Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.17 | ||
Root | \(2.58939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.a.383.18 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 12.3458 | − | 9.51744i | 0.791982 | − | 0.610544i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 26.7752i | 0.478970i | 0.970900 | + | 0.239485i | \(0.0769786\pi\) | ||||
−0.970900 | + | 0.239485i | \(0.923021\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 70.6872i | 0.545250i | 0.962120 | + | 0.272625i | \(0.0878918\pi\) | ||||
−0.962120 | + | 0.272625i | \(0.912108\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 61.8366 | − | 235.001i | 0.254472 | − | 0.967080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 98.7796 | 0.246142 | 0.123071 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123071 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −210.273 | −0.345084 | −0.172542 | − | 0.985002i | \(-0.555198\pi\) | ||||
−0.172542 | + | 0.985002i | \(0.555198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 254.832 | + | 330.561i | 0.292432 | + | 0.379336i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 524.555i | − | 0.440219i | −0.975475 | − | 0.220109i | \(-0.929359\pi\) | ||
0.975475 | − | 0.220109i | \(-0.0706414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1114.76i | − | 0.708434i | −0.935163 | − | 0.354217i | \(-0.884747\pi\) | ||
0.935163 | − | 0.354217i | \(-0.115253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 672.761 | + | 872.688i | 0.332899 | + | 0.431828i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −866.788 | −0.341659 | −0.170830 | − | 0.985301i | \(-0.554645\pi\) | ||||
−0.170830 | + | 0.985301i | \(0.554645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2408.09 | 0.770588 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1473.18 | − | 3489.79i | −0.388908 | − | 0.921276i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2162.01i | − | 0.477379i | −0.971096 | − | 0.238690i | \(-0.923282\pi\) | ||
0.971096 | − | 0.238690i | \(-0.0767179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1726.91i | 0.322750i | 0.986893 | + | 0.161375i | \(0.0515928\pi\) | ||||
−0.986893 | + | 0.161375i | \(0.948407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1219.51 | − | 940.129i | 0.194940 | − | 0.150281i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1892.66 | −0.261158 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12357.1 | 1.48393 | 0.741964 | − | 0.670440i | \(-0.233895\pi\) | ||||
0.741964 | + | 0.670440i | \(0.233895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2595.99 | + | 2001.26i | −0.273301 | + | 0.210689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1392.98i | − | 0.129415i | −0.997904 | − | 0.0647075i | \(-0.979389\pi\) | ||
0.997904 | − | 0.0647075i | \(-0.0206114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9131.49i | − | 0.753131i | −0.926390 | − | 0.376566i | \(-0.877105\pi\) | ||
0.926390 | − | 0.376566i | \(-0.122895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6292.19 | + | 1655.69i | 0.463202 | + | 0.121884i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21857.9 | 1.44332 | 0.721662 | − | 0.692246i | \(-0.243379\pi\) | ||||
0.721662 | + | 0.692246i | \(0.243379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11810.3 | 0.702703 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4992.42 | − | 6476.04i | −0.268773 | − | 0.348645i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7601.83i | 0.371731i | 0.982575 | + | 0.185865i | \(0.0595088\pi\) | ||||
−0.982575 | + | 0.185865i | \(0.940491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2644.85i | 0.117895i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10609.7 | − | 13762.6i | −0.432530 | − | 0.561067i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 40981.9 | 1.53272 | 0.766359 | − | 0.642413i | \(-0.222067\pi\) | ||||
0.766359 | + | 0.642413i | \(0.222067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24132.2 | 0.830370 | 0.415185 | − | 0.909737i | \(-0.363717\pi\) | ||||
0.415185 | + | 0.909737i | \(0.363717\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16611.5 | + | 4371.05i | 0.527300 | + | 0.138751i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5630.11i | − | 0.165285i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8969.02i | − | 0.244094i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) | ||
0.992524 | − | 0.122047i | \(-0.0389459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10701.2 | + | 8249.60i | −0.270588 | + | 0.208598i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4758.61 | −0.112030 | −0.0560150 | − | 0.998430i | \(-0.517839\pi\) | ||||
−0.0560150 | + | 0.998430i | \(0.517839\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65015.7 | −1.42794 | −0.713972 | − | 0.700174i | \(-0.753106\pi\) | ||||
−0.713972 | + | 0.700174i | \(0.753106\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29729.7 | − | 22918.8i | 0.610292 | − | 0.470478i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6982.45i | 0.134209i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 100325.i | − | 1.80860i | −0.426902 | − | 0.904298i | \(-0.640395\pi\) | ||
0.426902 | − | 0.904298i | \(-0.359605\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51401.5 | − | 29063.3i | −0.870488 | − | 0.492189i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −29063.3 | −0.463073 | −0.231537 | − | 0.972826i | \(-0.574375\pi\) | ||||
−0.231537 | + | 0.972826i | \(0.574375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14045.1 | 0.210851 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20576.8 | − | 26691.8i | −0.291461 | − | 0.378076i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 619.603i | 0.00829160i | 0.999991 | + | 0.00414580i | \(0.00131965\pi\) | ||||
−0.999991 | + | 0.00414580i | \(0.998680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14863.6i | − | 0.188157i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16435.8 | + | 21320.1i | 0.197053 | + | 0.255612i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29848.1 | 0.339318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −74920.5 | −0.808484 | −0.404242 | − | 0.914652i | \(-0.632465\pi\) | ||||
−0.404242 | + | 0.914652i | \(0.632465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6108.19 | − | 23213.3i | 0.0626361 | − | 0.238039i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 154823.i | 1.51019i | 0.655617 | + | 0.755094i | \(0.272409\pi\) | ||||
−0.655617 | + | 0.755094i | \(0.727591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 156724.i | − | 1.45560i | −0.685790 | − | 0.727799i | \(-0.740543\pi\) | ||
0.685790 | − | 0.727799i | \(-0.259457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −23366.4 | + | 18013.3i | −0.206833 | + | 0.159449i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 163885. | 1.38382 | 0.691910 | − | 0.721984i | \(-0.256769\pi\) | ||||
0.691910 | + | 0.721984i | \(0.256769\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 58919.6 | 0.475000 | 0.237500 | − | 0.971388i | \(-0.423672\pi\) | ||||
0.237500 | + | 0.971388i | \(0.423672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 152558. | − | 117608.i | 1.17524 | − | 0.906003i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 206289.i | − | 1.51978i | −0.650051 | − | 0.759890i | \(-0.725253\pi\) | ||
0.650051 | − | 0.759890i | \(-0.274747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 23208.4i | − | 0.163644i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13002.6 | + | 49414.3i | −0.0878142 | + | 0.333724i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 37079.3 | 0.240029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151294. | −0.939414 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13257.6 | − | 17197.4i | −0.0790135 | − | 0.102494i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 148150.i | 0.848058i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 34658.0i | − | 0.190675i | −0.995445 | − | 0.0953375i | \(-0.969607\pi\) | ||
0.995445 | − | 0.0953375i | \(-0.0303930\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −86908.4 | − | 112735.i | −0.459820 | − | 0.596466i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 146438. | 0.745548 | 0.372774 | − | 0.927922i | \(-0.378407\pi\) | ||||
0.372774 | + | 0.927922i | \(0.378407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 78799.5 | 0.386273 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 93439.9 | − | 39444.8i | 0.441264 | − | 0.186275i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 78954.6i | 0.359398i | 0.983722 | + | 0.179699i | \(0.0575124\pi\) | ||||
−0.983722 | + | 0.179699i | \(0.942488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 284001.i | − | 1.24676i | −0.781919 | − | 0.623380i | \(-0.785759\pi\) | ||
0.781919 | − | 0.623380i | \(-0.214241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 269853. | − | 208031.i | 1.14309 | − | 0.881213i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20770.7 | −0.0849398 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 57888.4 | 0.228650 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 145808. | − | 112404.i | 0.556528 | − | 0.429031i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 174820.i | 0.645097i | 0.946553 | + | 0.322549i | \(0.104540\pi\) | ||||
−0.946553 | + | 0.322549i | \(0.895460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 90430.8i | 0.322756i | 0.986893 | + | 0.161378i | \(0.0515938\pi\) | ||||
−0.986893 | + | 0.161378i | \(0.948406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −123271. | − | 32436.7i | −0.425727 | − | 0.112023i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −46238.4 | −0.154587 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 435845. | 1.41118 | 0.705591 | − | 0.708619i | \(-0.250681\pi\) | ||||
0.705591 | + | 0.708619i | \(0.250681\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 72350.0 | + | 93850.5i | 0.226958 | + | 0.294404i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 61270.8i | − | 0.186290i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 357566.i | − | 1.05411i | −0.849830 | − | 0.527057i | \(-0.823296\pi\) | ||
0.849830 | − | 0.527057i | \(-0.176704\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 25172.2 | + | 32652.7i | 0.0719798 | + | 0.0933704i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 206409. | 0.572714 | 0.286357 | − | 0.958123i | \(-0.407556\pi\) | ||||
0.286357 | + | 0.958123i | \(0.407556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −327078. | −0.880917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −261970. | − | 68933.2i | −0.685112 | − | 0.180276i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 425865.i | − | 1.08183i | −0.841079 | − | 0.540913i | \(-0.818079\pi\) | ||
0.841079 | − | 0.540913i | \(-0.181921\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 170221.i | 0.420163i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 505954. | − | 390043.i | 1.21388 | − | 0.935792i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 275598. | 0.642900 | 0.321450 | − | 0.946927i | \(-0.395830\pi\) | ||||
0.321450 | + | 0.946927i | \(0.395830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −160334. | −0.363773 | −0.181886 | − | 0.983320i | \(-0.558220\pi\) | ||||
−0.181886 | + | 0.983320i | \(0.558220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 297930. | − | 229676.i | 0.657638 | − | 0.506977i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 330864.i | 0.710756i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 51815.3i | − | 0.108356i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 246683. | − | 104135.i | 0.502326 | − | 0.212052i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −449025. | −0.890608 | −0.445304 | − | 0.895379i | \(-0.646904\pi\) | ||||
−0.445304 | + | 0.895379i | \(0.646904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 467575. | 0.903562 | 0.451781 | − | 0.892129i | \(-0.350789\pi\) | ||||
0.451781 | + | 0.892129i | \(0.350789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −53584.2 | − | 69508.1i | −0.100914 | − | 0.130903i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 888657.i | 1.63143i | 0.578453 | + | 0.815715i | \(0.303656\pi\) | ||||
−0.578453 | + | 0.815715i | \(0.696344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 90005.4i | 0.161115i | 0.996750 | + | 0.0805575i | \(0.0256701\pi\) | ||||
−0.996750 | + | 0.0805575i | \(0.974330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −85362.1 | − | 110729.i | −0.149030 | − | 0.193318i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 152827. | 0.260291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37297.3 | 0.0619858 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −53599.2 | + | 203696.i | −0.0869426 | + | 0.330412i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 110116.i | − | 0.174375i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 272052.i | 0.420674i | 0.977629 | + | 0.210337i | \(0.0674562\pi\) | ||||
−0.977629 | + | 0.210337i | \(0.932544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −58748.8 | + | 45289.8i | −0.0887258 | + | 0.0683993i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 244498. | 0.360727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −122070. | −0.175979 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −802670. | + | 618783.i | −1.13091 | + | 0.871823i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 110300.i | 0.151913i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 400949.i | − | 0.539917i | −0.962872 | − | 0.269958i | \(-0.912990\pi\) | ||
0.962872 | − | 0.269958i | \(-0.0870100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 148908. | − | 565902.i | 0.196093 | − | 0.745220i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 388147. | 0.499955 | 0.249978 | − | 0.968252i | \(-0.419577\pi\) | ||||
0.249978 | + | 0.968252i | \(0.419577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −999721. | −1.25977 | −0.629883 | − | 0.776690i | \(-0.716897\pi\) | ||||
−0.629883 | + | 0.776690i | \(0.716897\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 66455.1 | + | 86203.8i | 0.0819404 | + | 0.106291i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.53632e6i | 1.85392i | 0.375163 | + | 0.926959i | \(0.377587\pi\) | ||||
−0.375163 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 585250.i | 0.691308i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −954837. | − | 1.23859e6i | −1.10423 | − | 1.43238i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.24345e6 | −1.40810 | −0.704051 | − | 0.710150i | \(-0.748627\pi\) | ||||
−0.704051 | + | 0.710150i | \(0.748627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 227499. | 0.252311 | 0.126156 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126156 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −911199. | + | 130402.i | −0.989914 | + | 0.141667i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 316224.i | 0.336573i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 234405.i | 0.244469i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −358809. | + | 276608.i | −0.366746 | + | 0.282727i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 113966. | 0.114180 | 0.0570899 | − | 0.998369i | \(-0.481818\pi\) | ||||
0.0570899 | + | 0.998369i | \(0.481818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −85621.0 | −0.0840967 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 173397. | − | 133673.i | 0.166991 | − | 0.128734i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 114461.i | 0.108100i | 0.998538 | + | 0.0540501i | \(0.0172131\pi\) | ||||
−0.998538 | + | 0.0540501i | \(0.982787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 873489.i | 0.809111i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −508074. | − | 133692.i | −0.461664 | − | 0.121479i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.92150e6 | −1.71297 | −0.856487 | − | 0.516168i | \(-0.827358\pi\) | ||||
−0.856487 | + | 0.516168i | \(0.827358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −203541. | −0.178048 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5897.03 | + | 7649.48i | 0.00506239 | + | 0.00656680i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.09389e6i | − | 1.76431i | −0.470964 | − | 0.882153i | \(-0.656094\pi\) | ||
0.470964 | − | 0.882153i | \(-0.343906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 536501.i | 0.443759i | 0.975074 | + | 0.221880i | \(0.0712192\pi\) | ||||
−0.975074 | + | 0.221880i | \(0.928781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −141464. | − | 183503.i | −0.114878 | − | 0.149017i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 237870. | 0.189674 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.88269e6 | −1.47428 | −0.737141 | − | 0.675739i | \(-0.763825\pi\) | ||||
−0.737141 | + | 0.675739i | \(0.763825\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 405825. | + | 106786.i | 0.312125 | + | 0.0821306i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.07557e6i | 1.56809i | 0.620705 | + | 0.784045i | \(0.286847\pi\) | ||||
−0.620705 | + | 0.784045i | \(0.713153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 959147.i | 0.711900i | 0.934505 | + | 0.355950i | \(0.115843\pi\) | ||||
−0.934505 | + | 0.355950i | \(0.884157\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 368498. | − | 284077.i | 0.268734 | − | 0.207169i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 98465.6 | 0.0705635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14470e6 | 0.806207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −924952. | + | 713051.i | −0.640305 | + | 0.493615i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.40544e6i | 0.956406i | 0.878249 | + | 0.478203i | \(0.158712\pi\) | ||||
−0.878249 | + | 0.478203i | \(0.841288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.09730e6i | 0.734125i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −145520. | − | 344720.i | −0.0957267 | − | 0.226765i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 182262. | 0.117901 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 645479. | 0.410645 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.47352e6 | + | 1.91141e6i | 0.922036 | + | 1.19604i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 646144.i | 0.397722i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.45801e6i | 1.48846i | 0.667921 | + | 0.744232i | \(0.267184\pi\) | ||||
−0.667921 | + | 0.744232i | \(0.732816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.49161e6 | − | 1.93488e6i | −0.888707 | − | 1.15281i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.05824e6 | −1.20669 | −0.603344 | − | 0.797481i | \(-0.706165\pi\) | ||||
−0.603344 | + | 0.797481i | \(0.706165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08280e6 | 0.624722 | 0.312361 | − | 0.949964i | \(-0.398880\pi\) | ||||
0.312361 | + | 0.949964i | \(0.398880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −117036. | + | 444777.i | −0.0664573 | + | 0.252561i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.77359e6i | 1.55022i | 0.631824 | + | 0.775112i | \(0.282306\pi\) | ||||
−0.631824 | + | 0.775112i | \(0.717694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 213563.i | − | 0.117503i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.02329e6 | − | 1.55977e6i | 1.09596 | − | 0.844884i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −584755. | −0.311866 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −506356. | −0.265918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 727408. | − | 560764.i | 0.376191 | − | 0.290008i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.54507e6i | 0.786972i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.19074e6i | − | 0.597377i | −0.954351 | − | 0.298689i | \(-0.903451\pi\) | ||
0.954351 | − | 0.298689i | \(-0.0965492\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 764122. | − | 2.90393e6i | 0.377617 | − | 1.43508i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 240147. | 0.116914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.18912e6 | 1.05001 | 0.525006 | − | 0.851099i | \(-0.324063\pi\) | ||||
0.525006 | + | 0.851099i | \(0.324063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.96335e6 | − | 2.54680e6i | −0.927893 | − | 1.20364i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 170584.i | 0.0794422i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.02288e6i | 0.928398i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −220885. | − | 286526.i | −0.0999122 | − | 0.129604i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 806476. | 0.359557 | 0.179778 | − | 0.983707i | \(-0.442462\pi\) | ||||
0.179778 | + | 0.983707i | \(0.442462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.13913e6 | 0.500624 | 0.250312 | − | 0.968165i | \(-0.419467\pi\) | ||||
0.250312 | + | 0.968165i | \(0.419467\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 309771. | + | 733809.i | 0.134206 | + | 0.317918i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 405481.i | 0.173195i | 0.996243 | + | 0.0865973i | \(0.0275993\pi\) | ||||
−0.996243 | + | 0.0865973i | \(0.972401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 127413.i | − | 0.0536590i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 457773. | − | 352900.i | 0.190099 | − | 0.146548i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.48388e6 | −1.42668 | −0.713341 | − | 0.700817i | \(-0.752819\pi\) | ||||
−0.713341 | + | 0.700817i | \(0.752819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23340e6 | 0.498122 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.86784e6 | + | 1.43993e6i | −0.743999 | + | 0.573554i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.74081e6i | − | 0.683942i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 430810.i | − | 0.166963i | −0.996509 | − | 0.0834816i | \(-0.973396\pi\) | ||
0.996509 | − | 0.0834816i | \(-0.0266040\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −327350. | − | 86137.0i | −0.125155 | − | 0.0329324i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −537352. | −0.202686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.72685e6 | 0.642661 | 0.321330 | − | 0.946967i | \(-0.395870\pi\) | ||||
0.321330 | + | 0.946967i | \(0.395870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41001e6 | + | 1.82902e6i | 0.517777 | + | 0.671647i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 454614.i | 0.164736i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.14141e6i | − | 1.48098i | −0.672066 | − | 0.740491i | \(-0.734593\pi\) | ||
0.672066 | − | 0.740491i | \(-0.265407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −329855. | − | 427880.i | −0.116416 | − | 0.151011i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.77835e6 | −0.619469 | −0.309734 | − | 0.950823i | \(-0.600240\pi\) | ||||
−0.309734 | + | 0.950823i | \(0.600240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −186957. | −0.0642820 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.14591e6 | − | 564660.i | −0.728338 | − | 0.191650i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.42987e6i | 0.814159i | 0.913393 | + | 0.407079i | \(0.133453\pi\) | ||||
−0.913393 | + | 0.407079i | \(0.866547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 454678.i | 0.150405i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.80789e6 | − | 1.39372e6i | 0.590461 | − | 0.455190i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.68622e6 | 0.866263 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.87276e6 | −0.914794 | −0.457397 | − | 0.889263i | \(-0.651218\pi\) | ||||
−0.457397 | + | 0.889263i | \(0.651218\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 972842. | − | 749970.i | 0.305921 | − | 0.235837i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 622456.i | 0.193307i | 0.995318 | + | 0.0966535i | \(0.0308139\pi\) | ||||
−0.995318 | + | 0.0966535i | \(0.969186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 363123.i | − | 0.111376i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 778175. | − | 1.37629e6i | 0.235744 | − | 0.416938i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.22063e6 | 0.365257 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.35930e6 | −0.697389 | −0.348694 | − | 0.937236i | \(-0.613375\pi\) | ||||
−0.348694 | + | 0.937236i | \(0.613375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 751446. | + | 974756.i | 0.219429 | + | 0.284637i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.89689e6i | 0.835714i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 778177.i | − | 0.221798i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.70296e6 | − | 3.50622e6i | −0.761202 | − | 0.987412i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.85277e6 | 0.793839 | 0.396919 | − | 0.917854i | \(-0.370079\pi\) | ||||
0.396919 | + | 0.917854i | \(0.370079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.61879e6 | 0.720105 | 0.360052 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360052 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.35162e6 | − | 5.13662e6i | 0.367285 | − | 1.39581i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.26317e6i | − | 0.339227i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70583e6i | 0.452759i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −256430. | + | 197684.i | −0.0672708 | + | 0.0518595i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.48960e6 | 0.386257 | 0.193128 | − | 0.981173i | \(-0.438137\pi\) | ||||
0.193128 | + | 0.981173i | \(0.438137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.69553e6 | −0.947233 | −0.473617 | − | 0.880731i | \(-0.657052\pi\) | ||||
−0.473617 | + | 0.880731i | \(0.657052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 714678. | − | 550950.i | 0.181087 | − | 0.139601i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 966264.i | 0.242043i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97023e6i | 0.487927i | 0.969784 | + | 0.243963i | \(0.0784477\pi\) | ||||
−0.969784 | + | 0.243963i | \(0.921552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 730310. | − | 2.77543e6i | 0.178818 | − | 0.679570i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.26291e6 | 0.789943 | 0.394971 | − | 0.918693i | \(-0.370755\pi\) | ||||
0.394971 | + | 0.918693i | \(0.370755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16590.0 | −0.00397142 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.66384e6 | + | 2.15829e6i | 0.393860 | + | 0.510906i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.83012e6i | 1.36478i | 0.730989 | + | 0.682389i | \(0.239059\pi\) | ||||
−0.730989 | + | 0.682389i | \(0.760941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 137598.i | − | 0.0318544i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 860669. | + | 1.11644e6i | 0.197057 | + | 0.255617i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 397976. | 0.0901216 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.58653e6 | −0.803310 | −0.401655 | − | 0.915791i | \(-0.631565\pi\) | ||||
−0.401655 | + | 0.915791i | \(0.631565\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.83059e6 | + | 772765.i | −0.405563 | + | 0.171205i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.80727e6i | 0.834376i | 0.908820 | + | 0.417188i | \(0.136984\pi\) | ||||
−0.908820 | + | 0.417188i | \(0.863016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.35067e6i | − | 1.59358i | −0.604255 | − | 0.796791i | \(-0.706529\pi\) | ||
0.604255 | − | 0.796791i | \(-0.293471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −570850. | + | 440072.i | −0.122430 | + | 0.0943824i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.39614e6 | 1.78151 | 0.890753 | − | 0.454488i | \(-0.150178\pi\) | ||||
0.890753 | + | 0.454488i | \(0.150178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 633994. | 0.133092 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.38085e6 | − | 4.14813e6i | 1.11763 | − | 0.861589i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 902005.i | − | 0.185377i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.68445e6i | − | 0.545910i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.78643e6 | + | 470071.i | 0.359493 | + | 0.0945949i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.74882e6 | −0.945686 | −0.472843 | − | 0.881147i | \(-0.656772\pi\) | ||||
−0.472843 | + | 0.881147i | \(0.656772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.59837e6 | −0.512080 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −583141. | − | 756436.i | −0.113738 | − | 0.147538i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.00601e6i | − | 0.387239i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.94838e6i | − | 1.13652i | −0.822850 | − | 0.568259i | \(-0.807617\pi\) | ||
0.822850 | − | 0.568259i | \(-0.192383\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.40312e6 | − | 4.41443e6i | −0.643583 | − | 0.834839i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.20829e6 | −0.600579 | −0.300289 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300289 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.13410e6 | −0.210151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 621540. | + | 163548.i | 0.114013 | + | 0.0300008i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 336373.i | − | 0.0610843i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.23102e6i | 0.580882i | 0.956893 | + | 0.290441i | \(0.0938021\pi\) | ||||
−0.956893 | + | 0.290441i | \(0.906198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.54828e6 | − | 1.96449e6i | 0.453579 | − | 0.349667i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.43429e6 | 1.31014 | 0.655072 | − | 0.755566i | \(-0.272638\pi\) | ||||
0.655072 | + | 0.755566i | \(0.272638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.14541e6 | −0.723334 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.03804e6 | + | 3.11295e6i | −0.697670 | + | 0.537839i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.05706e6i | 1.37842i | 0.724560 | + | 0.689211i | \(0.242043\pi\) | ||||
−0.724560 | + | 0.689211i | \(0.757957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.59578e6i | − | 0.778586i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.89029e6 | + | 1.64225e6i | −0.652663 | + | 0.275516i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.19631e6 | 0.697188 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.15911e6 | 0.355262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.05315e6 | − | 5.25764e6i | −0.660502 | − | 0.856786i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.22668e6i | − | 0.197988i | −0.995088 | − | 0.0989939i | \(-0.968438\pi\) | ||
0.995088 | − | 0.0989939i | \(-0.0315624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.04029e6i | − | 0.965614i | −0.875727 | − | 0.482807i | \(-0.839617\pi\) | ||
0.875727 | − | 0.482807i | \(-0.160383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.62007e6 | + | 2.10151e6i | 0.256528 | + | 0.332762i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 905860. | 0.142080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.68502e6 | −0.883269 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.53418e6 | − | 9.63077e6i | 0.390033 | − | 1.48226i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 292906.i | 0.0446591i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.38806e6i | 0.662808i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.40247e6 | − | 2.62299e6i | 0.509165 | − | 0.392519i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.16662e6 | 0.172965 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 585938. | 0.0860714 | 0.0430357 | − | 0.999074i | \(-0.486297\pi\) | ||||
0.0430357 | + | 0.999074i | \(0.486297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.97945e6 | + | 1.52597e6i | −0.288102 | + | 0.222099i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.57758e6i | 0.227511i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.72451e6i | − | 0.246432i | −0.992380 | − | 0.123216i | \(-0.960679\pi\) | ||
0.992380 | − | 0.123216i | \(-0.0393208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.49225e6 | − | 5.67107e6i | 0.211305 | − | 0.803034i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.41014e6 | −0.338192 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.09169e6 | 0.986136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.14898e6 | + | 4.08478e6i | 0.433948 | + | 0.562906i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.06092e6i | 0.964325i | 0.876082 | + | 0.482163i | \(0.160149\pi\) | ||||
−0.876082 | + | 0.482163i | \(0.839851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.92011e6i | 0.259894i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −493149. | − | 639701.i | −0.0661563 | − | 0.0858163i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.79606e6 | −0.238809 | −0.119404 | − | 0.992846i | \(-0.538099\pi\) | ||||
−0.119404 | + | 0.992846i | \(0.538099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.52345e6 | 0.727929 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.05440e6 | − | 3.63342e6i | 0.268366 | − | 0.474634i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.28895e7i | − | 1.66899i | −0.551012 | − | 0.834497i | \(-0.685758\pi\) | ||
0.551012 | − | 0.834497i | \(-0.314242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.88344e6i | − | 1.26858i | −0.773095 | − | 0.634290i | \(-0.781293\pi\) | ||
0.773095 | − | 0.634290i | \(-0.218707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.54356e6 | + | 4.27357e6i | −0.705346 | + | 0.543756i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.08730e6 | −0.263279 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.24804e6 | −0.906319 | −0.453160 | − | 0.891429i | \(-0.649703\pi\) | ||||
−0.453160 | + | 0.891429i | \(0.649703\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.77258e6 | − | 4.45012e6i | 0.715605 | − | 0.551665i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.05440e6i | − | 0.252491i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 750906.i | 0.0914985i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.32308e6 | − | 348147.i | −0.159844 | − | 0.0420603i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.17837e6 | 0.141152 | 0.0705758 | − | 0.997506i | \(-0.477516\pi\) | ||||
0.0705758 | + | 0.997506i | \(0.477516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.92510e6 | 0.228647 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.45774e6 | + | 1.09712e7i | 0.996061 | + | 1.29206i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.11009e6i | − | 0.363191i | −0.983373 | − | 0.181596i | \(-0.941874\pi\) | ||
0.983373 | − | 0.181596i | \(-0.0581262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 992806.i | 0.114967i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 856621. | + | 1.11119e6i | 0.0983678 | + | 0.127600i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.95969e6 | 1.02030 | 0.510148 | − | 0.860087i | \(-0.329591\pi\) | ||||
0.510148 | + | 0.860087i | \(0.329591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.54483e7 | 1.74459 | 0.872294 | − | 0.488981i | \(-0.162631\pi\) | ||||
0.872294 | + | 0.488981i | \(0.162631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.10772e6 | − | 554613.i | −0.236059 | − | 0.0621151i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4.05092e6i | − | 0.449951i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.11892e7i | − | 1.23261i | −0.787507 | − | 0.616306i | \(-0.788629\pi\) | ||
0.787507 | − | 0.616306i | \(-0.211371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.88676e6 | − | 1.45452e6i | 0.206146 | − | 0.158919i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.59613e6 | −0.498068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.89608e6 | 0.848713 | 0.424356 | − | 0.905495i | \(-0.360500\pi\) | ||||
0.424356 | + | 0.905495i | \(0.360500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 460464. | − | 354975.i | 0.0490917 | − | 0.0378451i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.91077e6i | − | 0.202067i | −0.994883 | − | 0.101033i | \(-0.967785\pi\) | ||
0.994883 | − | 0.101033i | \(-0.0322149\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.94989e6i | − | 0.309441i | −0.987958 | − | 0.154721i | \(-0.950552\pi\) | ||
0.987958 | − | 0.154721i | \(-0.0494478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.27694e6 | + | 3.02491e6i | 0.132874 | + | 0.314763i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −43798.0 | −0.00452099 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.55853e6 | 0.364394 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.04802e6 | − | 1.35947e6i | −0.106464 | − | 0.138102i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.48198e6i | − | 0.653253i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.88150e7i | 1.88118i | 0.339546 | + | 0.940589i | \(0.389726\pi\) | ||||
−0.339546 | + | 0.940589i | \(0.610274\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.58924e6 | + | 3.35870e6i | 0.256840 | + | 0.333167i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 927975. | 0.0913276 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.48339e6 | −0.242492 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −294256. | + | 1.11828e6i | −0.0285085 | + | 0.108342i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.09172e7i | 1.04946i | 0.851267 | + | 0.524732i | \(0.175835\pi\) | ||||
−0.851267 | + | 0.524732i | \(0.824165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00191e7i | 0.955659i | 0.878453 | + | 0.477829i | \(0.158576\pi\) | ||||
−0.878453 | + | 0.477829i | \(0.841424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.01852e6 | − | 2.32699e6i | 0.285689 | − | 0.220240i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.37444e7 | −1.29082 | −0.645411 | − | 0.763836i | \(-0.723314\pi\) | ||||
−0.645411 | + | 0.763836i | \(0.723314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.04818e6 | 0.377266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.50706e6 | + | 1.16180e6i | −0.139372 | + | 0.107443i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.03271e6i | 0.553643i | 0.960921 | + | 0.276821i | \(0.0892811\pi\) | ||||
−0.960921 | + | 0.276821i | \(0.910719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.92091e6i | 0.357095i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.02035e6 | + | 1.52787e7i | −0.363371 | + | 1.38094i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.47900e7 | −1.32664 | −0.663320 | − | 0.748336i | \(-0.730853\pi\) | ||||
−0.663320 | + | 0.748336i | \(0.730853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.07054e7 | 0.953010 | 0.476505 | − | 0.879172i | \(-0.341903\pi\) | ||||
0.476505 | + | 0.879172i | \(0.341903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.04977e6 | + | 1.36174e6i | 0.0927494 | + | 0.120312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.10988e6i | 0.185013i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.87401e6i | 0.163101i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.81601e6 | − | 4.95003e6i | −0.329643 | − | 0.427605i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.38377e6 | 0.204389 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.90789e6 | −0.417693 | −0.208847 | − | 0.977948i | \(-0.566971\pi\) | ||||
−0.208847 | + | 0.977948i | \(0.566971\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.54755e6 | − | 8.40372e6i | −0.299688 | − | 0.709925i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.28439e7i | − | 1.07702i | −0.842618 | − | 0.538512i | \(-0.818987\pi\) | ||
0.842618 | − | 0.538512i | \(-0.181013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.29592e6i | − | 0.440825i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.79197e6 | − | 3.69416e6i | 0.395956 | − | 0.305245i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.31400e6 | 0.189807 | 0.0949033 | − | 0.995486i | \(-0.469746\pi\) | ||||
0.0949033 | + | 0.995486i | \(0.469746\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.11403e6 | −0.172141 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.23423e7 | + | 9.51478e6i | −0.997713 | + | 0.769143i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.59846e6i | − | 0.128279i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02912e7i | 0.819923i | 0.912103 | + | 0.409961i | \(0.134458\pi\) | ||||
−0.912103 | + | 0.409961i | \(0.865542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.64088e6 | + | 431771.i | 0.129791 | + | 0.0341523i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.60419e6 | 0.597161 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −730693. | −0.0569709 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.46218e7 | + | 1.89670e7i | 1.13190 | + | 1.46827i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.72471e7i | − | 1.32562i | −0.748786 | − | 0.662811i | \(-0.769363\pi\) | ||
0.748786 | − | 0.662811i | \(-0.230637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.37753e7i | − | 1.05126i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.57008e6 | + | 7.22537e6i | 0.422074 | + | 0.547504i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.09440e7 | −0.823429 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.52733e7 | −1.88819 | −0.944095 | − | 0.329673i | \(-0.893061\pi\) | ||||
−0.944095 | + | 0.329673i | \(0.893061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.35764e7 | − | 6.20376e6i | −1.74906 | − | 0.460236i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.49687e6i | − | 0.110270i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 556140.i | − | 0.0406836i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.53514e7 | + | 1.18345e7i | −1.11519 | + | 0.859708i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.71570e7 | 1.23771 | 0.618857 | − | 0.785504i | \(-0.287596\pi\) | ||||
0.618857 | + | 0.785504i | \(0.287596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.10784e7 | 0.793665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.80865e6 | − | 2.16521e6i | 0.199826 | − | 0.154047i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.20632e6i | − | 0.367863i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.67975e7i | 1.17871i | 0.807873 | + | 0.589357i | \(0.200619\pi\) | ||||
−0.807873 | + | 0.589357i | \(0.799381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00084e7 | + | 1.02822e7i | −0.697501 | + | 0.716584i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.78997e6 | −0.331542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.60515e7 | −1.10346 | −0.551730 | − | 0.834023i | \(-0.686032\pi\) | ||||
−0.551730 | + | 0.834023i | \(0.686032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.00964e6 | + | 3.90403e6i | 0.205493 | + | 0.266560i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 885956.i | − | 0.0600819i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81409e7i | 1.22194i | 0.791655 | + | 0.610968i | \(0.209220\pi\) | ||||
−0.791655 | + | 0.610968i | \(0.790780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.23094e6 | + | 2.89391e6i | 0.149259 | + | 0.193615i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.71782e7 | −1.14158 | −0.570790 | − | 0.821096i | \(-0.693363\pi\) | ||||
−0.570790 | + | 0.821096i | \(0.693363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.68084e6 | −0.308982 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.79718e6 | + | 6.82989e6i | −0.117839 | + | 0.447829i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.15846e7i | 0.754528i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.57900e6i | 0.619755i | 0.950776 | + | 0.309878i | \(0.100288\pi\) | ||||
−0.950776 | + | 0.309878i | \(0.899712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.40699e6 | − | 1.08466e6i | 0.0904284 | − | 0.0697119i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.42130e6 | −0.154590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.72136e7 | −1.09177 | −0.545886 | − | 0.837860i | \(-0.683807\pi\) | ||||
−0.545886 | + | 0.837860i | \(0.683807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.05706e6 | + | 814893.i | −0.0666031 | + | 0.0513448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.18209e7i | − | 0.739925i | −0.929047 | − | 0.369962i | \(-0.879371\pi\) | ||
0.929047 | − | 0.369962i | \(-0.120629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.16486e6i | 0.258993i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 868499. | − | 3.30060e6i | 0.0536557 | − | 0.203910i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.61739e6 | −0.528917 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28407e7 | 0.783021 | 0.391511 | − | 0.920174i | \(-0.371953\pi\) | ||||
0.391511 | + | 0.920174i | \(0.371953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08938e6 | + | 1.41312e6i | 0.0659999 | + | 0.0856134i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.84680e6i | − | 0.532522i | −0.963901 | − | 0.266261i | \(-0.914212\pi\) | ||
0.963901 | − | 0.266261i | \(-0.0857883\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.15855e6i | 0.248707i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.31338e6 | + | 1.07839e7i | 0.493998 | + | 0.640802i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.55284e6 | −0.0916819 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −470054. | −0.0275753 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.54498e6 | + | 3.18504e6i | −0.439798 | + | 0.185657i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.16699e7i | 0.675914i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.54331e7i | 1.46373i | 0.681447 | + | 0.731867i | \(0.261351\pi\) | ||||
−0.681447 | + | 0.731867i | \(0.738649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.37224e7 | + | 1.82878e7i | −1.35665 | + | 1.04585i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.45820e7 | 0.828660 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.07434e6 | −0.286548 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.51287e6 | + | 1.93719e6i | −0.141011 | + | 0.108706i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.09111e7i | − | 1.72373i | −0.507138 | − | 0.861865i | \(-0.669297\pi\) | ||
0.507138 | − | 0.861865i | \(-0.330703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.14657e7i | − | 0.635378i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 145607. | + | 38314.1i | 0.00801864 | + | 0.00210998i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.42223e6 | −0.351477 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.64054e6 | 0.0892271 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.99285e7 | − | 2.58507e7i | −1.07719 | − | 1.39730i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 797413.i | − | 0.0428363i | −0.999771 | − | 0.0214181i | \(-0.993182\pi\) | ||
0.999771 | − | 0.0214181i | \(-0.00681813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.10694e7i | − | 1.12487i | −0.826843 | − | 0.562433i | \(-0.809866\pi\) | ||
0.826843 | − | 0.562433i | \(-0.190134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.10612e6 | + | 6.62353e6i | 0.270935 | + | 0.351450i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.57391e6 | 0.504889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01795e7 | −0.533543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.49296e6 | − | 919115.i | −0.181963 | − | 0.0478807i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.22210e6i | − | 0.0632772i | −0.999499 | − | 0.0316386i | \(-0.989927\pi\) | ||
0.999499 | − | 0.0316386i | \(-0.0100726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.41506e7i | 1.24288i | 0.783463 | + | 0.621438i | \(0.213451\pi\) | ||||
−0.783463 | + | 0.621438i | \(0.786549\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.93669e6 | − | 2.26391e6i | 0.150218 | − | 0.115804i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.38595e7 | −1.72154 | −0.860769 | − | 0.508995i | \(-0.830017\pi\) | ||||
−0.860769 | + | 0.508995i | \(0.830017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.08299e7 | −0.547318 | −0.273659 | − | 0.961827i | \(-0.588234\pi\) | ||||
−0.273659 | + | 0.961827i | \(0.588234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.32433e7 | + | 1.79184e7i | −1.16760 | + | 0.900114i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.19516e6i | − | 0.309343i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.52665e6i | 0.274313i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.02656e6 | − | 2.54406e6i | 0.297342 | − | 0.125520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.78766e7 | −0.876760 | −0.438380 | − | 0.898790i | \(-0.644448\pi\) | ||||
−0.438380 | + | 0.898790i | \(0.644448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.58368e7 | 0.772109 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.97541e7 | + | 2.56245e7i | 0.957388 | + | 1.24190i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 8.75759e6i | − | 0.421932i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.06945e7i | − | 0.512215i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.12862e6 | + | 1.18414e7i | 0.434646 | + | 0.563812i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.07110e7 | −0.506998 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.17436e6 | 0.102320 | 0.0511599 | − | 0.998690i | \(-0.483708\pi\) | ||||
0.0511599 | + | 0.998690i | \(0.483708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.84570e6 | − | 7.01431e6i | 0.0863468 | − | 0.328148i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.34641e7i | 1.55642i | 0.628004 | + | 0.778210i | \(0.283872\pi\) | ||||
−0.628004 | + | 0.778210i | \(0.716128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.77403e6i | 0.266991i | 0.991049 | + | 0.133495i | \(0.0426202\pi\) | ||||
−0.991049 | + | 0.133495i | \(0.957380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.21563e6 | − | 937141.i | 0.0558850 | − | 0.0430821i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.35740e6 | −0.153453 | −0.0767267 | − | 0.997052i | \(-0.524447\pi\) | ||||
−0.0767267 | + | 0.997052i | \(0.524447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.14026e7 | 0.518162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.41322e7 | − | 1.08946e7i | 0.638502 | − | 0.492225i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.91007e6i | − | 0.445171i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.88594e6i | 0.0842332i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63283e6 | + | 1.76064e7i | −0.205736 | + | 0.781869i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.04723e7 | −0.462403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12595.7 | 0.000552997 | 0.000276498 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000276498 | 1.00000i | \(0.499912\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.33762e7 | + | 1.73512e7i | 0.583928 | + | 0.757457i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.16885e7i | − | 1.37551i | −0.725945 | − | 0.687753i | \(-0.758597\pi\) | ||
0.725945 | − | 0.687753i | \(-0.241403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.11571e7i | − | 0.913175i | −0.889678 | − | 0.456588i | \(-0.849071\pi\) | ||
0.889678 | − | 0.456588i | \(-0.150929\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.04435e7 | + | 1.35470e7i | 0.448216 | + | 0.581414i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.13156e7 | 1.76321 | 0.881607 | − | 0.471985i | \(-0.156462\pi\) | ||||
0.881607 | + | 0.471985i | \(0.156462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.44987e6 | 0.103966 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.07742e6 | − | 2.87086e6i | −0.214264 | − | 0.121148i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.43664e7i | − | 1.02250i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.37920e6i | 0.307930i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.25017e6 | − | 1.73467e6i | 0.0933757 | − | 0.0719840i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.73361e6 | 0.154074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.98758e6 | 0.163643 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.96894e6 | − | 6.14331e6i | 0.325223 | − | 0.250717i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.29299e6i | − | 0.174236i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 6.87161e6i | − | 0.277358i | −0.990337 | − | 0.138679i | \(-0.955714\pi\) | ||
0.990337 | − | 0.138679i | \(-0.0442856\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.63834e7 | + | 9.57370e6i | 1.46047 | + | 0.384300i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.68881e7 | 0.674195 | 0.337097 | − | 0.941470i | \(-0.390555\pi\) | ||||
0.337097 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87086e6 | −0.113982 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.14964e6 | + | 7.97715e6i | 0.242827 | + | 0.314989i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.03513e7i | 0.406510i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.85463e7i | 1.11497i | 0.830189 | + | 0.557483i | \(0.188233\pi\) | ||||
−0.830189 | + | 0.557483i | \(0.811767\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.33940e7 | + | 3.03461e7i | 0.908773 | + | 1.17884i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.00061e6 | 0.0386598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.97570e7 | 1.14350 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.68301e7 | − | 9.69126e6i | −1.40768 | − | 0.370408i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4.81809e7i | − | 1.83162i | −0.401610 | − | 0.915811i | \(-0.631549\pi\) | ||
0.401610 | − | 0.915811i | \(-0.368451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.31657e7i | − | 0.497818i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.54106e7 | + | 1.95892e7i | −0.955676 | + | 0.736737i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.38737e6 | 0.0518994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.81871e7 | −1.04882 | −0.524411 | − | 0.851465i | \(-0.675715\pi\) | ||||
−0.524411 | + | 0.851465i | \(0.675715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.33680e7 | − | 1.03055e7i | 0.494769 | − | 0.381420i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.40620e7i | − | 0.517693i | −0.965918 | − | 0.258847i | \(-0.916658\pi\) | ||
0.965918 | − | 0.258847i | \(-0.0833424\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20742e6i | 0.0442158i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.78824e6 | + | 6.60500e6i | 0.101567 | + | 0.240599i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.59975e7 | 0.942013 | 0.471006 | − | 0.882130i | \(-0.343891\pi\) | ||||
0.471006 | + | 0.882130i | \(0.343891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.36711e7 | 0.492761 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.63975e7 | + | 3.42422e7i | 0.946480 | + | 1.22775i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.29770e7i | − | 1.17619i | −0.808791 | − | 0.588096i | \(-0.799878\pi\) | ||
0.808791 | − | 0.588096i | \(-0.200122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.20227e7i | − | 0.426574i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.03257e6 | − | 2.63660e6i | −0.0717408 | − | 0.0930603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.58108e6 | −0.195962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.56469e7 | 0.895833 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.01341e7 | − | 3.85131e7i | 0.352143 | − | 1.33827i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.25194e7i | 0.432779i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.05302e7i | − | 1.04994i | −0.851122 | − | 0.524968i | \(-0.824077\pi\) | ||
0.851122 | − | 0.524968i | \(-0.175923\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.21926e6 | + | 5.56537e6i | −0.246992 | + | 0.190408i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.86270e7 | −0.974377 | −0.487189 | − | 0.873297i | \(-0.661978\pi\) | ||||
−0.487189 | + | 0.873297i | \(0.661978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00752e7 | 0.679796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.25136e6 | + | 4.81921e6i | −0.210602 | + | 0.162355i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.38661e7i | − | 0.464749i | −0.972626 | − | 0.232374i | \(-0.925351\pi\) | ||
0.972626 | − | 0.232374i | \(-0.0746495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61204.1i | 0.00204091i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.64339e6 | − | 1.38461e7i | 0.120874 | − | 0.459363i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.90160e7 | 1.61791 | 0.808954 | − | 0.587872i | \(-0.200034\pi\) | ||||
0.808954 | + | 0.587872i | \(0.200034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.37940e7 | −0.781406 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.47051e7 | + | 1.90751e7i | 0.480481 | + | 0.623268i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.91507e6i | 0.257314i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.29631e6i | 0.300695i | 0.988633 | + | 0.150348i | \(0.0480393\pi\) | ||||
−0.988633 | + | 0.150348i | \(0.951961\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.13328e7 | − | 1.47007e7i | −0.364725 | − | 0.473112i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.40991e6 | −0.0771692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.47793e7 | −1.10811 | −0.554055 | − | 0.832480i | \(-0.686920\pi\) | ||||
−0.554055 | + | 0.832480i | \(0.686920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.82043e7 | − | 4.31237e7i | −0.577112 | − | 1.36711i |
(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 | 384.6.c.a.383.17 | ✓ | 20 | |
3.2 | odd | 2 | 384.6.c.d.383.3 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.d.383.4 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.b.383.17 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.c.383.4 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.a.383.18 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.b.383.18 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.c.383.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.17 | ✓ | 20 | 1.1 | even | 1 | trivial | |
384.6.c.a.383.18 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.17 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.18 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.c.383.3 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.c.383.4 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.3 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.4 | yes | 20 | 4.3 | odd | 2 |