Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{70})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(-4.18330 - 4.18330i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.g.449.1 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 20.7332i | 1.33004i | 0.746828 | + | 0.665018i | \(0.231576\pi\) | ||||
−0.746828 | + | 0.665018i | \(0.768424\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 35.2668i | − 0.272033i | −0.990707 | − | 0.136016i | \(-0.956570\pi\) | ||||
0.990707 | − | 0.136016i | \(-0.0434300\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −186.866 | −0.768994 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.33201 | −0.0182701 | −0.00913505 | − | 0.999958i | \(-0.502908\pi\) | ||||
−0.00913505 | + | 0.999958i | \(0.502908\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 619.328i | 1.01639i | 0.861241 | + | 0.508197i | \(0.169688\pi\) | ||||
−0.861241 | + | 0.508197i | \(0.830312\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 959.328i | − 0.805091i | −0.915400 | − | 0.402545i | \(-0.868126\pi\) | ||||
0.915400 | − | 0.402545i | \(-0.131874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 309.328 | 0.196578 | 0.0982891 | − | 0.995158i | \(-0.468663\pi\) | ||||
0.0982891 | + | 0.995158i | \(0.468663\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 731.194 | 0.361813 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2467.12i | 0.972458i | 0.873831 | + | 0.486229i | \(0.161628\pi\) | ||||
−0.873831 | + | 0.486229i | \(0.838372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1163.85i | 0.307246i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1284.66 | 0.283656 | 0.141828 | − | 0.989891i | \(-0.454702\pi\) | ||||
0.141828 | + | 0.989891i | \(0.454702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7095.32 | 1.32607 | 0.663037 | − | 0.748587i | \(-0.269267\pi\) | ||||
0.663037 | + | 0.748587i | \(0.269267\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 152.016i | − 0.0242999i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6100.59i | 0.732601i | 0.930497 | + | 0.366301i | \(0.119376\pi\) | ||||
−0.930497 | + | 0.366301i | \(0.880624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12840.7 | −1.35184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18830.4 | −1.74945 | −0.874723 | − | 0.484623i | \(-0.838957\pi\) | ||||
−0.874723 | + | 0.484623i | \(0.838957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3147.48i | 0.259592i | 0.991541 | + | 0.129796i | \(0.0414323\pi\) | ||||
−0.991541 | + | 0.129796i | \(0.958568\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 20556.8i | − 1.35741i | −0.734411 | − | 0.678705i | \(-0.762541\pi\) | ||||
0.734411 | − | 0.678705i | \(-0.237459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15563.3 | 0.925998 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19889.9 | 1.07080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33741.9i | 1.64998i | 0.565146 | + | 0.824991i | \(0.308820\pi\) | ||||
−0.565146 | + | 0.824991i | \(0.691180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6413.36i | 0.261456i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15065.3 | −0.563441 | −0.281721 | − | 0.959496i | \(-0.590905\pi\) | ||||
−0.281721 | + | 0.959496i | \(0.590905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7542.11 | −0.259518 | −0.129759 | − | 0.991546i | \(-0.541420\pi\) | ||||
−0.129759 | + | 0.991546i | \(0.541420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6590.15i | 0.209192i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 25574.9i | − 0.696029i | −0.937489 | − | 0.348015i | \(-0.886856\pi\) | ||||
0.937489 | − | 0.348015i | \(-0.113144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −51151.3 | −1.29340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56232.3 | −1.32385 | −0.661926 | − | 0.749569i | \(-0.730261\pi\) | ||||
−0.661926 | + | 0.749569i | \(0.730261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58657.5i | 1.28830i | 0.764900 | + | 0.644149i | \(0.222788\pi\) | ||||
−0.764900 | + | 0.644149i | \(0.777212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 258.576i | 0.00497006i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −32238.7 | −0.581179 | −0.290589 | − | 0.956848i | \(-0.593851\pi\) | ||||
−0.290589 | + | 0.956848i | \(0.593851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69538.6 | −1.17764 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31173.4i | 0.496694i | 0.968671 | + | 0.248347i | \(0.0798874\pi\) | ||||
−0.968671 | + | 0.248347i | \(0.920113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26635.0i | 0.377272i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 75258.9 | 1.00712 | 0.503562 | − | 0.863959i | \(-0.332023\pi\) | ||||
0.503562 | + | 0.863959i | \(0.332023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21841.7 | 0.276492 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 147109.i | 1.76372i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 176059.i | 1.89989i | 0.312419 | + | 0.949944i | \(0.398861\pi\) | ||||
−0.312419 | + | 0.949944i | \(0.601139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1370.10 | 0.0140496 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −102454. | −0.999370 | −0.499685 | − | 0.866207i | \(-0.666551\pi\) | ||||
−0.499685 | + | 0.866207i | \(0.666551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 150320.i | − 1.39612i | −0.716038 | − | 0.698062i | \(-0.754046\pi\) | ||||
0.716038 | − | 0.698062i | \(-0.245954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 220857.i | 1.86488i | 0.361321 | + | 0.932441i | \(0.382326\pi\) | ||||
−0.361321 | + | 0.932441i | \(0.617674\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24621.0 | 0.198490 | 0.0992450 | − | 0.995063i | \(-0.468357\pi\) | ||||
0.0992450 | + | 0.995063i | \(0.468357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −126485. | −0.974386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 64568.7i | − 0.475692i | −0.971303 | − | 0.237846i | \(-0.923559\pi\) | ||||
0.971303 | − | 0.237846i | \(-0.0764413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 115731.i | − 0.781602i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −33832.4 | −0.219011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160997. | −0.999666 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 390415.i | − 2.32682i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 159599.i | − 0.878054i | −0.898474 | − | 0.439027i | \(-0.855323\pi\) | ||||
0.898474 | − | 0.439027i | \(-0.144677\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −65257.3 | −0.345267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 116112. | 0.591153 | 0.295577 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295577 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 10909.0i | − 0.0534757i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1446.13i | 0.00658272i | 0.999995 | + | 0.00329136i | \(0.00104767\pi\) | ||||
−0.999995 | + | 0.00329136i | \(0.998952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 135055. | 0.592891 | 0.296446 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296446 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 426209. | 1.80540 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4540.92i | − 0.0185696i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 322676.i | 1.23161i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16097.8 | −0.0594019 | −0.0297010 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0297010 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −467353. | −1.66802 | −0.834012 | − | 0.551746i | \(-0.813962\pi\) | ||||
−0.834012 | + | 0.551746i | \(0.813962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 179265.i | 0.619110i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 210478.i | − 0.681487i | −0.940156 | − | 0.340743i | \(-0.889321\pi\) | ||||
0.940156 | − | 0.340743i | \(-0.110679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −699577. | −2.19454 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87007.4 | 0.264540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 136230.i | − 0.401610i | −0.979631 | − | 0.200805i | \(-0.935644\pi\) | ||||
0.979631 | − | 0.200805i | \(-0.0643557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 246713.i | − 0.684542i | −0.939601 | − | 0.342271i | \(-0.888804\pi\) | ||||
0.939601 | − | 0.342271i | \(-0.111196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12274.2 | −0.0330580 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −57802.8 | −0.151167 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 652180.i | − 1.65673i | −0.560187 | − | 0.828366i | \(-0.689271\pi\) | ||||
0.560187 | − | 0.828366i | \(-0.310729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 312353.i | − 0.749397i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −786542. | −1.83480 | −0.917402 | − | 0.397962i | \(-0.869718\pi\) | ||||
−0.917402 | + | 0.397962i | \(0.869718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −974.027 | −0.00220991 | −0.00110495 | − | 0.999999i | \(-0.500352\pi\) | ||||
−0.00110495 | + | 0.999999i | \(0.500352\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 156372.i | − 0.345169i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7033.80i | 0.0147091i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41045.1 | 0.0835809 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −469675. | −0.931567 | −0.465783 | − | 0.884899i | \(-0.654227\pi\) | ||||
−0.465783 | + | 0.884899i | \(0.654227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 644811.i | − 1.24606i | −0.782198 | − | 0.623030i | \(-0.785901\pi\) | ||||
0.782198 | − | 0.623030i | \(-0.214099\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 521778.i | 0.957899i | 0.877842 | + | 0.478950i | \(0.158982\pi\) | ||||
−0.877842 | + | 0.478950i | \(0.841018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −394042. | −0.705358 | −0.352679 | − | 0.935744i | \(-0.614729\pi\) | ||||
−0.352679 | + | 0.935744i | \(0.614729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 530250. | 0.925744 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 45305.7i | − 0.0771637i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 461020.i | − 0.747814i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2267.99 | −0.00359150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 750041. | 1.15979 | 0.579894 | − | 0.814692i | \(-0.303094\pi\) | ||||
0.579894 | + | 0.814692i | \(0.303094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.16587e6i | − 1.76077i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 250229.i | − 0.360735i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.21616e6 | −1.71348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 594139. | 0.818290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.00328e6i | − 1.35102i | −0.737351 | − | 0.675509i | \(-0.763924\pi\) | ||||
0.737351 | − | 0.675509i | \(-0.236076\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 385367.i | − 0.496375i | −0.968712 | − | 0.248188i | \(-0.920165\pi\) | ||||
0.968712 | − | 0.248188i | \(-0.0798349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16601.6 | 0.0209200 | 0.0104600 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104600 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5361.12 | −0.00661036 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 933464.i | 1.12644i | 0.826307 | + | 0.563219i | \(0.190437\pi\) | ||||
−0.826307 | + | 0.563219i | \(0.809563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 668411.i | − 0.772988i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.34120e6 | −1.51880 | −0.759398 | − | 0.650626i | \(-0.774507\pi\) | ||||
−0.759398 | + | 0.650626i | \(0.774507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 390139. | 0.432690 | 0.216345 | − | 0.976317i | \(-0.430586\pi\) | ||||
0.216345 | + | 0.976317i | \(0.430586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.15894e6i | − 1.25906i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 191576.i | 0.199801i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −646325. | −0.660621 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 805856. | 0.807371 | 0.403686 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403686 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 18088.9i | − 0.0177669i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 153621.i | − 0.145084i | −0.997365 | − | 0.0725419i | \(-0.976889\pi\) | ||||
0.997365 | − | 0.0725419i | \(-0.0231111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 215148. | 0.199291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −240058. | −0.218130 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 28007.0i | − 0.0249676i | −0.999922 | − | 0.0124838i | \(-0.996026\pi\) | ||||
0.999922 | − | 0.0124838i | \(-0.00397382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.56036e6i | 1.33951i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −715607. | −0.602968 | −0.301484 | − | 0.953471i | \(-0.597482\pi\) | ||||
−0.301484 | + | 0.953471i | \(0.597482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.35674e6 | −1.12221 | −0.561104 | − | 0.827745i | \(-0.689623\pi\) | ||||
−0.561104 | + | 0.827745i | \(0.689623\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 452849.i | 0.367745i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 791037.i | 0.619437i | 0.950828 | + | 0.309719i | \(0.100235\pi\) | ||||
−0.950828 | + | 0.309719i | \(0.899765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.32587e6 | −1.01974 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −191136. | −0.144403 | −0.0722016 | − | 0.997390i | \(-0.523002\pi\) | ||||
−0.0722016 | + | 0.997390i | \(0.523002\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.16924e6i | − 0.867834i | −0.900953 | − | 0.433917i | \(-0.857131\pi\) | ||||
0.900953 | − | 0.433917i | \(-0.142869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 664089.i | 0.475906i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 499547. | 0.351829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.65026e6 | −2.52692 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 932811.i | − 0.634782i | −0.948295 | − | 0.317391i | \(-0.897193\pi\) | ||||
0.948295 | − | 0.317391i | \(-0.102807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 8533.32i | − 0.00561341i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.52796e6 | −0.988401 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 111001. | 0.0706175 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.12420e6i | − 1.32920i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 678740.i | 0.411015i | 0.978656 | + | 0.205507i | \(0.0658844\pi\) | ||||
−0.978656 | + | 0.205507i | \(0.934116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.11662e6 | 1.85689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.25645e6 | 0.736621 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.13670e6i | 1.80972i | 0.425708 | + | 0.904861i | \(0.360025\pi\) | ||||
−0.425708 | + | 0.904861i | \(0.639975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 353375.i | − 0.197510i | −0.995112 | − | 0.0987548i | \(-0.968514\pi\) | ||||
0.995112 | − | 0.0987548i | \(-0.0314859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9419.10 | −0.00518242 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.57907e6 | −2.48036 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 296747.i | − 0.158263i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 510471.i | 0.263999i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −724973. | −0.369260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.91561e6 | −1.46271 | −0.731356 | − | 0.681996i | \(-0.761112\pi\) | ||||
−0.731356 | + | 0.681996i | \(0.761112\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.13999e6i | − 0.563366i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.11496e6i | 1.49409i | 0.664772 | + | 0.747046i | \(0.268529\pi\) | ||||
−0.664772 | + | 0.747046i | \(0.731471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.33871e6 | 0.632687 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52022.9 | −0.0242275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.14160e6i | − 0.523934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.09755e6i | − 1.82684i | −0.407020 | − | 0.913419i | \(-0.633432\pi\) | ||||
0.407020 | − | 0.913419i | \(-0.366568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.46309e6 | −1.08247 | −0.541237 | − | 0.840870i | \(-0.682044\pi\) | ||||
−0.541237 | + | 0.840870i | \(0.682044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −720802. | −0.312283 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.56682e6i | 1.52350i | 0.647868 | + | 0.761752i | \(0.275661\pi\) | ||||
−0.647868 | + | 0.761752i | \(0.724339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 701455.i | − 0.291292i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 648318. | 0.265492 | 0.132746 | − | 0.991150i | \(-0.457620\pi\) | ||||
0.132746 | + | 0.991150i | \(0.457620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.38042e6 | −0.961357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.33799e6i | − 1.32959i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.84494e6i | 1.49013i | 0.666992 | + | 0.745065i | \(0.267581\pi\) | ||||
−0.666992 | + | 0.745065i | \(0.732419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.51876e6 | 1.34531 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.18997e6 | 0.448849 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.40550e6i | 0.895228i | 0.894227 | + | 0.447614i | \(0.147726\pi\) | ||||
−0.894227 | + | 0.447614i | \(0.852274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 795623.i | 0.288306i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.03689e6 | −1.80121 | −0.900605 | − | 0.434638i | \(-0.856876\pi\) | ||||
−0.900605 | + | 0.434638i | \(0.856876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.30900e6 | 1.16784 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.61371e6i | − 0.562121i | −0.959690 | − | 0.281060i | \(-0.909314\pi\) | ||||
0.959690 | − | 0.281060i | \(-0.0906861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 588155.i | − 0.199625i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.99508e6 | −0.668477 | −0.334238 | − | 0.942489i | \(-0.608479\pi\) | ||||
−0.334238 | + | 0.942489i | \(0.608479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.36678e6 | 0.782917 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.40738e6i | 0.786255i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.61674e6i | − 1.15170i | −0.817554 | − | 0.575852i | \(-0.804671\pi\) | ||||
0.817554 | − | 0.575852i | \(-0.195329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 226179. | 0.0711245 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.64534e6 | −0.821525 | −0.410763 | − | 0.911742i | \(-0.634738\pi\) | ||||
−0.410763 | + | 0.911742i | \(0.634738\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.39433e6i | 1.34781i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 44729.6i | − 0.0133847i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.86360e6 | −0.846456 | −0.423228 | − | 0.906023i | \(-0.639103\pi\) | ||||
−0.423228 | + | 0.906023i | \(0.639103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29982.9 | −0.00875525 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 531306.i | 0.153274i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.80013e6i | 0.788566i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.09856e6 | −0.305695 | −0.152847 | − | 0.988250i | \(-0.548844\pi\) | ||||
−0.152847 | + | 0.988250i | \(0.548844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.31987e6 | 0.637909 | 0.318955 | − | 0.947770i | \(-0.396668\pi\) | ||||
0.318955 | + | 0.947770i | \(0.396668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.84136e6i | 1.04384i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 265986.i | 0.0705975i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 94147.7 | 0.0246983 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.05072e6 | 1.30967 | 0.654833 | − | 0.755774i | \(-0.272739\pi\) | ||||
0.654833 | + | 0.755774i | \(0.272739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.01025e6i | − 0.258946i | −0.991583 | − | 0.129473i | \(-0.958671\pi\) | ||||
0.991583 | − | 0.129473i | \(-0.0413286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 763149.i | 0.191164i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.14635e6 | 1.27450 | 0.637248 | − | 0.770659i | \(-0.280073\pi\) | ||||
0.637248 | + | 0.770659i | \(0.280073\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.90824e6 | −0.712087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.25603e6i | 1.27247i | 0.771494 | + | 0.636236i | \(0.219510\pi\) | ||||
−0.771494 | + | 0.636236i | \(0.780490\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 333759.i | − 0.0790067i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.10261e6 | 0.960384 | 0.480192 | − | 0.877163i | \(-0.340567\pi\) | ||||
0.480192 | + | 0.877163i | \(0.340567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 138065. | 0.0319626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 9.68972e6i | − 2.21853i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.01053e6i | 0.898278i | 0.893462 | + | 0.449139i | \(0.148269\pi\) | ||||
−0.893462 | + | 0.449139i | \(0.851731\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11651e6 | 0.247361 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.83280e6 | 0.839971 | 0.419986 | − | 0.907531i | \(-0.362035\pi\) | ||||
0.419986 | + | 0.907531i | \(0.362035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.14398e6i | 0.248009i | 0.992282 | + | 0.124004i | \(0.0395737\pi\) | ||||
−0.992282 | + | 0.124004i | \(0.960426\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.12577e6i | − 1.51196i | −0.654596 | − | 0.755979i | \(-0.727161\pi\) | ||||
0.654596 | − | 0.755979i | \(-0.272839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −901946. | −0.189343 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.36388e6 | 0.906401 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 23077.3i | − 0.00474277i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.30519e6i | − 1.26883i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.45039e6 | −1.28454 | −0.642269 | − | 0.766479i | \(-0.722007\pi\) | ||||
−0.642269 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.77827e6 | −0.744612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.80394e6i | 0.351848i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.46947e6i | 0.280762i | 0.990098 | + | 0.140381i | \(0.0448327\pi\) | ||||
−0.990098 | + | 0.140381i | \(0.955167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.82449e6 | 0.534155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.19488e6 | −0.972460 | −0.486230 | − | 0.873831i | \(-0.661628\pi\) | ||||
−0.486230 | + | 0.873831i | \(0.661628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.23241e6i | − 0.228369i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.98313e6i | 0.360131i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.07689e6 | 1.27230 | 0.636152 | − | 0.771564i | \(-0.280525\pi\) | ||||
0.636152 | + | 0.771564i | \(0.280525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.11514e6 | 0.910465 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.92098e6i | 1.57215i | 0.618134 | + | 0.786073i | \(0.287889\pi\) | ||||
−0.618134 | + | 0.786073i | \(0.712111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 254483.i | − 0.0439683i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.79714e6 | −0.991789 | −0.495895 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495895 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.06866e6 | 0.350459 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 360010.i | 0.0603978i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 150723.i | 0.0248000i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.35218e7 | 2.20351 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.45721e6 | 1.20360 | 0.601800 | − | 0.798647i | \(-0.294450\pi\) | ||||
0.601800 | + | 0.798647i | \(0.294450\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.01015e7i | − 1.61485i | −0.589971 | − | 0.807424i | \(-0.700861\pi\) | ||||
0.589971 | − | 0.807424i | \(-0.299139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.80674e6i | − 1.06761i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 349660. | 0.0543258 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.81519e6 | 0.433283 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.16622e7i | − 1.77813i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.63075e7i | − 2.44035i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −114110. | −0.0169181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.23616e7 | 1.81585 | 0.907925 | − | 0.419132i | \(-0.137666\pi\) | ||||
0.907925 | + | 0.419132i | \(0.137666\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 20194.7i | − 0.00293926i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72735e6i | 0.532637i | 0.963885 | + | 0.266319i | \(0.0858073\pi\) | ||||
−0.963885 | + | 0.266319i | \(0.914193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.40936e6 | 0.199568 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 397380. | 0.0557606 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13696e6i | 0.158100i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.68294e6i | 0.229842i | 0.993375 | + | 0.114921i | \(0.0366615\pi\) | ||||
−0.993375 | + | 0.114921i | \(0.963338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.94932e6 | −0.263848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −145833. | −0.0195636 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.31501e7i | 1.74848i | 0.485498 | + | 0.874238i | \(0.338638\pi\) | ||||
−0.485498 | + | 0.874238i | \(0.661362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.45240e6i | 0.320357i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.91087e6 | −0.894854 | −0.447427 | − | 0.894320i | \(-0.647660\pi\) | ||||
−0.447427 | + | 0.894320i | \(0.647660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.49642e6 | 0.192072 | 0.0960361 | − | 0.995378i | \(-0.469384\pi\) | ||||
0.0960361 | + | 0.995378i | \(0.469384\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.73787e6i | − 1.23902i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.81857e6i | 0.352444i | 0.984350 | + | 0.176222i | \(0.0563876\pi\) | ||||
−0.984350 | + | 0.176222i | \(0.943612\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.33690e7 | 1.65730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.09939e6 | 0.135117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 247395.i | − 0.0301454i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.61995e6i | 1.15233i | 0.817333 | + | 0.576166i | \(0.195452\pi\) | ||||
−0.817333 | + | 0.576166i | \(0.804548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.19478e6 | 0.260677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.08181e7 | −1.27404 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.39724e6i | 0.863839i | 0.901912 | + | 0.431920i | \(0.142164\pi\) | ||||
−0.901912 | + | 0.431920i | \(0.857836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8.16975e6i | − 0.938152i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.14938e7 | 1.30887 | 0.654434 | − | 0.756119i | \(-0.272907\pi\) | ||||
0.654434 | + | 0.756119i | \(0.272907\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.58526e6 | −0.856612 | −0.428306 | − | 0.903634i | \(-0.640889\pi\) | ||||
−0.428306 | + | 0.903634i | \(0.640889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.77908e6i | 0.535243i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.36915e6i | 0.260988i | 0.991449 | + | 0.130494i | \(0.0416563\pi\) | ||||
−0.991449 | + | 0.130494i | \(0.958344\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 939332. | 0.102630 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.27314e7 | 1.37966 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.05992e7i | − 1.13926i | −0.821902 | − | 0.569629i | \(-0.807087\pi\) | ||||
0.821902 | − | 0.569629i | \(-0.192913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.22009e7i | 1.29026i | 0.764072 | + | 0.645131i | \(0.223197\pi\) | ||||
−0.764072 | + | 0.645131i | \(0.776803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.46019e7 | 1.53173 | 0.765865 | − | 0.643001i | \(-0.222311\pi\) | ||||
0.765865 | + | 0.643001i | \(0.222311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.87135e6 | −0.298784 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.65414e6i | − 0.273970i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 47022.8i | − 0.00477683i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.85247e6 | 0.589811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.40997e6 | −0.940838 | −0.470419 | − | 0.882443i | \(-0.655897\pi\) | ||||
−0.470419 | + | 0.882443i | \(0.655897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.55507e7i | 1.54256i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.63876e6i | 0.941180i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.05079e7 | 1.01804 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.44166e6 | −0.811489 | −0.405744 | − | 0.913987i | \(-0.632988\pi\) | ||||
−0.405744 | + | 0.913987i | \(0.632988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.03157e7i | 0.983942i | 0.870612 | + | 0.491971i | \(0.163723\pi\) | ||||
−0.870612 | + | 0.491971i | \(0.836277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3.52118e6i | − 0.330695i | −0.986235 | − | 0.165348i | \(-0.947125\pi\) | ||||
0.986235 | − | 0.165348i | \(-0.0528746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 110459. | 0.0102941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.18805e6 | 0.479791 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.20492e6i | − 0.202354i | −0.994868 | − | 0.101177i | \(-0.967739\pi\) | ||||
0.994868 | − | 0.101177i | \(-0.0322608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 1.09611e7i | − 0.990694i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.26903e7 | 1.13830 | 0.569152 | − | 0.822232i | \(-0.307271\pi\) | ||||
0.569152 | + | 0.822232i | \(0.307271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.20351e6 | 0.196160 | 0.0980801 | − | 0.995179i | \(-0.468730\pi\) | ||||
0.0980801 | + | 0.995179i | \(0.468730\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.23184e7i | 1.08835i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16940e6i | 0.275843i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.08013e7 | 1.79690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55298.8 | 0.00474143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.02905e6i | 0.172685i | 0.996266 | + | 0.0863424i | \(0.0275179\pi\) | ||||
−0.996266 | + | 0.0863424i | \(0.972482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.33080e7i | 1.11594i | 0.829860 | + | 0.557971i | \(0.188420\pi\) | ||||
−0.829860 | + | 0.557971i | \(0.811580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.20903e6 | 0.516832 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.98989e6 | 0.660196 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.95063e6i | − 0.488102i | −0.969762 | − | 0.244051i | \(-0.921524\pi\) | ||||
0.969762 | − | 0.244051i | \(-0.0784765\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 344204.i | 0.0278243i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.08973e7 | −1.67703 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.95555e7 | 1.55802 | 0.779010 | − | 0.627011i | \(-0.215722\pi\) | ||||
0.779010 | + | 0.627011i | \(0.215722\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 48319.0i | − 0.00382195i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.80646e7i | 1.40846i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.93537e7 | −1.49820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.70838e7 | −1.31308 | −0.656538 | − | 0.754293i | \(-0.727980\pi\) | ||||
−0.656538 | + | 0.754293i | \(0.727980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.88708e6i | 0.144013i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.61323e6i | 0.271861i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.47096e7 | −1.84608 | −0.923038 | − | 0.384710i | \(-0.874301\pi\) | ||||
−0.923038 | + | 0.384710i | \(0.874301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.02430e6 | 0.446923 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.75050e7i | 1.28955i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.78074e7i | − 2.02005i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.02894e7 | −1.46369 | −0.731843 | − | 0.681474i | \(-0.761339\pi\) | ||||
−0.731843 | + | 0.681474i | \(0.761339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.30131e6 | −0.379791 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.08882e6i | 0.575492i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.59786e7i | − 1.82297i | −0.411331 | − | 0.911486i | \(-0.634936\pi\) | ||||
0.411331 | − | 0.911486i | \(-0.365064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.13072e6 | 0.496952 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.01946e6 | 0.208995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.75705e7i | 1.20788i | 0.797030 | + | 0.603940i | \(0.206403\pi\) | ||||
−0.797030 | + | 0.603940i | \(0.793597\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 187516.i | 0.0127165i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.26188e7 | 1.52356 | 0.761779 | − | 0.647837i | \(-0.224326\pi\) | ||||
0.761779 | + | 0.647837i | \(0.224326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.97197e6 | −0.265742 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.75610e7i | 1.16701i | 0.812108 | + | 0.583507i | \(0.198320\pi\) | ||||
−0.812108 | + | 0.583507i | \(0.801680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.82524e6i | − 0.381955i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.78892e6 | 0.507309 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.36472e6 | 0.0882967 | 0.0441483 | − | 0.999025i | \(-0.485943\pi\) | ||||
0.0441483 | + | 0.999025i | \(0.485943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.67080e7i | 1.07383i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.89968e6i | 0.183912i | 0.995763 | + | 0.0919560i | \(0.0293119\pi\) | ||||
−0.995763 | + | 0.0919560i | \(0.970688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 375042. | 0.0236306 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.33991e6 | −0.584630 | −0.292315 | − | 0.956322i | \(-0.594426\pi\) | ||||
−0.292315 | + | 0.956322i | \(0.594426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 868303.i | − 0.0539958i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 9.33038e6i | − 0.572679i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.86030e7 | 1.13440 | 0.567200 | − | 0.823580i | \(-0.308026\pi\) | ||||
0.567200 | + | 0.823580i | \(0.308026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.18506e6 | 0.192967 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.71314e7i | 1.63314i | 0.577247 | + | 0.816570i | \(0.304127\pi\) | ||||
−0.577247 | + | 0.816570i | \(0.695873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.46071e6i | 0.265065i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.82478e6 | −0.343903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 412295. | 0.0241869 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.49514e6i | 0.0871521i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.16693e6i | 0.527579i | 0.964580 | + | 0.263789i | \(0.0849723\pi\) | ||||
−0.964580 | + | 0.263789i | \(0.915028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 580674. | 0.0332078 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.27713e6 | −0.129404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.67104e6i | − 0.263773i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.90109e7i | 1.06012i | 0.847959 | + | 0.530062i | \(0.177831\pi\) | ||||
−0.847959 | + | 0.530062i | \(0.822169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.97207e7 | −1.09284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.40633e7 | −0.774472 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 430077.i | − 0.0235373i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.48368e7i | − 0.801969i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.04747e6 | 0.217426 | 0.108713 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108713 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 984765. | 0.0525752 | 0.0262876 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262876 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.81296e7i | − 1.49258i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 973603.i | 0.0510301i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.08147e6 | −0.212621 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.53595e6 | 0.183083 | 0.0915415 | − | 0.995801i | \(-0.470821\pi\) | ||||
0.0915415 | + | 0.995801i | \(0.470821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.27174e6i | 0.477157i | 0.971123 | + | 0.238579i | \(0.0766815\pi\) | ||||
−0.971123 | + | 0.238579i | \(0.923319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.88822e6i | − 0.197691i | −0.995103 | − | 0.0988456i | \(-0.968485\pi\) | ||||
0.995103 | − | 0.0988456i | \(-0.0315150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.20046e7 | −1.11206 | −0.556028 | − | 0.831163i | \(-0.687675\pi\) | ||||
−0.556028 | + | 0.831163i | \(0.687675\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.64007e7 | −0.823874 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.49303e7i | − 0.745513i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.25785e6i | 0.407430i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −888779. | −0.0435902 | −0.0217951 | − | 0.999762i | \(-0.506938\pi\) | ||||
−0.0217951 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.88608e7 | −0.919539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.96286e6i | − 0.192061i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.67786e6i | 0.271942i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.42420e7 | 1.15425 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.50509e7 | −0.712424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.03265e7i | 0.956511i | 0.878221 | + | 0.478255i | \(0.158731\pi\) | ||||
−0.878221 | + | 0.478255i | \(0.841269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.96142e6i | − 0.0912258i | −0.998959 | − | 0.0456129i | \(-0.985476\pi\) | ||||
0.998959 | − | 0.0456129i | \(-0.0145241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.54216e7 | −0.713095 | −0.356548 | − | 0.934277i | \(-0.616046\pi\) | ||||
−0.356548 | + | 0.934277i | \(0.616046\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.37687e7 | −0.632972 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2.79115e7i | − 1.27572i | −0.770152 | − | 0.637860i | \(-0.779820\pi\) | ||||
0.770152 | − | 0.637860i | \(-0.220180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.03572e7i | 0.467945i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 236374. | 0.0106182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.58393e7 | 0.707440 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 3.28993e7i | − 1.46100i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.72191e7i | − 0.755980i | −0.925810 | − | 0.377990i | \(-0.876615\pi\) | ||||
0.925810 | − | 0.377990i | \(-0.123385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.93402e7 | 0.844282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.57166e7 | 1.55035 | 0.775177 | − | 0.631745i | \(-0.217661\pi\) | ||||
0.775177 | + | 0.631745i | \(0.217661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.78278e6i | 0.163271i | 0.996662 | + | 0.0816356i | \(0.0260144\pi\) | ||||
−0.996662 | + | 0.0816356i | \(0.973986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.45768e7i | 1.04886i | 0.851455 | + | 0.524428i | \(0.175721\pi\) | ||||
−0.851455 | + | 0.524428i | \(0.824279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.62855e6 | −0.238859 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 509857. | 0.0215156 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.35880e6i | − 0.266837i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.16794e7i | − 1.31461i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.11504e6 | 0.376149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.23695e7 | 1.32839 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.30142e6i | 0.0939238i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.47776e6i | 0.0596467i | 0.999555 | + | 0.0298234i | \(0.00949448\pi\) | ||||
−0.999555 | + | 0.0298234i | \(0.990506\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.91452e7 | 0.768510 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.62169e7 | −1.04661 | −0.523305 | − | 0.852146i | \(-0.675301\pi\) | ||||
−0.523305 | + | 0.852146i | \(0.675301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 228564.i | − 0.00907466i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.09491e6i | − 0.160813i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.10734e6 | −0.0432507 | −0.0216254 | − | 0.999766i | \(-0.506884\pi\) | ||||
−0.0216254 | + | 0.999766i | \(0.506884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.40724e7 | −0.546664 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.48262e7i | − 1.34556i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.80896e7i | 1.07361i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.36543e7 | −0.899229 | −0.449615 | − | 0.893223i | \(-0.648439\pi\) | ||||
−0.449615 | + | 0.893223i | \(0.648439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.81415e6 | 0.182031 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.60502e7i | 0.979732i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.28168e7i | 1.22109i | 0.791983 | + | 0.610544i | \(0.209049\pi\) | ||||
−0.791983 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.50338e7 | −2.40699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.66896e7 | 1.35073 | 0.675366 | − | 0.737483i | \(-0.263986\pi\) | ||||
0.675366 | + | 0.737483i | \(0.263986\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.64569e7i | − 1.70126i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 8.63334e6i | − 0.312827i | −0.987692 | − | 0.156413i | \(-0.950007\pi\) | ||||
0.987692 | − | 0.156413i | \(-0.0499932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.63282e7 | −1.30942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.32660e6 | 0.262695 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.76257e7i | − 0.628659i | −0.949314 | − | 0.314329i | \(-0.898220\pi\) | ||||
0.949314 | − | 0.314329i | \(-0.101780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 195288.i | − 0.00689281i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51000.3 | 0.00179071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.17144e7 | 0.758470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4.12706e7i | − 1.43408i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.87856e7i | 1.67774i | 0.544330 | + | 0.838871i | \(0.316784\pi\) | ||||
−0.544330 | + | 0.838871i | \(0.683216\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.15252e6 | 0.210496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.81830e7 | −1.29964 | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||||
−0.649818 | + | 0.760090i | \(0.725155\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.76297e6i | − 0.161286i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.64067e7i | − 1.22024i | −0.792309 | − | 0.610120i | \(-0.791121\pi\) | ||||
0.792309 | − | 0.610120i | \(-0.208879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −551799. | −0.0184003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.60081e6 | −0.152638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 4.61248e7i | − 1.52248i | −0.648472 | − | 0.761239i | \(-0.724592\pi\) | ||||
0.648472 | − | 0.761239i | \(-0.275408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.50310e7i | − 0.491129i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.76520e6 | −0.252442 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.77541e7 | 0.897725 | 0.448862 | − | 0.893601i | \(-0.351829\pi\) | ||||
0.448862 | + | 0.893601i | \(0.351829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 6.04499e7i | − 1.94546i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2.50394e7i | − 0.797784i | −0.916998 | − | 0.398892i | \(-0.869395\pi\) | ||||
0.916998 | − | 0.398892i | \(-0.130605\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.10015e6 | −0.225089 |
(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 | 800.6.c.g.449.4 | 4 | ||
4.3 | odd | 2 | 800.6.c.f.449.1 | 4 | |||
5.2 | odd | 4 | 160.6.a.e.1.2 | yes | 2 | ||
5.3 | odd | 4 | 800.6.a.g.1.1 | 2 | |||
5.4 | even | 2 | inner | 800.6.c.g.449.1 | 4 | ||
20.3 | even | 4 | 800.6.a.l.1.2 | 2 | |||
20.7 | even | 4 | 160.6.a.a.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 800.6.c.f.449.4 | 4 | |||
40.27 | even | 4 | 320.6.a.v.1.2 | 2 | |||
40.37 | odd | 4 | 320.6.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.a.1.1 | ✓ | 2 | 20.7 | even | 4 | ||
160.6.a.e.1.2 | yes | 2 | 5.2 | odd | 4 | ||
320.6.a.r.1.1 | 2 | 40.37 | odd | 4 | |||
320.6.a.v.1.2 | 2 | 40.27 | even | 4 | |||
800.6.a.g.1.1 | 2 | 5.3 | odd | 4 | |||
800.6.a.l.1.2 | 2 | 20.3 | even | 4 | |||
800.6.c.f.449.1 | 4 | 4.3 | odd | 2 | |||
800.6.c.f.449.4 | 4 | 20.19 | odd | 2 | |||
800.6.c.g.449.1 | 4 | 5.4 | even | 2 | inner | ||
800.6.c.g.449.4 | 4 | 1.1 | even | 1 | trivial |