | ||
0.834681 | − | 0.550734i | \(-0.185652\pi\) | |||||||
\(294\) | −5.88553e6 | −3.97116 | ||||||||
\(295\) | −33648.5 | −0.0225118 | ||||||||
\(296\) | 3.02611e6 | 2.00750 | ||||||||
\(297\) | 22770.3 | 0.0149788 | ||||||||
\(298\) | − | 2.69539e6i | − | 1.75825i | ||||||
\(299\) | −2.48463e6 | −1.60725 | ||||||||
\(300\) | 3.56328e6i | 2.28584i | ||||||||
\(301\) | − | 2.81343e6i | − | 1.78986i | ||||||
\(302\) | − | 3.26818e6i | − | 2.06200i | ||||||
\(303\) | −91363.0 | −0.0571694 | ||||||||
\(304\) | 1.02312e6i | 0.634956i | ||||||||
\(305\) | 120460.i | 0.0741471i | ||||||||
\(306\) | −1.67985e6 | −1.02557 | ||||||||
\(307\) | 909944.i | 0.551022i | 0.961298 | + | 0.275511i | \(0.0888470\pi\) | ||||
−0.961298 | + | 0.275511i | \(0.911153\pi\) | |||||||
\(308\) | 161405.i | 0.0969485i | ||||||||
\(309\) | 1.27238e6i | 0.758088i | ||||||||
\(310\) | −118810. | −0.0702178 | ||||||||
\(311\) | 2.84768e6i | 1.66952i | 0.550616 | + | 0.834758i | \(0.314393\pi\) | ||||
−0.550616 | + | 0.834758i | \(0.685607\pi\) | |||||||
\(312\) | −2.74814e6 | −1.59828 | ||||||||
\(313\) | −2.05227e6 | −1.18406 | −0.592029 | − | 0.805917i | \(-0.701673\pi\) | ||||
−0.592029 | + | 0.805917i | \(0.701673\pi\) | |||||||
\(314\) | −1.05913e6 | −0.606213 | ||||||||
\(315\) | 162905. | 0.0925034 | ||||||||
\(316\) | − | 1.99770e6i | − | 1.12541i | ||||||
\(317\) | 1.41233e6i | 0.789382i | 0.918814 | + | 0.394691i | \(0.129148\pi\) | ||||
−0.918814 | + | 0.394691i | \(0.870852\pi\) | |||||||
\(318\) | −4.13942e6 | −2.29547 | ||||||||
\(319\) | −26243.3 | − | 51510.0i | −0.0144392 | − | 0.0283410i | ||||
\(320\) | −229149. | −0.125096 | ||||||||
\(321\) | − | 771791.i | − | 0.418059i | ||||||
\(322\) | 9.09517e6i | 4.88845i | ||||||||
\(323\) | 2.57583e6 | 1.37376 | ||||||||
\(324\) | 4.20049e6 | 2.22299 | ||||||||
\(325\) | 1.75847e6 | 0.923476 | ||||||||
\(326\) | 5.33947e6 | 2.78262 | ||||||||
\(327\) | 3.17972e6i | 1.64445i | ||||||||
\(328\) | 898164. | 0.460968 | ||||||||
\(329\) | − | 1.51580e6i | − | 0.772062i | ||||||
\(330\) | − | 11664.9i | − | 0.00589651i | ||||||
\(331\) | − | 1.52835e6i | − | 0.766746i | −0.923594 | − | 0.383373i | \(-0.874762\pi\) | ||
0.923594 | − | 0.383373i | \(-0.125238\pi\) | |||||||
\(332\) | −1.26893e6 | −0.631818 | ||||||||
\(333\) | − | 1.90682e6i | − | 0.942319i | ||||||
\(334\) | 952151.i | 0.467024i | ||||||||
\(335\) | 213001. | 0.103698 | ||||||||
\(336\) | 2.00360e6i | 0.968197i | ||||||||
\(337\) | 935271.i | 0.448604i | 0.974520 | + | 0.224302i | \(0.0720101\pi\) | ||||
−0.974520 | + | 0.224302i | \(0.927990\pi\) | |||||||
\(338\) | − | 472025.i | − | 0.224736i | ||||||
\(339\) | 1.12912e6 | 0.533631 | ||||||||
\(340\) | − | 323321.i | − | 0.151683i | ||||||
\(341\) | −33041.2 | −0.0153875 | ||||||||
\(342\) | 3.23689e6 | 1.49645 | ||||||||
\(343\) | 3.15640e6 | 1.44863 | ||||||||
\(344\) | −3.12568e6 | −1.42412 | ||||||||
\(345\) | − | 422831.i | − | 0.191258i | ||||||
\(346\) | − | 4.94624e6i | − | 2.22119i | ||||||
\(347\) | 1.16833e6 | 0.520886 | 0.260443 | − | 0.965489i | \(-0.416131\pi\) | ||||
0.260443 | + | 0.965489i | \(0.416131\pi\) | |||||||
\(348\) | −2.36204e6 | − | 4.63617e6i | −1.04554 | − | 2.05216i | ||||
\(349\) | −3.70492e6 | −1.62823 | −0.814114 | − | 0.580706i | \(-0.802777\pi\) | ||||
−0.814114 | + | 0.580706i | \(0.802777\pi\) | |||||||
\(350\) | − | 6.43700e6i | − | 2.80875i | ||||||
\(351\) | − | 1.01140e6i | − | 0.438182i | ||||||
\(352\) | −43921.0 | −0.0188936 | ||||||||
\(353\) | −2.64790e6 | −1.13100 | −0.565502 | − | 0.824747i | \(-0.691318\pi\) | ||||
−0.565502 | + | 0.824747i | \(0.691318\pi\) | |||||||
\(354\) | −1.30931e6 | −0.555310 | ||||||||
\(355\) | 58440.7 | 0.0246119 | ||||||||
\(356\) | 3.71473e6i | 1.55347i | ||||||||
\(357\) | 5.04430e6 | 2.09474 | ||||||||
\(358\) | 6.63894e6i | 2.73773i | ||||||||
\(359\) | − | 3.45478e6i | − | 1.41476i | −0.706831 | − | 0.707382i | \(-0.749876\pi\) | ||
0.706831 | − | 0.707382i | \(-0.250124\pi\) | |||||||
\(360\) | − | 180985.i | − | 0.0736013i | ||||||
\(361\) | −2.48725e6 | −1.00450 | ||||||||
\(362\) | − | 2.16603e6i | − | 0.868746i | ||||||
\(363\) | 3.20326e6i | 1.27593i | ||||||||
\(364\) | 7.16920e6 | 2.83607 | ||||||||
\(365\) | − | 191060.i | − | 0.0750649i | ||||||
\(366\) | 4.68728e6i | 1.82902i | ||||||||
\(367\) | − | 1.44664e6i | − | 0.560654i | −0.959905 | − | 0.280327i | \(-0.909557\pi\) | ||
0.959905 | − | 0.280327i | \(-0.0904429\pi\) | |||||||
\(368\) | 2.01253e6 | 0.774680 | ||||||||
\(369\) | − | 565951.i | − | 0.216378i | ||||||
\(370\) | 570530. | 0.216658 | ||||||||
\(371\) | 4.81025e6 | 1.81440 | ||||||||
\(372\) | −2.97388e6 | −1.11421 | ||||||||
\(373\) | 1.80613e6 | 0.672168 | 0.336084 | − | 0.941832i | \(-0.390897\pi\) | ||||
0.336084 | + | 0.941832i | \(0.390897\pi\) | |||||||
\(374\) | − | 139779.i | − | 0.0516731i | ||||||
\(375\) | 600773.i | 0.220614i | ||||||||
\(376\) | −1.68403e6 | −0.614299 | ||||||||
\(377\) | −2.28794e6 | + | 1.16566e6i | −0.829069 | + | 0.422395i | ||||
\(378\) | −3.70230e6 | −1.33273 | ||||||||
\(379\) | 1.53246e6i | 0.548015i | 0.961728 | + | 0.274007i | \(0.0883492\pi\) | ||||
−0.961728 | + | 0.274007i | \(0.911651\pi\) | |||||||
\(380\) | 623006.i | 0.221326i | ||||||||
\(381\) | 3.16178e6 | 1.11588 | ||||||||
\(382\) | 7.81225e6 | 2.73916 | ||||||||
\(383\) | −3.49639e6 | −1.21793 | −0.608966 | − | 0.793197i | \(-0.708415\pi\) | ||||
−0.608966 | + | 0.793197i | \(0.708415\pi\) | |||||||
\(384\) | −6.72431e6 | −2.32712 | ||||||||
\(385\) | 13555.3i | 0.00466075i | ||||||||
\(386\) | −8.87526e6 | −3.03188 | ||||||||
\(387\) | 1.96955e6i | 0.668482i | ||||||||
\(388\) | 8.27833e6i | 2.79167i | ||||||||
\(389\) | − | 2.08406e6i | − | 0.698290i | −0.937069 | − | 0.349145i | \(-0.886472\pi\) | ||
0.937069 | − | 0.349145i | \(-0.113528\pi\) | |||||||
\(390\) | −518122. | −0.172493 | ||||||||
\(391\) | − | 5.06677e6i | − | 1.67606i | ||||||
\(392\) | − | 7.59838e6i | − | 2.49750i | ||||||
\(393\) | −1.79842e6 | −0.587367 | ||||||||
\(394\) | 423743.i | 0.137519i | ||||||||
\(395\) | − | 167772.i | − | 0.0541037i | ||||||
\(396\) | − | 112992.i | − | 0.0362085i | ||||||
\(397\) | −4.95385e6 | −1.57749 | −0.788745 | − | 0.614721i | \(-0.789269\pi\) | ||||
−0.788745 | + | 0.614721i | \(0.789269\pi\) | |||||||
\(398\) | − | 2.25395e6i | − | 0.713241i | ||||||
\(399\) | −9.71983e6 | −3.05652 | ||||||||
\(400\) | −1.42434e6 | −0.445107 | ||||||||
\(401\) | −967567. | −0.300483 | −0.150242 | − | 0.988649i | \(-0.548005\pi\) | ||||
−0.150242 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(402\) | 8.28819e6 | 2.55796 | ||||||||
\(403\) | 1.46760e6i | 0.450138i | ||||||||
\(404\) | − | 264795.i | − | 0.0807153i | ||||||
\(405\) | 352768. | 0.106869 | ||||||||
\(406\) | 4.26698e6 | + | 8.37516e6i | 1.28471 | + | 2.52161i | ||||
\(407\) | 158665. | 0.0474784 | ||||||||
\(408\) | − | 5.60413e6i | − | 1.66670i | ||||||
\(409\) | 1.99514e6i | 0.589745i | 0.955537 | + | 0.294872i | \(0.0952771\pi\) | ||||
−0.955537 | + | 0.294872i | \(0.904723\pi\) | |||||||
\(410\) | 169336. | 0.0497495 | ||||||||
\(411\) | 4.41770e6 | 1.29001 | ||||||||
\(412\) | −3.68770e6 | −1.07032 | ||||||||
\(413\) | 1.52150e6 | 0.438932 | ||||||||
\(414\) | − | 6.36710e6i | − | 1.82575i | ||||||
\(415\) | −106568. | −0.0303743 | ||||||||
\(416\) | 1.95085e6i | 0.552702i | ||||||||
\(417\) | − | 1.44644e6i | − | 0.407342i | ||||||
\(418\) | 269340.i | 0.0753981i | ||||||||
\(419\) | 2.26440e6 | 0.630113 | 0.315056 | − | 0.949073i | \(-0.397977\pi\) | ||||
0.315056 | + | 0.949073i | \(0.397977\pi\) | |||||||
\(420\) | 1.22005e6i | 0.337484i | ||||||||
\(421\) | − | 3.11193e6i | − | 0.855706i | −0.903848 | − | 0.427853i | \(-0.859270\pi\) | ||
0.903848 | − | 0.427853i | \(-0.140730\pi\) | |||||||
\(422\) | 1.84276e6 | 0.503719 | ||||||||
\(423\) | 1.06114e6i | 0.288351i | ||||||||
\(424\) | − | 5.34410e6i | − | 1.44364i | ||||||
\(425\) | 3.58594e6i | 0.963010i | ||||||||
\(426\) | 2.27401e6 | 0.607112 | ||||||||
\(427\) | − | 5.44690e6i | − | 1.44570i | ||||||
\(428\) | 2.23686e6 | 0.590241 | ||||||||
\(429\) | −144091. | −0.0378001 | ||||||||
\(430\) | −589301. | −0.153697 | ||||||||
\(431\) | −3.79285e6 | −0.983495 | −0.491747 | − | 0.870738i | \(-0.663642\pi\) | ||||
−0.491747 | + | 0.870738i | \(0.663642\pi\) | |||||||
\(432\) | 819223.i | 0.211199i | ||||||||
\(433\) | 3.89522e6i | 0.998418i | 0.866482 | + | 0.499209i | \(0.166376\pi\) | ||||
−0.866482 | + | 0.499209i | \(0.833624\pi\) | |||||||
\(434\) | 5.37226e6 | 1.36909 | ||||||||
\(435\) | −198371. | − | 389358.i | −0.0502636 | − | 0.0986566i | ||||
\(436\) | −9.21570e6 | −2.32173 | ||||||||
\(437\) | 9.76313e6i | 2.44560i | ||||||||
\(438\) | − | 7.43441e6i | − | 1.85166i | ||||||
\(439\) | 4.74191e6 | 1.17434 | 0.587168 | − | 0.809465i | \(-0.300243\pi\) | ||||
0.587168 | + | 0.809465i | \(0.300243\pi\) | |||||||
\(440\) | 15059.7 | 0.00370837 | ||||||||
\(441\) | −4.78789e6 | −1.17232 | ||||||||
\(442\) | −6.20863e6 | −1.51161 | ||||||||
\(443\) | 3.59596e6i | 0.870573i | 0.900292 | + | 0.435286i | \(0.143353\pi\) | ||||
−0.900292 | + | 0.435286i | \(0.856647\pi\) | |||||||
\(444\) | 1.42807e7 | 3.43790 | ||||||||
\(445\) | 311973.i | 0.0746822i | ||||||||
\(446\) | 2.29334e6i | 0.545922i | ||||||||
\(447\) | − | 5.66609e6i | − | 1.34126i | ||||||
\(448\) | 1.03615e7 | 2.43909 | ||||||||
\(449\) | 6.68678e6i | 1.56531i | 0.622454 | + | 0.782656i | \(0.286136\pi\) | ||||
−0.622454 | + | 0.782656i | \(0.713864\pi\) | |||||||
\(450\) | 4.50624e6i | 1.04902i | ||||||||
\(451\) | 47092.6 | 0.0109021 | ||||||||
\(452\) | 3.27250e6i | 0.753413i | ||||||||
\(453\) | − | 6.87019e6i | − | 1.57298i | ||||||
\(454\) | − | 1.20470e7i | − | 2.74309i | ||||||
\(455\) | 602089. | 0.136343 | ||||||||
\(456\) | 1.07986e7i | 2.43195i | ||||||||
\(457\) | 744507. | 0.166755 | 0.0833774 | − | 0.996518i | \(-0.473429\pi\) | ||||
0.0833774 | + | 0.996518i | \(0.473429\pi\) | |||||||
\(458\) | 463312. | 0.103207 | ||||||||
\(459\) | 2.06249e6 | 0.456940 | ||||||||
\(460\) | 1.22548e6 | 0.270030 | ||||||||
\(461\) | − | 4.37930e6i | − | 0.959738i | −0.877340 | − | 0.479869i | \(-0.840684\pi\) | ||
0.877340 | − | 0.479869i | \(-0.159316\pi\) | |||||||
\(462\) | 527455.i | 0.114969i | ||||||||
\(463\) | 201229. | 0.0436253 | 0.0218126 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218126 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(464\) | 1.85321e6 | − | 944173.i | 0.399603 | − | 0.203590i | ||||
\(465\) | −249754. | −0.0535650 | ||||||||
\(466\) | 4.42740e6i | 0.944461i | ||||||||
\(467\) | 1.00691e6i | 0.213647i | 0.994278 | + | 0.106824i | \(0.0340680\pi\) | ||||
−0.994278 | + | 0.106824i | \(0.965932\pi\) | |||||||
\(468\) | −5.01882e6 | −1.05922 | ||||||||
\(469\) | −9.63136e6 | −2.02188 | ||||||||
\(470\) | −317499. | −0.0662976 | ||||||||
\(471\) | −2.22644e6 | −0.462444 | ||||||||
\(472\) | − | 1.69036e6i | − | 0.349241i | ||||||
\(473\) | −163886. | −0.0336812 | ||||||||
\(474\) | − | 6.52826e6i | − | 1.33460i | ||||||
\(475\) | − | 6.90973e6i | − | 1.40516i | ||||||
\(476\) | 1.46197e7i | 2.95748i | ||||||||
\(477\) | −3.36743e6 | −0.677645 | ||||||||
\(478\) | 2.81383e6i | 0.563285i | ||||||||
\(479\) | 4.24063e6i | 0.844485i | 0.906483 | + | 0.422242i | \(0.138757\pi\) | ||||
−0.906483 | + | 0.422242i | \(0.861243\pi\) | |||||||
\(480\) | −331994. | −0.0657699 | ||||||||
\(481\) | − | 7.04750e6i | − | 1.38890i | ||||||
\(482\) | − | 2.01117e6i | − | 0.394303i | ||||||
\(483\) | 1.91193e7i | 3.72911i | ||||||||
\(484\) | −9.28392e6 | −1.80143 | ||||||||
\(485\) | 695236.i | 0.134208i | ||||||||
\(486\) | 9.62115e6 | 1.84772 | ||||||||
\(487\) | −2.67952e6 | −0.511959 | −0.255979 | − | 0.966682i | \(-0.582398\pi\) | ||||
−0.255979 | + | 0.966682i | \(0.582398\pi\) | |||||||
\(488\) | −6.05141e6 | −1.15029 | ||||||||
\(489\) | 1.12243e7 | 2.12270 | ||||||||
\(490\) | − | 1.43256e6i | − | 0.269540i | ||||||
\(491\) | − | 9.91828e6i | − | 1.85666i | −0.371756 | − | 0.928330i | \(-0.621244\pi\) | ||
0.371756 | − | 0.928330i | \(-0.378756\pi\) | |||||||
\(492\) | 4.23859e6 | 0.789420 | ||||||||
\(493\) | −2.37706e6 | − | 4.66566e6i | −0.440477 | − | 0.864561i | ||||
\(494\) | 1.19634e7 | 2.20565 | ||||||||
\(495\) | − | 9489.40i | − | 0.00174071i | ||||||
\(496\) | − | 1.18874e6i | − | 0.216962i | ||||||
\(497\) | −2.64254e6 | −0.479877 | ||||||||
\(498\) | −4.14672e6 | −0.749258 | ||||||||
\(499\) | 4.06076e6 | 0.730055 | 0.365028 | − | 0.930997i | \(-0.381060\pi\) | ||||
0.365028 | + | 0.930997i | \(0.381060\pi\) | |||||||
\(500\) | −1.74120e6 | −0.311476 | ||||||||
\(501\) | 2.00156e6i | 0.356265i | ||||||||
\(502\) | −5.03398e6 | −0.891564 | ||||||||
\(503\) | − | 9.67589e6i | − | 1.70518i | −0.522578 | − | 0.852592i | \(-0.675030\pi\) | ||
0.522578 | − | 0.852592i | \(-0.324970\pi\) | |||||||
\(504\) | 8.18366e6i | 1.43506i | ||||||||
\(505\) | − | 22238.2i | − | 0.00388035i | ||||||
\(506\) | 529804. | 0.0919897 | ||||||||
\(507\) | − | 992264.i | − | 0.171438i | ||||||
\(508\) | 9.16369e6i | 1.57547i | ||||||||
\(509\) | 7.29038e6 | 1.24726 | 0.623628 | − | 0.781721i | \(-0.285658\pi\) | ||||
0.623628 | + | 0.781721i | \(0.285658\pi\) | |||||||
\(510\) | − | 1.05658e6i | − | 0.179877i | ||||||
\(511\) | 8.63922e6i | 1.46360i | ||||||||
\(512\) | − | 5.15785e6i | − | 0.869548i | ||||||
\(513\) | −3.97420e6 | −0.666739 | ||||||||
\(514\) | − | 7.54799e6i | − | 1.26015i | ||||||
\(515\) | −309703. | −0.0514549 | ||||||||
\(516\) | −1.47506e7 | −2.43885 | ||||||||
\(517\) | −88297.1 | −0.0145285 | ||||||||
\(518\) | −2.57979e7 | −4.22435 | ||||||||
\(519\) | − | 1.03977e7i | − | 1.69441i | ||||||
\(520\) | − | 668910.i | − | 0.108482i | ||||||
\(521\) | 7.34925e6 | 1.18618 | 0.593088 | − | 0.805138i | \(-0.297909\pi\) | ||||
0.593088 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(522\) | −2.98711e6 | − | 5.86306e6i | −0.479817 | − | 0.941776i | ||||
\(523\) | 7.99648e6 | 1.27834 | 0.639168 | − | 0.769067i | \(-0.279279\pi\) | ||||
0.639168 | + | 0.769067i | \(0.279279\pi\) | |||||||
\(524\) | − | 5.21231e6i | − | 0.829282i | ||||||
\(525\) | − | 1.35315e7i | − | 2.14263i | ||||||
\(526\) | −917307. | −0.144561 | ||||||||
\(527\) | −2.99280e6 | −0.469408 | ||||||||
\(528\) | 116712. | 0.0182193 | ||||||||
\(529\) | 1.27682e7 | 1.98376 | ||||||||
\(530\) | − | 1.00755e6i | − | 0.155804i | ||||||
\(531\) | −1.06513e6 | −0.163933 | ||||||||
\(532\) | − | 2.81707e7i | − | 4.31538i | ||||||
\(533\) | − | 2.09173e6i | − | 0.318924i | ||||||
\(534\) | 1.21393e7i | 1.84222i | ||||||||
\(535\) | 187857. | 0.0283755 | ||||||||
\(536\) | 1.07003e7i | 1.60873i | ||||||||
\(537\) | 1.39560e7i | 2.08845i | ||||||||
\(538\) | −1.87305e7 | −2.78993 | ||||||||
\(539\) | − | 398399.i | − | 0.0590672i | ||||||
\(540\) | 498846.i | 0.0736177i | ||||||||
\(541\) | 1.20377e6i | 0.176828i | 0.996084 | + | 0.0884142i | \(0.0281799\pi\) | ||||
−0.996084 | + | 0.0884142i | \(0.971820\pi\) | |||||||
\(542\) | 4.18203e6 | 0.611490 | ||||||||
\(543\) | − | 4.55330e6i | − | 0.662715i | ||||||
\(544\) | −3.97827e6 | −0.576364 | ||||||||
\(545\) | −773959. | −0.111616 | ||||||||
\(546\) | 2.34282e7 | 3.36323 | ||||||||
\(547\) | 2.80819e6 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(548\) | 1.28037e7i | 1.82131i | ||||||||
\(549\) | 3.81312e6i | 0.539945i | ||||||||
\(550\) | −374963. | −0.0528544 | ||||||||
\(551\) | 4.58035e6 | + | 8.99024e6i | 0.642717 | + | 1.26151i | ||||
\(552\) | 2.12413e7 | 2.96710 | ||||||||
\(553\) | 7.58622e6i | 1.05490i | ||||||||
\(554\) | − | 4.19739e6i | − | 0.581039i | ||||||
\(555\) | 1.19933e6 | 0.165275 | ||||||||
\(556\) | 4.19217e6 | 0.575111 | ||||||||
\(557\) | 4.86294e6 | 0.664142 | 0.332071 | − | 0.943254i | \(-0.392253\pi\) | ||||
0.332071 | + | 0.943254i | \(0.392253\pi\) | |||||||
\(558\) | −3.76087e6 | −0.511331 | ||||||||
\(559\) | 7.27937e6i | 0.985290i | ||||||||
\(560\) | −487686. | −0.0657159 | ||||||||
\(561\) | − | 293836.i | − | 0.0394183i | ||||||
\(562\) | 1.29923e7i | 1.73518i | ||||||||
\(563\) | 2.75688e6i | 0.366562i | 0.983061 | + | 0.183281i | \(0.0586718\pi\) | ||||
−0.983061 | + | 0.183281i | \(0.941328\pi\) | |||||||
\(564\) | −7.94722e6 | −1.05200 | ||||||||
\(565\) | 274833.i | 0.0362200i | ||||||||
\(566\) | − | 6.97248e6i | − | 0.914843i | ||||||
\(567\) | −1.59513e7 | −2.08371 | ||||||||
\(568\) | 2.93582e6i | 0.381819i | ||||||||
\(569\) | − | 2.41402e6i | − | 0.312579i | −0.987711 | − | 0.156289i | \(-0.950047\pi\) | ||
0.987711 | − | 0.156289i | \(-0.0499533\pi\) | |||||||
\(570\) | 2.03591e6i | 0.262466i | ||||||||
\(571\) | −5.43385e6 | −0.697457 | −0.348729 | − | 0.937224i | \(-0.613386\pi\) | ||||
−0.348729 | + | 0.937224i | \(0.613386\pi\) | |||||||
\(572\) | − | 417614.i | − | 0.0533685i | ||||||
\(573\) | 1.64225e7 | 2.08954 | ||||||||
\(574\) | −7.65693e6 | −0.970007 | ||||||||
\(575\) | −1.35917e7 | −1.71437 | ||||||||
\(576\) | −7.25361e6 | −0.910958 | ||||||||
\(577\) | 407216.i | 0.0509197i | 0.999676 | + | 0.0254598i | \(0.00810500\pi\) | ||||
−0.999676 | + | 0.0254598i | \(0.991895\pi\) | |||||||
\(578\) | 786875.i | 0.0979684i | ||||||||
\(579\) | −1.86571e7 | −2.31285 | ||||||||
\(580\) | 1.12847e6 | − | 574931.i | 0.139290 | − | 0.0709653i | ||||
\(581\) | 4.81873e6 | 0.592233 | ||||||||
\(582\) | 2.70527e7i | 3.31057i | ||||||||
\(583\) | − | 280202.i | − | 0.0341429i | ||||||
\(584\) | 9.59803e6 | 1.16453 | ||||||||
\(585\) | −421494. | −0.0509216 | ||||||||
\(586\) | 1.53302e7 | 1.84418 | ||||||||
\(587\) | −3.72960e6 | −0.446752 | −0.223376 | − | 0.974732i | \(-0.571708\pi\) | ||||
−0.223376 | + | 0.974732i | \(0.571708\pi\) | |||||||
\(588\) | − | 3.58580e7i | − | 4.27704i | ||||||
\(589\) | 5.76680e6 | 0.684931 | ||||||||
\(590\) | − | 318693.i | − | 0.0376914i | ||||||
\(591\) | 890768.i | 0.104905i | ||||||||
\(592\) | 5.70841e6i | 0.669439i | ||||||||
\(593\) | −1.06458e7 | −1.24321 | −0.621603 | − | 0.783333i | \(-0.713518\pi\) | ||||
−0.621603 | + | 0.783333i | \(0.713518\pi\) | |||||||
\(594\) | 215663.i | 0.0250790i | ||||||||
\(595\) | 1.22781e6i | 0.142180i | ||||||||
\(596\) | 1.64219e7 | 1.89368 | ||||||||
\(597\) | − | 4.73812e6i | − | 0.544090i | ||||||
\(598\) | − | 2.35325e7i | − | 2.69101i | ||||||
\(599\) | − | 1.25592e7i | − | 1.43019i | −0.699027 | − | 0.715096i | \(-0.746383\pi\) | ||
0.699027 | − | 0.715096i | \(-0.253617\pi\) | |||||||
\(600\) | −1.50333e7 | −1.70481 | ||||||||
\(601\) | − | 3.82602e6i | − | 0.432077i | −0.976385 | − | 0.216038i | \(-0.930686\pi\) | ||
0.976385 | − | 0.216038i | \(-0.0693136\pi\) | |||||||
\(602\) | 2.66467e7 | 2.99676 | ||||||||
\(603\) | 6.74246e6 | 0.755136 | ||||||||
\(604\) | 1.99117e7 | 2.22083 | ||||||||
\(605\) | −779688. | −0.0866029 | ||||||||
\(606\) | − | 865320.i | − | 0.0957183i | ||||||
\(607\) | 1.49470e7i | 1.64658i | 0.567620 | + | 0.823291i | \(0.307864\pi\) | ||||
−0.567620 | + | 0.823291i | \(0.692136\pi\) | |||||||
\(608\) | 7.66570e6 | 0.840994 | ||||||||
\(609\) | 8.96980e6 | + | 1.76058e7i | 0.980031 | + | 1.92359i | ||||
\(610\) | −1.14091e6 | −0.124144 | ||||||||
\(611\) | 3.92193e6i | 0.425007i | ||||||||
\(612\) | − | 1.02346e7i | − | 1.10457i | ||||||
\(613\) | −3.48547e6 | −0.374636 | −0.187318 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187318 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(614\) | −8.61829e6 | −0.922572 | ||||||||
\(615\) | 355968. | 0.0379510 | ||||||||
\(616\) | −680959. | −0.0723052 | ||||||||
\(617\) | − | 5.45591e6i | − | 0.576971i | −0.957484 | − | 0.288486i | \(-0.906848\pi\) | ||
0.957484 | − | 0.288486i | \(-0.0931518\pi\) | |||||||
\(618\) | −1.20510e7 | −1.26926 | ||||||||
\(619\) | 1.36253e7i | 1.42929i | 0.699489 | + | 0.714644i | \(0.253411\pi\) | ||||
−0.699489 | + | 0.714644i | \(0.746589\pi\) | |||||||
\(620\) | − | 723856.i | − | 0.0756263i | ||||||
\(621\) | 7.81742e6i | 0.813456i | ||||||||
\(622\) | −2.69711e7 | −2.79526 | ||||||||
\(623\) | − | 1.41066e7i | − | 1.45614i | ||||||
\(624\) | − | 5.18405e6i | − | 0.532976i | ||||||
\(625\) | 9.54600e6 | 0.977511 | ||||||||
\(626\) | − | 1.94375e7i | − | 1.98246i | ||||||
\(627\) | 566192.i | 0.0575168i | ||||||||
\(628\) | − | 6.45283e6i | − | 0.652906i | ||||||
\(629\) | 1.43716e7 | 1.44836 | ||||||||
\(630\) | 1.54291e6i | 0.154878i | ||||||||
\(631\) | −4.70379e6 | −0.470299 | −0.235150 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235150 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(632\) | 8.42817e6 | 0.839345 | ||||||||
\(633\) | 3.87375e6 | 0.384257 | ||||||||
\(634\) | −1.33765e7 | −1.32166 | ||||||||
\(635\) | 769591.i | 0.0757401i | ||||||||
\(636\) | − | 2.52197e7i | − | 2.47228i | ||||||
\(637\) | −1.76958e7 | −1.72791 | ||||||||
\(638\) | 487863. | − | 248557.i | 0.0474511 | − | 0.0241754i | ||||
\(639\) | 1.84992e6 | 0.179226 | ||||||||
\(640\) | − | 1.63673e6i | − | 0.157952i | ||||||
\(641\) | − | 3.61550e6i | − | 0.347555i | −0.984785 | − | 0.173777i | \(-0.944403\pi\) | ||
0.984785 | − | 0.173777i | \(-0.0555973\pi\) | |||||||
\(642\) | 7.30981e6 | 0.699953 | ||||||||
\(643\) | 1.80915e6 | 0.172563 | 0.0862816 | − | 0.996271i | \(-0.472502\pi\) | ||||
0.0862816 | + | 0.996271i | \(0.472502\pi\) | |||||||
\(644\) | −5.54130e7 | −5.26499 | ||||||||
\(645\) | −1.23879e6 | −0.117246 | ||||||||
\(646\) | 2.43963e7i | 2.30007i | ||||||||
\(647\) | −1.01979e7 | −0.957749 | −0.478874 | − | 0.877883i | \(-0.658955\pi\) | ||||
−0.478874 | + | 0.877883i | \(0.658955\pi\) | |||||||
\(648\) | 1.77216e7i | 1.65793i | ||||||||
\(649\) | − | 88629.2i | − | 0.00825971i | ||||||
\(650\) | 1.66548e7i | 1.54617i | ||||||||
\(651\) | 1.12933e7 | 1.04440 | ||||||||
\(652\) | 3.25311e7i | 2.99695i | ||||||||
\(653\) | 1.40580e7i | 1.29015i | 0.764119 | + | 0.645076i | \(0.223174\pi\) | ||||
−0.764119 | + | 0.645076i | \(0.776826\pi\) | |||||||
\(654\) | −3.01159e7 | −2.75329 | ||||||||
\(655\) | − | 437744.i | − | 0.0398673i | ||||||
\(656\) | 1.69428e6i | 0.153718i | ||||||||
\(657\) | − | 6.04791e6i | − | 0.546628i | ||||||
\(658\) | 1.43565e7 | 1.29266 | ||||||||
\(659\) | − | 4.98482e6i | − | 0.447132i | −0.974689 | − | 0.223566i | \(-0.928230\pi\) | ||
0.974689 | − | 0.223566i | \(-0.0717698\pi\) | |||||||
\(660\) | 71069.1 | 0.00635069 | ||||||||
\(661\) | −1.50599e7 | −1.34066 | −0.670331 | − | 0.742062i | \(-0.733848\pi\) | ||||
−0.670331 | + | 0.742062i | \(0.733848\pi\) | |||||||
\(662\) | 1.44753e7 | 1.28376 | ||||||||
\(663\) | −1.30514e7 | −1.15312 | ||||||||
\(664\) | − | 5.35353e6i | − | 0.471216i | ||||||
\(665\) | − | 2.36585e6i | − | 0.207460i | ||||||
\(666\) | 1.80599e7 | 1.57772 | ||||||||
\(667\) | 1.76842e7 | − | 9.00975e6i | 1.53911 | − | 0.784149i | ||||
\(668\) | −5.80105e6 | −0.502997 | ||||||||
\(669\) | 4.82092e6i | 0.416452i | ||||||||
\(670\) | 2.01738e6i | 0.173621i | ||||||||
\(671\) | −317288. | −0.0272049 | ||||||||
\(672\) | 1.50119e7 | 1.28237 | ||||||||
\(673\) | −1.05492e7 | −0.897806 | −0.448903 | − | 0.893580i | \(-0.648185\pi\) | ||||
−0.448903 | + | 0.893580i | \(0.648185\pi\) | |||||||
\(674\) | −8.85817e6 | −0.751094 | ||||||||
\(675\) | − | 5.53268e6i | − | 0.467387i | ||||||
\(676\) | 2.87585e6 | 0.242047 | ||||||||
\(677\) | − | 1.35259e7i | − | 1.13421i | −0.823644 | − | 0.567107i | \(-0.808063\pi\) | ||
0.823644 | − | 0.567107i | \(-0.191937\pi\) | |||||||
\(678\) | 1.06942e7i | 0.893455i | ||||||||
\(679\) | − | 3.14368e7i | − | 2.61676i | ||||||
\(680\) | 1.36407e6 | 0.113127 | ||||||||
\(681\) | − | 2.53245e7i | − | 2.09254i | ||||||
\(682\) | − | 312940.i | − | 0.0257633i | ||||||
\(683\) | 2.06766e7 | 1.69600 | 0.848002 | − | 0.529993i | \(-0.177805\pi\) | ||||
0.848002 | + | 0.529993i | \(0.177805\pi\) | |||||||
\(684\) | 1.97210e7i | 1.61172i | ||||||||
\(685\) | 1.07529e6i | 0.0875586i | ||||||||
\(686\) | 2.98950e7i | 2.42543i | ||||||||
\(687\) | 973947. | 0.0787306 | ||||||||
\(688\) | − | 5.89622e6i | − | 0.474900i | ||||||
\(689\) | −1.24459e7 | −0.998795 | ||||||||
\(690\) | 4.00473e6 | 0.320222 | ||||||||
\(691\) | −9.29798e6 | −0.740787 | −0.370394 | − | 0.928875i | \(-0.620777\pi\) | ||||
−0.370394 | + | 0.928875i | \(0.620777\pi\) | |||||||
\(692\) | 3.01354e7 | 2.39227 | ||||||||
\(693\) | 429086.i | 0.0339400i | ||||||||
\(694\) | 1.10655e7i | 0.872116i | ||||||||
\(695\) | 352069. | 0.0276482 | ||||||||
\(696\) | 1.95597e7 | − | 9.96530e6i | 1.53052 | − | 0.779772i | ||||
\(697\) | 4.26555e6 | 0.332577 | ||||||||
\(698\) | − | 3.50901e7i | − | 2.72613i | ||||||
\(699\) | 9.30702e6i | 0.720473i | ||||||||
\(700\) | 3.92179e7 | 3.02510 | ||||||||
\(701\) | −593091. | −0.0455855 | −0.0227927 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227927 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(702\) | 9.57918e6 | 0.733645 | ||||||||
\(703\) | −2.76925e7 | −2.11336 | ||||||||
\(704\) | − | 603571.i | − | 0.0458983i | ||||||
\(705\) | −667428. | −0.0505745 | ||||||||
\(706\) | − | 2.50788e7i | − | 1.89363i | ||||||
\(707\) | 1.00555e6i | 0.0756582i | ||||||||
\(708\) | − | 7.97710e6i | − | 0.598084i | ||||||
\(709\) | 8.81645e6 | 0.658685 | 0.329343 | − | 0.944210i | \(-0.393173\pi\) | ||||
0.329343 | + | 0.944210i | \(0.393173\pi\) | |||||||
\(710\) | 553505.i | 0.0412075i | ||||||||
\(711\) | − | 5.31076e6i | − | 0.393988i | ||||||
\(712\) | −1.56722e7 | −1.15859 | ||||||||
\(713\) | − | 1.13436e7i | − | 0.835652i | ||||||
\(714\) | 4.77757e7i | 3.50721i | ||||||||
\(715\) | − | 35072.4i | − | 0.00256566i | ||||||
\(716\) | −4.04483e7 | −2.94861 | ||||||||
\(717\) | 5.91508e6i | 0.429697i | ||||||||
\(718\) | 3.27210e7 | 2.36873 | ||||||||
\(719\) | 2.04104e7 | 1.47241 | 0.736206 | − | 0.676758i | \(-0.236616\pi\) | ||||
0.736206 | + | 0.676758i | \(0.236616\pi\) | |||||||
\(720\) | 341406. | 0.0245437 | ||||||||
\(721\) | 1.40039e7 | 1.00326 | ||||||||
\(722\) | − | 2.35573e7i | − | 1.68183i | ||||||
\(723\) | − | 4.22776e6i | − | 0.300791i | ||||||
\(724\) | 1.31967e7 | 0.935661 | ||||||||
\(725\) | −1.25158e7 | + | 6.37654e6i | −0.884326 | + | 0.450547i | ||||
\(726\) | −3.03388e7 | −2.13627 | ||||||||
\(727\) | − | 1.37388e7i | − | 0.964077i | −0.876150 | − | 0.482038i | \(-0.839897\pi\) | ||
0.876150 | − | 0.482038i | \(-0.160103\pi\) | |||||||
\(728\) | 3.02464e7i | 2.11517i | ||||||||
\(729\) | 2.53622e6 | 0.176754 | ||||||||
\(730\) | 1.80957e6 | 0.125681 | ||||||||
\(731\) | −1.48444e7 | −1.02747 | ||||||||
\(732\) | −2.85576e7 | −1.96990 | ||||||||
\(733\) | 2.01671e7i | 1.38639i | 0.720752 | + | 0.693193i | \(0.243797\pi\) | ||||
−0.720752 | + | 0.693193i | \(0.756203\pi\) | |||||||
\(734\) | 1.37015e7 | 0.938699 | ||||||||
\(735\) | − | 3.01145e6i | − | 0.205616i | ||||||
\(736\) | − | 1.50788e7i | − | 1.02606i | ||||||
\(737\) | 561038.i | 0.0380473i | ||||||||
\(738\) | 5.36026e6 | 0.362280 | ||||||||
\(739\) | 8.07578e6i | 0.543968i | 0.962302 | + | 0.271984i | \(0.0876798\pi\) | ||||
−0.962302 | + | 0.271984i | \(0.912320\pi\) | |||||||
\(740\) | 3.47600e6i | 0.233346i | ||||||||
\(741\) | 2.51487e7 | 1.68256 | ||||||||
\(742\) | 4.55589e7i | 3.03783i | ||||||||
\(743\) | 189310.i | 0.0125806i | 0.999980 | + | 0.00629032i | \(0.00200228\pi\) | ||||
−0.999980 | + | 0.00629032i | \(0.997998\pi\) | |||||||
\(744\) | − | 1.25466e7i | − | 0.830987i | ||||||
\(745\) | 1.37915e6 | 0.0910377 | ||||||||
\(746\) | 1.71063e7i | 1.12541i | ||||||||
\(747\) | −3.37337e6 | −0.221188 | ||||||||
\(748\) | 851617. | 0.0556532 | ||||||||
\(749\) | −8.49443e6 | −0.553260 | ||||||||
\(750\) | −5.69006e6 | −0.369372 | ||||||||
\(751\) | 2.39016e7i | 1.54642i | 0.634153 | + | 0.773208i | \(0.281349\pi\) | ||||
−0.634153 | + | 0.773208i | \(0.718651\pi\) | |||||||
\(752\) | − | 3.17672e6i | − | 0.204849i | ||||||
\(753\) | −1.05821e7 | −0.680121 | ||||||||
\(754\) | −1.10402e7 | − | 2.16696e7i | −0.707212 | − | 1.38810i | ||||
\(755\) | 1.67223e6 | 0.106765 | ||||||||
\(756\) | − | 2.25565e7i | − | 1.43538i | ||||||
\(757\) | 1.42248e7i | 0.902208i | 0.892471 | + | 0.451104i | \(0.148970\pi\) | ||||
−0.892471 | + | 0.451104i | \(0.851030\pi\) | |||||||
\(758\) | −1.45143e7 | −0.917537 | ||||||||
\(759\) | 1.11372e6 | 0.0701735 | ||||||||
\(760\) | −2.62842e6 | −0.165067 | ||||||||
\(761\) | 8.90653e6 | 0.557502 | 0.278751 | − | 0.960363i | \(-0.410080\pi\) | ||||
0.278751 | + | 0.960363i | \(0.410080\pi\) | |||||||
\(762\) | 2.99459e7i | 1.86832i | ||||||||
\(763\) | 3.49964e7 | 2.17627 | ||||||||
\(764\) | 4.75967e7i | 2.95015i | ||||||||
\(765\) | − | 859529.i | − | 0.0531015i | ||||||
\(766\) | − | 3.31151e7i | − | 2.03917i | ||||||
\(767\) | −3.93667e6 | −0.241624 | ||||||||
\(768\) | − | 3.35616e7i | − | 2.05324i | ||||||
\(769\) | 1.35750e7i | 0.827795i | 0.910324 | + | 0.413897i | \(0.135833\pi\) | ||||
−0.910324 | + | 0.413897i | \(0.864167\pi\) | |||||||
\(770\) | −128385. | −0.00780346 | ||||||||
\(771\) | − | 1.58670e7i | − | 0.961297i | ||||||
\(772\) | − | 5.40732e7i | − | 3.26542i | ||||||
\(773\) | 2.44300e7i | 1.47054i | 0.677777 | + | 0.735268i | \(0.262943\pi\) | ||||
−0.677777 | + | 0.735268i | \(0.737057\pi\) | |||||||
\(774\) | −1.86541e7 | −1.11923 | ||||||||
\(775\) | 8.02826e6i | 0.480139i | ||||||||
\(776\) | −3.49257e7 | −2.08205 | ||||||||
\(777\) | −5.42308e7 | −3.22251 | ||||||||
\(778\) | 1.97386e7 | 1.16914 | ||||||||
\(779\) | −8.21926e6 | −0.485276 | ||||||||
\(780\) | − | 3.15670e6i | − | 0.185779i | ||||||
\(781\) | 153931.i | 0.00903022i | ||||||||
\(782\) | 4.79885e7 | 2.80621 | ||||||||
\(783\) | 3.66753e6 | + | 7.19856e6i | 0.213781 | + | 0.419605i | ||||
\(784\) | 1.43334e7 | 0.832838 | ||||||||
\(785\) | − | 541926.i | − | 0.0313881i | ||||||
\(786\) | − | 1.70333e7i | − | 0.983425i | ||||||
\(787\) | −9.09886e6 | −0.523661 | −0.261830 | − | 0.965114i | \(-0.584326\pi\) | ||||
−0.261830 | + | 0.965114i | \(0.584326\pi\) | |||||||
\(788\) | −2.58169e6 | −0.148111 | ||||||||
\(789\) | −1.92831e6 | −0.110277 | ||||||||
\(790\) | 1.58901e6 | 0.0905854 | ||||||||
\(791\) | − | 1.24272e7i | − | 0.706210i | ||||||
\(792\) | 476708. | 0.0270047 | ||||||||
\(793\) | 1.40931e7i | 0.795836i | ||||||||
\(794\) | − | 4.69190e7i | − | 2.64118i | ||||||
\(795\) | − | 2.11802e6i | − | 0.118854i | ||||||
\(796\) | 1.37324e7 | 0.768179 | ||||||||
\(797\) | − | 3.33609e6i | − | 0.186034i | −0.995665 | − | 0.0930170i | \(-0.970349\pi\) | ||
0.995665 | − | 0.0930170i | \(-0.0296511\pi\) | |||||||
\(798\) | − | 9.20588e7i | − | 5.11750i | ||||||
\(799\) | −7.99776e6 | −0.443202 | ||||||||
\(800\) | 1.06718e7i | 0.589540i | ||||||||
\(801\) | 9.87539e6i | 0.543842i | ||||||||
\(802\) | − | 9.16405e6i | − | 0.503097i | ||||||
\(803\) | 503245. | 0.0275417 | ||||||||
\(804\) | 5.04964e7i | 2.75499i | ||||||||
\(805\) | −4.65373e6 | −0.253111 | ||||||||
\(806\) | −1.39000e7 | −0.753662 | ||||||||
\(807\) | −3.93742e7 | −2.12828 | ||||||||
\(808\) | 1.11715e6 | 0.0601983 | ||||||||
\(809\) | − | 1.22656e7i | − | 0.658895i | −0.944174 | − | 0.329448i | \(-0.893137\pi\) | ||
0.944174 | − | 0.329448i | \(-0.106863\pi\) | |||||||
\(810\) | 3.34115e6i | 0.178930i | ||||||||
\(811\) | 1.58437e7 | 0.845873 | 0.422936 | − | 0.906159i | \(-0.360999\pi\) | ||||
0.422936 | + | 0.906159i | \(0.360999\pi\) | |||||||
\(812\) | −5.10263e7 | + | 2.59969e7i | −2.71584 | + | 1.38367i | ||||
\(813\) | 8.79123e6 | 0.466469 | ||||||||
\(814\) | 1.50276e6i | 0.0794928i | ||||||||
\(815\) | 2.73205e6i | 0.144077i | ||||||||
\(816\) | 1.05715e7 | 0.555793 | ||||||||
\(817\) | 2.86036e7 | 1.49922 | ||||||||
\(818\) | −1.88964e7 | −0.987405 | ||||||||
\(819\) | 1.90589e7 | 0.992858 | ||||||||
\(820\) | 1.03169e6i | 0.0535815i | ||||||||
\(821\) | 9.00970e6 | 0.466501 | 0.233251 | − | 0.972417i | \(-0.425064\pi\) | ||||
0.233251 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(822\) | 4.18411e7i | 2.15985i | ||||||||
\(823\) | − | 7.29604e6i | − | 0.375481i | −0.982219 | − | 0.187740i | \(-0.939884\pi\) | ||
0.982219 | − | 0.187740i | \(-0.0601163\pi\) | |||||||
\(824\) | − | 1.55582e7i | − | 0.798252i | ||||||
\(825\) | −788224. | −0.0403195 | ||||||||
\(826\) | 1.44105e7i | 0.734900i | ||||||||
\(827\) | − | 2.34866e7i | − | 1.19414i | −0.802188 | − | 0.597072i | \(-0.796331\pi\) | ||
0.802188 | − | 0.597072i | \(-0.203669\pi\) | |||||||
\(828\) | 3.87921e7 | 1.96638 | ||||||||
\(829\) | 1.67228e7i | 0.845127i | 0.906333 | + | 0.422564i | \(0.138870\pi\) | ||||
−0.906333 | + | 0.422564i | \(0.861130\pi\) | |||||||
\(830\) | − | 1.00933e6i | − | 0.0508555i | ||||||
\(831\) | − | 8.82351e6i | − | 0.443240i | ||||||
\(832\) | −2.68090e7 | −1.34268 | ||||||||
\(833\) | − | 3.60861e7i | − | 1.80189i | ||||||
\(834\) | 1.36995e7 | 0.682010 | ||||||||
\(835\) | −487188. | −0.0241813 | ||||||||
\(836\) | −1.64098e6 | −0.0812057 | ||||||||
\(837\) | 4.61753e6 | 0.227822 | ||||||||
\(838\) | 2.14467e7i | 1.05499i | ||||||||
\(839\) | 2.63609e7i | 1.29287i | 0.762968 | + | 0.646436i | \(0.223741\pi\) | ||||
−0.762968 | + | 0.646436i | \(0.776259\pi\) | |||||||
\(840\) | −5.14730e6 | −0.251699 | ||||||||
\(841\) | 1.20573e7 | − | 1.65930e7i | 0.587843 | − | 0.808975i | ||||
\(842\) | 2.94738e7 | 1.43270 | ||||||||
\(843\) | 2.73116e7i | 1.32367i | ||||||||
\(844\) | 1.12272e7i | 0.542518i | ||||||||
\(845\) | 241522. | 0.0116363 | ||||||||
\(846\) | −1.00503e7 | −0.482785 | ||||||||
\(847\) | 3.52555e7 | 1.68857 | ||||||||
\(848\) | 1.00810e7 | 0.481410 | ||||||||
\(849\) | − | 1.46571e7i | − | 0.697879i | ||||||
\(850\) | −3.39633e7 | −1.61236 | ||||||||
\(851\) | 5.44724e7i | 2.57841i | ||||||||
\(852\) | 1.38546e7i | 0.653876i | ||||||||
\(853\) | − | 1.49192e7i | − | 0.702060i | −0.936364 | − | 0.351030i | \(-0.885831\pi\) | ||
0.936364 | − | 0.351030i | \(-0.114169\pi\) | |||||||
\(854\) | 5.15888e7 | 2.42053 | ||||||||
\(855\) | 1.65622e6i | 0.0774824i | ||||||||
\(856\) | 9.43717e6i | 0.440208i | ||||||||
\(857\) | 8.16583e6 | 0.379794 | 0.189897 | − | 0.981804i | \(-0.439185\pi\) | ||||
0.189897 | + | 0.981804i | \(0.439185\pi\) | |||||||
\(858\) | − | 1.36472e6i | − | 0.0632885i | ||||||
\(859\) | 1.28694e7i | 0.595082i | 0.954709 | + | 0.297541i | \(0.0961665\pi\) | ||||
−0.954709 | + | 0.297541i | \(0.903833\pi\) | |||||||
\(860\) | − | 3.59036e6i | − | 0.165536i | ||||||
\(861\) | −1.60959e7 | −0.739961 | ||||||||
\(862\) | − | 3.59229e7i | − | 1.64666i | ||||||
\(863\) | −1.98390e7 | −0.906761 | −0.453381 | − | 0.891317i | \(-0.649782\pi\) | ||||
−0.453381 | + | 0.891317i | \(0.649782\pi\) | |||||||
\(864\) | 6.13799e6 | 0.279732 | ||||||||
\(865\) | 2.53085e6 | 0.115007 | ||||||||
\(866\) | −3.68925e7 | −1.67164 | ||||||||
\(867\) | 1.65412e6i | 0.0747343i | ||||||||
\(868\) | 3.27309e7i | 1.47455i | ||||||||
\(869\) | 441906. | 0.0198509 | ||||||||
\(870\) | 3.68770e6 | − | 1.87881e6i | 0.165180 | − | 0.0841561i | ||||
\(871\) | 2.49198e7 | 1.11301 | ||||||||
\(872\) | − | 3.88805e7i | − | 1.73157i | ||||||
\(873\) | 2.20074e7i | 0.977313i | ||||||||
\(874\) | −9.24688e7 | −4.09465 | ||||||||
\(875\) | 6.61219e6 | 0.291961 | ||||||||
\(876\) | 4.52947e7 | 1.99429 | ||||||||
\(877\) | −1.76108e7 | −0.773180 | −0.386590 | − | 0.922252i | \(-0.626347\pi\) | ||||
−0.386590 | + | 0.922252i | \(0.626347\pi\) | |||||||
\(878\) | 4.49118e7i | 1.96618i | ||||||||
\(879\) | 3.22262e7 | 1.40681 | ||||||||
\(880\) | 28408.3i | 0.00123663i | ||||||||
\(881\) | 2.13701e7i | 0.927611i | 0.885937 | + | 0.463805i | \(0.153516\pi\) | ||||
−0.885937 | + | 0.463805i | \(0.846484\pi\) | |||||||
\(882\) | − | 4.53472e7i | − | 1.96281i | ||||||
\(883\) | −4.74540e6 | −0.204819 | −0.102410 | − | 0.994742i | \(-0.532655\pi\) | ||||
−0.102410 | + | 0.994742i | \(0.532655\pi\) | |||||||
\(884\) | − | 3.78266e7i | − | 1.62805i | ||||||
\(885\) | − | 669938.i | − | 0.0287526i | ||||||
\(886\) | −3.40581e7 | −1.45759 | ||||||||
\(887\) | − | 3.34157e7i | − | 1.42607i | −0.701128 | − | 0.713035i | \(-0.747320\pi\) | ||
0.701128 | − | 0.713035i | \(-0.252680\pi\) | |||||||
\(888\) | 6.02496e7i | 2.56402i | ||||||||
\(889\) | − | 3.47989e7i | − | 1.47676i | ||||||
\(890\) | −2.95477e6 | −0.125040 | ||||||||
\(891\) | 929180.i | 0.0392108i | ||||||||
\(892\) | −1.39723e7 | −0.587972 | ||||||||
\(893\) | 1.54108e7 | 0.646692 | ||||||||
\(894\) | 5.36648e7 | 2.24567 | ||||||||
\(895\) | −3.39695e6 | −0.141753 | ||||||||
\(896\) | 7.40086e7i | 3.07972i | ||||||||
\(897\) | − | 4.94687e7i | − | 2.05281i | ||||||
\(898\) | −6.33320e7 | −2.62079 | ||||||||
\(899\) | −5.32181e6 | − | 1.04456e7i | −0.219614 | − | 0.431054i | ||||
\(900\) | −2.74546e7 | −1.12982 | ||||||||
\(901\) | − | 2.53801e7i | − | 1.04155i | ||||||
\(902\) | 446025.i | 0.0182534i | ||||||||
\(903\) | 5.60150e7 | 2.28605 | ||||||||
\(904\) | −1.38065e7 | −0.561903 | ||||||||
\(905\) | 1.10829e6 | 0.0449814 | ||||||||
\(906\) | 6.50691e7 | 2.63363 | ||||||||
\(907\) | − | 2.39221e7i | − | 0.965563i | −0.875741 | − | 0.482782i | \(-0.839627\pi\) | ||
0.875741 | − | 0.482782i | \(-0.160373\pi\) | |||||||
\(908\) | 7.33973e7 | 2.95437 | ||||||||
\(909\) | − | 703940.i | − | 0.0282570i | ||||||
\(910\) | 5.70252e6i | 0.228278i | ||||||||
\(911\) | 2.80696e7i | 1.12057i | 0.828299 | + | 0.560286i | \(0.189309\pi\) | ||||
−0.828299 | + | 0.560286i | \(0.810691\pi\) | |||||||
\(912\) | −2.03702e7 | −0.810978 | ||||||||
\(913\) | − | 280697.i | − | 0.0111445i | ||||||
\(914\) | 7.05140e6i | 0.279196i | ||||||||
\(915\) | −2.39835e6 | −0.0947020 | ||||||||
\(916\) | 2.82276e6i | 0.111157i | ||||||||
\(917\) | 1.97936e7i | 0.777325i | ||||||||
\(918\) | 1.95343e7i | 0.765052i | ||||||||
\(919\) | 1.78543e7 | 0.697356 | 0.348678 | − | 0.937243i | \(-0.386631\pi\) | ||||
0.348678 | + | 0.937243i | \(0.386631\pi\) | |||||||
\(920\) | 5.17022e6i | 0.201391i | ||||||||
\(921\) | −1.81169e7 | −0.703776 | ||||||||
\(922\) | 4.14774e7 | 1.60688 | ||||||||
\(923\) | 6.83720e6 | 0.264164 | ||||||||
\(924\) | −3.21356e6 | −0.123824 | ||||||||
\(925\) | − | 3.85522e7i | − | 1.48147i | ||||||
\(926\) | 1.90589e6i | 0.0730415i | ||||||||
\(927\) | −9.80351e6 | −0.374699 | ||||||||
\(928\) | −7.07418e6 | − | 1.38851e7i | −0.269653 | − | 0.529271i | ||||
\(929\) | −1.34684e7 | −0.512007 | −0.256004 | − | 0.966676i | \(-0.582406\pi\) | ||||
−0.256004 | + | 0.966676i | \(0.582406\pi\) | |||||||
\(930\) | − | 2.36548e6i | − | 0.0896835i | ||||||
\(931\) | 6.95341e7i | 2.62920i | ||||||||
\(932\) | −2.69743e7 | −1.01721 | ||||||||
\(933\) | −5.66970e7 | −2.13234 | ||||||||
\(934\) | −9.53665e6 | −0.357708 | ||||||||
\(935\) | 71521.1 | 0.00267550 | ||||||||
\(936\) | − | 2.11741e7i | − | 0.789978i | ||||||
\(937\) | −3.40806e7 | −1.26811 | −0.634056 | − | 0.773287i | \(-0.718611\pi\) | ||||
−0.634056 | + | 0.773287i | \(0.718611\pi\) | |||||||
\(938\) | − | 9.12208e7i | − | 3.38522i | ||||||
\(939\) | − | 4.08604e7i | − | 1.51230i | ||||||
\(940\) | − | 1.93439e6i | − | 0.0714042i | ||||||
\(941\) | −4.59724e7 | −1.69248 | −0.846239 | − | 0.532803i | \(-0.821139\pi\) | ||||
−0.846239 | + | 0.532803i | \(0.821139\pi\) | |||||||
\(942\) | − | 2.10871e7i | − | 0.774266i | ||||||
\(943\) | 1.61676e7i | 0.592062i | ||||||||
\(944\) | 3.18867e6 | 0.116461 | ||||||||
\(945\) | − | 1.89436e6i | − | 0.0690053i | ||||||
\(946\) | − | 1.55220e6i | − | 0.0563923i | ||||||
\(947\) | − | 1.76546e6i | − | 0.0639711i | −0.999488 | − | 0.0319856i | \(-0.989817\pi\) | ||
0.999488 | − | 0.0319856i | \(-0.0101831\pi\) | |||||||
\(948\) | 3.97739e7 | 1.43740 | ||||||||
\(949\) | − | 2.23528e7i | − | 0.805687i | ||||||
\(950\) | 6.54437e7 | 2.35266 | ||||||||
\(951\) | −2.81193e7 | −1.00821 | ||||||||
\(952\) | −6.16798e7 | −2.20572 | ||||||||
\(953\) | 7.46519e6 | 0.266262 | 0.133131 | − | 0.991098i | \(-0.457497\pi\) | ||||
0.133131 | + | 0.991098i | \(0.457497\pi\) | |||||||
\(954\) | − | 3.18937e7i | − | 1.13458i | ||||||
\(955\) | 3.99730e6i | 0.141827i | ||||||||
\(956\) | −1.71435e7 | −0.606673 | ||||||||
\(957\) | 1.02556e6 | − | 522501.i | 0.0361976 | − | 0.0184420i | ||||
\(958\) | −4.01640e7 | −1.41391 | ||||||||
\(959\) | − | 4.86218e7i | − | 1.70720i | ||||||
\(960\) | − | 4.56232e6i | − | 0.159775i | ||||||
\(961\) | 2.19288e7 | 0.765962 | ||||||||
\(962\) | 6.67485e7 | 2.32543 | ||||||||
\(963\) | 5.94655e6 | 0.206633 | ||||||||
\(964\) | 1.22532e7 | 0.424675 | ||||||||
\(965\) | − | 4.54121e6i | − | 0.156983i | ||||||
\(966\) | −1.81084e8 | −6.24362 | ||||||||
\(967\) | 4.13396e7i | 1.42167i | 0.703356 | + | 0.710837i | \(0.251684\pi\) | ||||
−0.703356 | + | 0.710837i | \(0.748316\pi\) | |||||||
\(968\) | − | 3.91683e7i | − | 1.34353i | ||||||
\(969\) | 5.12844e7i | 1.75459i | ||||||||
\(970\) | −6.58474e6 | −0.224703 | ||||||||
\(971\) | 1.41844e6i | 0.0482796i | 0.999709 | + | 0.0241398i | \(0.00768469\pi\) | ||||
−0.999709 | + | 0.0241398i | \(0.992315\pi\) | |||||||
\(972\) | 5.86176e7i | 1.99004i | ||||||||
\(973\) | −1.59197e7 | −0.539078 | ||||||||
\(974\) | − | 2.53784e7i | − | 0.857169i | ||||||
\(975\) | 3.50108e7i | 1.17948i | ||||||||
\(976\) | − | 1.14153e7i | − | 0.383585i | ||||||
\(977\) | 4.93091e7 | 1.65269 | 0.826344 | − | 0.563165i | \(-0.190417\pi\) | ||||
0.826344 | + | 0.563165i | \(0.190417\pi\) | |||||||
\(978\) | 1.06308e8i | 3.55401i | ||||||||
\(979\) | −821727. | −0.0274013 | ||||||||
\(980\) | 8.72801e6 | 0.290302 | ||||||||
\(981\) | −2.44994e7 | −0.812797 | ||||||||
\(982\) | 9.39383e7 | 3.10859 | ||||||||
\(983\) | 2.20571e7i | 0.728056i | 0.931388 | + | 0.364028i | \(0.118599\pi\) | ||||
−0.931388 | + | 0.364028i | \(0.881401\pi\) | |||||||
\(984\) | 1.78823e7i | 0.588758i | ||||||||
\(985\) | −216817. | −0.00712037 | ||||||||
\(986\) | 4.41895e7 | − | 2.25137e7i | 1.44753 | − | 0.737488i | ||||
\(987\) | 3.01794e7 | 0.986092 | ||||||||
\(988\) | 7.28878e7i | 2.37554i | ||||||||
\(989\) | − | 5.62645e7i | − | 1.82913i | ||||||
\(990\) | 89876.3 | 0.00291445 | ||||||||
\(991\) | −4.19924e7 | −1.35827 | −0.679135 | − | 0.734013i | \(-0.737645\pi\) | ||||
−0.679135 | + | 0.734013i | \(0.737645\pi\) | |||||||
\(992\) | −8.90660e6 | −0.287364 | ||||||||
\(993\) | 3.04292e7 | 0.979302 | ||||||||
\(994\) | − | 2.50281e7i | − | 0.803455i | ||||||
\(995\) | 1.15328e6 | 0.0369298 | ||||||||
\(996\) | − | 2.52642e7i | − | 0.806970i | ||||||
\(997\) | 3.76102e7i | 1.19831i | 0.800635 | + | 0.599153i | \(0.204496\pi\) | ||||
−0.800635 | + | 0.599153i | \(0.795504\pi\) | |||||||
\(998\) | 3.84604e7i | 1.22233i | ||||||||
\(999\) | −2.21736e7 | −0.702948 |
(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 | 29.6.b.a.28.12 | yes | 12 | |
3.2 | odd | 2 | 261.6.c.b.28.1 | 12 | |||
4.3 | odd | 2 | 464.6.e.c.289.4 | 12 | |||
29.12 | odd | 4 | 841.6.a.d.1.1 | 12 | |||
29.17 | odd | 4 | 841.6.a.d.1.12 | 12 | |||
29.28 | even | 2 | inner | 29.6.b.a.28.1 | ✓ | 12 | |
87.86 | odd | 2 | 261.6.c.b.28.12 | 12 | |||
116.115 | odd | 2 | 464.6.e.c.289.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.b.a.28.1 | ✓ | 12 | 29.28 | even | 2 | inner | |
29.6.b.a.28.12 | yes | 12 | 1.1 | even | 1 | trivial | |
261.6.c.b.28.1 | 12 | 3.2 | odd | 2 | |||
261.6.c.b.28.12 | 12 | 87.86 | odd | 2 | |||
464.6.e.c.289.4 | 12 | 4.3 | odd | 2 | |||
464.6.e.c.289.9 | 12 | 116.115 | odd | 2 | |||
841.6.a.d.1.1 | 12 | 29.12 | odd | 4 | |||
841.6.a.d.1.12 | 12 | 29.17 | odd | 4 |