Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.13 | ||
Root | \(675.810i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.4 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 675.810i | 1.08130i | 0.841249 | + | 0.540648i | \(0.181821\pi\) | ||||
−0.841249 | + | 0.540648i | \(0.818179\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 907.493 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18942.7i | 1.29381i | 0.762571 | + | 0.646905i | \(0.223937\pi\) | ||||
−0.762571 | + | 0.646905i | \(0.776063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6233.80 | 0.218263 | 0.109131 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109131 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 15144.2i | − 0.181322i | −0.995882 | − | 0.0906611i | \(-0.971102\pi\) | ||||
0.995882 | − | 0.0906611i | \(-0.0288980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 181701. | 1.39425 | 0.697127 | − | 0.716947i | \(-0.254461\pi\) | ||||
0.697127 | + | 0.716947i | \(0.254461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 421094.i | 1.50476i | 0.658728 | + | 0.752381i | \(0.271095\pi\) | ||||
−0.658728 | + | 0.752381i | \(0.728905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −66094.2 | −0.169201 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 190089.i | − 0.268760i | −0.990930 | − | 0.134380i | \(-0.957096\pi\) | ||||
0.990930 | − | 0.134380i | \(-0.0429043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −198070. | −0.214473 | −0.107236 | − | 0.994234i | \(-0.534200\pi\) | ||||
−0.107236 | + | 0.994234i | \(0.534200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 613293.i | 0.408692i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 700460. | 0.373746 | 0.186873 | − | 0.982384i | \(-0.440165\pi\) | ||||
0.186873 | + | 0.982384i | \(0.440165\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 628097.i | − 0.222275i | −0.993805 | − | 0.111138i | \(-0.964551\pi\) | ||||
0.993805 | − | 0.111138i | \(-0.0354495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.91651e6 | 1.73058 | 0.865290 | − | 0.501271i | \(-0.167134\pi\) | ||||
0.865290 | + | 0.501271i | \(0.167134\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.30001e6i | 1.29107i | 0.763730 | + | 0.645535i | \(0.223366\pi\) | ||||
−0.763730 | + | 0.645535i | \(0.776634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.32657e6i | − 0.294858i | −0.989073 | − | 0.147429i | \(-0.952900\pi\) | ||||
0.989073 | − | 0.147429i | \(-0.0470998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.28016e7 | −1.39899 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.34161e7i | − 1.10718i | −0.832788 | − | 0.553592i | \(-0.813257\pi\) | ||||
0.832788 | − | 0.553592i | \(-0.186743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.18165e6 | −0.663134 | −0.331567 | − | 0.943432i | \(-0.607577\pi\) | ||||
−0.331567 | + | 0.943432i | \(0.607577\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.21286e6i | 0.236007i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.29819e6 | 0.312548 | 0.156274 | − | 0.987714i | \(-0.450052\pi\) | ||||
0.156274 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.43966e7i | − 0.566536i | −0.959041 | − | 0.283268i | \(-0.908581\pi\) | ||||
0.959041 | − | 0.283268i | \(-0.0914186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.04114e7 | −1.42302 | −0.711512 | − | 0.702674i | \(-0.751989\pi\) | ||||
−0.711512 | + | 0.702674i | \(0.751989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.71903e7i | 0.489014i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00463e7 | −0.771406 | −0.385703 | − | 0.922623i | \(-0.626041\pi\) | ||||
−0.385703 | + | 0.922623i | \(0.626041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.01957e7i | 1.05768i | 0.848722 | + | 0.528840i | \(0.177373\pi\) | ||||
−0.848722 | + | 0.528840i | \(0.822627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.02346e7 | 0.196063 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.17353e6i | 0.0665186i | 0.999447 | + | 0.0332593i | \(0.0105887\pi\) | ||||
−0.999447 | + | 0.0332593i | \(0.989411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65713e6 | 0.0824955 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.22795e8i | 1.50760i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.41211e8 | 1.59507 | 0.797536 | − | 0.603272i | \(-0.206136\pi\) | ||||
0.797536 | + | 0.603272i | \(0.206136\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.22032e6i | − 0.0597761i | −0.999553 | − | 0.0298881i | \(-0.990485\pi\) | ||||
0.999553 | − | 0.0298881i | \(-0.00951508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.46907e7 | −0.485920 | −0.242960 | − | 0.970036i | \(-0.578118\pi\) | ||||
−0.242960 | + | 0.970036i | \(0.578118\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 6.90127e7i | − 0.526494i | −0.964728 | − | 0.263247i | \(-0.915207\pi\) | ||||
0.964728 | − | 0.263247i | \(-0.0847935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.93853e7 | 0.633228 | 0.316614 | − | 0.948554i | \(-0.397454\pi\) | ||||
0.316614 | + | 0.948554i | \(0.397454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.90457e8i | 1.78143i | 0.454565 | + | 0.890714i | \(0.349795\pi\) | ||||
−0.454565 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.84580e8 | −1.62709 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 1.37433e7i | − 0.0685334i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.44466e8 | −0.673943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.19321e8i | 0.898339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.37474e8 | −1.29725 | −0.648627 | − | 0.761107i | \(-0.724656\pi\) | ||||
−0.648627 | + | 0.761107i | \(0.724656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.80523e8i | 0.612982i | 0.951874 | + | 0.306491i | \(0.0991549\pi\) | ||||
−0.951874 | + | 0.306491i | \(0.900845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.64892e8 | 0.526979 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.75533e8i | 0.498283i | 0.968467 | + | 0.249141i | \(0.0801484\pi\) | ||||
−0.968467 | + | 0.249141i | \(0.919852\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.14176e8 | −0.305856 | −0.152928 | − | 0.988237i | \(-0.548870\pi\) | ||||
−0.152928 | + | 0.988237i | \(0.548870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.18085e8i | 0.282390i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.28464e8 | 0.290609 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.90588e8i | 1.19823i | 0.800663 | + | 0.599115i | \(0.204481\pi\) | ||||
−0.800663 | + | 0.599115i | \(0.795519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.52935e8 | −1.83297 | −0.916485 | − | 0.400069i | \(-0.868986\pi\) | ||||
−0.916485 | + | 0.400069i | \(0.868986\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.33858e8i | − 0.231908i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.02887e8 | −1.48605 | −0.743027 | − | 0.669261i | \(-0.766611\pi\) | ||||
−0.743027 | + | 0.669261i | \(0.766611\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.82140e8i | 0.568747i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.63169e8 | 0.231146 | 0.115573 | − | 0.993299i | \(-0.463130\pi\) | ||||
0.115573 | + | 0.993299i | \(0.463130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.25869e8i | 0.418964i | 0.977813 | + | 0.209482i | \(0.0671777\pi\) | ||||
−0.977813 | + | 0.209482i | \(0.932822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.76870e8 | −0.952361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.01042e9i | 1.12802i | 0.825768 | + | 0.564009i | \(0.190742\pi\) | ||||
−0.825768 | + | 0.564009i | \(0.809258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.99800e7 | −0.0639520 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.92198e7i | − 0.0869059i | −0.999055 | − | 0.0434530i | \(-0.986164\pi\) | ||||
0.999055 | − | 0.0434530i | \(-0.0138359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.63231e8 | −0.897463 | −0.448731 | − | 0.893667i | \(-0.648124\pi\) | ||||
−0.448731 | + | 0.893667i | \(0.648124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.73378e8i | 0.404130i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.86872e8 | 0.234597 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.36076e9i | 1.77386i | 0.461907 | + | 0.886928i | \(0.347165\pi\) | ||||
−0.461907 | + | 0.886928i | \(0.652835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.96485e8 | 0.213684 | 0.106842 | − | 0.994276i | \(-0.465926\pi\) | ||||
0.106842 | + | 0.994276i | \(0.465926\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.55058e9i | − 1.02951i | −0.857338 | − | 0.514754i | \(-0.827883\pi\) | ||||
0.857338 | − | 0.514754i | \(-0.172117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.31261e9 | 1.47465 | 0.737326 | − | 0.675537i | \(-0.236088\pi\) | ||||
0.737326 | + | 0.675537i | \(0.236088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.72504e8i | − 0.101582i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.24474e8 | 0.240345 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.44190e9i | 1.80390i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.86336e9 | −1.94910 | −0.974552 | − | 0.224163i | \(-0.928035\pi\) | ||||
−0.974552 | + | 0.224163i | \(0.928035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.99844e9i | 1.87127i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.79747e8 | −0.0810630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.44060e7i | − 0.0395759i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.06779e9 | 1.24053 | 0.620264 | − | 0.784393i | \(-0.287025\pi\) | ||||
0.620264 | + | 0.784393i | \(0.287025\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.63319e8i | 0.212154i | 0.994358 | + | 0.106077i | \(0.0338290\pi\) | ||||
−0.994358 | + | 0.106077i | \(0.966171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.34829e9 | 0.490278 | 0.245139 | − | 0.969488i | \(-0.421166\pi\) | ||||
0.245139 | + | 0.969488i | \(0.421166\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6.61906e8i | − 0.224581i | −0.993675 | − | 0.112290i | \(-0.964181\pi\) | ||||
0.993675 | − | 0.112290i | \(-0.0358187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.25761e9 | −1.39603 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4.96165e9i | − 1.52067i | −0.649531 | − | 0.760335i | \(-0.725035\pi\) | ||||
0.649531 | − | 0.760335i | \(-0.274965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.38994e9 | −1.00490 | −0.502452 | − | 0.864605i | \(-0.667569\pi\) | ||||
−0.502452 | + | 0.864605i | \(0.667569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.56559e8i | 0.154471i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.13269e9 | 0.304314 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.26441e9i | − 0.570507i | −0.958452 | − | 0.285253i | \(-0.907922\pi\) | ||||
0.958452 | − | 0.285253i | \(-0.0920777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.97665e9 | −1.94688 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 6.00346e9i | − 1.37616i | −0.725635 | − | 0.688080i | \(-0.758454\pi\) | ||||
0.725635 | − | 0.688080i | \(-0.241546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.35662e8 | 0.141263 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5.31075e8i | − 0.111003i | −0.998459 | − | 0.0555013i | \(-0.982324\pi\) | ||||
0.998459 | − | 0.0555013i | \(-0.0176757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.57232e9 | 0.318829 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46616e8i | 0.0661972i | 0.999452 | + | 0.0330986i | \(0.0105375\pi\) | ||||
−0.999452 | + | 0.0330986i | \(0.989462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.88625e9 | 1.46216 | 0.731078 | − | 0.682294i | \(-0.239018\pi\) | ||||
0.731078 | + | 0.682294i | \(0.239018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.25200e9i | − 0.218914i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.59726e9 | 0.441161 | 0.220580 | − | 0.975369i | \(-0.429205\pi\) | ||||
0.220580 | + | 0.975369i | \(0.429205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.57542e9i | 0.573459i | 0.958012 | + | 0.286729i | \(0.0925681\pi\) | ||||
−0.958012 | + | 0.286729i | \(0.907432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.40830e9 | −0.531365 | −0.265682 | − | 0.964061i | \(-0.585597\pi\) | ||||
−0.265682 | + | 0.964061i | \(0.585597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 5.69994e8i | − 0.0840122i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.74641e9 | 0.967122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6.14339e9i | − 0.833562i | −0.909007 | − | 0.416781i | \(-0.863158\pi\) | ||||
0.909007 | − | 0.416781i | \(-0.136842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.06676e9 | 1.19719 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.62502e9i | 0.328433i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.36919e9 | 0.654098 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 6.20505e9i | − 0.717045i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.89041e9 | 0.663120 | 0.331560 | − | 0.943434i | \(-0.392425\pi\) | ||||
0.331560 | + | 0.943434i | \(0.392425\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 1.47415e10i | − 1.57580i | −0.615803 | − | 0.787900i | \(-0.711168\pi\) | ||||
0.615803 | − | 0.787900i | \(-0.288832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.41159e9 | −0.251262 | −0.125631 | − | 0.992077i | \(-0.540096\pi\) | ||||
−0.125631 | + | 0.992077i | \(0.540096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.73533e9i | − 0.270877i | −0.990786 | − | 0.135438i | \(-0.956756\pi\) | ||||
0.990786 | − | 0.135438i | \(-0.0432443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.60079e9 | 0.347725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.75171e9i | − 0.252809i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.12018e8 | −0.0369303 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.71722e9i | 0.487979i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.97672e9 | 0.164677 | 0.0823387 | − | 0.996604i | \(-0.473761\pi\) | ||||
0.0823387 | + | 0.996604i | \(0.473761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.25638e9i | 0.337957i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00212e9 | 0.387824 | 0.193912 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193912 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.75197e9i | − 0.277487i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.47359e8 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.03079e9i | − 0.0710971i | −0.999368 | − | 0.0355485i | \(-0.988682\pi\) | ||||
0.999368 | − | 0.0355485i | \(-0.0113178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.68272e9 | 0.383049 | 0.191525 | − | 0.981488i | \(-0.438657\pi\) | ||||
0.191525 | + | 0.981488i | \(0.438657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7.38729e9i | − 0.475758i | −0.971295 | − | 0.237879i | \(-0.923548\pi\) | ||||
0.971295 | − | 0.237879i | \(-0.0764522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.72939e9 | 0.612593 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 1.75128e10i | − 1.05434i | −0.849761 | − | 0.527168i | \(-0.823254\pi\) | ||||
0.849761 | − | 0.527168i | \(-0.176746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.60316e10 | 0.943946 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.73104e10i | − 1.53871i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.61052e9 | −0.529764 | −0.264882 | − | 0.964281i | \(-0.585333\pi\) | ||||
−0.264882 | + | 0.964281i | \(0.585333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.11135e9i | − 0.111446i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.74568e10 | −0.901837 | −0.450919 | − | 0.892565i | \(-0.648904\pi\) | ||||
−0.450919 | + | 0.892565i | \(0.648904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.18498e9i | − 0.0586603i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.39385e10 | 1.64489 | 0.822444 | − | 0.568846i | \(-0.192610\pi\) | ||||
0.822444 | + | 0.568846i | \(0.192610\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 3.21374e10i | − 1.49354i | −0.665084 | − | 0.746769i | \(-0.731604\pi\) | ||||
0.665084 | − | 0.746769i | \(-0.268396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.16174e10 | −0.528769 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.89590e10i | 0.827977i | 0.910282 | + | 0.413988i | \(0.135865\pi\) | ||||
−0.910282 | + | 0.413988i | \(0.864135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.37714e9 | 0.272847 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.03056e10i | − 0.834119i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.73123e10 | −1.09950 | −0.549751 | − | 0.835328i | \(-0.685278\pi\) | ||||
−0.549751 | + | 0.835328i | \(0.685278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.05653e10i | 0.795349i | 0.917527 | + | 0.397675i | \(0.130183\pi\) | ||||
−0.917527 | + | 0.397675i | \(0.869817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23473e9 | −0.0468113 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.32686e10i | 0.483556i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.15906e10 | 1.48629 | 0.743143 | − | 0.669133i | \(-0.233334\pi\) | ||||
0.743143 | + | 0.669133i | \(0.233334\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.21751e10i | − 0.418476i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39228e10 | −1.14366 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8.09475e9i | − 0.262632i | −0.991341 | − | 0.131316i | \(-0.958080\pi\) | ||||
0.991341 | − | 0.131316i | \(-0.0419202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32776e10 | −0.422660 | −0.211330 | − | 0.977415i | \(-0.567780\pi\) | ||||
−0.211330 | + | 0.977415i | \(0.567780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00095e9i | 0.0306800i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.33228e9 | −0.250641 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 4.74178e10i | − 1.37415i | −0.726589 | − | 0.687073i | \(-0.758895\pi\) | ||||
0.726589 | − | 0.687073i | \(-0.241105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.31302e10 | −1.22696 | −0.613479 | − | 0.789711i | \(-0.710230\pi\) | ||||
−0.613479 | + | 0.789711i | \(0.710230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.65131e10i | 2.09802i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.81569e9 | 0.264279 | 0.132140 | − | 0.991231i | \(-0.457815\pi\) | ||||
0.132140 | + | 0.991231i | \(0.457815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.98569e10i | − 0.775229i | −0.921822 | − | 0.387614i | \(-0.873299\pi\) | ||||
0.921822 | − | 0.387614i | \(-0.126701\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.82051e9 | −0.0719263 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.45404e10i | 1.58798i | 0.607928 | + | 0.793992i | \(0.292001\pi\) | ||||
−0.607928 | + | 0.793992i | \(0.707999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.18978e10 | 0.287582 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.82314e9i | 0.0892021i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.79905e10 | 1.78804 | 0.894019 | − | 0.448029i | \(-0.147874\pi\) | ||||
0.894019 | + | 0.448029i | \(0.147874\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 3.74346e10i | − 0.828838i | −0.910086 | − | 0.414419i | \(-0.863985\pi\) | ||||
0.910086 | − | 0.414419i | \(-0.136015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.63866e10 | 0.356586 | 0.178293 | − | 0.983977i | \(-0.442943\pi\) | ||||
0.178293 | + | 0.983977i | \(0.442943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.06367e10i | 0.223634i | 0.993729 | + | 0.111817i | \(0.0356671\pi\) | ||||
−0.993729 | + | 0.111817i | \(0.964333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.71556e9 | 0.118132 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.12074e11i | 2.23904i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20094e10 | −0.235910 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.94703e10i | 1.31964i | 0.751422 | + | 0.659822i | \(0.229368\pi\) | ||||
−0.751422 | + | 0.659822i | \(0.770632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.36653e9 | 0.0815747 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.54315e10i | 1.72474i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.49782e10 | −0.977405 | −0.488703 | − | 0.872450i | \(-0.662530\pi\) | ||||
−0.488703 | + | 0.872450i | \(0.662530\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.04762e10i | 0.696424i | 0.937416 | + | 0.348212i | \(0.113211\pi\) | ||||
−0.937416 | + | 0.348212i | \(0.886789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.87875e9 | −0.0487322 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.30648e10i | − 0.214130i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.67410e10 | −0.753869 | −0.376935 | − | 0.926240i | \(-0.623022\pi\) | ||||
−0.376935 | + | 0.926240i | \(0.623022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4.28912e10i | − 0.670033i | −0.942212 | − | 0.335017i | \(-0.891258\pi\) | ||||
0.942212 | − | 0.335017i | \(-0.108742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.20376e9 | 0.0646357 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 6.68892e10i | − 0.996517i | −0.867028 | − | 0.498259i | \(-0.833973\pi\) | ||||
0.867028 | − | 0.498259i | \(-0.166027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.66730e10 | −0.537853 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.69606e10i | − 0.525424i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.19339e11 | −1.67040 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.09751e10i | 0.420399i | 0.977659 | + | 0.210199i | \(0.0674113\pi\) | ||||
−0.977659 | + | 0.210199i | \(0.932589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.58369e10 | 0.211672 | 0.105836 | − | 0.994384i | \(-0.466248\pi\) | ||||
0.105836 | + | 0.994384i | \(0.466248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.99961e9i | 0.0388886i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.90093e10 | −1.26431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.91543e9i | − 0.0485144i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.66395e10 | 0.569296 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.56001e10i | 0.184830i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.46603e11 | −1.71141 | −0.855705 | − | 0.517464i | \(-0.826876\pi\) | ||||
−0.855705 | + | 0.517464i | \(0.826876\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.04075e10i | 0.684707i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.52569e10 | 0.952314 | 0.476157 | − | 0.879360i | \(-0.342029\pi\) | ||||
0.476157 | + | 0.879360i | \(0.342029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 3.45393e10i | − 0.374720i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.72668e10 | −0.291564 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.05196e11i | 1.09289i | 0.837495 | + | 0.546445i | \(0.184019\pi\) | ||||
−0.837495 | + | 0.546445i | \(0.815981\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.68823e10 | 0.377721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.36005e10i | 0.433969i | 0.976175 | + | 0.216984i | \(0.0696220\pi\) | ||||
−0.976175 | + | 0.216984i | \(0.930378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.96294e11 | −1.92625 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1.63036e10i | − 0.155538i | −0.996971 | − | 0.0777688i | \(-0.975220\pi\) | ||||
0.996971 | − | 0.0777688i | \(-0.0247796\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.58110e10 | 0.619090 | 0.309545 | − | 0.950885i | \(-0.399823\pi\) | ||||
0.309545 | + | 0.950885i | \(0.399823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.78319e10i | − 0.254608i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.39333e11 | −1.25705 | −0.628523 | − | 0.777791i | \(-0.716340\pi\) | ||||
−0.628523 | + | 0.777791i | \(0.716340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.55522e10i | 0.399765i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.40715e10 | 0.381490 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50365e11i | 1.26647i | 0.773961 | + | 0.633233i | \(0.218272\pi\) | ||||
−0.773961 | + | 0.633233i | \(0.781728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.59894e10 | −0.299029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.73734e11i | 1.40497i | 0.711700 | + | 0.702484i | \(0.247926\pi\) | ||||
−0.711700 | + | 0.702484i | \(0.752074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.28784e9 | 0.0741049 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.75985e10i | 0.214377i | 0.994239 | + | 0.107189i | \(0.0341849\pi\) | ||||
−0.994239 | + | 0.107189i | \(0.965815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.52880e11 | 1.17180 | 0.585898 | − | 0.810385i | \(-0.300742\pi\) | ||||
0.585898 | + | 0.810385i | \(0.300742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 9.76314e10i | − 0.728732i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.35603e11 | 0.998884 | 0.499442 | − | 0.866347i | \(-0.333538\pi\) | ||||
0.499442 | + | 0.866347i | \(0.333538\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.92730e10i | 0.281793i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.37425e11 | 0.973249 | 0.486625 | − | 0.873611i | \(-0.338228\pi\) | ||||
0.486625 | + | 0.873611i | \(0.338228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 7.23941e10i | − 0.499531i | −0.968306 | − | 0.249765i | \(-0.919647\pi\) | ||||
0.968306 | − | 0.249765i | \(-0.0803535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.64909e10 | −0.112327 | −0.0561633 | − | 0.998422i | \(-0.517887\pi\) | ||||
−0.0561633 | + | 0.998422i | \(0.517887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.78744e9i | 0.0251417i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.74038e11 | −1.14057 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.06079e10i | − 0.0677684i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.52602e10 | 0.222417 | 0.111208 | − | 0.993797i | \(-0.464528\pi\) | ||||
0.111208 | + | 0.993797i | \(0.464528\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 2.28068e11i | − 1.40272i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.13380e9 | 0.0311804 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.76394e11i | 1.04484i | 0.852687 | + | 0.522422i | \(0.174971\pi\) | ||||
−0.852687 | + | 0.522422i | \(0.825029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.16256e11 | 0.680095 | 0.340048 | − | 0.940408i | \(-0.389557\pi\) | ||||
0.340048 | + | 0.940408i | \(0.389557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 7.89390e10i | − 0.450479i | −0.974303 | − | 0.225239i | \(-0.927684\pi\) | ||||
0.974303 | − | 0.225239i | \(-0.0723164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.54138e11 | 1.43248 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.76500e11i | 0.970713i | 0.874316 | + | 0.485357i | \(0.161310\pi\) | ||||
−0.874316 | + | 0.485357i | \(0.838690\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.21999e11 | −0.662815 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.00334e11i | − 1.06222i | −0.847304 | − | 0.531108i | \(-0.821776\pi\) | ||||
0.847304 | − | 0.531108i | \(-0.178224\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.06069e11 | −1.60330 | −0.801648 | − | 0.597796i | \(-0.796043\pi\) | ||||
−0.801648 | + | 0.597796i | \(0.796043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11436e11i | 0.569820i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00454e10 | 0.404420 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.73925e11i | − 0.857970i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.06648e11 | 0.519867 | 0.259934 | − | 0.965626i | \(-0.416299\pi\) | ||||
0.259934 | + | 0.965626i | \(0.416299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.42785e11i | − 1.63180i | −0.578192 | − | 0.815901i | \(-0.696241\pi\) | ||||
0.578192 | − | 0.815901i | \(-0.303759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.28148e11 | 0.602880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.20025e11i | − 0.551555i | −0.961222 | − | 0.275777i | \(-0.911065\pi\) | ||||
0.961222 | − | 0.275777i | \(-0.0889352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.18627e11 | −0.538791 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1.45034e10i | − 0.0643565i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.21637e11 | 0.972144 | 0.486072 | − | 0.873919i | \(-0.338429\pi\) | ||||
0.486072 | + | 0.873919i | \(0.338429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 7.71615e10i | − 0.330721i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.51204e9 | −0.0403035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.28038e11i | 0.530233i | 0.964216 | + | 0.265116i | \(0.0854104\pi\) | ||||
−0.964216 | + | 0.265116i | \(0.914590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.27274e11 | 0.521097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5.64490e9i | − 0.0225932i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.99426e11 | 0.789217 | 0.394608 | − | 0.918849i | \(-0.370880\pi\) | ||||
0.394608 | + | 0.918849i | \(0.370880\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.34061e10i | − 0.322730i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.98029e10 | −0.305348 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.72421e11i | − 1.39354i | −0.717296 | − | 0.696769i | \(-0.754620\pi\) | ||||
0.717296 | − | 0.696769i | \(-0.245380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.96314e10 | −0.183661 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.25638e10i | 0.0454746i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.45884e11 | 1.23821 | 0.619103 | − | 0.785310i | \(-0.287496\pi\) | ||||
0.619103 | + | 0.785310i | \(0.287496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 8.96009e10i | − 0.313793i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.42390e11 | 1.87887 | 0.939433 | − | 0.342733i | \(-0.111353\pi\) | ||||
0.939433 | + | 0.342733i | \(0.111353\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.19305e11i | 0.404378i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.62333e11 | −1.88545 | −0.942727 | − | 0.333565i | \(-0.891748\pi\) | ||||
−0.942727 | + | 0.333565i | \(0.891748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.74150e11i | − 1.55582i | −0.628374 | − | 0.777911i | \(-0.716279\pi\) | ||||
0.628374 | − | 0.777911i | \(-0.283721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.99126e11 | −1.29564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.26285e10i | − 0.198996i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.37525e11 | 0.432336 | 0.216168 | − | 0.976356i | \(-0.430644\pi\) | ||||
0.216168 | + | 0.976356i | \(0.430644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.44003e11i | − 1.98198i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.09476e11 | −1.85598 | −0.927990 | − | 0.372606i | \(-0.878464\pi\) | ||||
−0.927990 | + | 0.372606i | \(0.878464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.88452e11i | 1.15824i | 0.815242 | + | 0.579121i | \(0.196604\pi\) | ||||
−0.815242 | + | 0.579121i | \(0.803396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.11166e10 | 0.239338 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.36335e10i | − 0.241657i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.73576e10 | 0.192611 | 0.0963056 | − | 0.995352i | \(-0.469297\pi\) | ||||
0.0963056 | + | 0.995352i | \(0.469297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.57274e10i | 0.100065i | 0.998748 | + | 0.0500327i | \(0.0159325\pi\) | ||||
−0.998748 | + | 0.0500327i | \(0.984067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.30913e10 | 0.0362890 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.14126e11i | − 0.309908i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.72711e11 | 0.732990 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.10180e11i | − 1.60686i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.51060e11 | 1.43648 | 0.718240 | − | 0.695795i | \(-0.244948\pi\) | ||||
0.718240 | + | 0.695795i | \(0.244948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.63588e11i | 0.673316i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.72366e10 | −0.144737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.25775e11i | 1.55090i | 0.631406 | + | 0.775452i | \(0.282478\pi\) | ||||
−0.631406 | + | 0.775452i | \(0.717522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.54088e10 | 0.234100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.65499e11i | − 1.84112i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.58254e11 | −0.614984 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 3.34395e10i | − 0.0780667i | −0.999238 | − | 0.0390334i | \(-0.987572\pi\) | ||||
0.999238 | − | 0.0390334i | \(-0.0124279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.98789e11 | 1.38417 | 0.692086 | − | 0.721815i | \(-0.256692\pi\) | ||||
0.692086 | + | 0.721815i | \(0.256692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.10271e11i | 0.249938i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.07503e12 | 2.41287 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.98864e11i | 1.09802i | 0.835816 | + | 0.549009i | \(0.184995\pi\) | ||||
−0.835816 | + | 0.549009i | \(0.815005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.03490e11 | −0.225580 | −0.112790 | − | 0.993619i | \(-0.535979\pi\) | ||||
−0.112790 | + | 0.993619i | \(0.535979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.44947e11i | − 1.37880i | −0.724380 | − | 0.689401i | \(-0.757874\pi\) | ||||
0.724380 | − | 0.689401i | \(-0.242126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.99994e11 | 0.846906 | 0.423453 | − | 0.905918i | \(-0.360818\pi\) | ||||
0.423453 | + | 0.905918i | \(0.360818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.24719e10i | − 0.0259032i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.20225e11 | −0.453024 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.99830e11i | 0.806914i | 0.914999 | + | 0.403457i | \(0.132191\pi\) | ||||
−0.914999 | + | 0.403457i | \(0.867809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.64113e11 | 0.927768 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5.25017e11i | − 1.02978i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.31102e11 | −0.254727 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.94959e11i | 0.562398i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.79501e11 | −0.339055 | −0.169527 | − | 0.985525i | \(-0.554224\pi\) | ||||
−0.169527 | + | 0.985525i | \(0.554224\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.54874e11i | 1.77020i | 0.465398 | + | 0.885101i | \(0.345911\pi\) | ||||
−0.465398 | + | 0.885101i | \(0.654089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.02178e11 | −0.554997 | −0.277499 | − | 0.960726i | \(-0.589505\pi\) | ||||
−0.277499 | + | 0.960726i | \(0.589505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.97426e11i | 1.79820i | 0.437745 | + | 0.899099i | \(0.355777\pi\) | ||||
−0.437745 | + | 0.899099i | \(0.644223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.82850e11 | −1.21972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5.69158e11i | − 0.998053i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92617e10 | 0.0682176 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.99032e11i | 0.339540i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.40216e11 | −0.237028 | −0.118514 | − | 0.992952i | \(-0.537813\pi\) | ||||
−0.118514 | + | 0.992952i | \(0.537813\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1.02525e12i | − 1.70187i | −0.525268 | − | 0.850937i | \(-0.676035\pi\) | ||||
0.525268 | − | 0.850937i | \(-0.323965\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.77728e11 | 0.621350 | 0.310675 | − | 0.950516i | \(-0.399445\pi\) | ||||
0.310675 | + | 0.950516i | \(0.399445\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 4.25328e11i | − 0.687115i | −0.939132 | − | 0.343557i | \(-0.888368\pi\) | ||||
0.939132 | − | 0.343557i | \(-0.111632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.06255e11 | −0.490316 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.14472e12i | 1.80008i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.02957e10 | 0.0939710 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.76509e10i | 0.0576417i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.52341e10 | −0.0534644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.50961e11i | − 0.970423i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.30935e11 | −0.341241 | −0.170621 | − | 0.985337i | \(-0.554577\pi\) | ||||
−0.170621 | + | 0.985337i | \(0.554577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.01079e11i | 0.146753i | 0.997304 | + | 0.0733764i | \(0.0233774\pi\) | ||||
−0.997304 | + | 0.0733764i | \(0.976623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.50841e11 | −1.36844 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.63823e11i | 0.231685i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.67287e11 | −0.795317 | −0.397659 | − | 0.917533i | \(-0.630177\pi\) | ||||
−0.397659 | + | 0.917533i | \(0.630177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 8.97457e10i | − 0.123654i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.62963e10 | −0.0632382 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.04274e10i | 0.107979i | 0.998541 | + | 0.0539897i | \(0.0171938\pi\) | ||||
−0.998541 | + | 0.0539897i | \(0.982806\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49638e11 | 0.199179 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.93871e11i | 0.253668i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.25692e12 | −1.63061 | −0.815306 | − | 0.579030i | \(-0.803431\pi\) | ||||
−0.815306 | + | 0.579030i | \(0.803431\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.50994e11i | − 0.320115i | −0.987108 | − | 0.160057i | \(-0.948832\pi\) | ||||
0.987108 | − | 0.160057i | \(-0.0511679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.64488e11 | 0.334472 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.27838e11i | 0.407623i | 0.979010 | + | 0.203812i | \(0.0653330\pi\) | ||||
−0.979010 | + | 0.203812i | \(0.934667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.51916e11 | −0.310593 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.04603e12i | 1.26816i | 0.773268 | + | 0.634080i | \(0.218621\pi\) | ||||
−0.773268 | + | 0.634080i | \(0.781379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.59543e12 | −1.91806 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.59295e11i | 0.188333i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.13659e11 | −0.954002 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00367e11i | 0.231056i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.58893e11 | 0.753545 | 0.376773 | − | 0.926306i | \(-0.377034\pi\) | ||||
0.376773 | + | 0.926306i | \(0.377034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.55166e12i | − 1.74550i | −0.488170 | − | 0.872749i | \(-0.662335\pi\) | ||||
0.488170 | − | 0.872749i | \(-0.337665\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.03614e11 | −0.115603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.77778e11i | 0.743891i | 0.928255 | + | 0.371945i | \(0.121309\pi\) | ||||
−0.928255 | + | 0.371945i | \(0.878691\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.90577e10 | −0.0860624 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.15349e12i | 1.23538i | 0.786423 | + | 0.617688i | \(0.211930\pi\) | ||||
−0.786423 | + | 0.617688i | \(0.788070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04790e12 | 1.11320 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.49141e12i | 2.60411i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.26653e11 | −0.649730 | −0.324865 | − | 0.945760i | \(-0.605319\pi\) | ||||
−0.324865 | + | 0.945760i | \(0.605319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.56288e12i | 1.59454i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.43417e11 | 0.549987 | 0.274994 | − | 0.961446i | \(-0.411324\pi\) | ||||
0.274994 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.9.c.a.197.13 | yes | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.4 | ✓ | 16 | 3.2 | odd | 2 | inner | |
252.9.c.a.197.13 | yes | 16 | 1.1 | even | 1 | trivial |