Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.4244687775\) |
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: | \( x^{20} + 996 x^{18} + 408854 x^{16} + 89661524 x^{14} + 11414409521 x^{12} + 861580608848 x^{10} + \cdots + 34\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{50} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Root | \(-13.8615i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.f.113.18 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 13.8615i | − | 1.54017i | −0.637944 | − | 0.770083i | \(-0.720215\pi\) | ||
0.637944 | − | 0.770083i | \(-0.279785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.6305 | 0.665221 | 0.332611 | − | 0.943064i | \(-0.392070\pi\) | ||||
0.332611 | + | 0.943064i | \(0.392070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 34.1005 | 0.695929 | 0.347964 | − | 0.937508i | \(-0.386873\pi\) | ||||
0.347964 | + | 0.937508i | \(0.386873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −111.141 | −1.37211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 198.897 | 1.64378 | 0.821890 | − | 0.569646i | \(-0.192920\pi\) | ||||
0.821890 | + | 0.569646i | \(0.192920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 164.629i | 0.974138i | 0.873364 | + | 0.487069i | \(0.161934\pi\) | ||||
−0.873364 | + | 0.487069i | \(0.838066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 230.524i | − | 1.02455i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 463.763 | 1.60472 | 0.802358 | − | 0.596842i | \(-0.203578\pi\) | ||||
0.802358 | + | 0.596842i | \(0.203578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 176.546 | + | 314.885i | 0.489048 | + | 0.872257i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 472.684i | − | 1.07184i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 807.248 | 1.52599 | 0.762994 | − | 0.646405i | \(-0.223728\pi\) | ||||
0.762994 | + | 0.646405i | \(0.223728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −348.425 | −0.557480 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 417.796i | 0.573109i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 424.371i | 0.504603i | 0.967649 | + | 0.252302i | \(0.0811875\pi\) | ||||
−0.967649 | + | 0.252302i | \(0.918812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1283.92i | 1.33603i | 0.744148 | + | 0.668015i | \(0.232856\pi\) | ||||
−0.744148 | + | 0.668015i | \(0.767144\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2757.01i | − | 2.53169i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 567.110 | 0.462947 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1126.53i | 0.822883i | 0.911436 | + | 0.411441i | \(0.134975\pi\) | ||||
−0.911436 | + | 0.411441i | \(0.865025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2282.01 | 1.50033 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 408.190i | − | 0.242826i | −0.992602 | − | 0.121413i | \(-0.961257\pi\) | ||
0.992602 | − | 0.121413i | \(-0.0387425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1546.41 | −0.836350 | −0.418175 | − | 0.908366i | \(-0.637330\pi\) | ||||
−0.418175 | + | 0.908366i | \(0.637330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1848.33 | −0.912756 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −198.561 | −0.0898874 | −0.0449437 | − | 0.998990i | \(-0.514311\pi\) | ||||
−0.0449437 | + | 0.998990i | \(0.514311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1238.16 | −0.515683 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6428.45i | − | 2.47153i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1512.97i | − | 0.538617i | −0.963054 | − | 0.269308i | \(-0.913205\pi\) | ||
0.963054 | − | 0.269308i | \(-0.0867951\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3307.77 | 1.09348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4364.77 | − | 2447.19i | 1.34342 | − | 0.753214i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2476.47i | − | 0.711426i | −0.934595 | − | 0.355713i | \(-0.884238\pi\) | ||
0.934595 | − | 0.355713i | \(-0.115762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4116.57 | −1.10631 | −0.553153 | − | 0.833080i | \(-0.686576\pi\) | ||||
−0.553153 | + | 0.833080i | \(0.686576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3789.96 | −0.954890 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2737.87i | 0.648017i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8501.12i | − | 1.89377i | −0.321576 | − | 0.946884i | \(-0.604212\pi\) | ||
0.321576 | − | 0.946884i | \(-0.395788\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 11189.7i | − | 2.35027i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4053.08i | − | 0.804024i | −0.915634 | − | 0.402012i | \(-0.868311\pi\) | ||
0.915634 | − | 0.402012i | \(-0.131689\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.79120 | −0.00146204 | −0.000731019 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000731019 | 1.00000i | \(0.500233\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4829.69i | 0.858612i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6782.50 | 1.14395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4348.12i | 0.696703i | 0.937364 | + | 0.348351i | \(0.113258\pi\) | ||||
−0.937364 | + | 0.348351i | \(0.886742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3211.13 | −0.489426 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8742.26 | −1.26902 | −0.634509 | − | 0.772916i | \(-0.718797\pi\) | ||||
−0.634509 | + | 0.772916i | \(0.718797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7712.63 | 1.06749 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5882.42 | 0.777172 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8132.18i | 1.02666i | 0.858191 | + | 0.513331i | \(0.171589\pi\) | ||||
−0.858191 | + | 0.513331i | \(0.828411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5613.94i | 0.677930i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17797.1 | 2.05771 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2936.06 | + | 5236.70i | 0.325325 | + | 0.580244i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.4206i | 0.00748438i | 0.999993 | + | 0.00374219i | \(0.00119118\pi\) | ||||
−0.999993 | + | 0.00374219i | \(0.998809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22105.6 | −2.25545 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 249.501 | 0.0244585 | 0.0122292 | − | 0.999925i | \(-0.496107\pi\) | ||||
0.0122292 | + | 0.999925i | \(0.496107\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14423.2i | − | 1.35952i | −0.733433 | − | 0.679762i | \(-0.762083\pi\) | ||
0.733433 | − | 0.679762i | \(-0.237917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 7860.98i | − | 0.713014i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11154.7i | − | 0.974297i | −0.873319 | − | 0.487148i | \(-0.838037\pi\) | ||
0.873319 | − | 0.487148i | \(-0.161963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15364.9i | 1.29323i | 0.762815 | + | 0.646617i | \(0.223817\pi\) | ||||
−0.762815 | + | 0.646617i | \(0.776183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15615.3 | 1.26738 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5434.97i | 0.425638i | 0.977092 | + | 0.212819i | \(0.0682645\pi\) | ||||
−0.977092 | + | 0.212819i | \(0.931736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13425.0 | 1.01512 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 18297.0i | − | 1.33662i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15814.6 | 1.11677 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24919.2 | 1.70202 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5658.12 | −0.373992 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16188.6 | −1.03607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6910.69i | − | 0.428464i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) | ||
0.976783 | − | 0.214232i | \(-0.0687248\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21435.6i | 1.28812i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 25573.0 | 1.49018 | 0.745091 | − | 0.666962i | \(-0.232406\pi\) | ||||
0.745091 | + | 0.666962i | \(0.232406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6020.32 | + | 10737.7i | 0.340342 | + | 0.607029i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6948.18i | 0.381244i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −26984.5 | −1.43772 | −0.718859 | − | 0.695156i | \(-0.755335\pi\) | ||||
−0.718859 | + | 0.695156i | \(0.755335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −31644.5 | −1.63783 | −0.818914 | − | 0.573916i | \(-0.805424\pi\) | ||||
−0.818914 | + | 0.573916i | \(0.805424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2752.35i | 0.138441i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32744.4i | 1.60127i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7057.52i | 0.335673i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17162.7i | 0.794238i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25545.4 | −1.15064 | −0.575320 | − | 0.817928i | \(-0.695122\pi\) | ||||
−0.575320 | + | 0.817928i | \(0.695122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10722.8i | 0.470280i | 0.971962 | + | 0.235140i | \(0.0755548\pi\) | ||||
−0.971962 | + | 0.235140i | \(0.924445\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −51543.0 | −2.20185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21352.3i | 0.888755i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1380.26 | −0.0559964 | −0.0279982 | − | 0.999608i | \(-0.508913\pi\) | ||||
−0.0279982 | + | 0.999608i | \(0.508913\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20972.1 | −0.829559 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27527.6 | 1.06198 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18266.6 | −0.687516 | −0.343758 | − | 0.939058i | \(-0.611700\pi\) | ||||
−0.343758 | + | 0.939058i | \(0.611700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 45850.6i | − | 1.68414i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 34186.3i | − | 1.22580i | −0.790160 | − | 0.612900i | \(-0.790003\pi\) | ||
0.790160 | − | 0.612900i | \(-0.209997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1458.19 | 0.0510553 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19621.5 | − | 34996.5i | −0.671027 | − | 1.19683i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 47486.7i | − | 1.58665i | −0.608801 | − | 0.793323i | \(-0.708349\pi\) | ||
0.608801 | − | 0.793323i | \(-0.291651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11881.5 | −0.387967 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34327.6 | −1.09571 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 38613.4i | 1.20513i | 0.798072 | + | 0.602563i | \(0.205854\pi\) | ||||
−0.798072 | + | 0.602563i | \(0.794146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12404.6i | − | 0.378639i | −0.981915 | − | 0.189320i | \(-0.939372\pi\) | ||
0.981915 | − | 0.189320i | \(-0.0606283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 57061.7i | 1.70389i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18734.7i | 0.547399i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 92241.3 | 2.63780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14247.1i | 0.398843i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9053.96 | 0.248183 | 0.124091 | − | 0.992271i | \(-0.460398\pi\) | ||||
0.124091 | + | 0.992271i | \(0.460398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 29253.9i | 0.785362i | 0.919675 | + | 0.392681i | \(0.128452\pi\) | ||||
−0.919675 | + | 0.392681i | \(0.871548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 37951.0 | 0.998054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 37953.7 | 0.977962 | 0.488981 | − | 0.872294i | \(-0.337369\pi\) | ||||
0.488981 | + | 0.872294i | \(0.337369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41610.7 | −1.05075 | −0.525375 | − | 0.850871i | \(-0.676075\pi\) | ||||
−0.525375 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −117838. | −2.91672 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14471.3i | 0.351168i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 6788.42i | − | 0.161533i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −89718.2 | −2.09382 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 35114.6 | + | 62629.8i | 0.803887 | + | 1.43380i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 57280.1i | − | 1.28659i | −0.765620 | − | 0.643293i | \(-0.777568\pi\) | ||
0.765620 | − | 0.643293i | \(-0.222432\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −56181.8 | −1.23833 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25717.6 | −0.556358 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43782.4i | 0.929781i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 107.998i | 0.00225178i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 76349.0i | 1.56322i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 71207.6i | 1.43191i | 0.698145 | + | 0.715957i | \(0.254009\pi\) | ||||
−0.698145 | + | 0.715957i | \(0.745991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 38724.3 | 0.764924 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20746.3i | 0.402615i | 0.979528 | + | 0.201307i | \(0.0645190\pi\) | ||||
−0.979528 | + | 0.201307i | \(0.935481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 33103.0 | 0.631242 | 0.315621 | − | 0.948885i | \(-0.397787\pi\) | ||||
0.315621 | + | 0.948885i | \(0.397787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 94015.6i | − | 1.76188i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6773.66 | 0.124770 | 0.0623852 | − | 0.998052i | \(-0.480129\pi\) | ||||
0.0623852 | + | 0.998052i | \(0.480129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3302.18 | −0.0597950 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 60271.4 | 1.07304 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 99987.5 | 1.75045 | 0.875225 | − | 0.483716i | \(-0.160713\pi\) | ||||
0.875225 | + | 0.483716i | \(0.160713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9387.50i | − | 0.161628i | −0.996729 | − | 0.0808139i | \(-0.974248\pi\) | ||
0.996729 | − | 0.0808139i | \(-0.0257519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 78352.5i | 1.32691i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20591.2 | −0.343044 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −51839.3 | + | 29064.7i | −0.849699 | + | 0.476400i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 121181.i | 1.95450i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20871.7 | −0.331292 | −0.165646 | − | 0.986185i | \(-0.552971\pi\) | ||||
−0.165646 | + | 0.986185i | \(0.552971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 160560. | 2.50839 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 106909.i | − | 1.64411i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 51138.9i | − | 0.774258i | −0.922026 | − | 0.387129i | \(-0.873467\pi\) | ||
0.922026 | − | 0.387129i | \(-0.126533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38415.1i | 0.572668i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 47165.0i | − | 0.692371i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 52658.8 | 0.761306 | 0.380653 | − | 0.924718i | \(-0.375699\pi\) | ||||
0.380653 | + | 0.924718i | \(0.375699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 25161.6i | − | 0.358299i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 112724. | 1.58123 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 142239.i | − | 1.96569i | −0.184440 | − | 0.982844i | \(-0.559047\pi\) | ||
0.184440 | − | 0.982844i | \(-0.440953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −87901.2 | −1.19690 | −0.598448 | − | 0.801162i | \(-0.704216\pi\) | ||||
−0.598448 | + | 0.801162i | \(0.704216\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 77817.6 | 1.04412 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −69300.9 | −0.916376 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 43465.3 | 0.566478 | 0.283239 | − | 0.959049i | \(-0.408591\pi\) | ||||
0.283239 | + | 0.959049i | \(0.408591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 142696.i | − | 1.83318i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 44636.1i | − | 0.565293i | −0.959224 | − | 0.282647i | \(-0.908788\pi\) | ||
0.959224 | − | 0.282647i | \(-0.0912124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28005.9 | −0.349685 | −0.174842 | − | 0.984596i | \(-0.555942\pi\) | ||||
−0.174842 | + | 0.984596i | \(0.555942\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 72588.5 | − | 40698.1i | 0.893672 | − | 0.501054i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 13919.5i | − | 0.168989i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 131555. | 1.57512 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 976.134 | 0.0115272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 46994.9i | − | 0.547413i | −0.961813 | − | 0.273707i | \(-0.911750\pi\) | ||
0.961813 | − | 0.273707i | \(-0.0882497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 41185.1i | − | 0.473256i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 83098.7i | 0.942066i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 132897.i | 1.48652i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −52733.4 | −0.582040 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3458.46i | − | 0.0376701i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −68460.7 | −0.735939 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 181833.i | − | 1.92928i | −0.263573 | − | 0.964640i | \(-0.584901\pi\) | ||
0.263573 | − | 0.964640i | \(-0.415099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −199927. | −2.09389 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −85515.3 | −0.884144 | −0.442072 | − | 0.896980i | \(-0.645756\pi\) | ||||
−0.442072 | + | 0.896980i | \(0.645756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −84722.7 | −0.864790 | −0.432395 | − | 0.901684i | \(-0.642331\pi\) | ||||
−0.432395 | + | 0.901684i | \(0.642331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −63029.0 | −0.635213 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 52210.6i | 0.519565i | 0.965667 | + | 0.259783i | \(0.0836509\pi\) | ||||
−0.965667 | + | 0.259783i | \(0.916349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 84406.4i | 0.829457i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −154621. | −1.50058 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 81875.7 | + | 146032.i | 0.784783 | + | 1.39973i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 57361.0i | − | 0.543063i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 212981. | 1.99179 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6771.04 | −0.0625552 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 118412.i | − | 1.08079i | −0.841412 | − | 0.540394i | \(-0.818275\pi\) | ||
0.841412 | − | 0.540394i | \(-0.181725\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 125203.i | − | 1.12908i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 141378.i | − | 1.25977i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 59595.5i | 0.524752i | 0.964966 | + | 0.262376i | \(0.0845060\pi\) | ||||
−0.964966 | + | 0.262376i | \(0.915494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 75336.8 | 0.655553 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 255369.i | 2.19614i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −124097. | −1.05481 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 186090.i | − | 1.56345i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16642.0 | 0.138212 | 0.0691062 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691062 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 153463. | 1.25995 | 0.629973 | − | 0.776617i | \(-0.283066\pi\) | ||||
0.629973 | + | 0.776617i | \(0.283066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −68781.5 | −0.558287 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1766.45 | −0.0141760 | −0.00708799 | − | 0.999975i | \(-0.502256\pi\) | ||||
−0.00708799 | + | 0.999975i | \(0.502256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 67405.0i | − | 0.534854i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 219213.i | − | 1.72001i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −43498.4 | −0.337508 | −0.168754 | − | 0.985658i | \(-0.553974\pi\) | ||||
−0.168754 | + | 0.985658i | \(0.553974\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −67983.8 | + | 111183.i | −0.521665 | + | 0.853151i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 345417.i | − | 2.62139i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −129.572 | −0.000972579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 123157. | 0.914377 | 0.457189 | − | 0.889370i | \(-0.348856\pi\) | ||||
0.457189 | + | 0.889370i | \(0.348856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 45366.6i | 0.333183i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 51593.2i | − | 0.374839i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 251344.i | − | 1.80655i | −0.429059 | − | 0.903277i | \(-0.641155\pi\) | ||
0.429059 | − | 0.903277i | \(-0.358845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 224398.i | 1.59572i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −69864.0 | −0.491553 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 97859.0i | − | 0.681275i | −0.940195 | − | 0.340637i | \(-0.889357\pi\) | ||
0.940195 | − | 0.340637i | \(-0.110643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −95792.4 | −0.659905 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 255398.i | 1.74108i | 0.492095 | + | 0.870541i | \(0.336231\pi\) | ||||
−0.492095 | + | 0.870541i | \(0.663769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 112797. | 0.760983 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 171869. | 1.14756 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −250026. | −1.65229 | −0.826145 | − | 0.563458i | \(-0.809471\pi\) | ||||
−0.826145 | + | 0.563458i | \(0.809471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 374372. | 2.44878 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 354480.i | − | 2.29513i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 72311.6i | 0.463462i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 219854. | 1.39493 | 0.697466 | − | 0.716618i | \(-0.254311\pi\) | ||||
0.697466 | + | 0.716618i | \(0.254311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 148841. | − | 83450.5i | 0.934924 | − | 0.524183i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 88448.2i | − | 0.550047i | −0.961437 | − | 0.275024i | \(-0.911314\pi\) | ||
0.961437 | − | 0.275024i | \(-0.0886857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −211372. | −1.30148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −53402.8 | −0.325577 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 224063.i | 1.35264i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 104881.i | − | 0.626977i | −0.949592 | − | 0.313488i | \(-0.898502\pi\) | ||
0.949592 | − | 0.313488i | \(-0.101498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 374045.i | 2.21432i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 84449.0i | − | 0.495102i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −145388. | −0.844177 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 438640.i | 2.52253i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −112863. | −0.642868 | −0.321434 | − | 0.946932i | \(-0.604165\pi\) | ||||
−0.321434 | + | 0.946932i | \(0.604165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 216141.i | − | 1.21947i | −0.792604 | − | 0.609737i | \(-0.791275\pi\) | ||
0.792604 | − | 0.609737i | \(-0.208725\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22068.3 | 0.123335 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −161587. | −0.894598 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −140377. | −0.769910 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 453885. | 2.46622 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 274109.i | − | 1.47560i | −0.675019 | − | 0.737800i | \(-0.735865\pi\) | ||
0.675019 | − | 0.737800i | \(-0.264135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 304373.i | 1.62342i | 0.584062 | + | 0.811709i | \(0.301462\pi\) | ||||
−0.584062 | + | 0.811709i | \(0.698538\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 97827.8 | 0.516992 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 142517. | + | 254190.i | 0.746281 | + | 1.33105i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 237360.i | − | 1.23163i | −0.787892 | − | 0.615814i | \(-0.788827\pi\) | ||
0.787892 | − | 0.615814i | \(-0.211173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 137610. | 0.707574 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 158727. | 0.808804 | 0.404402 | − | 0.914581i | \(-0.367480\pi\) | ||||
0.404402 | + | 0.914581i | \(0.367480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 135243.i | 0.682957i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 354097.i | 1.77218i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 348261.i | 1.72747i | 0.503942 | + | 0.863737i | \(0.331882\pi\) | ||||
−0.503942 | + | 0.863737i | \(0.668118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 81188.0i | − | 0.399152i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 148635. | 0.724308 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 93362.9i | 0.450974i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −75791.2 | −0.362900 | −0.181450 | − | 0.983400i | \(-0.558079\pi\) | ||||
−0.181450 | + | 0.983400i | \(0.558079\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 193759.i | 0.919678i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −80904.8 | −0.380691 | −0.190346 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190346 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 265052. | 1.23643 | 0.618215 | − | 0.786009i | \(-0.287856\pi\) | ||||
0.618215 | + | 0.786009i | \(0.287856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 295975. | 1.36883 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −414041. | −1.89850 | −0.949248 | − | 0.314529i | \(-0.898153\pi\) | ||||
−0.949248 | + | 0.314529i | \(0.898153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 289893.i | − | 1.31793i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19132.4i | 0.0862438i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −307577. | −1.37478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −61513.2 | − | 109714.i | −0.272635 | − | 0.486266i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 168153.i | 0.739041i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 209176. | 0.911678 | 0.455839 | − | 0.890062i | \(-0.349339\pi\) | ||||
0.455839 | + | 0.890062i | \(0.349339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −185459. | −0.801601 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 381573.i | − | 1.63562i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1171.13i | 0.00497877i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 88387.7i | − | 0.372678i | −0.982485 | − | 0.186339i | \(-0.940338\pi\) | ||
0.982485 | − | 0.186339i | \(-0.0596623\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 253202.i | 1.05889i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −362034. | −1.50171 | −0.750856 | − | 0.660466i | \(-0.770359\pi\) | ||||
−0.750856 | + | 0.660466i | \(0.770359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 196808.i | 0.809745i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −367628. | −1.50037 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 138212.i | − | 0.559543i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −163151. | −0.655222 | −0.327611 | − | 0.944813i | \(-0.606244\pi\) | ||||
−0.327611 | + | 0.944813i | \(0.606244\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −473873. | −1.88793 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 437918. | 1.73084 | 0.865420 | − | 0.501048i | \(-0.167052\pi\) | ||||
0.865420 | + | 0.501048i | \(0.167052\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4149.34 | 0.0162703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 20212.7i | − | 0.0786336i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 321145.i | 1.23955i | 0.784778 | + | 0.619777i | \(0.212777\pi\) | ||||
−0.784778 | + | 0.619777i | \(0.787223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −265.684 | −0.00101747 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −131558. | + | 73760.4i | −0.499898 | + | 0.280278i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 239865.i | − | 0.904384i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39493.3 | −0.147755 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −658236. | −2.44370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 57254.3i | 0.210927i | 0.994423 | + | 0.105464i | \(0.0336327\pi\) | ||||
−0.994423 | + | 0.105464i | \(0.966367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 346981.i | 1.26854i | 0.773113 | + | 0.634268i | \(0.218698\pi\) | ||||
−0.773113 | + | 0.634268i | \(0.781302\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 164695.i | 0.597532i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 595437.i | 2.14395i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 371808. | 1.32864 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 275237.i | 0.976154i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 67200.1 | 0.236546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 185509.i | − | 0.648123i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 535239. | 1.85609 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −246266. | −0.847671 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −419291. | −1.43259 | −0.716294 | − | 0.697798i | \(-0.754163\pi\) | ||||
−0.716294 | + | 0.697798i | \(0.754163\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −171946. | −0.583167 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 255527.i | 0.860287i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 100244.i | 0.335029i | 0.985870 | + | 0.167515i | \(0.0535741\pi\) | ||||
−0.985870 | + | 0.167515i | \(0.946426\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 457518. | 1.51797 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −133628. | + | 74921.2i | −0.440144 | + | 0.246775i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 148273.i | 0.484855i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 259691. | 0.843085 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −472339. | −1.52245 | −0.761225 | − | 0.648487i | \(-0.775402\pi\) | ||||
−0.761225 | + | 0.648487i | \(0.775402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 254585.i | − | 0.814720i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.27860e6i | − | 4.06265i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 116539.i | − | 0.367667i | −0.982957 | − | 0.183833i | \(-0.941149\pi\) | ||
0.982957 | − | 0.183833i | \(-0.0588507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 90386.5i | 0.283144i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −109501. | −0.340606 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 356049.i | − | 1.09973i | −0.835254 | − | 0.549864i | \(-0.814680\pi\) | ||
0.835254 | − | 0.549864i | \(-0.185320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −543882. | −1.66814 | −0.834069 | − | 0.551660i | \(-0.813995\pi\) | ||||
−0.834069 | + | 0.551660i | \(0.813995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 125501.i | − | 0.382243i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −281266. | −0.850709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −168627. | −0.506497 | −0.253248 | − | 0.967401i | \(-0.581499\pi\) | ||||
−0.253248 | + | 0.967401i | \(0.581499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 405503. | 1.20959 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −298115. | −0.883145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 300927.i | − | 0.885368i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 304290.i | − | 0.889150i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 226344. | 0.656890 | 0.328445 | − | 0.944523i | \(-0.393475\pi\) | ||||
0.328445 | + | 0.944523i | \(0.393475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −404288. | + | 226672.i | −1.16536 | + | 0.653382i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 526095.i | − | 1.50622i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 138124. | 0.392790 | 0.196395 | − | 0.980525i | \(-0.437077\pi\) | ||||
0.196395 | + | 0.980525i | \(0.437077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 263005. | 0.742898 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 576787.i | 1.61833i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 85172.8i | − | 0.237382i | −0.992931 | − | 0.118691i | \(-0.962130\pi\) | ||
0.992931 | − | 0.118691i | \(-0.0378698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 323788.i | − | 0.896420i | −0.893928 | − | 0.448210i | \(-0.852062\pi\) | ||
0.893928 | − | 0.448210i | \(-0.147938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 944822.i | 2.59846i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 414420. | 1.13222 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 312727.i | 0.848766i | 0.905483 | + | 0.424383i | \(0.139509\pi\) | ||||
−0.905483 | + | 0.424383i | \(0.860491\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 200593. | 0.540856 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 32689.0i | − | 0.0875627i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −87167.0 | −0.231970 | −0.115985 | − | 0.993251i | \(-0.537002\pi\) | ||||
−0.115985 | + | 0.993251i | \(0.537002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −94097.6 | −0.248787 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 74773.6 | 0.196417 | 0.0982083 | − | 0.995166i | \(-0.468689\pi\) | ||||
0.0982083 | + | 0.995166i | \(0.468689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −517474. | −1.35054 | −0.675269 | − | 0.737571i | \(-0.735973\pi\) | ||||
−0.675269 | + | 0.737571i | \(0.735973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 337265.i | 0.874558i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 277311.i | 0.714483i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −51459.1 | −0.131735 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 868142. | − | 486741.i | 2.20829 | − | 1.23812i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 522442.i | 1.32049i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 234598. | 0.589205 | 0.294602 | − | 0.955620i | \(-0.404813\pi\) | ||||
0.294602 | + | 0.955620i | \(0.404813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −793987. | −1.98156 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 114928.i | − | 0.285023i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 203837.i | − | 0.502347i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 450463.i | 1.10321i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 201204.i | − | 0.489690i | −0.969562 | − | 0.244845i | \(-0.921263\pi\) | ||
0.969562 | − | 0.244845i | \(-0.0787371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 397450. | 0.961304 | 0.480652 | − | 0.876911i | \(-0.340400\pi\) | ||||
0.480652 | + | 0.876911i | \(0.340400\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 356485.i | 0.856883i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 319131. | 0.762360 | 0.381180 | − | 0.924501i | \(-0.375518\pi\) | ||||
0.381180 | + | 0.924501i | \(0.375518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 492565.i | − | 1.16943i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 606890. | 1.43202 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −615311. | −1.44301 | −0.721504 | − | 0.692411i | \(-0.756549\pi\) | ||||
−0.721504 | + | 0.692411i | \(0.756549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 425293. | 0.991302 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 865.920 | 0.00200608 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 389964.i | − | 0.897953i | −0.893544 | − | 0.448977i | \(-0.851789\pi\) | ||
0.893544 | − | 0.448977i | \(-0.148211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 202339.i | − | 0.463101i | −0.972823 | − | 0.231551i | \(-0.925620\pi\) | ||
0.972823 | − | 0.231551i | \(-0.0743799\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.05831e6 | 2.40761 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 100121. | + | 178574.i | 0.226403 | + | 0.403808i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 342573.i | 0.770019i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 987043. | 2.20538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −818775. | −1.81853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 564672.i | 1.24671i | 0.781938 | + | 0.623356i | \(0.214231\pi\) | ||||
−0.781938 | + | 0.623356i | \(0.785769\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 145571.i | − | 0.319497i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 157666.i | − | 0.344002i | −0.985097 | − | 0.172001i | \(-0.944977\pi\) | ||
0.985097 | − | 0.172001i | \(-0.0550232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2401.38i | 0.00520860i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 287575. | 0.620093 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 132840.i | 0.284765i | 0.989812 | + | 0.142382i | \(0.0454762\pi\) | ||||
−0.989812 | + | 0.142382i | \(0.954524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −448767. | −0.956400 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 458856.i | − | 0.972217i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 249080. | 0.524687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 822098. | 1.72174 | 0.860870 | − | 0.508826i | \(-0.169920\pi\) | ||||
0.860870 | + | 0.508826i | \(0.169920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −753813. | −1.56963 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −526265. | −1.08952 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 189304.i | − | 0.389667i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 93893.0i | − | 0.192167i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 524576. | 1.06751 | 0.533755 | − | 0.845639i | \(-0.320780\pi\) | ||||
0.533755 | + | 0.845639i | \(0.320780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −354726. | + | 198884.i | −0.717765 | + | 0.402429i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 45773.1i | 0.0920942i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8508.11 | 0.0170214 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 350588. | 0.697435 | 0.348718 | − | 0.937228i | \(-0.386617\pi\) | ||||
0.348718 | + | 0.937228i | \(0.386617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 483254.i | − | 0.955952i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.03645e6i | 2.03877i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 544556.i | 1.06520i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.38598e6i | − | 2.69598i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −105280. | −0.203652 | −0.101826 | − | 0.994802i | \(-0.532468\pi\) | ||||
−0.101826 | + | 0.994802i | \(0.532468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 491838.i | − | 0.946131i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −130125. | −0.248933 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 147862.i | − | 0.281306i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −142455. | −0.269531 | −0.134766 | − | 0.990878i | \(-0.543028\pi\) | ||||
−0.134766 | + | 0.990878i | \(0.543028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 825981. | 1.55423 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −717169. | −1.34211 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46226.2 | −0.0860361 | −0.0430180 | − | 0.999074i | \(-0.513697\pi\) | ||||
−0.0430180 | + | 0.999074i | \(0.513697\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 285425.i | 0.528344i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.69085e6i | − | 3.11294i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 383816. | 0.702803 | 0.351402 | − | 0.936225i | \(-0.385705\pi\) | ||||
0.351402 | + | 0.936225i | \(0.385705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 402880. | + | 718569.i | 0.733735 | + | 1.30868i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 289968.i | − | 0.525258i | −0.964897 | − | 0.262629i | \(-0.915410\pi\) | ||
0.964897 | − | 0.262629i | \(-0.0845895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −424833. | −0.765430 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 971622. | 1.74123 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 380382.i | − | 0.678041i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 701251.i | 1.24335i | 0.783275 | + | 0.621675i | \(0.213548\pi\) | ||||
−0.783275 | + | 0.621675i | \(0.786452\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 289313.i | 0.510244i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 178327.i | 0.312840i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 193035. | 0.336856 | 0.168428 | − | 0.985714i | \(-0.446131\pi\) | ||||
0.168428 | + | 0.985714i | \(0.446131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.22559e6i | − | 3.86334i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 882197. | 1.52334 | 0.761669 | − | 0.647966i | \(-0.224380\pi\) | ||||
0.761669 | + | 0.647966i | \(0.224380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 523951.i | 0.899998i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −857188. | −1.46472 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 407700. | 0.693027 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50360.6 | −0.0851605 | −0.0425803 | − | 0.999093i | \(-0.513558\pi\) | ||||
−0.0425803 | + | 0.999093i | \(0.513558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −708862. | −1.19248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 186023.i | 0.311320i | 0.987811 | + | 0.155660i | \(0.0497505\pi\) | ||||
−0.987811 | + | 0.155660i | \(0.950250\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 447352.i | − | 0.744810i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 532491. | 0.882003 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 128533. | − | 72064.4i | 0.211806 | − | 0.118753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 806148.i | − | 1.32164i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −177301. | −0.289193 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22954.4 | −0.0372500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 496717.i | − | 0.801973i | −0.916084 | − | 0.400987i | \(-0.868667\pi\) | ||
0.916084 | − | 0.400987i | \(-0.131333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 729929.i | − | 1.17254i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 185335.i | 0.296214i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 677707.i | − | 1.07769i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −348777. | −0.551840 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.16084e6i | 1.82749i | 0.406289 | + | 0.913745i | \(0.366823\pi\) | ||||
−0.406289 | + | 0.913745i | \(0.633177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −92085.4 | −0.144244 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 903817.i | − | 1.40869i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1549.65 | −0.00240327 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 457798. | 0.706451 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.97165e6 | −3.02748 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −327930. | −0.501054 | −0.250527 | − | 0.968110i | \(-0.580604\pi\) | ||||
−0.250527 | + | 0.968110i | \(0.580604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 921655.i | − | 1.40129i | −0.713512 | − | 0.700643i | \(-0.752897\pi\) | ||
0.713512 | − | 0.700643i | \(-0.247103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21844e6i | 1.84342i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −303783. | −0.457350 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −273013. | − | 486941.i | −0.409015 | − | 0.729512i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 623938.i | − | 0.930194i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −285899. | −0.424157 | −0.212078 | − | 0.977253i | \(-0.568023\pi\) | ||||
−0.212078 | + | 0.977253i | \(0.568023\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 127934. | 0.188880 | 0.0944398 | − | 0.995531i | \(-0.469894\pi\) | ||||
0.0944398 | + | 0.995531i | \(0.469894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 960614.i | 1.41137i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 244346.i | 0.357268i | 0.983916 | + | 0.178634i | \(0.0571679\pi\) | ||||
−0.983916 | + | 0.178634i | \(0.942832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 575618.i | 0.837579i | 0.908083 | + | 0.418789i | \(0.137545\pi\) | ||||
−0.908083 | + | 0.418789i | \(0.862455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 602494.i | − | 0.872470i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −574211. | −0.827526 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 568537.i | − | 0.815428i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −536419. | −0.765690 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.19220e6i | 1.69366i | 0.531866 | + | 0.846829i | \(0.321491\pi\) | ||||
−0.531866 | + | 0.846829i | \(0.678509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 527190. | 0.745376 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −618723. | −0.870645 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24250.5 | 0.0339631 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 849758. | 1.18448 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 388204.i | 0.538572i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 909386.i | 1.25571i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 661907. | 0.909702 | 0.454851 | − | 0.890568i | \(-0.349693\pi\) | ||||
0.454851 | + | 0.890568i | \(0.349693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −326316. | − | 582011.i | −0.446381 | − | 0.796158i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 982841.i | 1.33820i | 0.743171 | + | 0.669101i | \(0.233321\pi\) | ||||
−0.743171 | + | 0.669101i | \(0.766679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 521534. | 0.706800 | 0.353400 | − | 0.935472i | \(-0.385026\pi\) | ||||
0.353400 | + | 0.935472i | \(0.385026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −192945. | −0.260272 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 941751.i | − | 1.26449i | −0.774770 | − | 0.632243i | \(-0.782134\pi\) | ||
0.774770 | − | 0.632243i | \(-0.217866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 789730.i | − | 1.05547i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.82355e6i | − | 2.42594i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 864831.i | 1.14523i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.39953e6 | 1.84479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7826.60i | − | 0.0102694i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −552039. | −0.721030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 343716.i | 0.446890i | 0.974717 | + | 0.223445i | \(0.0717303\pi\) | ||||
−0.974717 | + | 0.223445i | \(0.928270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −651419. | −0.843107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 322791. | 0.415882 | 0.207941 | − | 0.978141i | \(-0.433324\pi\) | ||||
0.207941 | + | 0.978141i | \(0.433324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −555429. | −0.712372 | −0.356186 | − | 0.934415i | \(-0.615923\pi\) | ||||
−0.356186 | + | 0.934415i | \(0.615923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −570887. | −0.728892 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.26195e6i | 1.60396i | 0.597349 | + | 0.801981i | \(0.296221\pi\) | ||||
−0.597349 | + | 0.801981i | \(0.703779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 235658.i | − | 0.298180i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −638685. | −0.804510 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35055.2 | − | 62523.9i | −0.0439592 | − | 0.0784049i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 642162.i | 0.801675i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.84215e6 | 2.28949 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −544861. | −0.674165 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 701662.i | − | 0.864327i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 730963.i | 0.896438i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 206295.i | − | 0.251879i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 713110.i | − | 0.866846i | −0.901191 | − | 0.433423i | \(-0.857306\pi\) | ||
0.901191 | − | 0.433423i | \(-0.142694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27729.7 | −0.0335597 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 613356.i | 0.739054i | 0.929220 | + | 0.369527i | \(0.120480\pi\) | ||||
−0.929220 | + | 0.369527i | \(0.879520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.73881e6 | −2.08599 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 948967.i | 1.13347i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 872053. | 1.03706 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 341024. | 0.403788 | 0.201894 | − | 0.979407i | \(-0.435290\pi\) | ||||
0.201894 | + | 0.979407i | \(0.435290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.52047e6 | −2.97141 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 667257. | 0.783230 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 392510.i | − | 0.458741i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.60300e6i | 1.86541i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 396594. | 0.459531 | 0.229765 | − | 0.973246i | \(-0.426204\pi\) | ||||
0.229765 | + | 0.973246i | \(0.426204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −218592. | − | 389876.i | −0.252194 | − | 0.449809i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.18537e6i | 1.36173i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.53402e6 | 1.75472 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.60617e6 | 1.82941 | 0.914707 | − | 0.404119i | \(-0.132422\pi\) | ||||
0.914707 | + | 0.404119i | \(0.132422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.17438e6i | 1.33192i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 767970.i | 0.867292i | 0.901083 | + | 0.433646i | \(0.142773\pi\) | ||||
−0.901083 | + | 0.433646i | \(0.857227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 329511.i | − | 0.370549i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 236936.i | 0.265319i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 66938.4 | 0.0746406 | 0.0373203 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373203 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1282.66i | − | 0.00142423i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 723716. | 0.800216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 237880.i | 0.261922i | 0.991388 | + | 0.130961i | \(0.0418063\pi\) | ||||
−0.991388 | + | 0.130961i | \(0.958194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 150572. | 0.165097 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17000e6 | 1.27750 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −920185. | −1.00055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −724940. | −0.784974 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.23974e6i | 1.33684i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 486509.i | 0.522440i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36716e6 | 1.46206 | 0.731031 | − | 0.682345i | \(-0.239040\pi\) | ||||
0.731031 | + | 0.682345i | \(0.239040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.02422e6 | − | 1.13492e6i | 2.15581 | − | 1.20870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 72775.5i | 0.0771875i | 0.999255 | + | 0.0385937i | \(0.0122878\pi\) | ||||
−0.999255 | + | 0.0385937i | \(0.987712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.07909e6 | −1.13981 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −795109. | −0.836406 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 496154.i | − | 0.519789i | −0.965637 | − | 0.259895i | \(-0.916312\pi\) | ||
0.965637 | − | 0.259895i | \(-0.0836879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.61747e6i | 1.68761i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.70767e6i | − | 1.77446i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 354053.i | 0.366405i | 0.983075 | + | 0.183203i | \(0.0586465\pi\) | ||||
−0.983075 | + | 0.183203i | \(0.941354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 631191. | 0.650561 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 93856.6i | 0.0963453i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.24834e6 | −1.27626 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 431313.i | 0.439183i | 0.975592 | + | 0.219591i | \(0.0704724\pi\) | ||||
−0.975592 | + | 0.219591i | \(0.929528\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.64137e6 | −1.66459 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −692009. | −0.698981 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 522673. | 0.525823 | 0.262912 | − | 0.964820i | \(-0.415317\pi\) | ||||
0.262912 | + | 0.964820i | \(0.415317\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −470659. | −0.471602 |
(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 | 304.5.e.f.113.3 | 20 | ||
4.3 | odd | 2 | 152.5.e.a.113.18 | yes | 20 | ||
12.11 | even | 2 | 1368.5.o.a.721.6 | 20 | |||
19.18 | odd | 2 | inner | 304.5.e.f.113.18 | 20 | ||
76.75 | even | 2 | 152.5.e.a.113.3 | ✓ | 20 | ||
228.227 | odd | 2 | 1368.5.o.a.721.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.e.a.113.3 | ✓ | 20 | 76.75 | even | 2 | ||
152.5.e.a.113.18 | yes | 20 | 4.3 | odd | 2 | ||
304.5.e.f.113.3 | 20 | 1.1 | even | 1 | trivial | ||
304.5.e.f.113.18 | 20 | 19.18 | odd | 2 | inner | ||
1368.5.o.a.721.5 | 20 | 228.227 | odd | 2 | |||
1368.5.o.a.721.6 | 20 | 12.11 | even | 2 |