Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53113 | 1.60200 | 0.800998 | − | 0.598667i | \(-0.204303\pi\) | ||||
0.800998 | + | 0.598667i | \(0.204303\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.5311 | 1.56639 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 20.5311 | 0.907356 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.490023\pi\) | ||||
0.0313378 | + | 0.999509i | \(0.490023\pi\) | |||||||
\(14\) | 31.7179 | 0.605498 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.21984 | −0.112810 | ||||||||
\(17\) | −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 | \(-0.510448\pi\) | ||||
−0.0328173 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 86.3735 | 0.837041 | ||||||||
\(23\) | 49.3774 | 0.447648 | 0.223824 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223824 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.3113 | 0.100406 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 87.7179 | 0.592040 | ||||||||
\(29\) | 291.494 | 1.86652 | 0.933261 | − | 0.359200i | \(-0.116950\pi\) | ||||
0.933261 | + | 0.359200i | \(0.116950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 244.307 | 1.41545 | 0.707724 | − | 0.706489i | \(-0.249722\pi\) | ||||
0.707724 | + | 0.706489i | \(0.249722\pi\) | |||||||
\(32\) | −196.963 | −1.08808 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −29.4436 | −0.148516 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 193.121 | 0.858077 | 0.429038 | − | 0.903286i | \(-0.358853\pi\) | ||||
0.429038 | + | 0.903286i | \(0.358853\pi\) | |||||||
\(38\) | −24.6303 | −0.105147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −315.113 | −1.20030 | −0.600151 | − | 0.799887i | \(-0.704893\pi\) | ||||
−0.600151 | + | 0.799887i | \(0.704893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 300.996 | 1.06748 | 0.533738 | − | 0.845650i | \(-0.320787\pi\) | ||||
0.533738 | + | 0.845650i | \(0.320787\pi\) | |||||||
\(44\) | 238.872 | 0.818437 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 223.735 | 0.717130 | ||||||||
\(47\) | 86.5058 | 0.268472 | 0.134236 | − | 0.990949i | \(-0.457142\pi\) | ||||
0.134236 | + | 0.990949i | \(0.457142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 36.8132 | 0.0981745 | ||||||||
\(53\) | 509.677 | 1.32093 | 0.660467 | − | 0.750855i | \(-0.270358\pi\) | ||||
0.660467 | + | 0.750855i | \(0.270358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 143.718 | 0.342948 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1320.80 | 2.99016 | ||||||||
\(59\) | 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 | \(0.501755\pi\) | |||||||
\(62\) | 1106.99 | 2.26754 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −834.706 | −1.63029 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −205.992 | −0.375611 | −0.187806 | − | 0.982206i | \(-0.560138\pi\) | ||||
−0.187806 | + | 0.982206i | \(0.560138\pi\) | |||||||
\(68\) | −81.4281 | −0.145215 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.200823\pi\) | ||||
0.807494 | + | 0.589876i | \(0.200823\pi\) | |||||||
\(74\) | 875.055 | 1.37464 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −68.1168 | −0.102810 | ||||||||
\(77\) | 133.436 | 0.197486 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −863.237 | −1.22939 | −0.614695 | − | 0.788765i | \(-0.710721\pi\) | ||||
−0.614695 | + | 0.788765i | \(0.710721\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1427.82 | −1.92288 | ||||||||
\(83\) | 1334.72 | 1.76512 | 0.882560 | − | 0.470200i | \(-0.155818\pi\) | ||||
0.882560 | + | 0.470200i | \(0.155818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1363.85 | 1.71009 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 391.370 | 0.474093 | ||||||||
\(89\) | −326.249 | −0.388565 | −0.194283 | − | 0.980946i | \(-0.562238\pi\) | ||||
−0.194283 | + | 0.980946i | \(0.562238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.5642 | 0.0236892 | ||||||||
\(92\) | 618.755 | 0.701192 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 391.969 | 0.430091 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1526.77 | −1.59815 | −0.799075 | − | 0.601232i | \(-0.794677\pi\) | ||||
−0.799075 | + | 0.601232i | \(0.794677\pi\) | |||||||
\(98\) | 222.025 | 0.228857 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −96.8716 | −0.0954365 | −0.0477182 | − | 0.998861i | \(-0.515195\pi\) | ||||
−0.0477182 | + | 0.998861i | \(0.515195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1321.99 | −1.26466 | −0.632329 | − | 0.774700i | \(-0.717901\pi\) | ||||
−0.632329 | + | 0.774700i | \(0.717901\pi\) | |||||||
\(104\) | 60.3152 | 0.0568691 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2309.41 | 2.11613 | ||||||||
\(107\) | 1745.71 | 1.57724 | 0.788619 | − | 0.614883i | \(-0.210797\pi\) | ||||
0.788619 | + | 0.614883i | \(0.210797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 476.856 | 0.419032 | 0.209516 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209516 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −50.5389 | −0.0426382 | ||||||||
\(113\) | 1641.65 | 1.36666 | 0.683332 | − | 0.730108i | \(-0.260530\pi\) | ||||
0.683332 | + | 0.730108i | \(0.260530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3652.75 | 2.92370 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 377.829 | 0.294763 | ||||||||
\(119\) | −45.4864 | −0.0350398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −967.630 | −0.726995 | ||||||||
\(122\) | −23.8016 | −0.0176631 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3061.45 | 2.21715 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 844.016 | 0.589719 | 0.294859 | − | 0.955541i | \(-0.404727\pi\) | ||||
0.294859 | + | 0.955541i | \(0.404727\pi\) | |||||||
\(128\) | −2206.46 | −1.52363 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | −933.377 | −0.601728 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −133.413 | −0.0841179 | ||||||||
\(137\) | −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 | \(-0.678726\pi\) | ||||
−0.532444 | + | 0.846465i | \(0.678726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4550.65 | −2.68931 | ||||||||
\(143\) | 56.0000 | 0.0327479 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4564.15 | 2.58720 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2420.02 | 1.34408 | ||||||||
\(149\) | 1173.57 | 0.645254 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1540.07 | 0.829994 | 0.414997 | − | 0.909823i | \(-0.363783\pi\) | ||||
0.414997 | + | 0.909823i | \(0.363783\pi\) | |||||||
\(152\) | −111.603 | −0.0595540 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 604.615 | 0.316372 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2544.53 | 1.29348 | 0.646738 | − | 0.762712i | \(-0.276133\pi\) | ||||
0.646738 | + | 0.762712i | \(0.276133\pi\) | |||||||
\(158\) | −3911.44 | −1.96948 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | \(0.454361\pi\) | |||||||
\(164\) | −3948.72 | −1.88014 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6047.81 | 2.82772 | ||||||||
\(167\) | 928.498 | 0.430236 | 0.215118 | − | 0.976588i | \(-0.430986\pi\) | ||||
0.215118 | + | 0.976588i | \(0.430986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2188.37 | −0.996072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3771.82 | 1.67209 | ||||||||
\(173\) | −315.642 | −0.138716 | −0.0693578 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693578 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −137.626 | −0.0589431 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1478.28 | −0.622480 | ||||||||
\(179\) | 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 | \(0.623591\pi\) | |||||||
\(182\) | 93.1790 | 0.0379499 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1013.77 | 0.406176 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −123.868 | −0.0484391 | ||||||||
\(188\) | 1084.02 | 0.420532 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.395249\pi\) | ||||
0.323178 | + | 0.946338i | \(0.395249\pi\) | |||||||
\(194\) | −6918.01 | −2.56023 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 614.025 | 0.223770 | ||||||||
\(197\) | 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 | \(-0.693290\pi\) | ||||
−0.570601 | + | 0.821227i | \(0.693290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −438.938 | −0.152889 | ||||||||
\(203\) | 2040.46 | 0.705479 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5990.12 | −2.02598 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.2100 | −0.00707044 | ||||||||
\(209\) | −103.619 | −0.0342940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4943.16 | 1.61280 | 0.806401 | − | 0.591369i | \(-0.201412\pi\) | ||||
0.806401 | + | 0.591369i | \(0.201412\pi\) | |||||||
\(212\) | 6386.83 | 2.06910 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7910.05 | 2.52673 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1710.15 | 0.534989 | ||||||||
\(218\) | 2160.70 | 0.671288 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(0.657365\pi\) | |||||||
\(224\) | −1378.74 | −0.411255 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7438.51 | 2.18939 | ||||||||
\(227\) | −3651.11 | −1.06755 | −0.533773 | − | 0.845628i | \(-0.679226\pi\) | ||||
−0.533773 | + | 0.845628i | \(0.679226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4083.70 | −1.17842 | −0.589210 | − | 0.807980i | \(-0.700561\pi\) | ||||
−0.589210 | + | 0.807980i | \(0.700561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5984.70 | 1.69360 | ||||||||
\(233\) | −3682.51 | −1.03540 | −0.517702 | − | 0.855561i | \(-0.673212\pi\) | ||||
−0.517702 | + | 0.855561i | \(0.673212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1044.91 | 0.288211 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −206.105 | −0.0561336 | ||||||||
\(239\) | −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 | \(0.722813\pi\) | |||||||
\(242\) | −4384.46 | −1.16464 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −65.8249 | −0.0172705 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.9690 | −0.00411369 | ||||||||
\(248\) | 5015.91 | 1.28432 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | 3824.34 | 0.944727 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3320.09 | −0.810569 | ||||||||
\(257\) | −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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12670.0 | 2.98760 | ||||||||
\(263\) | 7319.00 | 1.71600 | 0.858002 | − | 0.513646i | \(-0.171706\pi\) | ||||
0.858002 | + | 0.513646i | \(0.171706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −172.412 | −0.0397416 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2581.32 | −0.588354 | ||||||||
\(269\) | 815.097 | 0.184749 | 0.0923743 | − | 0.995724i | \(-0.470554\pi\) | ||||
0.0923743 | + | 0.995724i | \(0.470554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5106.02 | −1.14453 | −0.572267 | − | 0.820068i | \(-0.693936\pi\) | ||||
−0.572267 | + | 0.820068i | \(0.693936\pi\) | |||||||
\(272\) | 46.9150 | 0.0104582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9321.13 | −2.05515 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1398.72 | −0.303398 | −0.151699 | − | 0.988427i | \(-0.548474\pi\) | ||||
−0.151699 | + | 0.988427i | \(0.548474\pi\) | |||||||
\(278\) | −7907.39 | −1.70595 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7102.38 | 1.50780 | 0.753901 | − | 0.656988i | \(-0.228170\pi\) | ||||
0.753901 | + | 0.656988i | \(0.228170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4465.18 | −0.937907 | −0.468953 | − | 0.883223i | \(-0.655369\pi\) | ||||
−0.468953 | + | 0.883223i | \(0.655369\pi\) | |||||||
\(284\) | −12585.1 | −2.62954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 253.743 | 0.0524621 | ||||||||
\(287\) | −2205.79 | −0.453671 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4870.78 | −0.991405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12622.5 | 2.52970 | ||||||||
\(293\) | 7590.61 | 1.51348 | 0.756738 | − | 0.653718i | \(-0.226792\pi\) | ||||
0.756738 | + | 0.653718i | \(0.226792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3964.98 | 0.778581 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5317.61 | 1.03369 | ||||||||
\(299\) | 145.058 | 0.0280566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2106.97 | 0.403468 | ||||||||
\(302\) | 6978.26 | 1.32965 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 39.2456 | 0.00740425 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9480.12 | −1.76241 | −0.881203 | − | 0.472737i | \(-0.843266\pi\) | ||||
−0.881203 | + | 0.472737i | \(0.843266\pi\) | |||||||
\(308\) | 1672.10 | 0.309340 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.668539\pi\) | ||||
−0.505084 | + | 0.863070i | \(0.668539\pi\) | |||||||
\(314\) | 11529.6 | 2.07214 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10817.3 | −1.92571 | ||||||||
\(317\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1566.15 | 0.271050 | ||||||||
\(323\) | 35.3222 | 0.00608477 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2694.70 | 0.457809 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6469.62 | −1.08910 | ||||||||
\(329\) | 605.541 | 0.101473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4389.67 | −0.728936 | −0.364468 | − | 0.931216i | \(-0.618749\pi\) | ||||
−0.364468 | + | 0.931216i | \(0.618749\pi\) | |||||||
\(332\) | 16725.6 | 2.76487 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4207.14 | 0.689236 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2348.83 | −0.379671 | −0.189835 | − | 0.981816i | \(-0.560795\pi\) | ||||
−0.189835 | + | 0.981816i | \(0.560795\pi\) | |||||||
\(338\) | −9915.79 | −1.59570 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4657.05 | 0.739570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 6179.79 | 0.968581 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1430.21 | −0.222222 | ||||||||
\(347\) | 558.436 | 0.0863931 | 0.0431965 | − | 0.999067i | \(-0.486246\pi\) | ||||
0.0431965 | + | 0.999067i | \(0.486246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3233.89 | 0.496006 | 0.248003 | − | 0.968759i | \(-0.420226\pi\) | ||||
0.248003 | + | 0.968759i | \(0.420226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3754.56 | −0.568519 | ||||||||
\(353\) | −7516.35 | −1.13330 | −0.566650 | − | 0.823959i | \(-0.691761\pi\) | ||||
−0.566650 | + | 0.823959i | \(0.691761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4088.27 | −0.608646 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6549.70 | 0.966935 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | −8354.56 | −1.21300 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 257.693 | 0.0371065 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8307.17 | −1.18155 | −0.590777 | − | 0.806835i | \(-0.701179\pi\) | ||||
−0.590777 | + | 0.806835i | \(0.701179\pi\) | |||||||
\(368\) | −356.497 | −0.0504992 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3567.74 | 0.499266 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4551.09 | 0.631760 | 0.315880 | − | 0.948799i | \(-0.397700\pi\) | ||||
0.315880 | + | 0.948799i | \(0.397700\pi\) | |||||||
\(374\) | −561.261 | −0.0775992 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1776.06 | 0.243599 | ||||||||
\(377\) | 856.335 | 0.116985 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1788.29 | −0.242370 | −0.121185 | − | 0.992630i | \(-0.538669\pi\) | ||||
−0.121185 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1105.93 | 0.148126 | ||||||||
\(383\) | −1358.47 | −0.181240 | −0.0906199 | − | 0.995886i | \(-0.528885\pi\) | ||||
−0.0906199 | + | 0.995886i | \(0.528885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7852.60 | 1.03546 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19132.2 | −2.50333 | ||||||||
\(389\) | −9722.54 | −1.26723 | −0.633615 | − | 0.773649i | \(-0.718430\pi\) | ||||
−0.633615 | + | 0.773649i | \(0.718430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −320.858 | −0.0414999 | ||||||||
\(392\) | 1006.03 | 0.129622 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1623.19 | 0.207551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4788.04 | 0.605302 | 0.302651 | − | 0.953101i | \(-0.402128\pi\) | ||||
0.302651 | + | 0.953101i | \(0.402128\pi\) | |||||||
\(398\) | −14516.1 | −1.82820 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9681.41 | −1.20565 | −0.602826 | − | 0.797873i | \(-0.705959\pi\) | ||||
−0.602826 | + | 0.797873i | \(0.705959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 717.712 | 0.0887141 | ||||||||
\(404\) | −1213.91 | −0.149491 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9245.58 | 1.13017 | ||||||||
\(407\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16566.1 | −1.98095 | ||||||||
\(413\) | 583.696 | 0.0695443 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −578.627 | −0.0681959 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −469.510 | −0.0549389 | ||||||||
\(419\) | 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 | \(0.753674\pi\) | |||||||
\(422\) | 22398.1 | 2.58370 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10464.2 | 1.19856 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.7703 | −0.00416731 | ||||||||
\(428\) | 21875.7 | 2.47057 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.487808\pi\) | ||||
0.0382939 | + | 0.999267i | \(0.487808\pi\) | |||||||
\(434\) | 7748.92 | 0.857051 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5975.55 | 0.656369 | ||||||||
\(437\) | −268.406 | −0.0293812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8408.79 | 0.914191 | 0.457095 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457095 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −86.4976 | −0.00930830 | ||||||||
\(443\) | 6568.55 | 0.704473 | 0.352236 | − | 0.935911i | \(-0.385421\pi\) | ||||
0.352236 | + | 0.935911i | \(0.385421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14319.0 | −1.52024 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5842.94 | −0.616190 | ||||||||
\(449\) | −2954.55 | −0.310543 | −0.155271 | − | 0.987872i | \(-0.549625\pi\) | ||||
−0.155271 | + | 0.987872i | \(0.549625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6006.76 | −0.627156 | ||||||||
\(452\) | 20571.7 | 2.14073 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16543.7 | −1.71020 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8144.84 | 0.833697 | 0.416849 | − | 0.908976i | \(-0.363135\pi\) | ||||
0.416849 | + | 0.908976i | \(0.363135\pi\) | |||||||
\(458\) | −18503.8 | −1.88782 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2495.26 | −0.252095 | −0.126048 | − | 0.992024i | \(-0.540229\pi\) | ||||
−0.126048 | + | 0.992024i | \(0.540229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5755.66 | 0.577728 | 0.288864 | − | 0.957370i | \(-0.406722\pi\) | ||||
0.288864 | + | 0.957370i | \(0.406722\pi\) | |||||||
\(464\) | −2104.54 | −0.210562 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16685.9 | −1.65871 | ||||||||
\(467\) | −4143.73 | −0.410598 | −0.205299 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205299 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1441.95 | −0.141968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1711.99 | 0.166951 | ||||||||
\(473\) | 5737.67 | 0.557755 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −569.996 | −0.0548860 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12047.3 | −1.15278 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | −21841.8 | −2.06404 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12125.5 | −1.13876 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6360.42 | −0.591824 | −0.295912 | − | 0.955215i | \(-0.595623\pi\) | ||||
−0.295912 | + | 0.955215i | \(0.595623\pi\) | |||||||
\(488\) | −107.848 | −0.0100042 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | −72.3576 | −0.00659012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1763.86 | −0.159677 | ||||||||
\(497\) | −7030.15 | −0.634498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18473.9 | −1.65732 | −0.828661 | − | 0.559751i | \(-0.810897\pi\) | ||||
−0.828661 | + | 0.559751i | \(0.810897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7577.28 | −0.673687 | ||||||||
\(503\) | 11379.2 | 1.00869 | 0.504347 | − | 0.863501i | \(-0.331733\pi\) | ||||
0.504347 | + | 0.863501i | \(0.331733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4264.90 | 0.374700 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10576.5 | 0.923730 | ||||||||
\(509\) | −6064.48 | −0.528101 | −0.264051 | − | 0.964509i | \(-0.585059\pi\) | ||||
−0.264051 | + | 0.964509i | \(0.585059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7051.02 | 0.610408 | ||||||||
\(512\) | 2607.89 | 0.225105 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16755.0 | −1.43780 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1649.00 | 0.140276 | ||||||||
\(518\) | 6125.38 | 0.519563 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2682.88 | −0.225603 | −0.112801 | − | 0.993618i | \(-0.535982\pi\) | ||||
−0.112801 | + | 0.993618i | \(0.535982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4309.02 | 0.360268 | 0.180134 | − | 0.983642i | \(-0.442347\pi\) | ||||
0.180134 | + | 0.983642i | \(0.442347\pi\) | |||||||
\(524\) | 35039.6 | 2.92120 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33163.3 | 2.74903 | ||||||||
\(527\) | −1587.52 | −0.131221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9728.87 | −0.799611 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −476.817 | −0.0388584 | ||||||||
\(533\) | −925.720 | −0.0752296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4229.25 | −0.340813 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3693.31 | 0.295966 | ||||||||
\(539\) | 934.051 | 0.0746427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4081.47 | 0.324355 | 0.162178 | − | 0.986762i | \(-0.448148\pi\) | ||||
0.162178 | + | 0.986762i | \(0.448148\pi\) | |||||||
\(542\) | −23136.0 | −1.83354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1279.88 | 0.100872 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8844.82 | −0.691366 | −0.345683 | − | 0.938351i | \(-0.612353\pi\) | ||||
−0.345683 | + | 0.938351i | \(0.612353\pi\) | |||||||
\(548\) | −25778.2 | −2.00947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1584.51 | −0.122509 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6042.66 | −0.464666 | ||||||||
\(554\) | −6337.80 | −0.486042 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21868.4 | −1.66803 | ||||||||
\(557\) | −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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32181.8 | 2.41549 | ||||||||
\(563\) | −21857.5 | −1.63621 | −0.818104 | − | 0.575071i | \(-0.804975\pi\) | ||||
−0.818104 | + | 0.575071i | \(0.804975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20232.3 | −1.50252 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20619.6 | −1.52320 | ||||||||
\(569\) | −23496.4 | −1.73115 | −0.865573 | − | 0.500783i | \(-0.833046\pi\) | ||||
−0.865573 | + | 0.500783i | \(0.833046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11067.8 | 0.811164 | 0.405582 | − | 0.914059i | \(-0.367069\pi\) | ||||
0.405582 | + | 0.914059i | \(0.367069\pi\) | |||||||
\(572\) | 701.743 | 0.0512961 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9994.72 | −0.726780 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20482.9 | −1.47784 | −0.738922 | − | 0.673791i | \(-0.764665\pi\) | ||||
−0.738922 | + | 0.673791i | \(0.764665\pi\) | |||||||
\(578\) | −22070.1 | −1.58823 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9343.07 | 0.667153 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9715.60 | 0.690187 | ||||||||
\(584\) | 20680.8 | 1.46537 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34394.1 | 2.42458 | ||||||||
\(587\) | −23444.3 | −1.64847 | −0.824235 | − | 0.566248i | \(-0.808394\pi\) | ||||
−0.824235 | + | 0.566248i | \(0.808394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1328.01 | −0.0929025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1394.30 | −0.0967996 | ||||||||
\(593\) | 4404.69 | 0.305024 | 0.152512 | − | 0.988302i | \(-0.451264\pi\) | ||||
0.152512 | + | 0.988302i | \(0.451264\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14706.2 | 1.01072 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 657.277 | 0.0449466 | ||||||||
\(599\) | −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 | \(0.660602\pi\) | |||||||
\(602\) | 9546.97 | 0.646354 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19298.8 | 1.30010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11446.5 | −0.765402 | −0.382701 | − | 0.923872i | \(-0.625006\pi\) | ||||
−0.382701 | + | 0.923872i | \(0.625006\pi\) | |||||||
\(608\) | 1070.65 | 0.0714156 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 254.132 | 0.0168266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19436.4 | 1.28063 | 0.640316 | − | 0.768111i | \(-0.278803\pi\) | ||||
0.640316 | + | 0.768111i | \(0.278803\pi\) | |||||||
\(614\) | −42955.6 | −2.82337 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2739.59 | 0.179190 | ||||||||
\(617\) | −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 | \(-0.439350\pi\) | ||||
0.189388 | + | 0.981902i | \(0.439350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32071.4 | −2.06744 | ||||||||
\(623\) | −2283.74 | −0.146864 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25346.4 | −1.61829 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31885.9 | 2.02609 | ||||||||
\(629\) | −1254.91 | −0.0795493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24776.6 | 1.56314 | 0.781568 | − | 0.623820i | \(-0.214420\pi\) | ||||
0.781568 | + | 0.623820i | \(0.214420\pi\) | |||||||
\(632\) | −17723.2 | −1.11549 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16166.2 | 1.01268 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 143.949 | 0.00895366 | ||||||||
\(638\) | 25177.4 | 1.56235 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27219.4 | −1.67723 | −0.838613 | − | 0.544728i | \(-0.816633\pi\) | ||||
−0.838613 | + | 0.544728i | \(0.816633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7091.79 | −0.434950 | −0.217475 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217475 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(644\) | 4331.28 | 0.265026 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 160.049 | 0.00974777 | ||||||||
\(647\) | 27773.0 | 1.68758 | 0.843792 | − | 0.536670i | \(-0.180318\pi\) | ||||
0.843792 | + | 0.536670i | \(0.180318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1589.51 | 0.0961382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7452.37 | 0.447634 | ||||||||
\(653\) | 21380.4 | 1.28129 | 0.640643 | − | 0.767839i | \(-0.278668\pi\) | ||||
0.640643 | + | 0.767839i | \(0.278668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2275.06 | 0.135406 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2743.78 | 0.162559 | ||||||||
\(659\) | 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 | \(0.214219\pi\) | |||||||
\(662\) | −19890.1 | −1.16775 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27403.4 | 1.60159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14393.2 | 0.835544 | ||||||||
\(668\) | 11635.1 | 0.673917 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −100.132 | −0.00576090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31695.2 | 1.81540 | 0.907698 | − | 0.419624i | \(-0.137838\pi\) | ||||
0.907698 | + | 0.419624i | \(0.137838\pi\) | |||||||
\(674\) | −10642.9 | −0.608231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27422.7 | −1.56024 | ||||||||
\(677\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21101.7 | 1.18479 | ||||||||
\(683\) | −22896.9 | −1.28276 | −0.641381 | − | 0.767223i | \(-0.721638\pi\) | ||||
−0.641381 | + | 0.767223i | \(0.721638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1554.18 | 0.0864997 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2173.14 | −0.120422 | ||||||||
\(689\) | 1497.30 | 0.0827904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23764.0 | −1.30829 | −0.654143 | − | 0.756371i | \(-0.726971\pi\) | ||||
−0.654143 | + | 0.756371i | \(0.726971\pi\) | |||||||
\(692\) | −3955.35 | −0.217283 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2530.34 | 0.138401 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2047.62 | 0.111276 | ||||||||
\(698\) | 14653.2 | 0.794600 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26259.5 | −1.41485 | −0.707423 | − | 0.706791i | \(-0.750142\pi\) | ||||
−0.707423 | + | 0.706791i | \(0.750142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1049.77 | −0.0563196 | ||||||||
\(704\) | −15911.4 | −0.851822 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34057.6 | −1.81554 | ||||||||
\(707\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6698.26 | −0.352567 | ||||||||
\(713\) | 12063.3 | 0.633623 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18113.6 | 0.945444 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29804.7 | 1.54916 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | −30945.1 | −1.59509 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23105.1 | −1.18604 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31306.2 | −1.59709 | −0.798544 | − | 0.601937i | \(-0.794396\pi\) | ||||
−0.798544 | + | 0.601937i | \(0.794396\pi\) | |||||||
\(728\) | 422.206 | 0.0214945 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1955.89 | −0.0989621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15765.8 | 0.794441 | 0.397220 | − | 0.917723i | \(-0.369975\pi\) | ||||
0.397220 | + | 0.917723i | \(0.369975\pi\) | |||||||
\(734\) | −37640.8 | −1.89285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9725.53 | −0.487076 | ||||||||
\(737\) | −3926.68 | −0.196256 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3966.51 | 0.197443 | 0.0987216 | − | 0.995115i | \(-0.468525\pi\) | ||||
0.0987216 | + | 0.995115i | \(0.468525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16165.9 | 0.799823 | ||||||||
\(743\) | 8224.50 | 0.406094 | 0.203047 | − | 0.979169i | \(-0.434916\pi\) | ||||
0.203047 | + | 0.979169i | \(0.434916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20621.6 | 1.01208 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1552.20 | −0.0758745 | ||||||||
\(749\) | 12220.0 | 0.596140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18929.2 | 0.919754 | 0.459877 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459877 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(752\) | −624.558 | −0.0302863 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3880.16 | 0.187410 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34906.8 | 1.67597 | 0.837984 | − | 0.545695i | \(-0.183734\pi\) | ||||
0.837984 | + | 0.545695i | \(0.183734\pi\) | |||||||
\(758\) | −8102.96 | −0.388276 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13683.4 | 0.651803 | 0.325902 | − | 0.945404i | \(-0.394332\pi\) | ||||
0.325902 | + | 0.945404i | \(0.394332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3337.99 | 0.158379 | ||||||||
\(764\) | 3058.52 | 0.144834 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6155.42 | −0.290345 | ||||||||
\(767\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21716.9 | 1.01245 | ||||||||
\(773\) | 19640.0 | 0.913843 | 0.456921 | − | 0.889507i | \(-0.348952\pi\) | ||||
0.456921 | + | 0.889507i | \(0.348952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31346.4 | −1.45009 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44054.1 | −2.03010 | ||||||||
\(779\) | 1712.89 | 0.0787814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19144.4 | −0.877131 | ||||||||
\(782\) | −1453.85 | −0.0664827 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −353.772 | −0.0161157 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24935.3 | −1.12941 | −0.564705 | − | 0.825293i | \(-0.691010\pi\) | ||||
−0.564705 | + | 0.825293i | \(0.691010\pi\) | |||||||
\(788\) | 4489.02 | 0.202938 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11491.5 | 0.516551 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4317 | −0.000691041 0 | ||||||||
\(794\) | 21695.2 | 0.969692 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40145.1 | −1.78757 | ||||||||
\(797\) | −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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −43867.7 | −1.93145 | ||||||||
\(803\) | 19201.2 | 0.843829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3252.05 | 0.142120 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1988.88 | −0.0865949 | ||||||||
\(809\) | 35175.7 | 1.52869 | 0.764345 | − | 0.644807i | \(-0.223062\pi\) | ||||
0.764345 | + | 0.644807i | \(0.223062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15256.5 | −0.660577 | −0.330288 | − | 0.943880i | \(-0.607146\pi\) | ||||
−0.330288 | + | 0.943880i | \(0.607146\pi\) | |||||||
\(812\) | 25569.3 | 1.10506 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16680.5 | 0.718245 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1636.16 | −0.0700635 | ||||||||
\(818\) | 50354.7 | 2.15233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15971.9 | 0.678956 | 0.339478 | − | 0.940614i | \(-0.389750\pi\) | ||||
0.339478 | + | 0.940614i | \(0.389750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2312.41 | −0.0979409 | −0.0489705 | − | 0.998800i | \(-0.515594\pi\) | ||||
−0.0489705 | + | 0.998800i | \(0.515594\pi\) | |||||||
\(824\) | −27142.0 | −1.14750 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2644.80 | 0.111410 | ||||||||
\(827\) | 10422.4 | 0.438238 | 0.219119 | − | 0.975698i | \(-0.429682\pi\) | ||||
0.219119 | + | 0.975698i | \(0.429682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13213.4 | −0.553584 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2452.15 | −0.102179 | ||||||||
\(833\) | −318.405 | −0.0132438 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1298.46 | −0.0537179 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5573.67 | 0.229761 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −55988.7 | −2.29157 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 61943.4 | 2.52628 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6773.41 | −0.274778 | ||||||||
\(848\) | −3679.79 | −0.149015 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9535.80 | 0.384116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35378.1 | −1.42007 | −0.710037 | − | 0.704165i | \(-0.751322\pi\) | ||||
−0.710037 | + | 0.704165i | \(0.751322\pi\) | |||||||
\(854\) | −166.611 | −0.00667602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35841.4 | 1.43112 | ||||||||
\(857\) | 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 | \(-0.660296\pi\) | ||||
−0.482568 | + | 0.875859i | \(0.660296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33418.3 | 1.32045 | ||||||||
\(863\) | 24942.9 | 0.983853 | 0.491926 | − | 0.870637i | \(-0.336293\pi\) | ||||
0.491926 | + | 0.870637i | \(0.336293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3126.78 | 0.122693 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21430.1 | 0.838002 | ||||||||
\(869\) | −16455.3 | −0.642355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −605.152 | −0.0235417 | ||||||||
\(872\) | 9790.39 | 0.380212 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1216.18 | −0.0470686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16276.6 | 0.626705 | 0.313353 | − | 0.949637i | \(-0.398548\pi\) | ||||
0.313353 | + | 0.949637i | \(0.398548\pi\) | |||||||
\(878\) | 38101.3 | 1.46453 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26636.5 | −1.01862 | −0.509311 | − | 0.860582i | \(-0.670100\pi\) | ||||
−0.509311 | + | 0.860582i | \(0.670100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21788.3 | 0.830392 | 0.415196 | − | 0.909732i | \(-0.363713\pi\) | ||||
0.415196 | + | 0.909732i | \(0.363713\pi\) | |||||||
\(884\) | −239.215 | −0.00910142 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29763.0 | 1.12856 | ||||||||
\(887\) | −26813.2 | −1.01499 | −0.507496 | − | 0.861654i | \(-0.669429\pi\) | ||||
−0.507496 | + | 0.861654i | \(0.669429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5908.11 | 0.222893 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39600.2 | −1.48645 | ||||||||
\(893\) | −470.229 | −0.0176211 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15445.2 | −0.575879 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13387.4 | −0.497488 | ||||||||
\(899\) | 71214.2 | 2.64196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3311.91 | −0.122459 | ||||||||
\(902\) | −27217.4 | −1.00470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33704.8 | 1.24005 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15543.0 | −0.569014 | −0.284507 | − | 0.958674i | \(-0.591830\pi\) | ||||
−0.284507 | + | 0.958674i | \(0.591830\pi\) | |||||||
\(908\) | −45752.6 | −1.67219 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | 36905.3 | 1.33558 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51173.3 | −1.84587 | ||||||||
\(917\) | 19573.4 | 0.704876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1030.47 | 0.0369883 | 0.0184941 | − | 0.999829i | \(-0.494113\pi\) | ||||
0.0184941 | + | 0.999829i | \(0.494113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11306.3 | −0.403855 | ||||||||
\(923\) | −2950.40 | −0.105215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26079.6 | 0.925518 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −57413.6 | −2.03092 | ||||||||
\(929\) | −879.756 | −0.0310698 | −0.0155349 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155349 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −266.354 | −0.00937638 | ||||||||
\(932\) | −46146.0 | −1.62185 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18775.8 | −0.657776 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18668.1 | 0.650864 | 0.325432 | − | 0.945565i | \(-0.394490\pi\) | ||||
0.325432 | + | 0.945565i | \(0.394490\pi\) | |||||||
\(938\) | −6533.64 | −0.227432 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29613.4 | −1.02590 | −0.512948 | − | 0.858420i | \(-0.671447\pi\) | ||||
−0.512948 | + | 0.858420i | \(0.671447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15559.5 | −0.537313 | ||||||||
\(944\) | −602.028 | −0.0207567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25998.1 | 0.893521 | ||||||||
\(947\) | 20738.9 | 0.711640 | 0.355820 | − | 0.934554i | \(-0.384202\pi\) | ||||
0.355820 | + | 0.934554i | \(0.384202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2959.15 | 0.101220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −933.888 | −0.0317936 | ||||||||
\(953\) | −45776.5 | −1.55598 | −0.777988 | − | 0.628279i | \(-0.783760\pi\) | ||||
−0.777988 | + | 0.628279i | \(0.783760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33317.5 | −1.12716 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30657.4 | 1.03392 | ||||||||
\(959\) | −14399.9 | −0.484878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29895.1 | 1.00349 | ||||||||
\(962\) | 2570.68 | 0.0861561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −60404.9 | −2.01817 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34461.0 | −1.14601 | −0.573005 | − | 0.819552i | \(-0.694222\pi\) | ||||
−0.573005 | + | 0.819552i | \(0.694222\pi\) | |||||||
\(968\) | −19866.5 | −0.659643 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −28819.9 | −0.948099 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.9251 | 0.00124381 | ||||||||
\(977\) | 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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32046.6 | 1.04139 | ||||||||
\(983\) | −27591.6 | −0.895256 | −0.447628 | − | 0.894220i | \(-0.647731\pi\) | ||||
−0.447628 | + | 0.894220i | \(0.647731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8582.63 | −0.277207 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −200.109 | −0.00644365 | ||||||||
\(989\) | 14862.4 | 0.477854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22263.4 | −0.713643 | −0.356822 | − | 0.934173i | \(-0.616140\pi\) | ||||
−0.356822 | + | 0.934173i | \(0.616140\pi\) | |||||||
\(992\) | −48119.5 | −1.54012 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −31854.5 | −1.01646 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30378.2 | −0.964983 | −0.482491 | − | 0.875901i | \(-0.660268\pi\) | ||||
−0.482491 | + | 0.875901i | \(0.660268\pi\) | |||||||
\(998\) | −83707.4 | −2.65502 | ||||||||
\(999\) | 0 | 0 |
(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 | 1575.4.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 525.4.a.k.1.1 | 2 | |||
5.4 | even | 2 | 315.4.a.i.1.1 | 2 | |||
15.2 | even | 4 | 525.4.d.h.274.1 | 4 | |||
15.8 | even | 4 | 525.4.d.h.274.4 | 4 | |||
15.14 | odd | 2 | 105.4.a.f.1.2 | ✓ | 2 | ||
35.34 | odd | 2 | 2205.4.a.z.1.1 | 2 | |||
60.59 | even | 2 | 1680.4.a.bg.1.2 | 2 | |||
105.104 | even | 2 | 735.4.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
315.4.a.i.1.1 | 2 | 5.4 | even | 2 | |||
525.4.a.k.1.1 | 2 | 3.2 | odd | 2 | |||
525.4.d.h.274.1 | 4 | 15.2 | even | 4 | |||
525.4.d.h.274.4 | 4 | 15.8 | even | 4 | |||
735.4.a.p.1.2 | 2 | 105.104 | even | 2 | |||
1575.4.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1680.4.a.bg.1.2 | 2 | 60.59 | even | 2 | |||
2205.4.a.z.1.1 | 2 | 35.34 | odd | 2 |