Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(-1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.i.449.4 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 6.32456i | − 0.405720i | −0.979208 | − | 0.202860i | \(-0.934976\pi\) | ||||
0.979208 | − | 0.202860i | \(-0.0650237\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.2719i | 0.341494i | 0.985315 | + | 0.170747i | \(0.0546181\pi\) | ||||
−0.985315 | + | 0.170747i | \(0.945382\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 203.000 | 0.835391 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 720.999 | 1.79661 | 0.898304 | − | 0.439375i | \(-0.144800\pi\) | ||||
0.898304 | + | 0.439375i | \(0.144800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 146.000i | − 0.239604i | −0.992798 | − | 0.119802i | \(-0.961774\pi\) | ||||
0.992798 | − | 0.119802i | \(-0.0382260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 702.000i | 0.589135i | 0.955631 | + | 0.294567i | \(0.0951756\pi\) | ||||
−0.955631 | + | 0.294567i | \(0.904824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2732.21 | 1.73632 | 0.868160 | − | 0.496285i | \(-0.165303\pi\) | ||||
0.868160 | + | 0.496285i | \(0.165303\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 280.000 | 0.138551 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4091.99i | 1.61293i | 0.591284 | + | 0.806463i | \(0.298621\pi\) | ||||
−0.591284 | + | 0.806463i | \(0.701379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2820.75i | − 0.744656i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4010.00 | 0.885420 | 0.442710 | − | 0.896665i | \(-0.354017\pi\) | ||||
0.442710 | + | 0.896665i | \(0.354017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4566.33 | −0.853420 | −0.426710 | − | 0.904388i | \(-0.640328\pi\) | ||||
−0.426710 | + | 0.904388i | \(0.640328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 4560.00i | − 0.728920i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14778.0i | 1.77464i | 0.461150 | + | 0.887322i | \(0.347437\pi\) | ||||
−0.461150 | + | 0.887322i | \(0.652563\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −923.385 | −0.0972123 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4350.00 | −0.404138 | −0.202069 | − | 0.979371i | \(-0.564767\pi\) | ||||
−0.202069 | + | 0.979371i | \(0.564767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 12427.8i | − 1.02499i | −0.858689 | − | 0.512497i | \(-0.828721\pi\) | ||||
0.858689 | − | 0.512497i | \(-0.171279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6014.65i | 0.397160i | 0.980085 | + | 0.198580i | \(0.0636330\pi\) | ||||
−0.980085 | + | 0.198580i | \(0.936367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14847.0 | 0.883382 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4439.84 | 0.239024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 18154.0i | − 0.887734i | −0.896093 | − | 0.443867i | \(-0.853606\pi\) | ||||
0.896093 | − | 0.443867i | \(-0.146394\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 17280.0i | − 0.704460i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −19707.3 | −0.737051 | −0.368525 | − | 0.929618i | \(-0.620137\pi\) | ||||
−0.368525 | + | 0.929618i | \(0.620137\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42130.0 | −1.44966 | −0.724831 | − | 0.688927i | \(-0.758082\pi\) | ||||
−0.724831 | + | 0.688927i | \(0.758082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8987.19i | 0.285281i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16184.5i | 0.440467i | 0.975447 | + | 0.220233i | \(0.0706819\pi\) | ||||
−0.975447 | + | 0.220233i | \(0.929318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25880.0 | 0.654397 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45448.3 | −1.06997 | −0.534985 | − | 0.844862i | \(-0.679683\pi\) | ||||
−0.534985 | + | 0.844862i | \(0.679683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26266.0i | 0.576882i | 0.957498 | + | 0.288441i | \(0.0931369\pi\) | ||||
−0.957498 | + | 0.288441i | \(0.906863\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31920.0i | 0.613530i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8677.29 | −0.156429 | −0.0782143 | − | 0.996937i | \(-0.524922\pi\) | ||||
−0.0782143 | + | 0.996937i | \(0.524922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31489.0 | 0.533269 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 98757.9i | 1.57354i | 0.617249 | + | 0.786768i | \(0.288247\pi\) | ||||
−0.617249 | + | 0.786768i | \(0.711753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 25361.5i | − 0.359233i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −30570.0 | −0.409091 | −0.204546 | − | 0.978857i | \(-0.565572\pi\) | ||||
−0.204546 | + | 0.978857i | \(0.565572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6463.70 | 0.0818234 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 28880.0i | 0.346250i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 66882.0i | − 0.721739i | −0.932616 | − | 0.360869i | \(-0.882480\pi\) | ||||
0.932616 | − | 0.360869i | \(-0.117520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 146363. | 1.50087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 42798.0 | 0.417465 | 0.208732 | − | 0.977973i | \(-0.433066\pi\) | ||||
0.208732 | + | 0.977973i | \(0.433066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10505.1i | − 0.0975678i | −0.998809 | − | 0.0487839i | \(-0.984465\pi\) | ||||
0.998809 | − | 0.0487839i | \(-0.0155346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 66856.9i | 0.564529i | 0.959337 | + | 0.282265i | \(0.0910857\pi\) | ||||
−0.959337 | + | 0.282265i | \(0.908914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 111714. | 0.900620 | 0.450310 | − | 0.892872i | \(-0.351314\pi\) | ||||
0.450310 | + | 0.892872i | \(0.351314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 93464.3 | 0.720009 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 216834.i | 1.59746i | 0.601686 | + | 0.798732i | \(0.294496\pi\) | ||||
−0.601686 | + | 0.798732i | \(0.705504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 29638.0i | − 0.200163i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31078.9 | −0.201186 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 358789. | 2.22780 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27511.8i | 0.163967i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 62277.9i | 0.342629i | 0.985216 | + | 0.171315i | \(0.0548015\pi\) | ||||
−0.985216 | + | 0.171315i | \(0.945199\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −78600.0 | −0.415861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −176189. | −0.897019 | −0.448510 | − | 0.893778i | \(-0.648045\pi\) | ||||
−0.448510 | + | 0.893778i | \(0.648045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 120960.i | 0.592943i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 99802.0i | − 0.454295i | −0.973860 | − | 0.227147i | \(-0.927060\pi\) | ||||
0.973860 | − | 0.227147i | \(-0.0729399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −271475. | −1.19177 | −0.595886 | − | 0.803069i | \(-0.703199\pi\) | ||||
−0.595886 | + | 0.803069i | \(0.703199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38040.0 | 0.161136 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 105266.i | − 0.430475i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 93900.7i | − 0.358406i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 413626. | 1.52631 | 0.763154 | − | 0.646217i | \(-0.223650\pi\) | ||||
0.763154 | + | 0.646217i | \(0.223650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −172496. | −0.615654 | −0.307827 | − | 0.951442i | \(-0.599602\pi\) | ||||
−0.307827 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 142506.i | 0.492158i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 179358.i | − 0.580726i | −0.956917 | − | 0.290363i | \(-0.906224\pi\) | ||||
0.956917 | − | 0.290363i | \(-0.0937761\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −114816. | −0.360172 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −181160. | −0.550805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 465924.i | − 1.37355i | −0.726868 | − | 0.686777i | \(-0.759025\pi\) | ||||
0.726868 | − | 0.686777i | \(-0.240975\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 609567.i | − 1.69134i | −0.533708 | − | 0.845669i | \(-0.679202\pi\) | ||||
0.533708 | − | 0.845669i | \(-0.320798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 349977. | 0.942590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 554638. | 1.45051 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 591086.i | 1.50153i | 0.660567 | + | 0.750767i | \(0.270316\pi\) | ||||
−0.660567 | + | 0.750767i | \(0.729684\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 124640.i | 0.299037i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 211215. | 0.492711 | 0.246355 | − | 0.969180i | \(-0.420767\pi\) | ||||
0.246355 | + | 0.969180i | \(0.420767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −97538.0 | −0.221298 | −0.110649 | − | 0.993860i | \(-0.535293\pi\) | ||||
−0.110649 | + | 0.993860i | \(0.535293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 266454.i | 0.588158i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 506142.i | 1.05844i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 124880. | 0.254295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −307158. | −0.609227 | −0.304613 | − | 0.952476i | \(-0.598527\pi\) | ||||
−0.304613 | + | 0.952476i | \(0.598527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12434.0i | 0.0240280i | 0.999928 | + | 0.0120140i | \(0.00382427\pi\) | ||||
−0.999928 | + | 0.0120140i | \(0.996176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 378858.i | 0.695522i | 0.937583 | + | 0.347761i | \(0.113058\pi\) | ||||
−0.937583 | + | 0.347761i | \(0.886942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 767194. | 1.37332 | 0.686661 | − | 0.726978i | \(-0.259076\pi\) | ||||
0.686661 | + | 0.726978i | \(0.259076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 102360. | 0.178706 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 177530.i | 0.302366i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 830673.i | 1.34742i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.96992e6 | 3.11948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 864529. | 1.33682 | 0.668411 | − | 0.743793i | \(-0.266975\pi\) | ||||
0.668411 | + | 0.743793i | \(0.266975\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 287440.i | 0.434108i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 202160.i | − 0.291438i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 166121. | 0.234053 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 102492. | 0.141159 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 639710.i | 0.861432i | 0.902488 | + | 0.430716i | \(0.141739\pi\) | ||||
−0.902488 | + | 0.430716i | \(0.858261\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 980515.i | − 1.26296i | −0.775392 | − | 0.631480i | \(-0.782448\pi\) | ||||
0.775392 | − | 0.631480i | \(-0.217552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01261e6 | 1.27601 | 0.638004 | − | 0.770033i | \(-0.279760\pi\) | ||||
0.638004 | + | 0.770033i | \(0.279760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 201880. | 0.248922 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 706326.i | − 0.852345i | −0.904642 | − | 0.426172i | \(-0.859862\pi\) | ||||
0.904642 | − | 0.426172i | \(-0.140138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 54880.0i | 0.0634663i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.19390e6 | −1.35199 | −0.675994 | − | 0.736907i | \(-0.736285\pi\) | ||||
−0.675994 | + | 0.736907i | \(0.736285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 404410. | 0.448517 | 0.224259 | − | 0.974530i | \(-0.428004\pi\) | ||||
0.224259 | + | 0.974530i | \(0.428004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 884597.i | − 0.961014i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 398902.i | − 0.416030i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 624600. | 0.638416 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.43258e6 | −1.43527 | −0.717634 | − | 0.696420i | \(-0.754775\pi\) | ||||
−0.717634 | + | 0.696420i | \(0.754775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.95032e6i | 2.89780i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 987982.i | 0.933074i | 0.884502 | + | 0.466537i | \(0.154499\pi\) | ||||
−0.884502 | + | 0.466537i | \(0.845501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −654250. | −0.606030 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 814030. | 0.739672 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2.06222e6i | − 1.83842i | −0.393767 | − | 0.919210i | \(-0.628828\pi\) | ||||
0.393767 | − | 0.919210i | \(-0.371172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 193342.i | 0.165977i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 780386. | 0.657550 | 0.328775 | − | 0.944408i | \(-0.393364\pi\) | ||||
0.328775 | + | 0.944408i | \(0.393364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 562291. | 0.465091 | 0.232545 | − | 0.972586i | \(-0.425295\pi\) | ||||
0.232545 | + | 0.972586i | \(0.425295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 40880.0i | − 0.0331974i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 386758.i | − 0.302859i | −0.988468 | − | 0.151429i | \(-0.951612\pi\) | ||||
0.988468 | − | 0.151429i | \(-0.0483876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −926965. | −0.712940 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.55485e6 | 1.17469 | 0.587344 | − | 0.809337i | \(-0.300173\pi\) | ||||
0.587344 | + | 0.809337i | \(0.300173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.75157e6i | 1.30005i | 0.759912 | + | 0.650026i | \(0.225242\pi\) | ||||
−0.759912 | + | 0.650026i | \(0.774758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 192583.i | − 0.138011i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 927053. | 0.652920 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −422999. | −0.292824 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.55309e6i | 1.05689i | 0.848968 | + | 0.528444i | \(0.177224\pi\) | ||||
−0.848968 | + | 0.528444i | \(0.822776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.03376e6i | − 1.33785i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 597430. | 0.386464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 550200. | 0.350029 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 270678.i | − 0.169374i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.60409e6i | 1.57692i | 0.615085 | + | 0.788461i | \(0.289122\pi\) | ||||
−0.615085 | + | 0.788461i | \(0.710878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −66440.0 | −0.0395853 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 302124. | 0.177127 | 0.0885634 | − | 0.996071i | \(-0.471772\pi\) | ||||
0.0885634 | + | 0.996071i | \(0.471772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.09455e6i | 1.20846i | 0.796812 | + | 0.604228i | \(0.206518\pi\) | ||||
−0.796812 | + | 0.604228i | \(0.793482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.07624e6i | − 0.601534i | −0.953698 | − | 0.300767i | \(-0.902757\pi\) | ||||
0.953698 | − | 0.300767i | \(-0.0972426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.89121e6 | 1.59075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 422840. | 0.229041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.91801e6i | 1.02293i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 706541.i | − 0.365400i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −266280. | −0.135628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −313002. | −0.157028 | −0.0785141 | − | 0.996913i | \(-0.525018\pi\) | ||||
−0.0785141 | + | 0.996913i | \(0.525018\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.99993e6i | 1.48252i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.55400e6i | − 0.745378i | −0.927956 | − | 0.372689i | \(-0.878436\pi\) | ||||
0.927956 | − | 0.372689i | \(-0.121564\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.37138e6 | 0.648124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.29232e6 | −1.53326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.40138e6i | 0.643163i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.22208e6i | − 0.990684i | −0.868698 | − | 0.495342i | \(-0.835043\pi\) | ||||
0.868698 | − | 0.495342i | \(-0.164957\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 774570. | 0.340406 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −411830. | −0.178423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.26217e6i | − 0.966249i | −0.875552 | − | 0.483125i | \(-0.839502\pi\) | ||||
0.875552 | − | 0.483125i | \(-0.160498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 196560.i | 0.0816253i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −869601. | −0.356110 | −0.178055 | − | 0.984021i | \(-0.556980\pi\) | ||||
−0.178055 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.98886e6 | 2.01481 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.26918e6i | − 0.903863i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.25361e6i | − 0.485844i | −0.970046 | − | 0.242922i | \(-0.921894\pi\) | ||||
0.970046 | − | 0.242922i | \(-0.0781059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −883050. | −0.337613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 803712. | 0.303156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 175206.i | 0.0652044i | 0.999468 | + | 0.0326022i | \(0.0103794\pi\) | ||||
−0.999468 | + | 0.0326022i | \(0.989621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 585460.i | − 0.212150i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −796945. | −0.284990 | −0.142495 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142495 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 393880. | 0.139012 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.36129e6i | 1.17087i | 0.810719 | + | 0.585436i | \(0.199077\pi\) | ||||
−0.810719 | + | 0.585436i | \(0.800923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.52283e6i | − 0.856271i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.51959e6 | 1.84941 | 0.924705 | − | 0.380685i | \(-0.124312\pi\) | ||||
0.924705 | + | 0.380685i | \(0.124312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.87258e6 | −0.950232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.11432e6i | 0.363939i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.74738e6i | 0.556430i | 0.960519 | + | 0.278215i | \(0.0897428\pi\) | ||||
−0.960519 | + | 0.278215i | \(0.910257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 765018. | 0.240569 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 541122. | 0.168048 | 0.0840242 | − | 0.996464i | \(-0.473223\pi\) | ||||
0.0840242 | + | 0.996464i | \(0.473223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 666684.i | 0.204483i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06549e7i | 3.18834i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.79699e6 | −1.12236 | −0.561179 | − | 0.827694i | \(-0.689652\pi\) | ||||
−0.561179 | + | 0.827694i | \(0.689652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −631203. | −0.184317 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 872480.i | − 0.251698i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.71696e6i | 0.483526i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.88108e6 | −1.07998 | −0.539992 | − | 0.841670i | \(-0.681573\pi\) | ||||
−0.539992 | + | 0.841670i | \(0.681573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.66081e6 | −1.83156 | −0.915781 | − | 0.401677i | \(-0.868427\pi\) | ||||
−0.915781 | + | 0.401677i | \(0.868427\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.22097e6i | 0.331784i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.86517e6i | − 0.495051i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −665760. | −0.174652 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.65337e6 | 1.20663 | 0.603315 | − | 0.797503i | \(-0.293846\pi\) | ||||
0.603315 | + | 0.797503i | \(0.293846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 6.23873e6i | − 1.59910i | −0.600597 | − | 0.799552i | \(-0.705070\pi\) | ||||
0.600597 | − | 0.799552i | \(-0.294930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.11802e7i | 2.80056i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.75743e6 | −1.17818 | −0.589089 | − | 0.808068i | \(-0.700513\pi\) | ||||
−0.589089 | + | 0.808068i | \(0.700513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.01394e6 | 0.737969 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.77073e6i | − 1.39708i | −0.715570 | − | 0.698541i | \(-0.753833\pi\) | ||||
0.715570 | − | 0.698541i | \(-0.246167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.61600e6i | − 0.619254i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.22765e6 | 0.989654 | 0.494827 | − | 0.868991i | \(-0.335231\pi\) | ||||
0.494827 | + | 0.868991i | \(0.335231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.13635e6 | −0.726077 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.09096e6i | 0.249783i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 4.31374e6i | − 0.966192i | −0.875567 | − | 0.483096i | \(-0.839512\pi\) | ||||
0.875567 | − | 0.483096i | \(-0.160488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.98017e6 | 0.438703 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.94820e6 | −1.30357 | −0.651784 | − | 0.758405i | \(-0.725979\pi\) | ||||
−0.651784 | + | 0.758405i | \(0.725979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.39722e6i | − 1.82047i | −0.414094 | − | 0.910234i | \(-0.635902\pi\) | ||||
0.414094 | − | 0.910234i | \(-0.364098\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.30976e6i | 1.12663i | 0.826241 | + | 0.563317i | \(0.190475\pi\) | ||||
−0.826241 | + | 0.563317i | \(0.809525\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −716520. | −0.150417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.13436e6 | −0.235613 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8.96040e6i | − 1.84151i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.68526e6i | − 0.741605i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.83653e6 | 1.16229 | 0.581147 | − | 0.813799i | \(-0.302604\pi\) | ||||
0.581147 | + | 0.813799i | \(0.302604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.15759e6 | 0.425212 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.14576e6i | 0.223473i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.75327e6i | − 1.67243i | −0.548402 | − | 0.836215i | \(-0.684764\pi\) | ||||
0.548402 | − | 0.836215i | \(-0.315236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.94676e6 | −0.557279 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.16834e6 | 0.967492 | 0.483746 | − | 0.875209i | \(-0.339276\pi\) | ||||
0.483746 | + | 0.875209i | \(0.339276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.81502e6i | 0.521632i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.01208e6i | − 0.365388i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.36171e6 | −0.963943 | −0.481972 | − | 0.876187i | \(-0.660079\pi\) | ||||
−0.481972 | + | 0.876187i | \(0.660079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.85524e6 | −0.686210 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.26635e6i | 0.928089i | 0.885812 | + | 0.464045i | \(0.153602\pi\) | ||||
−0.885812 | + | 0.464045i | \(0.846398\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.21345e6i | − 0.382428i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.46847e6 | −0.935559 | −0.467780 | − | 0.883845i | \(-0.654946\pi\) | ||||
−0.467780 | + | 0.883845i | \(0.654946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.16285e6 | −0.197002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 7.70688e6i | − 1.29296i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.33656e6i | 0.713541i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.73836e6 | 0.609203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.05762e6 | −0.493503 | −0.246751 | − | 0.969079i | \(-0.579363\pi\) | ||||
−0.246751 | + | 0.969079i | \(0.579363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.64117e6i | 1.54126i | 0.637284 | + | 0.770629i | \(0.280058\pi\) | ||||
−0.637284 | + | 0.770629i | \(0.719942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.20556e6i | − 0.502780i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.03080e7 | −1.60153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00058e6 | −0.615726 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 635100.i | 0.0968332i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.33584e6i | − 0.199903i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.07047e7 | 1.58709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.15820e6 | −0.610819 | −0.305409 | − | 0.952221i | \(-0.598793\pi\) | ||||
−0.305409 | + | 0.952221i | \(0.598793\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 616884.i | 0.0897851i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.32628e6i | 0.761125i | 0.924755 | + | 0.380562i | \(0.124270\pi\) | ||||
−0.924755 | + | 0.380562i | \(0.875730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.55239e6 | −1.21103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09562e7 | 1.53737 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 384160.i | − 0.0534194i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 999102.i | − 0.136449i | −0.997670 | − | 0.0682247i | \(-0.978267\pi\) | ||||
0.997670 | − | 0.0682247i | \(-0.0217335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.81445e6 | −0.245593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.20112e6 | 0.429432 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.31886e6i | − 0.707208i | −0.935395 | − | 0.353604i | \(-0.884956\pi\) | ||||
0.935395 | − | 0.353604i | \(-0.115044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.39408e6i | 0.182108i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.56759e6 | −0.850404 | −0.425202 | − | 0.905099i | \(-0.639797\pi\) | ||||
−0.425202 | + | 0.905099i | \(0.639797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 164173. | 0.0210723 | 0.0105361 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105361 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.94264e6i | 0.247176i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9.27762e6i | − 1.16010i | −0.814579 | − | 0.580052i | \(-0.803032\pi\) | ||||
0.814579 | − | 0.580052i | \(-0.196968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 78639.5 | 0.00974865 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.37220e6 | −0.537353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.30890e7i | − 1.59491i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.44474e6i | − 0.652202i | −0.945335 | − | 0.326101i | \(-0.894265\pi\) | ||||
0.945335 | − | 0.326101i | \(-0.105735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.24762e7 | −1.48181 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.39611e6 | 0.282187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.50978e7i | − 1.76310i | −0.472094 | − | 0.881548i | \(-0.656502\pi\) | ||||
0.472094 | − | 0.881548i | \(-0.343498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.85216e6i | − 0.557185i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.98593e6 | −0.795531 | −0.397765 | − | 0.917487i | \(-0.630214\pi\) | ||||
−0.397765 | + | 0.917487i | \(0.630214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.16941e6 | 0.696719 | 0.348359 | − | 0.937361i | \(-0.386739\pi\) | ||||
0.348359 | + | 0.937361i | \(0.386739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.28546e6i | 0.367962i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00769e7i | 1.11009i | 0.831822 | + | 0.555043i | \(0.187298\pi\) | ||||
−0.831822 | + | 0.555043i | \(0.812702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.12280e6 | 0.122676 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 878139. | 0.0951613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.26885e6i | 0.566324i | 0.959072 | + | 0.283162i | \(0.0913834\pi\) | ||||
−0.959072 | + | 0.283162i | \(0.908617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.38112e7i | 1.46056i | 0.683148 | + | 0.730280i | \(0.260610\pi\) | ||||
−0.683148 | + | 0.730280i | \(0.739390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.20903e6 | −0.336625 | −0.168313 | − | 0.985734i | \(-0.553832\pi\) | ||||
−0.168313 | + | 0.985734i | \(0.553832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15425e7 | 1.20108 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.35339e6i | − 0.139702i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.24589e7i | − 1.26564i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.03742e7 | −1.04551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.07204e6 | −0.607102 | −0.303551 | − | 0.952815i | \(-0.598172\pi\) | ||||
−0.303551 | + | 0.952815i | \(0.598172\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 5.46776e6i | − 0.542376i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.16766e6i | − 0.211662i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.22600e6 | −0.893843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.02767e6 | −0.194918 | −0.0974591 | − | 0.995240i | \(-0.531072\pi\) | ||||
−0.0974591 | + | 0.995240i | \(0.531072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.19769e7i | − 1.14240i | −0.820811 | − | 0.571199i | \(-0.806478\pi\) | ||||
0.820811 | − | 0.571199i | \(-0.193522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.44768e6i | 0.135961i | 0.997687 | + | 0.0679803i | \(0.0216555\pi\) | ||||
−0.997687 | + | 0.0679803i | \(0.978344\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.42090e7 | −1.32419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.27857e6 | −0.118242 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.82477e6i | 0.442785i | 0.975185 | + | 0.221393i | \(0.0710603\pi\) | ||||
−0.975185 | + | 0.221393i | \(0.928940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.33200e6i | 0.481922i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.37616e6 | −0.392536 | −0.196268 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196268 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.34953e6 | −0.654268 | −0.327134 | − | 0.944978i | \(-0.606083\pi\) | ||||
−0.327134 | + | 0.944978i | \(0.606083\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 648216.i | − 0.0572712i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.64089e7i | 1.42812i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.04588e6 | 0.349500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.03757e7 | −2.60447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1.75692e7i | − 1.49525i | −0.664119 | − | 0.747626i | \(-0.731193\pi\) | ||||
0.664119 | − | 0.747626i | \(-0.268807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.60338e6i | − 0.469871i | −0.972011 | − | 0.234935i | \(-0.924512\pi\) | ||||
0.972011 | − | 0.234935i | \(-0.0754879\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.96099e6 | 0.246469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.20132e6 | −0.512409 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.05809e6i | 0.414892i | 0.978246 | + | 0.207446i | \(0.0665152\pi\) | ||||
−0.978246 | + | 0.207446i | \(0.933485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 6.40431e6i | − 0.517703i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65048e6 | −0.212705 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.47421e7 | 1.17453 | 0.587267 | − | 0.809393i | \(-0.300204\pi\) | ||||
0.587267 | + | 0.809393i | \(0.300204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.47976e6i | 0.512538i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3.05370e6i | − 0.238092i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.46720e6 | −0.345814 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.83317e6 | −0.678925 | −0.339462 | − | 0.940620i | \(-0.610245\pi\) | ||||
−0.339462 | + | 0.940620i | \(0.610245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.03766e7i | 3.08135i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.89475e6i | 0.142562i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.93101e6 | 0.144268 | 0.0721338 | − | 0.997395i | \(-0.477019\pi\) | ||||
0.0721338 | + | 0.997395i | \(0.477019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.76149e6 | −0.130679 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.86854e7i | − 1.37650i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.55088e6i | 0.548529i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.22373e6 | 0.521122 | 0.260561 | − | 0.965457i | \(-0.416093\pi\) | ||||
0.260561 | + | 0.965457i | \(0.416093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 465080. | 0.0333188 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.55771e6i | − 0.181973i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 9.81106e6i | − 0.688462i | −0.938885 | − | 0.344231i | \(-0.888140\pi\) | ||||
0.938885 | − | 0.344231i | \(-0.111860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05715e6 | 0.143366 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.72428e6 | 0.603860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.40813e7i | − 1.65547i | −0.561122 | − | 0.827733i | \(-0.689630\pi\) | ||||
0.561122 | − | 0.827733i | \(-0.310370\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.16690e7i | 0.791346i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.40518e7 | 1.62008 | 0.810040 | − | 0.586374i | \(-0.199445\pi\) | ||||
0.810040 | + | 0.586374i | \(0.199445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.52288e6 | −0.168792 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.70160e6i | − 0.312445i | −0.987722 | − | 0.156223i | \(-0.950068\pi\) | ||||
0.987722 | − | 0.156223i | \(-0.0499317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.00479e7i | 1.31452i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.95988e6 | −0.192783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.31282e7 | 1.49638 | 0.748189 | − | 0.663485i | \(-0.230923\pi\) | ||||
0.748189 | + | 0.663485i | \(0.230923\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.06040e6i | 0.582318i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.26635e7i | 0.803181i | 0.915819 | + | 0.401591i | \(0.131542\pi\) | ||||
−0.915819 | + | 0.401591i | \(0.868458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.86595e7 | 1.17570 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.33524e6 | −0.271363 | −0.135682 | − | 0.990752i | \(-0.543322\pi\) | ||||
−0.135682 | + | 0.990752i | \(0.543322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.94579e6i | 0.307556i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.87727e6i | 0.176600i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 364270. | 0.0222130 | 0.0111065 | − | 0.999938i | \(-0.496465\pi\) | ||||
0.0111065 | + | 0.999938i | \(0.496465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.24855e6 | 0.378567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.03051e6i | − 0.0620300i | −0.999519 | − | 0.0310150i | \(-0.990126\pi\) | ||||
0.999519 | − | 0.0310150i | \(-0.00987396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.13784e6i | 0.245879i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.18851e7 | −0.701713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.27682e7 | −1.92231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.13112e7i | − 0.659333i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.95300e7i | − 1.12400i | −0.827138 | − | 0.561999i | \(-0.810032\pi\) | ||||
0.827138 | − | 0.561999i | \(-0.189968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.30426e7 | −0.745885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.59965e6 | −0.545524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.15098e6i | 0.347345i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7.86344e6i | − 0.438497i | −0.975669 | − | 0.219249i | \(-0.929639\pi\) | ||||
0.975669 | − | 0.219249i | \(-0.0703605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.22229e6 | −0.233981 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.20571e6 | −0.341751 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.89378e7i | 1.03643i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4.93559e6i | − 0.266781i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.05014e7 | 0.564127 | 0.282064 | − | 0.959396i | \(-0.408981\pi\) | ||||
0.282064 | + | 0.959396i | \(0.408981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.87803e7 | −1.00265 | −0.501325 | − | 0.865259i | \(-0.667154\pi\) | ||||
−0.501325 | + | 0.865259i | \(0.667154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.55624e6i | − 0.188697i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.39552e7i | − 1.77972i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.31213e6 | 0.0683545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.00558e7 | 1.03844 | 0.519220 | − | 0.854641i | \(-0.326223\pi\) | ||||
0.519220 | + | 0.854641i | \(0.326223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.02444e7i | − 0.527212i | −0.964630 | − | 0.263606i | \(-0.915088\pi\) | ||||
0.964630 | − | 0.263606i | \(-0.0849119\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 827524.i | 0.0420743i | 0.999779 | + | 0.0210371i | \(0.00669682\pi\) | ||||
−0.999779 | + | 0.0210371i | \(0.993303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.80328e7 | 1.92208 | 0.961041 | − | 0.276407i | \(-0.0891436\pi\) | ||||
0.961041 | + | 0.276407i | \(0.0891436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.44607e6 | −0.122876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.04226e7i | 0.520431i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.28805e7i | 0.635504i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.57628e7 | −1.75399 | −0.876993 | − | 0.480503i | \(-0.840454\pi\) | ||||
−0.876993 | + | 0.480503i | \(0.840454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.43105e6 | −0.216031 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 9.83373e6i | − 0.476595i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.58843e7i | 0.760779i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.10779e7 | 0.527457 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.04714e7 | −2.86237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 970214.i | 0.0456557i | 0.999739 | + | 0.0228278i | \(0.00726696\pi\) | ||||
−0.999739 | + | 0.0228278i | \(0.992733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.86468e6i | − 0.0867267i | −0.999059 | − | 0.0433633i | \(-0.986193\pi\) | ||||
0.999059 | − | 0.0433633i | \(-0.0138073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.05785e6 | 0.0489147 | 0.0244573 | − | 0.999701i | \(-0.492214\pi\) | ||||
0.0244573 | + | 0.999701i | \(0.492214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.21800e6 | −0.0559937 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 8.24333e6i | − 0.376769i | −0.982095 | − | 0.188385i | \(-0.939675\pi\) | ||||
0.982095 | − | 0.188385i | \(-0.0603252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5.86320e6i | − 0.264903i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.25632e6 | −0.281041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.36294e6 | 0.105538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.35770e7i | − 0.602934i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.40362e7i | 1.05528i | 0.849468 | + | 0.527640i | \(0.176923\pi\) | ||||
−0.849468 | + | 0.527640i | \(0.823077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.82263e6 | 0.428801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.68605e7 | 1.60000 | 0.800002 | − | 0.599997i | \(-0.204831\pi\) | ||||
0.800002 | + | 0.599997i | \(0.204831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.67403e7i | − 0.722541i | −0.932461 | − | 0.361271i | \(-0.882343\pi\) | ||||
0.932461 | − | 0.361271i | \(-0.117657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 9.25364e6i | − 0.394915i | −0.980311 | − | 0.197457i | \(-0.936732\pi\) | ||||
0.980311 | − | 0.197457i | \(-0.0632684\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.75716e6 | −0.117006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.27035e7 | 0.958075 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.64333e7i | 0.689597i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.77848e6i | − 0.156796i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.83110e7 | −0.755635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.27441e7 | 0.522995 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.47977e6i | − 0.142014i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.03030e7i | − 0.415859i | −0.978144 | − | 0.207929i | \(-0.933328\pi\) | ||||
0.978144 | − | 0.207929i | \(-0.0666724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.68799e6 | 0.348746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.82374e7 | 1.52649 | 0.763243 | − | 0.646111i | \(-0.223606\pi\) | ||||
0.763243 | + | 0.646111i | \(0.223606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.12044e7i | 2.82703i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7.80024e6i | − 0.306327i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.72150e6 | 0.301587 | 0.150794 | − | 0.988565i | \(-0.451817\pi\) | ||||
0.150794 | + | 0.988565i | \(0.451817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.64697e7 | 0.639790 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.63545e6i | 0.256369i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.13253e6i | − 0.0815073i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.39039e6 | −0.128888 | −0.0644438 | − | 0.997921i | \(-0.520527\pi\) | ||||
−0.0644438 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.05651e7 | 1.53383 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.91080e6i | − 0.0718640i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.67490e6i | 0.285577i | 0.989753 | + | 0.142789i | \(0.0456069\pi\) | ||||
−0.989753 | + | 0.142789i | \(0.954393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.32471e7 | 0.490295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.55115e7 | 1.67551 | 0.837756 | − | 0.546045i | \(-0.183867\pi\) | ||||
0.837756 | + | 0.546045i | \(0.183867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.78001e7i | − 0.651845i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.28294e7i | 0.827218i | 0.910455 | + | 0.413609i | \(0.135732\pi\) | ||||
−0.910455 | + | 0.413609i | \(0.864268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.83484e6 | 0.138223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.80673e6 | −0.244055 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.64478e7i | 1.65666i | 0.560241 | + | 0.828330i | \(0.310709\pi\) | ||||
−0.560241 | + | 0.828330i | \(0.689291\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.82856e7i | − 0.645401i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.41842e6 | 0.155139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.77779e6 | −0.271674 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.35719e7i | 0.471603i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.63000e7i | 0.904460i | 0.891901 | + | 0.452230i | \(0.149371\pi\) | ||||
−0.891901 | + | 0.452230i | \(0.850629\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.21306e7 | 0.415022 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.19967e7 | 0.748704 | 0.374352 | − | 0.927287i | \(-0.377865\pi\) | ||||
0.374352 | + | 0.927287i | \(0.377865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.20187e7i | − 0.406983i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 4.46750e7i | − 1.49737i | −0.662929 | − | 0.748683i | \(-0.730687\pi\) | ||||
0.662929 | − | 0.748683i | \(-0.269313\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.20409e7 | −0.734977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.26779e7 | 0.752369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.02740e7i | 0.669201i | 0.942360 | + | 0.334600i | \(0.108601\pi\) | ||||
−0.942360 | + | 0.334600i | \(0.891399\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.68410e6i | 0.0550270i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.08542e7 | 1.65324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.49135e7 | −0.482386 | −0.241193 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241193 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.97960e6i | 0.0637095i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.17032e7i | − 1.01010i | −0.863089 | − | 0.505052i | \(-0.831473\pi\) | ||||
0.863089 | − | 0.505052i | \(-0.168527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.16851e7 | 1.32150 |
(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 | 800.6.c.i.449.2 | 4 | ||
4.3 | odd | 2 | inner | 800.6.c.i.449.3 | 4 | ||
5.2 | odd | 4 | 160.6.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 800.6.a.h.1.2 | 2 | |||
5.4 | even | 2 | inner | 800.6.c.i.449.4 | 4 | ||
20.3 | even | 4 | 800.6.a.h.1.1 | 2 | |||
20.7 | even | 4 | 160.6.a.d.1.2 | yes | 2 | ||
20.19 | odd | 2 | inner | 800.6.c.i.449.1 | 4 | ||
40.27 | even | 4 | 320.6.a.s.1.1 | 2 | |||
40.37 | odd | 4 | 320.6.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
160.6.a.d.1.2 | yes | 2 | 20.7 | even | 4 | ||
320.6.a.s.1.1 | 2 | 40.27 | even | 4 | |||
320.6.a.s.1.2 | 2 | 40.37 | odd | 4 | |||
800.6.a.h.1.1 | 2 | 20.3 | even | 4 | |||
800.6.a.h.1.2 | 2 | 5.3 | odd | 4 | |||
800.6.c.i.449.1 | 4 | 20.19 | odd | 2 | inner | ||
800.6.c.i.449.2 | 4 | 1.1 | even | 1 | trivial | ||
800.6.c.i.449.3 | 4 | 4.3 | odd | 2 | inner | ||
800.6.c.i.449.4 | 4 | 5.4 | even | 2 | inner |