Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.a (trivial) |
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: | yes |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{70}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 70 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.36660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −20.7332 | −1.33004 | −0.665018 | − | 0.746828i | \(-0.731576\pi\) | ||||
−0.665018 | + | 0.746828i | \(0.731576\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.2668 | 0.272033 | 0.136016 | − | 0.990707i | \(-0.456570\pi\) | ||||
0.136016 | + | 0.990707i | \(0.456570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 186.866 | 0.768994 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.33201 | 0.0182701 | 0.00913505 | − | 0.999958i | \(-0.497092\pi\) | ||||
0.00913505 | + | 0.999958i | \(0.497092\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −619.328 | −1.01639 | −0.508197 | − | 0.861241i | \(-0.669688\pi\) | ||||
−0.508197 | + | 0.861241i | \(0.669688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 518.330 | 0.594810 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 959.328 | 0.805091 | 0.402545 | − | 0.915400i | \(-0.368126\pi\) | ||||
0.402545 | + | 0.915400i | \(0.368126\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 2467.12 | 0.972458 | 0.486229 | − | 0.873831i | \(-0.338372\pi\) | ||||
0.486229 | + | 0.873831i | \(0.338372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1163.85 | 0.307246 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | −152.016 | −0.0242999 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −881.670 | −0.121657 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6100.59 | 0.732601 | 0.366301 | − | 0.930497i | \(-0.380624\pi\) | ||||
0.366301 | + | 0.930497i | \(0.380624\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −3147.48 | −0.259592 | −0.129796 | − | 0.991541i | \(-0.541432\pi\) | ||||
−0.129796 | + | 0.991541i | \(0.541432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4671.64 | −0.343905 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20556.8 | 1.35741 | 0.678705 | − | 0.734411i | \(-0.262541\pi\) | ||||
0.678705 | + | 0.734411i | \(0.262541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15563.3 | −0.925998 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19889.9 | −1.07080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −33741.9 | −1.64998 | −0.824991 | − | 0.565146i | \(-0.808820\pi\) | ||||
−0.824991 | + | 0.565146i | \(0.808820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −183.300 | −0.00817064 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6413.36 | −0.261456 | ||||||||
\(58\) | 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 | \(-0.458580\pi\) | ||||
0.129759 | + | 0.991546i | \(0.458580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6590.15 | 0.209192 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15483.2 | 0.454545 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25574.9 | −0.696029 | −0.348015 | − | 0.937489i | \(-0.613144\pi\) | ||||
−0.348015 | + | 0.937489i | \(0.613144\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 58657.5 | 1.28830 | 0.644149 | − | 0.764900i | \(-0.277212\pi\) | ||||
0.644149 | + | 0.764900i | \(0.277212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12958.3 | −0.266007 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 258.576 | 0.00497006 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32238.7 | 0.581179 | 0.290589 | − | 0.956848i | \(-0.406149\pi\) | ||||
0.290589 | + | 0.956848i | \(0.406149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69538.6 | −1.17764 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31173.4 | −0.496694 | −0.248347 | − | 0.968671i | \(-0.579887\pi\) | ||||
−0.248347 | + | 0.968671i | \(0.579887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23983.2 | −0.360048 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −26635.0 | −0.377272 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −75258.9 | −1.00712 | −0.503562 | − | 0.863959i | \(-0.667977\pi\) | ||||
−0.503562 | + | 0.863959i | \(0.667977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21841.7 | −0.276492 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −147109. | −1.76372 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7733.20 | −0.0879124 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −176059. | −1.89989 | −0.949944 | − | 0.312419i | \(-0.898861\pi\) | ||||
−0.949944 | + | 0.312419i | \(0.898861\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1370.10 | 0.0140496 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 102454. | 0.999370 | 0.499685 | − | 0.866207i | \(-0.333449\pi\) | ||||
0.499685 | + | 0.866207i | \(0.333449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −150320. | −1.39612 | −0.698062 | − | 0.716038i | \(-0.745954\pi\) | ||||
−0.698062 | + | 0.716038i | \(0.745954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 18279.8 | 0.161808 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 220857. | 1.86488 | 0.932441 | − | 0.361321i | \(-0.117674\pi\) | ||||
0.932441 | + | 0.361321i | \(0.117674\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | −64568.7 | −0.475692 | −0.237846 | − | 0.971303i | \(-0.576441\pi\) | ||||
−0.237846 | + | 0.971303i | \(0.576441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −61678.0 | −0.434896 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −115731. | −0.781602 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 33832.4 | 0.219011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160997. | −0.999666 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 390415. | 2.32682 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 159599. | 0.878054 | 0.439027 | − | 0.898474i | \(-0.355323\pi\) | ||||
0.439027 | + | 0.898474i | \(0.355323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 65257.3 | 0.345267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −116112. | −0.591153 | −0.295577 | − | 0.955319i | \(-0.595512\pi\) | ||||
−0.295577 | + | 0.955319i | \(0.595512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10909.0 | 0.0534757 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −29096.1 | −0.137405 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1446.13 | −0.00658272 | −0.00329136 | − | 0.999995i | \(-0.501048\pi\) | ||||
−0.00329136 | + | 0.999995i | \(0.501048\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −4540.92 | −0.0185696 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32116.4 | −0.126855 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 322676. | 1.23161 | ||||||||
\(148\) | 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. | 0.619110 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −177383. | −0.593038 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −210478. | −0.681487 | −0.340743 | − | 0.940156i | \(-0.610679\pi\) | ||||
−0.340743 | + | 0.940156i | \(0.610679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 699577. | 2.19454 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87007.4 | 0.264540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 136230. | 0.401610 | 0.200805 | − | 0.979631i | \(-0.435644\pi\) | ||||
0.200805 | + | 0.979631i | \(0.435644\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3800.40 | 0.0108672 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 246713. | 0.684542 | 0.342271 | − | 0.939601i | \(-0.388804\pi\) | ||||
0.342271 | + | 0.939601i | \(0.388804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12274.2 | 0.0330580 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57802.8 | 0.151167 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 652180. | 1.65673 | 0.828366 | − | 0.560187i | \(-0.189271\pi\) | ||||
0.828366 | + | 0.560187i | \(0.189271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22041.7 | 0.0544065 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 312353. | 0.749397 | ||||||||
\(178\) | 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 | \(-0.499648\pi\) | ||||
0.00110495 | + | 0.999999i | \(0.499648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −156372. | −0.345169 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −152515. | −0.327629 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7033.80 | 0.0147091 | ||||||||
\(188\) | 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. | −1.24606 | −0.623030 | − | 0.782198i | \(-0.714099\pi\) | ||||
−0.623030 | + | 0.782198i | \(0.714099\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −321016. | −0.604562 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 521778. | 0.957899 | 0.478950 | − | 0.877842i | \(-0.341018\pi\) | ||||
0.478950 | + | 0.877842i | \(0.341018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 394042. | 0.705358 | 0.352679 | − | 0.935744i | \(-0.385271\pi\) | ||||
0.352679 | + | 0.935744i | \(0.385271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 530250. | 0.925744 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 45305.7 | 0.0771637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 470761. | 0.782376 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 461020. | 0.747814 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2267.99 | 0.00359150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −750041. | −1.15979 | −0.579894 | − | 0.814692i | \(-0.696906\pi\) | ||||
−0.579894 | + | 0.814692i | \(0.696906\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.16587e6 | 1.76077 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 78686.9 | 0.116093 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 250229. | 0.360735 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.21616e6 | −1.71348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −594139. | −0.818290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00328e6 | −1.35102 | −0.675509 | − | 0.737351i | \(-0.736076\pi\) | ||||
−0.675509 | + | 0.737351i | \(0.736076\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 116791. | 0.153799 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −385367. | −0.496375 | −0.248188 | − | 0.968712i | \(-0.579835\pi\) | ||||
−0.248188 | + | 0.968712i | \(0.579835\pi\) | |||||||
\(228\) | 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. | 1.12644 | 0.563219 | − | 0.826307i | \(-0.309563\pi\) | ||||
0.563219 | + | 0.826307i | \(0.309563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −513920. | −0.607052 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −668411. | −0.772988 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.34120e6 | 1.51880 | 0.759398 | − | 0.650626i | \(-0.225493\pi\) | ||||
0.759398 | + | 0.650626i | \(0.225493\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 390139. | 0.432690 | 0.216345 | − | 0.976317i | \(-0.430586\pi\) | ||||
0.216345 | + | 0.976317i | \(0.430586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.15894e6 | 1.25906 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 389081. | 0.414119 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −191576. | −0.199801 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 646325. | 0.660621 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −805856. | −0.807371 | −0.403686 | − | 0.914898i | \(-0.632271\pi\) | ||||
−0.403686 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18088.9 | 0.0177669 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 497249. | 0.478876 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 153621. | 0.145084 | 0.0725419 | − | 0.997365i | \(-0.476889\pi\) | ||||
0.0725419 | + | 0.997365i | \(0.476889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 215148. | 0.199291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 240058. | 0.218130 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28007.0 | −0.0249676 | −0.0124838 | − | 0.999922i | \(-0.503974\pi\) | ||||
−0.0124838 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 843546. | 0.737895 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.56036e6 | 1.33951 | ||||||||
\(268\) | 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. | 0.367745 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4582.50 | 0.00365402 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 791037. | 0.619437 | 0.309719 | − | 0.950828i | \(-0.399765\pi\) | ||||
0.309719 | + | 0.950828i | \(0.399765\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 1.16924e6 | 0.867834 | 0.433917 | − | 0.900953i | \(-0.357131\pi\) | ||||
0.433917 | + | 0.900953i | \(0.357131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 160334. | 0.116927 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −664089. | −0.475906 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −499547. | −0.351829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.65026e6 | 2.52692 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 932811. | 0.634782 | 0.317391 | − | 0.948295i | \(-0.397193\pi\) | ||||
0.317391 | + | 0.948295i | \(0.397193\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 376633. | 0.251979 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8533.32 | 0.00561341 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.52796e6 | −0.988401 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −111001. | −0.0706175 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.12420e6 | −1.32920 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −188553. | −0.116060 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 678740. | 0.411015 | 0.205507 | − | 0.978656i | \(-0.434116\pi\) | ||||
0.205507 | + | 0.978656i | \(0.434116\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 3.13670e6 | 1.80972 | 0.904861 | − | 0.425708i | \(-0.139975\pi\) | ||||
0.904861 | + | 0.425708i | \(0.139975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −164754. | −0.0935533 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −353375. | −0.197510 | −0.0987548 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987548 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9419.10 | 0.00518242 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.57907e6 | −2.48036 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 296747. | 0.158263 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −387080. | −0.203279 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −510471. | −0.263999 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 724973. | 0.369260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.91561e6 | 1.46271 | 0.731356 | − | 0.681996i | \(-0.238888\pi\) | ||||
0.731356 | + | 0.681996i | \(0.238888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.13999e6 | 0.563366 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 639373. | 0.311274 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.11496e6 | −1.49409 | −0.747046 | − | 0.664772i | \(-0.768529\pi\) | ||||
−0.747046 | + | 0.664772i | \(0.768529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.33871e6 | 0.632687 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52022.9 | 0.0242275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.14160e6 | −0.523934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.27878e6 | 0.578428 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.09755e6 | −1.82684 | −0.913419 | − | 0.407020i | \(-0.866568\pi\) | ||||
−0.913419 | + | 0.407020i | \(0.866568\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 3.56682e6 | 1.52350 | 0.761752 | − | 0.647868i | \(-0.224339\pi\) | ||||
0.761752 | + | 0.647868i | \(0.224339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.40581e6 | 0.592045 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −701455. | −0.291292 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −648318. | −0.265492 | −0.132746 | − | 0.991150i | \(-0.542380\pi\) | ||||
−0.132746 | + | 0.991150i | \(0.542380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.38042e6 | −0.961357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.33799e6 | 1.32959 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.46644e6 | −0.576145 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.84494e6 | −1.49013 | −0.745065 | − | 0.666992i | \(-0.767581\pi\) | ||||
−0.745065 | + | 0.666992i | \(0.767581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.51876e6 | −1.34531 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.18997e6 | −0.448849 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.40550e6 | −0.895228 | −0.447614 | − | 0.894227i | \(-0.647726\pi\) | ||||
−0.447614 | + | 0.894227i | \(0.647726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 323956. | 0.118962 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −795623. | −0.288306 | ||||||||
\(378\) | 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 | ||||||||
\(383\) | −1.61371e6 | −0.562121 | −0.281060 | − | 0.959690i | \(-0.590686\pi\) | ||||
−0.281060 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6464.41 | −0.00222268 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −588155. | −0.199625 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 2.40738e6 | 0.786255 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −805967. | −0.259911 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.61674e6 | −1.15170 | −0.575852 | − | 0.817554i | \(-0.695329\pi\) | ||||
−0.575852 | + | 0.817554i | \(0.695329\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −4.39433e6 | −1.34781 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.73846e6 | 0.526658 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44729.6 | 0.0133847 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.86360e6 | 0.846456 | 0.423228 | − | 0.906023i | \(-0.360897\pi\) | ||||
0.423228 | + | 0.906023i | \(0.360897\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29982.9 | 0.00875525 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −531306. | −0.153274 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 779336. | 0.222129 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.80013e6 | −0.788566 | ||||||||
\(418\) | 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 | \(-0.603332\pi\) | ||||
−0.318955 | + | 0.947770i | \(0.603332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.84136e6 | 1.04384 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 599580. | 0.161018 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 265986. | 0.0705975 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −1.01025e6 | −0.258946 | −0.129473 | − | 0.991583i | \(-0.541329\pi\) | ||||
−0.129473 | + | 0.991583i | \(0.541329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 665876. | 0.168721 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 763149. | 0.191164 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.14635e6 | −1.27450 | −0.637248 | − | 0.770659i | \(-0.719927\pi\) | ||||
−0.637248 | + | 0.770659i | \(0.719927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.90824e6 | −0.712087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25603e6 | −1.27247 | −0.636236 | − | 0.771494i | \(-0.719510\pi\) | ||||
−0.636236 | + | 0.771494i | \(0.719510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.88147e6 | 0.450399 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 333759. | 0.0790067 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.10261e6 | −0.960384 | −0.480192 | − | 0.877163i | \(-0.659433\pi\) | ||||
−0.480192 | + | 0.877163i | \(0.659433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −138065. | −0.0319626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.68972e6 | 2.21853 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 546043. | 0.123651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.01053e6 | −0.898278 | −0.449139 | − | 0.893462i | \(-0.648269\pi\) | ||||
−0.449139 | + | 0.893462i | \(0.648269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11651e6 | 0.247361 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.83280e6 | −0.839971 | −0.419986 | − | 0.907531i | \(-0.637965\pi\) | ||||
−0.419986 | + | 0.907531i | \(0.637965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.14398e6 | 0.248009 | 0.124004 | − | 0.992282i | \(-0.460426\pi\) | ||||
0.124004 | + | 0.992282i | \(0.460426\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.67772e6 | 0.788762 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.12577e6 | −1.51196 | −0.755979 | − | 0.654596i | \(-0.772839\pi\) | ||||
−0.755979 | + | 0.654596i | \(0.772839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −901946. | −0.189343 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.36388e6 | 0.906401 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23077.3 | −0.00474277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 193330. | 0.0393156 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.30519e6 | −1.26883 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.45039e6 | 1.28454 | 0.642269 | − | 0.766479i | \(-0.277993\pi\) | ||||
0.642269 | + | 0.766479i | \(0.277993\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.77827e6 | −0.744612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.80394e6 | −0.351848 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.40147e6 | 0.849656 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.46947e6 | −0.280762 | −0.140381 | − | 0.990098i | \(-0.544833\pi\) | ||||
−0.140381 | + | 0.990098i | \(0.544833\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.82449e6 | −0.534155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.19488e6 | 0.972460 | 0.486230 | − | 0.873831i | \(-0.338372\pi\) | ||||
0.486230 | + | 0.873831i | \(0.338372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.23241e6 | 0.228369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34252.5 | −0.00628317 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.98313e6 | −0.360131 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 8.92098e6 | 1.57215 | 0.786073 | − | 0.618134i | \(-0.212111\pi\) | ||||
0.786073 | + | 0.618134i | \(0.212111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.56135e6 | −0.446932 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −254483. | −0.0439683 | ||||||||
\(508\) | 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. | 0.0603978 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.75800e6 | 0.624365 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 150723. | 0.0248000 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 1.01015e7 | 1.61485 | 0.807424 | − | 0.589971i | \(-0.200861\pi\) | ||||
0.807424 | + | 0.589971i | \(0.200861\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −456996. | −0.0723626 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.80674e6 | 1.06761 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −349660. | −0.0543258 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.81519e6 | −0.433283 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.16622e7 | 1.77813 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.52142e6 | −0.834001 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.63075e7 | 2.44035 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −114110. | −0.0169181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.23616e7 | −1.81585 | −0.907925 | − | 0.419132i | \(-0.862334\pi\) | ||||
−0.907925 | + | 0.419132i | \(0.862334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20194.7 | −0.00293926 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −615524. | −0.0887675 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72735e6 | 0.532637 | 0.266319 | − | 0.963885i | \(-0.414193\pi\) | ||||
0.266319 | + | 0.963885i | \(0.414193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.40936e6 | 0.199568 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 397380. | 0.0557606 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13696e6 | 0.158100 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.16212e6 | 0.435759 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.68294e6 | 0.229842 | 0.114921 | − | 0.993375i | \(-0.463338\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.94932e6 | 0.263848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −145833. | −0.0195636 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.31501e7 | −1.74848 | −0.874238 | − | 0.485498i | \(-0.838638\pi\) | ||||
−0.874238 | + | 0.485498i | \(0.838638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.61422e6 | 0.212736 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.45240e6 | −0.320357 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.91087e6 | 0.894854 | 0.447427 | − | 0.894320i | \(-0.352340\pi\) | ||||
0.447427 | + | 0.894320i | \(0.352340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49642e6 | −0.192072 | −0.0960361 | − | 0.995378i | \(-0.530616\pi\) | ||||
−0.0960361 | + | 0.995378i | \(0.530616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.73787e6 | 1.23902 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.54195e6 | 0.194492 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.81857e6 | −0.352444 | −0.176222 | − | 0.984350i | \(-0.556388\pi\) | ||||
−0.176222 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.33690e7 | 1.65730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.09939e6 | −0.135117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −247395. | −0.0301454 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.89328e6 | 0.349543 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.61995e6 | 1.15233 | 0.576166 | − | 0.817333i | \(-0.304548\pi\) | ||||
0.576166 | + | 0.817333i | \(0.304548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.19478e6 | 0.260677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.08181e7 | −1.27404 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.39724e6 | 0.863839 | 0.431920 | − | 0.901912i | \(-0.357836\pi\) | ||||
0.431920 | + | 0.901912i | \(0.357836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −845811. | −0.0979447 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.16975e6 | −0.938152 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.14938e7 | −1.30887 | −0.654434 | − | 0.756119i | \(-0.727093\pi\) | ||||
−0.654434 | + | 0.756119i | \(0.727093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.58526e6 | −0.856612 | −0.428306 | − | 0.903634i | \(-0.640889\pi\) | ||||
−0.428306 | + | 0.903634i | \(0.640889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.77908e6 | −0.535243 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.02493e6 | 0.447064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.36915e6 | −0.260988 | −0.130494 | − | 0.991449i | \(-0.541656\pi\) | ||||
−0.130494 | + | 0.991449i | \(0.541656\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −939332. | −0.102630 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.27314e7 | −1.37966 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.05992e7 | 1.13926 | 0.569629 | − | 0.821902i | \(-0.307087\pi\) | ||||
0.569629 | + | 0.821902i | \(0.307087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.76037e6 | −1.04059 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.22009e7 | −1.29026 | −0.645131 | − | 0.764072i | \(-0.723197\pi\) | ||||
−0.645131 | + | 0.764072i | \(0.723197\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −2.65414e6 | −0.273970 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −47022.8 | −0.00477683 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 1.55507e7 | 1.54256 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.98998e6 | −0.392678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.63876e6 | 0.941180 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −1.03157e7 | −0.983942 | −0.491971 | − | 0.870612i | \(-0.663723\pi\) | ||||
−0.491971 | + | 0.870612i | \(0.663723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.63143e6 | −0.154408 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.52118e6 | 0.330695 | 0.165348 | − | 0.986235i | \(-0.447125\pi\) | ||||
0.165348 | + | 0.986235i | \(0.447125\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −110459. | −0.0102941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.18805e6 | −0.479791 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.20492e6 | 0.202354 | 0.101177 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101177 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.90281e6 | 0.264372 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.09611e7 | 0.990694 | ||||||||
\(658\) | 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 | \(-0.531270\pi\) | ||||
−0.0980801 | + | 0.995179i | \(0.531270\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.23184e7 | 1.08835 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −272725. | −0.0239150 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16940e6 | 0.275843 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.08013e7 | 1.79690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55298.8 | 0.00474143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.02905e6 | 0.172685 | 0.0863424 | − | 0.996266i | \(-0.472482\pi\) | ||||
0.0863424 | + | 0.996266i | \(0.472482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 727404. | 0.0614492 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.33080e7 | 1.11594 | 0.557971 | − | 0.829860i | \(-0.311580\pi\) | ||||
0.557971 | + | 0.829860i | \(0.311580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.20903e6 | −0.516832 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.98989e6 | 0.660196 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.95063e6 | 0.488102 | 0.244051 | − | 0.969762i | \(-0.421524\pi\) | ||||
0.244051 | + | 0.969762i | \(0.421524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36153.2 | 0.00294388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −344204. | −0.0278243 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.08973e7 | 1.67703 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.95555e7 | −1.55802 | −0.779010 | − | 0.627011i | \(-0.784278\pi\) | ||||
−0.779010 | + | 0.627011i | \(0.784278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 48319.0 | 0.00382195 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.37639e6 | −0.265149 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.80646e7 | −1.40846 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.93537e7 | −1.49820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.70838e7 | 1.31308 | 0.656538 | − | 0.754293i | \(-0.272020\pi\) | ||||
0.656538 | + | 0.754293i | \(0.272020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.88708e6 | 0.144013 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.06552e7 | 0.807401 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.61323e6 | 0.271861 | ||||||||
\(708\) | 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 | ||||||||
\(713\) | 1.75050e7 | 1.28955 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 113523. | 0.00830459 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.78074e7 | −2.02005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.02894e7 | 1.46369 | 0.731843 | − | 0.681474i | \(-0.238661\pi\) | ||||
0.731843 | + | 0.681474i | \(0.238661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.30131e6 | −0.379791 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.08882e6 | −0.575492 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 802910. | 0.0567312 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.59786e7 | 1.82297 | 0.911486 | − | 0.411331i | \(-0.134936\pi\) | ||||
0.911486 | + | 0.411331i | \(0.134936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.13072e6 | −0.496952 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.01946e6 | −0.208995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.75705e7 | −1.20788 | −0.603940 | − | 0.797030i | \(-0.706403\pi\) | ||||
−0.603940 | + | 0.797030i | \(0.706403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.06690e6 | −0.550793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −187516. | −0.0127165 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 1.75610e7 | 1.16701 | 0.583507 | − | 0.812108i | \(-0.301680\pi\) | ||||
0.583507 | + | 0.812108i | \(0.301680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 402445. | 0.0265653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.82524e6 | −0.381955 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 1.67080e7 | 1.07383 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.16838e7 | 0.745963 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.89968e6 | 0.183912 | 0.0919560 | − | 0.995763i | \(-0.470688\pi\) | ||||
0.0919560 | + | 0.995763i | \(0.470688\pi\) | |||||||
\(758\) | 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. | 0.0539958 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.48164e6 | −0.276874 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.33038e6 | 0.572679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.86030e7 | −1.13440 | −0.567200 | − | 0.823580i | \(-0.691974\pi\) | ||||
−0.567200 | + | 0.823580i | \(0.691974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.18506e6 | −0.192967 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.71314e7 | −1.63314 | −0.816570 | − | 0.577247i | \(-0.804127\pi\) | ||||
−0.816570 | + | 0.577247i | \(0.804127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.43457e6 | 0.265215 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.46071e6 | −0.265065 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.82478e6 | −0.343903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −412295. | −0.0241869 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.49514e6 | 0.0871521 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.26195e6 | 0.304770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.16693e6 | 0.527579 | 0.263789 | − | 0.964580i | \(-0.415028\pi\) | ||||
0.263789 | + | 0.964580i | \(0.415028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 580674. | 0.0332078 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.27713e6 | −0.129404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.67104e6 | −0.263773 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.74894e7 | −0.981426 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.90109e7 | 1.06012 | 0.530062 | − | 0.847959i | \(-0.322169\pi\) | ||||
0.530062 | + | 0.847959i | \(0.322169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.97207e7 | 1.09284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.40633e7 | −0.774472 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 430077. | 0.0235373 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.17519e6 | −0.118306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.48368e7 | 0.801969 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.04747e6 | −0.217426 | −0.108713 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108713 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −984765. | −0.0525752 | −0.0262876 | − | 0.999654i | \(-0.508369\pi\) | ||||
−0.0262876 | + | 0.999654i | \(0.508369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.81296e7 | 1.49258 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.40575e6 | −0.179605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −973603. | −0.0510301 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.08147e6 | −0.212621 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.53595e6 | −0.183083 | −0.0915415 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915415 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.27174e6 | 0.477157 | 0.238579 | − | 0.971123i | \(-0.423319\pi\) | ||||
0.238579 | + | 0.971123i | \(0.423319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −95010.0 | −0.00485998 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.88822e6 | −0.197691 | −0.0988456 | − | 0.995103i | \(-0.531515\pi\) | ||||
−0.0988456 | + | 0.995103i | \(0.531515\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | −1.49303e7 | −0.745513 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.16781e6 | −0.306136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.25785e6 | 0.407430 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 888779. | 0.0435902 | 0.0217951 | − | 0.999762i | \(-0.493062\pi\) | ||||
0.0217951 | + | 0.999762i | \(0.493062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.88608e7 | −0.919539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.96286e6 | 0.192061 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −306855. | −0.0147840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.67786e6 | −0.271942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.42420e7 | −1.15425 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50509e7 | 0.712424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.03265e7 | −0.956511 | −0.478255 | − | 0.878221i | \(-0.658731\pi\) | ||||
−0.478255 | + | 0.878221i | \(0.658731\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.44507e6 | −0.0676041 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.96142e6 | 0.0912258 | 0.0456129 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456129 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −2.79115e7 | −1.27572 | −0.637860 | − | 0.770152i | \(-0.720180\pi\) | ||||
−0.637860 | + | 0.770152i | \(0.720180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63045e7 | −0.740913 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.03572e7 | 0.467945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 236374. | 0.0106182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.58393e7 | 0.707440 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.28993e7 | −1.46100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −551044. | −0.0243313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.72191e7 | −0.755980 | −0.377990 | − | 0.925810i | \(-0.623385\pi\) | ||||
−0.377990 | + | 0.925810i | \(0.623385\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −3.78278e6 | −0.163271 | −0.0816356 | − | 0.996662i | \(-0.526014\pi\) | ||||
−0.0816356 | + | 0.996662i | \(0.526014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.80882e6 | −0.335141 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.45768e7 | −1.04886 | −0.524428 | − | 0.851455i | \(-0.675721\pi\) | ||||
−0.524428 | + | 0.851455i | \(0.675721\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.62855e6 | 0.238859 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −509857. | −0.0215156 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.35880e6 | 0.266837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.96636e7 | 0.820549 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.16794e7 | 1.31461 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.11504e6 | 0.376149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.23695e7 | −1.32839 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.30142e6 | 0.0939238 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24350.7 | −0.000988301 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.47776e6 | 0.0596467 | 0.0298234 | − | 0.999555i | \(-0.490506\pi\) | ||||
0.0298234 | + | 0.999555i | \(0.490506\pi\) | |||||||
\(908\) | 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. | −0.00907466 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.90930e6 | 0.154364 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.09491e6 | −0.160813 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.10734e6 | 0.0432507 | 0.0216254 | − | 0.999766i | \(-0.493116\pi\) | ||||
0.0216254 | + | 0.999766i | \(0.493116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.40724e7 | −0.546664 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.48262e7 | 1.34556 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.81287e6 | 0.146520 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.80896e7 | −1.07361 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.36543e7 | 0.899229 | 0.449615 | − | 0.893223i | \(-0.351561\pi\) | ||||
0.449615 | + | 0.893223i | \(0.351561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.81415e6 | −0.182031 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.60502e7 | −0.979732 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −175845. | −0.00657811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.28168e7 | −1.22109 | −0.610544 | − | 0.791983i | \(-0.709049\pi\) | ||||
−0.610544 | + | 0.791983i | \(0.709049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.50338e7 | −2.40699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.66896e7 | −1.35073 | −0.675366 | − | 0.737483i | \(-0.736014\pi\) | ||||
−0.675366 | + | 0.737483i | \(0.736014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.64569e7 | −1.70126 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.02613e6 | −0.0373785 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.63334e6 | −0.312827 | −0.156413 | − | 0.987692i | \(-0.549993\pi\) | ||||
−0.156413 | + | 0.987692i | \(0.549993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.63282e7 | −1.30942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.32660e6 | 0.262695 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.76257e7 | −0.628659 | −0.314329 | − | 0.949314i | \(-0.601780\pi\) | ||||
−0.314329 | + | 0.949314i | \(0.601780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17419e7 | 0.416609 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −195288. | −0.00689281 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51000.3 | −0.00179071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.17144e7 | 0.758470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.12706e7 | 1.43408 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.61203e7 | 0.557255 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.87856e7 | −1.67774 | −0.838871 | − | 0.544330i | \(-0.816784\pi\) | ||||
−0.838871 | + | 0.544330i | \(0.816784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.15252e6 | −0.210496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.81830e7 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.76297e6 | 0.161286 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.02541e6 | 0.270368 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.64067e7 | 1.22024 | 0.610120 | − | 0.792309i | \(-0.291121\pi\) | ||||
0.610120 | + | 0.792309i | \(0.291121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −551799. | −0.0184003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.60081e6 | 0.152638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.61248e7 | −1.52248 | −0.761239 | − | 0.648472i | \(-0.775408\pi\) | ||||
−0.761239 | + | 0.648472i | \(0.775408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.30444e7 | −0.428386 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.50310e7 | −0.491129 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −6.04499e7 | −1.94546 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.85105e6 | −0.315446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50394e7 | −0.797784 | −0.398892 | − | 0.916998i | \(-0.630605\pi\) | ||||
−0.398892 | + | 0.916998i | \(0.630605\pi\) | |||||||
\(998\) | 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 | 320.6.a.r.1.1 | 2 | ||
4.3 | odd | 2 | 320.6.a.v.1.2 | 2 | |||
8.3 | odd | 2 | 160.6.a.a.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 160.6.a.e.1.2 | yes | 2 | ||
40.3 | even | 4 | 800.6.c.f.449.1 | 4 | |||
40.13 | odd | 4 | 800.6.c.g.449.4 | 4 | |||
40.19 | odd | 2 | 800.6.a.l.1.2 | 2 | |||
40.27 | even | 4 | 800.6.c.f.449.4 | 4 | |||
40.29 | even | 2 | 800.6.a.g.1.1 | 2 | |||
40.37 | odd | 4 | 800.6.c.g.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.a.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
160.6.a.e.1.2 | yes | 2 | 8.5 | even | 2 | ||
320.6.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
320.6.a.v.1.2 | 2 | 4.3 | odd | 2 | |||
800.6.a.g.1.1 | 2 | 40.29 | even | 2 | |||
800.6.a.l.1.2 | 2 | 40.19 | odd | 2 | |||
800.6.c.f.449.1 | 4 | 40.3 | even | 4 | |||
800.6.c.f.449.4 | 4 | 40.27 | even | 4 | |||
800.6.c.g.449.1 | 4 | 40.37 | odd | 4 | |||
800.6.c.g.449.4 | 4 | 40.13 | odd | 4 |