Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.a (trivial) |
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: | yes |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 8.00000 | 0.513200 | 0.256600 | − | 0.966518i | \(-0.417398\pi\) | ||||
0.256600 | + | 0.966518i | \(0.417398\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 108.000 | 0.833065 | 0.416532 | − | 0.909121i | \(-0.363245\pi\) | ||||
0.416532 | + | 0.909121i | \(0.363245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −179.000 | −0.736626 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 604.000 | 1.50506 | 0.752532 | − | 0.658555i | \(-0.228832\pi\) | ||||
0.752532 | + | 0.658555i | \(0.228832\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −306.000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 200.000 | 0.229510 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 930.000 | 0.780478 | 0.390239 | − | 0.920714i | \(-0.372392\pi\) | ||||
0.390239 | + | 0.920714i | \(0.372392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1324.00 | 0.841403 | 0.420701 | − | 0.907199i | \(-0.361784\pi\) | ||||
0.420701 | + | 0.907199i | \(0.361784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 864.000 | 0.427529 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 852.000 | 0.335830 | 0.167915 | − | 0.985801i | \(-0.446297\pi\) | ||||
0.167915 | + | 0.985801i | \(0.446297\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3376.00 | −0.891237 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5902.00 | 1.30318 | 0.651590 | − | 0.758572i | \(-0.274102\pi\) | ||||
0.651590 | + | 0.758572i | \(0.274102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3320.00 | 0.620489 | 0.310244 | − | 0.950657i | \(-0.399589\pi\) | ||||
0.310244 | + | 0.950657i | \(0.399589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4832.00 | 0.772400 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2700.00 | 0.372558 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10774.0 | 1.29382 | 0.646908 | − | 0.762568i | \(-0.276062\pi\) | ||||
0.646908 | + | 0.762568i | \(0.276062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2448.00 | −0.257721 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17958.0 | −1.66839 | −0.834196 | − | 0.551467i | \(-0.814068\pi\) | ||||
−0.834196 | + | 0.551467i | \(0.814068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9264.00 | −0.764060 | −0.382030 | − | 0.924150i | \(-0.624775\pi\) | ||||
−0.382030 | + | 0.924150i | \(0.624775\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4475.00 | −0.329429 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9796.00 | 0.646851 | 0.323425 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323425 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5143.00 | −0.306003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7440.00 | 0.400541 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31434.0 | −1.53713 | −0.768564 | − | 0.639773i | \(-0.779028\pi\) | ||||
−0.768564 | + | 0.639773i | \(0.779028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15100.0 | 0.673085 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10592.0 | 0.431808 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −33228.0 | −1.24272 | −0.621361 | − | 0.783524i | \(-0.713420\pi\) | ||||
−0.621361 | + | 0.783524i | \(0.713420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40210.0 | −1.38360 | −0.691798 | − | 0.722091i | \(-0.743181\pi\) | ||||
−0.691798 | + | 0.722091i | \(0.743181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19332.0 | −0.613657 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7650.00 | −0.224584 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −58864.0 | −1.60200 | −0.801000 | − | 0.598664i | \(-0.795699\pi\) | ||||
−0.801000 | + | 0.598664i | \(0.795699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6816.00 | 0.172348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 55312.0 | 1.30219 | 0.651094 | − | 0.758997i | \(-0.274310\pi\) | ||||
0.651094 | + | 0.758997i | \(0.274310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27258.0 | 0.598669 | 0.299335 | − | 0.954148i | \(-0.403235\pi\) | ||||
0.299335 | + | 0.954148i | \(0.403235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5000.00 | 0.102640 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 65232.0 | 1.25382 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31456.0 | −0.567069 | −0.283534 | − | 0.958962i | \(-0.591507\pi\) | ||||
−0.283534 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16489.0 | 0.279243 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −24552.0 | −0.391194 | −0.195597 | − | 0.980684i | \(-0.562664\pi\) | ||||
−0.195597 | + | 0.980684i | \(0.562664\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23250.0 | 0.349040 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 47216.0 | 0.668792 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −90854.0 | −1.21582 | −0.607910 | − | 0.794006i | \(-0.707992\pi\) | ||||
−0.607910 | + | 0.794006i | \(0.707992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −33048.0 | −0.418352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26560.0 | 0.318435 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 33100.0 | 0.376287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 154706. | 1.66947 | 0.834733 | − | 0.550654i | \(-0.185622\pi\) | ||||
0.834733 | + | 0.550654i | \(0.185622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108116. | −1.10867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −72714.0 | −0.709275 | −0.354637 | − | 0.935004i | \(-0.615396\pi\) | ||||
−0.354637 | + | 0.935004i | \(0.615396\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 129396. | 1.20179 | 0.600894 | − | 0.799329i | \(-0.294811\pi\) | ||||
0.600894 | + | 0.799329i | \(0.294811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21600.0 | 0.191197 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 206680. | 1.74518 | 0.872588 | − | 0.488458i | \(-0.162440\pi\) | ||||
0.872588 | + | 0.488458i | \(0.162440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −70146.0 | −0.565505 | −0.282753 | − | 0.959193i | \(-0.591248\pi\) | ||||
−0.282753 | + | 0.959193i | \(0.591248\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86192.0 | 0.663987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −151854. | −1.11874 | −0.559371 | − | 0.828917i | \(-0.688957\pi\) | ||||
−0.559371 | + | 0.828917i | \(0.688957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21300.0 | 0.150188 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54774.0 | 0.369922 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 100440. | 0.650189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 203765. | 1.26522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −143664. | −0.856220 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 336596. | 1.85182 | 0.925912 | − | 0.377740i | \(-0.123299\pi\) | ||||
0.925912 | + | 0.377740i | \(0.123299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −74112.0 | −0.392116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −275308. | −1.40165 | −0.700827 | − | 0.713332i | \(-0.747185\pi\) | ||||
−0.700827 | + | 0.713332i | \(0.747185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 142992. | 0.700943 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −84400.0 | −0.398573 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −228502. | −1.04013 | −0.520066 | − | 0.854126i | \(-0.674093\pi\) | ||||
−0.520066 | + | 0.854126i | \(0.674093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −224284. | −0.984603 | −0.492302 | − | 0.870425i | \(-0.663844\pi\) | ||||
−0.492302 | + | 0.870425i | \(0.663844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 78368.0 | 0.331964 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −184824. | −0.755820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 147550. | 0.582800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41144.0 | −0.157041 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −183802. | −0.678242 | −0.339121 | − | 0.940743i | \(-0.610130\pi\) | ||||
−0.339121 | + | 0.940743i | \(0.610130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −296032. | −1.05657 | −0.528283 | − | 0.849069i | \(-0.677164\pi\) | ||||
−0.528283 | + | 0.849069i | \(0.677164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −166470. | −0.574920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 83000.0 | 0.277491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 134766. | 0.436346 | 0.218173 | − | 0.975910i | \(-0.429990\pi\) | ||||
0.218173 | + | 0.975910i | \(0.429990\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −251472. | −0.788854 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 92016.0 | 0.279768 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 60248.0 | 0.177613 | 0.0888063 | − | 0.996049i | \(-0.471695\pi\) | ||||
0.0888063 | + | 0.996049i | \(0.471695\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 120800. | 0.345428 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 62012.0 | 0.172062 | 0.0860309 | − | 0.996292i | \(-0.472582\pi\) | ||||
0.0860309 | + | 0.996292i | \(0.472582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −277657. | −0.747811 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −236996. | −0.619799 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −591682. | −1.50305 | −0.751524 | − | 0.659705i | \(-0.770681\pi\) | ||||
−0.751524 | + | 0.659705i | \(0.770681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 67500.0 | 0.166613 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −265824. | −0.637766 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 241404. | 0.563134 | 0.281567 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281567 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 187622. | 0.425684 | 0.212842 | − | 0.977087i | \(-0.431728\pi\) | ||||
0.212842 | + | 0.977087i | \(0.431728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −321680. | −0.710062 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 269350. | 0.578612 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 561720. | 1.17467 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −364608. | −0.742458 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −37560.0 | −0.0744976 | −0.0372488 | − | 0.999306i | \(-0.511859\pi\) | ||||
−0.0372488 | + | 0.999306i | \(0.511859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 164434. | 0.317759 | 0.158880 | − | 0.987298i | \(-0.449212\pi\) | ||||
0.158880 | + | 0.987298i | \(0.449212\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −61200.0 | −0.115256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 360518. | 0.661853 | 0.330926 | − | 0.943657i | \(-0.392639\pi\) | ||||
0.330926 | + | 0.943657i | \(0.392639\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 654168. | 1.17100 | 0.585500 | − | 0.810673i | \(-0.300898\pi\) | ||||
0.585500 | + | 0.810673i | \(0.300898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −470912. | −0.822147 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 637416. | 1.08563 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −448950. | −0.746128 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −152508. | −0.247381 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 799696. | 1.26637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 693156. | 1.07183 | 0.535914 | − | 0.844273i | \(-0.319967\pi\) | ||||
0.535914 | + | 0.844273i | \(0.319967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 442496. | 0.668283 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −231600. | −0.341698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 358560. | 0.516907 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 218064. | 0.307237 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −284580. | −0.391944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −494756. | −0.666237 | −0.333119 | − | 0.942885i | \(-0.608101\pi\) | ||||
−0.333119 | + | 0.942885i | \(0.608101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −111875. | −0.147325 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −907088. | −1.16838 | −0.584191 | − | 0.811616i | \(-0.698588\pi\) | ||||
−0.584191 | + | 0.811616i | \(0.698588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.08949e6 | 1.37289 | 0.686446 | − | 0.727181i | \(-0.259170\pi\) | ||||
0.686446 | + | 0.727181i | \(0.259170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 521856. | 0.643459 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 499706. | 0.603010 | 0.301505 | − | 0.953465i | \(-0.402511\pi\) | ||||
0.301505 | + | 0.953465i | \(0.402511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 244900. | 0.289280 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −251648. | −0.291020 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.62038e6 | −1.83495 | −0.917473 | − | 0.397799i | \(-0.869774\pi\) | ||||
−0.917473 | + | 0.397799i | \(0.869774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00122e6 | 1.11042 | 0.555208 | − | 0.831711i | \(-0.312638\pi\) | ||||
0.555208 | + | 0.831711i | \(0.312638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 952280. | 1.03454 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −128575. | −0.136849 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −405144. | −0.422539 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −196416. | −0.200761 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −368980. | −0.369674 | −0.184837 | − | 0.982769i | \(-0.559176\pi\) | ||||
−0.184837 | + | 0.982769i | \(0.559176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 514608. | 0.505447 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 186000. | 0.179128 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 279010. | 0.263504 | 0.131752 | − | 0.991283i | \(-0.457940\pi\) | ||||
0.131752 | + | 0.991283i | \(0.457940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16359e6 | 1.07783 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05646e6 | −0.959955 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −811740. | −0.723648 | −0.361824 | − | 0.932246i | \(-0.617846\pi\) | ||||
−0.361824 | + | 0.932246i | \(0.617846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −785850. | −0.687424 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −726832. | −0.623959 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 353214. | 0.297617 | 0.148808 | − | 0.988866i | \(-0.452456\pi\) | ||||
0.148808 | + | 0.988866i | \(0.452456\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.71622e6 | 1.41954 | 0.709772 | − | 0.704432i | \(-0.248798\pi\) | ||||
0.709772 | + | 0.704432i | \(0.248798\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −264384. | −0.214698 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 377500. | 0.301013 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −245882. | −0.192543 | −0.0962714 | − | 0.995355i | \(-0.530692\pi\) | ||||
−0.0962714 | + | 0.995355i | \(0.530692\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −594280. | −0.457068 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.67618e6 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718250\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.25882e6 | 0.934321 | 0.467161 | − | 0.884173i | \(-0.345277\pi\) | ||||
0.467161 | + | 0.884173i | \(0.345277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 264800. | 0.193110 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.93946e6 | −1.38988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −554957. | −0.390854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.23765e6 | 0.856771 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 719158. | 0.489390 | 0.244695 | − | 0.969600i | \(-0.421312\pi\) | ||||
0.244695 | + | 0.969600i | \(0.421312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −830700. | −0.555762 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.03910e6 | −1.34137 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −260712. | −0.168649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00051e6 | −0.636511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −581712. | −0.364000 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00525e6 | −0.618763 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.86013e6 | −1.12641 | −0.563206 | − | 0.826317i | \(-0.690432\pi\) | ||||
−0.563206 | + | 0.826317i | \(0.690432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.03517e6 | 0.616758 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −278384. | −0.163209 | −0.0816043 | − | 0.996665i | \(-0.526004\pi\) | ||||
−0.0816043 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −474182. | −0.273580 | −0.136790 | − | 0.990600i | \(-0.543679\pi\) | ||||
−0.136790 | + | 0.990600i | \(0.543679\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −483300. | −0.274436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.83738e6 | −1.02695 | −0.513476 | − | 0.858104i | \(-0.671643\pi\) | ||||
−0.513476 | + | 0.858104i | \(0.671643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.56481e6 | 1.96137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65344e6 | 0.895624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23132e6 | 0.656696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −191250. | −0.100437 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −561168. | −0.290217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.05797e6 | 0.538868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.99743e6 | −1.50376 | −0.751880 | − | 0.659299i | \(-0.770853\pi\) | ||||
−0.751880 | + | 0.659299i | \(0.770853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.92855e6 | −0.953058 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.47160e6 | −0.716437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.87531e6 | 0.899496 | 0.449748 | − | 0.893155i | \(-0.351514\pi\) | ||||
0.449748 | + | 0.893155i | \(0.351514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.21483e6 | −0.574139 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00528e6 | 0.933876 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.37060e6 | −1.08799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 170400. | 0.0770765 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −180312. | −0.0803898 | −0.0401949 | − | 0.999192i | \(-0.512798\pi\) | ||||
−0.0401949 | + | 0.999192i | \(0.512798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −87058.0 | −0.0382600 | −0.0191300 | − | 0.999817i | \(-0.506090\pi\) | ||||
−0.0191300 | + | 0.999817i | \(0.506090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.03306e6 | 0.447565 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.65901e6 | 1.13575 | 0.567876 | − | 0.823114i | \(-0.307765\pi\) | ||||
0.567876 | + | 0.823114i | \(0.307765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.38280e6 | 0.582356 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 803520. | 0.333677 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.14937e6 | 0.880186 | 0.440093 | − | 0.897952i | \(-0.354945\pi\) | ||||
0.440093 | + | 0.897952i | \(0.354945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −723123. | −0.292041 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.63012e6 | 0.649311 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 681450. | 0.267733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.08258e6 | 1.19467 | 0.597337 | − | 0.801991i | \(-0.296226\pi\) | ||||
0.597337 | + | 0.801991i | \(0.296226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.21448e6 | 1.22898 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.39487e6 | −1.28053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28727e6 | 0.851227 | 0.425613 | − | 0.904905i | \(-0.360058\pi\) | ||||
0.425613 | + | 0.904905i | \(0.360058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 125000. | 0.0459020 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.80601e6 | −0.654436 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30154e6 | 0.465435 | 0.232718 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232718 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.69277e6 | 0.950356 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.03276e6 | 0.708093 | 0.354046 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354046 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.63080e6 | 0.560724 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65826e6 | 0.562826 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 94230.0 | 0.0315730 | 0.0157865 | − | 0.999875i | \(-0.494975\pi\) | ||||
0.0157865 | + | 0.999875i | \(0.494975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 792360. | 0.262108 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.20246e6 | −0.719329 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −786400. | −0.253601 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.55551e6 | −1.76908 | −0.884540 | − | 0.466465i | \(-0.845527\pi\) | ||||
−0.884540 | + | 0.466465i | \(0.845527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.14394e6 | 0.359724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −784814. | −0.243728 | −0.121864 | − | 0.992547i | \(-0.538887\pi\) | ||||
−0.121864 | + | 0.992547i | \(0.538887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.01592e6 | −0.311600 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 412225. | 0.124881 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.50750e6 | 1.94728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59401e6 | −1.35795 | −0.678974 | − | 0.734162i | \(-0.737575\pi\) | ||||
−0.678974 | + | 0.734162i | \(0.737575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.82802e6 | −0.533796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.58862e6 | −1.03527 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −613800. | −0.174947 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.79427e6 | −0.505299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.41301e6 | −0.393198 | −0.196599 | − | 0.980484i | \(-0.562990\pi\) | ||||
−0.196599 | + | 0.980484i | \(0.562990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.94556e6 | 1.63489 | 0.817443 | − | 0.576010i | \(-0.195391\pi\) | ||||
0.817443 | + | 0.576010i | \(0.195391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.75348e6 | −0.476487 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 581250. | 0.156096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.34268e6 | −1.15263 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.47859e6 | −0.387887 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.48114e6 | 1.68058 | 0.840289 | − | 0.542139i | \(-0.182385\pi\) | ||||
0.840289 | + | 0.542139i | \(0.182385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.05597e6 | 1.03962 | 0.519810 | − | 0.854282i | \(-0.326003\pi\) | ||||
0.519810 | + | 0.854282i | \(0.326003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.18040e6 | 0.299093 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.12805e6 | 0.282569 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.21450e6 | 0.300772 | 0.150386 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150386 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 920597. | 0.225410 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.53154e6 | 1.33917 | 0.669586 | − | 0.742734i | \(-0.266472\pi\) | ||||
0.669586 | + | 0.742734i | \(0.266472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.27135e6 | −0.543731 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.47042e6 | −0.348074 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.20111e6 | 0.515258 | 0.257629 | − | 0.966244i | \(-0.417059\pi\) | ||||
0.257629 | + | 0.966244i | \(0.417059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.08466e7 | −2.51104 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.36826e6 | −0.542229 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −826200. | −0.187093 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.29835e6 | 0.738764 | 0.369382 | − | 0.929278i | \(-0.379569\pi\) | ||||
0.369382 | + | 0.929278i | \(0.379569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.13968e6 | −0.695591 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.94266e6 | −0.864046 | −0.432023 | − | 0.901863i | \(-0.642200\pi\) | ||||
−0.432023 | + | 0.901863i | \(0.642200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.82040e6 | −1.91221 | −0.956106 | − | 0.293021i | \(-0.905339\pi\) | ||||
−0.956106 | + | 0.293021i | \(0.905339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 664000. | 0.142408 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.28709e6 | 0.273096 | 0.136548 | − | 0.990633i | \(-0.456399\pi\) | ||||
0.136548 | + | 0.990633i | \(0.456399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.35731e6 | −1.33457 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.07813e6 | 0.223933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.59546e6 | −1.14996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 827500. | 0.168281 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.62669e6 | 1.13229 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.51179e6 | −1.29677 | −0.648383 | − | 0.761314i | \(-0.724555\pi\) | ||||
−0.648383 | + | 0.761314i | \(0.724555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.29684e6 | −0.649734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 736128. | 0.143577 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.86765e6 | 0.746608 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.79523e6 | 1.10726 | 0.553628 | − | 0.832764i | \(-0.313243\pi\) | ||||
0.553628 | + | 0.832764i | \(0.313243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 481984. | 0.0911508 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −990276. | −0.185376 | −0.0926878 | − | 0.995695i | \(-0.529546\pi\) | ||||
−0.0926878 | + | 0.995695i | \(0.529546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.48886e6 | 1.01710 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.70290e6 | −0.495812 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.97370e6 | 1.08481 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.91500e6 | −0.524067 | −0.262033 | − | 0.965059i | \(-0.584393\pi\) | ||||
−0.262033 | + | 0.965059i | \(0.584393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 496096. | 0.0883022 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.47872e6 | −0.436824 | −0.218412 | − | 0.975857i | \(-0.570088\pi\) | ||||
−0.218412 | + | 0.975857i | \(0.570088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.81785e6 | −0.317197 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.22126e6 | −0.383777 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.75807e6 | −1.15619 | −0.578093 | − | 0.815971i | \(-0.696203\pi\) | ||||
−0.578093 | + | 0.815971i | \(0.696203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.94386e6 | 0.498730 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.46982e6 | −0.749889 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.23490e6 | 0.537456 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.91678e6 | 0.973552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.73346e6 | −0.771365 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.33903e6 | −1.02312 | −0.511562 | − | 0.859246i | \(-0.670933\pi\) | ||||
−0.511562 | + | 0.859246i | \(0.670933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −231920. | −0.0370752 | −0.0185376 | − | 0.999828i | \(-0.505901\pi\) | ||||
−0.0185376 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 540000. | 0.0855058 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.08760e6 | 0.484278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.71044e6 | −0.887218 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.94781e6 | 0.915421 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.49515e6 | 0.837841 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.16700e6 | 0.780466 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.93123e6 | 0.289001 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.10637e6 | −0.460555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.44440e6 | −1.38733 | −0.693667 | − | 0.720295i | \(-0.744006\pi\) | ||||
−0.693667 | + | 0.720295i | \(0.744006\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.50098e6 | 0.218461 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.75365e6 | −0.252902 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.10162e6 | −0.443220 | −0.221610 | − | 0.975135i | \(-0.571131\pi\) | ||||
−0.221610 | + | 0.975135i | \(0.571131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.19759e6 | 1.01919 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.81425e6 | 1.09650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.39725e6 | −0.472405 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.15480e6 | 0.296944 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.22330e6 | −0.167068 | −0.0835342 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835342 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.83478e6 | 0.383699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.49376e6 | 0.602841 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.40896e7 | 1.87339 | 0.936693 | − | 0.350151i | \(-0.113870\pi\) | ||||
0.936693 | + | 0.350151i | \(0.113870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.79635e6 | −0.500317 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.78081e6 | 0.232627 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.48468e6 | 0.192244 | 0.0961220 | − | 0.995370i | \(-0.469356\pi\) | ||||
0.0961220 | + | 0.995370i | \(0.469356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.86470e6 | 0.367696 | 0.183848 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183848 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −300480. | −0.0382322 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 532500. | 0.0671661 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.21728e6 | 0.527343 | 0.263671 | − | 0.964613i | \(-0.415067\pi\) | ||||
0.263671 | + | 0.964613i | \(0.415067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.31547e6 | 0.163074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.65162e6 | −0.325889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.89861e7 | −2.31348 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.36935e6 | 0.165434 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.01047e6 | 0.240826 | 0.120413 | − | 0.992724i | \(-0.461578\pi\) | ||||
0.120413 | + | 0.992724i | \(0.461578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.39568e6 | 0.522081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.88414e6 | 0.339663 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.33691e6 | 0.856795 | 0.428397 | − | 0.903590i | \(-0.359078\pi\) | ||||
0.428397 | + | 0.903590i | \(0.359078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.51100e6 | 0.290773 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.23334e6 | 0.600957 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.14884e6 | −0.130826 | −0.0654128 | − | 0.997858i | \(-0.520836\pi\) | ||||
−0.0654128 | + | 0.997858i | \(0.520836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16409e7 | 1.31462 | 0.657312 | − | 0.753618i | \(-0.271693\pi\) | ||||
0.657312 | + | 0.753618i | \(0.271693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.05367e7 | 1.18007 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.09412e6 | 0.565824 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 155540. | 0.0171345 | 0.00856723 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856723 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.09933e6 | 0.557147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.99758e6 | −0.324838 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.18137e7 | −1.26980 | −0.634899 | − | 0.772595i | \(-0.718958\pi\) | ||||
−0.634899 | + | 0.772595i | \(0.718958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.59160e6 | −0.382913 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.42252e6 | 0.679192 | 0.339596 | − | 0.940571i | \(-0.389710\pi\) | ||||
0.339596 | + | 0.940571i | \(0.389710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.85252e6 | −0.404128 | −0.202064 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202064 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.87635e6 | −0.299304 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.81223e6 | −1.01286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.39757e6 | 0.649899 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.00198e7 | 1.00980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.75136e6 | 0.675022 | 0.337511 | − | 0.941322i | \(-0.390415\pi\) | ||||
0.337511 | + | 0.941322i | \(0.390415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.54525e6 | 0.550062 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.41490e6 | 0.828161 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.57376e6 | 0.153670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.90085e6 | −0.959224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.35493e6 | −0.707022 | −0.353511 | − | 0.935430i | \(-0.615012\pi\) | ||||
−0.353511 | + | 0.935430i | \(0.615012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.59694e7 | −1.52322 | −0.761610 | − | 0.648036i | \(-0.775591\pi\) | ||||
−0.761610 | + | 0.648036i | \(0.775591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.85280e6 | −0.175359 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.72667e7 | −1.62162 | −0.810809 | − | 0.585311i | \(-0.800972\pi\) | ||||
−0.810809 | + | 0.585311i | \(0.800972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00697e7 | −1.87038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.86848e6 | 0.265277 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.36251e6 | −0.125043 | −0.0625213 | − | 0.998044i | \(-0.519914\pi\) | ||||
−0.0625213 | + | 0.998044i | \(0.519914\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.88270e6 | −0.626838 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.87918e6 | −0.440995 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.81808e6 | 0.790971 | 0.395485 | − | 0.918472i | \(-0.370576\pi\) | ||||
0.395485 | + | 0.918472i | \(0.370576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.52035e6 | −0.135344 | −0.0676720 | − | 0.997708i | \(-0.521557\pi\) | ||||
−0.0676720 | + | 0.997708i | \(0.521557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.27664e6 | −0.201146 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.57480e6 | 0.313471 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.02850e6 | 0.437647 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.95805e6 | −0.341913 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.42868e7 | −2.08240 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −315086. | −0.0268158 | −0.0134079 | − | 0.999910i | \(-0.504268\pi\) | ||||
−0.0134079 | + | 0.999910i | \(0.504268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.11000e6 | −0.178247 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.74092e6 | −0.145985 | −0.0729924 | − | 0.997332i | \(-0.523255\pi\) | ||||
−0.0729924 | + | 0.997332i | \(0.523255\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.67082e7 | 1.39077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.25670e6 | −0.599614 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.98935e7 | 1.63177 | 0.815885 | − | 0.578214i | \(-0.196250\pi\) | ||||
0.815885 | + | 0.578214i | \(0.196250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.71255e6 | −0.465161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.71595e6 | 0.704568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.61880e6 | 0.771921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01519e7 | −1.60554 | −0.802770 | − | 0.596289i | \(-0.796641\pi\) | ||||
−0.802770 | + | 0.596289i | \(0.796641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.16765e7 | −0.923593 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.60710e6 | −0.440328 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.67009e7 | −1.30214 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.99765e6 | 0.309465 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.10766e6 | 0.623161 | 0.311581 | − | 0.950220i | \(-0.399142\pi\) | ||||
0.311581 | + | 0.950220i | \(0.399142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.42648e7 | 1.08862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.95920e6 | 0.148459 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.85311e6 | −0.590872 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.35613e7 | −1.01317 | −0.506587 | − | 0.862189i | \(-0.669093\pi\) | ||||
−0.506587 | + | 0.862189i | \(0.669093\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.63062e6 | 0.417717 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.82864e6 | 0.208379 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.62060e6 | −0.338013 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.29631e7 | −0.941695 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.28314e6 | −0.308987 | −0.154493 | − | 0.987994i | \(-0.549375\pi\) | ||||
−0.154493 | + | 0.987994i | \(0.549375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.39748e7 | 1.00117 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.00974e6 | 0.569866 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.68875e6 | 0.260636 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12084e7 | −0.786515 | −0.393258 | − | 0.919428i | \(-0.628652\pi\) | ||||
−0.393258 | + | 0.919428i | \(0.628652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.61141e6 | 0.251686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.61552e6 | −0.596332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.70549e6 | 0.323478 | 0.161739 | − | 0.986834i | \(-0.448290\pi\) | ||||
0.161739 | + | 0.986834i | \(0.448290\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.02860e6 | −0.0702309 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.55539e7 | −2.41112 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.31099e7 | 1.55663 | 0.778317 | − | 0.627872i | \(-0.216074\pi\) | ||||
0.778317 | + | 0.627872i | \(0.216074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.24115e6 | −0.216847 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.75294e6 | −0.382312 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.59505e6 | −0.303319 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.39481e6 | 0.288163 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.23214e7 | 1.45384 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.92424e7 | 1.24497 | 0.622485 | − | 0.782632i | \(-0.286123\pi\) | ||||
0.622485 | + | 0.782632i | \(0.286123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.95184e6 | −0.189717 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.40080e6 | −0.472510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.49210e6 | 0.284911 | 0.142456 | − | 0.989801i | \(-0.454500\pi\) | ||||
0.142456 | + | 0.989801i | \(0.454500\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.11686e6 | 0.259395 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.33500e6 | 0.459133 | 0.229567 | − | 0.973293i | \(-0.426269\pi\) | ||||
0.229567 | + | 0.973293i | \(0.426269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.57577e6 | −0.471102 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.16175e6 | −0.257112 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.01678e7 | 0.624076 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.85526e6 | −0.357051 | −0.178526 | − | 0.983935i | \(-0.557133\pi\) | ||||
−0.178526 | + | 0.983935i | \(0.557133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.23208e6 | 0.135230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.34558e7 | 0.809952 | 0.404976 | − | 0.914327i | \(-0.367280\pi\) | ||||
0.404976 | + | 0.914327i | \(0.367280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.07500e6 | 0.124098 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.30874e6 | 0.553144 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.37764e7 | −1.40379 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.34084e7 | 1.95988 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.99252e7 | −1.16144 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.36915e6 | 0.195140 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.00706e7 | −0.579587 | −0.289794 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289794 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.49392e6 | −0.371377 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.64002e7 | −0.931985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.23043e7 | 0.694820 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.28680e6 | −0.352786 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.18844e7 | −0.662723 | −0.331362 | − | 0.943504i | \(-0.607508\pi\) | ||||
−0.331362 | + | 0.943504i | \(0.607508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.11028e6 | 0.504853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.62629e7 | 0.895604 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.64638e7 | 0.901036 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.30040e6 | 0.125116 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.82571e6 | 0.152737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.06053e7 | 0.569705 | 0.284852 | − | 0.958571i | \(-0.408055\pi\) | ||||
0.284852 | + | 0.958571i | \(0.408055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38944e6 | 0.0741799 | 0.0370900 | − | 0.999312i | \(-0.488191\pi\) | ||||
0.0370900 | + | 0.999312i | \(0.488191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37297e7 | 0.728510 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.50620e6 | 0.0794307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.22655e7 | −0.642882 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.91559e6 | 0.308169 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.12661e7 | −0.583334 | −0.291667 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291667 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.77093e7 | 1.42602 | 0.713011 | − | 0.701152i | \(-0.247331\pi\) | ||||
0.713011 | + | 0.701152i | \(0.247331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.02000e6 | 0.154480 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.23662e7 | −0.628740 | −0.314370 | − | 0.949300i | \(-0.601793\pi\) | ||||
−0.314370 | + | 0.949300i | \(0.601793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.23182e7 | 0.622530 | 0.311265 | − | 0.950323i | \(-0.399247\pi\) | ||||
0.311265 | + | 0.950323i | \(0.399247\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.96706e6 | −0.0988130 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.78299e6 | −0.238829 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.55030e6 | 0.0769484 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.12083e7 | −0.553002 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17277e7 | 0.575183 | 0.287592 | − | 0.957753i | \(-0.407145\pi\) | ||||
0.287592 | + | 0.957753i | \(0.407145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.43225e7 | 0.698277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.34095e7 | −0.649894 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.94142e6 | −0.334431 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.20066e7 | 1.05401 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00705e7 | 0.479494 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.17945e6 | 0.434503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.57059e7 | 0.739077 | 0.369538 | − | 0.929215i | \(-0.379516\pi\) | ||||
0.369538 | + | 0.929215i | \(0.379516\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.92490e6 | −0.277182 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.52390e7 | 1.17387 | 0.586935 | − | 0.809634i | \(-0.300334\pi\) | ||||
0.586935 | + | 0.809634i | \(0.300334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.66248e6 | −0.169353 | −0.0846763 | − | 0.996409i | \(-0.526986\pi\) | ||||
−0.0846763 | + | 0.996409i | \(0.526986\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.55157e7 | −0.713286 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.17938e7 | 1.91023 | 0.955113 | − | 0.296243i | \(-0.0957338\pi\) | ||||
0.955113 | + | 0.296243i | \(0.0957338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.47920e7 | −0.672184 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.43966e6 | −0.200586 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.89994e7 | −0.853475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.80124e7 | 0.804500 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.76924e7 | −1.22977 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.68750e6 | 0.0745116 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.08990e7 | 0.478505 | 0.239253 | − | 0.970957i | \(-0.423098\pi\) | ||||
0.239253 | + | 0.970957i | \(0.423098\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.75326e6 | 0.251155 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.04336e7 | −1.32103 | −0.660517 | − | 0.750811i | \(-0.729663\pi\) | ||||
−0.660517 | + | 0.750811i | \(0.729663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.09028e6 | −0.262867 | −0.131433 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131433 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.64560e6 | −0.285217 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.77908e7 | −1.18602 | −0.593010 | − | 0.805195i | \(-0.702060\pi\) | ||||
−0.593010 | + | 0.805195i | \(0.702060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.63524e7 | 1.54269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.95936e6 | 0.420278 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.29699e7 | 0.544262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.03510e6 | 0.251841 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.08570e6 | −0.0865506 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.95946e7 | 0.808608 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.92336e7 | −1.19969 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.00410e6 | −0.326658 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.69055e6 | 0.190372 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.71510e7 | −1.49952 | −0.749761 | − | 0.661709i | \(-0.769831\pi\) | ||||
−0.749761 | + | 0.661709i | \(0.769831\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.30158e7 | 0.522470 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.85959e6 | 0.313765 | 0.156882 | − | 0.987617i | \(-0.449856\pi\) | ||||
0.156882 | + | 0.987617i | \(0.449856\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.48294e7 | −0.588772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.04200e6 | −0.317549 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.97333e7 | −1.16767 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.62693e7 | 0.635448 | 0.317724 | − | 0.948183i | \(-0.397081\pi\) | ||||
0.317724 | + | 0.948183i | \(0.397081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48810e7 | −0.578074 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.69255e7 | −0.653938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.73375e6 | 0.258763 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.31619e7 | −0.885268 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.69365e7 | −1.40416 | −0.702079 | − | 0.712099i | \(-0.747745\pi\) | ||||
−0.702079 | + | 0.712099i | \(0.747745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.80933e6 | −0.257472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.22707e6 | −0.0837587 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.40430e7 | 0.525328 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.89705e6 | 0.182216 | 0.0911078 | − | 0.995841i | \(-0.470959\pi\) | ||||
0.0911078 | + | 0.995841i | \(0.470959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.79346e6 | −0.140401 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.83943e6 | −0.251794 | −0.125897 | − | 0.992043i | \(-0.540181\pi\) | ||||
−0.125897 | + | 0.992043i | \(0.540181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.53002e7 | −0.560297 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.11520e6 | −0.332037 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.03790e7 | −0.376082 | −0.188041 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188041 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.34095e6 | −0.300642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.46990e7 | −0.527032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.59587e7 | 0.925873 | 0.462937 | − | 0.886391i | \(-0.346796\pi\) | ||||
0.462937 | + | 0.886391i | \(0.346796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −939000. | −0.0333163 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.85185e7 | 1.00658 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.46782e7 | −0.866497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76068e7 | −0.614994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.69957e7 | −1.28554 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.11085e6 | 0.142106 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.92120e7 | 1.34851 | 0.674253 | − | 0.738501i | \(-0.264466\pi\) | ||||
0.674253 | + | 0.738501i | \(0.264466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.85056e6 | 0.337017 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.06876e7 | 0.363774 | 0.181887 | − | 0.983319i | \(-0.441779\pi\) | ||||
0.181887 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.42227e7 | −0.820238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.53000e6 | −0.0515442 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.77266e7 | 0.929308 | 0.464654 | − | 0.885492i | \(-0.346179\pi\) | ||||
0.464654 | + | 0.885492i | \(0.346179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.48758e7 | −1.82989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.25561e7 | 0.416566 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.49272e6 | 0.313334 | 0.156667 | − | 0.987652i | \(-0.449925\pi\) | ||||
0.156667 | + | 0.987652i | \(0.449925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.01295e6 | 0.295990 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.46374e6 | 0.276547 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.89293e6 | −0.256595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.03243e7 | 0.657403 | 0.328702 | − | 0.944434i | \(-0.393389\pi\) | ||||
0.328702 | + | 0.944434i | \(0.393389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.39794e7 | −0.771730 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.63542e7 | 0.523687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.70508e7 | 1.49909 | 0.749547 | − | 0.661951i | \(-0.230271\pi\) | ||||
0.749547 | + | 0.661951i | \(0.230271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.63730e7 | −1.15310 |
(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 | 80.6.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 720.6.a.h.1.1 | 1 | |||
4.3 | odd | 2 | 40.6.a.b.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 400.6.c.h.49.1 | 2 | |||
5.3 | odd | 4 | 400.6.c.h.49.2 | 2 | |||
5.4 | even | 2 | 400.6.a.f.1.1 | 1 | |||
8.3 | odd | 2 | 320.6.a.l.1.1 | 1 | |||
8.5 | even | 2 | 320.6.a.e.1.1 | 1 | |||
12.11 | even | 2 | 360.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 200.6.c.c.49.1 | 2 | |||
20.7 | even | 4 | 200.6.c.c.49.2 | 2 | |||
20.19 | odd | 2 | 200.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
80.6.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
200.6.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
200.6.c.c.49.1 | 2 | 20.3 | even | 4 | |||
200.6.c.c.49.2 | 2 | 20.7 | even | 4 | |||
320.6.a.e.1.1 | 1 | 8.5 | even | 2 | |||
320.6.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
360.6.a.b.1.1 | 1 | 12.11 | even | 2 | |||
400.6.a.f.1.1 | 1 | 5.4 | even | 2 | |||
400.6.c.h.49.1 | 2 | 5.2 | odd | 4 | |||
400.6.c.h.49.2 | 2 | 5.3 | odd | 4 | |||
720.6.a.h.1.1 | 1 | 3.2 | odd | 2 |