Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.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: | \(13.8032450172\) |
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: | \( x^{12} + 1880 x^{10} + 1266870 x^{8} + 399545800 x^{6} + 62009694600 x^{4} + 4432082624000 x^{2} + 109931031040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 5^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.9 | ||
Root | \(-7.15535i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.7.b.a.29.10 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 22.8848 | − | 14.3278i | 0.847585 | − | 0.530659i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −93.9389 | + | 82.4651i | −0.751511 | + | 0.659720i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 279.744i | − | 0.815581i | −0.913076 | − | 0.407791i | \(-0.866299\pi\) | ||
0.913076 | − | 0.407791i | \(-0.133701\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 318.429 | − | 655.777i | 0.436802 | − | 0.899558i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 772.624i | − | 0.580484i | −0.956953 | − | 0.290242i | \(-0.906264\pi\) | ||
0.956953 | − | 0.290242i | \(-0.0937358\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2877.85i | − | 1.30990i | −0.755672 | − | 0.654950i | \(-0.772690\pi\) | ||
0.755672 | − | 0.654950i | \(-0.227310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −968.231 | + | 3233.13i | −0.286883 | + | 0.957966i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2794.21 | 0.568738 | 0.284369 | − | 0.958715i | \(-0.408216\pi\) | ||||
0.284369 | + | 0.958715i | \(0.408216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13069.1 | −1.90539 | −0.952697 | − | 0.303922i | \(-0.901704\pi\) | ||||
−0.952697 | + | 0.303922i | \(0.901704\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4008.12 | − | 6401.89i | −0.432795 | − | 0.691275i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10557.8 | 0.867740 | 0.433870 | − | 0.900975i | \(-0.357148\pi\) | ||||
0.433870 | + | 0.900975i | \(0.357148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2024.03 | − | 15493.4i | 0.129538 | − | 0.991574i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2108.66 | − | 19569.7i | −0.107131 | − | 0.994245i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 37261.6i | − | 1.52780i | −0.645332 | − | 0.763902i | \(-0.723281\pi\) | ||
0.645332 | − | 0.763902i | \(-0.276719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8711.04 | −0.292405 | −0.146203 | − | 0.989255i | \(-0.546705\pi\) | ||||
−0.146203 | + | 0.989255i | \(0.546705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11070.0 | − | 17681.4i | −0.308039 | − | 0.492010i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 23069.1 | + | 26278.9i | 0.538055 | + | 0.612918i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3555.10i | − | 0.0701854i | −0.999384 | − | 0.0350927i | \(-0.988827\pi\) | ||
0.999384 | − | 0.0350927i | \(-0.0111726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −41233.2 | − | 65859.0i | −0.695110 | − | 1.11025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 108887.i | 1.57988i | 0.613187 | + | 0.789938i | \(0.289887\pi\) | ||||
−0.613187 | + | 0.789938i | \(0.710113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66697.5i | 0.838889i | 0.907781 | + | 0.419444i | \(0.137775\pi\) | ||||
−0.907781 | + | 0.419444i | \(0.862225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24165.9 | + | 87862.3i | 0.265195 | + | 0.964195i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4022.16 | −0.0387405 | −0.0193703 | − | 0.999812i | \(-0.506166\pi\) | ||||
−0.0193703 | + | 0.999812i | \(0.506166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 39392.1 | 0.334828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 63944.9 | − | 40034.8i | 0.482054 | − | 0.301806i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79567.7 | 0.534453 | 0.267226 | − | 0.963634i | \(-0.413893\pi\) | ||||
0.267226 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63714.5 | + | 72579.5i | 0.382957 | + | 0.436240i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −299084. | + | 187251.i | −1.61498 | + | 1.01111i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 151116.i | 0.735793i | 0.929867 | + | 0.367897i | \(0.119922\pi\) | ||||
−0.929867 | + | 0.367897i | \(0.880078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 207998. | 0.916369 | 0.458184 | − | 0.888857i | \(-0.348500\pi\) | ||||
0.458184 | + | 0.888857i | \(0.348500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −183450. | − | 89078.6i | −0.733662 | − | 0.356248i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 237322. | + | 270342.i | 0.864168 | + | 0.984404i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 363435.i | − | 1.20838i | −0.796842 | − | 0.604188i | \(-0.793498\pi\) | ||
0.796842 | − | 0.604188i | \(-0.206502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 241613. | − | 151270.i | 0.735484 | − | 0.460474i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37954.2i | 0.106044i | 0.998593 | + | 0.0530218i | \(0.0168853\pi\) | ||||
−0.998593 | + | 0.0530218i | \(0.983115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 461513.i | 1.18636i | 0.805071 | + | 0.593179i | \(0.202127\pi\) | ||||
−0.805071 | + | 0.593179i | \(0.797873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −175666. | − | 383562.i | −0.416393 | − | 0.909185i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −216137. | −0.473432 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −227372. | −0.461164 | −0.230582 | − | 0.973053i | \(-0.574063\pi\) | ||||
−0.230582 | + | 0.973053i | \(0.574063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −328647. | − | 417637.i | −0.618408 | − | 0.785857i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 998762. | 1.74674 | 0.873369 | − | 0.487060i | \(-0.161931\pi\) | ||||
0.873369 | + | 0.487060i | \(0.161931\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −262485. | + | 230425.i | −0.427413 | + | 0.375208i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −533877. | − | 852725.i | −0.810743 | − | 1.29494i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.03916e6i | 1.47405i | 0.675864 | + | 0.737026i | \(0.263771\pi\) | ||||
−0.675864 | + | 0.737026i | \(0.736229\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −805062. | −1.06833 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −199350. | + | 124810.i | −0.247838 | + | 0.155167i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.22770e6 | − | 1.07774e6i | 1.43192 | − | 1.25703i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 734512.i | − | 0.804792i | −0.915466 | − | 0.402396i | \(-0.868178\pi\) | ||
0.915466 | − | 0.402396i | \(-0.131822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −506670. | − | 246026.i | −0.522179 | − | 0.253557i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 184614.i | − | 0.179184i | −0.995979 | − | 0.0895922i | \(-0.971444\pi\) | ||
0.995979 | − | 0.0895922i | \(-0.0285564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.69989e6i | − | 1.55564i | −0.628489 | − | 0.777818i | \(-0.716326\pi\) | ||
0.628489 | − | 0.777818i | \(-0.283674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 904451. | + | 270857.i | 0.781299 | + | 0.233977i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.51250e6 | −1.23465 | −0.617325 | − | 0.786708i | \(-0.711784\pi\) | ||||
−0.617325 | + | 0.786708i | \(0.711784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.08425e6 | 0.837237 | 0.418618 | − | 0.908162i | \(-0.362514\pi\) | ||||
0.418618 | + | 0.908162i | \(0.362514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −50936.7 | − | 81357.8i | −0.0372445 | − | 0.0594881i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 639940. | 0.443511 | 0.221755 | − | 0.975102i | \(-0.428821\pi\) | ||||
0.221755 | + | 0.975102i | \(0.428821\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −991787. | + | 870649.i | −0.652116 | + | 0.572466i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.88723e6 | − | 916390.i | −1.17833 | − | 0.572167i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 781664.i | − | 0.463852i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.17461e6 | 0.663038 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.56010e6 | + | 2.49185e6i | 0.838375 | + | 1.33908i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.08753e6 | + | 1.62234e6i | 0.556813 | + | 0.830638i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 215399.i | − | 0.105155i | −0.998617 | − | 0.0525777i | \(-0.983256\pi\) | ||
0.998617 | − | 0.0525777i | \(-0.0167437\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 955628. | + | 1.52636e6i | 0.445164 | + | 0.711030i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.27781e6i | 0.568399i | 0.958765 | + | 0.284199i | \(0.0917278\pi\) | ||||
−0.958765 | + | 0.284199i | \(0.908272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65601e6i | 1.55400i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.81190e6 | + | 1.66447e6i | 0.736434 | + | 0.676509i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.09410e6 | −1.98110 | −0.990548 | − | 0.137166i | \(-0.956200\pi\) | ||||
−0.990548 | + | 0.137166i | \(0.956200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.88792e6 | −0.702975 | −0.351488 | − | 0.936193i | \(-0.614324\pi\) | ||||
−0.351488 | + | 0.936193i | \(0.614324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −92046.3 | + | 57628.6i | −0.0328359 | + | 0.0205580i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.22350e6 | −0.760376 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.07278e6 | + | 3.50032e6i | 1.00792 | + | 1.14816i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 901481. | − | 564402.i | 0.283795 | − | 0.177679i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.41329e6i | − | 0.729542i | −0.931097 | − | 0.364771i | \(-0.881147\pi\) | ||
0.931097 | − | 0.364771i | \(-0.118853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.39450e6 | 1.56682 | 0.783412 | − | 0.621502i | \(-0.213477\pi\) | ||||
0.783412 | + | 0.621502i | \(0.213477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 889756. | − | 1.83238e6i | 0.248426 | − | 0.511612i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 818305. | − | 718356.i | 0.219746 | − | 0.192906i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.66333e6i | − | 1.20503i | −0.798108 | − | 0.602514i | \(-0.794166\pi\) | ||
0.798108 | − | 0.602514i | \(-0.205834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.82089e6 | − | 1.14003e6i | 0.452994 | − | 0.283612i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.95348e6i | − | 0.707712i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 172365.i | − | 0.0398003i | −0.999802 | − | 0.0199002i | \(-0.993665\pi\) | ||
0.999802 | − | 0.0199002i | \(-0.00633484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.49800e6 | + | 748079.i | 0.556084 | + | 0.166531i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.56485e6 | −1.40953 | −0.704767 | − | 0.709439i | \(-0.748948\pi\) | ||||
−0.704767 | + | 0.709439i | \(0.748948\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.45521e6 | −0.715837 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.16158e6 | + | 8.57042e6i | −0.832280 | + | 1.71401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.35829e6 | 0.841740 | 0.420870 | − | 0.907121i | \(-0.361725\pi\) | ||||
0.420870 | + | 0.907121i | \(0.361725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.33418e6 | − | 566211.i | −0.808709 | − | 0.105649i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.16517e6 | + | 3.45827e6i | 0.390455 | + | 0.623648i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.77899e6i | − | 1.53068i | −0.643624 | − | 0.765341i | \(-0.722570\pi\) | ||
0.643624 | − | 0.765341i | \(-0.277430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.19153e6 | −1.21279 | −0.606395 | − | 0.795164i | \(-0.707385\pi\) | ||||
−0.606395 | + | 0.795164i | \(0.707385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.76000e6 | − | 2.98016e6i | 0.776701 | − | 0.486279i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 293171. | + | 333962.i | 0.0463027 | + | 0.0527451i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.15887e6i | − | 0.330143i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.47452e6 | + | 589886.i | −0.810887 | + | 0.0873741i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.04101e6i | − | 0.292917i | −0.989217 | − | 0.146459i | \(-0.953212\pi\) | ||
0.989217 | − | 0.146459i | \(-0.0467875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.28380e6i | − | 0.595878i | −0.954585 | − | 0.297939i | \(-0.903701\pi\) | ||
0.954585 | − | 0.297939i | \(-0.0962992\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.30447e6 | + | 2.78642e6i | 1.25484 | + | 0.375788i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.19176e6 | 0.809870 | 0.404935 | − | 0.914345i | \(-0.367294\pi\) | ||||
0.404935 | + | 0.914345i | \(0.367294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.95373e6 | 0.247917 | 0.123958 | − | 0.992287i | \(-0.460441\pi\) | ||||
0.123958 | + | 0.992287i | \(0.460441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.20722e6 | − | 8.31713e6i | −0.641235 | − | 1.02420i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.04237e7 | −1.24605 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.97934e6 | − | 1.02287e7i | −1.04228 | − | 1.18729i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.36191e6 | − | 6.92356e6i | 0.379031 | − | 0.780582i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00975e7i | 1.10605i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.15179e7 | 1.22610 | 0.613051 | − | 0.790043i | \(-0.289942\pi\) | ||||
0.613051 | + | 0.790043i | \(0.289942\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 543799. | + | 868574.i | 0.0562730 | + | 0.0898810i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.50021e6 | − | 6.26549e6i | −0.553432 | − | 0.630434i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.43686e6i | 0.238480i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.61247e6 | + | 1.05616e7i | 0.629552 | + | 1.00554i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.04131e6i | − | 0.744989i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19993e7i | 1.08204i | 0.841010 | + | 0.541019i | \(0.181961\pi\) | ||||
−0.841010 | + | 0.541019i | \(0.818039\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.51568e6 | − | 6.26084e6i | −0.835396 | − | 0.549649i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.97219e6 | 0.681553 | 0.340777 | − | 0.940144i | \(-0.389310\pi\) | ||||
0.340777 | + | 0.940144i | \(0.389310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −192826. | −0.0160568 | −0.00802840 | − | 0.999968i | \(-0.502556\pi\) | ||||
−0.00802840 | + | 0.999968i | \(0.502556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.94626e6 | + | 3.09677e6i | −0.401274 | + | 0.251231i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.89892e6 | 0.466343 | 0.233171 | − | 0.972436i | \(-0.425090\pi\) | ||||
0.233171 | + | 0.972436i | \(0.425090\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 377837. | − | 331687.i | 0.0291139 | − | 0.0255579i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.20336e6 | + | 3.25774e6i | −0.390876 | + | 0.244721i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.92581e7i | 1.41065i | 0.708884 | + | 0.705325i | \(0.249199\pi\) | ||||
−0.708884 | + | 0.705325i | \(0.750801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.83867e7 | 1.31357 | 0.656785 | − | 0.754078i | \(-0.271916\pi\) | ||||
0.656785 | + | 0.754078i | \(0.271916\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.35048e7 | − | 4.84875e6i | −0.941176 | − | 0.337918i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.70045e6 | + | 3.24847e6i | −0.251627 | + | 0.220893i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.76109e7i | 2.49587i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.28565e7 | − | 1.43100e7i | 1.48051 | − | 0.926922i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.31637e7i | 0.832449i | 0.909262 | + | 0.416224i | \(0.136647\pi\) | ||||
−0.909262 | + | 0.416224i | \(0.863353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.15721e6i | − | 0.503709i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.70544e6 | + | 9.03405e6i | −0.163161 | + | 0.544831i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.19050e7 | 1.29046 | 0.645230 | − | 0.763988i | \(-0.276762\pi\) | ||||
0.645230 | + | 0.763988i | \(0.276762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −994519. | −0.0572419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.44353e7 | − | 1.18652e7i | −1.37435 | − | 0.667348i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.12229e7 | −0.616930 | −0.308465 | − | 0.951236i | \(-0.599815\pi\) | ||||
−0.308465 | + | 0.951236i | \(0.599815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.47450e6 | + | 6.56155e6i | −0.401647 | + | 0.352589i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48889e7 | + | 2.37810e7i | 0.782219 | + | 1.24939i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.28826e6i | 0.0661829i | 0.999452 | + | 0.0330914i | \(0.0105353\pi\) | ||||
−0.999452 | + | 0.0330914i | \(0.989465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.45523e7 | 0.731178 | 0.365589 | − | 0.930776i | \(-0.380868\pi\) | ||||
0.365589 | + | 0.930776i | \(0.380868\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.84237e7 | + | 1.15348e7i | −0.905500 | + | 0.566919i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.19705e7 | − | 1.56381e6i | −0.575593 | − | 0.0751947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.52269e7i | − | 0.716426i | −0.933640 | − | 0.358213i | \(-0.883386\pi\) | ||
0.933640 | − | 0.358213i | \(-0.116614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.77385e6 | + | 5.71250e6i | −0.127723 | + | 0.263035i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.16226e7i | 1.87590i | 0.346770 | + | 0.937950i | \(0.387279\pi\) | ||||
−0.346770 | + | 0.937950i | \(0.612721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.10241e7i | − | 1.36880i | −0.729107 | − | 0.684400i | \(-0.760064\pi\) | ||
0.729107 | − | 0.684400i | \(-0.239936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26539e7 | − | 4.22541e7i | 0.546626 | − | 1.82530i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.04604e7 | 1.28852 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.63300e7 | −0.676537 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.05239e7 | − | 1.68092e7i | −0.427070 | − | 0.682130i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.84645e7 | 1.13162 | 0.565810 | − | 0.824536i | \(-0.308564\pi\) | ||||
0.565810 | + | 0.824536i | \(0.308564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.24618e7 | − | 1.41957e7i | −0.485418 | − | 0.552957i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.51200e7 | + | 1.62920e6i | −0.577143 | + | 0.0621879i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3.03837e7i | − | 1.13665i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.86583e7 | 0.684182 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.64511e6 | − | 4.22485e6i | −0.0950858 | − | 0.151874i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.95391e7 | + | 1.71526e7i | −0.688661 | + | 0.604547i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.58731e7i | − | 0.548587i | −0.961646 | − | 0.274293i | \(-0.911556\pi\) | ||
0.961646 | − | 0.274293i | \(-0.0884440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.43556e7 | − | 3.89016e7i | −0.825512 | − | 1.31853i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.36168e7i | − | 1.45002i | −0.688741 | − | 0.725008i | \(-0.741836\pi\) | ||
0.688741 | − | 0.725008i | \(-0.258164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.86898e7i | 0.609498i | 0.952433 | + | 0.304749i | \(0.0985726\pi\) | ||||
−0.952433 | + | 0.304749i | \(0.901427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.45790e7 | − | 6.76027e6i | 0.786379 | − | 0.216288i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.05789e7 | 1.90171 | 0.950853 | − | 0.309642i | \(-0.100209\pi\) | ||||
0.950853 | + | 0.309642i | \(0.100209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87892e7 | −0.886866 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.46132e7 | + | 2.16708e7i | −1.04647 | + | 0.655178i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.65178e7 | −1.08367 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.45875e7 | − | 5.82485e6i | −1.29886 | − | 0.169682i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.48128e7 | − | 1.55349e7i | 0.709630 | − | 0.444287i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.12518e6i | 0.0315960i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 889460. | 0.0245269 | 0.0122634 | − | 0.999925i | \(-0.496096\pi\) | ||||
0.0122634 | + | 0.999925i | \(0.496096\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.33135e6 | − | 1.13205e6i | −0.0631358 | − | 0.0306571i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.99707e7 | + | 3.41406e7i | 0.797190 | + | 0.908108i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.44293e7i | 1.68343i | 0.539926 | + | 0.841713i | \(0.318452\pi\) | ||||
−0.539926 | + | 0.841713i | \(0.681548\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.46449e7 | − | 9.16893e6i | 0.375913 | − | 0.235353i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.73036e6i | 0.169736i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.39314e7i | − | 1.08866i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.02224e7 | + | 3.41348e7i | −0.248940 | + | 0.831265i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.40907e7 | −0.576582 | −0.288291 | − | 0.957543i | \(-0.593087\pi\) | ||||
−0.288291 | + | 0.957543i | \(0.593087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.95136e7 | −0.459051 | −0.229525 | − | 0.973303i | \(-0.573717\pi\) | ||||
−0.229525 | + | 0.973303i | \(0.573717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63187e7 | + | 6.06841e6i | −1.30236 | + | 0.140331i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.83518e7 | 0.871891 | 0.435945 | − | 0.899973i | \(-0.356414\pi\) | ||||
0.435945 | + | 0.899973i | \(0.356414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.12989e6 | − | 3.56537e6i | −0.0699591 | − | 0.0796929i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.11995e7 | − | 1.78882e7i | −0.246147 | − | 0.393154i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.82974e7i | − | 0.395463i | −0.980256 | − | 0.197732i | \(-0.936643\pi\) | ||
0.980256 | − | 0.197732i | \(-0.0633574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23755e8 | 2.63053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.68808e7 | − | 1.68296e7i | 0.561982 | − | 0.351847i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.80587e7 | − | 4.33541e7i | −0.782665 | − | 0.891561i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.49800e6i | 0.0303049i | 0.999885 | + | 0.0151525i | \(0.00482336\pi\) | ||||
−0.999885 | + | 0.0151525i | \(0.995177\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.14054e7 | + | 3.46726e7i | 1.42119 | + | 0.690093i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.22586e7i | − | 0.435889i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.34299e7i | 0.836878i | 0.908245 | + | 0.418439i | \(0.137423\pi\) | ||||
−0.908245 | + | 0.418439i | \(0.862577\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.81323e7 | + | 2.15451e7i | 0.912732 | + | 0.408559i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.07233e8 | −2.00127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.39252e7 | −0.439480 | −0.219740 | − | 0.975559i | \(-0.570521\pi\) | ||||
−0.219740 | + | 0.975559i | \(0.570521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.08619e6 | − | 4.92936e6i | −0.0558017 | − | 0.0891283i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.46356e7 | −1.68445 | −0.842225 | − | 0.539126i | \(-0.818754\pi\) | ||||
−0.842225 | + | 0.539126i | \(0.818754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.03037e7 | − | 1.78238e7i | 0.355789 | − | 0.312333i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.37387e7 | + | 2.12384e7i | 0.754629 | + | 0.366428i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.73483e7i | 1.14414i | 0.820206 | + | 0.572068i | \(0.193859\pi\) | ||||
−0.820206 | + | 0.572068i | \(0.806141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.95007e7 | 0.493516 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.83082e7 | + | 2.92425e7i | 0.301626 | + | 0.481767i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.13591e7 | − | 1.87502e7i | 0.346570 | − | 0.304239i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.88724e7i | − | 0.781073i | −0.920587 | − | 0.390537i | \(-0.872289\pi\) | ||
0.920587 | − | 0.390537i | \(-0.127711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.23825e7 | + | 8.36670e7i | 0.824646 | + | 1.31715i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.51763e7i | 0.700612i | 0.936635 | + | 0.350306i | \(0.113922\pi\) | ||||
−0.936635 | + | 0.350306i | \(0.886078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.50691e7i | 0.383021i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.53132e7 | + | 1.21304e7i | 0.983186 | + | 0.182604i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74676e6 | −0.0407415 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.79302e7 | 0.992871 | 0.496436 | − | 0.868074i | \(-0.334642\pi\) | ||||
0.496436 | + | 0.868074i | \(0.334642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.16577e8 | + | 7.29872e7i | −1.67915 | + | 1.05129i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.22740e7 | 0.600099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.38225e7 | + | 8.23629e7i | −1.31269 | + | 1.15236i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.32048e7 | + | 2.70498e7i | −0.595832 | + | 0.373040i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.84851e7i | − | 0.523179i | −0.965179 | − | 0.261590i | \(-0.915753\pi\) | ||
0.965179 | − | 0.261590i | \(-0.0842467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.01299e6 | −0.120788 | −0.0603939 | − | 0.998175i | \(-0.519236\pi\) | ||||
−0.0603939 | + | 0.998175i | \(0.519236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.28077e6 | + | 2.63764e6i | −0.0169219 | + | 0.0348493i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.65556e6 | − | 4.32916e7i | 0.0736731 | − | 0.563946i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.81863e7i | − | 0.747373i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.08843e7 | + | 3.18578e7i | −0.644484 | + | 0.403500i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.03193e8i | − | 1.28889i | −0.764650 | − | 0.644446i | \(-0.777088\pi\) | ||
0.764650 | − | 0.644446i | \(-0.222912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.44510e8i | 1.78006i | 0.455900 | + | 0.890031i | \(0.349318\pi\) | ||||
−0.455900 | + | 0.890031i | \(0.650682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.20472e8 | + | 3.60779e7i | 1.46358 | + | 0.438302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.37981e8 | −1.65339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.69066e7 | 0.199831 | 0.0999156 | − | 0.994996i | \(-0.468143\pi\) | ||||
0.0999156 | + | 0.994996i | \(0.468143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.25436e7 | − | 2.58325e7i | 0.146253 | − | 0.301197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.78401e7 | 0.320228 | 0.160114 | − | 0.987099i | \(-0.448814\pi\) | ||||
0.160114 | + | 0.987099i | \(0.448814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.56945e7 | − | 9.76177e7i | −0.972463 | − | 1.10777i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.45771e7 | − | 5.52276e7i | −0.387138 | − | 0.618349i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.38092e7i | − | 0.483979i | −0.970279 | − | 0.241990i | \(-0.922200\pi\) | ||
0.970279 | − | 0.241990i | \(-0.0778000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.41285e7 | 0.917093 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.23452e8 | − | 7.72913e7i | 1.32802 | − | 0.831450i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.56266e7 | − | 6.63895e7i | 0.802861 | − | 0.704799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.14940e8i | − | 1.20426i | −0.798397 | − | 0.602131i | \(-0.794318\pi\) | ||
0.798397 | − | 0.602131i | \(-0.205682\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.89204e6 | − | 5.46819e7i | −0.0609295 | − | 0.565465i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.03087e7i | − | 0.105221i | −0.998615 | − | 0.0526104i | \(-0.983246\pi\) | ||
0.998615 | − | 0.0526104i | \(-0.0167542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.09209e8i | − | 1.10032i | −0.835061 | − | 0.550158i | \(-0.814568\pi\) | ||
0.835061 | − | 0.550158i | \(-0.185432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.43430e6 | − | 2.81640e7i | 0.0838861 | − | 0.280114i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.33692e7 | −0.916755 | −0.458377 | − | 0.888758i | \(-0.651569\pi\) | ||||
−0.458377 | + | 0.888758i | \(0.651569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.01669e8 | −0.985528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.68153e7 | − | 1.06719e8i | −0.639459 | − | 1.02137i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.15321e7 | 0.486962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.64522e7 | + | 2.02484e8i | −0.246821 | + | 1.88934i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.53366e7 | − | 5.21787e7i | 0.233450 | − | 0.480771i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.21460e8i | 1.10516i | 0.833459 | + | 0.552581i | \(0.186357\pi\) | ||||
−0.833459 | + | 0.552581i | \(0.813643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.02310e7 | −0.0919358 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.23169e7 | − | 6.75899e7i | −0.375554 | − | 0.599847i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.05715e7 | + | 6.89992e7i | 0.530937 | + | 0.604810i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.28588e7i | − | 0.630805i | −0.948958 | − | 0.315402i | \(-0.897861\pi\) | ||
0.948958 | − | 0.315402i | \(-0.102139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.46961e6 | − | 3.94455e6i | −0.0211204 | − | 0.0337342i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.10666e7i | − | 0.0934911i | −0.998907 | − | 0.0467456i | \(-0.985115\pi\) | ||
0.998907 | − | 0.0467456i | \(-0.0148850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.04117e8i | − | 0.868920i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.78845e7 | − | 1.86711e7i | 0.559700 | − | 0.153941i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.06175e7 | 0.0864872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.65048e8 | −1.32834 | −0.664168 | − | 0.747584i | \(-0.731214\pi\) | ||||
−0.664168 | + | 0.747584i | \(0.731214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50235e8 | + | 9.40598e7i | −1.19470 | + | 0.747982i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.48649e7 | −0.431112 | −0.215556 | − | 0.976491i | \(-0.569156\pi\) | ||||
−0.215556 | + | 0.976491i | \(0.569156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.52242e7 | + | 1.73424e7i | 0.118212 | + | 0.134659i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.90718e7 | + | 4.95055e7i | −0.606733 | + | 0.379865i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.47827e8i | − | 1.87929i | −0.342147 | − | 0.939647i | \(-0.611154\pi\) | ||
0.342147 | − | 0.939647i | \(-0.388846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.29106e8 | 0.967571 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.75583e7 | + | 2.55759e8i | 0.204127 | + | 1.89443i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.40181e8 | + | 1.59685e8i | 1.02629 | + | 1.16908i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.10762e6i | 0.0224883i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.97386e7 | − | 6.24447e7i | 0.713446 | − | 0.446677i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.86823e6i | − | 0.0344237i | −0.999852 | − | 0.0172118i | \(-0.994521\pi\) | ||
0.999852 | − | 0.0172118i | \(-0.00547897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.30392e7i | 0.370759i | 0.982667 | + | 0.185379i | \(0.0593514\pi\) | ||||
−0.982667 | + | 0.185379i | \(0.940649\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.07299e8 | + | 4.91416e7i | −0.741514 | + | 0.339603i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.43405e7 | −0.166302 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.65689e7 | −0.247027 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.90988e7 | + | 4.81198e7i | 0.661888 | + | 0.321396i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.13359e8 | 2.06948 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.42082e8 | − | 1.24728e8i | 0.927853 | − | 0.814523i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.25783e8 | − | 2.00905e8i | −0.812271 | − | 1.29738i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.04353e7i | − | 0.194362i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.43394e7 | −0.153716 | −0.0768578 | − | 0.997042i | \(-0.524489\pi\) | ||||
−0.0768578 | + | 0.997042i | \(0.524489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.64577e8 | + | 1.03039e8i | −1.02794 | + | 0.643578i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.01853e8 | + | 8.94124e7i | −0.629193 | + | 0.552342i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.94157e8i | 1.18629i | 0.805094 | + | 0.593147i | \(0.202115\pi\) | ||||
−0.805094 | + | 0.593147i | \(0.797885\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.62326e7 | − | 1.36401e8i | 0.400272 | − | 0.824326i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.86976e8i | 2.91107i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.36060e7i | 0.376117i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.14941e7 | + | 3.44216e6i | 0.0672352 | + | 0.0201350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.28160e7 | −0.189898 | −0.0949490 | − | 0.995482i | \(-0.530269\pi\) | ||||
−0.0949490 | + | 0.995482i | \(0.530269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.91945e8 | 1.09886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.09319e7 | − | 4.94054e7i | −0.175193 | − | 0.279825i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.44281e8 | −1.36888 | −0.684439 | − | 0.729070i | \(-0.739953\pi\) | ||||
−0.684439 | + | 0.729070i | \(0.739953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.01153e7 | + | 5.27727e7i | −0.333303 | + | 0.292593i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.16832e8 | + | 9.19372e7i | −0.640930 | + | 0.504362i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.53339e8i | 1.37520i | 0.726090 | + | 0.687600i | \(0.241336\pi\) | ||||
−0.726090 | + | 0.687600i | \(0.758664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.40185e8 | 0.752999 | 0.376499 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376499 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.92432e7 | − | 4.67081e7i | −0.155439 | − | 0.248272i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.13693e7 | − | 1.63576e8i | 0.112405 | − | 0.860429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.11319e7i | 0.266173i | 0.991104 | + | 0.133087i | \(0.0424888\pi\) | ||||
−0.991104 | + | 0.133087i | \(0.957511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.13774e7 | − | 9.80339e7i | −0.316208 | − | 0.505057i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.79398e8i | − | 1.42461i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.14759e7i | − | 0.310241i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.52854e8 | − | 6.95458e7i | 1.26300 | − | 0.347379i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.47081e8 | 1.71599 | 0.857997 | − | 0.513654i | \(-0.171709\pi\) | ||||
0.857997 | + | 0.513654i | \(0.171709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.13845e8 | 0.557147 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.41697e8 | − | 8.87142e7i | 0.686434 | − | 0.429765i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.55958e7 | 0.122745 | 0.0613725 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613725 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.44599e7 | + | 7.34286e7i | 0.306012 | + | 0.348590i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.47108e7 | − | 2.79927e7i | 0.210131 | − | 0.131559i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.40177e8i | 1.11751i | 0.829333 | + | 0.558755i | \(0.188721\pi\) | ||||
−0.829333 | + | 0.558755i | \(0.811279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 103123. | 0.000475041 | 0.000237520 | − | 1.00000i | \(-0.499924\pi\) | ||||
0.000237520 | 1.00000i | \(0.499924\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.38332e8 | − | 1.15728e8i | −1.08700 | − | 0.527821i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.10342e8 | + | 9.68645e7i | −0.498281 | + | 0.437420i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50975e8i | 0.675053i | 0.941316 | + | 0.337526i | \(0.109590\pi\) | ||||
−0.941316 | + | 0.337526i | \(0.890410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.38545e8 | + | 1.49349e8i | −1.05613 | + | 0.661227i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.15752e7i | 0.0507462i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.49042e7i | 0.194942i | 0.995238 | + | 0.0974711i | \(0.0310754\pi\) | ||||
−0.995238 | + | 0.0974711i | \(0.968925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.52045e8 | − | 1.05427e8i | −1.51347 | − | 0.453240i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.74818e7 | −0.202149 | −0.101074 | − | 0.994879i | \(-0.532228\pi\) | ||||
−0.101074 | + | 0.994879i | \(0.532228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.46225e7 | −0.230303 | −0.115152 | − | 0.993348i | \(-0.536735\pi\) | ||||
−0.115152 | + | 0.993348i | \(0.536735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.22628e7 | − | 2.06613e8i | −0.0929619 | − | 0.862746i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.90699e8 | 1.20221 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.35947e8 | − | 6.27180e7i | −0.966440 | − | 0.256893i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.44675e8 | + | 2.31079e8i | 0.586936 | + | 0.937473i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.93369e6i | − | 0.0399171i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.24138e8 | −1.68818 | −0.844090 | − | 0.536201i | \(-0.819859\pi\) | ||||
−0.844090 | + | 0.536201i | \(0.819859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.63585e8 | − | 1.65026e8i | 1.03923 | − | 0.650642i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.77629e7 | + | 2.02343e7i | 0.0693732 | + | 0.0790255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.13365e8i | − | 0.438591i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.48895e7 | + | 1.20857e7i | 0.0953923 | + | 0.0463201i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.86487e7i | − | 0.146744i | −0.997305 | − | 0.0733721i | \(-0.976624\pi\) | ||
0.997305 | − | 0.0733721i | \(-0.0233761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.25945e7i | − | 0.197837i | −0.995096 | − | 0.0989185i | \(-0.968462\pi\) | ||
0.995096 | − | 0.0989185i | \(-0.0315383\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.15642e8 | − | 6.45786e7i | −0.803626 | − | 0.240663i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.78974e8 | 1.39925 | 0.699626 | − | 0.714509i | \(-0.253350\pi\) | ||||
0.699626 | + | 0.714509i | \(0.253350\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.16756e8 | 0.427116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.49149e7 | + | 5.57671e7i | 0.126552 | + | 0.202132i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.47799e8 | −0.889940 | −0.444970 | − | 0.895546i | \(-0.646786\pi\) | ||||
−0.444970 | + | 0.895546i | \(0.646786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.05375e8 | − | 1.20036e8i | −0.374984 | − | 0.427158i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.02650e8 | + | 1.46959e8i | 1.06720 | + | 0.518204i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.29762e8i | − | 0.453410i | −0.973963 | − | 0.226705i | \(-0.927205\pi\) | ||
0.973963 | − | 0.226705i | \(-0.0727954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.47342e8 | −0.510180 | −0.255090 | − | 0.966917i | \(-0.582105\pi\) | ||||
−0.255090 | + | 0.966917i | \(0.582105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.15214e8 | − | 1.84024e8i | −0.395335 | − | 0.631442i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.01493e8 | − | 3.43441e8i | −1.02521 | − | 1.16785i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.93400e8i | − | 1.32574i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.71924e8 | + | 2.74603e8i | 0.574194 | + | 0.917120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.60705e8i | − | 0.531937i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.34333e8i | − | 0.768756i | −0.923176 | − | 0.384378i | \(-0.874416\pi\) | ||
0.923176 | − | 0.384378i | \(-0.125584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.07469e8 | − | 6.93945e6i | −0.999745 | − | 0.0225639i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.68160e8 | 1.18651 | 0.593254 | − | 0.805015i | \(-0.297843\pi\) | ||||
0.593254 | + | 0.805015i | \(0.297843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.05475e8 | −0.656373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.82442e8 | − | 1.14224e8i | 0.577675 | − | 0.361672i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.78221e8 | −1.18709 | −0.593545 | − | 0.804801i | \(-0.702272\pi\) | ||||
−0.593545 | + | 0.804801i | \(0.702272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.78534e8 | − | 4.20085e8i | 1.48882 | − | 1.30697i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.41278e6 | + | 2.76277e6i | −0.0136095 | + | 0.00852068i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.28984e8i | − | 0.700079i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.94037e6 | −0.00891186 | −0.00445593 | − | 0.999990i | \(-0.501418\pi\) | ||||
−0.00445593 | + | 0.999990i | \(0.501418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.88243e7 | + | 1.41738e8i | −0.206796 | + | 0.425879i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.77349e8 | − | 1.55688e8i | 0.528294 | − | 0.463767i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.04252e8i | 0.898535i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.34996e8 | − | 8.45186e7i | 0.395265 | − | 0.247469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.90944e7i | − | 0.258640i | −0.991603 | − | 0.129320i | \(-0.958720\pi\) | ||
0.991603 | − | 0.129320i | \(-0.0412795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.64619e7i | 0.133731i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.89438e6 | − | 1.30042e7i | 0.0111140 | − | 0.0371121i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.16447e7 | −0.146139 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.18589e7 | 0.145507 | 0.0727536 | − | 0.997350i | \(-0.476821\pi\) | ||||
0.0727536 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.24018e7 | + | 1.49105e8i | −0.201438 | + | 0.414844i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.19693e7 | −0.253732 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.08873e8 | − | 1.83361e8i | 0.571431 | − | 0.501636i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.75926e8 | + | 4.40717e8i | 0.748574 | + | 1.19565i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.07056e8i | 0.557059i | 0.960428 | + | 0.278530i | \(0.0898471\pi\) | ||||
−0.960428 | + | 0.278530i | \(0.910153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.75533e8 | −1.26875 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.20776e8 | − | 2.63441e8i | 1.11336 | − | 0.697057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.77307e8 | − | 7.54186e7i | −1.51493 | − | 0.197909i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.83279e8i | 1.25775i | 0.777506 | + | 0.628875i | \(0.216484\pi\) | ||||
−0.777506 | + | 0.628875i | \(0.783516\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.78528e8 | + | 8.25318e7i | −0.977046 | + | 0.213029i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.86367e8i | 0.477108i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.32007e8i | 1.60476i | 0.596813 | + | 0.802380i | \(0.296433\pi\) | ||||
−0.596813 | + | 0.802380i | \(0.703567\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.81407e7 | + | 1.27360e8i | −0.0960565 | + | 0.320753i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.80798e8 | −0.701443 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.40814e7 | 0.158781 | 0.0793905 | − | 0.996844i | \(-0.474703\pi\) | ||||
0.0793905 | + | 0.996844i | \(0.474703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.38881e8 | + | 8.60718e8i | 1.32446 | + | 2.11547i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.46058e8 | −0.356089 | −0.178045 | − | 0.984022i | \(-0.556977\pi\) | ||||
−0.178045 | + | 0.984022i | \(0.556977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99012e8 | + | 2.26701e8i | 0.481294 | + | 0.548259i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.18034e8 | − | 6.54965e8i | 0.762979 | − | 1.57129i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.23113e8i | 1.00696i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.06104e7 | 0.166705 | 0.0833526 | − | 0.996520i | \(-0.473437\pi\) | ||||
0.0833526 | + | 0.996520i | \(0.473437\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.88607e8 | + | 3.01249e8i | 0.441746 | + | 0.705571i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.06753e8 | + | 4.44858e8i | −1.17749 | + | 1.03367i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.20517e8i | 1.43043i | 0.698905 | + | 0.715215i | \(0.253671\pi\) | ||||
−0.698905 | + | 0.715215i | \(0.746329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.16875e8 | − | 1.86676e8i | −0.267298 | − | 0.426937i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.01803e8i | − | 0.457904i | −0.973438 | − | 0.228952i | \(-0.926470\pi\) | ||
0.973438 | − | 0.228952i | \(-0.0735298\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.03312e8i | − | 0.682835i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.75245e7 | + | 2.45505e8i | 0.150826 | + | 0.548374i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.34891e8 | 0.963815 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.56998e8 | 1.66462 | 0.832311 | − | 0.554308i | \(-0.187017\pi\) | ||||
0.832311 | + | 0.554308i | \(0.187017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.01293e8 | − | 3.13851e8i | 1.09378 | − | 0.684794i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.74970e8 | −1.24482 | −0.622410 | − | 0.782691i | \(-0.713846\pi\) | ||||
−0.622410 | + | 0.782691i | \(0.713846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.76314e7 | + | 1.34963e8i | −0.0378775 | + | 0.289941i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.27594e7 | + | 1.42493e7i | −0.0485174 | + | 0.0303759i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.42305e9i | − | 3.01029i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.93243e7 | 0.0615566 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.29200e8 | + | 7.85721e7i | −1.51901 | + | 0.163675i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.84562e8 | + | 4.38068e8i | 0.794982 | + | 0.905593i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.48390e8i | 0.714729i | 0.933965 | + | 0.357365i | \(0.116325\pi\) | ||||
−0.933965 | + | 0.357365i | \(0.883675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.56833e8 | + | 1.60799e8i | −0.522901 | + | 0.327380i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.79020e8i | − | 0.361719i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.98588e8i | − | 1.20035i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.70399e7 | + | 2.57253e8i | −0.153326 | + | 0.511987i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.25438e8 | −1.03788 | −0.518939 | − | 0.854811i | \(-0.673673\pi\) | ||||
−0.518939 | + | 0.854811i | \(0.673673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.12387e7 | −0.0220332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.81459e8 | + | 3.30899e8i | 1.32600 | + | 0.643869i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.56577e8 | 0.688662 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.43559e8 | + | 2.77447e8i | 0.466892 | + | 0.531854i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.84579e7 | + | 2.94815e7i | 0.0351205 | + | 0.0560956i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.86771e8i | − | 1.10821i | −0.832446 | − | 0.554106i | \(-0.813060\pi\) | ||
0.832446 | − | 0.554106i | \(-0.186940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.92475e8 | −0.548309 | −0.274155 | − | 0.961686i | \(-0.588398\pi\) | ||||
−0.274155 | + | 0.961686i | \(0.588398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.33026e8 | − | 2.08502e8i | 0.619736 | − | 0.388006i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.42141e7 | + | 1.61918e7i | 0.0262571 | + | 0.0299104i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.71676e8i | − | 1.59841i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.56355e8 | + | 5.27942e8i | −0.466649 | + | 0.961024i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.82491e8i | 0.329770i | 0.986313 | + | 0.164885i | \(0.0527254\pi\) | ||||
−0.986313 | + | 0.164885i | \(0.947275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.87227e8i | − | 0.515259i | −0.966244 | − | 0.257629i | \(-0.917059\pi\) | ||
0.966244 | − | 0.257629i | \(-0.0829413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.96350e8 | + | 1.35724e8i | −0.527767 | + | 0.241710i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.52810e8 | −0.800570 | −0.400285 | − | 0.916391i | \(-0.631089\pi\) | ||||
−0.400285 | + | 0.916391i | \(0.631089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.05808e8 | 0.185719 | 0.0928594 | − | 0.995679i | \(-0.470399\pi\) | ||||
0.0928594 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.18167e8 | − | 3.48464e8i | −0.380178 | − | 0.607232i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.10070e8 | 0.190429 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.16695e8 | − | 5.41371e8i | 1.05928 | − | 0.929898i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.83686e7 | + | 1.70473e8i | 0.0313257 | + | 0.290722i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09165e9i | 1.84841i | 0.381896 | + | 0.924205i | \(0.375271\pi\) | ||||
−0.381896 | + | 0.924205i | \(0.624729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.93605e8 | −1.33419 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.96359e8 | + | 9.52524e8i | 0.995463 | + | 1.58999i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.24579e8 | − | 2.84934e8i | 0.537960 | − | 0.472253i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.28591e8i | − | 0.540761i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.44507e8 | − | 7.09981e8i | −0.726366 | − | 1.16017i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.75340e7i | − | 0.0609027i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.70719e8i | 1.24179i | 0.783893 | + | 0.620896i | \(0.213231\pi\) | ||||
−0.783893 | + | 0.620896i | \(0.786769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.15826e8 | − | 1.14828e9i | −0.505301 | − | 1.83717i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.95426e8 | 0.310485 | 0.155242 | − | 0.987876i | \(-0.450384\pi\) | ||||
0.155242 | + | 0.987876i | \(0.450384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.88095e8 | −1.55890 | −0.779451 | − | 0.626463i | \(-0.784502\pi\) | ||||
−0.779451 | + | 0.626463i | \(0.784502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.97081e8 | − | 4.36430e8i | 1.09213 | − | 0.683763i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.59608e8 | 1.02625 | 0.513125 | − | 0.858314i | \(-0.328488\pi\) | ||||
0.513125 | + | 0.858314i | \(0.328488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.09413e8 | + | 3.59407e8i | −0.632577 | + | 0.555313i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.73708e8 | + | 2.33972e8i | −0.573423 | + | 0.359011i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75673e8i | 0.267698i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04591e9 | −1.58285 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.81676e8 | − | 2.33890e8i | −0.723956 | − | 0.351535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.53840e8 | − | 3.04229e8i | 0.677453 | − | 0.454126i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.54769e8i | − | 1.41547i | −0.706480 | − | 0.707733i | \(-0.749718\pi\) | ||
0.706480 | − | 0.707733i | \(-0.250282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.51404e8 | − | 4.07833e8i | 0.959145 | − | 0.600504i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.27849e7i | − | 0.0333211i | −0.999861 | − | 0.0166606i | \(-0.994697\pi\) | ||
0.999861 | − | 0.0166606i | \(-0.00530346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.64348e8i | − | 0.238717i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) | ||
0.992851 | − | 0.119359i | \(-0.0380838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.88580e8 | − | 1.46316e8i | −0.704865 | − | 0.211087i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.76046e8 | −0.252265 | −0.126132 | − | 0.992013i | \(-0.540256\pi\) | ||||
−0.126132 | + | 0.992013i | \(0.540256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.02566e7 | −0.0857628 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.22676e8 | + | 2.53921e8i | −0.456178 | + | 0.358976i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.25660e7 | 0.0738159 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.23960e8 | + | 8.24688e8i | 1.00982 | + | 1.15033i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.35332e8 | − | 6.95326e8i | −0.603175 | − | 0.963410i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.24587e8i | 0.446738i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.22329e8 | 0.303963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.26990e8 | − | 2.67332e8i | 0.579902 | − | 0.363067i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.75564e8 | − | 5.93050e8i | 0.911425 | − | 0.800102i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.07506e8i | − | 0.144083i | −0.997402 | − | 0.0720413i | \(-0.977049\pi\) | ||
0.997402 | − | 0.0720413i | \(-0.0229513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.21066e8 | − | 5.87864e7i | −0.161187 | − | 0.0782681i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.74267e8i | 0.230494i | 0.993337 | + | 0.115247i | \(0.0367659\pi\) | ||||
−0.993337 | + | 0.115247i | \(0.963234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.71667e8i | − | 1.01395i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.01390e8 | + | 6.72486e8i | −0.262891 | + | 0.877850i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.57461e8 | 0.463575 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.89452e8 | 0.888296 | 0.444148 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444148 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.27426e8 | − | 3.63252e8i | −0.291113 | − | 0.464974i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.09226e8 | 0.138906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.50804e7 | − | 7.19562e6i | −0.0695940 | − | 0.00909166i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.11475e9 | − | 5.41293e8i | −1.39938 | − | 0.679505i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.86093e8i | − | 0.481554i | −0.970580 | − | 0.240777i | \(-0.922598\pi\) | ||
0.970580 | − | 0.240777i | \(-0.0774022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.14820e8 | −0.637978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.24932e8 | − | 9.98162e8i | −0.769464 | − | 1.22901i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.78032e8 | + | 2.02802e8i | 0.217802 | + | 0.248106i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.56424e7i | 0.0311702i | 0.999879 | + | 0.0155851i | \(0.00496109\pi\) | ||||
−0.999879 | + | 0.0155851i | \(0.995039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.67784e8 | + | 4.27713e8i | 0.323436 | + | 0.516602i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.32023e9i | 1.58446i | 0.610224 | + | 0.792229i | \(0.291080\pi\) | ||||
−0.610224 | + | 0.792229i | \(0.708920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.14960e9i | 1.37092i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.65625e8 | − | 5.06870e8i | 0.551748 | − | 0.600622i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.59807e8 | −1.13014 | −0.565072 | − | 0.825041i | \(-0.691152\pi\) | ||||
−0.565072 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.32817e9 | 1.55401 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.38634e9 | − | 8.67962e8i | 1.61186 | − | 1.00916i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.86881e8 | 1.14021 | 0.570106 | − | 0.821571i | \(-0.306902\pi\) | ||||
0.570106 | + | 0.821571i | \(0.306902\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.68312e8 | + | 1.91730e8i | 0.193244 | + | 0.220131i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.58836e8 | + | 4.12486e8i | −0.751695 | + | 0.470623i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.42504e9i | 1.61574i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.11621e8 | −0.914499 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.81623e8 | + | 9.91862e8i | −0.539298 | + | 1.11064i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.53264e8 | + | 4.02415e8i | 0.393113 | + | 0.447809i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.20291e8i | − | 0.907170i | −0.891213 | − | 0.453585i | \(-0.850145\pi\) | ||
0.891213 | − | 0.453585i | \(-0.149855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.35702e8 | + | 5.23219e8i | −0.918502 | + | 0.575059i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.18742e9i | − | 1.29702i | −0.761205 | − | 0.648512i | \(-0.775392\pi\) | ||
0.761205 | − | 0.648512i | \(-0.224608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.28136e8i | 0.573333i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.10383e9 | + | 5.05540e8i | −1.19094 | + | 0.545434i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.04362e8 | −0.755287 | −0.377644 | − | 0.925951i | \(-0.623266\pi\) | ||||
−0.377644 | + | 0.925951i | \(0.623266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.02881e8 | 0.855664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.45255e8 | − | 7.11024e8i | 0.365707 | − | 0.753143i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.07712e9 | 1.13398 | 0.566988 | − | 0.823726i | \(-0.308108\pi\) | ||||
0.566988 | + | 0.823726i | \(0.308108\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.81647e8 | + | 5.10604e8i | −0.608626 | + | 0.534288i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.61213e7 | + | 2.57494e7i | 0.0167667 | + | 0.0267803i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.04179e8i | 0.727937i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.19667e9 | 1.22957 | 0.614786 | − | 0.788694i | \(-0.289242\pi\) | ||||
0.614786 | + | 0.788694i | \(0.289242\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.03551e7 | − | 1.27440e7i | 0.0207886 | − | 0.0130154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.83531e8 | + | 1.61115e8i | −0.186312 | + | 0.163556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.14696e9i | 1.15735i | 0.815559 | + | 0.578674i | \(0.196430\pi\) | ||||
−0.815559 | + | 0.578674i | \(0.803570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.95723e7 | + | 7.49650e6i | −0.0697814 | + | 0.00751904i |
(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 | 60.7.b.a.29.9 | yes | 12 | |
3.2 | odd | 2 | inner | 60.7.b.a.29.3 | ✓ | 12 | |
4.3 | odd | 2 | 240.7.c.e.209.4 | 12 | |||
5.2 | odd | 4 | 300.7.g.i.101.3 | 12 | |||
5.3 | odd | 4 | 300.7.g.i.101.10 | 12 | |||
5.4 | even | 2 | inner | 60.7.b.a.29.4 | yes | 12 | |
12.11 | even | 2 | 240.7.c.e.209.10 | 12 | |||
15.2 | even | 4 | 300.7.g.i.101.4 | 12 | |||
15.8 | even | 4 | 300.7.g.i.101.9 | 12 | |||
15.14 | odd | 2 | inner | 60.7.b.a.29.10 | yes | 12 | |
20.19 | odd | 2 | 240.7.c.e.209.9 | 12 | |||
60.59 | even | 2 | 240.7.c.e.209.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.b.a.29.3 | ✓ | 12 | 3.2 | odd | 2 | inner | |
60.7.b.a.29.4 | yes | 12 | 5.4 | even | 2 | inner | |
60.7.b.a.29.9 | yes | 12 | 1.1 | even | 1 | trivial | |
60.7.b.a.29.10 | yes | 12 | 15.14 | odd | 2 | inner | |
240.7.c.e.209.3 | 12 | 60.59 | even | 2 | |||
240.7.c.e.209.4 | 12 | 4.3 | odd | 2 | |||
240.7.c.e.209.9 | 12 | 20.19 | odd | 2 | |||
240.7.c.e.209.10 | 12 | 12.11 | even | 2 | |||
300.7.g.i.101.3 | 12 | 5.2 | odd | 4 | |||
300.7.g.i.101.4 | 12 | 15.2 | even | 4 | |||
300.7.g.i.101.9 | 12 | 15.8 | even | 4 | |||
300.7.g.i.101.10 | 12 | 5.3 | odd | 4 |