Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,8,Mod(257,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.257");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.i (of order \(4\), degree \(2\), 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: | \(93.7155076452\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 132 x^{14} - 784 x^{13} + 5524236 x^{12} - 33135588 x^{11} - 49457570 x^{10} + \cdots + 18\!\cdots\!21 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{12}\cdot 5^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.8 | ||
Root | \(27.4835 - 23.4128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.293 |
Dual form | 300.8.i.c.257.8 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 46.0669 | + | 8.05216i | 0.985065 | + | 0.172182i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 565.187 | − | 565.187i | 0.622800 | − | 0.622800i | −0.323446 | − | 0.946247i | \(-0.604841\pi\) |
0.946247 | + | 0.323446i | \(0.104841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2057.33 | + | 741.876i | 0.940707 | + | 0.339221i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2361.39i | 0.534926i | 0.963568 | + | 0.267463i | \(0.0861852\pi\) | ||||
−0.963568 | + | 0.267463i | \(0.913815\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −732.128 | − | 732.128i | −0.0924241 | − | 0.0924241i | 0.659383 | − | 0.751807i | \(-0.270818\pi\) |
−0.751807 | + | 0.659383i | \(0.770818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22896.0 | − | 22896.0i | −1.13029 | − | 1.13029i | −0.990129 | − | 0.140157i | \(-0.955239\pi\) |
−0.140157 | − | 0.990129i | \(-0.544761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 38729.0i | − | 1.29539i | −0.761902 | − | 0.647693i | \(-0.775734\pi\) | ||
0.761902 | − | 0.647693i | \(-0.224266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30587.4 | − | 21485.4i | 0.720734 | − | 0.506264i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23922.4 | − | 23922.4i | 0.409975 | − | 0.409975i | −0.471755 | − | 0.881730i | \(-0.656379\pi\) |
0.881730 | + | 0.471755i | \(0.156379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 88801.0 | + | 50741.9i | 0.868250 | + | 0.496128i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 172492. | 1.31333 | 0.656667 | − | 0.754181i | \(-0.271966\pi\) | ||||
0.656667 | + | 0.754181i | \(0.271966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −119020. | −0.717551 | −0.358776 | − | 0.933424i | \(-0.616806\pi\) | ||||
−0.358776 | + | 0.933424i | \(0.616806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19014.3 | + | 108782.i | −0.0921046 | + | 0.526937i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −93692.5 | + | 93692.5i | −0.304088 | + | 0.304088i | −0.842611 | − | 0.538523i | \(-0.818983\pi\) |
0.538523 | + | 0.842611i | \(0.318983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27831.7 | − | 39622.1i | −0.0751300 | − | 0.106958i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 673768.i | − | 1.52675i | −0.645958 | − | 0.763373i | \(-0.723542\pi\) | ||
0.645958 | − | 0.763373i | \(-0.276458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −265451. | − | 265451.i | −0.509148 | − | 0.509148i | 0.405117 | − | 0.914265i | \(-0.367231\pi\) |
−0.914265 | + | 0.405117i | \(0.867231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 218777. | + | 218777.i | 0.307368 | + | 0.307368i | 0.843888 | − | 0.536520i | \(-0.180261\pi\) |
−0.536520 | + | 0.843888i | \(0.680261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 184671.i | 0.224240i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −870387. | − | 1.23911e6i | −0.918791 | − | 1.30802i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9795.00 | − | 9795.00i | 0.00903730 | − | 0.00903730i | −0.702574 | − | 0.711611i | \(-0.747966\pi\) |
0.711611 | + | 0.702574i | \(0.247966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 311852. | − | 1.78413e6i | 0.223042 | − | 1.27604i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.54803e6 | 0.981292 | 0.490646 | − | 0.871359i | \(-0.336761\pi\) | ||||
0.490646 | + | 0.871359i | \(0.336761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −394224. | −0.222376 | −0.111188 | − | 0.993799i | \(-0.535466\pi\) | ||||
−0.111188 | + | 0.993799i | \(0.535466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.58207e6 | − | 743474.i | 0.797139 | − | 0.374605i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −898446. | + | 898446.i | −0.364947 | + | 0.364947i | −0.865631 | − | 0.500683i | \(-0.833082\pi\) |
0.500683 | + | 0.865631i | \(0.333082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.29466e6 | − | 909405.i | 0.474442 | − | 0.333262i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.33054e6i | − | 0.772772i | −0.922337 | − | 0.386386i | \(-0.873723\pi\) | ||
0.922337 | − | 0.386386i | \(-0.126277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.64459e6 | − | 2.64459e6i | −0.795663 | − | 0.795663i | 0.186745 | − | 0.982408i | \(-0.440206\pi\) |
−0.982408 | + | 0.186745i | \(0.940206\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.33463e6 | + | 1.33463e6i | 0.333152 | + | 0.333152i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.05235e6i | − | 0.696530i | −0.937396 | − | 0.348265i | \(-0.886771\pi\) | ||
0.937396 | − | 0.348265i | \(-0.113229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.68221e6 | + | 3.05256e6i | 0.769858 | + | 0.638215i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.34959e6 | − | 2.34959e6i | 0.451044 | − | 0.451044i | −0.444657 | − | 0.895701i | \(-0.646674\pi\) |
0.895701 | + | 0.444657i | \(0.146674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.94617e6 | + | 1.38893e6i | 1.29372 | + | 0.226133i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.61447e6 | −0.543475 | −0.271738 | − | 0.962371i | \(-0.587598\pi\) | ||||
−0.271738 | + | 0.962371i | \(0.587598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −827578. | −0.115124 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.48287e6 | − | 958365.i | −0.706835 | − | 0.123549i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.89118e6 | − | 3.89118e6i | 0.432892 | − | 0.432892i | −0.456719 | − | 0.889611i | \(-0.650975\pi\) |
0.889611 | + | 0.456719i | \(0.150975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75186e6 | + | 4.85815e6i | −0.181458 | + | 0.503208i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.34688e7i | 1.30078i | 0.759599 | + | 0.650392i | \(0.225395\pi\) | ||||
−0.759599 | + | 0.650392i | \(0.774605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.12200e7 | − | 1.12200e7i | −1.01172 | − | 1.01172i | −0.999930 | − | 0.0117938i | \(-0.996246\pi\) |
−0.0117938 | − | 0.999930i | \(-0.503754\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −513749. | − | 513749.i | −0.0405423 | − | 0.0405423i | 0.686545 | − | 0.727087i | \(-0.259126\pi\) |
−0.727087 | + | 0.686545i | \(0.759126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.44407e7i | 1.06806i | 0.845466 | + | 0.534030i | \(0.179323\pi\) | ||||
−0.845466 | + | 0.534030i | \(0.820677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.07056e6 | + | 3.56170e6i | −0.351905 | + | 0.247188i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.81341e7 | − | 1.81341e7i | 1.18228 | − | 1.18228i | 0.203131 | − | 0.979152i | \(-0.434888\pi\) |
0.979152 | − | 0.203131i | \(-0.0651118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −963077. | − | 2.04937e6i | −0.0555918 | − | 0.118296i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.58810e7 | −1.40789 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.39110e7 | 0.713855 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.42528e6 | − | 3.10384e7i | 0.262878 | − | 1.50394i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.98952e7 | − | 2.98952e7i | 1.29506 | − | 1.29506i | 0.363438 | − | 0.931618i | \(-0.381603\pi\) |
0.931618 | − | 0.363438i | \(-0.118397\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00910e7 | − | 1.43659e7i | −0.413878 | − | 0.589210i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04475e7i | 0.406035i | 0.979175 | + | 0.203018i | \(0.0650748\pi\) | ||||
−0.979175 | + | 0.203018i | \(0.934925\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.18891e7 | − | 2.18891e7i | −0.806767 | − | 0.806767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.55355e7 | + | 3.55355e7i | 1.18070 | + | 1.18070i | 0.979563 | + | 0.201138i | \(0.0644640\pi\) |
0.201138 | + | 0.979563i | \(0.435536\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50412e6i | 0.0790865i | 0.999218 | + | 0.0395433i | \(0.0125903\pi\) | ||||
−0.999218 | + | 0.0395433i | \(0.987410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.31675e6 | + | 1.18400e7i | 0.249854 | + | 0.355701i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.72884e6 | − | 1.72884e6i | 0.0494400 | − | 0.0494400i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.48700e6 | + | 8.50723e6i | −0.0386100 | + | 0.220891i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.78790e7 | 1.92872 | 0.964358 | − | 0.264602i | \(-0.0852406\pi\) | ||||
0.964358 | + | 0.264602i | \(0.0852406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.59598e7 | −0.377231 | −0.188615 | − | 0.982051i | \(-0.560400\pi\) | ||||
−0.188615 | + | 0.982051i | \(0.560400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.01185e7 | − | 6.40905e7i | −0.679851 | − | 1.44668i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.04188e7 | − | 4.04188e7i | 0.833555 | − | 0.833555i | −0.154446 | − | 0.988001i | \(-0.549359\pi\) |
0.988001 | + | 0.154446i | \(0.0493593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 530096. | − | 372355.i | 0.0104584 | − | 0.00734627i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.70412e7i | − | 0.510665i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.56387e7 | − | 6.56387e7i | −1.18714 | − | 1.18714i | −0.977854 | − | 0.209290i | \(-0.932885\pi\) |
−0.209290 | − | 0.977854i | \(-0.567115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.17012e7 | + | 2.17012e7i | 0.360559 | + | 0.360559i | 0.864019 | − | 0.503459i | \(-0.167940\pi\) |
−0.503459 | + | 0.864019i | \(0.667940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.16765e7i | − | 0.982916i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.87322e7 | − | 7.96782e7i | 0.439422 | − | 1.21858i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.65454e7 | − | 8.65454e7i | 1.27082 | − | 1.27082i | 0.325154 | − | 0.945661i | \(-0.394584\pi\) |
0.945661 | − | 0.325154i | \(-0.105416\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.13132e7 | + | 1.24650e7i | 0.966637 | + | 0.168961i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.55469e7 | −0.723892 | −0.361946 | − | 0.932199i | \(-0.617888\pi\) | ||||
−0.361946 | + | 0.932199i | \(0.617888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.21040e7 | −1.02917 | −0.514587 | − | 0.857438i | \(-0.672055\pi\) | ||||
−0.514587 | + | 0.857438i | \(0.672055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.81607e7 | − | 3.17435e6i | −0.219055 | − | 0.0382892i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.40664e7 | − | 5.40664e7i | 0.604619 | − | 0.604619i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.88678e7 | − | 2.15105e7i | 0.849735 | − | 0.231758i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.27821e8i | − | 1.32735i | −0.748021 | − | 0.663675i | \(-0.768996\pi\) | ||
0.748021 | − | 0.663675i | \(-0.231004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.53151e7 | − | 4.53151e7i | −0.453724 | − | 0.453724i | 0.442864 | − | 0.896589i | \(-0.353962\pi\) |
−0.896589 | + | 0.442864i | \(0.853962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.34501e7 | − | 6.34501e7i | −0.591290 | − | 0.591290i | 0.346690 | − | 0.937980i | \(-0.387306\pi\) |
−0.937980 | + | 0.346690i | \(0.887306\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.01928e8i | 1.81640i | 0.418538 | + | 0.908199i | \(0.362543\pi\) | ||||
−0.418538 | + | 0.908199i | \(0.637457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.86231e7 | + | 3.41542e7i | −0.422334 | + | 0.296659i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.74900e7 | − | 9.74900e7i | 0.817945 | − | 0.817945i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.69636e7 | − | 3.14687e7i | 0.524738 | − | 0.246594i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.14544e7 | 0.692935 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.55270e6 | −0.0480210 | −0.0240105 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240105 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.87658e7 | − | 1.07361e8i | 0.133057 | − | 0.761231i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.72683e7 | + | 6.72683e7i | −0.446891 | + | 0.446891i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00534e8 | − | 1.43123e8i | −0.646781 | − | 0.920779i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.35256e7i | 0.208931i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.30061e8 | − | 1.30061e8i | −0.785380 | − | 0.785380i | 0.195353 | − | 0.980733i | \(-0.437415\pi\) |
−0.980733 | + | 0.195353i | \(0.937415\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.84611e8 | + | 1.84611e8i | 1.04753 | + | 1.04753i | 0.998812 | + | 0.0487216i | \(0.0155147\pi\) |
0.0487216 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.37952e7i | − | 0.185965i | −0.995668 | − | 0.0929825i | \(-0.970360\pi\) | ||
0.995668 | − | 0.0929825i | \(-0.0296401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.07355e7 | + | 7.22288e7i | 0.270813 | + | 0.385539i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.26237e8 | + | 2.26237e8i | −1.17170 | + | 1.17170i | −0.189898 | + | 0.981804i | \(0.560816\pi\) |
−0.981804 | + | 0.189898i | \(0.939184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.45780e7 | − | 1.40612e8i | 0.119930 | − | 0.686127i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.17366e8 | −1.02991 | −0.514954 | − | 0.857218i | \(-0.672191\pi\) | ||||
−0.514954 | + | 0.857218i | \(0.672191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.52613e8 | 0.702316 | 0.351158 | − | 0.936316i | \(-0.385788\pi\) | ||||
0.351158 | + | 0.936316i | \(0.385788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.45048e8 | + | 1.70272e8i | 0.648471 | + | 0.761239i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.83546e7 | + | 2.83546e7i | −0.119725 | + | 0.119725i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.27158e8 | − | 8.93191e7i | 0.521969 | − | 0.366646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.18158e8i | 1.26994i | 0.772535 | + | 0.634972i | \(0.218988\pi\) | ||||
−0.772535 | + | 0.634972i | \(0.781012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.64901e7 | + | 5.64901e7i | 0.219306 | + | 0.219306i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.37997e7 | − | 2.37997e7i | −0.0874591 | − | 0.0874591i | 0.662024 | − | 0.749483i | \(-0.269698\pi\) |
−0.749483 | + | 0.662024i | \(0.769698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.05908e8i | 0.378772i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.54872e8 | + | 1.27968e8i | 1.23546 | + | 0.445511i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.33888e7 | − | 8.33888e7i | 0.282659 | − | 0.282659i | −0.551510 | − | 0.834169i | \(-0.685948\pi\) |
0.834169 | + | 0.551510i | \(0.185948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.66508e8 | − | 2.91043e7i | −0.535358 | − | 0.0935766i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.61377e6 | 0.0175842 | 0.00879208 | − | 0.999961i | \(-0.497201\pi\) | ||||
0.00879208 | + | 0.999961i | \(0.497201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.57656e8 | −1.09162 | −0.545812 | − | 0.837907i | \(-0.683779\pi\) | ||||
−0.545812 | + | 0.837907i | \(0.683779\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.81240e7 | − | 6.66379e6i | −0.113404 | − | 0.0198222i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.65642e8 | + | 2.65642e8i | −0.750962 | + | 0.750962i | −0.974659 | − | 0.223697i | \(-0.928187\pi\) |
0.223697 | + | 0.974659i | \(0.428187\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.44862e8 | − | 8.82979e7i | −0.675005 | − | 0.243408i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.57465e8i | 1.22995i | 0.788548 | + | 0.614973i | \(0.210833\pi\) | ||||
−0.788548 | + | 0.614973i | \(0.789167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.81936e8 | + | 3.81936e8i | 1.00170 | + | 1.00170i | 0.999999 | + | 0.00170342i | \(0.000542216\pi\) |
0.00170342 | + | 0.999999i | \(0.499458\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.80805e8 | − | 3.80805e8i | −0.950858 | − | 0.950858i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.38115e8i | 1.55509i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.10587e8 | − | 1.47922e8i | 0.500963 | − | 0.351891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.69493e6 | − | 7.69493e6i | 0.0178718 | − | 0.0178718i | −0.698114 | − | 0.715986i | \(-0.745977\pi\) |
0.715986 | + | 0.698114i | \(0.245977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.19821e8 | + | 2.09694e8i | −0.265391 | + | 0.464449i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.50285e7 | −0.0757832 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00058e8 | −0.634195 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.08453e8 | + | 6.20468e8i | −0.223971 | + | 1.28136i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12115e8 | − | 2.12115e8i | 0.418396 | − | 0.418396i | −0.466254 | − | 0.884651i | \(-0.654397\pi\) |
0.884651 | + | 0.466254i | \(0.154397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.26525e8 | − | 6.07216e8i | −0.822414 | − | 1.17082i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.81144e8i | − | 1.66106i | −0.556973 | − | 0.830531i | \(-0.688037\pi\) | ||
0.556973 | − | 0.830531i | \(-0.311963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.14996e8 | + | 5.14996e8i | 0.949289 | + | 0.949289i | 0.998775 | − | 0.0494862i | \(-0.0157584\pi\) |
−0.0494862 | + | 0.998775i | \(0.515758\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.34448e8 | − | 3.34448e8i | −0.589687 | − | 0.589687i | 0.347860 | − | 0.937547i | \(-0.386909\pi\) |
−0.937547 | + | 0.347860i | \(0.886909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.07320e8i | 0.702536i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.95301e7 | − | 2.78036e7i | −0.0329561 | − | 0.0469174i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.86740e8 | + | 8.86740e8i | −1.46416 | + | 1.46416i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.16279e8 | + | 6.65239e8i | −0.183901 | + | 1.05211i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.47299e8 | 0.382858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.49153e8 | −0.226065 | −0.113033 | − | 0.993591i | \(-0.536056\pi\) | ||||
−0.113033 | + | 0.993591i | \(0.536056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.62264e8 | + | 1.23248e8i | −0.389210 | + | 0.182904i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81331e8 | + | 6.81331e8i | −0.969736 | + | 0.969736i | −0.999555 | − | 0.0298192i | \(-0.990507\pi\) |
0.0298192 | + | 0.999555i | \(0.490507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.81401e8 | − | 6.89364e8i | 1.36819 | − | 0.961058i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.81052e8i | − | 0.383836i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.69829e8 | + | 5.69829e8i | 0.762457 | + | 0.762457i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.34509e8 | + | 2.34509e8i | 0.301305 | + | 0.301305i | 0.841524 | − | 0.540219i | \(-0.181659\pi\) |
−0.540219 | + | 0.841524i | \(0.681659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.82894e8i | 0.859932i | 0.902845 | + | 0.429966i | \(0.141474\pi\) | ||||
−0.902845 | + | 0.429966i | \(0.858526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.78641e7 | − | 1.02163e8i | −0.0343931 | − | 0.126101i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.59877e7 | + | 3.59877e7i | −0.0435454 | + | 0.0435454i | −0.728544 | − | 0.684999i | \(-0.759803\pi\) |
0.684999 | + | 0.728544i | \(0.259803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.19226e9 | − | 2.08398e8i | −1.38686 | − | 0.242413i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.87990e8 | 0.898856 | 0.449428 | − | 0.893317i | \(-0.351628\pi\) | ||||
0.449428 | + | 0.893317i | \(0.351628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.06066e8 | −0.678024 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.40838e8 | + | 1.12014e8i | 0.703193 | + | 0.122913i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.88227e8 | − | 2.88227e8i | 0.304371 | − | 0.304371i | −0.538350 | − | 0.842721i | \(-0.680952\pi\) |
0.842721 | + | 0.538350i | \(0.180952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.99853e8 | − | 1.38616e9i | 0.517904 | − | 1.43622i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.10720e7i | − | 0.0112569i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.75486e8 | + | 9.75486e8i | 0.973285 | + | 0.973285i | 0.999652 | − | 0.0263674i | \(-0.00839398\pi\) |
−0.0263674 | + | 0.999652i | \(0.508394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.26286e8 | − | 1.26286e8i | −0.121384 | − | 0.121384i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.44236e7i | 0.0230448i | 0.999934 | + | 0.0115224i | \(0.00366777\pi\) | ||||
−0.999934 | + | 0.0115224i | \(0.996332\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.61790e9 | − | 1.13646e9i | 1.49870 | − | 1.05273i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.30215e8 | + | 8.30215e8i | −0.755083 | + | 0.755083i | −0.975423 | − | 0.220340i | \(-0.929283\pi\) |
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.49187e8 | − | 7.43050e8i | −0.306245 | − | 0.651673i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.85170e8 | −0.762435 | −0.381218 | − | 0.924485i | \(-0.624495\pi\) | ||||
−0.381218 | + | 0.924485i | \(0.624495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.09545e9 | −0.926778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.41250e7 | + | 4.81285e8i | −0.0699119 | + | 0.399971i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.72503e8 | + | 4.72503e8i | −0.378999 | + | 0.378999i | −0.870741 | − | 0.491742i | \(-0.836360\pi\) |
0.491742 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.32111e8 | − | 1.18462e9i | −0.655807 | − | 0.933628i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.26513e9i | − | 0.979784i | −0.871783 | − | 0.489892i | \(-0.837036\pi\) | ||
0.871783 | − | 0.489892i | \(-0.162964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.71377e7 | + | 8.71377e7i | 0.0663190 | + | 0.0663190i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.21245e8 | − | 2.21245e8i | −0.162664 | − | 0.162664i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.15154e9i | 1.55495i | 0.628911 | + | 0.777477i | \(0.283501\pi\) | ||||
−0.628911 | + | 0.777477i | \(0.716499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.35087e9 | + | 1.92315e9i | 0.959772 | + | 1.36636i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.74928e8 | − | 8.74928e8i | 0.611149 | − | 0.611149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.01635e7 | + | 1.15357e8i | −0.0136173 | + | 0.0779054i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.48977e8 | 0.497415 | 0.248708 | − | 0.968579i | \(-0.419994\pi\) | ||||
0.248708 | + | 0.968579i | \(0.419994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.49357e9 | −1.62867 | −0.814337 | − | 0.580392i | \(-0.802899\pi\) | ||||
−0.814337 | + | 0.580392i | \(0.802899\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.87790e8 | + | 6.12400e8i | 0.184877 | + | 0.393409i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.22810e8 | + | 2.22810e8i | −0.138496 | + | 0.138496i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.35633e7 | − | 6.57215e7i | 0.0572143 | − | 0.0401890i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.00871e9i | 1.20850i | 0.796794 | + | 0.604251i | \(0.206527\pi\) | ||||
−0.796794 | + | 0.604251i | \(0.793473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.15215e9 | − | 2.15215e9i | −1.27399 | − | 1.27399i | −0.943977 | − | 0.330011i | \(-0.892948\pi\) |
−0.330011 | − | 0.943977i | \(-0.607052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.26492e8 | − | 9.26492e8i | −0.531076 | − | 0.531076i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.52076e9i | 1.98615i | 0.117499 | + | 0.993073i | \(0.462512\pi\) | ||||
−0.117499 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.37003e8 | + | 3.79928e8i | −0.0760668 | + | 0.210944i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.05454e8 | + | 4.05454e8i | −0.221579 | + | 0.221579i | −0.809163 | − | 0.587584i | \(-0.800079\pi\) |
0.587584 | + | 0.809163i | \(0.300079\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.58764e9 | + | 6.27094e8i | 1.89991 | + | 0.332090i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.04161e9 | −1.58578 | −0.792888 | − | 0.609367i | \(-0.791424\pi\) | ||||
−0.792888 | + | 0.609367i | \(0.791424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.59103e9 | 0.816695 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.35217e8 | − | 1.28510e8i | −0.371597 | − | 0.0649523i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.04947e9 | + | 1.04947e9i | −0.514355 | + | 0.514355i | −0.915858 | − | 0.401502i | \(-0.868488\pi\) |
0.401502 | + | 0.915858i | \(0.368488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.71401e8 | − | 3.19497e9i | −0.420604 | − | 1.54214i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.42379e9i | 0.676851i | 0.940993 | + | 0.338425i | \(0.109894\pi\) | ||||
−0.940993 | + | 0.338425i | \(0.890106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.31932e9 | + | 1.31932e9i | 0.617754 | + | 0.617754i | 0.944955 | − | 0.327201i | \(-0.106105\pi\) |
−0.327201 | + | 0.944955i | \(0.606105\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.20143e9 | + | 2.20143e9i | 1.00022 | + | 1.00022i | 1.00000 | 0.000219918i | \(7.00021e-5\pi\) | |
0.000219918 | 1.00000i | \(0.499930\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.01558e9i | 0.454578i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.18743e9 | − | 1.53651e9i | 0.964629 | − | 0.677583i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.26832e8 | − | 6.26832e8i | 0.272356 | − | 0.272356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.74182e7 | − | 1.28848e7i | 0.0115671 | − | 0.00543581i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.19523e9 | 0.496910 | 0.248455 | − | 0.968643i | \(-0.420077\pi\) | ||||
0.248455 | + | 0.968643i | \(0.420077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.37190e8 | 0.0562101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.17740e8 | − | 1.24571e9i | 0.0879274 | − | 0.503038i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.43704e9 | − | 2.43704e9i | 0.956117 | − | 0.956117i | −0.0429600 | − | 0.999077i | \(-0.513679\pi\) |
0.999077 | + | 0.0429600i | \(0.0136788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.49524e9 | − | 3.55231e9i | −0.965009 | − | 1.37382i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.69275e9i | 1.40788i | 0.710261 | + | 0.703938i | \(0.248577\pi\) | ||||
−0.710261 | + | 0.703938i | \(0.751423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.94937e9 | − | 3.94937e9i | −1.48444 | − | 1.48444i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.31719e9 | − | 1.31719e9i | −0.481283 | − | 0.481283i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.10681e9i | 1.11934i | 0.828715 | + | 0.559671i | \(0.189072\pi\) | ||||
−0.828715 | + | 0.559671i | \(0.810928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.24968e8 | + | 1.17445e9i | 0.293093 | + | 0.417256i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.71686e9 | − | 3.71686e9i | 1.30223 | − | 1.30223i | 0.375345 | − | 0.926885i | \(-0.377524\pi\) |
0.926885 | − | 0.375345i | \(-0.122476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.96629e8 | − | 2.84125e9i | 0.169240 | − | 0.968236i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.98710e9 | 0.667894 | 0.333947 | − | 0.942592i | \(-0.391619\pi\) | ||||
0.333947 | + | 0.942592i | \(0.391619\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.98938e9 | −0.991078 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.96518e9 | − | 3.43918e9i | 0.642677 | − | 1.12472i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.16617e8 | + | 5.16617e8i | −0.164419 | + | 0.164419i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.68376e9 | − | 3.29000e9i | 1.47065 | − | 1.03302i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.68557e9i | − | 0.831963i | −0.909373 | − | 0.415982i | \(-0.863438\pi\) | ||
0.909373 | − | 0.415982i | \(-0.136562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.83283e9 | − | 1.83283e9i | −0.560231 | − | 0.560231i | 0.369142 | − | 0.929373i | \(-0.379652\pi\) |
−0.929373 | + | 0.369142i | \(0.879652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.72508e9 | + | 2.72508e9i | 0.811038 | + | 0.811038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.26026e9i | 0.663841i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.18481e9 | + | 1.14845e9i | 0.923108 | + | 0.332875i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.93284e8 | + | 4.93284e8i | −0.141108 | + | 0.141108i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.55887e9 | − | 4.47272e8i | −0.713081 | − | 0.124641i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.36080e8 | −0.119951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.09705e9 | −0.840925 | −0.420463 | − | 0.907310i | \(-0.638132\pi\) | ||||
−0.420463 | + | 0.907310i | \(0.638132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.78228e9 | − | 6.61114e8i | −1.01380 | − | 0.177205i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.08212e9 | − | 5.08212e9i | 1.32767 | − | 1.32767i | 0.420267 | − | 0.907401i | \(-0.361936\pi\) |
0.907401 | − | 0.420267i | \(-0.138064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.11047e8 | − | 2.92466e8i | −0.209191 | − | 0.0754348i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.68044e9i | − | 1.70127i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.72515e9 | − | 1.72515e9i | −0.433799 | − | 0.433799i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.22298e9 | + | 2.22298e9i | 0.545059 | + | 0.545059i | 0.925008 | − | 0.379949i | \(-0.124058\pi\) |
−0.379949 | + | 0.925008i | \(0.624058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.88688e8i | 0.0941151i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.92602e9 | − | 2.05532e9i | 0.699694 | − | 0.491485i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.57065e8 | + | 3.57065e8i | −0.0843273 | + | 0.0843273i | −0.748012 | − | 0.663685i | \(-0.768992\pi\) |
0.663685 | + | 0.748012i | \(0.268992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.80640e9 | − | 3.55867e8i | 0.876948 | − | 0.0819874i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.15255e8 | 0.0489848 | 0.0244924 | − | 0.999700i | \(-0.492203\pi\) | ||||
0.0244924 | + | 0.999700i | \(0.492203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.21269e9 | −1.39654 | −0.698270 | − | 0.715834i | \(-0.746047\pi\) | ||||
−0.698270 | + | 0.715834i | \(0.746047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.02924e9 | − | 5.88832e9i | 0.228546 | − | 1.30753i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.09785e9 | − | 1.09785e9i | 0.237918 | − | 0.237918i | −0.578069 | − | 0.815988i | \(-0.696194\pi\) |
0.815988 | + | 0.578069i | \(0.196194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.72264e9 | − | 2.45241e9i | −0.368825 | − | 0.525071i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.65591e9i | − | 0.561820i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.31298e7 | + | 2.31298e7i | 0.00483428 | + | 0.00483428i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.05457e9 | + | 3.05457e9i | 0.623329 | + | 0.623329i | 0.946381 | − | 0.323052i | \(-0.104709\pi\) |
−0.323052 | + | 0.946381i | \(0.604709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.60952e9i | 0.929505i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41204e9 | − | 3.43386e9i | −0.480650 | − | 0.684269i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.59943e9 | − | 5.59943e9i | 1.10269 | − | 1.10269i | 0.108602 | − | 0.994085i | \(-0.465363\pi\) |
0.994085 | − | 0.108602i | \(-0.0346374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.62596e9 | + | 9.30221e9i | −0.312751 | + | 1.78927i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.22831e8 | −0.137418 | −0.0687088 | − | 0.997637i | \(-0.521888\pi\) | ||||
−0.0687088 | + | 0.997637i | \(0.521888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31712e9 | −0.247493 | −0.123747 | − | 0.992314i | \(-0.539491\pi\) | ||||
−0.123747 | + | 0.992314i | \(0.539491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.51493e9 | + | 1.18186e9i | −0.467106 | + | 0.219511i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.78474e9 | − | 1.78474e9i | 0.323903 | − | 0.323903i | −0.526360 | − | 0.850262i | \(-0.676443\pi\) |
0.850262 | + | 0.526360i | \(0.176443\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.27607e9 | − | 3.70606e9i | 0.946564 | − | 0.664894i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.20345e8i | − | 0.0568164i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.53669e9 | − | 5.53669e9i | −0.970819 | − | 0.970819i | 0.0287671 | − | 0.999586i | \(-0.490842\pi\) |
−0.999586 | + | 0.0287671i | \(0.990842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.29818e9 | − | 6.29818e9i | −1.07949 | − | 1.07949i | −0.996555 | − | 0.0829309i | \(-0.973572\pi\) |
−0.0829309 | − | 0.996555i | \(-0.526428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.02532e9i | 0.682155i | 0.940035 | + | 0.341078i | \(0.110792\pi\) | ||||
−0.940035 | + | 0.341078i | \(0.889208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.33820e9 | − | 9.10465e8i | 0.559361 | − | 0.152561i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.04285e9 | + | 2.04285e9i | −0.338476 | + | 0.338476i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.21302e9 | + | 7.36405e8i | 0.682586 | + | 0.119311i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.29037e9 | 0.687413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00012e9 | 0.158471 | 0.0792357 | − | 0.996856i | \(-0.474752\pi\) | ||||
0.0792357 | + | 0.996856i | \(0.474752\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.01863e8 | − | 5.27633e7i | −0.0473038 | − | 0.00826836i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.35203e8 | − | 1.35203e8i | 0.0207252 | − | 0.0207252i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72897e9 | − | 4.79467e9i | 0.262141 | − | 0.726952i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.84409e9i | 0.876423i | 0.898872 | + | 0.438211i | \(0.144388\pi\) | ||||
−0.898872 | + | 0.438211i | \(0.855612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.70724e9 | + | 7.70724e9i | 1.14330 | + | 1.14330i | 0.987842 | + | 0.155458i | \(0.0496854\pi\) |
0.155458 | + | 0.987842i | \(0.450315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.26457e9 | − | 1.26457e9i | −0.183560 | − | 0.183560i | 0.609345 | − | 0.792905i | \(-0.291432\pi\) |
−0.792905 | + | 0.609345i | \(0.791432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.65551e9i | 0.524918i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.64050e9 | + | 2.55719e9i | −0.517163 | + | 0.363270i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.06128e9 | − | 4.06128e9i | 0.570777 | − | 0.570777i | −0.361569 | − | 0.932345i | \(-0.617759\pi\) |
0.932345 | + | 0.361569i | \(0.117759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.47883e9 | − | 7.40275e9i | −0.478580 | − | 1.01839i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.05577e9 | −0.552045 | −0.276022 | − | 0.961151i | \(-0.589016\pi\) | ||||
−0.276022 | + | 0.961151i | \(0.589016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.61381e9 | 0.486698 | 0.243349 | − | 0.969939i | \(-0.421754\pi\) | ||||
0.243349 | + | 0.969939i | \(0.421754\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.69954e8 | + | 1.54442e9i | −0.0359742 | + | 0.205811i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.12642e9 | − | 4.12642e9i | 0.538434 | − | 0.538434i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.94424e9 | − | 7.03878e9i | −0.638422 | − | 0.908879i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.30917e8i | − | 0.118955i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.83270e9 | − | 2.83270e9i | −0.358218 | − | 0.358218i | 0.504938 | − | 0.863156i | \(-0.331515\pi\) |
−0.863156 | + | 0.504938i | \(0.831515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.30153e9 | − | 1.30153e9i | −0.161211 | − | 0.161211i | 0.621892 | − | 0.783103i | \(-0.286364\pi\) |
−0.783103 | + | 0.621892i | \(0.786364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.39848e9i | − | 0.539211i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.01796e9 | + | 9.99100e9i | 0.851523 | + | 1.21226i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.66517e9 | + | 6.66517e9i | −0.800458 | + | 0.800458i | −0.983167 | − | 0.182709i | \(-0.941513\pi\) |
0.182709 | + | 0.983167i | \(0.441513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.72124e8 | − | 1.55684e9i | 0.0320198 | − | 0.183188i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.43424e7 | −0.00167053 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.08878e9 | 0.932631 | 0.466316 | − | 0.884618i | \(-0.345581\pi\) | ||||
0.466316 | + | 0.884618i | \(0.345581\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.75563e9 | + | 3.73589e9i | 0.200386 | + | 0.426410i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.54266e10 | + | 1.54266e10i | −1.72566 | + | 1.72566i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.22437e10 | + | 8.60034e9i | −1.35595 | + | 0.952457i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.03327e9i | 0.990448i | 0.868765 | + | 0.495224i | \(0.164914\pi\) | ||||
−0.868765 | + | 0.495224i | \(0.835086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.62862e9 | + | 3.62862e9i | 0.393911 | + | 0.393911i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.61240e9 | + | 7.61240e9i | 0.810128 | + | 0.810128i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.76635e9i | − | 0.502255i | −0.967954 | − | 0.251127i | \(-0.919199\pi\) | ||
0.967954 | − | 0.251127i | \(-0.0808013\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.26447e9 | − | 6.27968e9i | 0.236278 | − | 0.655230i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.84724e9 | + | 2.84724e9i | −0.294178 | + | 0.294178i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.00134e10 | − | 1.75026e9i | −1.01453 | − | 0.177332i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.15153e8 | −0.0316206 | −0.0158103 | − | 0.999875i | \(-0.505033\pi\) | ||||
−0.0158103 | + | 0.999875i | \(0.505033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.26828e10 | −1.26020 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.03043e9 | + | 1.22887e9i | 0.691827 | + | 0.120926i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.64502e8 | + | 9.64502e8i | −0.0930963 | + | 0.0930963i | −0.752121 | − | 0.659025i | \(-0.770969\pi\) |
0.659025 | + | 0.752121i | \(0.270969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.31088e9 | + | 9.01186e9i | 0.507715 | + | 0.861525i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.21555e10i | 1.15097i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.00690e9 | + | 7.00690e9i | 0.657147 | + | 0.657147i | 0.954704 | − | 0.297557i | \(-0.0961720\pi\) |
−0.297557 | + | 0.954704i | \(0.596172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.12158e9 | − | 2.12158e9i | −0.195220 | − | 0.195220i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.63138e10i | 1.48696i | 0.668757 | + | 0.743481i | \(0.266826\pi\) | ||||
−0.668757 | + | 0.743481i | \(0.733174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.53453e9 | + | 1.07789e9i | −0.138551 | + | 0.0973223i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.77965e9 | + | 9.77965e9i | −0.874707 | + | 0.874707i | −0.992981 | − | 0.118274i | \(-0.962264\pi\) |
0.118274 | + | 0.992981i | \(0.462264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.57697e9 | − | 3.09076e9i | 0.577303 | − | 0.271296i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.80729e8 | −0.0504995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45113e9 | −0.125016 | −0.0625082 | − | 0.998044i | \(-0.519910\pi\) | ||||
−0.0625082 | + | 0.998044i | \(0.519910\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.56186e9 | + | 1.46566e10i | −0.218662 | + | 1.25098i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.94867e9 | + | 8.94867e9i | −0.749761 | + | 0.749761i | −0.974434 | − | 0.224673i | \(-0.927869\pi\) |
0.224673 | + | 0.974434i | \(0.427869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.14746e9 | + | 3.05719e9i | 0.178270 | + | 0.253791i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.51046e8i | − | 0.0288747i | −0.999896 | − | 0.0144374i | \(-0.995404\pi\) | ||
0.999896 | − | 0.0144374i | \(-0.00459572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.16169e9 | + | 8.16169e9i | 0.665188 | + | 0.665188i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.13336e9 | − | 1.13336e9i | −0.0906951 | − | 0.0906951i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.06835e10i | − | 0.847170i | −0.905856 | − | 0.423585i | \(-0.860771\pi\) | ||
0.905856 | − | 0.423585i | \(-0.139229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.04739e8 | − | 1.28802e9i | −0.0710940 | − | 0.101212i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.62442e9 | + | 9.62442e9i | −0.749457 | + | 0.749457i | −0.974377 | − | 0.224921i | \(-0.927788\pi\) |
0.224921 | + | 0.974377i | \(0.427788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.52784e8 | + | 4.87884e9i | −0.0652177 | + | 0.373115i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.60944e10 | −1.97772 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.50330e9 | 0.413376 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.53174e10 | + | 8.75255e9i | 1.14030 | + | 0.651581i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.14739e9 | + | 3.14739e9i | −0.230165 | + | 0.230165i | −0.812762 | − | 0.582597i | \(-0.802037\pi\) |
0.582597 | + | 0.812762i | \(0.302037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.51293e9 | − | 3.17001e9i | 0.327106 | − | 0.229769i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.04983e10i | − | 1.47265i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.88623e8 | + | 2.88623e8i | 0.0205529 | + | 0.0205529i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.69169e10 | − | 1.69169e10i | −1.18363 | − | 1.18363i | −0.978797 | − | 0.204835i | \(-0.934334\pi\) |
−0.204835 | − | 0.978797i | \(-0.565666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.00182e10i | − | 0.694828i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.43614e9 | − | 2.68149e9i | −0.511251 | − | 0.184358i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.24492e9 | − | 6.24492e9i | 0.425620 | − | 0.425620i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.58609e8 | + | 4.52030e7i | 0.0173215 | + | 0.00302768i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.86006e10 | 1.23511 | 0.617556 | − | 0.786527i | \(-0.288123\pi\) | ||||
0.617556 | + | 0.786527i | \(0.288123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.00449e10 | 0.661263 | 0.330632 | − | 0.943760i | \(-0.392738\pi\) | ||||
0.330632 | + | 0.943760i | \(0.392738\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.64761e10 | − | 2.87991e9i | −1.07532 | − | 0.187958i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.02806e10 | + | 1.02806e10i | −0.659543 | + | 0.659543i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.70260e9 | − | 6.13961e8i | −0.108297 | − | 0.0390523i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.37544e10i | − | 0.867444i | −0.901047 | − | 0.433722i | \(-0.857200\pi\) | ||
0.901047 | − | 0.433722i | \(-0.142800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.26443e10 | + | 1.26443e10i | 0.790669 | + | 0.790669i | 0.981603 | − | 0.190934i | \(-0.0611517\pi\) |
−0.190934 | + | 0.981603i | \(0.561152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.86210e10 | − | 1.86210e10i | −1.14481 | − | 1.14481i | −0.987559 | − | 0.157252i | \(-0.949737\pi\) |
−0.157252 | − | 0.987559i | \(-0.550263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.21215e10i | − | 0.738949i | −0.929241 | − | 0.369475i | \(-0.879538\pi\) | ||
0.929241 | − | 0.369475i | \(-0.120462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.43763e10 | + | 1.00983e10i | −0.869049 | + | 0.610444i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.22823e9 | − | 4.22823e9i | 0.253455 | − | 0.253455i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.05691e10 | − | 6.03928e9i | −0.623014 | − | 0.355997i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.12593e10 | 1.82731 | 0.913656 | − | 0.406488i | \(-0.133247\pi\) | ||||
0.913656 | + | 0.406488i | \(0.133247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25035e10 | 0.724847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.68358e9 | + | 2.10740e10i | −0.211775 | + | 1.21158i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.86232e9 | − | 7.86232e9i | 0.444589 | − | 0.444589i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.45192e10 | + | 2.06701e10i | 0.814267 | + | 1.15922i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.48270e9i | 0.249337i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.01070e10 | + | 1.01070e10i | 0.557570 | + | 0.557570i | 0.928615 | − | 0.371045i | \(-0.121000\pi\) |
−0.371045 | + | 0.928615i | \(0.621000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.22083e9 | + | 5.22083e9i | 0.283339 | + | 0.283339i | 0.834439 | − | 0.551100i | \(-0.185792\pi\) |
−0.551100 | + | 0.834439i | \(0.685792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.06595e10i | − | 0.573798i | −0.957961 | − | 0.286899i | \(-0.907376\pi\) | ||
0.957961 | − | 0.286899i | \(-0.0926244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.44762e10 | − | 2.06088e10i | −0.772936 | − | 1.10038i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.81636e10 | + | 1.81636e10i | −0.961978 | + | 0.961978i | −0.999303 | − | 0.0373248i | \(-0.988116\pi\) |
0.0373248 | + | 0.999303i | \(0.488116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.13820e9 | + | 2.93960e10i | −0.267759 | + | 1.53187i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.20779e9 | 0.372592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.31555e9 | 0.0674599 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.08922e10 | − | 5.11864e9i | 0.554071 | − | 0.260378i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.91061e9 | − | 4.91061e9i | 0.245831 | − | 0.245831i | −0.573426 | − | 0.819257i | \(-0.694386\pi\) |
0.819257 | + | 0.573426i | \(0.194386\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.16443e8 | − | 2.92521e8i | 0.0206821 | − | 0.0145277i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.36282e9i | − | 0.313497i | −0.987639 | − | 0.156749i | \(-0.949899\pi\) | ||
0.987639 | − | 0.156749i | \(-0.0501013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.25527e8 | − | 9.25527e8i | −0.0452404 | − | 0.0452404i | 0.684125 | − | 0.729365i | \(-0.260184\pi\) |
−0.729365 | + | 0.684125i | \(0.760184\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.78070e10 | + | 2.78070e10i | 1.33789 | + | 1.33789i | 0.898099 | + | 0.439794i | \(0.144949\pi\) |
0.439794 | + | 0.898099i | \(0.355051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.37928e10i | − | 1.61312i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.20829e9 | + | 8.69513e9i | −0.341398 | + | 0.411817i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.47301e9 | − | 8.47301e9i | 0.398160 | − | 0.398160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.61366e9 | − | 2.82055e8i | −0.0746514 | − | 0.0130485i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.05299e10 | −0.942385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.48533e8 | −0.0204295 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.38228e10 | − | 2.41612e9i | −0.624723 | − | 0.109197i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.17395e9 | − | 4.17395e9i | 0.185747 | − | 0.185747i | −0.608108 | − | 0.793855i | \(-0.708071\pi\) |
0.793855 | + | 0.608108i | \(0.208071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.99220e9 | + | 2.77098e10i | −0.441253 | + | 1.22366i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.10265e10i | − | 1.35962i | −0.733386 | − | 0.679812i | \(-0.762061\pi\) | ||
0.733386 | − | 0.679812i | \(-0.237939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.54830e9 | + | 5.54830e9i | 0.241275 | + | 0.241275i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.90480e9 | + | 5.90480e9i | 0.252879 | + | 0.252879i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.00910e10i | − | 0.428876i | −0.976738 | − | 0.214438i | \(-0.931208\pi\) | ||
0.976738 | − | 0.214438i | \(-0.0687920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.14795e10 | − | 8.06352e9i | 0.484188 | − | 0.340107i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.70625e9 | + | 1.70625e9i | −0.0714228 | + | 0.0714228i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.47593e10 | − | 3.14070e10i | −0.608538 | − | 1.29493i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.63018e10 | −1.48550 | −0.742751 | − | 0.669568i | \(-0.766479\pi\) | ||||
−0.742751 | + | 0.669568i | \(0.766479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.15213e9 | 0.290477 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.09511e9 | − | 4.05916e10i | 0.286005 | − | 1.63625i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.89509e9 | + | 6.89509e9i | −0.273811 | + | 0.273811i | −0.830632 | − | 0.556821i | \(-0.812021\pi\) |
0.556821 | + | 0.830632i | \(0.312021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.95774e10 | + | 2.78711e10i | 0.771661 | + | 1.09856i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.05738e10i | 1.58739i | 0.608319 | + | 0.793693i | \(0.291844\pi\) | ||||
−0.608319 | + | 0.793693i | \(0.708156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.61181e10 | − | 1.61181e10i | −0.625928 | − | 0.625928i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.16883e9 | − | 6.16883e9i | −0.236036 | − | 0.236036i | 0.579171 | − | 0.815206i | \(-0.303377\pi\) |
−0.815206 | + | 0.579171i | \(0.803377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87236e9i | 0.147077i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.27140e10 | − | 1.81000e10i | −0.479346 | − | 0.682413i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.73175e10 | + | 1.73175e10i | −0.648125 | + | 0.648125i | −0.952540 | − | 0.304415i | \(-0.901539\pi\) |
0.304415 | + | 0.952540i | \(0.401539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.27981e9 | + | 1.87640e10i | −0.120964 | + | 0.692044i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.01683e10 | 1.47068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.33469e10 | −0.485120 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.75811e8 | − | 1.43809e9i | −0.0243856 | − | 0.0518912i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.11183e10 | − | 2.11183e10i | 0.751045 | − | 0.751045i | −0.223630 | − | 0.974674i | \(-0.571791\pi\) |
0.974674 | + | 0.223630i | \(0.0717906\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.79896e10 | + | 3.37092e10i | −1.69439 | + | 1.19019i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.83642e10i | 1.34480i | 0.740186 | + | 0.672402i | \(0.234737\pi\) | ||||
−0.740186 | + | 0.672402i | \(0.765263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.41529e9 | + | 1.41529e9i | 0.0492551 | + | 0.0492551i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.73015e9 | − | 5.73015e9i | −0.196578 | − | 0.196578i | 0.601953 | − | 0.798531i | \(-0.294389\pi\) |
−0.798531 | + | 0.601953i | \(0.794389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.53517e9i | − | 0.290719i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.07132e10 | + | 2.97092e10i | −0.362308 | + | 1.00473i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.73867e10 | − | 2.73867e10i | 0.919607 | − | 0.919607i | −0.0773933 | − | 0.997001i | \(-0.524660\pi\) |
0.997001 | + | 0.0773933i | \(0.0246597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.13923e10 | + | 1.99129e9i | 0.377140 | + | 0.0659212i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.27004e10 | −0.417476 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.97037e10 | 1.62230 | 0.811149 | − | 0.584840i | \(-0.198843\pi\) | ||||
0.811149 | + | 0.584840i | \(0.198843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.87102e9 | − | 1.20100e9i | −0.222689 | − | 0.0389244i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.87057e10 | − | 2.87057e10i | 0.917349 | − | 0.917349i | −0.0794873 | − | 0.996836i | \(-0.525328\pi\) |
0.996836 | + | 0.0794873i | \(0.0253283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.30741e10 | + | 3.56585e9i | −0.414890 | + | 0.113158i |
(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 | 300.8.i.c.293.8 | yes | 16 | |
3.2 | odd | 2 | inner | 300.8.i.c.293.5 | yes | 16 | |
5.2 | odd | 4 | inner | 300.8.i.c.257.5 | yes | 16 | |
5.3 | odd | 4 | inner | 300.8.i.c.257.4 | yes | 16 | |
5.4 | even | 2 | inner | 300.8.i.c.293.1 | yes | 16 | |
15.2 | even | 4 | inner | 300.8.i.c.257.8 | yes | 16 | |
15.8 | even | 4 | inner | 300.8.i.c.257.1 | ✓ | 16 | |
15.14 | odd | 2 | inner | 300.8.i.c.293.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.8.i.c.257.1 | ✓ | 16 | 15.8 | even | 4 | inner | |
300.8.i.c.257.4 | yes | 16 | 5.3 | odd | 4 | inner | |
300.8.i.c.257.5 | yes | 16 | 5.2 | odd | 4 | inner | |
300.8.i.c.257.8 | yes | 16 | 15.2 | even | 4 | inner | |
300.8.i.c.293.1 | yes | 16 | 5.4 | even | 2 | inner | |
300.8.i.c.293.4 | yes | 16 | 15.14 | odd | 2 | inner | |
300.8.i.c.293.5 | yes | 16 | 3.2 | odd | 2 | inner | |
300.8.i.c.293.8 | yes | 16 | 1.1 | even | 1 | trivial |