Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(13,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.k (of order \(4\), degree \(2\), 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: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 8x^{6} + 28x^{5} + 97x^{4} - 168x^{3} + 288x^{2} + 864x + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Root | \(3.17086 + 3.17086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.13 |
Dual form | 60.5.k.a.37.3 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 3.67423 | + | 3.67423i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.4961 | + | 12.7640i | −0.859842 | + | 0.510560i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.2390 | + | 29.2390i | −0.596715 | + | 0.596715i | −0.939437 | − | 0.342722i | \(-0.888651\pi\) |
0.342722 | + | 0.939437i | \(0.388651\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −100.806 | −0.833109 | −0.416555 | − | 0.909111i | \(-0.636763\pi\) | ||||
−0.416555 | + | 0.909111i | \(0.636763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.5718 | + | 65.5718i | 0.387999 | + | 0.387999i | 0.873973 | − | 0.485974i | \(-0.161535\pi\) |
−0.485974 | + | 0.873973i | \(0.661535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −125.879 | − | 32.0836i | −0.559464 | − | 0.142594i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −206.336 | + | 206.336i | −0.713967 | + | 0.713967i | −0.967363 | − | 0.253396i | \(-0.918452\pi\) |
0.253396 | + | 0.967363i | \(0.418452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 260.194i | 0.720758i | 0.932806 | + | 0.360379i | \(0.117353\pi\) | ||||
−0.932806 | + | 0.360379i | \(0.882647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −214.862 | −0.487216 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 210.067 | + | 210.067i | 0.397101 | + | 0.397101i | 0.877209 | − | 0.480108i | \(-0.159403\pi\) |
−0.480108 | + | 0.877209i | \(0.659403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 299.160 | − | 548.751i | 0.478657 | − | 0.878002i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −99.2043 | + | 99.2043i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 503.161i | − | 0.598289i | −0.954208 | − | 0.299145i | \(-0.903299\pi\) | ||
0.954208 | − | 0.299145i | \(-0.0967013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1252.33 | 1.30316 | 0.651578 | − | 0.758581i | \(-0.274107\pi\) | ||||
0.651578 | + | 0.758581i | \(0.274107\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −370.386 | − | 370.386i | −0.340115 | − | 0.340115i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 255.317 | − | 1001.73i | 0.208422 | − | 0.817739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1812.07 | − | 1812.07i | 1.32364 | − | 1.32364i | 0.412838 | − | 0.910805i | \(-0.364538\pi\) |
0.910805 | − | 0.412838i | \(-0.135462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 481.852i | 0.316800i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3129.49 | −1.86168 | −0.930842 | − | 0.365423i | \(-0.880924\pi\) | ||||
−0.930842 | + | 0.365423i | \(0.880924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2140.10 | + | 2140.10i | 1.15744 | + | 1.15744i | 0.985025 | + | 0.172413i | \(0.0551563\pi\) |
0.172413 | + | 0.985025i | \(0.444844\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −344.628 | − | 580.393i | −0.170187 | − | 0.286614i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 838.104 | − | 838.104i | 0.379404 | − | 0.379404i | −0.491483 | − | 0.870887i | \(-0.663545\pi\) |
0.870887 | + | 0.491483i | \(0.163545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 691.158i | 0.287863i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1516.26 | −0.582951 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 883.512 | + | 883.512i | 0.314529 | + | 0.314529i | 0.846661 | − | 0.532132i | \(-0.178609\pi\) |
−0.532132 | + | 0.846661i | \(0.678609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2166.94 | − | 1286.69i | 0.716342 | − | 0.425352i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −956.012 | + | 956.012i | −0.294248 | + | 0.294248i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4933.68i | 1.41732i | 0.705551 | + | 0.708659i | \(0.250700\pi\) | ||||
−0.705551 | + | 0.708659i | \(0.749300\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5873.12 | −1.57837 | −0.789186 | − | 0.614154i | \(-0.789497\pi\) | ||||
−0.789186 | + | 0.614154i | \(0.789497\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −789.454 | − | 789.454i | −0.198905 | − | 0.198905i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2246.49 | − | 572.576i | −0.531714 | − | 0.135521i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −932.560 | + | 932.560i | −0.207743 | + | 0.207743i | −0.803308 | − | 0.595564i | \(-0.796929\pi\) |
0.595564 | + | 0.803308i | \(0.296929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1543.67i | 0.324232i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4439.96 | −0.880769 | −0.440385 | − | 0.897809i | \(-0.645158\pi\) | ||||
−0.440385 | + | 0.897809i | \(0.645158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −412.029 | − | 412.029i | −0.0773183 | − | 0.0773183i | 0.667390 | − | 0.744708i | \(-0.267411\pi\) |
−0.744708 | + | 0.667390i | \(0.767411\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3115.43 | − | 917.056i | 0.553854 | − | 0.163032i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2947.48 | − | 2947.48i | 0.497129 | − | 0.497129i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8658.90i | 1.38742i | 0.720254 | + | 0.693711i | \(0.244025\pi\) | ||||
−0.720254 | + | 0.693711i | \(0.755975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5223.10 | + | 5223.10i | 0.758180 | + | 0.758180i | 0.975991 | − | 0.217811i | \(-0.0698917\pi\) |
−0.217811 | + | 0.975991i | \(0.569892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1801.74 | − | 7069.09i | 0.249376 | − | 0.978421i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1848.73 | − | 1848.73i | 0.244251 | − | 0.244251i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5102.20i | − | 0.644136i | −0.946717 | − | 0.322068i | \(-0.895622\pi\) | ||
0.946717 | − | 0.322068i | \(-0.104378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3834.51 | −0.463049 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4601.37 | + | 4601.37i | 0.532012 | + | 0.532012i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3321.11 | − | 5593.13i | −0.367990 | − | 0.619738i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2418.77 | + | 2418.77i | −0.257070 | + | 0.257070i | −0.823861 | − | 0.566791i | \(-0.808185\pi\) |
0.566791 | + | 0.823861i | \(0.308185\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2721.77i | − | 0.277703i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4380.82 | 0.429450 | 0.214725 | − | 0.976675i | \(-0.431114\pi\) | ||||
0.214725 | + | 0.976675i | \(0.431114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6844.96 | − | 6844.96i | −0.645203 | − | 0.645203i | 0.306627 | − | 0.951830i | \(-0.400800\pi\) |
−0.951830 | + | 0.306627i | \(0.900800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4618.69 | − | 2742.50i | 0.418929 | − | 0.248753i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12713.4 | − | 12713.4i | 1.11044 | − | 1.11044i | 0.117350 | − | 0.993091i | \(-0.462560\pi\) |
0.993091 | − | 0.117350i | \(-0.0374398\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11845.5i | − | 0.997011i | −0.866887 | − | 0.498505i | \(-0.833882\pi\) | ||
0.866887 | − | 0.498505i | \(-0.166118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13315.9 | 1.08075 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16798.8 | + | 16798.8i | 1.31559 | + | 1.31559i | 0.917226 | + | 0.398367i | \(0.130423\pi\) |
0.398367 | + | 0.917226i | \(0.369577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7196.89 | − | 1834.31i | −0.544188 | − | 0.138700i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1770.44 | + | 1770.44i | −0.129333 | + | 0.129333i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 12066.1i | − | 0.852069i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4479.11 | −0.305929 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11498.5 | − | 11498.5i | −0.760029 | − | 0.760029i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 573.499 | + | 15614.5i | 0.0367039 | + | 0.999326i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14949.7 | + | 14949.7i | −0.926882 | + | 0.926882i | −0.997503 | − | 0.0706214i | \(-0.977502\pi\) |
0.0706214 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15726.5i | 0.945044i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3761.56 | −0.219193 | −0.109596 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109596 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7607.81 | − | 7607.81i | −0.430087 | − | 0.430087i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 866.257 | − | 3398.75i | 0.0475312 | − | 0.186488i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13779.0 | + | 13779.0i | −0.734139 | + | 0.734139i | −0.971437 | − | 0.237298i | \(-0.923738\pi\) |
0.237298 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25283.6i | 1.30861i | 0.756232 | + | 0.654303i | \(0.227038\pi\) | ||||
−0.756232 | + | 0.654303i | \(0.772962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6158.78 | 0.309782 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6610.04 | − | 6610.04i | −0.323245 | − | 0.323245i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6422.36 | + | 10816.0i | 0.305463 | + | 0.514434i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2539.48 | + | 2539.48i | −0.117519 | + | 0.117519i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13593.6i | − | 0.612295i | −0.951984 | − | 0.306147i | \(-0.900960\pi\) | ||
0.951984 | − | 0.306147i | \(-0.0990400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17658.0 | 0.774440 | 0.387220 | − | 0.921987i | \(-0.373435\pi\) | ||||
0.387220 | + | 0.921987i | \(0.373435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5571.08 | − | 5571.08i | −0.237989 | − | 0.237989i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26920.2 | + | 15984.8i | −1.12051 | + | 0.665340i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2986.67 | − | 2986.67i | 0.121168 | − | 0.121168i | −0.643923 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643923i | \(0.222694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6492.46i | 0.256812i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12284.3 | −0.473913 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14591.9 | − | 14591.9i | −0.549207 | − | 0.549207i | 0.377005 | − | 0.926211i | \(-0.376954\pi\) |
−0.926211 | + | 0.377005i | \(0.876954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12689.4 | + | 3234.22i | 0.466095 | + | 0.118796i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4074.21 | − | 4074.21i | 0.146087 | − | 0.146087i | −0.630281 | − | 0.776367i | \(-0.717060\pi\) |
0.776367 | + | 0.630281i | \(0.217060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19961.7i | − | 0.698914i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7025.23 | −0.240253 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10988.5 | + | 10988.5i | 0.367152 | + | 0.367152i | 0.866437 | − | 0.499286i | \(-0.166404\pi\) |
−0.499286 | + | 0.866437i | \(0.666404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7297.80 | + | 24792.1i | 0.238295 | + | 0.809539i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18127.5 | + | 18127.5i | −0.578618 | + | 0.578618i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 55895.4i | − | 1.74450i | −0.489063 | − | 0.872248i | \(-0.662661\pi\) | ||
0.489063 | − | 0.872248i | \(-0.337339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 61470.9 | 1.87634 | 0.938171 | − | 0.346171i | \(-0.112518\pi\) | ||||
0.938171 | + | 0.346171i | \(0.112518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21579.2 | − | 21579.2i | −0.644368 | − | 0.644368i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15823.0 | + | 62081.5i | −0.462324 | + | 1.81392i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20800.0 | − | 20800.0i | 0.594812 | − | 0.594812i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5801.28i | − | 0.162405i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21064.5 | 0.577411 | 0.288706 | − | 0.957418i | \(-0.406775\pi\) | ||||
0.288706 | + | 0.957418i | \(0.406775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16416.6 | − | 16416.6i | −0.440726 | − | 0.440726i | 0.451530 | − | 0.892256i | \(-0.350878\pi\) |
−0.892256 | + | 0.451530i | \(0.850878\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6150.36 | − | 10357.9i | −0.161745 | − | 0.272398i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 37084.2 | − | 37084.2i | 0.955556 | − | 0.955556i | −0.0434975 | − | 0.999054i | \(-0.513850\pi\) |
0.999054 | + | 0.0434975i | \(0.0138500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15577.7i | 0.393366i | 0.980467 | + | 0.196683i | \(0.0630170\pi\) | ||||
−0.980467 | + | 0.196683i | \(0.936983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6852.89 | −0.169622 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14712.0 | + | 14712.0i | 0.357008 | + | 0.357008i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 67271.7 | − | 39944.8i | 1.60075 | − | 0.950501i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5671.80 | + | 5671.80i | −0.132367 | + | 0.132367i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 26229.1i | − | 0.600470i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 71670.6 | 1.60981 | 0.804907 | − | 0.593401i | \(-0.202215\pi\) | ||||
0.804907 | + | 0.593401i | \(0.202215\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16313.4 | − | 16313.4i | −0.359573 | − | 0.359573i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −73320.0 | − | 18687.5i | −1.58615 | − | 0.404272i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36617.0 | + | 36617.0i | −0.777613 | + | 0.777613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3027.78i | − | 0.0631301i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27059.7 | −0.554036 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10834.2 | + | 10834.2i | 0.217864 | + | 0.217864i | 0.807598 | − | 0.589734i | \(-0.200767\pi\) |
−0.589734 | + | 0.807598i | \(0.700767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14816.3 | + | 8077.33i | 0.292667 | + | 0.159552i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8536.10 | − | 8536.10i | 0.165656 | − | 0.165656i | −0.619411 | − | 0.785067i | \(-0.712628\pi\) |
0.785067 | + | 0.619411i | \(0.212628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 53172.3i | − | 1.01395i | −0.861962 | − | 0.506973i | \(-0.830765\pi\) | ||
0.861962 | − | 0.506973i | \(-0.169235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21659.4 | 0.405904 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8276.62 | − | 8276.62i | −0.152455 | − | 0.152455i | 0.626759 | − | 0.779213i | \(-0.284381\pi\) |
−0.779213 | + | 0.626759i | \(0.784381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7318.36 | + | 28713.5i | −0.132519 | + | 0.519936i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31814.8 | + | 31814.8i | −0.566412 | + | 0.566412i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 64206.9i | 1.12405i | 0.827120 | + | 0.562025i | \(0.189978\pi\) | ||||
−0.827120 | + | 0.562025i | \(0.810022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −52792.1 | −0.908940 | −0.454470 | − | 0.890762i | \(-0.650171\pi\) | ||||
−0.454470 | + | 0.890762i | \(0.650171\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2678.52 | − | 2678.52i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8821.94 | − | 14857.2i | −0.146971 | − | 0.247516i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17061.4 | + | 17061.4i | −0.279653 | + | 0.279653i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38381.8i | 0.619051i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7619.52 | 0.120943 | 0.0604714 | − | 0.998170i | \(-0.480740\pi\) | ||||
0.0604714 | + | 0.998170i | \(0.480740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21176.0 | − | 21176.0i | −0.330829 | − | 0.330829i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32593.5 | − | 19353.5i | 0.501246 | − | 0.297632i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −56900.1 | + | 56900.1i | −0.861483 | + | 0.861483i | −0.991510 | − | 0.130027i | \(-0.958494\pi\) |
0.130027 | + | 0.991510i | \(0.458494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 105966.i | 1.57967i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13585.4 | 0.199430 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 78565.0 | + | 78565.0i | 1.13584 | + | 1.13584i | 0.989188 | + | 0.146653i | \(0.0468502\pi\) |
0.146653 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30269.2 | − | 7714.86i | −0.431031 | − | 0.109859i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18746.7 | − | 18746.7i | 0.262967 | − | 0.262967i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 108837.i | − | 1.50409i | −0.659114 | − | 0.752043i | \(-0.729068\pi\) | ||
0.659114 | − | 0.752043i | \(-0.270932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −51081.3 | −0.695542 | −0.347771 | − | 0.937580i | \(-0.613061\pi\) | ||||
−0.347771 | + | 0.937580i | \(0.613061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14088.9 | − | 14088.9i | −0.189039 | − | 0.189039i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30157.2 | + | 55317.5i | −0.398773 | + | 0.731472i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −37506.3 | + | 37506.3i | −0.488815 | + | 0.488815i | −0.907932 | − | 0.419117i | \(-0.862340\pi\) |
0.419117 | + | 0.907932i | \(0.362340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33813.0i | 0.434386i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −101190. | −1.28152 | −0.640758 | − | 0.767743i | \(-0.721380\pi\) | ||||
−0.640758 | + | 0.767743i | \(0.721380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4039.24 | − | 4039.24i | −0.0504344 | − | 0.0504344i | 0.681440 | − | 0.731874i | \(-0.261354\pi\) |
−0.731874 | + | 0.681440i | \(0.761354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8347.94 | − | 32753.0i | 0.102776 | − | 0.403238i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 91503.2 | − | 91503.2i | 1.11089 | − | 1.11089i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1628.37i | − | 0.0194966i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17774.3 | −0.209897 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 92563.9 | + | 92563.9i | 1.07822 | + | 1.07822i | 0.996669 | + | 0.0815481i | \(0.0259864\pi\) |
0.0815481 | + | 0.996669i | \(0.474014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −62973.6 | − | 106055.i | −0.723626 | − | 1.21867i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10000.4 | − | 10000.4i | 0.113372 | − | 0.113372i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27548.9i | 0.308150i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −125149. | −1.38132 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16096.2 | + | 16096.2i | 0.175322 | + | 0.175322i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 126249. | − | 74964.6i | 1.35715 | − | 0.805854i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 82316.5 | − | 82316.5i | 0.873394 | − | 0.873394i | −0.119447 | − | 0.992841i | \(-0.538112\pi\) |
0.992841 | + | 0.119447i | \(0.0381121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 50300.0i | − | 0.526806i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 66895.0 | 0.691628 | 0.345814 | − | 0.938303i | \(-0.387603\pi\) | ||||
0.345814 | + | 0.938303i | \(0.387603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12902.7 | + | 12902.7i | 0.131702 | + | 0.131702i | 0.769885 | − | 0.638183i | \(-0.220314\pi\) |
−0.638183 | + | 0.769885i | \(0.720314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27046.7 | + | 6893.55i | 0.272580 | + | 0.0694739i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 87261.9 | − | 87261.9i | 0.868373 | − | 0.868373i | −0.123919 | − | 0.992292i | \(-0.539546\pi\) |
0.992292 | + | 0.123919i | \(0.0395464\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 50721.8i | 0.498440i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 93424.2 | 0.906671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −53687.4 | − | 53687.4i | −0.514597 | − | 0.514597i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55599.1 | − | 16366.1i | 0.526382 | − | 0.154946i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43523.1 | − | 43523.1i | 0.407028 | − | 0.407028i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 49010.7i | 0.452792i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −89537.0 | −0.817234 | −0.408617 | − | 0.912706i | \(-0.633989\pi\) | ||||
−0.408617 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 48925.8 | + | 48925.8i | 0.441214 | + | 0.441214i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8143.16 | − | 31949.6i | 0.0725610 | − | 0.284692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10633.8 | + | 10633.8i | −0.0936326 | + | 0.0936326i | −0.752372 | − | 0.658739i | \(-0.771090\pi\) |
0.658739 | + | 0.752372i | \(0.271090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 123446.i | 1.07418i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −126243. | −1.08567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −90411.7 | − | 90411.7i | −0.768487 | − | 0.768487i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19703.4 | − | 33182.8i | −0.165540 | − | 0.278788i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −37803.6 | + | 37803.6i | −0.313960 | + | 0.313960i | −0.846442 | − | 0.532482i | \(-0.821260\pi\) |
0.532482 | + | 0.846442i | \(0.321260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 68613.6i | 0.563325i | 0.959514 | + | 0.281663i | \(0.0908859\pi\) | ||||
−0.959514 | + | 0.281663i | \(0.909114\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13010.0 | −0.105600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31348.2 | + | 31348.2i | 0.251572 | + | 0.251572i | 0.821615 | − | 0.570043i | \(-0.193073\pi\) |
−0.570043 | + | 0.821615i | \(0.693073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 95441.6 | − | 56671.7i | 0.757323 | − | 0.449686i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44333.9 | − | 44333.9i | 0.347856 | − | 0.347856i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 85046.4i | − | 0.659883i | −0.944001 | − | 0.329941i | \(-0.892971\pi\) | ||
0.944001 | − | 0.329941i | \(-0.107029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 62620.3 | 0.480508 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16457.3 | − | 16457.3i | −0.124895 | − | 0.124895i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14116.1 | + | 3597.86i | 0.105957 | + | 0.0270059i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19597.4 | + | 19597.4i | −0.145501 | + | 0.145501i | −0.776105 | − | 0.630604i | \(-0.782807\pi\) |
0.630604 | + | 0.776105i | \(0.282807\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 84496.2i | − | 0.620561i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −51666.0 | −0.375368 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 88837.3 | + | 88837.3i | 0.638525 | + | 0.638525i | 0.950191 | − | 0.311667i | \(-0.100887\pi\) |
−0.311667 | + | 0.950191i | \(0.600887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −55264.1 | + | 59478.4i | −0.392989 | + | 0.422958i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32993.2 | − | 32993.2i | 0.232136 | − | 0.232136i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 55861.4i | − | 0.388896i | −0.980913 | − | 0.194448i | \(-0.937708\pi\) | ||
0.980913 | − | 0.194448i | \(-0.0622916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −109857. | −0.756796 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 77604.9 | + | 77604.9i | 0.529044 | + | 0.529044i | 0.920287 | − | 0.391244i | \(-0.127955\pi\) |
−0.391244 | + | 0.920287i | \(0.627955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25737.5 | + | 100981.i | −0.173638 | + | 0.681266i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −57782.8 | + | 57782.8i | −0.385813 | + | 0.385813i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 210631.i | 1.39195i | 0.718067 | + | 0.695974i | \(0.245027\pi\) | ||||
−0.718067 | + | 0.695974i | \(0.754973\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −86688.7 | −0.567034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13820.9 | − | 13820.9i | −0.0894850 | − | 0.0894850i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −110522. | − | 186132.i | −0.708362 | − | 1.19296i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −47327.7 | + | 47327.7i | −0.300285 | + | 0.300285i | −0.841125 | − | 0.540840i | \(-0.818106\pi\) |
0.540840 | + | 0.841125i | \(0.318106\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 55905.7i | − | 0.351164i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16778.8 | −0.104345 | −0.0521726 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521726 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 82117.7 | + | 82117.7i | 0.505623 | + | 0.505623i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15670.6 | − | 9304.96i | 0.0955380 | − | 0.0567289i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −182667. | + | 182667.i | −1.10274 | + | 1.10274i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33710.4i | 0.201520i | 0.994911 | + | 0.100760i | \(0.0321274\pi\) | ||||
−0.994911 | + | 0.100760i | \(0.967873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −101255. | −0.599422 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −144256. | − | 144256.i | −0.845735 | − | 0.845735i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −178944. | − | 45608.4i | −1.03901 | − | 0.264818i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −92897.9 | + | 92897.9i | −0.534237 | + | 0.534237i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 293984.i | 1.67454i | 0.546789 | + | 0.837270i | \(0.315850\pi\) | ||||
−0.546789 | + | 0.837270i | \(0.684150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 90452.8 | 0.510338 | 0.255169 | − | 0.966896i | \(-0.417869\pi\) | ||||
0.255169 | + | 0.966896i | \(0.417869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22628.8 | + | 22628.8i | 0.126468 | + | 0.126468i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51499.7 | + | 174955.i | 0.285119 | + | 0.968609i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 171724. | − | 171724.i | 0.941838 | − | 0.941838i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 48573.7i | − | 0.263929i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 193225. | 1.04018 | 0.520091 | − | 0.854111i | \(-0.325898\pi\) | ||||
0.520091 | + | 0.854111i | \(0.325898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 233890. | + | 233890.i | 1.24749 | + | 1.24749i | 0.956826 | + | 0.290661i | \(0.0938753\pi\) |
0.290661 | + | 0.956826i | \(0.406125\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16143.2 | + | 63337.7i | −0.0853123 | + | 0.334722i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54658.0 | + | 54658.0i | −0.286214 | + | 0.286214i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 256431.i | − | 1.33058i | −0.746583 | − | 0.665292i | \(-0.768307\pi\) | ||
0.746583 | − | 0.665292i | \(-0.231693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18661.3 | −0.0959542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −271033. | − | 271033.i | −1.38107 | − | 1.38107i | −0.842732 | − | 0.538333i | \(-0.819054\pi\) |
−0.538333 | − | 0.842732i | \(-0.680946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 65124.5 | + | 109677.i | 0.328870 | + | 0.553855i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49945.9 | − | 49945.9i | 0.249968 | − | 0.249968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 346521.i | − | 1.71885i | −0.511265 | − | 0.859423i | \(-0.670823\pi\) | ||
0.511265 | − | 0.859423i | \(-0.329177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 315472. | 1.55099 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 64879.7 | + | 64879.7i | 0.316164 | + | 0.316164i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 82426.8 | − | 48943.7i | 0.398149 | − | 0.236414i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37089.6 | − | 37089.6i | 0.177590 | − | 0.177590i | −0.612714 | − | 0.790305i | \(-0.709922\pi\) |
0.790305 | + | 0.612714i | \(0.209922\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 40938.9i | − | 0.194317i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 178438. | 0.839627 | 0.419813 | − | 0.907610i | \(-0.362096\pi\) | ||||
0.419813 | + | 0.907610i | \(0.362096\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −137047. | − | 137047.i | −0.639303 | − | 0.639303i | 0.311081 | − | 0.950383i | \(-0.399309\pi\) |
−0.950383 | + | 0.311081i | \(0.899309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −157643. | − | 40179.4i | −0.729070 | − | 0.185822i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −137506. | + | 137506.i | −0.630503 | + | 0.630503i | −0.948194 | − | 0.317691i | \(-0.897092\pi\) |
0.317691 | + | 0.948194i | \(0.397092\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 54534.3i | − | 0.247927i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21947.5 | 0.0989334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −215736. | − | 215736.i | −0.964272 | − | 0.964272i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 142782. | + | 77839.6i | 0.632827 | + | 0.344995i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23854.8 | + | 23854.8i | −0.104843 | + | 0.104843i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 17228.2i | − | 0.0750879i | −0.999295 | − | 0.0375439i | \(-0.988047\pi\) | ||
0.999295 | − | 0.0375439i | \(-0.0119534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 237641. | 1.02714 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −45135.4 | − | 45135.4i | −0.193474 | − | 0.193474i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21120.8 | − | 82867.2i | 0.0897898 | − | 0.352289i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 55195.9 | − | 55195.9i | 0.232728 | − | 0.232728i | −0.581102 | − | 0.813830i | \(-0.697378\pi\) |
0.813830 | + | 0.581102i | \(0.197378\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 107228.i | − | 0.448425i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 99534.3 | 0.412867 | 0.206433 | − | 0.978461i | \(-0.433814\pi\) | ||||
0.206433 | + | 0.978461i | \(0.433814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 103820. | + | 103820.i | 0.427159 | + | 0.427159i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34740.6 | + | 58507.2i | 0.141784 | + | 0.238781i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 129820. | − | 129820.i | 0.525568 | − | 0.525568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 222798.i | − | 0.894769i | −0.894342 | − | 0.447385i | \(-0.852355\pi\) | ||
0.894342 | − | 0.447385i | \(-0.147645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29939.2 | 0.119279 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18900.9 | − | 18900.9i | −0.0747045 | − | 0.0747045i | 0.668767 | − | 0.743472i | \(-0.266822\pi\) |
−0.743472 | + | 0.668767i | \(0.766822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −94170.3 | + | 55916.8i | −0.369259 | + | 0.219260i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 73343.9 | − | 73343.9i | 0.285330 | − | 0.285330i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 294705.i | 1.13750i | 0.822510 | + | 0.568750i | \(0.192573\pi\) | ||||
−0.822510 | + | 0.568750i | \(0.807427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24094.7 | 0.0922739 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25812.3 | − | 25812.3i | −0.0980827 | − | 0.0980827i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 234509. | + | 59770.5i | 0.884187 | + | 0.225358i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −84486.0 | + | 84486.0i | −0.316085 | + | 0.316085i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 80748.6i | 0.299778i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 284288. | 1.04733 | 0.523664 | − | 0.851925i | \(-0.324565\pi\) | ||||
0.523664 | + | 0.851925i | \(0.324565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −121118. | − | 121118.i | −0.442796 | − | 0.442796i | 0.450154 | − | 0.892951i | \(-0.351369\pi\) |
−0.892951 | + | 0.450154i | \(0.851369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −64278.2 | + | 117906.i | −0.233209 | + | 0.427776i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −258402. | + | 258402.i | −0.930411 | + | 0.930411i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 191585.i | − | 0.684621i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −133209. | −0.472439 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −205206. | − | 205206.i | −0.722331 | − | 0.722331i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −111014. | + | 435563.i | −0.387857 | + | 1.52175i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 205373. | − | 205373.i | 0.712188 | − | 0.712188i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 69673.0i | − | 0.239821i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −434885. | −1.48587 | −0.742933 | − | 0.669366i | \(-0.766566\pi\) | ||||
−0.742933 | + | 0.669366i | \(0.766566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 225858. | + | 225858.i | 0.766014 | + | 0.766014i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 151196. | + | 254631.i | 0.509034 | + | 0.857272i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7758.44 | − | 7758.44i | 0.0259298 | − | 0.0259298i | −0.694023 | − | 0.719953i | \(-0.744163\pi\) |
0.719953 | + | 0.694023i | \(0.244163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 158574.i | − | 0.526124i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130919. | 0.431222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −253178. | − | 253178.i | −0.827895 | − | 0.827895i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −286240. | + | 169964.i | −0.929274 | + | 0.551788i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22166.3 | + | 22166.3i | −0.0714470 | + | 0.0714470i | −0.741927 | − | 0.670480i | \(-0.766088\pi\) |
0.670480 | + | 0.741927i | \(0.266088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 280661.i | 0.898168i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 152848. | 0.485662 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 253305. | + | 253305.i | 0.799147 | + | 0.799147i | 0.982961 | − | 0.183814i | \(-0.0588445\pi\) |
−0.183814 | + | 0.982961i | \(0.558844\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −575528. | − | 146688.i | −1.80289 | − | 0.459513i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21315.3 | − | 21315.3i | 0.0663017 | − | 0.0663017i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4947.07i | − | 0.0152800i | −0.999971 | − | 0.00764001i | \(-0.997568\pi\) | ||
0.999971 | − | 0.00764001i | \(-0.00243191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −205345. | −0.629813 | −0.314907 | − | 0.949123i | \(-0.601973\pi\) | ||||
−0.314907 | + | 0.949123i | \(0.601973\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 77396.1 | + | 77396.1i | 0.235727 | + | 0.235727i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 178118. | − | 52430.7i | 0.538731 | − | 0.158581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −178874. | + | 178874.i | −0.537274 | + | 0.537274i | −0.922727 | − | 0.385453i | \(-0.874045\pi\) |
0.385453 | + | 0.922727i | \(0.374045\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 120637.i | − | 0.359851i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −305437. | −0.904835 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −89063.4 | − | 89063.4i | −0.262037 | − | 0.262037i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15459.5 | − | 60655.3i | 0.0451736 | − | 0.177238i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −240208. | + | 240208.i | −0.697126 | + | 0.697126i | −0.963790 | − | 0.266663i | \(-0.914079\pi\) |
0.266663 | + | 0.963790i | \(0.414079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 325849.i | 0.939260i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 272512. | 0.780208 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −481681. | − | 481681.i | −1.36978 | − | 1.36978i | −0.860752 | − | 0.509025i | \(-0.830006\pi\) |
−0.509025 | − | 0.860752i | \(-0.669994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 154012. | + | 259375.i | 0.435033 | + | 0.732645i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −57236.1 | + | 57236.1i | −0.160591 | + | 0.160591i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 154606.i | − | 0.430896i | −0.976515 | − | 0.215448i | \(-0.930879\pi\) | ||
0.976515 | − | 0.215448i | \(-0.0691211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 439313. | 1.21626 | 0.608128 | − | 0.793839i | \(-0.291921\pi\) | ||||
0.608128 | + | 0.793839i | \(0.291921\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25179.1 | − | 25179.1i | −0.0692478 | − | 0.0692478i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 96283.2 | − | 57171.4i | 0.263051 | − | 0.156195i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37796.8 | + | 37796.8i | −0.102584 | + | 0.102584i | −0.756536 | − | 0.653952i | \(-0.773110\pi\) |
0.653952 | + | 0.756536i | \(0.273110\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 108110.i | 0.291496i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 109912. | 0.294417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 140335. | + | 140335.i | 0.373461 | + | 0.373461i | 0.868736 | − | 0.495275i | \(-0.164933\pi\) |
−0.495275 | + | 0.868736i | \(0.664933\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 393939. | + | 100405.i | 1.04155 | + | 0.265464i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 54366.7 | − | 54366.7i | 0.142811 | − | 0.142811i | −0.632086 | − | 0.774898i | \(-0.717801\pi\) |
0.774898 | + | 0.632086i | \(0.217801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 273964.i | − | 0.715011i | −0.933911 | − | 0.357505i | \(-0.883627\pi\) | ||
0.933911 | − | 0.357505i | \(-0.116373\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41679.0 | −0.108077 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 149183. | + | 149183.i | 0.384365 | + | 0.384365i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −211631. | − | 328329.i | −0.541776 | − | 0.840523i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 96371.9 | − | 96371.9i | 0.245141 | − | 0.245141i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 747790.i | 1.89007i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −770840. | −1.93600 | −0.968001 | − | 0.250947i | \(-0.919258\pi\) | ||||
−0.968001 | + | 0.250947i | \(0.919258\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 263334. | + | 263334.i | 0.657204 | + | 0.657204i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 130541. | − | 512177.i | 0.323743 | − | 1.27020i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −45320.5 | + | 45320.5i | −0.111690 | + | 0.111690i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 119879.i | − | 0.293590i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 404369. | 0.984152 | 0.492076 | − | 0.870552i | \(-0.336238\pi\) | ||||
0.492076 | + | 0.870552i | \(0.336238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 438578. | + | 438578.i | 1.06078 | + | 1.06078i | 0.998029 | + | 0.0627491i | \(0.0199868\pi\) |
0.0627491 | + | 0.998029i | \(0.480013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −200733. | − | 338057.i | −0.482502 | − | 0.812588i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 190458. | − | 190458.i | 0.454978 | − | 0.454978i | −0.442025 | − | 0.897003i | \(-0.645740\pi\) |
0.897003 | + | 0.442025i | \(0.145740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 497346.i | − | 1.18078i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −269079. | −0.634919 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −184154. | − | 184154.i | −0.431872 | − | 0.431872i | 0.457393 | − | 0.889265i | \(-0.348783\pi\) |
−0.889265 | + | 0.457393i | \(0.848783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 80858.8 | − | 48012.6i | 0.188471 | − | 0.111911i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11124.8 | − | 11124.8i | 0.0257728 | − | 0.0257728i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 136158.i | − | 0.313525i | −0.987636 | − | 0.156762i | \(-0.949894\pi\) | ||
0.987636 | − | 0.156762i | \(-0.0501057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −302378. | −0.692065 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −99423.6 | − | 99423.6i | −0.226184 | − | 0.226184i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 260644. | + | 66431.7i | 0.589392 | + | 0.150222i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 105697. | − | 105697.i | 0.237582 | − | 0.237582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 79614.5i | 0.177885i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 592047. | 1.31496 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −273891. | − | 273891.i | −0.604710 | − | 0.604710i | 0.336849 | − | 0.941559i | \(-0.390639\pi\) |
−0.941559 | + | 0.336849i | \(0.890639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24760.5 | + | 84116.5i | 0.0543441 | + | 0.184618i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 178343. | − | 178343.i | 0.389116 | − | 0.389116i | −0.485256 | − | 0.874372i | \(-0.661274\pi\) |
0.874372 | + | 0.485256i | \(0.161274\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 141445.i | − | 0.306795i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 62727.3 | 0.135258 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 238606. | + | 238606.i | 0.511494 | + | 0.511494i | 0.914984 | − | 0.403490i | \(-0.132203\pi\) |
−0.403490 | + | 0.914984i | \(0.632203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 120319. | − | 472071.i | 0.256421 | − | 1.00607i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 195367. | − | 195367.i | 0.413941 | − | 0.413941i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 115867.i | 0.244074i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 207226. | 0.433998 | 0.216999 | − | 0.976172i | \(-0.430373\pi\) | ||||
0.216999 | + | 0.976172i | \(0.430373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 79581.8 | + | 79581.8i | 0.165710 | + | 0.165710i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −322720. | − | 543497.i | −0.668123 | − | 1.12520i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 645727. | − | 645727.i | 1.32918 | − | 1.32918i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 60820.5i | − | 0.124479i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −472139. | −0.960803 | −0.480401 | − | 0.877049i | \(-0.659509\pi\) | ||||
−0.480401 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 471488. | + | 471488.i | 0.954025 | + | 0.954025i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −132389. | + | 78610.7i | −0.266364 | + | 0.158162i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −128091. | + | 128091.i | −0.256259 | + | 0.256259i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 180630.i | 0.359333i | 0.983728 | + | 0.179667i | \(0.0575019\pi\) | ||||
−0.983728 | + | 0.179667i | \(0.942498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −233790. | −0.462474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 263073. | + | 263073.i | 0.517485 | + | 0.517485i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 226460. | + | 57719.2i | 0.442976 | + | 0.112904i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −235911. | + | 235911.i | −0.458892 | + | 0.458892i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 71380.5i | 0.138077i | 0.997614 | + | 0.0690386i | \(0.0219932\pi\) | ||||
−0.997614 | + | 0.0690386i | \(0.978007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 400280. | 0.770004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −193971. | − | 193971.i | −0.371073 | − | 0.371073i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −276111. | − | 150526.i | −0.525299 | − | 0.286375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −520312. | + | 520312.i | −0.984453 | + | 0.984453i | −0.999881 | − | 0.0154283i | \(-0.995089\pi\) |
0.0154283 | + | 0.999881i | \(0.495089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 19683.0i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −883162. | −1.65274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 304781. | + | 304781.i | 0.567258 | + | 0.567258i | 0.931359 | − | 0.364101i | \(-0.118624\pi\) |
−0.364101 | + | 0.931359i | \(0.618624\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22174.8 | − | 87002.6i | 0.0410474 | − | 0.161049i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 94007.8 | − | 94007.8i | 0.173073 | − | 0.173073i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 422739.i | 0.774076i | 0.922064 | + | 0.387038i | \(0.126502\pi\) | ||||
−0.922064 | + | 0.387038i | \(0.873498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −125375. | −0.228336 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −309220. | − | 309220.i | −0.560131 | − | 0.560131i | 0.369214 | − | 0.929344i | \(-0.379627\pi\) |
−0.929344 | + | 0.369214i | \(0.879627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 173508. | + | 292208.i | 0.312613 | + | 0.526477i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −141024. | + | 141024.i | −0.252727 | + | 0.252727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 743457.i | 1.32523i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −830203. | −1.47199 | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||||
−0.735994 | + | 0.676988i | \(0.763285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27995.9 | + | 27995.9i | 0.0493747 | + | 0.0493747i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −379578. | + | 225387.i | −0.665896 | + | 0.395398i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 319294. | − | 319294.i | 0.557184 | − | 0.557184i | −0.371321 | − | 0.928505i | \(-0.621095\pi\) |
0.928505 | + | 0.371321i | \(0.121095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 155611.i | − | 0.270120i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −668943. | −1.15510 | −0.577550 | − | 0.816355i | \(-0.695991\pi\) | ||||
−0.577550 | + | 0.816355i | \(0.695991\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 346351. | + | 346351.i | 0.594931 | + | 0.594931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 190866. | + | 48646.9i | 0.326140 | + | 0.0831252i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −323510. | + | 323510.i | −0.549917 | + | 0.549917i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 831330.i | 1.40579i | 0.711293 | + | 0.702896i | \(0.248110\pi\) | ||||
−0.711293 | + | 0.702896i | \(0.751890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −418129. | −0.703398 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 457925. | + | 457925.i | 0.766364 | + | 0.766364i | 0.977464 | − | 0.211100i | \(-0.0677047\pi\) |
−0.211100 | + | 0.977464i | \(0.567705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 374649. | − | 687220.i | 0.623765 | − | 1.14417i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −389344. | + | 389344.i | −0.644899 | + | 0.644899i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 814273.i | − | 1.34182i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 447575. | 0.733777 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 49915.8 | + | 49915.8i | 0.0814169 | + | 0.0814169i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26079.8 | + | 102324.i | −0.0423218 | + | 0.166049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 440089. | − | 440089.i | 0.710544 | − | 0.710544i | −0.256105 | − | 0.966649i | \(-0.582439\pi\) |
0.966649 | + | 0.256105i | \(0.0824394\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 577333.i | 0.927411i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −982362. | −1.57007 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −385111. | − | 385111.i | −0.612406 | − | 0.612406i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −82869.8 | − | 139562.i | −0.131118 | − | 0.220818i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 874514. | − | 874514.i | 1.37673 | − | 1.37673i | 0.526654 | − | 0.850080i | \(-0.323446\pi\) |
0.850080 | − | 0.526654i | \(-0.176554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 345862.i | 0.541764i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 137759. | 0.214712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41535.1 | + | 41535.1i | 0.0644146 | + | 0.0644146i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 264064. | − | 156797.i | 0.407490 | − | 0.241961i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 399893. | − | 399893.i | 0.614041 | − | 0.614041i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 900682.i | 1.37618i | 0.725627 | + | 0.688088i | \(0.241550\pi\) | ||||
−0.725627 | + | 0.688088i | \(0.758450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 560145. | 0.851645 | 0.425822 | − | 0.904807i | \(-0.359985\pi\) | ||||
0.425822 | + | 0.904807i | \(0.359985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −187685. | − | 187685.i | −0.283954 | − | 0.283954i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 499918. | + | 127417.i | 0.752634 | + | 0.191828i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −556841. | + | 556841.i | −0.834232 | + | 0.834232i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 103532.i | − | 0.154350i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −391487. | −0.580805 | −0.290403 | − | 0.956905i | \(-0.593789\pi\) | ||||
−0.290403 | + | 0.956905i | \(0.593789\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −877887. | − | 877887.i | −1.29610 | − | 1.29610i | −0.930947 | − | 0.365154i | \(-0.881017\pi\) |
−0.365154 | − | 0.930947i | \(-0.618983\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −314054. | + | 92444.9i | −0.461420 | + | 0.135824i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −796044. | + | 796044.i | −1.16393 | + | 1.16393i | −0.180320 | + | 0.983608i | \(0.557713\pi\) |
−0.983608 | + | 0.180320i | \(0.942287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 83808.3i | − | 0.121949i | −0.998139 | − | 0.0609745i | \(-0.980579\pi\) | ||
0.998139 | − | 0.0609745i | \(-0.0194208\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −275614. | −0.399116 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −142611. | − | 142611.i | −0.205524 | − | 0.205524i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35576.2 | + | 139583.i | −0.0510254 | + | 0.200198i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −124237. | + | 124237.i | −0.177337 | + | 0.177337i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.03825e6i | − | 1.47495i | −0.675372 | − | 0.737477i | \(-0.736017\pi\) | ||
0.675372 | − | 0.737477i | \(-0.263983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 454110. | 0.642050 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −371795. | − | 371795.i | −0.523176 | − | 0.523176i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 254791. | + | 429097.i | 0.356838 | + | 0.600956i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 130965. | − | 130965.i | 0.182553 | − | 0.182553i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 29682.2i | − | 0.0411795i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 761309. | 1.05124 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 417742. | + | 417742.i | 0.574130 | + | 0.574130i | 0.933280 | − | 0.359150i | \(-0.116933\pi\) |
−0.359150 | + | 0.933280i | \(0.616933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 151015. | − | 89670.0i | 0.206579 | − | 0.122663i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 295564. | − | 295564.i | 0.402430 | − | 0.402430i | −0.476659 | − | 0.879088i | \(-0.658152\pi\) |
0.879088 | + | 0.476659i | \(0.158152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 156574.i | − | 0.212194i | −0.994356 | − | 0.106097i | \(-0.966165\pi\) | ||
0.994356 | − | 0.106097i | \(-0.0338354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 672409. | 0.907041 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 852253. | + | 852253.i | 1.14432 | + | 1.14432i | 0.987652 | + | 0.156667i | \(0.0500748\pi\) |
0.156667 | + | 0.987652i | \(0.449925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −376466. | − | 95952.0i | −0.503146 | − | 0.128239i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5983.02 | − | 5983.02i | 0.00795944 | − | 0.00795944i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 872871.i | − | 1.15587i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −122299. | −0.161208 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −65306.8 | − | 65306.8i | −0.0856900 | − | 0.0856900i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −473321. | − | 439783.i | −0.618215 | − | 0.574411i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 673537. | − | 673537.i | 0.875713 | − | 0.875713i | −0.117374 | − | 0.993088i | \(-0.537448\pi\) |
0.993088 | + | 0.117374i | \(0.0374477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 680203.i | 0.880361i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 801878. | 1.03313 | 0.516567 | − | 0.856247i | \(-0.327210\pi\) | ||||
0.516567 | + | 0.856247i | \(0.327210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 419877. | + | 419877.i | 0.538519 | + | 0.538519i | 0.923094 | − | 0.384575i | \(-0.125652\pi\) |
−0.384575 | + | 0.923094i | \(0.625652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 158290. | − | 621050.i | 0.202101 | − | 0.792939i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 700728. | − | 700728.i | 0.890640 | − | 0.890640i | −0.103943 | − | 0.994583i | \(-0.533146\pi\) |
0.994583 | + | 0.103943i | \(0.0331461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 874228.i | − | 1.10617i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 73487.7 | 0.0925677 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 218069. | + | 218069.i | 0.273458 | + | 0.273458i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 713449. | + | 1.20153e6i | 0.890670 | + | 1.49999i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −101221. | + | 101221.i | −0.125802 | + | 0.125802i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 630126.i | − | 0.779665i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −364601. | −0.449126 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −459827. | − | 459827.i | −0.563922 | − | 0.563922i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.32138e6 | + | 784614.i | −1.61336 | + | 0.957986i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −226251. | + | 226251.i | −0.275027 | + | 0.275027i | −0.831120 | − | 0.556093i | \(-0.812300\pi\) |
0.556093 | + | 0.831120i | \(0.312300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 118282.i | 0.143150i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 840996. | 1.01334 | 0.506672 | − | 0.862139i | \(-0.330875\pi\) | ||||
0.506672 | + | 0.862139i | \(0.330875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −526521. | − | 526521.i | −0.631647 | − | 0.631647i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 739306. | + | 188431.i | 0.883043 | + | 0.225066i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 109985. | − | 109985.i | 0.130796 | − | 0.130796i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 131956.i | 0.156242i | 0.996944 | + | 0.0781208i | \(0.0248920\pi\) | ||||
−0.996944 | + | 0.0781208i | \(0.975108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 604900. | 0.713123 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −291136. | − | 291136.i | −0.341737 | − | 0.341737i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −452275. | − | 1.53647e6i | −0.528591 | − | 1.79573i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 184814. | − | 184814.i | 0.215068 | − | 0.215068i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 789125.i | − | 0.914354i | −0.889376 | − | 0.457177i | \(-0.848861\pi\) | ||
0.889376 | − | 0.457177i | \(-0.151139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −179835. | −0.207479 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 245788. | + | 245788.i | 0.282356 | + | 0.282356i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −181626. | + | 712609.i | −0.207757 | + | 0.815132i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −979642. | + | 979642.i | −1.11580 | + | 1.11580i | −0.123454 | + | 0.992350i | \(0.539397\pi\) |
−0.992350 | + | 0.123454i | \(0.960603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 94815.1i | 0.107534i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −961058. | −1.08535 | −0.542675 | − | 0.839942i | \(-0.682589\pi\) | ||||
−0.542675 | + | 0.839942i | \(0.682589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −657401. | − | 657401.i | −0.739277 | − | 0.739277i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 74047.5 | + | 124705.i | 0.0829176 | + | 0.139643i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −96791.3 | + | 96791.3i | −0.107929 | + | 0.107929i | −0.759009 | − | 0.651080i | \(-0.774316\pi\) |
0.651080 | + | 0.759009i | \(0.274316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 54035.0i | − | 0.0599988i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 641242. | 0.709024 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 280586. | + | 280586.i | 0.308944 | + | 0.308944i | 0.844500 | − | 0.535556i | \(-0.179898\pi\) |
−0.535556 | + | 0.844500i | \(0.679898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −452804. | + | 268868.i | −0.496482 | + | 0.294803i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −186364. | + | 186364.i | −0.203487 | + | 0.203487i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 805772.i | − | 0.876143i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 644819. | 0.698218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 343263. | + | 343263.i | 0.370147 | + | 0.370147i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 562433. | + | 143350.i | 0.603972 | + | 0.153938i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.05482e6 | + | 1.05482e6i | −1.12805 | + | 1.12805i | −0.137551 | + | 0.990495i | \(0.543923\pi\) |
−0.990495 | + | 0.137551i | \(0.956077\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 394520.i | − | 0.420167i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 494524. | 0.524504 | 0.262252 | − | 0.964999i | \(-0.415535\pi\) | ||||
0.262252 | + | 0.964999i | \(0.415535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −739268. | − | 739268.i | −0.780865 | − | 0.780865i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 264417. | + | 144151.i | 0.278151 | + | 0.151638i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −391473. | + | 391473.i | −0.410121 | + | 0.410121i | −0.881781 | − | 0.471660i | \(-0.843655\pi\) |
0.471660 | + | 0.881781i | \(0.343655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 514333.i | 0.536635i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 319828. | 0.332337 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 657131. | + | 657131.i | 0.680057 | + | 0.680057i | 0.960013 | − | 0.279956i | \(-0.0903200\pi\) |
−0.279956 | + | 0.960013i | \(0.590320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −323821. | + | 1.27051e6i | −0.333758 | + | 1.30950i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −180077. | + | 180077.i | −0.184852 | + | 0.184852i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 899128.i | 0.919240i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 443257. | 0.451344 | 0.225672 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225672 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −328980. | − | 328980.i | −0.333634 | − | 0.333634i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −198834. | − | 334859.i | −0.200837 | − | 0.338233i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −667384. | + | 667384.i | −0.671407 | + | 0.671407i | −0.958040 | − | 0.286634i | \(-0.907464\pi\) |
0.286634 | + | 0.958040i | \(0.407464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 359530.i | 0.360250i |
(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 | 60.5.k.a.13.3 | ✓ | 8 | |
3.2 | odd | 2 | 180.5.l.b.73.4 | 8 | |||
4.3 | odd | 2 | 240.5.bg.d.193.1 | 8 | |||
5.2 | odd | 4 | inner | 60.5.k.a.37.3 | yes | 8 | |
5.3 | odd | 4 | 300.5.k.d.157.2 | 8 | |||
5.4 | even | 2 | 300.5.k.d.193.2 | 8 | |||
15.2 | even | 4 | 180.5.l.b.37.4 | 8 | |||
15.8 | even | 4 | 900.5.l.k.757.3 | 8 | |||
15.14 | odd | 2 | 900.5.l.k.793.3 | 8 | |||
20.7 | even | 4 | 240.5.bg.d.97.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.k.a.13.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
60.5.k.a.37.3 | yes | 8 | 5.2 | odd | 4 | inner | |
180.5.l.b.37.4 | 8 | 15.2 | even | 4 | |||
180.5.l.b.73.4 | 8 | 3.2 | odd | 2 | |||
240.5.bg.d.97.1 | 8 | 20.7 | even | 4 | |||
240.5.bg.d.193.1 | 8 | 4.3 | odd | 2 | |||
300.5.k.d.157.2 | 8 | 5.3 | odd | 4 | |||
300.5.k.d.193.2 | 8 | 5.4 | even | 2 | |||
900.5.l.k.757.3 | 8 | 15.8 | even | 4 | |||
900.5.l.k.793.3 | 8 | 15.14 | odd | 2 |