Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,4,Mod(1,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.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: | \(99.1232088096\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.0623 | 0.522499 | 0.261249 | − | 0.965271i | \(-0.415865\pi\) | ||||
0.261249 | + | 0.965271i | \(0.415865\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93774 | −0.0626756 | −0.0313378 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313378 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.49806 | −0.0927066 | −0.0463533 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463533 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.43580 | 0.0656347 | 0.0328173 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328173 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −49.3774 | −0.447648 | −0.223824 | − | 0.974630i | \(-0.571854\pi\) | ||||
−0.223824 | + | 0.974630i | \(0.571854\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −291.494 | −1.86652 | −0.933261 | − | 0.359200i | \(-0.883050\pi\) | ||||
−0.933261 | + | 0.359200i | \(0.883050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −244.307 | −1.41545 | −0.707724 | − | 0.706489i | \(-0.750278\pi\) | ||||
−0.707724 | + | 0.706489i | \(0.750278\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −57.1868 | −0.301665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −193.121 | −0.858077 | −0.429038 | − | 0.903286i | \(-0.641147\pi\) | ||||
−0.429038 | + | 0.903286i | \(0.641147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.81323 | 0.0361858 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 315.113 | 1.20030 | 0.600151 | − | 0.799887i | \(-0.295107\pi\) | ||||
0.600151 | + | 0.799887i | \(0.295107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 300.996 | 1.06748 | 0.533738 | − | 0.845650i | \(-0.320787\pi\) | ||||
0.533738 | + | 0.845650i | \(0.320787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −86.5058 | −0.268472 | −0.134236 | − | 0.990949i | \(-0.542858\pi\) | ||||
−0.134236 | + | 0.990949i | \(0.542858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.4942 | 0.0535242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 509.677 | 1.32093 | 0.660467 | − | 0.750855i | \(-0.270358\pi\) | ||||
0.660467 | + | 0.750855i | \(0.270358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 95.3113 | 0.233669 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.3074 | −0.0378942 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 83.3852 | 0.183997 | 0.0919985 | − | 0.995759i | \(-0.470674\pi\) | ||||
0.0919985 | + | 0.995759i | \(0.470674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.25291 | −0.0110257 | −0.00551283 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551283 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.6887 | −0.0280294 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −205.992 | −0.375611 | −0.187806 | − | 0.982206i | \(-0.560138\pi\) | ||||
−0.187806 | + | 0.982206i | \(0.560138\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 148.132 | 0.258450 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1004.31 | −1.67872 | −0.839362 | − | 0.543573i | \(-0.817071\pi\) | ||||
−0.839362 | + | 0.543573i | \(0.817071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1007.29 | −1.61499 | −0.807494 | − | 0.589876i | \(-0.799177\pi\) | ||||
−0.807494 | + | 0.589876i | \(0.799177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 133.436 | 0.197486 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 863.237 | 1.22939 | 0.614695 | − | 0.788765i | \(-0.289279\pi\) | ||||
0.614695 | + | 0.788765i | \(0.289279\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1334.72 | −1.76512 | −0.882560 | − | 0.470200i | \(-0.844182\pi\) | ||||
−0.882560 | + | 0.470200i | \(0.844182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32.4903 | −0.0414596 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 874.483 | 1.07764 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 326.249 | 0.388565 | 0.194283 | − | 0.980946i | \(-0.437762\pi\) | ||||
0.194283 | + | 0.980946i | \(0.437762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.5642 | −0.0236892 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 732.922 | 0.817210 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.1790 | 0.0293527 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1526.77 | 1.59815 | 0.799075 | − | 0.601232i | \(-0.205323\pi\) | ||||
0.799075 | + | 0.601232i | \(0.205323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 171.560 | 0.174166 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 96.8716 | 0.0954365 | 0.0477182 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477182 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1321.99 | −1.26466 | −0.632329 | − | 0.774700i | \(-0.717901\pi\) | ||||
−0.632329 | + | 0.774700i | \(0.717901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −105.000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1745.71 | −1.57724 | −0.788619 | − | 0.614883i | \(-0.789203\pi\) | ||||
−0.788619 | + | 0.614883i | \(0.789203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 476.856 | 0.419032 | 0.209516 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209516 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 579.362 | 0.495411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1641.65 | 1.36666 | 0.683332 | − | 0.730108i | \(-0.260530\pi\) | ||||
0.683332 | + | 0.730108i | \(0.260530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −246.887 | −0.200194 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −26.4397 | −0.0208919 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −45.4864 | −0.0350398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −967.630 | −0.726995 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −945.339 | −0.692994 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 844.016 | 0.589719 | 0.294859 | − | 0.955541i | \(-0.404727\pi\) | ||||
0.294859 | + | 0.955541i | \(0.404727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −902.988 | −0.616308 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2796.20 | 1.86493 | 0.932463 | − | 0.361265i | \(-0.117655\pi\) | ||||
0.932463 | + | 0.361265i | \(0.117655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 38.0506 | 0.0248076 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2057.13 | −1.28287 | −0.641433 | − | 0.767179i | \(-0.721660\pi\) | ||||
−0.641433 | + | 0.767179i | \(0.721660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1745.12 | 1.06489 | 0.532444 | − | 0.846465i | \(-0.321274\pi\) | ||||
0.532444 | + | 0.846465i | \(0.321274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 259.517 | 0.155002 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −56.0000 | −0.0327479 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1457.47 | −0.834734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1173.57 | −0.645254 | −0.322627 | − | 0.946526i | \(-0.604566\pi\) | ||||
−0.322627 | + | 0.946526i | \(0.604566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1540.07 | −0.829994 | −0.414997 | − | 0.909823i | \(-0.636217\pi\) | ||||
−0.414997 | + | 0.909823i | \(0.636217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −58.4826 | −0.0309022 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1221.54 | −0.633008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2544.53 | −1.29348 | −0.646738 | − | 0.762712i | \(-0.723867\pi\) | ||||
−0.646738 | + | 0.762712i | \(0.723867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1529.03 | −0.762642 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −345.642 | −0.169195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 594.708 | 0.285774 | 0.142887 | − | 0.989739i | \(-0.454361\pi\) | ||||
0.142887 | + | 0.989739i | \(0.454361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −285.934 | −0.134909 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −928.498 | −0.430236 | −0.215118 | − | 0.976588i | \(-0.569014\pi\) | ||||
−0.215118 | + | 0.976588i | \(0.569014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2188.37 | −0.996072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 48.9222 | 0.0218782 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −315.642 | −0.138716 | −0.0693578 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693578 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −250.156 | −0.106231 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1445.49 | 0.603581 | 0.301791 | − | 0.953374i | \(-0.402416\pi\) | ||||
0.301791 | + | 0.953374i | \(0.402416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1843.81 | −0.757180 | −0.378590 | − | 0.925564i | \(-0.623591\pi\) | ||||
−0.378590 | + | 0.925564i | \(0.623591\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7587 | 0.00636567 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −965.603 | −0.383744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −123.868 | −0.0484391 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 244.074 | 0.0924637 | 0.0462318 | − | 0.998931i | \(-0.485279\pi\) | ||||
0.0462318 | + | 0.998931i | \(0.485279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1733.03 | −0.646355 | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||||
−0.323178 | + | 0.946338i | \(0.604751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 44.0661 | 0.0161828 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 358.230 | 0.129557 | 0.0647787 | − | 0.997900i | \(-0.479366\pi\) | ||||
0.0647787 | + | 0.997900i | \(0.479366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3203.63 | 1.14120 | 0.570601 | − | 0.821227i | \(-0.306710\pi\) | ||||
0.570601 | + | 0.821227i | \(0.306710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 617.977 | 0.216859 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2040.46 | −0.705479 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1575.56 | 0.536791 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −444.397 | −0.149216 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 103.619 | 0.0342940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4943.16 | −1.61280 | −0.806401 | − | 0.591369i | \(-0.798588\pi\) | ||||
−0.806401 | + | 0.591369i | \(0.798588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3012.92 | 0.969211 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1504.98 | 0.477390 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1710.15 | −0.534989 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3021.86 | 0.932414 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.0896 | 0.00581044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3160.15 | −0.948965 | −0.474482 | − | 0.880265i | \(-0.657365\pi\) | ||||
−0.474482 | + | 0.880265i | \(0.657365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3651.11 | 1.06755 | 0.533773 | − | 0.845628i | \(-0.320774\pi\) | ||||
0.533773 | + | 0.845628i | \(0.320774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4083.70 | −1.17842 | −0.589210 | − | 0.807980i | \(-0.700561\pi\) | ||||
−0.589210 | + | 0.807980i | \(0.700561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −400.307 | −0.114019 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3682.51 | −1.03540 | −0.517702 | − | 0.855561i | \(-0.673212\pi\) | ||||
−0.517702 | + | 0.855561i | \(0.673212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −432.529 | −0.120064 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2589.71 | −0.709789 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2658.78 | −0.719591 | −0.359796 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359796 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4820.39 | −1.28842 | −0.644209 | − | 0.764850i | \(-0.722813\pi\) | ||||
−0.644209 | + | 0.764850i | \(0.722813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.9690 | −0.00411369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4004.17 | 1.01909 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1672.27 | −0.420530 | −0.210265 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210265 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −941.245 | −0.233896 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 97.4709 | 0.0239367 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3697.74 | −0.897506 | −0.448753 | − | 0.893656i | \(-0.648132\pi\) | ||||
−0.448753 | + | 0.893656i | \(0.648132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1351.84 | −0.324323 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2623.45 | −0.622174 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7319.00 | −1.71600 | −0.858002 | − | 0.513646i | \(-0.828294\pi\) | ||||
−0.858002 | + | 0.513646i | \(0.828294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2548.39 | 0.590740 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −978.747 | −0.224338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −815.097 | −0.184749 | −0.0923743 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923743 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5106.02 | 1.14453 | 0.572267 | − | 0.820068i | \(-0.306064\pi\) | ||||
0.572267 | + | 0.820068i | \(0.306064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 61.6926 | 0.0136769 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 476.556 | 0.104500 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1398.72 | 0.303398 | 0.151699 | − | 0.988427i | \(-0.451526\pi\) | ||||
0.151699 | + | 0.988427i | \(0.451526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2198.77 | −0.471816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7102.38 | −1.50780 | −0.753901 | − | 0.656988i | \(-0.771830\pi\) | ||||
−0.753901 | + | 0.656988i | \(0.771830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4465.18 | −0.937907 | −0.468953 | − | 0.883223i | \(-0.655369\pi\) | ||||
−0.468953 | + | 0.883223i | \(0.655369\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −81.5371 | −0.0169468 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2205.79 | 0.453671 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4870.78 | −0.991405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4580.32 | −0.922692 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7590.61 | 1.51348 | 0.756738 | − | 0.653718i | \(-0.226792\pi\) | ||||
0.756738 | + | 0.653718i | \(0.226792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 416.926 | 0.0822860 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −514.681 | −0.100555 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 145.058 | 0.0280566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2106.97 | 0.403468 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −290.615 | −0.0551003 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.2645 | −0.00493083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9480.12 | −1.76241 | −0.881203 | − | 0.472737i | \(-0.843266\pi\) | ||||
−0.881203 | + | 0.472737i | \(0.843266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3965.98 | 0.730151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7078.01 | −1.29054 | −0.645268 | − | 0.763956i | \(-0.723254\pi\) | ||||
−0.645268 | + | 0.763956i | \(0.723254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5593.84 | 1.01017 | 0.505084 | − | 0.863070i | \(-0.331461\pi\) | ||||
0.505084 | + | 0.863070i | \(0.331461\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 315.000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3567.81 | 0.632139 | 0.316070 | − | 0.948736i | \(-0.397637\pi\) | ||||
0.316070 | + | 0.948736i | \(0.397637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5556.54 | −0.975255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5237.14 | 0.910618 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.3222 | −0.00608477 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −73.4436 | −0.0125351 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1430.57 | −0.241928 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −605.541 | −0.101473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4389.67 | 0.728936 | 0.364468 | − | 0.931216i | \(-0.381251\pi\) | ||||
0.364468 | + | 0.931216i | \(0.381251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1738.09 | −0.286026 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1029.96 | −0.167978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2348.83 | 0.379671 | 0.189835 | − | 0.981816i | \(-0.439205\pi\) | ||||
0.189835 | + | 0.981816i | \(0.439205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4924.94 | −0.789044 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4657.05 | −0.739570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 740.661 | 0.115582 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −558.436 | −0.0863931 | −0.0431965 | − | 0.999067i | \(-0.513754\pi\) | ||||
−0.0431965 | + | 0.999067i | \(0.513754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3233.89 | 0.496006 | 0.248003 | − | 0.968759i | \(-0.420226\pi\) | ||||
0.248003 | + | 0.968759i | \(0.420226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 79.3190 | 0.0120619 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7516.35 | −1.13330 | −0.566650 | − | 0.823959i | \(-0.691761\pi\) | ||||
−0.566650 | + | 0.823959i | \(0.691761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5021.54 | −0.750748 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 136.459 | 0.0202302 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6577.76 | 0.967021 | 0.483511 | − | 0.875338i | \(-0.339361\pi\) | ||||
0.483511 | + | 0.875338i | \(0.339361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6829.45 | −0.995692 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2902.89 | 0.419731 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5036.44 | −0.722245 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8307.17 | −1.18155 | −0.590777 | − | 0.806835i | \(-0.701179\pi\) | ||||
−0.590777 | + | 0.806835i | \(0.701179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2836.02 | 0.400101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3567.74 | 0.499266 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4551.09 | −0.631760 | −0.315880 | − | 0.948799i | \(-0.602300\pi\) | ||||
−0.315880 | + | 0.948799i | \(0.602300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 856.335 | 0.116985 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1788.29 | 0.242370 | 0.121185 | − | 0.992630i | \(-0.461331\pi\) | ||||
0.121185 | + | 0.992630i | \(0.461331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2532.05 | −0.340474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1358.47 | 0.181240 | 0.0906199 | − | 0.995886i | \(-0.471115\pi\) | ||||
0.0906199 | + | 0.995886i | \(0.471115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 667.179 | 0.0883184 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2708.97 | 0.355825 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9722.54 | 1.26723 | 0.633615 | − | 0.773649i | \(-0.281570\pi\) | ||||
0.633615 | + | 0.773649i | \(0.281570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 320.858 | 0.0414999 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8388.61 | −1.07672 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4316.19 | 0.549800 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4788.04 | −0.605302 | −0.302651 | − | 0.953101i | \(-0.597872\pi\) | ||||
−0.302651 | + | 0.953101i | \(0.597872\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −114.152 | −0.0143227 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9681.41 | 1.20565 | 0.602826 | − | 0.797873i | \(-0.294041\pi\) | ||||
0.602826 | + | 0.797873i | \(0.294041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 717.712 | 0.0887141 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3681.32 | −0.448344 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11113.1 | 1.34353 | 0.671767 | − | 0.740763i | \(-0.265536\pi\) | ||||
0.671767 | + | 0.740763i | \(0.265536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6171.40 | 0.740663 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 583.696 | 0.0695443 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6673.62 | −0.789386 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5235.37 | −0.614814 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1230.09 | 0.143421 | 0.0717107 | − | 0.997425i | \(-0.477154\pi\) | ||||
0.0717107 | + | 0.997425i | \(0.477154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12356.5 | −1.43044 | −0.715222 | − | 0.698897i | \(-0.753674\pi\) | ||||
−0.715222 | + | 0.698897i | \(0.753674\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −778.552 | −0.0894906 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −162.452 | −0.0185413 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.7703 | −0.00416731 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 168.000 | 0.0189070 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7375.27 | 0.824256 | 0.412128 | − | 0.911126i | \(-0.364786\pi\) | ||||
0.412128 | + | 0.911126i | \(0.364786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −690.067 | −0.0765877 | −0.0382939 | − | 0.999267i | \(-0.512192\pi\) | ||||
−0.0382939 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4372.41 | 0.481934 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −268.406 | −0.0293812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8408.79 | −0.914191 | −0.457095 | − | 0.889418i | \(-0.651110\pi\) | ||||
−0.457095 | + | 0.889418i | \(0.651110\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6568.55 | −0.704473 | −0.352236 | − | 0.935911i | \(-0.614579\pi\) | ||||
−0.352236 | + | 0.935911i | \(0.614579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1631.25 | 0.173772 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3520.72 | 0.372537 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2954.55 | 0.310543 | 0.155271 | − | 0.987872i | \(-0.450375\pi\) | ||||
0.155271 | + | 0.987872i | \(0.450375\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6006.76 | 0.627156 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4620.21 | 0.479197 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −102.821 | −0.0105941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8144.84 | −0.833697 | −0.416849 | − | 0.908976i | \(-0.636865\pi\) | ||||
−0.416849 | + | 0.908976i | \(0.636865\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 175.448 | 0.0178414 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2495.26 | 0.252095 | 0.126048 | − | 0.992024i | \(-0.459771\pi\) | ||||
0.126048 | + | 0.992024i | \(0.459771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5755.66 | 0.577728 | 0.288864 | − | 0.957370i | \(-0.406722\pi\) | ||||
0.288864 | + | 0.957370i | \(0.406722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3664.61 | 0.365467 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4143.73 | 0.410598 | 0.205299 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205299 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1441.95 | −0.141968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7633.60 | 0.746789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5737.67 | 0.557755 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 135.895 | 0.0131269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4587.09 | 0.440312 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6765.96 | 0.645396 | 0.322698 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322698 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 567.339 | 0.0537805 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1036.93 | 0.0976848 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7633.87 | 0.714714 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6360.42 | −0.591824 | −0.295912 | − | 0.955215i | \(-0.595623\pi\) | ||||
−0.295912 | + | 0.955215i | \(0.595623\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1784.12 | −0.164992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7072.54 | 0.650060 | 0.325030 | − | 0.945704i | \(-0.394626\pi\) | ||||
0.325030 | + | 0.945704i | \(0.394626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1894.15 | 0.173039 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 857.802 | 0.0778895 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7030.15 | −0.634498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18473.9 | 1.65732 | 0.828661 | − | 0.559751i | \(-0.189103\pi\) | ||||
0.828661 | + | 0.559751i | \(0.189103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2785.49 | 0.248397 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11379.2 | −1.00869 | −0.504347 | − | 0.863501i | \(-0.668267\pi\) | ||||
−0.504347 | + | 0.863501i | \(0.668267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 484.358 | 0.0426805 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6565.11 | 0.575082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6064.48 | 0.528101 | 0.264051 | − | 0.964509i | \(-0.414941\pi\) | ||||
0.264051 | + | 0.964509i | \(0.414941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7051.02 | −0.610408 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −146.767 | −0.0126314 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6609.96 | −0.565572 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1649.00 | −0.140276 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 946.926 | 0.0800875 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2682.88 | 0.225603 | 0.112801 | − | 0.993618i | \(-0.464018\pi\) | ||||
0.112801 | + | 0.993618i | \(0.464018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4309.02 | 0.360268 | 0.180134 | − | 0.983642i | \(-0.442347\pi\) | ||||
0.180134 | + | 0.983642i | \(0.442347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1587.52 | 0.131221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9728.87 | −0.799611 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 750.467 | 0.0613323 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −925.720 | −0.0752296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8728.56 | −0.705362 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4336.47 | −0.348478 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 934.051 | 0.0746427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4081.47 | 0.324355 | 0.162178 | − | 0.986762i | \(-0.448148\pi\) | ||||
0.162178 | + | 0.986762i | \(0.448148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5531.44 | 0.437158 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2384.28 | 0.187397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8844.82 | −0.691366 | −0.345683 | − | 0.938351i | \(-0.612353\pi\) | ||||
−0.345683 | + | 0.938351i | \(0.612353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −47.2762 | −0.00367522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1584.51 | −0.122509 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6042.66 | 0.464666 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2896.81 | 0.221554 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11144.7 | −0.847787 | −0.423894 | − | 0.905712i | \(-0.639337\pi\) | ||||
−0.423894 | + | 0.905712i | \(0.639337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −884.249 | −0.0669047 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 371.603 | 0.0279663 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21857.5 | 1.63621 | 0.818104 | − | 0.575071i | \(-0.195025\pi\) | ||||
0.818104 | + | 0.575071i | \(0.195025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8208.23 | 0.611191 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23496.4 | 1.73115 | 0.865573 | − | 0.500783i | \(-0.166954\pi\) | ||||
0.865573 | + | 0.500783i | \(0.166954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11067.8 | −0.811164 | −0.405582 | − | 0.914059i | \(-0.632931\pi\) | ||||
−0.405582 | + | 0.914059i | \(0.632931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −732.222 | −0.0533839 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1234.44 | −0.0895296 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20482.9 | 1.47784 | 0.738922 | − | 0.673791i | \(-0.235335\pi\) | ||||
0.738922 | + | 0.673791i | \(0.235335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5199.10 | 0.373173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9343.07 | −0.667153 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9715.60 | 0.690187 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −132.198 | −0.00934313 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23444.3 | 1.64847 | 0.824235 | − | 0.566248i | \(-0.191606\pi\) | ||||
0.824235 | + | 0.566248i | \(0.191606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1328.01 | −0.0929025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1074.69 | −0.0748000 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4404.69 | 0.305024 | 0.152512 | − | 0.988302i | \(-0.451264\pi\) | ||||
0.152512 | + | 0.988302i | \(0.451264\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −227.432 | −0.0156703 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9610.89 | −0.658874 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3327.05 | −0.226945 | −0.113472 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113472 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14244.8 | −0.966818 | −0.483409 | − | 0.875395i | \(-0.660602\pi\) | ||||
−0.483409 | + | 0.875395i | \(0.660602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1853.93 | −0.125204 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4838.15 | −0.325122 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11446.5 | −0.765402 | −0.382701 | − | 0.923872i | \(-0.625006\pi\) | ||||
−0.382701 | + | 0.923872i | \(0.625006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6121.38 | 0.407308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 254.132 | 0.0168266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19436.4 | −1.28063 | −0.640316 | − | 0.768111i | \(-0.721197\pi\) | ||||
−0.640316 | + | 0.768111i | \(0.721197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4726.69 | −0.309917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20530.1 | −1.33956 | −0.669781 | − | 0.742558i | \(-0.733612\pi\) | ||||
−0.669781 | + | 0.742558i | \(0.733612\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5833.35 | −0.378776 | −0.189388 | − | 0.981902i | \(-0.560650\pi\) | ||||
−0.189388 | + | 0.981902i | \(0.560650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1333.19 | 0.0861499 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2283.74 | 0.146864 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −310.856 | −0.0197997 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1254.91 | 0.0795493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24776.6 | −1.56314 | −0.781568 | − | 0.623820i | \(-0.785580\pi\) | ||||
−0.781568 | + | 0.623820i | \(0.785580\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14829.5 | 0.931152 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4220.08 | 0.263730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −143.949 | −0.00895366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9038.77 | −0.559574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27219.4 | 1.67723 | 0.838613 | − | 0.544728i | \(-0.183367\pi\) | ||||
0.838613 | + | 0.544728i | \(0.183367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7091.79 | −0.434950 | −0.217475 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217475 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4514.94 | −0.275621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27773.0 | −1.68758 | −0.843792 | − | 0.536670i | \(-0.819682\pi\) | ||||
−0.843792 | + | 0.536670i | \(0.819682\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1589.51 | 0.0961382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5130.46 | 0.308876 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21380.4 | 1.28129 | 0.640643 | − | 0.767839i | \(-0.278668\pi\) | ||||
0.640643 | + | 0.767839i | \(0.278668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13981.0 | 0.834020 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9065.59 | −0.538329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17232.3 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26577.7 | 1.56392 | 0.781962 | − | 0.623326i | \(-0.214219\pi\) | ||||
0.781962 | + | 0.623326i | \(0.214219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −57.2689 | −0.00335466 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 190.253 | 0.0110943 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14393.2 | 0.835544 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9480.44 | 0.547885 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −100.132 | −0.00576090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31695.2 | −1.81540 | −0.907698 | − | 0.419624i | \(-0.862162\pi\) | ||||
−0.907698 | + | 0.419624i | \(0.862162\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20440.3 | 1.16039 | 0.580195 | − | 0.814477i | \(-0.302976\pi\) | ||||
0.580195 | + | 0.814477i | \(0.302976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10687.4 | 0.604044 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10953.3 | −0.616348 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22896.9 | 1.28276 | 0.641381 | − | 0.767223i | \(-0.278362\pi\) | ||||
0.641381 | + | 0.767223i | \(0.278362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10285.7 | −0.573715 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12251.1 | 0.680361 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1497.30 | −0.0827904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23764.0 | 1.30829 | 0.654143 | − | 0.756371i | \(-0.273029\pi\) | ||||
0.654143 | + | 0.756371i | \(0.273029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1200.92 | 0.0658287 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8725.62 | 0.476233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2047.62 | −0.111276 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11047.5 | 0.597791 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26259.5 | 1.41485 | 0.707423 | − | 0.706791i | \(-0.249858\pi\) | ||||
0.707423 | + | 0.706791i | \(0.249858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1049.77 | −0.0563196 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1297.59 | 0.0693191 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 678.101 | 0.0360716 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12783.0 | 0.677116 | 0.338558 | − | 0.940945i | \(-0.390061\pi\) | ||||
0.338558 | + | 0.940945i | \(0.390061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7769.14 | 0.409797 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12063.3 | 0.633623 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −280.000 | −0.0146453 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7976.35 | 0.415456 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27609.0 | 1.43205 | 0.716025 | − | 0.698075i | \(-0.245960\pi\) | ||||
0.716025 | + | 0.698075i | \(0.245960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9253.95 | −0.477996 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14461.2 | 0.743868 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7287.35 | −0.373304 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31306.2 | −1.59709 | −0.798544 | − | 0.601937i | \(-0.794396\pi\) | ||||
−0.798544 | + | 0.601937i | \(0.794396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1955.89 | −0.0989621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15765.8 | −0.794441 | −0.397220 | − | 0.917723i | \(-0.630025\pi\) | ||||
−0.397220 | + | 0.917723i | \(0.630025\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −735.000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3926.68 | −0.196256 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3966.51 | −0.197443 | −0.0987216 | − | 0.995115i | \(-0.531475\pi\) | ||||
−0.0987216 | + | 0.995115i | \(0.531475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 47.9070 | 0.00237504 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8224.50 | −0.406094 | −0.203047 | − | 0.979169i | \(-0.565084\pi\) | ||||
−0.203047 | + | 0.979169i | \(0.565084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5867.86 | −0.288566 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12012.5 | −0.588373 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12220.0 | −0.596140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18929.2 | −0.919754 | −0.459877 | − | 0.887983i | \(-0.652106\pi\) | ||||
−0.459877 | + | 0.887983i | \(0.652106\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5016.82 | 0.242793 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7700.35 | −0.371185 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34906.8 | −1.67597 | −0.837984 | − | 0.545695i | \(-0.816266\pi\) | ||||
−0.837984 | + | 0.545695i | \(0.816266\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2823.74 | 0.135040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13683.4 | −0.651803 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3337.99 | 0.158379 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −292.413 | −0.0138199 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −244.964 | −0.0115321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41837.3 | 1.96189 | 0.980943 | − | 0.194294i | \(-0.0622416\pi\) | ||||
0.980943 | + | 0.194294i | \(0.0622416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11093.2 | 0.518175 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19640.0 | 0.913843 | 0.456921 | − | 0.889507i | \(-0.348952\pi\) | ||||
0.456921 | + | 0.889507i | \(0.348952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6107.69 | −0.283090 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4055.53 | 0.187248 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1712.89 | 0.0787814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19144.4 | −0.877131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7870.34 | 0.359212 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12722.7 | −0.578460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24935.3 | −1.12941 | −0.564705 | − | 0.825293i | \(-0.691010\pi\) | ||||
−0.564705 | + | 0.825293i | \(0.691010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21957.0 | 0.990736 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11491.5 | 0.516551 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4317 | 0.000691041 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7645.16 | −0.341064 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1168.33 | −0.0519251 | −0.0259625 | − | 0.999663i | \(-0.508265\pi\) | ||||
−0.0259625 | + | 0.999663i | \(0.508265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 562.120 | 0.0248891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2936.24 | 0.129522 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19201.2 | −0.843829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1728.21 | −0.0756663 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2445.29 | 0.106665 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35175.7 | −1.52869 | −0.764345 | − | 0.644807i | \(-0.776938\pi\) | ||||
−0.764345 | + | 0.644807i | \(0.776938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15256.5 | 0.660577 | 0.330288 | − | 0.943880i | \(-0.392854\pi\) | ||||
0.330288 | + | 0.943880i | \(0.392854\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15318.1 | −0.660797 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2973.54 | 0.127802 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1636.16 | 0.0700635 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −185.078 | −0.00789639 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15971.9 | −0.678956 | −0.339478 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339478 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2312.41 | −0.0979409 | −0.0489705 | − | 0.998800i | \(-0.515594\pi\) | ||||
−0.0489705 | + | 0.998800i | \(0.515594\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1429.67 | −0.0603330 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10422.4 | −0.438238 | −0.219119 | − | 0.975698i | \(-0.570318\pi\) | ||||
−0.219119 | + | 0.975698i | \(0.570318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13213.4 | −0.553584 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4196.17 | −0.175167 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −318.405 | −0.0132438 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4642.49 | −0.192407 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6596.30 | 0.272403 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10119.6 | 0.416409 | 0.208205 | − | 0.978085i | \(-0.433238\pi\) | ||||
0.208205 | + | 0.978085i | \(0.433238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60579.9 | 2.48390 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21307.1 | 0.870530 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10941.8 | −0.445457 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6773.41 | −0.274778 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13395.5 | 0.541501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9535.80 | 0.384116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35378.1 | 1.42007 | 0.710037 | − | 0.704165i | \(-0.248678\pi\) | ||||
0.710037 | + | 0.704165i | \(0.248678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 244.611 | 0.00978424 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6697.57 | 0.266960 | 0.133480 | − | 0.991052i | \(-0.457385\pi\) | ||||
0.133480 | + | 0.991052i | \(0.457385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24298.4 | 0.965135 | 0.482568 | − | 0.875859i | \(-0.339704\pi\) | ||||
0.482568 | + | 0.875859i | \(0.339704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6617.37 | −0.261927 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24942.9 | −0.983853 | −0.491926 | − | 0.870637i | \(-0.663707\pi\) | ||||
−0.491926 | + | 0.870637i | \(0.663707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1578.21 | −0.0620355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14612.3 | 0.572388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16455.3 | 0.642355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 605.152 | 0.0235417 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13741.0 | 0.532716 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16276.6 | −0.626705 | −0.313353 | − | 0.949637i | \(-0.601452\pi\) | ||||
−0.313353 | + | 0.949637i | \(0.601452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22771.8 | −0.873806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26636.5 | 1.01862 | 0.509311 | − | 0.860582i | \(-0.329900\pi\) | ||||
0.509311 | + | 0.860582i | \(0.329900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21788.3 | 0.830392 | 0.415196 | − | 0.909732i | \(-0.363713\pi\) | ||||
0.415196 | + | 0.909732i | \(0.363713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1250.78 | −0.0475078 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26813.2 | 1.01499 | 0.507496 | − | 0.861654i | \(-0.330571\pi\) | ||||
0.507496 | + | 0.861654i | \(0.330571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5908.11 | 0.222893 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1544.04 | 0.0580554 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −470.229 | −0.0176211 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7227.45 | 0.269930 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −435.174 | −0.0161985 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71214.2 | 2.64196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3311.91 | −0.122459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6320.92 | −0.232942 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9219.07 | −0.338621 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15543.0 | −0.569014 | −0.284507 | − | 0.958674i | \(-0.591830\pi\) | ||||
−0.284507 | + | 0.958674i | \(0.591830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 871.844 | 0.0318122 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48711.1 | −1.77154 | −0.885768 | − | 0.464128i | \(-0.846368\pi\) | ||||
−0.885768 | + | 0.464128i | \(0.846368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25442.8 | −0.922273 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 78.7936 | 0.00284682 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19573.4 | 0.704876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1030.47 | −0.0369883 | −0.0184941 | − | 0.999829i | \(-0.505887\pi\) | ||||
−0.0184941 | + | 0.999829i | \(0.505887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28440.4 | 1.01753 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2950.40 | 0.105215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4828.02 | −0.171615 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11897.9 | −0.421553 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 879.756 | 0.0310698 | 0.0155349 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155349 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 266.354 | 0.00937638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21234.0 | 0.745092 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −619.339 | −0.0216626 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18668.1 | −0.650864 | −0.325432 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325432 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16781.5 | −0.583221 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29613.4 | 1.02590 | 0.512948 | − | 0.858420i | \(-0.328553\pi\) | ||||
0.512948 | + | 0.858420i | \(0.328553\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15559.5 | −0.537313 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −945.000 | −0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20738.9 | −0.711640 | −0.355820 | − | 0.934554i | \(-0.615798\pi\) | ||||
−0.355820 | + | 0.934554i | \(0.615798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2959.15 | 0.101220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10703.4 | −0.364966 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45776.5 | −1.55598 | −0.777988 | − | 0.628279i | \(-0.783760\pi\) | ||||
−0.777988 | + | 0.628279i | \(0.783760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1220.37 | 0.0413510 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16669.6 | 0.563064 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14399.9 | −0.484878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29895.1 | 1.00349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15711.4 | −0.525746 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8665.17 | −0.289059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34461.0 | −1.14601 | −0.573005 | − | 0.819552i | \(-0.694222\pi\) | ||||
−0.573005 | + | 0.819552i | \(0.694222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 105.967 | 0.00351304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22762.8 | 0.752309 | 0.376154 | − | 0.926557i | \(-0.377246\pi\) | ||||
0.376154 | + | 0.926557i | \(0.377246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12215.9 | 0.402490 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 220.331 | 0.00723716 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4809.57 | 0.157494 | 0.0787470 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787470 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6219.04 | 0.203025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4291.70 | 0.139677 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27591.6 | 0.895256 | 0.447628 | − | 0.894220i | \(-0.352269\pi\) | ||||
0.447628 | + | 0.894220i | \(0.352269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1791.15 | 0.0579399 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1816.62 | 0.0585853 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14862.4 | −0.477854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22263.4 | 0.713643 | 0.356822 | − | 0.934173i | \(-0.383860\pi\) | ||||
0.356822 | + | 0.934173i | \(0.383860\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13169.0 | −0.420851 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16018.2 | 0.510361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30378.2 | 0.964983 | 0.482491 | − | 0.875901i | \(-0.339732\pi\) | ||||
0.482491 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5214.26 | 0.165137 |
(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 | 1680.4.a.bg.1.2 | 2 | ||
4.3 | odd | 2 | 105.4.a.f.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 315.4.a.i.1.1 | 2 | |||
20.3 | even | 4 | 525.4.d.h.274.1 | 4 | |||
20.7 | even | 4 | 525.4.d.h.274.4 | 4 | |||
20.19 | odd | 2 | 525.4.a.k.1.1 | 2 | |||
28.27 | even | 2 | 735.4.a.p.1.2 | 2 | |||
60.59 | even | 2 | 1575.4.a.w.1.2 | 2 | |||
84.83 | odd | 2 | 2205.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
315.4.a.i.1.1 | 2 | 12.11 | even | 2 | |||
525.4.a.k.1.1 | 2 | 20.19 | odd | 2 | |||
525.4.d.h.274.1 | 4 | 20.3 | even | 4 | |||
525.4.d.h.274.4 | 4 | 20.7 | even | 4 | |||
735.4.a.p.1.2 | 2 | 28.27 | even | 2 | |||
1575.4.a.w.1.2 | 2 | 60.59 | even | 2 | |||
1680.4.a.bg.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2205.4.a.z.1.1 | 2 | 84.83 | odd | 2 |