Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,10,Mod(99,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.99");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(180.262542657\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.99 |
Dual form | 350.10.c.b.99.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 16.0000i | − 0.707107i | ||||||||
\(3\) | 6.00000i | 0.0427667i | 0.999771 | + | 0.0213833i | \(0.00680705\pi\) | ||||
−0.999771 | + | 0.0213833i | \(0.993193\pi\) | |||||||
\(4\) | −256.000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 96.0000 | 0.0302406 | ||||||||
\(7\) | − 2401.00i | − 0.377964i | ||||||||
\(8\) | 4096.00i | 0.353553i | ||||||||
\(9\) | 19647.0 | 0.998171 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54152.0 | −1.11519 | −0.557593 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557593 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(12\) | − 1536.00i | − 0.0213833i | ||||||||
\(13\) | 113172.i | 1.09899i | 0.835497 | + | 0.549495i | \(0.185180\pi\) | ||||
−0.835497 | + | 0.549495i | \(0.814820\pi\) | |||||||
\(14\) | −38416.0 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 6262.00i | 0.0181841i | 0.999959 | + | 0.00909207i | \(0.00289414\pi\) | ||||
−0.999959 | + | 0.00909207i | \(0.997106\pi\) | |||||||
\(18\) | − 314352.i | − 0.705813i | ||||||||
\(19\) | −257078. | −0.452557 | −0.226279 | − | 0.974063i | \(-0.572656\pi\) | ||||
−0.226279 | + | 0.974063i | \(0.572656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14406.0 | 0.0161643 | ||||||||
\(22\) | 866432.i | 0.788556i | ||||||||
\(23\) | 266000.i | 0.198201i | 0.995077 | + | 0.0991006i | \(0.0315966\pi\) | ||||
−0.995077 | + | 0.0991006i | \(0.968403\pi\) | |||||||
\(24\) | −24576.0 | −0.0151203 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.81075e6 | 0.777104 | ||||||||
\(27\) | 235980.i | 0.0854552i | ||||||||
\(28\) | 614656.i | 0.188982i | ||||||||
\(29\) | −1.57471e6 | −0.413438 | −0.206719 | − | 0.978400i | \(-0.566279\pi\) | ||||
−0.206719 | + | 0.978400i | \(0.566279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.63748e6 | −0.901893 | −0.450946 | − | 0.892551i | \(-0.648913\pi\) | ||||
−0.450946 | + | 0.892551i | \(0.648913\pi\) | |||||||
\(32\) | − 1.04858e6i | − 0.176777i | ||||||||
\(33\) | − 324912.i | − 0.0476928i | ||||||||
\(34\) | 100192. | 0.0128581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.02963e6 | −0.499086 | ||||||||
\(37\) | − 1.19462e7i | − 1.04791i | −0.851746 | − | 0.523954i | \(-0.824456\pi\) | ||||
0.851746 | − | 0.523954i | \(-0.175544\pi\) | |||||||
\(38\) | 4.11325e6i | 0.320006i | ||||||||
\(39\) | −679032. | −0.0470002 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.19091e7 | 1.21087 | 0.605435 | − | 0.795895i | \(-0.292999\pi\) | ||||
0.605435 | + | 0.795895i | \(0.292999\pi\) | |||||||
\(42\) | − 230496.i | − 0.0114299i | ||||||||
\(43\) | − 2.75206e7i | − 1.22758i | −0.789469 | − | 0.613790i | \(-0.789644\pi\) | ||||
0.789469 | − | 0.613790i | \(-0.210356\pi\) | |||||||
\(44\) | 1.38629e7 | 0.557593 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.25600e6 | 0.140149 | ||||||||
\(47\) | 5.29278e7i | 1.58214i | 0.611728 | + | 0.791068i | \(0.290475\pi\) | ||||
−0.611728 | + | 0.791068i | \(0.709525\pi\) | |||||||
\(48\) | 393216.i | 0.0106917i | ||||||||
\(49\) | −5.76480e6 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −37572.0 | −0.000777676 0 | ||||||||
\(52\) | − 2.89720e7i | − 0.549495i | ||||||||
\(53\) | − 1.62212e7i | − 0.282385i | −0.989982 | − | 0.141193i | \(-0.954906\pi\) | ||||
0.989982 | − | 0.141193i | \(-0.0450937\pi\) | |||||||
\(54\) | 3.77568e6 | 0.0604259 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.83450e6 | 0.133631 | ||||||||
\(57\) | − 1.54247e6i | − 0.0193544i | ||||||||
\(58\) | 2.51954e7i | 0.292345i | ||||||||
\(59\) | 1.40510e8 | 1.50964 | 0.754818 | − | 0.655935i | \(-0.227725\pi\) | ||||
0.754818 | + | 0.655935i | \(0.227725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.02964e8 | −1.87687 | −0.938434 | − | 0.345458i | \(-0.887724\pi\) | ||||
−0.938434 | + | 0.345458i | \(0.887724\pi\) | |||||||
\(62\) | 7.41997e7i | 0.637734i | ||||||||
\(63\) | − 4.71724e7i | − 0.377273i | ||||||||
\(64\) | −1.67772e7 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.19859e6 | −0.0337239 | ||||||||
\(67\) | 1.53735e8i | 0.932041i | 0.884774 | + | 0.466020i | \(0.154313\pi\) | ||||
−0.884774 | + | 0.466020i | \(0.845687\pi\) | |||||||
\(68\) | − 1.60307e6i | − 0.00909207i | ||||||||
\(69\) | −1.59600e6 | −0.00847641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.79656e8 | 1.30606 | 0.653028 | − | 0.757334i | \(-0.273499\pi\) | ||||
0.653028 | + | 0.757334i | \(0.273499\pi\) | |||||||
\(72\) | 8.04741e7i | 0.352907i | ||||||||
\(73\) | 4.04023e8i | 1.66515i | 0.553913 | + | 0.832574i | \(0.313134\pi\) | ||||
−0.553913 | + | 0.832574i | \(0.686866\pi\) | |||||||
\(74\) | −1.91140e8 | −0.740983 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.58120e7 | 0.226279 | ||||||||
\(77\) | 1.30019e8i | 0.421501i | ||||||||
\(78\) | 1.08645e7i | 0.0332341i | ||||||||
\(79\) | 1.30690e8 | 0.377503 | 0.188751 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188751 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.85296e8 | 0.994516 | ||||||||
\(82\) | − 3.50546e8i | − 0.856215i | ||||||||
\(83\) | − 4.20134e8i | − 0.971709i | −0.874040 | − | 0.485855i | \(-0.838508\pi\) | ||||
0.874040 | − | 0.485855i | \(-0.161492\pi\) | |||||||
\(84\) | −3.68794e6 | −0.00808214 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.40329e8 | −0.868030 | ||||||||
\(87\) | − 9.44828e6i | − 0.0176814i | ||||||||
\(88\) | − 2.21807e8i | − 0.394278i | ||||||||
\(89\) | 4.69542e8 | 0.793268 | 0.396634 | − | 0.917977i | \(-0.370178\pi\) | ||||
0.396634 | + | 0.917977i | \(0.370178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.71726e8 | 0.415379 | ||||||||
\(92\) | − 6.80960e7i | − 0.0991006i | ||||||||
\(93\) | − 2.78249e7i | − 0.0385710i | ||||||||
\(94\) | 8.46845e8 | 1.11874 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.29146e6 | 0.00756015 | ||||||||
\(97\) | − 8.72502e8i | − 1.00068i | −0.865830 | − | 0.500338i | \(-0.833209\pi\) | ||||
0.865830 | − | 0.500338i | \(-0.166791\pi\) | |||||||
\(98\) | 9.22368e7i | 0.101015i | ||||||||
\(99\) | −1.06392e9 | −1.11315 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.20901e9 | −1.15607 | −0.578037 | − | 0.816011i | \(-0.696181\pi\) | ||||
−0.578037 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(102\) | 601152.i | 0 0.000549900i | ||||||||
\(103\) | − 6.90563e8i | − 0.604555i | −0.953220 | − | 0.302277i | \(-0.902253\pi\) | ||||
0.953220 | − | 0.302277i | \(-0.0977469\pi\) | |||||||
\(104\) | −4.63553e8 | −0.388552 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.59540e8 | −0.199677 | ||||||||
\(107\) | 1.79499e8i | 0.132384i | 0.997807 | + | 0.0661921i | \(0.0210850\pi\) | ||||
−0.997807 | + | 0.0661921i | \(0.978915\pi\) | |||||||
\(108\) | − 6.04109e7i | − 0.0427276i | ||||||||
\(109\) | 1.60361e9 | 1.08813 | 0.544063 | − | 0.839044i | \(-0.316885\pi\) | ||||
0.544063 | + | 0.839044i | \(0.316885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.16774e7 | 0.0448156 | ||||||||
\(112\) | − 1.57352e8i | − 0.0944911i | ||||||||
\(113\) | − 1.42785e9i | − 0.823815i | −0.911226 | − | 0.411908i | \(-0.864863\pi\) | ||||
0.911226 | − | 0.411908i | \(-0.135137\pi\) | |||||||
\(114\) | −2.46795e7 | −0.0136856 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.03127e8 | 0.206719 | ||||||||
\(117\) | 2.22349e9i | 1.09698i | ||||||||
\(118\) | − 2.24815e9i | − 1.06747i | ||||||||
\(119\) | 1.50351e7 | 0.00687296 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.74491e8 | 0.243640 | ||||||||
\(122\) | 3.24742e9i | 1.32715i | ||||||||
\(123\) | 1.31455e8i | 0.0517849i | ||||||||
\(124\) | 1.18720e9 | 0.450946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.54759e8 | −0.266772 | ||||||||
\(127\) | − 2.35873e9i | − 0.804565i | −0.915516 | − | 0.402282i | \(-0.868217\pi\) | ||||
0.915516 | − | 0.402282i | \(-0.131783\pi\) | |||||||
\(128\) | 2.68435e8i | 0.0883883i | ||||||||
\(129\) | 1.65124e8 | 0.0524995 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.01665e8 | 0.178498 | 0.0892492 | − | 0.996009i | \(-0.471553\pi\) | ||||
0.0892492 | + | 0.996009i | \(0.471553\pi\) | |||||||
\(132\) | 8.31775e7i | 0.0238464i | ||||||||
\(133\) | 6.17244e8i | 0.171051i | ||||||||
\(134\) | 2.45975e9 | 0.659052 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.56492e7 | −0.00642907 | ||||||||
\(137\) | − 5.16009e9i | − 1.25145i | −0.780043 | − | 0.625726i | \(-0.784803\pi\) | ||||
0.780043 | − | 0.625726i | \(-0.215197\pi\) | |||||||
\(138\) | 2.55360e7i | 0.00599373i | ||||||||
\(139\) | 7.14356e9 | 1.62311 | 0.811556 | − | 0.584275i | \(-0.198621\pi\) | ||||
0.811556 | + | 0.584275i | \(0.198621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.17567e8 | −0.0676627 | ||||||||
\(142\) | − 4.47449e9i | − 0.923520i | ||||||||
\(143\) | − 6.12849e9i | − 1.22558i | ||||||||
\(144\) | 1.28759e9 | 0.249543 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.46437e9 | 1.17744 | ||||||||
\(147\) | − 3.45888e7i | − 0.00610953i | ||||||||
\(148\) | 3.05824e9i | 0.523954i | ||||||||
\(149\) | −9.10424e9 | −1.51323 | −0.756616 | − | 0.653859i | \(-0.773149\pi\) | ||||
−0.756616 | + | 0.653859i | \(0.773149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89432e8 | −0.0453054 | −0.0226527 | − | 0.999743i | \(-0.507211\pi\) | ||||
−0.0226527 | + | 0.999743i | \(0.507211\pi\) | |||||||
\(152\) | − 1.05299e9i | − 0.160003i | ||||||||
\(153\) | 1.23030e8i | 0.0181509i | ||||||||
\(154\) | 2.08030e9 | 0.298046 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.73832e8 | 0.0235001 | ||||||||
\(157\) | 1.39068e10i | 1.82675i | 0.407124 | + | 0.913373i | \(0.366532\pi\) | ||||
−0.407124 | + | 0.913373i | \(0.633468\pi\) | |||||||
\(158\) | − 2.09104e9i | − 0.266935i | ||||||||
\(159\) | 9.73273e7 | 0.0120767 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.38666e8 | 0.0749130 | ||||||||
\(162\) | − 6.16474e9i | − 0.703229i | ||||||||
\(163\) | − 1.66232e10i | − 1.84447i | −0.386629 | − | 0.922235i | \(-0.626361\pi\) | ||||
0.386629 | − | 0.922235i | \(-0.373639\pi\) | |||||||
\(164\) | −5.60874e9 | −0.605435 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.72214e9 | −0.687102 | ||||||||
\(167\) | − 1.58019e10i | − 1.57212i | −0.618149 | − | 0.786061i | \(-0.712117\pi\) | ||||
0.618149 | − | 0.786061i | \(-0.287883\pi\) | |||||||
\(168\) | 5.90070e7i | 0.00571494i | ||||||||
\(169\) | −2.20340e9 | −0.207780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.05081e9 | −0.451730 | ||||||||
\(172\) | 7.04527e9i | 0.613790i | ||||||||
\(173\) | − 3.23125e9i | − 0.274260i | −0.990553 | − | 0.137130i | \(-0.956212\pi\) | ||||
0.990553 | − | 0.137130i | \(-0.0437879\pi\) | |||||||
\(174\) | −1.51173e8 | −0.0125026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.54891e9 | −0.278797 | ||||||||
\(177\) | 8.43058e8i | 0.0645621i | ||||||||
\(178\) | − 7.51268e9i | − 0.560925i | ||||||||
\(179\) | 2.41408e10 | 1.75757 | 0.878785 | − | 0.477218i | \(-0.158355\pi\) | ||||
0.878785 | + | 0.477218i | \(0.158355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.89332e9 | −0.269629 | −0.134814 | − | 0.990871i | \(-0.543044\pi\) | ||||
−0.134814 | + | 0.990871i | \(0.543044\pi\) | |||||||
\(182\) | − 4.34762e9i | − 0.293718i | ||||||||
\(183\) | − 1.21778e9i | − 0.0802674i | ||||||||
\(184\) | −1.08954e9 | −0.0700747 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.45198e8 | −0.0272738 | ||||||||
\(187\) | − 3.39100e8i | − 0.0202787i | ||||||||
\(188\) | − 1.35495e10i | − 0.791068i | ||||||||
\(189\) | 5.66588e8 | 0.0322990 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.58988e10 | −1.40809 | −0.704043 | − | 0.710157i | \(-0.748624\pi\) | ||||
−0.704043 | + | 0.710157i | \(0.748624\pi\) | |||||||
\(192\) | − 1.00663e8i | − 0.00534584i | ||||||||
\(193\) | − 1.59367e10i | − 0.826783i | −0.910553 | − | 0.413391i | \(-0.864344\pi\) | ||||
0.910553 | − | 0.413391i | \(-0.135656\pi\) | |||||||
\(194\) | −1.39600e10 | −0.707585 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.47579e9 | 0.0714286 | ||||||||
\(197\) | − 3.34685e9i | − 0.158321i | −0.996862 | − | 0.0791604i | \(-0.974776\pi\) | ||||
0.996862 | − | 0.0791604i | \(-0.0252239\pi\) | |||||||
\(198\) | 1.70228e10i | 0.787114i | ||||||||
\(199\) | 1.34261e10 | 0.606891 | 0.303445 | − | 0.952849i | \(-0.401863\pi\) | ||||
0.303445 | + | 0.952849i | \(0.401863\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.22407e8 | −0.0398603 | ||||||||
\(202\) | 1.93442e10i | 0.817467i | ||||||||
\(203\) | 3.78089e9i | 0.156265i | ||||||||
\(204\) | 9.61843e6 | 0.000388838 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.10490e10 | −0.427485 | ||||||||
\(207\) | 5.22610e9i | 0.197839i | ||||||||
\(208\) | 7.41684e9i | 0.274748i | ||||||||
\(209\) | 1.39213e10 | 0.504686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.01702e10 | 1.04787 | 0.523935 | − | 0.851759i | \(-0.324464\pi\) | ||||
0.523935 | + | 0.851759i | \(0.324464\pi\) | |||||||
\(212\) | 4.15263e9i | 0.141193i | ||||||||
\(213\) | 1.67794e9i | 0.0558556i | ||||||||
\(214\) | 2.87199e9 | 0.0936097 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.66574e8 | −0.0302130 | ||||||||
\(217\) | 1.11346e10i | 0.340883i | ||||||||
\(218\) | − 2.56577e10i | − 0.769421i | ||||||||
\(219\) | −2.42414e9 | −0.0712129 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.08683e8 | −0.0199842 | ||||||||
\(222\) | − 1.14684e9i | − 0.0316894i | ||||||||
\(223\) | − 5.35030e10i | − 1.44879i | −0.689384 | − | 0.724396i | \(-0.742119\pi\) | ||||
0.689384 | − | 0.724396i | \(-0.257881\pi\) | |||||||
\(224\) | −2.51763e9 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.28456e10 | −0.582525 | ||||||||
\(227\) | − 4.02704e10i | − 1.00663i | −0.864103 | − | 0.503315i | \(-0.832114\pi\) | ||||
0.864103 | − | 0.503315i | \(-0.167886\pi\) | |||||||
\(228\) | 3.94872e8i | 0.00967719i | ||||||||
\(229\) | −1.90247e10 | −0.457150 | −0.228575 | − | 0.973526i | \(-0.573407\pi\) | ||||
−0.228575 | + | 0.973526i | \(0.573407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.80114e8 | −0.0180262 | ||||||||
\(232\) | − 6.45003e9i | − 0.146173i | ||||||||
\(233\) | 3.67748e10i | 0.817426i | 0.912663 | + | 0.408713i | \(0.134022\pi\) | ||||
−0.912663 | + | 0.408713i | \(0.865978\pi\) | |||||||
\(234\) | 3.55758e10 | 0.775682 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.59705e10 | −0.754818 | ||||||||
\(237\) | 7.84139e8i | 0.0161445i | ||||||||
\(238\) | − 2.40561e8i | − 0.00485992i | ||||||||
\(239\) | −6.56110e9 | −0.130073 | −0.0650363 | − | 0.997883i | \(-0.520716\pi\) | ||||
−0.0650363 | + | 0.997883i | \(0.520716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.96818e10 | −1.71249 | −0.856244 | − | 0.516572i | \(-0.827208\pi\) | ||||
−0.856244 | + | 0.516572i | \(0.827208\pi\) | |||||||
\(242\) | − 9.19186e9i | − 0.172280i | ||||||||
\(243\) | 6.95657e9i | 0.127987i | ||||||||
\(244\) | 5.19587e10 | 0.938434 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.10328e9 | 0.0366175 | ||||||||
\(247\) | − 2.90940e10i | − 0.497356i | ||||||||
\(248\) | − 1.89951e10i | − 0.318867i | ||||||||
\(249\) | 2.52080e9 | 0.0415568 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.33703e9 | 0.0848727 | 0.0424363 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424363 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(252\) | 1.20761e10i | 0.188637i | ||||||||
\(253\) | − 1.44044e10i | − 0.221031i | ||||||||
\(254\) | −3.77396e10 | −0.568913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | − 8.35575e10i | − 1.19478i | −0.801952 | − | 0.597388i | \(-0.796205\pi\) | ||||
0.801952 | − | 0.597388i | \(-0.203795\pi\) | |||||||
\(258\) | − 2.64198e9i | − 0.0371228i | ||||||||
\(259\) | −2.86829e10 | −0.396072 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.09384e10 | −0.412682 | ||||||||
\(262\) | − 9.62665e9i | − 0.126217i | ||||||||
\(263\) | − 1.08635e11i | − 1.40013i | −0.714079 | − | 0.700065i | \(-0.753154\pi\) | ||||
0.714079 | − | 0.700065i | \(-0.246846\pi\) | |||||||
\(264\) | 1.33084e9 | 0.0168620 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.87591e9 | 0.120951 | ||||||||
\(267\) | 2.81725e9i | 0.0339254i | ||||||||
\(268\) | − 3.93561e10i | − 0.466020i | ||||||||
\(269\) | −1.41401e11 | −1.64652 | −0.823258 | − | 0.567668i | \(-0.807846\pi\) | ||||
−0.823258 | + | 0.567668i | \(0.807846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.08353e10 | −1.02304 | −0.511520 | − | 0.859271i | \(-0.670917\pi\) | ||||
−0.511520 | + | 0.859271i | \(0.670917\pi\) | |||||||
\(272\) | 4.10386e8i | 0.00454604i | ||||||||
\(273\) | 1.63036e9i | 0.0177644i | ||||||||
\(274\) | −8.25614e10 | −0.884911 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.08576e8 | 0.00423821 | ||||||||
\(277\) | − 2.65075e10i | − 0.270527i | −0.990810 | − | 0.135263i | \(-0.956812\pi\) | ||||
0.990810 | − | 0.135263i | \(-0.0431880\pi\) | |||||||
\(278\) | − 1.14297e11i | − 1.14771i | ||||||||
\(279\) | −9.11126e10 | −0.900243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.86968e11 | −1.78891 | −0.894455 | − | 0.447158i | \(-0.852436\pi\) | ||||
−0.894455 | + | 0.447158i | \(0.852436\pi\) | |||||||
\(282\) | 5.08107e9i | 0.0478448i | ||||||||
\(283\) | 5.33413e9i | 0.0494338i | 0.999694 | + | 0.0247169i | \(0.00786844\pi\) | ||||
−0.999694 | + | 0.0247169i | \(0.992132\pi\) | |||||||
\(284\) | −7.15919e10 | −0.653028 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.80558e10 | −0.866615 | ||||||||
\(287\) | − 5.26038e10i | − 0.457666i | ||||||||
\(288\) | − 2.06014e10i | − 0.176453i | ||||||||
\(289\) | 1.18549e11 | 0.999669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.23501e9 | 0.0427956 | ||||||||
\(292\) | − 1.03430e11i | − 0.832574i | ||||||||
\(293\) | − 7.65433e10i | − 0.606741i | −0.952873 | − | 0.303370i | \(-0.901888\pi\) | ||||
0.952873 | − | 0.303370i | \(-0.0981119\pi\) | |||||||
\(294\) | −5.53421e8 | −0.00432009 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.89318e10 | 0.370492 | ||||||||
\(297\) | − 1.27788e10i | − 0.0952984i | ||||||||
\(298\) | 1.45668e11i | 1.07002i | ||||||||
\(299\) | −3.01038e10 | −0.217821 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.60769e10 | −0.463982 | ||||||||
\(302\) | 4.63091e9i | 0.0320358i | ||||||||
\(303\) | − 7.25409e9i | − 0.0494414i | ||||||||
\(304\) | −1.68479e10 | −0.113139 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.96847e9 | 0.0128346 | ||||||||
\(307\) | − 7.51944e10i | − 0.483128i | −0.970385 | − | 0.241564i | \(-0.922340\pi\) | ||||
0.970385 | − | 0.241564i | \(-0.0776605\pi\) | |||||||
\(308\) | − 3.32849e10i | − 0.210750i | ||||||||
\(309\) | 4.14338e9 | 0.0258548 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.15134e11 | 1.30403 | 0.652014 | − | 0.758207i | \(-0.273924\pi\) | ||||
0.652014 | + | 0.758207i | \(0.273924\pi\) | |||||||
\(312\) | − 2.78132e9i | − 0.0166171i | ||||||||
\(313\) | − 9.59075e10i | − 0.564811i | −0.959295 | − | 0.282405i | \(-0.908868\pi\) | ||||
0.959295 | − | 0.282405i | \(-0.0911323\pi\) | |||||||
\(314\) | 2.22508e11 | 1.29170 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.34566e10 | −0.188751 | ||||||||
\(317\) | 1.70586e11i | 0.948807i | 0.880308 | + | 0.474403i | \(0.157336\pi\) | ||||
−0.880308 | + | 0.474403i | \(0.842664\pi\) | |||||||
\(318\) | − 1.55724e9i | − 0.00853951i | ||||||||
\(319\) | 8.52739e10 | 0.461061 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.07700e9 | −0.00566163 | ||||||||
\(322\) | − 1.02187e10i | − 0.0529715i | ||||||||
\(323\) | − 1.60982e9i | − 0.00822937i | ||||||||
\(324\) | −9.86358e10 | −0.497258 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.65972e11 | −1.30424 | ||||||||
\(327\) | 9.62165e9i | 0.0465355i | ||||||||
\(328\) | 8.97398e10i | 0.428107i | ||||||||
\(329\) | 1.27080e11 | 0.597991 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23992e11 | −0.567762 | −0.283881 | − | 0.958859i | \(-0.591622\pi\) | ||||
−0.283881 | + | 0.958859i | \(0.591622\pi\) | |||||||
\(332\) | 1.07554e11i | 0.485855i | ||||||||
\(333\) | − 2.34708e11i | − 1.04599i | ||||||||
\(334\) | −2.52831e11 | −1.11166 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.44112e8 | 0.00404107 | ||||||||
\(337\) | − 7.29335e10i | − 0.308030i | −0.988069 | − | 0.154015i | \(-0.950780\pi\) | ||||
0.988069 | − | 0.154015i | \(-0.0492204\pi\) | |||||||
\(338\) | 3.52544e10i | 0.146923i | ||||||||
\(339\) | 8.56710e9 | 0.0352318 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.51129e11 | 1.00578 | ||||||||
\(342\) | 8.08130e10i | 0.319421i | ||||||||
\(343\) | 1.38413e10i | 0.0539949i | ||||||||
\(344\) | 1.12724e11 | 0.434015 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.17000e10 | −0.193931 | ||||||||
\(347\) | − 1.55720e11i | − 0.576584i | −0.957542 | − | 0.288292i | \(-0.906913\pi\) | ||||
0.957542 | − | 0.288292i | \(-0.0930874\pi\) | |||||||
\(348\) | 2.41876e9i | 0.00884069i | ||||||||
\(349\) | −1.08728e11 | −0.392310 | −0.196155 | − | 0.980573i | \(-0.562846\pi\) | ||||
−0.196155 | + | 0.980573i | \(0.562846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.67063e10 | −0.0939144 | ||||||||
\(352\) | 5.67825e10i | 0.197139i | ||||||||
\(353\) | − 3.25585e11i | − 1.11604i | −0.829829 | − | 0.558018i | \(-0.811562\pi\) | ||||
0.829829 | − | 0.558018i | \(-0.188438\pi\) | |||||||
\(354\) | 1.34889e10 | 0.0456523 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.20203e11 | −0.396634 | ||||||||
\(357\) | 9.02104e7i | 0 0.000293934i | ||||||||
\(358\) | − 3.86252e11i | − 1.24279i | ||||||||
\(359\) | 2.27550e11 | 0.723022 | 0.361511 | − | 0.932368i | \(-0.382261\pi\) | ||||
0.361511 | + | 0.932368i | \(0.382261\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.56599e11 | −0.795192 | ||||||||
\(362\) | 6.22931e10i | 0.190656i | ||||||||
\(363\) | 3.44695e9i | 0.0104197i | ||||||||
\(364\) | −6.95618e10 | −0.207690 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.94845e10 | −0.0567577 | ||||||||
\(367\) | − 4.21993e11i | − 1.21425i | −0.794607 | − | 0.607125i | \(-0.792323\pi\) | ||||
0.794607 | − | 0.607125i | \(-0.207677\pi\) | |||||||
\(368\) | 1.74326e10i | 0.0495503i | ||||||||
\(369\) | 4.30449e11 | 1.20866 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.89472e10 | −0.106732 | ||||||||
\(372\) | 7.12318e9i | 0.0192855i | ||||||||
\(373\) | − 3.83283e11i | − 1.02525i | −0.858613 | − | 0.512625i | \(-0.828673\pi\) | ||||
0.858613 | − | 0.512625i | \(-0.171327\pi\) | |||||||
\(374\) | −5.42560e9 | −0.0143392 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.16792e11 | −0.559370 | ||||||||
\(377\) | − 1.78214e11i | − 0.454365i | ||||||||
\(378\) | − 9.06541e9i | − 0.0228389i | ||||||||
\(379\) | 1.21462e11 | 0.302386 | 0.151193 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151193 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.41524e10 | 0.0344086 | ||||||||
\(382\) | 4.14381e11i | 0.995667i | ||||||||
\(383\) | 3.97721e11i | 0.944461i | 0.881475 | + | 0.472230i | \(0.156551\pi\) | ||||
−0.881475 | + | 0.472230i | \(0.843449\pi\) | |||||||
\(384\) | −1.61061e9 | −0.00378008 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.54988e11 | −0.584624 | ||||||||
\(387\) | − 5.40697e11i | − 1.22533i | ||||||||
\(388\) | 2.23360e11i | 0.500338i | ||||||||
\(389\) | −6.75462e10 | −0.149564 | −0.0747821 | − | 0.997200i | \(-0.523826\pi\) | ||||
−0.0747821 | + | 0.997200i | \(0.523826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.66569e9 | −0.00360412 | ||||||||
\(392\) | − 2.36126e10i | − 0.0505076i | ||||||||
\(393\) | 3.60999e9i | 0.00763378i | ||||||||
\(394\) | −5.35495e10 | −0.111950 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.72365e11 | 0.556573 | ||||||||
\(397\) | 1.24656e11i | 0.251857i | 0.992039 | + | 0.125929i | \(0.0401911\pi\) | ||||
−0.992039 | + | 0.125929i | \(0.959809\pi\) | |||||||
\(398\) | − 2.14817e11i | − 0.429136i | ||||||||
\(399\) | −3.70347e9 | −0.00731527 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.51196e11 | 0.678265 | 0.339133 | − | 0.940739i | \(-0.389866\pi\) | ||||
0.339133 | + | 0.940739i | \(0.389866\pi\) | |||||||
\(402\) | 1.47585e10i | 0.0281855i | ||||||||
\(403\) | − 5.24833e11i | − 0.991171i | ||||||||
\(404\) | 3.09508e11 | 0.578037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.04942e10 | 0.110496 | ||||||||
\(407\) | 6.46913e11i | 1.16861i | ||||||||
\(408\) | − 1.53895e8i | 0 0.000274950i | ||||||||
\(409\) | 3.81956e10 | 0.0674930 | 0.0337465 | − | 0.999430i | \(-0.489256\pi\) | ||||
0.0337465 | + | 0.999430i | \(0.489256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.09605e10 | 0.0535205 | ||||||||
\(412\) | 1.76784e11i | 0.302277i | ||||||||
\(413\) | − 3.37364e11i | − 0.570588i | ||||||||
\(414\) | 8.36176e10 | 0.139893 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.18669e11 | 0.194276 | ||||||||
\(417\) | 4.28614e10i | 0.0694151i | ||||||||
\(418\) | − 2.22741e11i | − 0.356867i | ||||||||
\(419\) | −2.15268e11 | −0.341205 | −0.170603 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170603 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.19933e12 | 1.86066 | 0.930332 | − | 0.366718i | \(-0.119519\pi\) | ||||
0.930332 | + | 0.366718i | \(0.119519\pi\) | |||||||
\(422\) | − 4.82723e11i | − 0.740955i | ||||||||
\(423\) | 1.03987e12i | 1.57924i | ||||||||
\(424\) | 6.64421e10 | 0.0998383 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.68470e10 | 0.0394959 | ||||||||
\(427\) | 4.87316e11i | 0.709390i | ||||||||
\(428\) | − 4.59518e10i | − 0.0661921i | ||||||||
\(429\) | 3.67709e10 | 0.0524140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.91117e11 | 1.10432 | 0.552158 | − | 0.833740i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833740i | \(0.313805\pi\) | |||||||
\(432\) | 1.54652e10i | 0.0213638i | ||||||||
\(433\) | 1.15451e12i | 1.57834i | 0.614174 | + | 0.789170i | \(0.289489\pi\) | ||||
−0.614174 | + | 0.789170i | \(0.710511\pi\) | |||||||
\(434\) | 1.78154e11 | 0.241041 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.10524e11 | −0.544063 | ||||||||
\(437\) | − 6.83827e10i | − 0.0896974i | ||||||||
\(438\) | 3.87862e10i | 0.0503551i | ||||||||
\(439\) | 2.12728e11 | 0.273360 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.13261e11 | −0.142596 | ||||||||
\(442\) | 1.13389e10i | 0.0141310i | ||||||||
\(443\) | 6.48300e10i | 0.0799759i | 0.999200 | + | 0.0399880i | \(0.0127320\pi\) | ||||
−0.999200 | + | 0.0399880i | \(0.987268\pi\) | |||||||
\(444\) | −1.83494e10 | −0.0224078 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.56047e11 | −1.02445 | ||||||||
\(447\) | − 5.46255e10i | − 0.0647159i | ||||||||
\(448\) | 4.02821e10i | 0.0472456i | ||||||||
\(449\) | 1.08031e12 | 1.25441 | 0.627207 | − | 0.778853i | \(-0.284198\pi\) | ||||
0.627207 | + | 0.778853i | \(0.284198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18642e12 | −1.35035 | ||||||||
\(452\) | 3.65530e11i | 0.411908i | ||||||||
\(453\) | − 1.73659e9i | − 0.00193756i | ||||||||
\(454\) | −6.44326e11 | −0.711794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.31795e9 | 0.00684281 | ||||||||
\(457\) | − 6.46725e10i | − 0.0693581i | −0.999399 | − | 0.0346790i | \(-0.988959\pi\) | ||||
0.999399 | − | 0.0346790i | \(-0.0110409\pi\) | |||||||
\(458\) | 3.04395e11i | 0.323254i | ||||||||
\(459\) | −1.47771e9 | −0.00155393 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.29254e11 | 0.442649 | 0.221325 | − | 0.975200i | \(-0.428962\pi\) | ||||
0.221325 | + | 0.975200i | \(0.428962\pi\) | |||||||
\(462\) | 1.24818e10i | 0.0127464i | ||||||||
\(463\) | − 1.61883e12i | − 1.63715i | −0.574401 | − | 0.818574i | \(-0.694765\pi\) | ||||
0.574401 | − | 0.818574i | \(-0.305235\pi\) | |||||||
\(464\) | −1.03200e11 | −0.103360 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.88396e11 | 0.578007 | ||||||||
\(467\) | 3.27321e11i | 0.318455i | 0.987242 | + | 0.159228i | \(0.0509003\pi\) | ||||
−0.987242 | + | 0.159228i | \(0.949100\pi\) | |||||||
\(468\) | − 5.69214e11i | − 0.548490i | ||||||||
\(469\) | 3.69117e11 | 0.352278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.34407e10 | −0.0781239 | ||||||||
\(472\) | 5.75527e11i | 0.533737i | ||||||||
\(473\) | 1.49030e12i | 1.36898i | ||||||||
\(474\) | 1.25462e10 | 0.0114159 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.84898e9 | −0.00343648 | ||||||||
\(477\) | − 3.18698e11i | − 0.281869i | ||||||||
\(478\) | 1.04978e11i | 0.0919752i | ||||||||
\(479\) | −2.84811e11 | −0.247199 | −0.123600 | − | 0.992332i | \(-0.539444\pi\) | ||||
−0.123600 | + | 0.992332i | \(0.539444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.35198e12 | 1.15164 | ||||||||
\(482\) | 1.43491e12i | 1.21091i | ||||||||
\(483\) | 3.83200e9i | 0.00320378i | ||||||||
\(484\) | −1.47070e11 | −0.121820 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.11305e11 | 0.0905007 | ||||||||
\(487\) | − 7.14776e11i | − 0.575824i | −0.957657 | − | 0.287912i | \(-0.907039\pi\) | ||||
0.957657 | − | 0.287912i | \(-0.0929610\pi\) | |||||||
\(488\) | − 8.31339e11i | − 0.663573i | ||||||||
\(489\) | 9.97395e10 | 0.0788819 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01506e12 | 0.788176 | 0.394088 | − | 0.919073i | \(-0.371061\pi\) | ||||
0.394088 | + | 0.919073i | \(0.371061\pi\) | |||||||
\(492\) | − 3.36524e10i | − 0.0258925i | ||||||||
\(493\) | − 9.86086e9i | − 0.00751802i | ||||||||
\(494\) | −4.65505e11 | −0.351684 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.03922e11 | −0.225473 | ||||||||
\(497\) | − 6.71454e11i | − 0.493642i | ||||||||
\(498\) | − 4.03329e10i | − 0.0293851i | ||||||||
\(499\) | −1.33412e12 | −0.963260 | −0.481630 | − | 0.876375i | \(-0.659955\pi\) | ||||
−0.481630 | + | 0.876375i | \(0.659955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.48116e10 | 0.0672345 | ||||||||
\(502\) | − 8.53925e10i | − 0.0600140i | ||||||||
\(503\) | 5.68445e11i | 0.395943i | 0.980208 | + | 0.197971i | \(0.0634353\pi\) | ||||
−0.980208 | + | 0.197971i | \(0.936565\pi\) | |||||||
\(504\) | 1.93218e11 | 0.133386 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.30471e11 | −0.156293 | ||||||||
\(507\) | − 1.32204e10i | − 0.00888606i | ||||||||
\(508\) | 6.03834e11i | 0.402282i | ||||||||
\(509\) | −3.57173e11 | −0.235857 | −0.117928 | − | 0.993022i | \(-0.537625\pi\) | ||||
−0.117928 | + | 0.993022i | \(0.537625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.70059e11 | 0.629367 | ||||||||
\(512\) | − 6.87195e10i | − 0.0441942i | ||||||||
\(513\) | − 6.06653e10i | − 0.0386734i | ||||||||
\(514\) | −1.33692e12 | −0.844834 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.22716e10 | −0.0262498 | ||||||||
\(517\) | − 2.86615e12i | − 1.76438i | ||||||||
\(518\) | 4.58927e11i | 0.280065i | ||||||||
\(519\) | 1.93875e10 | 0.0117292 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.17972e12 | 1.29608 | 0.648040 | − | 0.761606i | \(-0.275589\pi\) | ||||
0.648040 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(522\) | 4.95014e11i | 0.291810i | ||||||||
\(523\) | 1.57081e12i | 0.918048i | 0.888424 | + | 0.459024i | \(0.151801\pi\) | ||||
−0.888424 | + | 0.459024i | \(0.848199\pi\) | |||||||
\(524\) | −1.54026e11 | −0.0892492 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.73816e12 | −0.990042 | ||||||||
\(527\) | − 2.90399e10i | − 0.0164001i | ||||||||
\(528\) | − 2.12934e10i | − 0.0119232i | ||||||||
\(529\) | 1.73040e12 | 0.960716 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.76059e12 | 1.50687 | ||||||||
\(532\) | − 1.58015e11i | − 0.0855253i | ||||||||
\(533\) | 2.47950e12i | 1.33074i | ||||||||
\(534\) | 4.50761e10 | 0.0239889 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.29697e11 | −0.329526 | ||||||||
\(537\) | 1.44845e11i | 0.0751655i | ||||||||
\(538\) | 2.26241e12i | 1.16426i | ||||||||
\(539\) | 3.12176e11 | 0.159312 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.24544e12 | 1.12697 | 0.563486 | − | 0.826126i | \(-0.309460\pi\) | ||||
0.563486 | + | 0.826126i | \(0.309460\pi\) | |||||||
\(542\) | 1.45336e12i | 0.723399i | ||||||||
\(543\) | − 2.33599e10i | − 0.0115311i | ||||||||
\(544\) | 6.56618e9 | 0.00321453 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.60857e10 | 0.0125613 | ||||||||
\(547\) | − 3.86062e11i | − 0.184380i | −0.995741 | − | 0.0921899i | \(-0.970613\pi\) | ||||
0.995741 | − | 0.0921899i | \(-0.0293867\pi\) | |||||||
\(548\) | 1.32098e12i | 0.625726i | ||||||||
\(549\) | −3.98763e12 | −1.87344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.04824e11 | 0.187105 | ||||||||
\(552\) | − 6.53722e9i | − 0.00299686i | ||||||||
\(553\) | − 3.13786e11i | − 0.142683i | ||||||||
\(554\) | −4.24120e11 | −0.191291 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.82875e12 | −0.811556 | ||||||||
\(557\) | − 7.95102e11i | − 0.350005i | −0.984568 | − | 0.175003i | \(-0.944007\pi\) | ||||
0.984568 | − | 0.175003i | \(-0.0559934\pi\) | |||||||
\(558\) | 1.45780e12i | 0.636568i | ||||||||
\(559\) | 3.11456e12 | 1.34910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.03460e9 | 0.000867253 0 | ||||||||
\(562\) | 2.99149e12i | 1.26495i | ||||||||
\(563\) | 2.13667e12i | 0.896292i | 0.893960 | + | 0.448146i | \(0.147916\pi\) | ||||
−0.893960 | + | 0.448146i | \(0.852084\pi\) | |||||||
\(564\) | 8.12972e10 | 0.0338314 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.53460e10 | 0.0349550 | ||||||||
\(567\) | − 9.25096e11i | − 0.375892i | ||||||||
\(568\) | 1.14547e12i | 0.461760i | ||||||||
\(569\) | −2.17461e12 | −0.869714 | −0.434857 | − | 0.900500i | \(-0.643201\pi\) | ||||
−0.434857 | + | 0.900500i | \(0.643201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95075e11 | 0.391736 | 0.195868 | − | 0.980630i | \(-0.437248\pi\) | ||||
0.195868 | + | 0.980630i | \(0.437248\pi\) | |||||||
\(572\) | 1.56889e12i | 0.612790i | ||||||||
\(573\) | − 1.55393e11i | − 0.0602192i | ||||||||
\(574\) | −8.41661e11 | −0.323619 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.29622e11 | −0.124771 | ||||||||
\(577\) | 4.30588e12i | 1.61723i | 0.588340 | + | 0.808614i | \(0.299782\pi\) | ||||
−0.588340 | + | 0.808614i | \(0.700218\pi\) | |||||||
\(578\) | − 1.89678e12i | − 0.706873i | ||||||||
\(579\) | 9.56204e10 | 0.0353588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00874e12 | −0.367272 | ||||||||
\(582\) | − 8.37602e10i | − 0.0302611i | ||||||||
\(583\) | 8.78412e11i | 0.314912i | ||||||||
\(584\) | −1.65488e12 | −0.588719 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.22469e12 | −0.429030 | ||||||||
\(587\) | 5.05762e12i | 1.75822i | 0.476615 | + | 0.879112i | \(0.341864\pi\) | ||||
−0.476615 | + | 0.879112i | \(0.658136\pi\) | |||||||
\(588\) | 8.85473e9i | 0.00305476i | ||||||||
\(589\) | 1.19220e12 | 0.408158 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.00811e10 | 0.00677085 | ||||||||
\(592\) | − 7.82909e11i | − 0.261977i | ||||||||
\(593\) | 2.80300e12i | 0.930844i | 0.885089 | + | 0.465422i | \(0.154097\pi\) | ||||
−0.885089 | + | 0.465422i | \(0.845903\pi\) | |||||||
\(594\) | −2.04461e11 | −0.0673862 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.33069e12 | 0.756616 | ||||||||
\(597\) | 8.05565e10i | 0.0259547i | ||||||||
\(598\) | 4.81660e11i | 0.154023i | ||||||||
\(599\) | −3.20907e12 | −1.01849 | −0.509247 | − | 0.860620i | \(-0.670076\pi\) | ||||
−0.509247 | + | 0.860620i | \(0.670076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.49502e11 | 0.234335 | 0.117168 | − | 0.993112i | \(-0.462619\pi\) | ||||
0.117168 | + | 0.993112i | \(0.462619\pi\) | |||||||
\(602\) | 1.05723e12i | 0.328084i | ||||||||
\(603\) | 3.02042e12i | 0.930336i | ||||||||
\(604\) | 7.40946e10 | 0.0226527 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.16065e11 | −0.0349604 | ||||||||
\(607\) | − 1.74097e12i | − 0.520526i | −0.965538 | − | 0.260263i | \(-0.916191\pi\) | ||||
0.965538 | − | 0.260263i | \(-0.0838092\pi\) | |||||||
\(608\) | 2.69566e11i | 0.0800016i | ||||||||
\(609\) | −2.26853e10 | −0.00668294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.98995e12 | −1.73875 | ||||||||
\(612\) | − 3.14956e10i | − 0.00907544i | ||||||||
\(613\) | 4.03977e12i | 1.15554i | 0.816200 | + | 0.577770i | \(0.196077\pi\) | ||||
−0.816200 | + | 0.577770i | \(0.803923\pi\) | |||||||
\(614\) | −1.20311e12 | −0.341623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.32558e11 | −0.149023 | ||||||||
\(617\) | − 2.93367e12i | − 0.814945i | −0.913218 | − | 0.407472i | \(-0.866410\pi\) | ||||
0.913218 | − | 0.407472i | \(-0.133590\pi\) | |||||||
\(618\) | − 6.62940e10i | − 0.0182821i | ||||||||
\(619\) | 5.77691e12 | 1.58157 | 0.790784 | − | 0.612095i | \(-0.209673\pi\) | ||||
0.790784 | + | 0.612095i | \(0.209673\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.27707e10 | −0.0169373 | ||||||||
\(622\) | − 3.44214e12i | − 0.922088i | ||||||||
\(623\) | − 1.12737e12i | − 0.299827i | ||||||||
\(624\) | −4.45010e10 | −0.0117500 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.53452e12 | −0.399381 | ||||||||
\(627\) | 8.35277e10i | 0.0215837i | ||||||||
\(628\) | − 3.56014e12i | − 0.913373i | ||||||||
\(629\) | 7.48073e10 | 0.0190553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.99985e12 | 1.00441 | 0.502206 | − | 0.864748i | \(-0.332522\pi\) | ||||
0.502206 | + | 0.864748i | \(0.332522\pi\) | |||||||
\(632\) | 5.35305e11i | 0.133467i | ||||||||
\(633\) | 1.81021e11i | 0.0448139i | ||||||||
\(634\) | 2.72938e12 | 0.670908 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.49158e10 | −0.00603834 | ||||||||
\(637\) | − 6.52414e11i | − 0.156999i | ||||||||
\(638\) | − 1.36438e12i | − 0.326019i | ||||||||
\(639\) | 5.49440e12 | 1.30367 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.68328e12 | 1.09569 | 0.547846 | − | 0.836579i | \(-0.315448\pi\) | ||||
0.547846 | + | 0.836579i | \(0.315448\pi\) | |||||||
\(642\) | 1.72319e10i | 0.00400338i | ||||||||
\(643\) | 1.54877e12i | 0.357304i | 0.983912 | + | 0.178652i | \(0.0571736\pi\) | ||||
−0.983912 | + | 0.178652i | \(0.942826\pi\) | |||||||
\(644\) | −1.63498e11 | −0.0374565 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.57572e10 | −0.00581904 | ||||||||
\(647\) | − 8.14493e12i | − 1.82733i | −0.406463 | − | 0.913667i | \(-0.633238\pi\) | ||||
0.406463 | − | 0.913667i | \(-0.366762\pi\) | |||||||
\(648\) | 1.57817e12i | 0.351615i | ||||||||
\(649\) | −7.60888e12 | −1.68352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.68076e10 | −0.0145785 | ||||||||
\(652\) | 4.25555e12i | 0.922235i | ||||||||
\(653\) | 2.88925e12i | 0.621836i | 0.950437 | + | 0.310918i | \(0.100636\pi\) | ||||
−0.950437 | + | 0.310918i | \(0.899364\pi\) | |||||||
\(654\) | 1.53946e11 | 0.0329056 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.43584e12 | 0.302718 | ||||||||
\(657\) | 7.93784e12i | 1.66210i | ||||||||
\(658\) | − 2.03328e12i | − 0.422844i | ||||||||
\(659\) | −5.20255e12 | −1.07456 | −0.537281 | − | 0.843403i | \(-0.680549\pi\) | ||||
−0.537281 | + | 0.843403i | \(0.680549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.88973e12 | 0.588777 | 0.294388 | − | 0.955686i | \(-0.404884\pi\) | ||||
0.294388 | + | 0.955686i | \(0.404884\pi\) | |||||||
\(662\) | 1.98387e12i | 0.401469i | ||||||||
\(663\) | − 4.25210e9i | 0 0.000854658i | ||||||||
\(664\) | 1.72087e12 | 0.343551 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.75532e12 | −0.739628 | ||||||||
\(667\) | − 4.18874e11i | − 0.0819440i | ||||||||
\(668\) | 4.04530e12i | 0.786061i | ||||||||
\(669\) | 3.21018e11 | 0.0619600 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09909e13 | 2.09306 | ||||||||
\(672\) | − 1.51058e10i | − 0.00285747i | ||||||||
\(673\) | − 9.46362e12i | − 1.77824i | −0.457677 | − | 0.889119i | \(-0.651318\pi\) | ||||
0.457677 | − | 0.889119i | \(-0.348682\pi\) | |||||||
\(674\) | −1.16694e12 | −0.217810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.64071e11 | 0.103890 | ||||||||
\(677\) | − 6.52268e12i | − 1.19338i | −0.802474 | − | 0.596688i | \(-0.796483\pi\) | ||||
0.802474 | − | 0.596688i | \(-0.203517\pi\) | |||||||
\(678\) | − 1.37074e11i | − 0.0249127i | ||||||||
\(679\) | −2.09488e12 | −0.378220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.41622e11 | 0.0430502 | ||||||||
\(682\) | − 4.01806e12i | − 0.711193i | ||||||||
\(683\) | − 5.37240e12i | − 0.944660i | −0.881422 | − | 0.472330i | \(-0.843413\pi\) | ||||
0.881422 | − | 0.472330i | \(-0.156587\pi\) | |||||||
\(684\) | 1.29301e12 | 0.225865 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.21461e11 | 0.0381802 | ||||||||
\(687\) | − 1.14148e11i | − 0.0195508i | ||||||||
\(688\) | − 1.80359e12i | − 0.306895i | ||||||||
\(689\) | 1.83579e12 | 0.310339 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.01563e12 | 0.336325 | 0.168163 | − | 0.985759i | \(-0.446217\pi\) | ||||
0.168163 | + | 0.985759i | \(0.446217\pi\) | |||||||
\(692\) | 8.27200e11i | 0.137130i | ||||||||
\(693\) | 2.55448e12i | 0.420730i | ||||||||
\(694\) | −2.49153e12 | −0.407707 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.87002e10 | 0.00625131 | ||||||||
\(697\) | 1.37195e11i | 0.0220186i | ||||||||
\(698\) | 1.73966e12i | 0.277405i | ||||||||
\(699\) | −2.20649e11 | −0.0349586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.06523e13 | −1.66614 | −0.833068 | − | 0.553171i | \(-0.813418\pi\) | ||||
−0.833068 | + | 0.553171i | \(0.813418\pi\) | |||||||
\(702\) | 4.27301e11i | 0.0664075i | ||||||||
\(703\) | 3.07111e12i | 0.474239i | ||||||||
\(704\) | 9.08520e11 | 0.139398 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.20936e12 | −0.789157 | ||||||||
\(707\) | 2.90284e12i | 0.436955i | ||||||||
\(708\) | − 2.15823e11i | − 0.0322810i | ||||||||
\(709\) | −3.46187e12 | −0.514520 | −0.257260 | − | 0.966342i | \(-0.582820\pi\) | ||||
−0.257260 | + | 0.966342i | \(0.582820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.56766e12 | 0.376812 | ||||||||
\(712\) | 1.92325e12i | 0.280462i | ||||||||
\(713\) | − 1.23357e12i | − 0.178756i | ||||||||
\(714\) | 1.44337e9 | 0.000207843 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.18004e12 | −0.878785 | ||||||||
\(717\) | − 3.93666e10i | − 0.00556277i | ||||||||
\(718\) | − 3.64080e12i | − 0.511253i | ||||||||
\(719\) | 9.62025e12 | 1.34248 | 0.671238 | − | 0.741242i | \(-0.265763\pi\) | ||||
0.671238 | + | 0.741242i | \(0.265763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.65804e12 | −0.228500 | ||||||||
\(722\) | 4.10558e12i | 0.562285i | ||||||||
\(723\) | − 5.38091e11i | − 0.0732374i | ||||||||
\(724\) | 9.96689e11 | 0.134814 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.51512e10 | 0.00736784 | ||||||||
\(727\) | − 3.13479e12i | − 0.416202i | −0.978107 | − | 0.208101i | \(-0.933272\pi\) | ||||
0.978107 | − | 0.208101i | \(-0.0667282\pi\) | |||||||
\(728\) | 1.11299e12i | 0.146859i | ||||||||
\(729\) | 7.54204e12 | 0.989043 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.72334e11 | 0.0223225 | ||||||||
\(732\) | 3.11752e11i | 0.0401337i | ||||||||
\(733\) | − 6.47775e12i | − 0.828812i | −0.910092 | − | 0.414406i | \(-0.863989\pi\) | ||||
0.910092 | − | 0.414406i | \(-0.136011\pi\) | |||||||
\(734\) | −6.75189e12 | −0.858604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.78921e11 | 0.0350374 | ||||||||
\(737\) | − 8.32503e12i | − 1.03940i | ||||||||
\(738\) | − 6.88718e12i | − 0.854649i | ||||||||
\(739\) | 1.12510e12 | 0.138769 | 0.0693843 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693843 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.74564e11 | 0.0212703 | ||||||||
\(742\) | 6.23154e11i | 0.0754707i | ||||||||
\(743\) | − 1.65266e12i | − 0.198945i | −0.995040 | − | 0.0994725i | \(-0.968284\pi\) | ||||
0.995040 | − | 0.0994725i | \(-0.0317155\pi\) | |||||||
\(744\) | 1.13971e11 | 0.0136369 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.13253e12 | −0.724961 | ||||||||
\(747\) | − 8.25437e12i | − 0.969932i | ||||||||
\(748\) | 8.68096e10i | 0.0101394i | ||||||||
\(749\) | 4.30978e11 | 0.0500365 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.03299e12 | 0.692074 | 0.346037 | − | 0.938221i | \(-0.387527\pi\) | ||||
0.346037 | + | 0.938221i | \(0.387527\pi\) | |||||||
\(752\) | 3.46868e12i | 0.395534i | ||||||||
\(753\) | 3.20222e10i | 0.00362972i | ||||||||
\(754\) | −2.85142e12 | −0.321284 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.45047e11 | −0.0161495 | ||||||||
\(757\) | − 8.02798e12i | − 0.888535i | −0.895894 | − | 0.444268i | \(-0.853464\pi\) | ||||
0.895894 | − | 0.444268i | \(-0.146536\pi\) | |||||||
\(758\) | − 1.94338e12i | − 0.213820i | ||||||||
\(759\) | 8.64266e10 | 0.00945278 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.51923e12 | −0.704637 | −0.352318 | − | 0.935880i | \(-0.614607\pi\) | ||||
−0.352318 | + | 0.935880i | \(0.614607\pi\) | |||||||
\(762\) | − 2.26438e11i | − 0.0243305i | ||||||||
\(763\) | − 3.85026e12i | − 0.411273i | ||||||||
\(764\) | 6.63009e12 | 0.704043 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.36354e12 | 0.667835 | ||||||||
\(767\) | 1.59018e13i | 1.65907i | ||||||||
\(768\) | 2.57698e10i | 0.00267292i | ||||||||
\(769\) | 1.34250e13 | 1.38435 | 0.692175 | − | 0.721730i | \(-0.256653\pi\) | ||||
0.692175 | + | 0.721730i | \(0.256653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.01345e11 | 0.0510966 | ||||||||
\(772\) | 4.07980e12i | 0.413391i | ||||||||
\(773\) | − 7.85934e12i | − 0.791733i | −0.918308 | − | 0.395866i | \(-0.870444\pi\) | ||||
0.918308 | − | 0.395866i | \(-0.129556\pi\) | |||||||
\(774\) | −8.65115e12 | −0.866442 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.57377e12 | 0.353792 | ||||||||
\(777\) | − 1.72098e11i | − 0.0169387i | ||||||||
\(778\) | 1.08074e12i | 0.105758i | ||||||||
\(779\) | −5.63235e12 | −0.547988 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.51439e13 | −1.45649 | ||||||||
\(782\) | 2.66511e10i | 0.00254850i | ||||||||
\(783\) | − 3.71601e11i | − 0.0353304i | ||||||||
\(784\) | −3.77802e11 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.77599e10 | 0.00539790 | ||||||||
\(787\) | − 1.47720e12i | − 0.137263i | −0.997642 | − | 0.0686316i | \(-0.978137\pi\) | ||||
0.997642 | − | 0.0686316i | \(-0.0218633\pi\) | |||||||
\(788\) | 8.56793e11i | 0.0791604i | ||||||||
\(789\) | 6.51809e11 | 0.0598789 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.42827e12 | −0.311373 | ||||||||
\(792\) | − 4.35783e12i | − 0.393557i | ||||||||
\(793\) | − 2.29698e13i | − 2.06266i | ||||||||
\(794\) | 1.99449e12 | 0.178090 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.43708e12 | −0.303445 | ||||||||
\(797\) | − 6.47327e12i | − 0.568278i | −0.958783 | − | 0.284139i | \(-0.908292\pi\) | ||||
0.958783 | − | 0.284139i | \(-0.0917078\pi\) | |||||||
\(798\) | 5.92555e10i | 0.00517268i | ||||||||
\(799\) | −3.31434e11 | −0.0287698 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.22510e12 | 0.791817 | ||||||||
\(802\) | − 5.61913e12i | − 0.479606i | ||||||||
\(803\) | − 2.18786e13i | − 1.85695i | ||||||||
\(804\) | 2.36136e11 | 0.0199301 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.39733e12 | −0.700864 | ||||||||
\(807\) | − 8.48403e11i | − 0.0704160i | ||||||||
\(808\) | − 4.95212e12i | − 0.408734i | ||||||||
\(809\) | 1.53631e13 | 1.26099 | 0.630493 | − | 0.776195i | \(-0.282853\pi\) | ||||
0.630493 | + | 0.776195i | \(0.282853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.29056e13 | −1.04757 | −0.523787 | − | 0.851849i | \(-0.675481\pi\) | ||||
−0.523787 | + | 0.851849i | \(0.675481\pi\) | |||||||
\(812\) | − 9.67907e11i | − 0.0781325i | ||||||||
\(813\) | − 5.45012e11i | − 0.0437520i | ||||||||
\(814\) | 1.03506e13 | 0.826334 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.46232e9 | −0.000194419 0 | ||||||||
\(817\) | 7.07494e12i | 0.555550i | ||||||||
\(818\) | − 6.11130e11i | − 0.0477247i | ||||||||
\(819\) | 5.33860e12 | 0.414620 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.93771e11 | 0.0686566 | 0.0343283 | − | 0.999411i | \(-0.489071\pi\) | ||||
0.0343283 | + | 0.999411i | \(0.489071\pi\) | |||||||
\(822\) | − 4.95368e11i | − 0.0378447i | ||||||||
\(823\) | 2.29844e13i | 1.74636i | 0.487394 | + | 0.873182i | \(0.337947\pi\) | ||||
−0.487394 | + | 0.873182i | \(0.662053\pi\) | |||||||
\(824\) | 2.82854e12 | 0.213742 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.39782e12 | −0.403467 | ||||||||
\(827\) | − 2.75618e12i | − 0.204896i | −0.994738 | − | 0.102448i | \(-0.967333\pi\) | ||||
0.994738 | − | 0.102448i | \(-0.0326675\pi\) | |||||||
\(828\) | − 1.33788e12i | − 0.0989194i | ||||||||
\(829\) | 3.15925e12 | 0.232321 | 0.116160 | − | 0.993230i | \(-0.462941\pi\) | ||||
0.116160 | + | 0.993230i | \(0.462941\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.59045e11 | 0.0115695 | ||||||||
\(832\) | − 1.89871e12i | − 0.137374i | ||||||||
\(833\) | − 3.60992e10i | − 0.00259774i | ||||||||
\(834\) | 6.85782e11 | 0.0490839 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.56385e12 | −0.252343 | ||||||||
\(837\) | − 1.09435e12i | − 0.0770714i | ||||||||
\(838\) | 3.44428e12i | 0.241269i | ||||||||
\(839\) | −1.92403e13 | −1.34055 | −0.670277 | − | 0.742111i | \(-0.733825\pi\) | ||||
−0.670277 | + | 0.742111i | \(0.733825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20274e13 | −0.829069 | ||||||||
\(842\) | − 1.91892e13i | − 1.31569i | ||||||||
\(843\) | − 1.12181e12i | − 0.0765058i | ||||||||
\(844\) | −7.72357e12 | −0.523935 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.66380e13 | 1.11669 | ||||||||
\(847\) | − 1.37935e12i | − 0.0920874i | ||||||||
\(848\) | − 1.06307e12i | − 0.0705963i | ||||||||
\(849\) | −3.20048e10 | −0.00211412 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.17770e12 | 0.207697 | ||||||||
\(852\) | − 4.29552e11i | − 0.0279278i | ||||||||
\(853\) | 2.60804e13i | 1.68672i | 0.537345 | + | 0.843362i | \(0.319427\pi\) | ||||
−0.537345 | + | 0.843362i | \(0.680573\pi\) | |||||||
\(854\) | 7.79705e12 | 0.501614 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.35229e11 | −0.0468049 | ||||||||
\(857\) | 2.19177e13i | 1.38797i | 0.719988 | + | 0.693986i | \(0.244147\pi\) | ||||
−0.719988 | + | 0.693986i | \(0.755853\pi\) | |||||||
\(858\) | − 5.88335e11i | − 0.0370623i | ||||||||
\(859\) | 3.55588e12 | 0.222832 | 0.111416 | − | 0.993774i | \(-0.464461\pi\) | ||||
0.111416 | + | 0.993774i | \(0.464461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.15623e11 | 0.0195729 | ||||||||
\(862\) | − 1.26579e13i | − 0.780869i | ||||||||
\(863\) | − 2.22084e13i | − 1.36292i | −0.731858 | − | 0.681458i | \(-0.761346\pi\) | ||||
0.731858 | − | 0.681458i | \(-0.238654\pi\) | |||||||
\(864\) | 2.47443e11 | 0.0151065 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.84721e13 | 1.11606 | ||||||||
\(867\) | 7.11292e11i | 0.0427525i | ||||||||
\(868\) | − 2.85046e12i | − 0.170442i | ||||||||
\(869\) | −7.07711e12 | −0.420986 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.73984e13 | −1.02430 | ||||||||
\(872\) | 6.56838e12i | 0.384711i | ||||||||
\(873\) | − 1.71420e13i | − 0.998846i | ||||||||
\(874\) | −1.09412e12 | −0.0634257 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.20579e11 | 0.0356064 | ||||||||
\(877\) | 3.38004e12i | 0.192941i | 0.995336 | + | 0.0964703i | \(0.0307553\pi\) | ||||
−0.995336 | + | 0.0964703i | \(0.969245\pi\) | |||||||
\(878\) | − 3.40365e12i | − 0.193295i | ||||||||
\(879\) | 4.59260e11 | 0.0259483 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.25103e11 | 0.0293665 | 0.0146833 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146833 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(882\) | 1.81218e12i | 0.100830i | ||||||||
\(883\) | − 3.33972e13i | − 1.84879i | −0.381441 | − | 0.924393i | \(-0.624572\pi\) | ||||
0.381441 | − | 0.924393i | \(-0.375428\pi\) | |||||||
\(884\) | 1.81423e11 | 0.00999210 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.03728e12 | 0.0565515 | ||||||||
\(887\) | − 9.61964e12i | − 0.521798i | −0.965366 | − | 0.260899i | \(-0.915981\pi\) | ||||
0.965366 | − | 0.260899i | \(-0.0840190\pi\) | |||||||
\(888\) | 2.93591e11i | 0.0158447i | ||||||||
\(889\) | −5.66331e12 | −0.304097 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.08646e13 | −1.10907 | ||||||||
\(892\) | 1.36968e13i | 0.724396i | ||||||||
\(893\) | − 1.36066e13i | − 0.716007i | ||||||||
\(894\) | −8.74007e11 | −0.0457611 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.44514e11 | 0.0334077 | ||||||||
\(897\) | − 1.80623e11i | − 0.00931549i | ||||||||
\(898\) | − 1.72850e13i | − 0.887004i | ||||||||
\(899\) | 7.30271e12 | 0.372877 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01577e11 | 0.00513494 | ||||||||
\(902\) | 1.89828e13i | 0.954839i | ||||||||
\(903\) | − 3.96462e11i | − 0.0198430i | ||||||||
\(904\) | 5.84848e12 | 0.291263 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.77855e10 | −0.00137006 | ||||||||
\(907\) | − 2.08341e13i | − 1.02221i | −0.859517 | − | 0.511107i | \(-0.829236\pi\) | ||||
0.859517 | − | 0.511107i | \(-0.170764\pi\) | |||||||
\(908\) | 1.03092e13i | 0.503315i | ||||||||
\(909\) | −2.37535e13 | −1.15396 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.33789e13 | −0.643560 | −0.321780 | − | 0.946814i | \(-0.604281\pi\) | ||||
−0.321780 | + | 0.946814i | \(0.604281\pi\) | |||||||
\(912\) | − 1.01087e11i | − 0.00483860i | ||||||||
\(913\) | 2.27511e13i | 1.08364i | ||||||||
\(914\) | −1.03476e12 | −0.0490436 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.87033e12 | 0.228575 | ||||||||
\(917\) | − 1.44460e12i | − 0.0674660i | ||||||||
\(918\) | 2.36433e10i | 0.00109879i | ||||||||
\(919\) | 1.38352e13 | 0.639830 | 0.319915 | − | 0.947446i | \(-0.396346\pi\) | ||||
0.319915 | + | 0.947446i | \(0.396346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.51166e11 | 0.0206618 | ||||||||
\(922\) | − 6.86806e12i | − 0.313000i | ||||||||
\(923\) | 3.16492e13i | 1.43534i | ||||||||
\(924\) | 1.99709e11 | 0.00901310 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.59013e13 | −1.15764 | ||||||||
\(927\) | − 1.35675e13i | − 0.603449i | ||||||||
\(928\) | 1.65121e12i | 0.0730863i | ||||||||
\(929\) | 1.74073e13 | 0.766761 | 0.383380 | − | 0.923591i | \(-0.374760\pi\) | ||||
0.383380 | + | 0.923591i | \(0.374760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48200e12 | 0.0646511 | ||||||||
\(932\) | − 9.41434e12i | − 0.408713i | ||||||||
\(933\) | 1.29080e12i | 0.0557690i | ||||||||
\(934\) | 5.23714e12 | 0.225182 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.10742e12 | −0.387841 | ||||||||
\(937\) | 1.98361e12i | 0.0840676i | 0.999116 | + | 0.0420338i | \(0.0133837\pi\) | ||||
−0.999116 | + | 0.0420338i | \(0.986616\pi\) | |||||||
\(938\) | − 5.90587e12i | − 0.249098i | ||||||||
\(939\) | 5.75445e11 | 0.0241551 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.33533e13 | −0.970946 | −0.485473 | − | 0.874252i | \(-0.661353\pi\) | ||||
−0.485473 | + | 0.874252i | \(0.661353\pi\) | |||||||
\(942\) | 1.33505e12i | 0.0552419i | ||||||||
\(943\) | 5.82783e12i | 0.239996i | ||||||||
\(944\) | 9.20844e12 | 0.377409 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.38447e13 | 0.968015 | ||||||||
\(947\) | 3.59882e13i | 1.45407i | 0.686600 | + | 0.727035i | \(0.259102\pi\) | ||||
−0.686600 | + | 0.727035i | \(0.740898\pi\) | |||||||
\(948\) | − 2.00740e11i | − 0.00807227i | ||||||||
\(949\) | −4.57241e13 | −1.82998 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.02352e12 | −0.0405773 | ||||||||
\(952\) | 6.15836e10i | 0.00242996i | ||||||||
\(953\) | 1.37662e13i | 0.540624i | 0.962773 | + | 0.270312i | \(0.0871268\pi\) | ||||
−0.962773 | + | 0.270312i | \(0.912873\pi\) | |||||||
\(954\) | −5.09917e12 | −0.199311 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.67964e12 | 0.0650363 | ||||||||
\(957\) | 5.11643e11i | 0.0197180i | ||||||||
\(958\) | 4.55698e12i | 0.174796i | ||||||||
\(959\) | −1.23894e13 | −0.473005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.93336e12 | −0.186590 | ||||||||
\(962\) | − 2.16317e13i | − 0.814334i | ||||||||
\(963\) | 3.52662e12i | 0.132142i | ||||||||
\(964\) | 2.29585e13 | 0.856244 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.13119e10 | 0.00226542 | ||||||||
\(967\) | − 3.02718e12i | − 0.111332i | −0.998449 | − | 0.0556659i | \(-0.982272\pi\) | ||||
0.998449 | − | 0.0556659i | \(-0.0177282\pi\) | |||||||
\(968\) | 2.35312e12i | 0.0861399i | ||||||||
\(969\) | 9.65893e9 | 0.000351943 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.53183e13 | −0.914003 | −0.457002 | − | 0.889466i | \(-0.651077\pi\) | ||||
−0.457002 | + | 0.889466i | \(0.651077\pi\) | |||||||
\(972\) | − 1.78088e12i | − 0.0639937i | ||||||||
\(973\) | − 1.71517e13i | − 0.613478i | ||||||||
\(974\) | −1.14364e13 | −0.407169 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.33014e13 | −0.469217 | ||||||||
\(977\) | 9.90729e12i | 0.347880i | 0.984756 | + | 0.173940i | \(0.0556499\pi\) | ||||
−0.984756 | + | 0.173940i | \(0.944350\pi\) | |||||||
\(978\) | − 1.59583e12i | − 0.0557779i | ||||||||
\(979\) | −2.54267e13 | −0.884641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.15061e13 | 1.08614 | ||||||||
\(982\) | − 1.62409e13i | − 0.557325i | ||||||||
\(983\) | − 2.40523e13i | − 0.821610i | −0.911723 | − | 0.410805i | \(-0.865248\pi\) | ||||
0.911723 | − | 0.410805i | \(-0.134752\pi\) | |||||||
\(984\) | −5.38439e11 | −0.0183087 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.57774e11 | −0.00531604 | ||||||||
\(987\) | 7.62478e11i | 0.0255741i | ||||||||
\(988\) | 7.44807e12i | 0.248678i | ||||||||
\(989\) | 7.32048e12 | 0.243308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.15782e13 | 1.04005 | 0.520027 | − | 0.854150i | \(-0.325922\pi\) | ||||
0.520027 | + | 0.854150i | \(0.325922\pi\) | |||||||
\(992\) | 4.86275e12i | 0.159434i | ||||||||
\(993\) | − 7.43950e11i | − 0.0242813i | ||||||||
\(994\) | −1.07433e13 | −0.349058 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.45326e11 | −0.0207784 | ||||||||
\(997\) | 9.32241e12i | 0.298813i | 0.988776 | + | 0.149407i | \(0.0477364\pi\) | ||||
−0.988776 | + | 0.149407i | \(0.952264\pi\) | |||||||
\(998\) | 2.13460e13i | 0.681128i | ||||||||
\(999\) | 2.81907e12 | 0.0895492 |
(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 | 350.10.c.b.99.1 | 2 | ||
5.2 | odd | 4 | 350.10.a.c.1.1 | 1 | |||
5.3 | odd | 4 | 14.10.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 350.10.c.b.99.2 | 2 | ||
15.8 | even | 4 | 126.10.a.e.1.1 | 1 | |||
20.3 | even | 4 | 112.10.a.b.1.1 | 1 | |||
35.3 | even | 12 | 98.10.c.e.79.1 | 2 | |||
35.13 | even | 4 | 98.10.a.a.1.1 | 1 | |||
35.18 | odd | 12 | 98.10.c.f.79.1 | 2 | |||
35.23 | odd | 12 | 98.10.c.f.67.1 | 2 | |||
35.33 | even | 12 | 98.10.c.e.67.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
98.10.a.a.1.1 | 1 | 35.13 | even | 4 | |||
98.10.c.e.67.1 | 2 | 35.33 | even | 12 | |||
98.10.c.e.79.1 | 2 | 35.3 | even | 12 | |||
98.10.c.f.67.1 | 2 | 35.23 | odd | 12 | |||
98.10.c.f.79.1 | 2 | 35.18 | odd | 12 | |||
112.10.a.b.1.1 | 1 | 20.3 | even | 4 | |||
126.10.a.e.1.1 | 1 | 15.8 | even | 4 | |||
350.10.a.c.1.1 | 1 | 5.2 | odd | 4 | |||
350.10.c.b.99.1 | 2 | 1.1 | even | 1 | trivial | ||
350.10.c.b.99.2 | 2 | 5.4 | even | 2 | inner |