Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
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: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-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 | \(0.204303\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 12.5311 | 1.56639 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 13.5934 | 0.924913 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 20.5311 | 0.907356 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 22.6556 | 0.716434 | ||||||||
\(11\) | −19.0623 | −0.522499 | −0.261249 | − | 0.965271i | \(-0.584135\pi\) | ||||
−0.261249 | + | 0.965271i | \(0.584135\pi\) | |||||||
\(12\) | 37.5934 | 0.904356 | ||||||||
\(13\) | −2.93774 | −0.0626756 | −0.0313378 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313378 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(14\) | −31.7179 | −0.605498 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −7.21984 | −0.112810 | ||||||||
\(17\) | −6.49806 | −0.0927066 | −0.0463533 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463533 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(18\) | 40.7802 | 0.533999 | ||||||||
\(19\) | −5.43580 | −0.0656347 | −0.0328173 | − | 0.999461i | \(-0.510448\pi\) | ||||
−0.0328173 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(20\) | 62.6556 | 0.700511 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −86.3735 | −0.837041 | ||||||||
\(23\) | 49.3774 | 0.447648 | 0.223824 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223824 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(24\) | 61.5934 | 0.523862 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −13.3113 | −0.100406 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −87.7179 | −0.592040 | ||||||||
\(29\) | −291.494 | −1.86652 | −0.933261 | − | 0.359200i | \(-0.883050\pi\) | ||||
−0.933261 | + | 0.359200i | \(0.883050\pi\) | |||||||
\(30\) | 67.9669 | 0.413634 | ||||||||
\(31\) | 244.307 | 1.41545 | 0.707724 | − | 0.706489i | \(-0.249722\pi\) | ||||
0.707724 | + | 0.706489i | \(0.249722\pi\) | |||||||
\(32\) | −196.963 | −1.08808 | ||||||||
\(33\) | −57.1868 | −0.301665 | ||||||||
\(34\) | −29.4436 | −0.148516 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 112.780 | 0.522130 | ||||||||
\(37\) | −193.121 | −0.858077 | −0.429038 | − | 0.903286i | \(-0.641147\pi\) | ||||
−0.429038 | + | 0.903286i | \(0.641147\pi\) | |||||||
\(38\) | −24.6303 | −0.105147 | ||||||||
\(39\) | −8.81323 | −0.0361858 | ||||||||
\(40\) | 102.656 | 0.405782 | ||||||||
\(41\) | 315.113 | 1.20030 | 0.600151 | − | 0.799887i | \(-0.295107\pi\) | ||||
0.600151 | + | 0.799887i | \(0.295107\pi\) | |||||||
\(42\) | −95.1537 | −0.349584 | ||||||||
\(43\) | −300.996 | −1.06748 | −0.533738 | − | 0.845650i | \(-0.679213\pi\) | ||||
−0.533738 | + | 0.845650i | \(0.679213\pi\) | |||||||
\(44\) | −238.872 | −0.818437 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 223.735 | 0.717130 | ||||||||
\(47\) | 86.5058 | 0.268472 | 0.134236 | − | 0.990949i | \(-0.457142\pi\) | ||||
0.134236 | + | 0.990949i | \(0.457142\pi\) | |||||||
\(48\) | −21.6595 | −0.0651309 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 113.278 | 0.320399 | ||||||||
\(51\) | −19.4942 | −0.0535242 | ||||||||
\(52\) | −36.8132 | −0.0981745 | ||||||||
\(53\) | 509.677 | 1.32093 | 0.660467 | − | 0.750855i | \(-0.270358\pi\) | ||||
0.660467 | + | 0.750855i | \(0.270358\pi\) | |||||||
\(54\) | 122.340 | 0.308304 | ||||||||
\(55\) | −95.3113 | −0.233669 | ||||||||
\(56\) | −143.718 | −0.342948 | ||||||||
\(57\) | −16.3074 | −0.0378942 | ||||||||
\(58\) | −1320.80 | −2.99016 | ||||||||
\(59\) | −83.3852 | −0.183997 | −0.0919985 | − | 0.995759i | \(-0.529326\pi\) | ||||
−0.0919985 | + | 0.995759i | \(0.529326\pi\) | |||||||
\(60\) | 187.967 | 0.404440 | ||||||||
\(61\) | −5.25291 | −0.0110257 | −0.00551283 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551283 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(62\) | 1106.99 | 2.26754 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −834.706 | −1.63029 | ||||||||
\(65\) | −14.6887 | −0.0280294 | ||||||||
\(66\) | −259.121 | −0.483266 | ||||||||
\(67\) | 205.992 | 0.375611 | 0.187806 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187806 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(68\) | −81.4281 | −0.145215 | ||||||||
\(69\) | 148.132 | 0.258450 | ||||||||
\(70\) | −158.590 | −0.270787 | ||||||||
\(71\) | 1004.31 | 1.67872 | 0.839362 | − | 0.543573i | \(-0.182929\pi\) | ||||
0.839362 | + | 0.543573i | \(0.182929\pi\) | |||||||
\(72\) | 184.780 | 0.302452 | ||||||||
\(73\) | −1007.29 | −1.61499 | −0.807494 | − | 0.589876i | \(-0.799177\pi\) | ||||
−0.807494 | + | 0.589876i | \(0.799177\pi\) | |||||||
\(74\) | −875.055 | −1.37464 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −68.1168 | −0.102810 | ||||||||
\(77\) | 133.436 | 0.197486 | ||||||||
\(78\) | −39.9339 | −0.0579695 | ||||||||
\(79\) | −863.237 | −1.22939 | −0.614695 | − | 0.788765i | \(-0.710721\pi\) | ||||
−0.614695 | + | 0.788765i | \(0.710721\pi\) | |||||||
\(80\) | −36.0992 | −0.0504502 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1427.82 | 1.92288 | ||||||||
\(83\) | 1334.72 | 1.76512 | 0.882560 | − | 0.470200i | \(-0.155818\pi\) | ||||
0.882560 | + | 0.470200i | \(0.155818\pi\) | |||||||
\(84\) | −263.154 | −0.341815 | ||||||||
\(85\) | −32.4903 | −0.0414596 | ||||||||
\(86\) | −1363.85 | −1.71009 | ||||||||
\(87\) | −874.483 | −1.07764 | ||||||||
\(88\) | −391.370 | −0.474093 | ||||||||
\(89\) | 326.249 | 0.388565 | 0.194283 | − | 0.980946i | \(-0.437762\pi\) | ||||
0.194283 | + | 0.980946i | \(0.437762\pi\) | |||||||
\(90\) | 203.901 | 0.238811 | ||||||||
\(91\) | 20.5642 | 0.0236892 | ||||||||
\(92\) | 618.755 | 0.701192 | ||||||||
\(93\) | 732.922 | 0.817210 | ||||||||
\(94\) | 391.969 | 0.430091 | ||||||||
\(95\) | −27.1790 | −0.0293527 | ||||||||
\(96\) | −590.889 | −0.628202 | ||||||||
\(97\) | 1526.77 | 1.59815 | 0.799075 | − | 0.601232i | \(-0.205323\pi\) | ||||
0.799075 | + | 0.601232i | \(0.205323\pi\) | |||||||
\(98\) | 222.025 | 0.228857 | ||||||||
\(99\) | −171.560 | −0.174166 | ||||||||
\(100\) | 313.278 | 0.313278 | ||||||||
\(101\) | 96.8716 | 0.0954365 | 0.0477182 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477182 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(102\) | −88.3307 | −0.0857455 | ||||||||
\(103\) | 1321.99 | 1.26466 | 0.632329 | − | 0.774700i | \(-0.282099\pi\) | ||||
0.632329 | + | 0.774700i | \(0.282099\pi\) | |||||||
\(104\) | −60.3152 | −0.0568691 | ||||||||
\(105\) | −105.000 | −0.0975900 | ||||||||
\(106\) | 2309.41 | 2.11613 | ||||||||
\(107\) | 1745.71 | 1.57724 | 0.788619 | − | 0.614883i | \(-0.210797\pi\) | ||||
0.788619 | + | 0.614883i | \(0.210797\pi\) | |||||||
\(108\) | 338.340 | 0.301452 | ||||||||
\(109\) | 476.856 | 0.419032 | 0.209516 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209516 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(110\) | −431.868 | −0.374336 | ||||||||
\(111\) | −579.362 | −0.495411 | ||||||||
\(112\) | 50.5389 | 0.0426382 | ||||||||
\(113\) | 1641.65 | 1.36666 | 0.683332 | − | 0.730108i | \(-0.260530\pi\) | ||||
0.683332 | + | 0.730108i | \(0.260530\pi\) | |||||||
\(114\) | −73.8910 | −0.0607064 | ||||||||
\(115\) | 246.887 | 0.200194 | ||||||||
\(116\) | −3652.75 | −2.92370 | ||||||||
\(117\) | −26.4397 | −0.0208919 | ||||||||
\(118\) | −377.829 | −0.294763 | ||||||||
\(119\) | 45.4864 | 0.0350398 | ||||||||
\(120\) | 307.967 | 0.234278 | ||||||||
\(121\) | −967.630 | −0.726995 | ||||||||
\(122\) | −23.8016 | −0.0176631 | ||||||||
\(123\) | 945.339 | 0.692994 | ||||||||
\(124\) | 3061.45 | 2.21715 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −285.461 | −0.201833 | ||||||||
\(127\) | −844.016 | −0.589719 | −0.294859 | − | 0.955541i | \(-0.595273\pi\) | ||||
−0.294859 | + | 0.955541i | \(0.595273\pi\) | |||||||
\(128\) | −2206.46 | −1.52363 | ||||||||
\(129\) | −902.988 | −0.616308 | ||||||||
\(130\) | −66.5564 | −0.0449030 | ||||||||
\(131\) | −2796.20 | −1.86493 | −0.932463 | − | 0.361265i | \(-0.882345\pi\) | ||||
−0.932463 | + | 0.361265i | \(0.882345\pi\) | |||||||
\(132\) | −716.615 | −0.472525 | ||||||||
\(133\) | 38.0506 | 0.0248076 | ||||||||
\(134\) | 933.377 | 0.601728 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | −133.413 | −0.0841179 | ||||||||
\(137\) | −2057.13 | −1.28287 | −0.641433 | − | 0.767179i | \(-0.721660\pi\) | ||||
−0.641433 | + | 0.767179i | \(0.721660\pi\) | |||||||
\(138\) | 671.206 | 0.414035 | ||||||||
\(139\) | −1745.12 | −1.06489 | −0.532444 | − | 0.846465i | \(-0.678726\pi\) | ||||
−0.532444 | + | 0.846465i | \(0.678726\pi\) | |||||||
\(140\) | −438.590 | −0.264768 | ||||||||
\(141\) | 259.517 | 0.155002 | ||||||||
\(142\) | 4550.65 | 2.68931 | ||||||||
\(143\) | 56.0000 | 0.0327479 | ||||||||
\(144\) | −64.9786 | −0.0376033 | ||||||||
\(145\) | −1457.47 | −0.834734 | ||||||||
\(146\) | −4564.15 | −2.58720 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | −2420.02 | −1.34408 | ||||||||
\(149\) | −1173.57 | −0.645254 | −0.322627 | − | 0.946526i | \(-0.604566\pi\) | ||||
−0.322627 | + | 0.946526i | \(0.604566\pi\) | |||||||
\(150\) | 339.835 | 0.184983 | ||||||||
\(151\) | 1540.07 | 0.829994 | 0.414997 | − | 0.909823i | \(-0.363783\pi\) | ||||
0.414997 | + | 0.909823i | \(0.363783\pi\) | |||||||
\(152\) | −111.603 | −0.0595540 | ||||||||
\(153\) | −58.4826 | −0.0309022 | ||||||||
\(154\) | 604.615 | 0.316372 | ||||||||
\(155\) | 1221.54 | 0.633008 | ||||||||
\(156\) | −110.440 | −0.0566811 | ||||||||
\(157\) | −2544.53 | −1.29348 | −0.646738 | − | 0.762712i | \(-0.723867\pi\) | ||||
−0.646738 | + | 0.762712i | \(0.723867\pi\) | |||||||
\(158\) | −3911.44 | −1.96948 | ||||||||
\(159\) | 1529.03 | 0.762642 | ||||||||
\(160\) | −984.815 | −0.486603 | ||||||||
\(161\) | −345.642 | −0.169195 | ||||||||
\(162\) | 367.021 | 0.178000 | ||||||||
\(163\) | −594.708 | −0.285774 | −0.142887 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142887 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(164\) | 3948.72 | 1.88014 | ||||||||
\(165\) | −285.934 | −0.134909 | ||||||||
\(166\) | 6047.81 | 2.82772 | ||||||||
\(167\) | 928.498 | 0.430236 | 0.215118 | − | 0.976588i | \(-0.430986\pi\) | ||||
0.215118 | + | 0.976588i | \(0.430986\pi\) | |||||||
\(168\) | −431.154 | −0.198001 | ||||||||
\(169\) | −2188.37 | −0.996072 | ||||||||
\(170\) | −147.218 | −0.0664182 | ||||||||
\(171\) | −48.9222 | −0.0218782 | ||||||||
\(172\) | −3771.82 | −1.67209 | ||||||||
\(173\) | −315.642 | −0.138716 | −0.0693578 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693578 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(174\) | −3962.39 | −1.72637 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | 137.626 | 0.0589431 | ||||||||
\(177\) | −250.156 | −0.106231 | ||||||||
\(178\) | 1478.28 | 0.622480 | ||||||||
\(179\) | −1445.49 | −0.603581 | −0.301791 | − | 0.953374i | \(-0.597584\pi\) | ||||
−0.301791 | + | 0.953374i | \(0.597584\pi\) | |||||||
\(180\) | 563.901 | 0.233504 | ||||||||
\(181\) | −1843.81 | −0.757180 | −0.378590 | − | 0.925564i | \(-0.623591\pi\) | ||||
−0.378590 | + | 0.925564i | \(0.623591\pi\) | |||||||
\(182\) | 93.1790 | 0.0379499 | ||||||||
\(183\) | −15.7587 | −0.00636567 | ||||||||
\(184\) | 1013.77 | 0.406176 | ||||||||
\(185\) | −965.603 | −0.383744 | ||||||||
\(186\) | 3320.97 | 1.30917 | ||||||||
\(187\) | 123.868 | 0.0484391 | ||||||||
\(188\) | 1084.02 | 0.420532 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −123.152 | −0.0470229 | ||||||||
\(191\) | −244.074 | −0.0924637 | −0.0462318 | − | 0.998931i | \(-0.514721\pi\) | ||||
−0.0462318 | + | 0.998931i | \(0.514721\pi\) | |||||||
\(192\) | −2504.12 | −0.941246 | ||||||||
\(193\) | −1733.03 | −0.646355 | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||||
−0.323178 | + | 0.946338i | \(0.604751\pi\) | |||||||
\(194\) | 6918.01 | 2.56023 | ||||||||
\(195\) | −44.0661 | −0.0161828 | ||||||||
\(196\) | 614.025 | 0.223770 | ||||||||
\(197\) | 358.230 | 0.129557 | 0.0647787 | − | 0.997900i | \(-0.479366\pi\) | ||||
0.0647787 | + | 0.997900i | \(0.479366\pi\) | |||||||
\(198\) | −777.362 | −0.279014 | ||||||||
\(199\) | −3203.63 | −1.14120 | −0.570601 | − | 0.821227i | \(-0.693290\pi\) | ||||
−0.570601 | + | 0.821227i | \(0.693290\pi\) | |||||||
\(200\) | 513.278 | 0.181471 | ||||||||
\(201\) | 617.977 | 0.216859 | ||||||||
\(202\) | 438.938 | 0.152889 | ||||||||
\(203\) | 2040.46 | 0.705479 | ||||||||
\(204\) | −244.284 | −0.0838398 | ||||||||
\(205\) | 1575.56 | 0.536791 | ||||||||
\(206\) | 5990.12 | 2.02598 | ||||||||
\(207\) | 444.397 | 0.149216 | ||||||||
\(208\) | 21.2100 | 0.00707044 | ||||||||
\(209\) | 103.619 | 0.0342940 | ||||||||
\(210\) | −475.769 | −0.156339 | ||||||||
\(211\) | 4943.16 | 1.61280 | 0.806401 | − | 0.591369i | \(-0.201412\pi\) | ||||
0.806401 | + | 0.591369i | \(0.201412\pi\) | |||||||
\(212\) | 6386.83 | 2.06910 | ||||||||
\(213\) | 3012.92 | 0.969211 | ||||||||
\(214\) | 7910.05 | 2.52673 | ||||||||
\(215\) | −1504.98 | −0.477390 | ||||||||
\(216\) | 554.340 | 0.174621 | ||||||||
\(217\) | −1710.15 | −0.534989 | ||||||||
\(218\) | 2160.70 | 0.671288 | ||||||||
\(219\) | −3021.86 | −0.932414 | ||||||||
\(220\) | −1194.36 | −0.366016 | ||||||||
\(221\) | 19.0896 | 0.00581044 | ||||||||
\(222\) | −2625.16 | −0.793646 | ||||||||
\(223\) | 3160.15 | 0.948965 | 0.474482 | − | 0.880265i | \(-0.342635\pi\) | ||||
0.474482 | + | 0.880265i | \(0.342635\pi\) | |||||||
\(224\) | 1378.74 | 0.411255 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 7438.51 | 2.18939 | ||||||||
\(227\) | −3651.11 | −1.06755 | −0.533773 | − | 0.845628i | \(-0.679226\pi\) | ||||
−0.533773 | + | 0.845628i | \(0.679226\pi\) | |||||||
\(228\) | −204.350 | −0.0593571 | ||||||||
\(229\) | −4083.70 | −1.17842 | −0.589210 | − | 0.807980i | \(-0.700561\pi\) | ||||
−0.589210 | + | 0.807980i | \(0.700561\pi\) | |||||||
\(230\) | 1118.68 | 0.320710 | ||||||||
\(231\) | 400.307 | 0.114019 | ||||||||
\(232\) | −5984.70 | −1.69360 | ||||||||
\(233\) | −3682.51 | −1.03540 | −0.517702 | − | 0.855561i | \(-0.673212\pi\) | ||||
−0.517702 | + | 0.855561i | \(0.673212\pi\) | |||||||
\(234\) | −119.802 | −0.0334687 | ||||||||
\(235\) | 432.529 | 0.120064 | ||||||||
\(236\) | −1044.91 | −0.288211 | ||||||||
\(237\) | −2589.71 | −0.709789 | ||||||||
\(238\) | 206.105 | 0.0561336 | ||||||||
\(239\) | 2658.78 | 0.719591 | 0.359796 | − | 0.933031i | \(-0.382846\pi\) | ||||
0.359796 | + | 0.933031i | \(0.382846\pi\) | |||||||
\(240\) | −108.298 | −0.0291274 | ||||||||
\(241\) | −4820.39 | −1.28842 | −0.644209 | − | 0.764850i | \(-0.722813\pi\) | ||||
−0.644209 | + | 0.764850i | \(0.722813\pi\) | |||||||
\(242\) | −4384.46 | −1.16464 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −65.8249 | −0.0172705 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 4283.45 | 1.11017 | ||||||||
\(247\) | 15.9690 | 0.00411369 | ||||||||
\(248\) | 5015.91 | 1.28432 | ||||||||
\(249\) | 4004.17 | 1.01909 | ||||||||
\(250\) | 566.391 | 0.143287 | ||||||||
\(251\) | 1672.27 | 0.420530 | 0.210265 | − | 0.977644i | \(-0.432567\pi\) | ||||
0.210265 | + | 0.977644i | \(0.432567\pi\) | |||||||
\(252\) | −789.461 | −0.197347 | ||||||||
\(253\) | −941.245 | −0.233896 | ||||||||
\(254\) | −3824.34 | −0.944727 | ||||||||
\(255\) | −97.4709 | −0.0239367 | ||||||||
\(256\) | −3320.09 | −0.810569 | ||||||||
\(257\) | −3697.74 | −0.897506 | −0.448753 | − | 0.893656i | \(-0.648132\pi\) | ||||
−0.448753 | + | 0.893656i | \(0.648132\pi\) | |||||||
\(258\) | −4091.56 | −0.987322 | ||||||||
\(259\) | 1351.84 | 0.324323 | ||||||||
\(260\) | −184.066 | −0.0439050 | ||||||||
\(261\) | −2623.45 | −0.622174 | ||||||||
\(262\) | −12670.0 | −2.98760 | ||||||||
\(263\) | 7319.00 | 1.71600 | 0.858002 | − | 0.513646i | \(-0.171706\pi\) | ||||
0.858002 | + | 0.513646i | \(0.171706\pi\) | |||||||
\(264\) | −1174.11 | −0.273717 | ||||||||
\(265\) | 2548.39 | 0.590740 | ||||||||
\(266\) | 172.412 | 0.0397416 | ||||||||
\(267\) | 978.747 | 0.224338 | ||||||||
\(268\) | 2581.32 | 0.588354 | ||||||||
\(269\) | −815.097 | −0.184749 | −0.0923743 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923743 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(270\) | 611.702 | 0.137878 | ||||||||
\(271\) | −5106.02 | −1.14453 | −0.572267 | − | 0.820068i | \(-0.693936\pi\) | ||||
−0.572267 | + | 0.820068i | \(0.693936\pi\) | |||||||
\(272\) | 46.9150 | 0.0104582 | ||||||||
\(273\) | 61.6926 | 0.0136769 | ||||||||
\(274\) | −9321.13 | −2.05515 | ||||||||
\(275\) | −476.556 | −0.104500 | ||||||||
\(276\) | 1856.26 | 0.404833 | ||||||||
\(277\) | 1398.72 | 0.303398 | 0.151699 | − | 0.988427i | \(-0.451526\pi\) | ||||
0.151699 | + | 0.988427i | \(0.451526\pi\) | |||||||
\(278\) | −7907.39 | −1.70595 | ||||||||
\(279\) | 2198.77 | 0.471816 | ||||||||
\(280\) | −718.590 | −0.153371 | ||||||||
\(281\) | −7102.38 | −1.50780 | −0.753901 | − | 0.656988i | \(-0.771830\pi\) | ||||
−0.753901 | + | 0.656988i | \(0.771830\pi\) | |||||||
\(282\) | 1175.91 | 0.248313 | ||||||||
\(283\) | 4465.18 | 0.937907 | 0.468953 | − | 0.883223i | \(-0.344631\pi\) | ||||
0.468953 | + | 0.883223i | \(0.344631\pi\) | |||||||
\(284\) | 12585.1 | 2.62954 | ||||||||
\(285\) | −81.5371 | −0.0169468 | ||||||||
\(286\) | 253.743 | 0.0524621 | ||||||||
\(287\) | −2205.79 | −0.453671 | ||||||||
\(288\) | −1772.67 | −0.362692 | ||||||||
\(289\) | −4870.78 | −0.991405 | ||||||||
\(290\) | −6603.99 | −1.33724 | ||||||||
\(291\) | 4580.32 | 0.922692 | ||||||||
\(292\) | −12622.5 | −2.52970 | ||||||||
\(293\) | 7590.61 | 1.51348 | 0.756738 | − | 0.653718i | \(-0.226792\pi\) | ||||
0.756738 | + | 0.653718i | \(0.226792\pi\) | |||||||
\(294\) | 666.076 | 0.132130 | ||||||||
\(295\) | −416.926 | −0.0822860 | ||||||||
\(296\) | −3964.98 | −0.778581 | ||||||||
\(297\) | −514.681 | −0.100555 | ||||||||
\(298\) | −5317.61 | −1.03369 | ||||||||
\(299\) | −145.058 | −0.0280566 | ||||||||
\(300\) | 939.835 | 0.180871 | ||||||||
\(301\) | 2106.97 | 0.403468 | ||||||||
\(302\) | 6978.26 | 1.32965 | ||||||||
\(303\) | 290.615 | 0.0551003 | ||||||||
\(304\) | 39.2456 | 0.00740425 | ||||||||
\(305\) | −26.2645 | −0.00493083 | ||||||||
\(306\) | −264.992 | −0.0495052 | ||||||||
\(307\) | 9480.12 | 1.76241 | 0.881203 | − | 0.472737i | \(-0.156734\pi\) | ||||
0.881203 | + | 0.472737i | \(0.156734\pi\) | |||||||
\(308\) | 1672.10 | 0.309340 | ||||||||
\(309\) | 3965.98 | 0.730151 | ||||||||
\(310\) | 5534.94 | 1.01408 | ||||||||
\(311\) | 7078.01 | 1.29054 | 0.645268 | − | 0.763956i | \(-0.276746\pi\) | ||||
0.645268 | + | 0.763956i | \(0.276746\pi\) | |||||||
\(312\) | −180.945 | −0.0328334 | ||||||||
\(313\) | 5593.84 | 1.01017 | 0.505084 | − | 0.863070i | \(-0.331461\pi\) | ||||
0.505084 | + | 0.863070i | \(0.331461\pi\) | |||||||
\(314\) | −11529.6 | −2.07214 | ||||||||
\(315\) | −315.000 | −0.0563436 | ||||||||
\(316\) | −10817.3 | −1.92571 | ||||||||
\(317\) | 3567.81 | 0.632139 | 0.316070 | − | 0.948736i | \(-0.397637\pi\) | ||||
0.316070 | + | 0.948736i | \(0.397637\pi\) | |||||||
\(318\) | 6928.24 | 1.22175 | ||||||||
\(319\) | 5556.54 | 0.975255 | ||||||||
\(320\) | −4173.53 | −0.729086 | ||||||||
\(321\) | 5237.14 | 0.910618 | ||||||||
\(322\) | −1566.15 | −0.271050 | ||||||||
\(323\) | 35.3222 | 0.00608477 | ||||||||
\(324\) | 1015.02 | 0.174043 | ||||||||
\(325\) | −73.4436 | −0.0125351 | ||||||||
\(326\) | −2694.70 | −0.457809 | ||||||||
\(327\) | 1430.57 | 0.241928 | ||||||||
\(328\) | 6469.62 | 1.08910 | ||||||||
\(329\) | −605.541 | −0.101473 | ||||||||
\(330\) | −1295.60 | −0.216123 | ||||||||
\(331\) | −4389.67 | −0.728936 | −0.364468 | − | 0.931216i | \(-0.618749\pi\) | ||||
−0.364468 | + | 0.931216i | \(0.618749\pi\) | |||||||
\(332\) | 16725.6 | 2.76487 | ||||||||
\(333\) | −1738.09 | −0.286026 | ||||||||
\(334\) | 4207.14 | 0.689236 | ||||||||
\(335\) | 1029.96 | 0.167978 | ||||||||
\(336\) | 151.617 | 0.0246172 | ||||||||
\(337\) | 2348.83 | 0.379671 | 0.189835 | − | 0.981816i | \(-0.439205\pi\) | ||||
0.189835 | + | 0.981816i | \(0.439205\pi\) | |||||||
\(338\) | −9915.79 | −1.59570 | ||||||||
\(339\) | 4924.94 | 0.789044 | ||||||||
\(340\) | −407.140 | −0.0649420 | ||||||||
\(341\) | −4657.05 | −0.739570 | ||||||||
\(342\) | −221.673 | −0.0350488 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −6179.79 | −0.968581 | ||||||||
\(345\) | 740.661 | 0.115582 | ||||||||
\(346\) | −1430.21 | −0.222222 | ||||||||
\(347\) | 558.436 | 0.0863931 | 0.0431965 | − | 0.999067i | \(-0.486246\pi\) | ||||
0.0431965 | + | 0.999067i | \(0.486246\pi\) | |||||||
\(348\) | −10958.3 | −1.68800 | ||||||||
\(349\) | 3233.89 | 0.496006 | 0.248003 | − | 0.968759i | \(-0.420226\pi\) | ||||
0.248003 | + | 0.968759i | \(0.420226\pi\) | |||||||
\(350\) | −792.948 | −0.121100 | ||||||||
\(351\) | −79.3190 | −0.0120619 | ||||||||
\(352\) | 3754.56 | 0.568519 | ||||||||
\(353\) | −7516.35 | −1.13330 | −0.566650 | − | 0.823959i | \(-0.691761\pi\) | ||||
−0.566650 | + | 0.823959i | \(0.691761\pi\) | |||||||
\(354\) | −1133.49 | −0.170181 | ||||||||
\(355\) | 5021.54 | 0.750748 | ||||||||
\(356\) | 4088.27 | 0.608646 | ||||||||
\(357\) | 136.459 | 0.0202302 | ||||||||
\(358\) | −6549.70 | −0.966935 | ||||||||
\(359\) | −6577.76 | −0.967021 | −0.483511 | − | 0.875338i | \(-0.660639\pi\) | ||||
−0.483511 | + | 0.875338i | \(0.660639\pi\) | |||||||
\(360\) | 923.901 | 0.135261 | ||||||||
\(361\) | −6829.45 | −0.995692 | ||||||||
\(362\) | −8354.56 | −1.21300 | ||||||||
\(363\) | −2902.89 | −0.419731 | ||||||||
\(364\) | 257.693 | 0.0371065 | ||||||||
\(365\) | −5036.44 | −0.722245 | ||||||||
\(366\) | −71.4048 | −0.0101978 | ||||||||
\(367\) | 8307.17 | 1.18155 | 0.590777 | − | 0.806835i | \(-0.298821\pi\) | ||||
0.590777 | + | 0.806835i | \(0.298821\pi\) | |||||||
\(368\) | −356.497 | −0.0504992 | ||||||||
\(369\) | 2836.02 | 0.400101 | ||||||||
\(370\) | −4375.27 | −0.614756 | ||||||||
\(371\) | −3567.74 | −0.499266 | ||||||||
\(372\) | 9184.34 | 1.28007 | ||||||||
\(373\) | −4551.09 | −0.631760 | −0.315880 | − | 0.948799i | \(-0.602300\pi\) | ||||
−0.315880 | + | 0.948799i | \(0.602300\pi\) | |||||||
\(374\) | 561.261 | 0.0775992 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 1776.06 | 0.243599 | ||||||||
\(377\) | 856.335 | 0.116985 | ||||||||
\(378\) | −856.383 | −0.116528 | ||||||||
\(379\) | −1788.29 | −0.242370 | −0.121185 | − | 0.992630i | \(-0.538669\pi\) | ||||
−0.121185 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(380\) | −340.584 | −0.0459778 | ||||||||
\(381\) | −2532.05 | −0.340474 | ||||||||
\(382\) | −1105.93 | −0.148126 | ||||||||
\(383\) | −1358.47 | −0.181240 | −0.0906199 | − | 0.995886i | \(-0.528885\pi\) | ||||
−0.0906199 | + | 0.995886i | \(0.528885\pi\) | |||||||
\(384\) | −6619.37 | −0.879670 | ||||||||
\(385\) | 667.179 | 0.0883184 | ||||||||
\(386\) | −7852.60 | −1.03546 | ||||||||
\(387\) | −2708.97 | −0.355825 | ||||||||
\(388\) | 19132.2 | 2.50333 | ||||||||
\(389\) | 9722.54 | 1.26723 | 0.633615 | − | 0.773649i | \(-0.281570\pi\) | ||||
0.633615 | + | 0.773649i | \(0.281570\pi\) | |||||||
\(390\) | −199.669 | −0.0259247 | ||||||||
\(391\) | −320.858 | −0.0414999 | ||||||||
\(392\) | 1006.03 | 0.129622 | ||||||||
\(393\) | −8388.61 | −1.07672 | ||||||||
\(394\) | 1623.19 | 0.207551 | ||||||||
\(395\) | −4316.19 | −0.549800 | ||||||||
\(396\) | −2149.84 | −0.272812 | ||||||||
\(397\) | −4788.04 | −0.605302 | −0.302651 | − | 0.953101i | \(-0.597872\pi\) | ||||
−0.302651 | + | 0.953101i | \(0.597872\pi\) | |||||||
\(398\) | −14516.1 | −1.82820 | ||||||||
\(399\) | 114.152 | 0.0143227 | ||||||||
\(400\) | −180.496 | −0.0225620 | ||||||||
\(401\) | 9681.41 | 1.20565 | 0.602826 | − | 0.797873i | \(-0.294041\pi\) | ||||
0.602826 | + | 0.797873i | \(0.294041\pi\) | |||||||
\(402\) | 2800.13 | 0.347408 | ||||||||
\(403\) | −717.712 | −0.0887141 | ||||||||
\(404\) | 1213.91 | 0.149491 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 9245.58 | 1.13017 | ||||||||
\(407\) | 3681.32 | 0.448344 | ||||||||
\(408\) | −400.238 | −0.0485655 | ||||||||
\(409\) | 11113.1 | 1.34353 | 0.671767 | − | 0.740763i | \(-0.265536\pi\) | ||||
0.671767 | + | 0.740763i | \(0.265536\pi\) | |||||||
\(410\) | 7139.09 | 0.859937 | ||||||||
\(411\) | −6171.40 | −0.740663 | ||||||||
\(412\) | 16566.1 | 1.98095 | ||||||||
\(413\) | 583.696 | 0.0695443 | ||||||||
\(414\) | 2013.62 | 0.239043 | ||||||||
\(415\) | 6673.62 | 0.789386 | ||||||||
\(416\) | 578.627 | 0.0681959 | ||||||||
\(417\) | −5235.37 | −0.614814 | ||||||||
\(418\) | 469.510 | 0.0549389 | ||||||||
\(419\) | −1230.09 | −0.143421 | −0.0717107 | − | 0.997425i | \(-0.522846\pi\) | ||||
−0.0717107 | + | 0.997425i | \(0.522846\pi\) | |||||||
\(420\) | −1315.77 | −0.152864 | ||||||||
\(421\) | −12356.5 | −1.43044 | −0.715222 | − | 0.698897i | \(-0.753674\pi\) | ||||
−0.715222 | + | 0.698897i | \(0.753674\pi\) | |||||||
\(422\) | 22398.1 | 2.58370 | ||||||||
\(423\) | 778.552 | 0.0894906 | ||||||||
\(424\) | 10464.2 | 1.19856 | ||||||||
\(425\) | −162.452 | −0.0185413 | ||||||||
\(426\) | 13651.9 | 1.55267 | ||||||||
\(427\) | 36.7703 | 0.00416731 | ||||||||
\(428\) | 21875.7 | 2.47057 | ||||||||
\(429\) | 168.000 | 0.0189070 | ||||||||
\(430\) | −6819.26 | −0.764777 | ||||||||
\(431\) | −7375.27 | −0.824256 | −0.412128 | − | 0.911126i | \(-0.635214\pi\) | ||||
−0.412128 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(432\) | −194.936 | −0.0217103 | ||||||||
\(433\) | −690.067 | −0.0765877 | −0.0382939 | − | 0.999267i | \(-0.512192\pi\) | ||||
−0.0382939 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(434\) | −7748.92 | −0.857051 | ||||||||
\(435\) | −4372.41 | −0.481934 | ||||||||
\(436\) | 5975.55 | 0.656369 | ||||||||
\(437\) | −268.406 | −0.0293812 | ||||||||
\(438\) | −13692.5 | −1.49372 | ||||||||
\(439\) | 8408.79 | 0.914191 | 0.457095 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457095 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(440\) | −1956.85 | −0.212021 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 86.4976 | 0.00930830 | ||||||||
\(443\) | 6568.55 | 0.704473 | 0.352236 | − | 0.935911i | \(-0.385421\pi\) | ||||
0.352236 | + | 0.935911i | \(0.385421\pi\) | |||||||
\(444\) | −7260.06 | −0.776007 | ||||||||
\(445\) | 1631.25 | 0.173772 | ||||||||
\(446\) | 14319.0 | 1.52024 | ||||||||
\(447\) | −3520.72 | −0.372537 | ||||||||
\(448\) | 5842.94 | 0.616190 | ||||||||
\(449\) | 2954.55 | 0.310543 | 0.155271 | − | 0.987872i | \(-0.450375\pi\) | ||||
0.155271 | + | 0.987872i | \(0.450375\pi\) | |||||||
\(450\) | 1019.50 | 0.106800 | ||||||||
\(451\) | −6006.76 | −0.627156 | ||||||||
\(452\) | 20571.7 | 2.14073 | ||||||||
\(453\) | 4620.21 | 0.479197 | ||||||||
\(454\) | −16543.7 | −1.71020 | ||||||||
\(455\) | 102.821 | 0.0105941 | ||||||||
\(456\) | −334.810 | −0.0343835 | ||||||||
\(457\) | −8144.84 | −0.833697 | −0.416849 | − | 0.908976i | \(-0.636865\pi\) | ||||
−0.416849 | + | 0.908976i | \(0.636865\pi\) | |||||||
\(458\) | −18503.8 | −1.88782 | ||||||||
\(459\) | −175.448 | −0.0178414 | ||||||||
\(460\) | 3093.77 | 0.313583 | ||||||||
\(461\) | 2495.26 | 0.252095 | 0.126048 | − | 0.992024i | \(-0.459771\pi\) | ||||
0.126048 | + | 0.992024i | \(0.459771\pi\) | |||||||
\(462\) | 1813.84 | 0.182657 | ||||||||
\(463\) | −5755.66 | −0.577728 | −0.288864 | − | 0.957370i | \(-0.593278\pi\) | ||||
−0.288864 | + | 0.957370i | \(0.593278\pi\) | |||||||
\(464\) | 2104.54 | 0.210562 | ||||||||
\(465\) | 3664.61 | 0.365467 | ||||||||
\(466\) | −16685.9 | −1.65871 | ||||||||
\(467\) | −4143.73 | −0.410598 | −0.205299 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205299 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(468\) | −331.319 | −0.0327248 | ||||||||
\(469\) | −1441.95 | −0.141968 | ||||||||
\(470\) | 1959.84 | 0.192342 | ||||||||
\(471\) | −7633.60 | −0.746789 | ||||||||
\(472\) | −1711.99 | −0.166951 | ||||||||
\(473\) | 5737.67 | 0.557755 | ||||||||
\(474\) | −11734.3 | −1.13708 | ||||||||
\(475\) | −135.895 | −0.0131269 | ||||||||
\(476\) | 569.996 | 0.0548860 | ||||||||
\(477\) | 4587.09 | 0.440312 | ||||||||
\(478\) | 12047.3 | 1.15278 | ||||||||
\(479\) | −6765.96 | −0.645396 | −0.322698 | − | 0.946502i | \(-0.604590\pi\) | ||||
−0.322698 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(480\) | −2954.45 | −0.280940 | ||||||||
\(481\) | 567.339 | 0.0537805 | ||||||||
\(482\) | −21841.8 | −2.06404 | ||||||||
\(483\) | −1036.93 | −0.0976848 | ||||||||
\(484\) | −12125.5 | −1.13876 | ||||||||
\(485\) | 7633.87 | 0.714714 | ||||||||
\(486\) | 1101.06 | 0.102768 | ||||||||
\(487\) | 6360.42 | 0.591824 | 0.295912 | − | 0.955215i | \(-0.404377\pi\) | ||||
0.295912 | + | 0.955215i | \(0.404377\pi\) | |||||||
\(488\) | −107.848 | −0.0100042 | ||||||||
\(489\) | −1784.12 | −0.164992 | ||||||||
\(490\) | 1110.13 | 0.102348 | ||||||||
\(491\) | −7072.54 | −0.650060 | −0.325030 | − | 0.945704i | \(-0.605374\pi\) | ||||
−0.325030 | + | 0.945704i | \(0.605374\pi\) | |||||||
\(492\) | 11846.2 | 1.08550 | ||||||||
\(493\) | 1894.15 | 0.173039 | ||||||||
\(494\) | 72.3576 | 0.00659012 | ||||||||
\(495\) | −857.802 | −0.0778895 | ||||||||
\(496\) | −1763.86 | −0.159677 | ||||||||
\(497\) | −7030.15 | −0.634498 | ||||||||
\(498\) | 18143.4 | 1.63258 | ||||||||
\(499\) | −18473.9 | −1.65732 | −0.828661 | − | 0.559751i | \(-0.810897\pi\) | ||||
−0.828661 | + | 0.559751i | \(0.810897\pi\) | |||||||
\(500\) | 1566.39 | 0.140102 | ||||||||
\(501\) | 2785.49 | 0.248397 | ||||||||
\(502\) | 7577.28 | 0.673687 | ||||||||
\(503\) | 11379.2 | 1.00869 | 0.504347 | − | 0.863501i | \(-0.331733\pi\) | ||||
0.504347 | + | 0.863501i | \(0.331733\pi\) | |||||||
\(504\) | −1293.46 | −0.114316 | ||||||||
\(505\) | 484.358 | 0.0426805 | ||||||||
\(506\) | −4264.90 | −0.374700 | ||||||||
\(507\) | −6565.11 | −0.575082 | ||||||||
\(508\) | −10576.5 | −0.923730 | ||||||||
\(509\) | 6064.48 | 0.528101 | 0.264051 | − | 0.964509i | \(-0.414941\pi\) | ||||
0.264051 | + | 0.964509i | \(0.414941\pi\) | |||||||
\(510\) | −441.653 | −0.0383465 | ||||||||
\(511\) | 7051.02 | 0.610408 | ||||||||
\(512\) | 2607.89 | 0.225105 | ||||||||
\(513\) | −146.767 | −0.0126314 | ||||||||
\(514\) | −16755.0 | −1.43780 | ||||||||
\(515\) | 6609.96 | 0.565572 | ||||||||
\(516\) | −11315.5 | −0.965379 | ||||||||
\(517\) | −1649.00 | −0.140276 | ||||||||
\(518\) | 6125.38 | 0.519563 | ||||||||
\(519\) | −946.926 | −0.0800875 | ||||||||
\(520\) | −301.576 | −0.0254326 | ||||||||
\(521\) | 2682.88 | 0.225603 | 0.112801 | − | 0.993618i | \(-0.464018\pi\) | ||||
0.112801 | + | 0.993618i | \(0.464018\pi\) | |||||||
\(522\) | −11887.2 | −0.996720 | ||||||||
\(523\) | −4309.02 | −0.360268 | −0.180134 | − | 0.983642i | \(-0.557653\pi\) | ||||
−0.180134 | + | 0.983642i | \(0.557653\pi\) | |||||||
\(524\) | −35039.6 | −2.92120 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 33163.3 | 2.74903 | ||||||||
\(527\) | −1587.52 | −0.131221 | ||||||||
\(528\) | 412.879 | 0.0340308 | ||||||||
\(529\) | −9728.87 | −0.799611 | ||||||||
\(530\) | 11547.1 | 0.946363 | ||||||||
\(531\) | −750.467 | −0.0613323 | ||||||||
\(532\) | 476.817 | 0.0388584 | ||||||||
\(533\) | −925.720 | −0.0752296 | ||||||||
\(534\) | 4434.83 | 0.359389 | ||||||||
\(535\) | 8728.56 | 0.705362 | ||||||||
\(536\) | 4229.25 | 0.340813 | ||||||||
\(537\) | −4336.47 | −0.348478 | ||||||||
\(538\) | −3693.31 | −0.295966 | ||||||||
\(539\) | −934.051 | −0.0746427 | ||||||||
\(540\) | 1691.70 | 0.134813 | ||||||||
\(541\) | 4081.47 | 0.324355 | 0.162178 | − | 0.986762i | \(-0.448148\pi\) | ||||
0.162178 | + | 0.986762i | \(0.448148\pi\) | |||||||
\(542\) | −23136.0 | −1.83354 | ||||||||
\(543\) | −5531.44 | −0.437158 | ||||||||
\(544\) | 1279.88 | 0.100872 | ||||||||
\(545\) | 2384.28 | 0.187397 | ||||||||
\(546\) | 279.537 | 0.0219104 | ||||||||
\(547\) | 8844.82 | 0.691366 | 0.345683 | − | 0.938351i | \(-0.387647\pi\) | ||||
0.345683 | + | 0.938351i | \(0.387647\pi\) | |||||||
\(548\) | −25778.2 | −2.00947 | ||||||||
\(549\) | −47.2762 | −0.00367522 | ||||||||
\(550\) | −2159.34 | −0.167408 | ||||||||
\(551\) | 1584.51 | 0.122509 | ||||||||
\(552\) | 3041.32 | 0.234506 | ||||||||
\(553\) | 6042.66 | 0.464666 | ||||||||
\(554\) | 6337.80 | 0.486042 | ||||||||
\(555\) | −2896.81 | −0.221554 | ||||||||
\(556\) | −21868.4 | −1.66803 | ||||||||
\(557\) | −11144.7 | −0.847787 | −0.423894 | − | 0.905712i | \(-0.639337\pi\) | ||||
−0.423894 | + | 0.905712i | \(0.639337\pi\) | |||||||
\(558\) | 9962.90 | 0.755848 | ||||||||
\(559\) | 884.249 | 0.0669047 | ||||||||
\(560\) | 252.694 | 0.0190684 | ||||||||
\(561\) | 371.603 | 0.0279663 | ||||||||
\(562\) | −32181.8 | −2.41549 | ||||||||
\(563\) | −21857.5 | −1.63621 | −0.818104 | − | 0.575071i | \(-0.804975\pi\) | ||||
−0.818104 | + | 0.575071i | \(0.804975\pi\) | |||||||
\(564\) | 3252.05 | 0.242794 | ||||||||
\(565\) | 8208.23 | 0.611191 | ||||||||
\(566\) | 20232.3 | 1.50252 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 20619.6 | 1.52320 | ||||||||
\(569\) | 23496.4 | 1.73115 | 0.865573 | − | 0.500783i | \(-0.166954\pi\) | ||||
0.865573 | + | 0.500783i | \(0.166954\pi\) | |||||||
\(570\) | −369.455 | −0.0271487 | ||||||||
\(571\) | 11067.8 | 0.811164 | 0.405582 | − | 0.914059i | \(-0.367069\pi\) | ||||
0.405582 | + | 0.914059i | \(0.367069\pi\) | |||||||
\(572\) | 701.743 | 0.0512961 | ||||||||
\(573\) | −732.222 | −0.0533839 | ||||||||
\(574\) | −9994.72 | −0.726780 | ||||||||
\(575\) | 1234.44 | 0.0895296 | ||||||||
\(576\) | −7512.36 | −0.543429 | ||||||||
\(577\) | 20482.9 | 1.47784 | 0.738922 | − | 0.673791i | \(-0.235335\pi\) | ||||
0.738922 | + | 0.673791i | \(0.235335\pi\) | |||||||
\(578\) | −22070.1 | −1.58823 | ||||||||
\(579\) | −5199.10 | −0.373173 | ||||||||
\(580\) | −18263.8 | −1.30752 | ||||||||
\(581\) | −9343.07 | −0.667153 | ||||||||
\(582\) | 20754.0 | 1.47815 | ||||||||
\(583\) | −9715.60 | −0.690187 | ||||||||
\(584\) | −20680.8 | −1.46537 | ||||||||
\(585\) | −132.198 | −0.00934313 | ||||||||
\(586\) | 34394.1 | 2.42458 | ||||||||
\(587\) | −23444.3 | −1.64847 | −0.824235 | − | 0.566248i | \(-0.808394\pi\) | ||||
−0.824235 | + | 0.566248i | \(0.808394\pi\) | |||||||
\(588\) | 1842.08 | 0.129194 | ||||||||
\(589\) | −1328.01 | −0.0929025 | ||||||||
\(590\) | −1889.14 | −0.131822 | ||||||||
\(591\) | 1074.69 | 0.0748000 | ||||||||
\(592\) | 1394.30 | 0.0967996 | ||||||||
\(593\) | 4404.69 | 0.305024 | 0.152512 | − | 0.988302i | \(-0.451264\pi\) | ||||
0.152512 | + | 0.988302i | \(0.451264\pi\) | |||||||
\(594\) | −2332.09 | −0.161089 | ||||||||
\(595\) | 227.432 | 0.0156703 | ||||||||
\(596\) | −14706.2 | −1.01072 | ||||||||
\(597\) | −9610.89 | −0.658874 | ||||||||
\(598\) | −657.277 | −0.0449466 | ||||||||
\(599\) | 3327.05 | 0.226945 | 0.113472 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113472 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(600\) | 1539.83 | 0.104772 | ||||||||
\(601\) | −14244.8 | −0.966818 | −0.483409 | − | 0.875395i | \(-0.660602\pi\) | ||||
−0.483409 | + | 0.875395i | \(0.660602\pi\) | |||||||
\(602\) | 9546.97 | 0.646354 | ||||||||
\(603\) | 1853.93 | 0.125204 | ||||||||
\(604\) | 19298.8 | 1.30010 | ||||||||
\(605\) | −4838.15 | −0.325122 | ||||||||
\(606\) | 1316.81 | 0.0882704 | ||||||||
\(607\) | 11446.5 | 0.765402 | 0.382701 | − | 0.923872i | \(-0.374994\pi\) | ||||
0.382701 | + | 0.923872i | \(0.374994\pi\) | |||||||
\(608\) | 1070.65 | 0.0714156 | ||||||||
\(609\) | 6121.38 | 0.407308 | ||||||||
\(610\) | −119.008 | −0.00789917 | ||||||||
\(611\) | −254.132 | −0.0168266 | ||||||||
\(612\) | −732.852 | −0.0484049 | ||||||||
\(613\) | −19436.4 | −1.28063 | −0.640316 | − | 0.768111i | \(-0.721197\pi\) | ||||
−0.640316 | + | 0.768111i | \(0.721197\pi\) | |||||||
\(614\) | 42955.6 | 2.82337 | ||||||||
\(615\) | 4726.69 | 0.309917 | ||||||||
\(616\) | 2739.59 | 0.179190 | ||||||||
\(617\) | −20530.1 | −1.33956 | −0.669781 | − | 0.742558i | \(-0.733612\pi\) | ||||
−0.669781 | + | 0.742558i | \(0.733612\pi\) | |||||||
\(618\) | 17970.4 | 1.16970 | ||||||||
\(619\) | 5833.35 | 0.378776 | 0.189388 | − | 0.981902i | \(-0.439350\pi\) | ||||
0.189388 | + | 0.981902i | \(0.439350\pi\) | |||||||
\(620\) | 15307.2 | 0.991538 | ||||||||
\(621\) | 1333.19 | 0.0861499 | ||||||||
\(622\) | 32071.4 | 2.06744 | ||||||||
\(623\) | −2283.74 | −0.146864 | ||||||||
\(624\) | 63.6301 | 0.00408212 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 25346.4 | 1.61829 | ||||||||
\(627\) | 310.856 | 0.0197997 | ||||||||
\(628\) | −31885.9 | −2.02609 | ||||||||
\(629\) | 1254.91 | 0.0795493 | ||||||||
\(630\) | −1427.31 | −0.0902622 | ||||||||
\(631\) | 24776.6 | 1.56314 | 0.781568 | − | 0.623820i | \(-0.214420\pi\) | ||||
0.781568 | + | 0.623820i | \(0.214420\pi\) | |||||||
\(632\) | −17723.2 | −1.11549 | ||||||||
\(633\) | 14829.5 | 0.931152 | ||||||||
\(634\) | 16166.2 | 1.01268 | ||||||||
\(635\) | −4220.08 | −0.263730 | ||||||||
\(636\) | 19160.5 | 1.19460 | ||||||||
\(637\) | −143.949 | −0.00895366 | ||||||||
\(638\) | 25177.4 | 1.56235 | ||||||||
\(639\) | 9038.77 | 0.559574 | ||||||||
\(640\) | −11032.3 | −0.681390 | ||||||||
\(641\) | 27219.4 | 1.67723 | 0.838613 | − | 0.544728i | \(-0.183367\pi\) | ||||
0.838613 | + | 0.544728i | \(0.183367\pi\) | |||||||
\(642\) | 23730.1 | 1.45881 | ||||||||
\(643\) | 7091.79 | 0.434950 | 0.217475 | − | 0.976066i | \(-0.430218\pi\) | ||||
0.217475 | + | 0.976066i | \(0.430218\pi\) | |||||||
\(644\) | −4331.28 | −0.265026 | ||||||||
\(645\) | −4514.94 | −0.275621 | ||||||||
\(646\) | 160.049 | 0.00974777 | ||||||||
\(647\) | 27773.0 | 1.68758 | 0.843792 | − | 0.536670i | \(-0.180318\pi\) | ||||
0.843792 | + | 0.536670i | \(0.180318\pi\) | |||||||
\(648\) | 1663.02 | 0.100817 | ||||||||
\(649\) | 1589.51 | 0.0961382 | ||||||||
\(650\) | −332.782 | −0.0200812 | ||||||||
\(651\) | −5130.46 | −0.308876 | ||||||||
\(652\) | −7452.37 | −0.447634 | ||||||||
\(653\) | 21380.4 | 1.28129 | 0.640643 | − | 0.767839i | \(-0.278668\pi\) | ||||
0.640643 | + | 0.767839i | \(0.278668\pi\) | |||||||
\(654\) | 6482.09 | 0.387568 | ||||||||
\(655\) | −13981.0 | −0.834020 | ||||||||
\(656\) | −2275.06 | −0.135406 | ||||||||
\(657\) | −9065.59 | −0.538329 | ||||||||
\(658\) | −2743.78 | −0.162559 | ||||||||
\(659\) | −17232.3 | −1.01863 | −0.509315 | − | 0.860580i | \(-0.670101\pi\) | ||||
−0.509315 | + | 0.860580i | \(0.670101\pi\) | |||||||
\(660\) | −3583.07 | −0.211320 | ||||||||
\(661\) | 26577.7 | 1.56392 | 0.781962 | − | 0.623326i | \(-0.214219\pi\) | ||||
0.781962 | + | 0.623326i | \(0.214219\pi\) | |||||||
\(662\) | −19890.1 | −1.16775 | ||||||||
\(663\) | 57.2689 | 0.00335466 | ||||||||
\(664\) | 27403.4 | 1.60159 | ||||||||
\(665\) | 190.253 | 0.0110943 | ||||||||
\(666\) | −7875.49 | −0.458212 | ||||||||
\(667\) | −14393.2 | −0.835544 | ||||||||
\(668\) | 11635.1 | 0.673917 | ||||||||
\(669\) | 9480.44 | 0.547885 | ||||||||
\(670\) | 4666.89 | 0.269101 | ||||||||
\(671\) | 100.132 | 0.00576090 | ||||||||
\(672\) | 4136.22 | 0.237438 | ||||||||
\(673\) | −31695.2 | −1.81540 | −0.907698 | − | 0.419624i | \(-0.862162\pi\) | ||||
−0.907698 | + | 0.419624i | \(0.862162\pi\) | |||||||
\(674\) | 10642.9 | 0.608231 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −27422.7 | −1.56024 | ||||||||
\(677\) | 20440.3 | 1.16039 | 0.580195 | − | 0.814477i | \(-0.302976\pi\) | ||||
0.580195 | + | 0.814477i | \(0.302976\pi\) | |||||||
\(678\) | 22315.5 | 1.26405 | ||||||||
\(679\) | −10687.4 | −0.604044 | ||||||||
\(680\) | −667.063 | −0.0376187 | ||||||||
\(681\) | −10953.3 | −0.616348 | ||||||||
\(682\) | −21101.7 | −1.18479 | ||||||||
\(683\) | −22896.9 | −1.28276 | −0.641381 | − | 0.767223i | \(-0.721638\pi\) | ||||
−0.641381 | + | 0.767223i | \(0.721638\pi\) | |||||||
\(684\) | −613.051 | −0.0342699 | ||||||||
\(685\) | −10285.7 | −0.573715 | ||||||||
\(686\) | −1554.18 | −0.0864997 | ||||||||
\(687\) | −12251.1 | −0.680361 | ||||||||
\(688\) | 2173.14 | 0.120422 | ||||||||
\(689\) | −1497.30 | −0.0827904 | ||||||||
\(690\) | 3356.03 | 0.185162 | ||||||||
\(691\) | −23764.0 | −1.30829 | −0.654143 | − | 0.756371i | \(-0.726971\pi\) | ||||
−0.654143 | + | 0.756371i | \(0.726971\pi\) | |||||||
\(692\) | −3955.35 | −0.217283 | ||||||||
\(693\) | 1200.92 | 0.0658287 | ||||||||
\(694\) | 2530.34 | 0.138401 | ||||||||
\(695\) | −8725.62 | −0.476233 | ||||||||
\(696\) | −17954.1 | −0.977800 | ||||||||
\(697\) | −2047.62 | −0.111276 | ||||||||
\(698\) | 14653.2 | 0.794600 | ||||||||
\(699\) | −11047.5 | −0.597791 | ||||||||
\(700\) | −2192.95 | −0.118408 | ||||||||
\(701\) | 26259.5 | 1.41485 | 0.707423 | − | 0.706791i | \(-0.249858\pi\) | ||||
0.707423 | + | 0.706791i | \(0.249858\pi\) | |||||||
\(702\) | −359.405 | −0.0193232 | ||||||||
\(703\) | 1049.77 | 0.0563196 | ||||||||
\(704\) | 15911.4 | 0.851822 | ||||||||
\(705\) | 1297.59 | 0.0693191 | ||||||||
\(706\) | −34057.6 | −1.81554 | ||||||||
\(707\) | −678.101 | −0.0360716 | ||||||||
\(708\) | −3134.73 | −0.166399 | ||||||||
\(709\) | 12783.0 | 0.677116 | 0.338558 | − | 0.940945i | \(-0.390061\pi\) | ||||
0.338558 | + | 0.940945i | \(0.390061\pi\) | |||||||
\(710\) | 22753.2 | 1.20270 | ||||||||
\(711\) | −7769.14 | −0.409797 | ||||||||
\(712\) | 6698.26 | 0.352567 | ||||||||
\(713\) | 12063.3 | 0.633623 | ||||||||
\(714\) | 618.315 | 0.0324087 | ||||||||
\(715\) | 280.000 | 0.0146453 | ||||||||
\(716\) | −18113.6 | −0.945444 | ||||||||
\(717\) | 7976.35 | 0.415456 | ||||||||
\(718\) | −29804.7 | −1.54916 | ||||||||
\(719\) | −27609.0 | −1.43205 | −0.716025 | − | 0.698075i | \(-0.754040\pi\) | ||||
−0.716025 | + | 0.698075i | \(0.754040\pi\) | |||||||
\(720\) | −324.893 | −0.0168167 | ||||||||
\(721\) | −9253.95 | −0.477996 | ||||||||
\(722\) | −30945.1 | −1.59509 | ||||||||
\(723\) | −14461.2 | −0.743868 | ||||||||
\(724\) | −23105.1 | −1.18604 | ||||||||
\(725\) | −7287.35 | −0.373304 | ||||||||
\(726\) | −13153.4 | −0.672407 | ||||||||
\(727\) | 31306.2 | 1.59709 | 0.798544 | − | 0.601937i | \(-0.205604\pi\) | ||||
0.798544 | + | 0.601937i | \(0.205604\pi\) | |||||||
\(728\) | 422.206 | 0.0214945 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −22820.8 | −1.15703 | ||||||||
\(731\) | 1955.89 | 0.0989621 | ||||||||
\(732\) | −197.475 | −0.00997113 | ||||||||
\(733\) | −15765.8 | −0.794441 | −0.397220 | − | 0.917723i | \(-0.630025\pi\) | ||||
−0.397220 | + | 0.917723i | \(0.630025\pi\) | |||||||
\(734\) | 37640.8 | 1.89285 | ||||||||
\(735\) | 735.000 | 0.0368856 | ||||||||
\(736\) | −9725.53 | −0.487076 | ||||||||
\(737\) | −3926.68 | −0.196256 | ||||||||
\(738\) | 12850.4 | 0.640959 | ||||||||
\(739\) | 3966.51 | 0.197443 | 0.0987216 | − | 0.995115i | \(-0.468525\pi\) | ||||
0.0987216 | + | 0.995115i | \(0.468525\pi\) | |||||||
\(740\) | −12100.1 | −0.601093 | ||||||||
\(741\) | 47.9070 | 0.00237504 | ||||||||
\(742\) | −16165.9 | −0.799823 | ||||||||
\(743\) | 8224.50 | 0.406094 | 0.203047 | − | 0.979169i | \(-0.434916\pi\) | ||||
0.203047 | + | 0.979169i | \(0.434916\pi\) | |||||||
\(744\) | 15047.7 | 0.741500 | ||||||||
\(745\) | −5867.86 | −0.288566 | ||||||||
\(746\) | −20621.6 | −1.01208 | ||||||||
\(747\) | 12012.5 | 0.588373 | ||||||||
\(748\) | 1552.20 | 0.0758745 | ||||||||
\(749\) | −12220.0 | −0.596140 | ||||||||
\(750\) | 1699.17 | 0.0827267 | ||||||||
\(751\) | 18929.2 | 0.919754 | 0.459877 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459877 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(752\) | −624.558 | −0.0302863 | ||||||||
\(753\) | 5016.82 | 0.242793 | ||||||||
\(754\) | 3880.16 | 0.187410 | ||||||||
\(755\) | 7700.35 | 0.371185 | ||||||||
\(756\) | −2368.38 | −0.113938 | ||||||||
\(757\) | −34906.8 | −1.67597 | −0.837984 | − | 0.545695i | \(-0.816266\pi\) | ||||
−0.837984 | + | 0.545695i | \(0.816266\pi\) | |||||||
\(758\) | −8102.96 | −0.388276 | ||||||||
\(759\) | −2823.74 | −0.135040 | ||||||||
\(760\) | −558.016 | −0.0266334 | ||||||||
\(761\) | −13683.4 | −0.651803 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(762\) | −11473.0 | −0.545438 | ||||||||
\(763\) | −3337.99 | −0.158379 | ||||||||
\(764\) | −3058.52 | −0.144834 | ||||||||
\(765\) | −292.413 | −0.0138199 | ||||||||
\(766\) | −6155.42 | −0.290345 | ||||||||
\(767\) | 244.964 | 0.0115321 | ||||||||
\(768\) | −9960.28 | −0.467982 | ||||||||
\(769\) | 41837.3 | 1.96189 | 0.980943 | − | 0.194294i | \(-0.0622416\pi\) | ||||
0.980943 | + | 0.194294i | \(0.0622416\pi\) | |||||||
\(770\) | 3023.07 | 0.141486 | ||||||||
\(771\) | −11093.2 | −0.518175 | ||||||||
\(772\) | −21716.9 | −1.01245 | ||||||||
\(773\) | 19640.0 | 0.913843 | 0.456921 | − | 0.889507i | \(-0.348952\pi\) | ||||
0.456921 | + | 0.889507i | \(0.348952\pi\) | |||||||
\(774\) | −12274.7 | −0.570031 | ||||||||
\(775\) | 6107.69 | 0.283090 | ||||||||
\(776\) | 31346.4 | 1.45009 | ||||||||
\(777\) | 4055.53 | 0.187248 | ||||||||
\(778\) | 44054.1 | 2.03010 | ||||||||
\(779\) | −1712.89 | −0.0787814 | ||||||||
\(780\) | −552.198 | −0.0253486 | ||||||||
\(781\) | −19144.4 | −0.877131 | ||||||||
\(782\) | −1453.85 | −0.0664827 | ||||||||
\(783\) | −7870.34 | −0.359212 | ||||||||
\(784\) | −353.772 | −0.0161157 | ||||||||
\(785\) | −12722.7 | −0.578460 | ||||||||
\(786\) | −38009.9 | −1.72489 | ||||||||
\(787\) | 24935.3 | 1.12941 | 0.564705 | − | 0.825293i | \(-0.308990\pi\) | ||||
0.564705 | + | 0.825293i | \(0.308990\pi\) | |||||||
\(788\) | 4489.02 | 0.202938 | ||||||||
\(789\) | 21957.0 | 0.990736 | ||||||||
\(790\) | −19557.2 | −0.880777 | ||||||||
\(791\) | −11491.5 | −0.516551 | ||||||||
\(792\) | −3522.33 | −0.158031 | ||||||||
\(793\) | 15.4317 | 0.000691041 0 | ||||||||
\(794\) | −21695.2 | −0.969692 | ||||||||
\(795\) | 7645.16 | 0.341064 | ||||||||
\(796\) | −40145.1 | −1.78757 | ||||||||
\(797\) | −1168.33 | −0.0519251 | −0.0259625 | − | 0.999663i | \(-0.508265\pi\) | ||||
−0.0259625 | + | 0.999663i | \(0.508265\pi\) | |||||||
\(798\) | 517.237 | 0.0229448 | ||||||||
\(799\) | −562.120 | −0.0248891 | ||||||||
\(800\) | −4924.08 | −0.217615 | ||||||||
\(801\) | 2936.24 | 0.129522 | ||||||||
\(802\) | 43867.7 | 1.93145 | ||||||||
\(803\) | 19201.2 | 0.843829 | ||||||||
\(804\) | 7743.95 | 0.339686 | ||||||||
\(805\) | −1728.21 | −0.0756663 | ||||||||
\(806\) | −3252.05 | −0.142120 | ||||||||
\(807\) | −2445.29 | −0.106665 | ||||||||
\(808\) | 1988.88 | 0.0865949 | ||||||||
\(809\) | −35175.7 | −1.52869 | −0.764345 | − | 0.644807i | \(-0.776938\pi\) | ||||
−0.764345 | + | 0.644807i | \(0.776938\pi\) | |||||||
\(810\) | 1835.11 | 0.0796038 | ||||||||
\(811\) | −15256.5 | −0.660577 | −0.330288 | − | 0.943880i | \(-0.607146\pi\) | ||||
−0.330288 | + | 0.943880i | \(0.607146\pi\) | |||||||
\(812\) | 25569.3 | 1.10506 | ||||||||
\(813\) | −15318.1 | −0.660797 | ||||||||
\(814\) | 16680.5 | 0.718245 | ||||||||
\(815\) | −2973.54 | −0.127802 | ||||||||
\(816\) | 140.745 | 0.00603806 | ||||||||
\(817\) | 1636.16 | 0.0700635 | ||||||||
\(818\) | 50354.7 | 2.15233 | ||||||||
\(819\) | 185.078 | 0.00789639 | ||||||||
\(820\) | 19743.6 | 0.840825 | ||||||||
\(821\) | −15971.9 | −0.678956 | −0.339478 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339478 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(822\) | −27963.4 | −1.18654 | ||||||||
\(823\) | 2312.41 | 0.0979409 | 0.0489705 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489705 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(824\) | 27142.0 | 1.14750 | ||||||||
\(825\) | −1429.67 | −0.0603330 | ||||||||
\(826\) | 2644.80 | 0.111410 | ||||||||
\(827\) | 10422.4 | 0.438238 | 0.219119 | − | 0.975698i | \(-0.429682\pi\) | ||||
0.219119 | + | 0.975698i | \(0.429682\pi\) | |||||||
\(828\) | 5568.79 | 0.233731 | ||||||||
\(829\) | −13213.4 | −0.553584 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(830\) | 30239.0 | 1.26459 | ||||||||
\(831\) | 4196.17 | 0.175167 | ||||||||
\(832\) | 2452.15 | 0.102179 | ||||||||
\(833\) | −318.405 | −0.0132438 | ||||||||
\(834\) | −23722.2 | −0.984929 | ||||||||
\(835\) | 4642.49 | 0.192407 | ||||||||
\(836\) | 1298.46 | 0.0537179 | ||||||||
\(837\) | 6596.30 | 0.272403 | ||||||||
\(838\) | −5573.67 | −0.229761 | ||||||||
\(839\) | −10119.6 | −0.416409 | −0.208205 | − | 0.978085i | \(-0.566762\pi\) | ||||
−0.208205 | + | 0.978085i | \(0.566762\pi\) | |||||||
\(840\) | −2155.77 | −0.0885489 | ||||||||
\(841\) | 60579.9 | 2.48390 | ||||||||
\(842\) | −55988.7 | −2.29157 | ||||||||
\(843\) | −21307.1 | −0.870530 | ||||||||
\(844\) | 61943.4 | 2.52628 | ||||||||
\(845\) | −10941.8 | −0.445457 | ||||||||
\(846\) | 3527.72 | 0.143364 | ||||||||
\(847\) | 6773.41 | 0.274778 | ||||||||
\(848\) | −3679.79 | −0.149015 | ||||||||
\(849\) | 13395.5 | 0.541501 | ||||||||
\(850\) | −736.089 | −0.0297031 | ||||||||
\(851\) | −9535.80 | −0.384116 | ||||||||
\(852\) | 37755.3 | 1.51816 | ||||||||
\(853\) | 35378.1 | 1.42007 | 0.710037 | − | 0.704165i | \(-0.248678\pi\) | ||||
0.710037 | + | 0.704165i | \(0.248678\pi\) | |||||||
\(854\) | 166.611 | 0.00667602 | ||||||||
\(855\) | −244.611 | −0.00978424 | ||||||||
\(856\) | 35841.4 | 1.43112 | ||||||||
\(857\) | 6697.57 | 0.266960 | 0.133480 | − | 0.991052i | \(-0.457385\pi\) | ||||
0.133480 | + | 0.991052i | \(0.457385\pi\) | |||||||
\(858\) | 761.230 | 0.0302890 | ||||||||
\(859\) | −24298.4 | −0.965135 | −0.482568 | − | 0.875859i | \(-0.660296\pi\) | ||||
−0.482568 | + | 0.875859i | \(0.660296\pi\) | |||||||
\(860\) | −18859.1 | −0.747779 | ||||||||
\(861\) | −6617.37 | −0.261927 | ||||||||
\(862\) | −33418.3 | −1.32045 | ||||||||
\(863\) | 24942.9 | 0.983853 | 0.491926 | − | 0.870637i | \(-0.336293\pi\) | ||||
0.491926 | + | 0.870637i | \(0.336293\pi\) | |||||||
\(864\) | −5318.00 | −0.209401 | ||||||||
\(865\) | −1578.21 | −0.0620355 | ||||||||
\(866\) | −3126.78 | −0.122693 | ||||||||
\(867\) | −14612.3 | −0.572388 | ||||||||
\(868\) | −21430.1 | −0.838002 | ||||||||
\(869\) | 16455.3 | 0.642355 | ||||||||
\(870\) | −19812.0 | −0.772056 | ||||||||
\(871\) | −605.152 | −0.0235417 | ||||||||
\(872\) | 9790.39 | 0.380212 | ||||||||
\(873\) | 13741.0 | 0.532716 | ||||||||
\(874\) | −1216.18 | −0.0470686 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | −37867.4 | −1.46052 | ||||||||
\(877\) | −16276.6 | −0.626705 | −0.313353 | − | 0.949637i | \(-0.601452\pi\) | ||||
−0.313353 | + | 0.949637i | \(0.601452\pi\) | |||||||
\(878\) | 38101.3 | 1.46453 | ||||||||
\(879\) | 22771.8 | 0.873806 | ||||||||
\(880\) | 688.132 | 0.0263602 | ||||||||
\(881\) | 26636.5 | 1.01862 | 0.509311 | − | 0.860582i | \(-0.329900\pi\) | ||||
0.509311 | + | 0.860582i | \(0.329900\pi\) | |||||||
\(882\) | 1998.23 | 0.0762855 | ||||||||
\(883\) | −21788.3 | −0.830392 | −0.415196 | − | 0.909732i | \(-0.636287\pi\) | ||||
−0.415196 | + | 0.909732i | \(0.636287\pi\) | |||||||
\(884\) | 239.215 | 0.00910142 | ||||||||
\(885\) | −1250.78 | −0.0475078 | ||||||||
\(886\) | 29763.0 | 1.12856 | ||||||||
\(887\) | −26813.2 | −1.01499 | −0.507496 | − | 0.861654i | \(-0.669429\pi\) | ||||
−0.507496 | + | 0.861654i | \(0.669429\pi\) | |||||||
\(888\) | −11895.0 | −0.449514 | ||||||||
\(889\) | 5908.11 | 0.222893 | ||||||||
\(890\) | 7391.38 | 0.278382 | ||||||||
\(891\) | −1544.04 | −0.0580554 | ||||||||
\(892\) | 39600.2 | 1.48645 | ||||||||
\(893\) | −470.229 | −0.0176211 | ||||||||
\(894\) | −15952.8 | −0.596803 | ||||||||
\(895\) | −7227.45 | −0.269930 | ||||||||
\(896\) | 15445.2 | 0.575879 | ||||||||
\(897\) | −435.174 | −0.0161985 | ||||||||
\(898\) | 13387.4 | 0.497488 | ||||||||
\(899\) | −71214.2 | −2.64196 | ||||||||
\(900\) | 2819.50 | 0.104426 | ||||||||
\(901\) | −3311.91 | −0.122459 | ||||||||
\(902\) | −27217.4 | −1.00470 | ||||||||
\(903\) | 6320.92 | 0.232942 | ||||||||
\(904\) | 33704.8 | 1.24005 | ||||||||
\(905\) | −9219.07 | −0.338621 | ||||||||
\(906\) | 20934.8 | 0.767672 | ||||||||
\(907\) | 15543.0 | 0.569014 | 0.284507 | − | 0.958674i | \(-0.408170\pi\) | ||||
0.284507 | + | 0.958674i | \(0.408170\pi\) | |||||||
\(908\) | −45752.6 | −1.67219 | ||||||||
\(909\) | 871.844 | 0.0318122 | ||||||||
\(910\) | 465.895 | 0.0169717 | ||||||||
\(911\) | 48711.1 | 1.77154 | 0.885768 | − | 0.464128i | \(-0.153632\pi\) | ||||
0.885768 | + | 0.464128i | \(0.153632\pi\) | |||||||
\(912\) | 117.737 | 0.00427485 | ||||||||
\(913\) | −25442.8 | −0.922273 | ||||||||
\(914\) | −36905.3 | −1.33558 | ||||||||
\(915\) | −78.7936 | −0.00284682 | ||||||||
\(916\) | −51173.3 | −1.84587 | ||||||||
\(917\) | 19573.4 | 0.704876 | ||||||||
\(918\) | −794.976 | −0.0285818 | ||||||||
\(919\) | 1030.47 | 0.0369883 | 0.0184941 | − | 0.999829i | \(-0.494113\pi\) | ||||
0.0184941 | + | 0.999829i | \(0.494113\pi\) | |||||||
\(920\) | 5068.87 | 0.181648 | ||||||||
\(921\) | 28440.4 | 1.01753 | ||||||||
\(922\) | 11306.3 | 0.403855 | ||||||||
\(923\) | −2950.40 | −0.105215 | ||||||||
\(924\) | 5016.30 | 0.178598 | ||||||||
\(925\) | −4828.02 | −0.171615 | ||||||||
\(926\) | −26079.6 | −0.925518 | ||||||||
\(927\) | 11897.9 | 0.421553 | ||||||||
\(928\) | 57413.6 | 2.03092 | ||||||||
\(929\) | 879.756 | 0.0310698 | 0.0155349 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155349 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(930\) | 16604.8 | 0.585477 | ||||||||
\(931\) | −266.354 | −0.00937638 | ||||||||
\(932\) | −46146.0 | −1.62185 | ||||||||
\(933\) | 21234.0 | 0.745092 | ||||||||
\(934\) | −18775.8 | −0.657776 | ||||||||
\(935\) | 619.339 | 0.0216626 | ||||||||
\(936\) | −542.836 | −0.0189564 | ||||||||
\(937\) | −18668.1 | −0.650864 | −0.325432 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325432 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(938\) | −6533.64 | −0.227432 | ||||||||
\(939\) | 16781.5 | 0.583221 | ||||||||
\(940\) | 5420.08 | 0.188067 | ||||||||
\(941\) | 29613.4 | 1.02590 | 0.512948 | − | 0.858420i | \(-0.328553\pi\) | ||||
0.512948 | + | 0.858420i | \(0.328553\pi\) | |||||||
\(942\) | −34588.8 | −1.19635 | ||||||||
\(943\) | 15559.5 | 0.537313 | ||||||||
\(944\) | 602.028 | 0.0207567 | ||||||||
\(945\) | −945.000 | −0.0325300 | ||||||||
\(946\) | 25998.1 | 0.893521 | ||||||||
\(947\) | 20738.9 | 0.711640 | 0.355820 | − | 0.934554i | \(-0.384202\pi\) | ||||
0.355820 | + | 0.934554i | \(0.384202\pi\) | |||||||
\(948\) | −32452.0 | −1.11181 | ||||||||
\(949\) | 2959.15 | 0.101220 | ||||||||
\(950\) | −615.758 | −0.0210293 | ||||||||
\(951\) | 10703.4 | 0.364966 | ||||||||
\(952\) | 933.888 | 0.0317936 | ||||||||
\(953\) | −45776.5 | −1.55598 | −0.777988 | − | 0.628279i | \(-0.783760\pi\) | ||||
−0.777988 | + | 0.628279i | \(0.783760\pi\) | |||||||
\(954\) | 20784.7 | 0.705377 | ||||||||
\(955\) | −1220.37 | −0.0413510 | ||||||||
\(956\) | 33317.5 | 1.12716 | ||||||||
\(957\) | 16669.6 | 0.563064 | ||||||||
\(958\) | −30657.4 | −1.03392 | ||||||||
\(959\) | 14399.9 | 0.484878 | ||||||||
\(960\) | −12520.6 | −0.420938 | ||||||||
\(961\) | 29895.1 | 1.00349 | ||||||||
\(962\) | 2570.68 | 0.0861561 | ||||||||
\(963\) | 15711.4 | 0.525746 | ||||||||
\(964\) | −60404.9 | −2.01817 | ||||||||
\(965\) | −8665.17 | −0.289059 | ||||||||
\(966\) | −4698.44 | −0.156491 | ||||||||
\(967\) | 34461.0 | 1.14601 | 0.573005 | − | 0.819552i | \(-0.305778\pi\) | ||||
0.573005 | + | 0.819552i | \(0.305778\pi\) | |||||||
\(968\) | −19866.5 | −0.659643 | ||||||||
\(969\) | 105.967 | 0.00351304 | ||||||||
\(970\) | 34590.1 | 1.14497 | ||||||||
\(971\) | −22762.8 | −0.752309 | −0.376154 | − | 0.926557i | \(-0.622754\pi\) | ||||
−0.376154 | + | 0.926557i | \(0.622754\pi\) | |||||||
\(972\) | 3045.06 | 0.100484 | ||||||||
\(973\) | 12215.9 | 0.402490 | ||||||||
\(974\) | 28819.9 | 0.948099 | ||||||||
\(975\) | −220.331 | −0.00723716 | ||||||||
\(976\) | 37.9251 | 0.00124381 | ||||||||
\(977\) | 4809.57 | 0.157494 | 0.0787470 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787470 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(978\) | −8084.10 | −0.264316 | ||||||||
\(979\) | −6219.04 | −0.203025 | ||||||||
\(980\) | 3070.13 | 0.100073 | ||||||||
\(981\) | 4291.70 | 0.139677 | ||||||||
\(982\) | −32046.6 | −1.04139 | ||||||||
\(983\) | −27591.6 | −0.895256 | −0.447628 | − | 0.894220i | \(-0.647731\pi\) | ||||
−0.447628 | + | 0.894220i | \(0.647731\pi\) | |||||||
\(984\) | 19408.9 | 0.628793 | ||||||||
\(985\) | 1791.15 | 0.0579399 | ||||||||
\(986\) | 8582.63 | 0.277207 | ||||||||
\(987\) | −1816.62 | −0.0585853 | ||||||||
\(988\) | 200.109 | 0.00644365 | ||||||||
\(989\) | −14862.4 | −0.477854 | ||||||||
\(990\) | −3886.81 | −0.124779 | ||||||||
\(991\) | −22263.4 | −0.713643 | −0.356822 | − | 0.934173i | \(-0.616140\pi\) | ||||
−0.356822 | + | 0.934173i | \(0.616140\pi\) | |||||||
\(992\) | −48119.5 | −1.54012 | ||||||||
\(993\) | −13169.0 | −0.420851 | ||||||||
\(994\) | −31854.5 | −1.01646 | ||||||||
\(995\) | −16018.2 | −0.510361 | ||||||||
\(996\) | 50176.8 | 1.59630 | ||||||||
\(997\) | 30378.2 | 0.964983 | 0.482491 | − | 0.875901i | \(-0.339732\pi\) | ||||
0.482491 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(998\) | −83707.4 | −2.65502 | ||||||||
\(999\) | −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 | 105.4.a.f.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 315.4.a.i.1.1 | 2 | |||
4.3 | odd | 2 | 1680.4.a.bg.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.h.274.4 | 4 | |||
5.3 | odd | 4 | 525.4.d.h.274.1 | 4 | |||
5.4 | even | 2 | 525.4.a.k.1.1 | 2 | |||
7.6 | odd | 2 | 735.4.a.p.1.2 | 2 | |||
15.14 | odd | 2 | 1575.4.a.w.1.2 | 2 | |||
21.20 | even | 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 | 1.1 | even | 1 | trivial | |
315.4.a.i.1.1 | 2 | 3.2 | odd | 2 | |||
525.4.a.k.1.1 | 2 | 5.4 | even | 2 | |||
525.4.d.h.274.1 | 4 | 5.3 | odd | 4 | |||
525.4.d.h.274.4 | 4 | 5.2 | odd | 4 | |||
735.4.a.p.1.2 | 2 | 7.6 | odd | 2 | |||
1575.4.a.w.1.2 | 2 | 15.14 | odd | 2 | |||
1680.4.a.bg.1.2 | 2 | 4.3 | odd | 2 | |||
2205.4.a.z.1.1 | 2 | 21.20 | even | 2 |