Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 14x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.29360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.12311 | −1.45774 | −0.728869 | − | 0.684653i | \(-0.759954\pi\) | ||||
−0.728869 | + | 0.684653i | \(0.759954\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 9.00000 | 1.12500 | ||||||||
\(5\) | 3.05006 | 0.272806 | 0.136403 | − | 0.990653i | \(-0.456446\pi\) | ||||
0.136403 | + | 0.990653i | \(0.456446\pi\) | |||||||
\(6\) | 12.3693 | 0.841625 | ||||||||
\(7\) | 6.68324 | 0.360861 | 0.180431 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180431 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(8\) | −4.12311 | −0.182217 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −12.5757 | −0.397679 | ||||||||
\(11\) | −32.2500 | −0.883975 | −0.441988 | − | 0.897021i | \(-0.645727\pi\) | ||||
−0.441988 | + | 0.897021i | \(0.645727\pi\) | |||||||
\(12\) | −27.0000 | −0.649519 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −27.5557 | −0.526041 | ||||||||
\(15\) | −9.15018 | −0.157504 | ||||||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | −28.8586 | −0.411720 | −0.205860 | − | 0.978582i | \(-0.565999\pi\) | ||||
−0.205860 | + | 0.978582i | \(0.565999\pi\) | |||||||
\(18\) | −37.1080 | −0.485913 | ||||||||
\(19\) | 101.194 | 1.22187 | 0.610933 | − | 0.791682i | \(-0.290794\pi\) | ||||
0.610933 | + | 0.791682i | \(0.290794\pi\) | |||||||
\(20\) | 27.4505 | 0.306906 | ||||||||
\(21\) | −20.0497 | −0.208343 | ||||||||
\(22\) | 132.970 | 1.28860 | ||||||||
\(23\) | −118.990 | −1.07874 | −0.539372 | − | 0.842067i | \(-0.681338\pi\) | ||||
−0.539372 | + | 0.842067i | \(0.681338\pi\) | |||||||
\(24\) | 12.3693 | 0.105203 | ||||||||
\(25\) | −115.697 | −0.925577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 60.1492 | 0.405969 | ||||||||
\(29\) | 160.111 | 1.02524 | 0.512620 | − | 0.858616i | \(-0.328675\pi\) | ||||
0.512620 | + | 0.858616i | \(0.328675\pi\) | |||||||
\(30\) | 37.7271 | 0.229600 | ||||||||
\(31\) | 38.0705 | 0.220570 | 0.110285 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110285 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(32\) | 259.756 | 1.43496 | ||||||||
\(33\) | 96.7499 | 0.510363 | ||||||||
\(34\) | 118.987 | 0.600179 | ||||||||
\(35\) | 20.3843 | 0.0984449 | ||||||||
\(36\) | 81.0000 | 0.375000 | ||||||||
\(37\) | 327.568 | 1.45545 | 0.727727 | − | 0.685866i | \(-0.240577\pi\) | ||||
0.727727 | + | 0.685866i | \(0.240577\pi\) | |||||||
\(38\) | −417.233 | −1.78116 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.5757 | −0.0497099 | ||||||||
\(41\) | −56.0846 | −0.213633 | −0.106816 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106816 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(42\) | 82.6671 | 0.303710 | ||||||||
\(43\) | 127.879 | 0.453519 | 0.226759 | − | 0.973951i | \(-0.427187\pi\) | ||||
0.226759 | + | 0.973951i | \(0.427187\pi\) | |||||||
\(44\) | −290.250 | −0.994472 | ||||||||
\(45\) | 27.4505 | 0.0909352 | ||||||||
\(46\) | 490.608 | 1.57253 | ||||||||
\(47\) | 517.983 | 1.60757 | 0.803783 | − | 0.594923i | \(-0.202817\pi\) | ||||
0.803783 | + | 0.594923i | \(0.202817\pi\) | |||||||
\(48\) | 165.000 | 0.496160 | ||||||||
\(49\) | −298.334 | −0.869779 | ||||||||
\(50\) | 477.032 | 1.34925 | ||||||||
\(51\) | 86.5757 | 0.237706 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −695.546 | −1.80265 | −0.901326 | − | 0.433141i | \(-0.857405\pi\) | ||||
−0.901326 | + | 0.433141i | \(0.857405\pi\) | |||||||
\(54\) | 111.324 | 0.280542 | ||||||||
\(55\) | −98.3643 | −0.241153 | ||||||||
\(56\) | −27.5557 | −0.0657551 | ||||||||
\(57\) | −303.581 | −0.705445 | ||||||||
\(58\) | −660.156 | −1.49453 | ||||||||
\(59\) | −656.523 | −1.44868 | −0.724339 | − | 0.689444i | \(-0.757855\pi\) | ||||
−0.724339 | + | 0.689444i | \(0.757855\pi\) | |||||||
\(60\) | −82.3516 | −0.177192 | ||||||||
\(61\) | 701.304 | 1.47201 | 0.736007 | − | 0.676974i | \(-0.236709\pi\) | ||||
0.736007 | + | 0.676974i | \(0.236709\pi\) | |||||||
\(62\) | −156.969 | −0.321533 | ||||||||
\(63\) | 60.1492 | 0.120287 | ||||||||
\(64\) | −631.000 | −1.23242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −398.910 | −0.743976 | ||||||||
\(67\) | 57.1750 | 0.104254 | 0.0521271 | − | 0.998640i | \(-0.483400\pi\) | ||||
0.0521271 | + | 0.998640i | \(0.483400\pi\) | |||||||
\(68\) | −259.727 | −0.463184 | ||||||||
\(69\) | 356.970 | 0.622814 | ||||||||
\(70\) | −84.0465 | −0.143507 | ||||||||
\(71\) | −309.226 | −0.516879 | −0.258440 | − | 0.966027i | \(-0.583208\pi\) | ||||
−0.258440 | + | 0.966027i | \(0.583208\pi\) | |||||||
\(72\) | −37.1080 | −0.0607391 | ||||||||
\(73\) | 389.711 | 0.624826 | 0.312413 | − | 0.949946i | \(-0.398863\pi\) | ||||
0.312413 | + | 0.949946i | \(0.398863\pi\) | |||||||
\(74\) | −1350.60 | −2.12167 | ||||||||
\(75\) | 347.091 | 0.534382 | ||||||||
\(76\) | 910.744 | 1.37460 | ||||||||
\(77\) | −215.534 | −0.318992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 901.820 | 1.28434 | 0.642169 | − | 0.766563i | \(-0.278035\pi\) | ||||
0.642169 | + | 0.766563i | \(0.278035\pi\) | |||||||
\(80\) | −167.753 | −0.234442 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 231.243 | 0.311421 | ||||||||
\(83\) | −687.095 | −0.908657 | −0.454328 | − | 0.890834i | \(-0.650121\pi\) | ||||
−0.454328 | + | 0.890834i | \(0.650121\pi\) | |||||||
\(84\) | −180.448 | −0.234386 | ||||||||
\(85\) | −88.0203 | −0.112319 | ||||||||
\(86\) | −527.257 | −0.661111 | ||||||||
\(87\) | −480.334 | −0.591922 | ||||||||
\(88\) | 132.970 | 0.161076 | ||||||||
\(89\) | −1070.54 | −1.27502 | −0.637510 | − | 0.770442i | \(-0.720036\pi\) | ||||
−0.637510 | + | 0.770442i | \(0.720036\pi\) | |||||||
\(90\) | −113.181 | −0.132560 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1070.91 | −1.21359 | ||||||||
\(93\) | −114.211 | −0.127346 | ||||||||
\(94\) | −2135.70 | −2.34341 | ||||||||
\(95\) | 308.647 | 0.333332 | ||||||||
\(96\) | −779.267 | −0.828475 | ||||||||
\(97\) | −1754.48 | −1.83650 | −0.918251 | − | 0.395998i | \(-0.870399\pi\) | ||||
−0.918251 | + | 0.395998i | \(0.870399\pi\) | |||||||
\(98\) | 1230.06 | 1.26791 | ||||||||
\(99\) | −290.250 | −0.294658 | ||||||||
\(100\) | −1041.27 | −1.04127 | ||||||||
\(101\) | −640.840 | −0.631346 | −0.315673 | − | 0.948868i | \(-0.602230\pi\) | ||||
−0.315673 | + | 0.948868i | \(0.602230\pi\) | |||||||
\(102\) | −356.961 | −0.346514 | ||||||||
\(103\) | −693.153 | −0.663091 | −0.331546 | − | 0.943439i | \(-0.607570\pi\) | ||||
−0.331546 | + | 0.943439i | \(0.607570\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −61.1528 | −0.0568372 | ||||||||
\(106\) | 2867.81 | 2.62779 | ||||||||
\(107\) | −405.676 | −0.366525 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(108\) | −243.000 | −0.216506 | ||||||||
\(109\) | 479.516 | 0.421370 | 0.210685 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210685 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(110\) | 405.566 | 0.351538 | ||||||||
\(111\) | −982.704 | −0.840307 | ||||||||
\(112\) | −367.578 | −0.310115 | ||||||||
\(113\) | −1547.20 | −1.28804 | −0.644021 | − | 0.765008i | \(-0.722735\pi\) | ||||
−0.644021 | + | 0.765008i | \(0.722735\pi\) | |||||||
\(114\) | 1251.70 | 1.02835 | ||||||||
\(115\) | −362.926 | −0.294288 | ||||||||
\(116\) | 1441.00 | 1.15339 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2706.91 | 2.11179 | ||||||||
\(119\) | −192.869 | −0.148574 | ||||||||
\(120\) | 37.7271 | 0.0287000 | ||||||||
\(121\) | −290.940 | −0.218588 | ||||||||
\(122\) | −2891.55 | −2.14581 | ||||||||
\(123\) | 168.254 | 0.123341 | ||||||||
\(124\) | 342.634 | 0.248141 | ||||||||
\(125\) | −734.140 | −0.525308 | ||||||||
\(126\) | −248.001 | −0.175347 | ||||||||
\(127\) | −2495.15 | −1.74338 | −0.871690 | − | 0.490059i | \(-0.836975\pi\) | ||||
−0.871690 | + | 0.490059i | \(0.836975\pi\) | |||||||
\(128\) | 523.634 | 0.361587 | ||||||||
\(129\) | −383.636 | −0.261839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 43.7571 | 0.0291838 | 0.0145919 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145919 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(132\) | 870.749 | 0.574159 | ||||||||
\(133\) | 676.303 | 0.440924 | ||||||||
\(134\) | −235.739 | −0.151975 | ||||||||
\(135\) | −82.3516 | −0.0525015 | ||||||||
\(136\) | 118.987 | 0.0750224 | ||||||||
\(137\) | 206.194 | 0.128586 | 0.0642932 | − | 0.997931i | \(-0.479521\pi\) | ||||
0.0642932 | + | 0.997931i | \(0.479521\pi\) | |||||||
\(138\) | −1471.83 | −0.907899 | ||||||||
\(139\) | −100.000 | −0.0610208 | −0.0305104 | − | 0.999534i | \(-0.509713\pi\) | ||||
−0.0305104 | + | 0.999534i | \(0.509713\pi\) | |||||||
\(140\) | 183.459 | 0.110751 | ||||||||
\(141\) | −1553.95 | −0.928128 | ||||||||
\(142\) | 1274.97 | 0.753474 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −495.000 | −0.286458 | ||||||||
\(145\) | 488.349 | 0.279691 | ||||||||
\(146\) | −1606.82 | −0.910832 | ||||||||
\(147\) | 895.003 | 0.502167 | ||||||||
\(148\) | 2948.11 | 1.63739 | ||||||||
\(149\) | −380.451 | −0.209179 | −0.104590 | − | 0.994515i | \(-0.533353\pi\) | ||||
−0.104590 | + | 0.994515i | \(0.533353\pi\) | |||||||
\(150\) | −1431.09 | −0.778989 | ||||||||
\(151\) | 1517.45 | 0.817805 | 0.408902 | − | 0.912578i | \(-0.365912\pi\) | ||||
0.408902 | + | 0.912578i | \(0.365912\pi\) | |||||||
\(152\) | −417.233 | −0.222645 | ||||||||
\(153\) | −259.727 | −0.137240 | ||||||||
\(154\) | 888.671 | 0.465007 | ||||||||
\(155\) | 116.117 | 0.0601726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1450.16 | 0.737166 | 0.368583 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368583 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(158\) | −3718.30 | −1.87223 | ||||||||
\(159\) | 2086.64 | 1.04076 | ||||||||
\(160\) | 792.270 | 0.391465 | ||||||||
\(161\) | −795.239 | −0.389277 | ||||||||
\(162\) | −333.972 | −0.161971 | ||||||||
\(163\) | −2342.36 | −1.12557 | −0.562785 | − | 0.826603i | \(-0.690270\pi\) | ||||
−0.562785 | + | 0.826603i | \(0.690270\pi\) | |||||||
\(164\) | −504.762 | −0.240337 | ||||||||
\(165\) | 295.093 | 0.139230 | ||||||||
\(166\) | 2832.97 | 1.32458 | ||||||||
\(167\) | 40.0731 | 0.0185686 | 0.00928428 | − | 0.999957i | \(-0.497045\pi\) | ||||
0.00928428 | + | 0.999957i | \(0.497045\pi\) | |||||||
\(168\) | 82.6671 | 0.0379637 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 362.917 | 0.163732 | ||||||||
\(171\) | 910.744 | 0.407289 | ||||||||
\(172\) | 1150.91 | 0.510208 | ||||||||
\(173\) | 1909.54 | 0.839189 | 0.419594 | − | 0.907712i | \(-0.362172\pi\) | ||||
0.419594 | + | 0.907712i | \(0.362172\pi\) | |||||||
\(174\) | 1980.47 | 0.862868 | ||||||||
\(175\) | −773.232 | −0.334005 | ||||||||
\(176\) | 1773.75 | 0.759666 | ||||||||
\(177\) | 1969.57 | 0.836395 | ||||||||
\(178\) | 4413.94 | 1.85864 | ||||||||
\(179\) | −509.959 | −0.212939 | −0.106470 | − | 0.994316i | \(-0.533955\pi\) | ||||
−0.106470 | + | 0.994316i | \(0.533955\pi\) | |||||||
\(180\) | 247.055 | 0.102302 | ||||||||
\(181\) | −2136.88 | −0.877531 | −0.438766 | − | 0.898602i | \(-0.644584\pi\) | ||||
−0.438766 | + | 0.898602i | \(0.644584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2103.91 | −0.849867 | ||||||||
\(184\) | 490.608 | 0.196566 | ||||||||
\(185\) | 999.101 | 0.397056 | ||||||||
\(186\) | 470.906 | 0.185637 | ||||||||
\(187\) | 930.688 | 0.363950 | ||||||||
\(188\) | 4661.85 | 1.80851 | ||||||||
\(189\) | −180.448 | −0.0694478 | ||||||||
\(190\) | −1272.58 | −0.485911 | ||||||||
\(191\) | 4057.74 | 1.53721 | 0.768607 | − | 0.639721i | \(-0.220950\pi\) | ||||
0.768607 | + | 0.639721i | \(0.220950\pi\) | |||||||
\(192\) | 1893.00 | 0.711539 | ||||||||
\(193\) | −873.394 | −0.325742 | −0.162871 | − | 0.986647i | \(-0.552075\pi\) | ||||
−0.162871 | + | 0.986647i | \(0.552075\pi\) | |||||||
\(194\) | 7233.92 | 2.67714 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2685.01 | −0.978502 | ||||||||
\(197\) | −4147.25 | −1.49989 | −0.749947 | − | 0.661498i | \(-0.769921\pi\) | ||||
−0.749947 | + | 0.661498i | \(0.769921\pi\) | |||||||
\(198\) | 1196.73 | 0.429535 | ||||||||
\(199\) | −2404.06 | −0.856379 | −0.428189 | − | 0.903689i | \(-0.640848\pi\) | ||||
−0.428189 | + | 0.903689i | \(0.640848\pi\) | |||||||
\(200\) | 477.032 | 0.168656 | ||||||||
\(201\) | −171.525 | −0.0601912 | ||||||||
\(202\) | 2642.25 | 0.920337 | ||||||||
\(203\) | 1070.06 | 0.369969 | ||||||||
\(204\) | 779.181 | 0.267420 | ||||||||
\(205\) | −171.061 | −0.0582802 | ||||||||
\(206\) | 2857.94 | 0.966613 | ||||||||
\(207\) | −1070.91 | −0.359582 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3263.50 | −1.08010 | ||||||||
\(210\) | 252.140 | 0.0828538 | ||||||||
\(211\) | 3868.85 | 1.26229 | 0.631144 | − | 0.775665i | \(-0.282586\pi\) | ||||
0.631144 | + | 0.775665i | \(0.282586\pi\) | |||||||
\(212\) | −6259.91 | −2.02798 | ||||||||
\(213\) | 927.679 | 0.298420 | ||||||||
\(214\) | 1672.64 | 0.534297 | ||||||||
\(215\) | 390.037 | 0.123722 | ||||||||
\(216\) | 111.324 | 0.0350677 | ||||||||
\(217\) | 254.434 | 0.0795950 | ||||||||
\(218\) | −1977.09 | −0.614246 | ||||||||
\(219\) | −1169.13 | −0.360743 | ||||||||
\(220\) | −885.279 | −0.271298 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4051.79 | 1.22495 | ||||||||
\(223\) | −2813.55 | −0.844885 | −0.422443 | − | 0.906390i | \(-0.638827\pi\) | ||||
−0.422443 | + | 0.906390i | \(0.638827\pi\) | |||||||
\(224\) | 1736.01 | 0.517822 | ||||||||
\(225\) | −1041.27 | −0.308526 | ||||||||
\(226\) | 6379.29 | 1.87763 | ||||||||
\(227\) | 4518.37 | 1.32112 | 0.660561 | − | 0.750772i | \(-0.270318\pi\) | ||||
0.660561 | + | 0.750772i | \(0.270318\pi\) | |||||||
\(228\) | −2732.23 | −0.793625 | ||||||||
\(229\) | 1305.27 | 0.376658 | 0.188329 | − | 0.982106i | \(-0.439693\pi\) | ||||
0.188329 | + | 0.982106i | \(0.439693\pi\) | |||||||
\(230\) | 1496.38 | 0.428994 | ||||||||
\(231\) | 646.603 | 0.184170 | ||||||||
\(232\) | −660.156 | −0.186816 | ||||||||
\(233\) | −3360.55 | −0.944879 | −0.472440 | − | 0.881363i | \(-0.656627\pi\) | ||||
−0.472440 | + | 0.881363i | \(0.656627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1579.88 | 0.438553 | ||||||||
\(236\) | −5908.71 | −1.62976 | ||||||||
\(237\) | −2705.46 | −0.741513 | ||||||||
\(238\) | 795.219 | 0.216581 | ||||||||
\(239\) | 4737.17 | 1.28210 | 0.641050 | − | 0.767499i | \(-0.278499\pi\) | ||||
0.641050 | + | 0.767499i | \(0.278499\pi\) | |||||||
\(240\) | 503.260 | 0.135355 | ||||||||
\(241\) | −4785.28 | −1.27903 | −0.639516 | − | 0.768778i | \(-0.720865\pi\) | ||||
−0.639516 | + | 0.768778i | \(0.720865\pi\) | |||||||
\(242\) | 1199.58 | 0.318643 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 6311.74 | 1.65601 | ||||||||
\(245\) | −909.937 | −0.237281 | ||||||||
\(246\) | −693.729 | −0.179799 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −156.969 | −0.0401916 | ||||||||
\(249\) | 2061.29 | 0.524613 | ||||||||
\(250\) | 3026.94 | 0.765762 | ||||||||
\(251\) | −3273.86 | −0.823284 | −0.411642 | − | 0.911346i | \(-0.635045\pi\) | ||||
−0.411642 | + | 0.911346i | \(0.635045\pi\) | |||||||
\(252\) | 541.343 | 0.135323 | ||||||||
\(253\) | 3837.42 | 0.953584 | ||||||||
\(254\) | 10287.8 | 2.54139 | ||||||||
\(255\) | 264.061 | 0.0648476 | ||||||||
\(256\) | 2889.00 | 0.705322 | ||||||||
\(257\) | −6545.81 | −1.58878 | −0.794390 | − | 0.607408i | \(-0.792209\pi\) | ||||
−0.794390 | + | 0.607408i | \(0.792209\pi\) | |||||||
\(258\) | 1581.77 | 0.381693 | ||||||||
\(259\) | 2189.22 | 0.525217 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1441.00 | 0.341746 | ||||||||
\(262\) | −180.415 | −0.0425424 | ||||||||
\(263\) | 88.2014 | 0.0206796 | 0.0103398 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103398 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(264\) | −398.910 | −0.0929970 | ||||||||
\(265\) | −2121.46 | −0.491773 | ||||||||
\(266\) | −2788.47 | −0.642752 | ||||||||
\(267\) | 3211.61 | 0.736133 | ||||||||
\(268\) | 514.575 | 0.117286 | ||||||||
\(269\) | −4527.60 | −1.02622 | −0.513109 | − | 0.858324i | \(-0.671506\pi\) | ||||
−0.513109 | + | 0.858324i | \(0.671506\pi\) | |||||||
\(270\) | 339.544 | 0.0765334 | ||||||||
\(271\) | −8321.82 | −1.86537 | −0.932684 | − | 0.360695i | \(-0.882540\pi\) | ||||
−0.932684 | + | 0.360695i | \(0.882540\pi\) | |||||||
\(272\) | 1587.22 | 0.353821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −850.160 | −0.187445 | ||||||||
\(275\) | 3731.23 | 0.818187 | ||||||||
\(276\) | 3212.73 | 0.700665 | ||||||||
\(277\) | −2881.31 | −0.624986 | −0.312493 | − | 0.949920i | \(-0.601164\pi\) | ||||
−0.312493 | + | 0.949920i | \(0.601164\pi\) | |||||||
\(278\) | 412.311 | 0.0889523 | ||||||||
\(279\) | 342.634 | 0.0735232 | ||||||||
\(280\) | −84.0465 | −0.0179384 | ||||||||
\(281\) | 2817.99 | 0.598247 | 0.299123 | − | 0.954214i | \(-0.403306\pi\) | ||||
0.299123 | + | 0.954214i | \(0.403306\pi\) | |||||||
\(282\) | 6407.10 | 1.35297 | ||||||||
\(283\) | 264.601 | 0.0555792 | 0.0277896 | − | 0.999614i | \(-0.491153\pi\) | ||||
0.0277896 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(284\) | −2783.04 | −0.581489 | ||||||||
\(285\) | −925.941 | −0.192449 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −374.827 | −0.0770918 | ||||||||
\(288\) | 2337.80 | 0.478320 | ||||||||
\(289\) | −4080.18 | −0.830487 | ||||||||
\(290\) | −2013.52 | −0.407716 | ||||||||
\(291\) | 5263.45 | 1.06031 | ||||||||
\(292\) | 3507.40 | 0.702929 | ||||||||
\(293\) | −4292.52 | −0.855877 | −0.427938 | − | 0.903808i | \(-0.640760\pi\) | ||||
−0.427938 | + | 0.903808i | \(0.640760\pi\) | |||||||
\(294\) | −3690.19 | −0.732028 | ||||||||
\(295\) | −2002.43 | −0.395208 | ||||||||
\(296\) | −1350.60 | −0.265209 | ||||||||
\(297\) | 870.749 | 0.170121 | ||||||||
\(298\) | 1568.64 | 0.304929 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3123.82 | 0.601180 | ||||||||
\(301\) | 854.643 | 0.163657 | ||||||||
\(302\) | −6256.62 | −1.19214 | ||||||||
\(303\) | 1922.52 | 0.364508 | ||||||||
\(304\) | −5565.66 | −1.05004 | ||||||||
\(305\) | 2139.02 | 0.401573 | ||||||||
\(306\) | 1070.88 | 0.200060 | ||||||||
\(307\) | −7026.26 | −1.30622 | −0.653110 | − | 0.757263i | \(-0.726536\pi\) | ||||
−0.653110 | + | 0.757263i | \(0.726536\pi\) | |||||||
\(308\) | −1939.81 | −0.358866 | ||||||||
\(309\) | 2079.46 | 0.382836 | ||||||||
\(310\) | −478.763 | −0.0877159 | ||||||||
\(311\) | −1133.21 | −0.206618 | −0.103309 | − | 0.994649i | \(-0.532943\pi\) | ||||
−0.103309 | + | 0.994649i | \(0.532943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5285.95 | −0.954566 | −0.477283 | − | 0.878750i | \(-0.658378\pi\) | ||||
−0.477283 | + | 0.878750i | \(0.658378\pi\) | |||||||
\(314\) | −5979.15 | −1.07459 | ||||||||
\(315\) | 183.459 | 0.0328150 | ||||||||
\(316\) | 8116.38 | 1.44488 | ||||||||
\(317\) | 4782.16 | 0.847296 | 0.423648 | − | 0.905827i | \(-0.360749\pi\) | ||||
0.423648 | + | 0.905827i | \(0.360749\pi\) | |||||||
\(318\) | −8603.43 | −1.51716 | ||||||||
\(319\) | −5163.59 | −0.906286 | ||||||||
\(320\) | −1924.59 | −0.336212 | ||||||||
\(321\) | 1217.03 | 0.211613 | ||||||||
\(322\) | 3278.85 | 0.567464 | ||||||||
\(323\) | −2920.31 | −0.503066 | ||||||||
\(324\) | 729.000 | 0.125000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9657.80 | 1.64079 | ||||||||
\(327\) | −1438.55 | −0.243278 | ||||||||
\(328\) | 231.243 | 0.0389276 | ||||||||
\(329\) | 3461.81 | 0.580108 | ||||||||
\(330\) | −1216.70 | −0.202961 | ||||||||
\(331\) | −8669.98 | −1.43971 | −0.719857 | − | 0.694122i | \(-0.755793\pi\) | ||||
−0.719857 | + | 0.694122i | \(0.755793\pi\) | |||||||
\(332\) | −6183.86 | −1.02224 | ||||||||
\(333\) | 2948.11 | 0.485152 | ||||||||
\(334\) | −165.226 | −0.0270681 | ||||||||
\(335\) | 174.387 | 0.0284412 | ||||||||
\(336\) | 1102.73 | 0.179045 | ||||||||
\(337\) | 8526.59 | 1.37826 | 0.689129 | − | 0.724639i | \(-0.257993\pi\) | ||||
0.689129 | + | 0.724639i | \(0.257993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4641.61 | 0.743651 | ||||||||
\(340\) | −792.183 | −0.126359 | ||||||||
\(341\) | −1227.77 | −0.194978 | ||||||||
\(342\) | −3755.10 | −0.593720 | ||||||||
\(343\) | −4286.19 | −0.674731 | ||||||||
\(344\) | −527.257 | −0.0826389 | ||||||||
\(345\) | 1088.78 | 0.169907 | ||||||||
\(346\) | −7873.23 | −1.22332 | ||||||||
\(347\) | −12581.5 | −1.94643 | −0.973213 | − | 0.229907i | \(-0.926158\pi\) | ||||
−0.973213 | + | 0.229907i | \(0.926158\pi\) | |||||||
\(348\) | −4323.01 | −0.665913 | ||||||||
\(349\) | 8961.18 | 1.37444 | 0.687222 | − | 0.726447i | \(-0.258830\pi\) | ||||
0.687222 | + | 0.726447i | \(0.258830\pi\) | |||||||
\(350\) | 3188.12 | 0.486892 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8377.11 | −1.26847 | ||||||||
\(353\) | 5357.99 | 0.807868 | 0.403934 | − | 0.914788i | \(-0.367643\pi\) | ||||
0.403934 | + | 0.914788i | \(0.367643\pi\) | |||||||
\(354\) | −8120.74 | −1.21924 | ||||||||
\(355\) | −943.159 | −0.141007 | ||||||||
\(356\) | −9634.84 | −1.43440 | ||||||||
\(357\) | 578.606 | 0.0857790 | ||||||||
\(358\) | 2102.61 | 0.310409 | ||||||||
\(359\) | 2705.40 | 0.397731 | 0.198866 | − | 0.980027i | \(-0.436274\pi\) | ||||
0.198866 | + | 0.980027i | \(0.436274\pi\) | |||||||
\(360\) | −113.181 | −0.0165700 | ||||||||
\(361\) | 3381.19 | 0.492957 | ||||||||
\(362\) | 8810.59 | 1.27921 | ||||||||
\(363\) | 872.820 | 0.126202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1188.64 | 0.170456 | ||||||||
\(366\) | 8674.65 | 1.23888 | ||||||||
\(367\) | 10473.8 | 1.48972 | 0.744858 | − | 0.667223i | \(-0.232517\pi\) | ||||
0.744858 | + | 0.667223i | \(0.232517\pi\) | |||||||
\(368\) | 6544.45 | 0.927046 | ||||||||
\(369\) | −504.762 | −0.0712110 | ||||||||
\(370\) | −4119.40 | −0.578804 | ||||||||
\(371\) | −4648.50 | −0.650507 | ||||||||
\(372\) | −1027.90 | −0.143264 | ||||||||
\(373\) | −12763.0 | −1.77170 | −0.885850 | − | 0.463973i | \(-0.846424\pi\) | ||||
−0.885850 | + | 0.463973i | \(0.846424\pi\) | |||||||
\(374\) | −3837.32 | −0.530544 | ||||||||
\(375\) | 2202.42 | 0.303287 | ||||||||
\(376\) | −2135.70 | −0.292926 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 744.004 | 0.101237 | ||||||||
\(379\) | 2318.02 | 0.314166 | 0.157083 | − | 0.987585i | \(-0.449791\pi\) | ||||
0.157083 | + | 0.987585i | \(0.449791\pi\) | |||||||
\(380\) | 2777.82 | 0.374998 | ||||||||
\(381\) | 7485.46 | 1.00654 | ||||||||
\(382\) | −16730.5 | −2.24086 | ||||||||
\(383\) | −1983.34 | −0.264606 | −0.132303 | − | 0.991209i | \(-0.542237\pi\) | ||||
−0.132303 | + | 0.991209i | \(0.542237\pi\) | |||||||
\(384\) | −1570.90 | −0.208763 | ||||||||
\(385\) | −657.392 | −0.0870229 | ||||||||
\(386\) | 3601.10 | 0.474847 | ||||||||
\(387\) | 1150.91 | 0.151173 | ||||||||
\(388\) | −15790.3 | −2.06607 | ||||||||
\(389\) | −3244.51 | −0.422887 | −0.211444 | − | 0.977390i | \(-0.567816\pi\) | ||||
−0.211444 | + | 0.977390i | \(0.567816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3433.88 | 0.444140 | ||||||||
\(392\) | 1230.06 | 0.158489 | ||||||||
\(393\) | −131.271 | −0.0168493 | ||||||||
\(394\) | 17099.5 | 2.18645 | ||||||||
\(395\) | 2750.60 | 0.350374 | ||||||||
\(396\) | −2612.25 | −0.331491 | ||||||||
\(397\) | −3759.72 | −0.475302 | −0.237651 | − | 0.971351i | \(-0.576378\pi\) | ||||
−0.237651 | + | 0.971351i | \(0.576378\pi\) | |||||||
\(398\) | 9912.20 | 1.24838 | ||||||||
\(399\) | −2028.91 | −0.254568 | ||||||||
\(400\) | 6363.34 | 0.795418 | ||||||||
\(401\) | 1997.55 | 0.248760 | 0.124380 | − | 0.992235i | \(-0.460306\pi\) | ||||
0.124380 | + | 0.992235i | \(0.460306\pi\) | |||||||
\(402\) | 707.216 | 0.0877431 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5767.56 | −0.710264 | ||||||||
\(405\) | 247.055 | 0.0303117 | ||||||||
\(406\) | −4411.98 | −0.539318 | ||||||||
\(407\) | −10564.1 | −1.28659 | ||||||||
\(408\) | −356.961 | −0.0433142 | ||||||||
\(409\) | 5195.23 | 0.628087 | 0.314044 | − | 0.949409i | \(-0.398316\pi\) | ||||
0.314044 | + | 0.949409i | \(0.398316\pi\) | |||||||
\(410\) | 705.304 | 0.0849573 | ||||||||
\(411\) | −618.582 | −0.0742394 | ||||||||
\(412\) | −6238.38 | −0.745977 | ||||||||
\(413\) | −4387.70 | −0.522772 | ||||||||
\(414\) | 4415.48 | 0.524176 | ||||||||
\(415\) | −2095.68 | −0.247887 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 300.000 | 0.0352304 | ||||||||
\(418\) | 13455.7 | 1.57450 | ||||||||
\(419\) | −6822.11 | −0.795422 | −0.397711 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397711 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(420\) | −550.376 | −0.0639419 | ||||||||
\(421\) | −7537.70 | −0.872601 | −0.436300 | − | 0.899801i | \(-0.643712\pi\) | ||||
−0.436300 | + | 0.899801i | \(0.643712\pi\) | |||||||
\(422\) | −15951.7 | −1.84009 | ||||||||
\(423\) | 4661.85 | 0.535855 | ||||||||
\(424\) | 2867.81 | 0.328474 | ||||||||
\(425\) | 3338.85 | 0.381078 | ||||||||
\(426\) | −3824.92 | −0.435019 | ||||||||
\(427\) | 4686.99 | 0.531192 | ||||||||
\(428\) | −3651.08 | −0.412340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1608.16 | −0.180355 | ||||||||
\(431\) | 13404.2 | 1.49805 | 0.749023 | − | 0.662544i | \(-0.230523\pi\) | ||||
0.749023 | + | 0.662544i | \(0.230523\pi\) | |||||||
\(432\) | 1485.00 | 0.165387 | ||||||||
\(433\) | −17715.9 | −1.96622 | −0.983110 | − | 0.183014i | \(-0.941415\pi\) | ||||
−0.983110 | + | 0.183014i | \(0.941415\pi\) | |||||||
\(434\) | −1049.06 | −0.116029 | ||||||||
\(435\) | −1465.05 | −0.161480 | ||||||||
\(436\) | 4315.64 | 0.474041 | ||||||||
\(437\) | −12041.1 | −1.31808 | ||||||||
\(438\) | 4820.46 | 0.525869 | ||||||||
\(439\) | 7163.47 | 0.778801 | 0.389401 | − | 0.921068i | \(-0.372682\pi\) | ||||
0.389401 | + | 0.921068i | \(0.372682\pi\) | |||||||
\(440\) | 405.566 | 0.0439423 | ||||||||
\(441\) | −2685.01 | −0.289926 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10169.2 | −1.09064 | −0.545321 | − | 0.838227i | \(-0.683592\pi\) | ||||
−0.545321 | + | 0.838227i | \(0.683592\pi\) | |||||||
\(444\) | −8844.33 | −0.945346 | ||||||||
\(445\) | −3265.20 | −0.347833 | ||||||||
\(446\) | 11600.6 | 1.23162 | ||||||||
\(447\) | 1141.35 | 0.120770 | ||||||||
\(448\) | −4217.13 | −0.444733 | ||||||||
\(449\) | 17142.5 | 1.80179 | 0.900895 | − | 0.434037i | \(-0.142911\pi\) | ||||
0.900895 | + | 0.434037i | \(0.142911\pi\) | |||||||
\(450\) | 4293.28 | 0.449750 | ||||||||
\(451\) | 1808.73 | 0.188846 | ||||||||
\(452\) | −13924.8 | −1.44905 | ||||||||
\(453\) | −4552.36 | −0.472160 | ||||||||
\(454\) | −18629.7 | −1.92585 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1251.70 | 0.128544 | ||||||||
\(457\) | −14091.1 | −1.44235 | −0.721177 | − | 0.692750i | \(-0.756399\pi\) | ||||
−0.721177 | + | 0.692750i | \(0.756399\pi\) | |||||||
\(458\) | −5381.76 | −0.549068 | ||||||||
\(459\) | 779.181 | 0.0792355 | ||||||||
\(460\) | −3266.34 | −0.331074 | ||||||||
\(461\) | 2922.22 | 0.295231 | 0.147616 | − | 0.989045i | \(-0.452840\pi\) | ||||
0.147616 | + | 0.989045i | \(0.452840\pi\) | |||||||
\(462\) | −2666.01 | −0.268472 | ||||||||
\(463\) | 2072.61 | 0.208040 | 0.104020 | − | 0.994575i | \(-0.466829\pi\) | ||||
0.104020 | + | 0.994575i | \(0.466829\pi\) | |||||||
\(464\) | −8806.13 | −0.881065 | ||||||||
\(465\) | −348.352 | −0.0347407 | ||||||||
\(466\) | 13855.9 | 1.37739 | ||||||||
\(467\) | −2664.19 | −0.263992 | −0.131996 | − | 0.991250i | \(-0.542139\pi\) | ||||
−0.131996 | + | 0.991250i | \(0.542139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 382.114 | 0.0376213 | ||||||||
\(470\) | −6514.01 | −0.639295 | ||||||||
\(471\) | −4350.47 | −0.425603 | ||||||||
\(472\) | 2706.91 | 0.263974 | ||||||||
\(473\) | −4124.08 | −0.400899 | ||||||||
\(474\) | 11154.9 | 1.08093 | ||||||||
\(475\) | −11707.8 | −1.13093 | ||||||||
\(476\) | −1735.82 | −0.167145 | ||||||||
\(477\) | −6259.91 | −0.600884 | ||||||||
\(478\) | −19531.8 | −1.86897 | ||||||||
\(479\) | 5220.70 | 0.497995 | 0.248998 | − | 0.968504i | \(-0.419899\pi\) | ||||
0.248998 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(480\) | −2376.81 | −0.226013 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19730.2 | 1.86449 | ||||||||
\(483\) | 2385.72 | 0.224749 | ||||||||
\(484\) | −2618.46 | −0.245911 | ||||||||
\(485\) | −5351.28 | −0.501008 | ||||||||
\(486\) | 1001.91 | 0.0935139 | ||||||||
\(487\) | 12224.6 | 1.13747 | 0.568737 | − | 0.822520i | \(-0.307432\pi\) | ||||
0.568737 | + | 0.822520i | \(0.307432\pi\) | |||||||
\(488\) | −2891.55 | −0.268226 | ||||||||
\(489\) | 7027.08 | 0.649848 | ||||||||
\(490\) | 3751.77 | 0.345893 | ||||||||
\(491\) | 19653.2 | 1.80639 | 0.903195 | − | 0.429231i | \(-0.141216\pi\) | ||||
0.903195 | + | 0.429231i | \(0.141216\pi\) | |||||||
\(492\) | 1514.29 | 0.138759 | ||||||||
\(493\) | −4620.59 | −0.422111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −885.279 | −0.0803845 | ||||||||
\(496\) | −2093.88 | −0.189552 | ||||||||
\(497\) | −2066.63 | −0.186522 | ||||||||
\(498\) | −8498.90 | −0.764749 | ||||||||
\(499\) | 11713.6 | 1.05084 | 0.525422 | − | 0.850842i | \(-0.323907\pi\) | ||||
0.525422 | + | 0.850842i | \(0.323907\pi\) | |||||||
\(500\) | −6607.26 | −0.590972 | ||||||||
\(501\) | −120.219 | −0.0107206 | ||||||||
\(502\) | 13498.5 | 1.20013 | ||||||||
\(503\) | 13003.3 | 1.15266 | 0.576332 | − | 0.817216i | \(-0.304483\pi\) | ||||
0.576332 | + | 0.817216i | \(0.304483\pi\) | |||||||
\(504\) | −248.001 | −0.0219184 | ||||||||
\(505\) | −1954.60 | −0.172235 | ||||||||
\(506\) | −15822.1 | −1.39008 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22456.4 | −1.96130 | ||||||||
\(509\) | 5328.93 | 0.464049 | 0.232024 | − | 0.972710i | \(-0.425465\pi\) | ||||
0.232024 | + | 0.972710i | \(0.425465\pi\) | |||||||
\(510\) | −1088.75 | −0.0945308 | ||||||||
\(511\) | 2604.54 | 0.225475 | ||||||||
\(512\) | −16100.7 | −1.38976 | ||||||||
\(513\) | −2732.23 | −0.235148 | ||||||||
\(514\) | 26989.1 | 2.31603 | ||||||||
\(515\) | −2114.16 | −0.180895 | ||||||||
\(516\) | −3452.72 | −0.294569 | ||||||||
\(517\) | −16704.9 | −1.42105 | ||||||||
\(518\) | −9026.37 | −0.765629 | ||||||||
\(519\) | −5728.62 | −0.484506 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11700.3 | −0.983876 | −0.491938 | − | 0.870630i | \(-0.663711\pi\) | ||||
−0.491938 | + | 0.870630i | \(0.663711\pi\) | |||||||
\(522\) | −5941.41 | −0.498177 | ||||||||
\(523\) | −4535.04 | −0.379165 | −0.189583 | − | 0.981865i | \(-0.560714\pi\) | ||||
−0.189583 | + | 0.981865i | \(0.560714\pi\) | |||||||
\(524\) | 393.814 | 0.0328318 | ||||||||
\(525\) | 2319.70 | 0.192838 | ||||||||
\(526\) | −363.664 | −0.0301454 | ||||||||
\(527\) | −1098.66 | −0.0908128 | ||||||||
\(528\) | −5321.24 | −0.438594 | ||||||||
\(529\) | 1991.62 | 0.163690 | ||||||||
\(530\) | 8746.98 | 0.716877 | ||||||||
\(531\) | −5908.71 | −0.482893 | ||||||||
\(532\) | 6086.73 | 0.496040 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −13241.8 | −1.07309 | ||||||||
\(535\) | −1237.33 | −0.0999900 | ||||||||
\(536\) | −235.739 | −0.0189969 | ||||||||
\(537\) | 1529.88 | 0.122940 | ||||||||
\(538\) | 18667.8 | 1.49596 | ||||||||
\(539\) | 9621.27 | 0.768863 | ||||||||
\(540\) | −741.164 | −0.0590641 | ||||||||
\(541\) | 5184.89 | 0.412044 | 0.206022 | − | 0.978547i | \(-0.433948\pi\) | ||||
0.206022 | + | 0.978547i | \(0.433948\pi\) | |||||||
\(542\) | 34311.7 | 2.71922 | ||||||||
\(543\) | 6410.64 | 0.506643 | ||||||||
\(544\) | −7496.18 | −0.590801 | ||||||||
\(545\) | 1462.55 | 0.114952 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5609.12 | 0.438443 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(548\) | 1855.75 | 0.144660 | ||||||||
\(549\) | 6311.74 | 0.490671 | ||||||||
\(550\) | −15384.2 | −1.19270 | ||||||||
\(551\) | 16202.3 | 1.25271 | ||||||||
\(552\) | −1471.83 | −0.113487 | ||||||||
\(553\) | 6027.08 | 0.463468 | ||||||||
\(554\) | 11879.9 | 0.911066 | ||||||||
\(555\) | −2997.30 | −0.229241 | ||||||||
\(556\) | −900.000 | −0.0686484 | ||||||||
\(557\) | 20150.5 | 1.53286 | 0.766432 | − | 0.642326i | \(-0.222030\pi\) | ||||
0.766432 | + | 0.642326i | \(0.222030\pi\) | |||||||
\(558\) | −1412.72 | −0.107178 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1121.14 | −0.0846011 | ||||||||
\(561\) | −2792.06 | −0.210127 | ||||||||
\(562\) | −11618.9 | −0.872087 | ||||||||
\(563\) | 16292.2 | 1.21960 | 0.609800 | − | 0.792556i | \(-0.291250\pi\) | ||||
0.609800 | + | 0.792556i | \(0.291250\pi\) | |||||||
\(564\) | −13985.5 | −1.04414 | ||||||||
\(565\) | −4719.06 | −0.351385 | ||||||||
\(566\) | −1090.98 | −0.0810200 | ||||||||
\(567\) | 541.343 | 0.0400957 | ||||||||
\(568\) | 1274.97 | 0.0941843 | ||||||||
\(569\) | 10460.5 | 0.770700 | 0.385350 | − | 0.922770i | \(-0.374081\pi\) | ||||
0.385350 | + | 0.922770i | \(0.374081\pi\) | |||||||
\(570\) | 3817.75 | 0.280541 | ||||||||
\(571\) | 2225.96 | 0.163141 | 0.0815705 | − | 0.996668i | \(-0.474006\pi\) | ||||
0.0815705 | + | 0.996668i | \(0.474006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12173.2 | −0.887511 | ||||||||
\(574\) | 1545.45 | 0.112380 | ||||||||
\(575\) | 13766.8 | 0.998461 | ||||||||
\(576\) | −5679.00 | −0.410807 | ||||||||
\(577\) | −4686.23 | −0.338112 | −0.169056 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169056 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(578\) | 16823.0 | 1.21063 | ||||||||
\(579\) | 2620.18 | 0.188067 | ||||||||
\(580\) | 4395.14 | 0.314652 | ||||||||
\(581\) | −4592.03 | −0.327899 | ||||||||
\(582\) | −21701.8 | −1.54565 | ||||||||
\(583\) | 22431.3 | 1.59350 | ||||||||
\(584\) | −1606.82 | −0.113854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17698.5 | 1.24764 | ||||||||
\(587\) | −12090.6 | −0.850138 | −0.425069 | − | 0.905161i | \(-0.639750\pi\) | ||||
−0.425069 | + | 0.905161i | \(0.639750\pi\) | |||||||
\(588\) | 8055.03 | 0.564938 | ||||||||
\(589\) | 3852.50 | 0.269507 | ||||||||
\(590\) | 8256.25 | 0.576109 | ||||||||
\(591\) | 12441.7 | 0.865964 | ||||||||
\(592\) | −18016.2 | −1.25078 | ||||||||
\(593\) | −6135.97 | −0.424914 | −0.212457 | − | 0.977170i | \(-0.568147\pi\) | ||||
−0.212457 | + | 0.977170i | \(0.568147\pi\) | |||||||
\(594\) | −3590.19 | −0.247992 | ||||||||
\(595\) | −588.261 | −0.0405317 | ||||||||
\(596\) | −3424.06 | −0.235327 | ||||||||
\(597\) | 7212.18 | 0.494431 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6198.80 | −0.422831 | −0.211416 | − | 0.977396i | \(-0.567807\pi\) | ||||
−0.211416 | + | 0.977396i | \(0.567807\pi\) | |||||||
\(600\) | −1431.09 | −0.0973737 | ||||||||
\(601\) | 18345.4 | 1.24513 | 0.622565 | − | 0.782568i | \(-0.286091\pi\) | ||||
0.622565 | + | 0.782568i | \(0.286091\pi\) | |||||||
\(602\) | −3523.79 | −0.238569 | ||||||||
\(603\) | 514.575 | 0.0347514 | ||||||||
\(604\) | 13657.1 | 0.920030 | ||||||||
\(605\) | −887.384 | −0.0596319 | ||||||||
\(606\) | −7926.75 | −0.531357 | ||||||||
\(607\) | 10388.1 | 0.694631 | 0.347315 | − | 0.937748i | \(-0.387093\pi\) | ||||
0.347315 | + | 0.937748i | \(0.387093\pi\) | |||||||
\(608\) | 26285.7 | 1.75333 | ||||||||
\(609\) | −3210.19 | −0.213602 | ||||||||
\(610\) | −8819.40 | −0.585389 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2337.54 | −0.154395 | ||||||||
\(613\) | 804.480 | 0.0530060 | 0.0265030 | − | 0.999649i | \(-0.491563\pi\) | ||||
0.0265030 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(614\) | 28970.0 | 1.90413 | ||||||||
\(615\) | 513.184 | 0.0336481 | ||||||||
\(616\) | 888.671 | 0.0581259 | ||||||||
\(617\) | −15218.3 | −0.992973 | −0.496486 | − | 0.868044i | \(-0.665377\pi\) | ||||
−0.496486 | + | 0.868044i | \(0.665377\pi\) | |||||||
\(618\) | −8573.83 | −0.558074 | ||||||||
\(619\) | 11462.5 | 0.744291 | 0.372145 | − | 0.928174i | \(-0.378622\pi\) | ||||
0.372145 | + | 0.928174i | \(0.378622\pi\) | |||||||
\(620\) | 1045.05 | 0.0676942 | ||||||||
\(621\) | 3212.73 | 0.207605 | ||||||||
\(622\) | 4672.33 | 0.301195 | ||||||||
\(623\) | −7154.66 | −0.460105 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12223.0 | 0.782270 | ||||||||
\(626\) | 21794.5 | 1.39151 | ||||||||
\(627\) | 9790.49 | 0.623596 | ||||||||
\(628\) | 13051.4 | 0.829311 | ||||||||
\(629\) | −9453.14 | −0.599239 | ||||||||
\(630\) | −756.419 | −0.0478356 | ||||||||
\(631\) | 4468.68 | 0.281926 | 0.140963 | − | 0.990015i | \(-0.454980\pi\) | ||||
0.140963 | + | 0.990015i | \(0.454980\pi\) | |||||||
\(632\) | −3718.30 | −0.234028 | ||||||||
\(633\) | −11606.6 | −0.728783 | ||||||||
\(634\) | −19717.3 | −1.23514 | ||||||||
\(635\) | −7610.37 | −0.475603 | ||||||||
\(636\) | 18779.7 | 1.17086 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21290.0 | 1.32113 | ||||||||
\(639\) | −2783.04 | −0.172293 | ||||||||
\(640\) | 1597.12 | 0.0986430 | ||||||||
\(641\) | 6142.36 | 0.378484 | 0.189242 | − | 0.981930i | \(-0.439397\pi\) | ||||
0.189242 | + | 0.981930i | \(0.439397\pi\) | |||||||
\(642\) | −5017.93 | −0.308477 | ||||||||
\(643\) | −20738.2 | −1.27190 | −0.635951 | − | 0.771729i | \(-0.719392\pi\) | ||||
−0.635951 | + | 0.771729i | \(0.719392\pi\) | |||||||
\(644\) | −7157.15 | −0.437937 | ||||||||
\(645\) | −1170.11 | −0.0714312 | ||||||||
\(646\) | 12040.7 | 0.733339 | ||||||||
\(647\) | 852.757 | 0.0518166 | 0.0259083 | − | 0.999664i | \(-0.491752\pi\) | ||||
0.0259083 | + | 0.999664i | \(0.491752\pi\) | |||||||
\(648\) | −333.972 | −0.0202464 | ||||||||
\(649\) | 21172.8 | 1.28060 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −763.303 | −0.0459542 | ||||||||
\(652\) | −21081.3 | −1.26627 | ||||||||
\(653\) | −7345.75 | −0.440217 | −0.220108 | − | 0.975475i | \(-0.570641\pi\) | ||||
−0.220108 | + | 0.975475i | \(0.570641\pi\) | |||||||
\(654\) | 5931.28 | 0.354635 | ||||||||
\(655\) | 133.462 | 0.00796151 | ||||||||
\(656\) | 3084.65 | 0.183591 | ||||||||
\(657\) | 3507.40 | 0.208275 | ||||||||
\(658\) | −14273.4 | −0.845645 | ||||||||
\(659\) | 12540.7 | 0.741297 | 0.370648 | − | 0.928773i | \(-0.379136\pi\) | ||||
0.370648 | + | 0.928773i | \(0.379136\pi\) | |||||||
\(660\) | 2655.84 | 0.156634 | ||||||||
\(661\) | 2242.95 | 0.131983 | 0.0659915 | − | 0.997820i | \(-0.478979\pi\) | ||||
0.0659915 | + | 0.997820i | \(0.478979\pi\) | |||||||
\(662\) | 35747.3 | 2.09873 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2832.97 | 0.165573 | ||||||||
\(665\) | 2062.76 | 0.120287 | ||||||||
\(666\) | −12155.4 | −0.707224 | ||||||||
\(667\) | −19051.7 | −1.10597 | ||||||||
\(668\) | 360.658 | 0.0208896 | ||||||||
\(669\) | 8440.66 | 0.487795 | ||||||||
\(670\) | −719.016 | −0.0414597 | ||||||||
\(671\) | −22617.0 | −1.30122 | ||||||||
\(672\) | −5208.03 | −0.298964 | ||||||||
\(673\) | −4776.46 | −0.273579 | −0.136790 | − | 0.990600i | \(-0.543678\pi\) | ||||
−0.136790 | + | 0.990600i | \(0.543678\pi\) | |||||||
\(674\) | −35156.0 | −2.00914 | ||||||||
\(675\) | 3123.82 | 0.178127 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7933.57 | −0.450387 | −0.225193 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225193 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(678\) | −19137.9 | −1.08405 | ||||||||
\(679\) | −11725.6 | −0.662723 | ||||||||
\(680\) | 362.917 | 0.0204665 | ||||||||
\(681\) | −13555.1 | −0.762750 | ||||||||
\(682\) | 5062.23 | 0.284227 | ||||||||
\(683\) | −23573.8 | −1.32068 | −0.660340 | − | 0.750967i | \(-0.729588\pi\) | ||||
−0.660340 | + | 0.750967i | \(0.729588\pi\) | |||||||
\(684\) | 8196.70 | 0.458200 | ||||||||
\(685\) | 628.904 | 0.0350791 | ||||||||
\(686\) | 17672.4 | 0.983581 | ||||||||
\(687\) | −3915.81 | −0.217463 | ||||||||
\(688\) | −7033.32 | −0.389743 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4489.15 | −0.247680 | ||||||||
\(691\) | 12543.8 | 0.690575 | 0.345288 | − | 0.938497i | \(-0.387781\pi\) | ||||
0.345288 | + | 0.938497i | \(0.387781\pi\) | |||||||
\(692\) | 17185.9 | 0.944087 | ||||||||
\(693\) | −1939.81 | −0.106331 | ||||||||
\(694\) | 51874.8 | 2.83738 | ||||||||
\(695\) | −305.006 | −0.0166468 | ||||||||
\(696\) | 1980.47 | 0.107858 | ||||||||
\(697\) | 1618.52 | 0.0879568 | ||||||||
\(698\) | −36947.9 | −2.00358 | ||||||||
\(699\) | 10081.6 | 0.545526 | ||||||||
\(700\) | −6959.09 | −0.375755 | ||||||||
\(701\) | −581.786 | −0.0313463 | −0.0156731 | − | 0.999877i | \(-0.504989\pi\) | ||||
−0.0156731 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33147.9 | 1.77837 | ||||||||
\(704\) | 20349.7 | 1.08943 | ||||||||
\(705\) | −4739.64 | −0.253199 | ||||||||
\(706\) | −22091.6 | −1.17766 | ||||||||
\(707\) | −4282.89 | −0.227828 | ||||||||
\(708\) | 17726.1 | 0.940944 | ||||||||
\(709\) | 20742.0 | 1.09871 | 0.549353 | − | 0.835590i | \(-0.314874\pi\) | ||||
0.549353 | + | 0.835590i | \(0.314874\pi\) | |||||||
\(710\) | 3888.74 | 0.205552 | ||||||||
\(711\) | 8116.38 | 0.428113 | ||||||||
\(712\) | 4413.94 | 0.232331 | ||||||||
\(713\) | −4530.01 | −0.237938 | ||||||||
\(714\) | −2385.66 | −0.125043 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4589.63 | −0.239556 | ||||||||
\(717\) | −14211.5 | −0.740221 | ||||||||
\(718\) | −11154.6 | −0.579788 | ||||||||
\(719\) | 25350.2 | 1.31489 | 0.657443 | − | 0.753504i | \(-0.271638\pi\) | ||||
0.657443 | + | 0.753504i | \(0.271638\pi\) | |||||||
\(720\) | −1509.78 | −0.0781474 | ||||||||
\(721\) | −4632.51 | −0.239284 | ||||||||
\(722\) | −13941.0 | −0.718602 | ||||||||
\(723\) | 14355.8 | 0.738449 | ||||||||
\(724\) | −19231.9 | −0.987223 | ||||||||
\(725\) | −18524.4 | −0.948938 | ||||||||
\(726\) | −3598.73 | −0.183969 | ||||||||
\(727\) | 33428.2 | 1.70534 | 0.852672 | − | 0.522447i | \(-0.174981\pi\) | ||||
0.852672 | + | 0.522447i | \(0.174981\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −4900.90 | −0.248480 | ||||||||
\(731\) | −3690.39 | −0.186722 | ||||||||
\(732\) | −18935.2 | −0.956101 | ||||||||
\(733\) | 3842.67 | 0.193632 | 0.0968160 | − | 0.995302i | \(-0.469134\pi\) | ||||
0.0968160 | + | 0.995302i | \(0.469134\pi\) | |||||||
\(734\) | −43184.4 | −2.17162 | ||||||||
\(735\) | 2729.81 | 0.136994 | ||||||||
\(736\) | −30908.3 | −1.54796 | ||||||||
\(737\) | −1843.89 | −0.0921582 | ||||||||
\(738\) | 2081.19 | 0.103807 | ||||||||
\(739\) | −29029.6 | −1.44502 | −0.722511 | − | 0.691359i | \(-0.757012\pi\) | ||||
−0.722511 | + | 0.691359i | \(0.757012\pi\) | |||||||
\(740\) | 8991.91 | 0.446688 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19166.3 | 0.948269 | ||||||||
\(743\) | 34996.7 | 1.72800 | 0.864000 | − | 0.503492i | \(-0.167952\pi\) | ||||
0.864000 | + | 0.503492i | \(0.167952\pi\) | |||||||
\(744\) | 470.906 | 0.0232046 | ||||||||
\(745\) | −1160.40 | −0.0570653 | ||||||||
\(746\) | 52623.2 | 2.58267 | ||||||||
\(747\) | −6183.86 | −0.302886 | ||||||||
\(748\) | 8376.19 | 0.409444 | ||||||||
\(749\) | −2711.23 | −0.132265 | ||||||||
\(750\) | −9080.82 | −0.442113 | ||||||||
\(751\) | 10454.1 | 0.507957 | 0.253979 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253979 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(752\) | −28489.1 | −1.38150 | ||||||||
\(753\) | 9821.58 | 0.475323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4628.32 | 0.223102 | ||||||||
\(756\) | −1624.03 | −0.0781287 | ||||||||
\(757\) | −28130.4 | −1.35062 | −0.675308 | − | 0.737536i | \(-0.735989\pi\) | ||||
−0.675308 | + | 0.737536i | \(0.735989\pi\) | |||||||
\(758\) | −9557.45 | −0.457971 | ||||||||
\(759\) | −11512.3 | −0.550552 | ||||||||
\(760\) | −1272.58 | −0.0607388 | ||||||||
\(761\) | −21087.0 | −1.00447 | −0.502236 | − | 0.864731i | \(-0.667489\pi\) | ||||
−0.502236 | + | 0.864731i | \(0.667489\pi\) | |||||||
\(762\) | −30863.4 | −1.46727 | ||||||||
\(763\) | 3204.72 | 0.152056 | ||||||||
\(764\) | 36519.7 | 1.72937 | ||||||||
\(765\) | −792.183 | −0.0374398 | ||||||||
\(766\) | 8177.54 | 0.385727 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8667.00 | −0.407218 | ||||||||
\(769\) | −19527.9 | −0.915728 | −0.457864 | − | 0.889022i | \(-0.651385\pi\) | ||||
−0.457864 | + | 0.889022i | \(0.651385\pi\) | |||||||
\(770\) | 2710.50 | 0.126857 | ||||||||
\(771\) | 19637.4 | 0.917283 | ||||||||
\(772\) | −7860.55 | −0.366460 | ||||||||
\(773\) | 29352.0 | 1.36574 | 0.682870 | − | 0.730540i | \(-0.260731\pi\) | ||||
0.682870 | + | 0.730540i | \(0.260731\pi\) | |||||||
\(774\) | −4745.31 | −0.220370 | ||||||||
\(775\) | −4404.64 | −0.204154 | ||||||||
\(776\) | 7233.92 | 0.334643 | ||||||||
\(777\) | −6567.65 | −0.303234 | ||||||||
\(778\) | 13377.5 | 0.616459 | ||||||||
\(779\) | −5675.42 | −0.261031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9972.54 | 0.456908 | ||||||||
\(782\) | −14158.3 | −0.647440 | ||||||||
\(783\) | −4323.01 | −0.197307 | ||||||||
\(784\) | 16408.4 | 0.747467 | ||||||||
\(785\) | 4423.06 | 0.201103 | ||||||||
\(786\) | 541.246 | 0.0245618 | ||||||||
\(787\) | −4463.12 | −0.202151 | −0.101076 | − | 0.994879i | \(-0.532228\pi\) | ||||
−0.101076 | + | 0.994879i | \(0.532228\pi\) | |||||||
\(788\) | −37325.2 | −1.68738 | ||||||||
\(789\) | −264.604 | −0.0119394 | ||||||||
\(790\) | −11341.0 | −0.510754 | ||||||||
\(791\) | −10340.3 | −0.464804 | ||||||||
\(792\) | 1196.73 | 0.0536919 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 15501.7 | 0.692866 | ||||||||
\(795\) | 6364.37 | 0.283926 | ||||||||
\(796\) | −21636.6 | −0.963426 | ||||||||
\(797\) | −34785.5 | −1.54600 | −0.773002 | − | 0.634404i | \(-0.781246\pi\) | ||||
−0.773002 | + | 0.634404i | \(0.781246\pi\) | |||||||
\(798\) | 8365.40 | 0.371093 | ||||||||
\(799\) | −14948.2 | −0.661866 | ||||||||
\(800\) | −30053.0 | −1.32817 | ||||||||
\(801\) | −9634.84 | −0.425007 | ||||||||
\(802\) | −8236.09 | −0.362627 | ||||||||
\(803\) | −12568.2 | −0.552330 | ||||||||
\(804\) | −1543.72 | −0.0677152 | ||||||||
\(805\) | −2425.53 | −0.106197 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13582.8 | 0.592487 | ||||||||
\(808\) | 2642.25 | 0.115042 | ||||||||
\(809\) | −10620.0 | −0.461530 | −0.230765 | − | 0.973010i | \(-0.574123\pi\) | ||||
−0.230765 | + | 0.973010i | \(0.574123\pi\) | |||||||
\(810\) | −1018.63 | −0.0441866 | ||||||||
\(811\) | −5497.87 | −0.238047 | −0.119024 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119024 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(812\) | 9630.57 | 0.416215 | ||||||||
\(813\) | 24965.5 | 1.07697 | ||||||||
\(814\) | 43556.7 | 1.87551 | ||||||||
\(815\) | −7144.34 | −0.307062 | ||||||||
\(816\) | −4761.66 | −0.204279 | ||||||||
\(817\) | 12940.5 | 0.554139 | ||||||||
\(818\) | −21420.5 | −0.915587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1539.55 | −0.0655653 | ||||||||
\(821\) | −21305.3 | −0.905678 | −0.452839 | − | 0.891592i | \(-0.649589\pi\) | ||||
−0.452839 | + | 0.891592i | \(0.649589\pi\) | |||||||
\(822\) | 2550.48 | 0.108222 | ||||||||
\(823\) | 17342.6 | 0.734537 | 0.367268 | − | 0.930115i | \(-0.380293\pi\) | ||||
0.367268 | + | 0.930115i | \(0.380293\pi\) | |||||||
\(824\) | 2857.94 | 0.120827 | ||||||||
\(825\) | −11193.7 | −0.472381 | ||||||||
\(826\) | 18091.0 | 0.762064 | ||||||||
\(827\) | −5129.96 | −0.215703 | −0.107851 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107851 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(828\) | −9638.19 | −0.404529 | ||||||||
\(829\) | −8471.81 | −0.354931 | −0.177466 | − | 0.984127i | \(-0.556790\pi\) | ||||
−0.177466 | + | 0.984127i | \(0.556790\pi\) | |||||||
\(830\) | 8640.72 | 0.361354 | ||||||||
\(831\) | 8643.93 | 0.360836 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8609.50 | 0.358105 | ||||||||
\(834\) | −1236.93 | −0.0513566 | ||||||||
\(835\) | 122.225 | 0.00506561 | ||||||||
\(836\) | −29371.5 | −1.21511 | ||||||||
\(837\) | −1027.90 | −0.0424486 | ||||||||
\(838\) | 28128.3 | 1.15952 | ||||||||
\(839\) | 19155.0 | 0.788207 | 0.394103 | − | 0.919066i | \(-0.371055\pi\) | ||||
0.394103 | + | 0.919066i | \(0.371055\pi\) | |||||||
\(840\) | 252.140 | 0.0103567 | ||||||||
\(841\) | 1246.67 | 0.0511160 | ||||||||
\(842\) | 31078.7 | 1.27202 | ||||||||
\(843\) | −8453.98 | −0.345398 | ||||||||
\(844\) | 34819.7 | 1.42007 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19221.3 | −0.781136 | ||||||||
\(847\) | −1944.42 | −0.0788797 | ||||||||
\(848\) | 38255.0 | 1.54915 | ||||||||
\(849\) | −793.804 | −0.0320887 | ||||||||
\(850\) | −13766.4 | −0.555512 | ||||||||
\(851\) | −38977.3 | −1.57006 | ||||||||
\(852\) | 8349.11 | 0.335723 | ||||||||
\(853\) | 18075.1 | 0.725532 | 0.362766 | − | 0.931880i | \(-0.381832\pi\) | ||||
0.362766 | + | 0.931880i | \(0.381832\pi\) | |||||||
\(854\) | −19324.9 | −0.774339 | ||||||||
\(855\) | 2777.82 | 0.111111 | ||||||||
\(856\) | 1672.64 | 0.0667871 | ||||||||
\(857\) | −21054.6 | −0.839219 | −0.419609 | − | 0.907705i | \(-0.637833\pi\) | ||||
−0.419609 | + | 0.907705i | \(0.637833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 920.322 | 0.0365553 | 0.0182776 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182776 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(860\) | 3510.33 | 0.139188 | ||||||||
\(861\) | 1124.48 | 0.0445090 | ||||||||
\(862\) | −55267.0 | −2.18376 | ||||||||
\(863\) | 19427.5 | 0.766304 | 0.383152 | − | 0.923685i | \(-0.374839\pi\) | ||||
0.383152 | + | 0.923685i | \(0.374839\pi\) | |||||||
\(864\) | −7013.40 | −0.276158 | ||||||||
\(865\) | 5824.21 | 0.228935 | ||||||||
\(866\) | 73044.7 | 2.86623 | ||||||||
\(867\) | 12240.5 | 0.479482 | ||||||||
\(868\) | 2289.91 | 0.0895444 | ||||||||
\(869\) | −29083.7 | −1.13532 | ||||||||
\(870\) | 6040.55 | 0.235395 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1977.09 | −0.0767808 | ||||||||
\(873\) | −15790.3 | −0.612168 | ||||||||
\(874\) | 49646.5 | 1.92142 | ||||||||
\(875\) | −4906.44 | −0.189563 | ||||||||
\(876\) | −10522.2 | −0.405836 | ||||||||
\(877\) | −14872.2 | −0.572632 | −0.286316 | − | 0.958135i | \(-0.592431\pi\) | ||||
−0.286316 | + | 0.958135i | \(0.592431\pi\) | |||||||
\(878\) | −29535.7 | −1.13529 | ||||||||
\(879\) | 12877.6 | 0.494141 | ||||||||
\(880\) | 5410.04 | 0.207241 | ||||||||
\(881\) | −12940.6 | −0.494870 | −0.247435 | − | 0.968905i | \(-0.579588\pi\) | ||||
−0.247435 | + | 0.968905i | \(0.579588\pi\) | |||||||
\(882\) | 11070.6 | 0.422637 | ||||||||
\(883\) | −25585.5 | −0.975108 | −0.487554 | − | 0.873093i | \(-0.662111\pi\) | ||||
−0.487554 | + | 0.873093i | \(0.662111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6007.30 | 0.228173 | ||||||||
\(886\) | 41928.8 | 1.58987 | ||||||||
\(887\) | 3716.46 | 0.140684 | 0.0703418 | − | 0.997523i | \(-0.477591\pi\) | ||||
0.0703418 | + | 0.997523i | \(0.477591\pi\) | |||||||
\(888\) | 4051.79 | 0.153118 | ||||||||
\(889\) | −16675.7 | −0.629118 | ||||||||
\(890\) | 13462.8 | 0.507049 | ||||||||
\(891\) | −2612.25 | −0.0982195 | ||||||||
\(892\) | −25322.0 | −0.950496 | ||||||||
\(893\) | 52416.7 | 1.96423 | ||||||||
\(894\) | −4705.92 | −0.176051 | ||||||||
\(895\) | −1555.40 | −0.0580910 | ||||||||
\(896\) | 3499.58 | 0.130483 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70680.3 | −2.62654 | ||||||||
\(899\) | 6095.52 | 0.226137 | ||||||||
\(900\) | −9371.47 | −0.347091 | ||||||||
\(901\) | 20072.5 | 0.742187 | ||||||||
\(902\) | −7457.57 | −0.275288 | ||||||||
\(903\) | −2563.93 | −0.0944876 | ||||||||
\(904\) | 6379.29 | 0.234703 | ||||||||
\(905\) | −6517.61 | −0.239395 | ||||||||
\(906\) | 18769.8 | 0.688285 | ||||||||
\(907\) | −12960.4 | −0.474469 | −0.237235 | − | 0.971452i | \(-0.576241\pi\) | ||||
−0.237235 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(908\) | 40665.3 | 1.48626 | ||||||||
\(909\) | −5767.56 | −0.210449 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36607.1 | −1.33134 | −0.665668 | − | 0.746248i | \(-0.731853\pi\) | ||||
−0.665668 | + | 0.746248i | \(0.731853\pi\) | |||||||
\(912\) | 16697.0 | 0.606242 | ||||||||
\(913\) | 22158.8 | 0.803230 | ||||||||
\(914\) | 58099.3 | 2.10258 | ||||||||
\(915\) | −6417.06 | −0.231849 | ||||||||
\(916\) | 11747.4 | 0.423740 | ||||||||
\(917\) | 292.440 | 0.0105313 | ||||||||
\(918\) | −3212.65 | −0.115505 | ||||||||
\(919\) | 20356.3 | 0.730676 | 0.365338 | − | 0.930875i | \(-0.380953\pi\) | ||||
0.365338 | + | 0.930875i | \(0.380953\pi\) | |||||||
\(920\) | 1496.38 | 0.0536243 | ||||||||
\(921\) | 21078.8 | 0.754147 | ||||||||
\(922\) | −12048.6 | −0.430370 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5819.43 | 0.207192 | ||||||||
\(925\) | −37898.7 | −1.34714 | ||||||||
\(926\) | −8545.61 | −0.303268 | ||||||||
\(927\) | −6238.38 | −0.221030 | ||||||||
\(928\) | 41589.8 | 1.47118 | ||||||||
\(929\) | 45069.7 | 1.59170 | 0.795849 | − | 0.605495i | \(-0.207025\pi\) | ||||
0.795849 | + | 0.605495i | \(0.207025\pi\) | |||||||
\(930\) | 1436.29 | 0.0506428 | ||||||||
\(931\) | −30189.6 | −1.06275 | ||||||||
\(932\) | −30244.9 | −1.06299 | ||||||||
\(933\) | 3399.62 | 0.119291 | ||||||||
\(934\) | 10984.7 | 0.384831 | ||||||||
\(935\) | 2838.65 | 0.0992876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6771.10 | −0.236075 | −0.118037 | − | 0.993009i | \(-0.537660\pi\) | ||||
−0.118037 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(938\) | −1575.50 | −0.0548420 | ||||||||
\(939\) | 15857.8 | 0.551119 | ||||||||
\(940\) | 14218.9 | 0.493372 | ||||||||
\(941\) | −36690.7 | −1.27108 | −0.635538 | − | 0.772070i | \(-0.719222\pi\) | ||||
−0.635538 | + | 0.772070i | \(0.719222\pi\) | |||||||
\(942\) | 17937.4 | 0.620417 | ||||||||
\(943\) | 6673.51 | 0.230455 | ||||||||
\(944\) | 36108.8 | 1.24496 | ||||||||
\(945\) | −550.376 | −0.0189457 | ||||||||
\(946\) | 17004.0 | 0.584406 | ||||||||
\(947\) | 50861.2 | 1.74527 | 0.872634 | − | 0.488375i | \(-0.162410\pi\) | ||||
0.872634 | + | 0.488375i | \(0.162410\pi\) | |||||||
\(948\) | −24349.1 | −0.834202 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48272.6 | 1.64860 | ||||||||
\(951\) | −14346.5 | −0.489187 | ||||||||
\(952\) | 795.219 | 0.0270727 | ||||||||
\(953\) | 11855.6 | 0.402980 | 0.201490 | − | 0.979491i | \(-0.435422\pi\) | ||||
0.201490 | + | 0.979491i | \(0.435422\pi\) | |||||||
\(954\) | 25810.3 | 0.875931 | ||||||||
\(955\) | 12376.4 | 0.419361 | ||||||||
\(956\) | 42634.5 | 1.44236 | ||||||||
\(957\) | 15490.8 | 0.523245 | ||||||||
\(958\) | −21525.5 | −0.725947 | ||||||||
\(959\) | 1378.04 | 0.0464019 | ||||||||
\(960\) | 5773.76 | 0.194112 | ||||||||
\(961\) | −28341.6 | −0.951349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3651.08 | −0.122175 | ||||||||
\(964\) | −43067.5 | −1.43891 | ||||||||
\(965\) | −2663.90 | −0.0888643 | ||||||||
\(966\) | −9836.56 | −0.327625 | ||||||||
\(967\) | −40661.7 | −1.35221 | −0.676107 | − | 0.736803i | \(-0.736334\pi\) | ||||
−0.676107 | + | 0.736803i | \(0.736334\pi\) | |||||||
\(968\) | 1199.58 | 0.0398304 | ||||||||
\(969\) | 8760.93 | 0.290445 | ||||||||
\(970\) | 22063.9 | 0.730339 | ||||||||
\(971\) | 57318.3 | 1.89437 | 0.947184 | − | 0.320690i | \(-0.103915\pi\) | ||||
0.947184 | + | 0.320690i | \(0.103915\pi\) | |||||||
\(972\) | −2187.00 | −0.0721688 | ||||||||
\(973\) | −668.324 | −0.0220200 | ||||||||
\(974\) | −50403.3 | −1.65814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38571.7 | −1.26501 | ||||||||
\(977\) | 3026.73 | 0.0991134 | 0.0495567 | − | 0.998771i | \(-0.484219\pi\) | ||||
0.0495567 | + | 0.998771i | \(0.484219\pi\) | |||||||
\(978\) | −28973.4 | −0.947308 | ||||||||
\(979\) | 34524.8 | 1.12709 | ||||||||
\(980\) | −8189.43 | −0.266941 | ||||||||
\(981\) | 4315.64 | 0.140457 | ||||||||
\(982\) | −81032.3 | −2.63324 | ||||||||
\(983\) | −33942.5 | −1.10132 | −0.550659 | − | 0.834730i | \(-0.685624\pi\) | ||||
−0.550659 | + | 0.834730i | \(0.685624\pi\) | |||||||
\(984\) | −693.729 | −0.0224749 | ||||||||
\(985\) | −12649.3 | −0.409179 | ||||||||
\(986\) | 19051.2 | 0.615327 | ||||||||
\(987\) | −10385.4 | −0.334925 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15216.3 | −0.489231 | ||||||||
\(990\) | 3650.10 | 0.117179 | ||||||||
\(991\) | 21637.5 | 0.693580 | 0.346790 | − | 0.937943i | \(-0.387272\pi\) | ||||
0.346790 | + | 0.937943i | \(0.387272\pi\) | |||||||
\(992\) | 9889.02 | 0.316509 | ||||||||
\(993\) | 26009.9 | 0.831219 | ||||||||
\(994\) | 8520.95 | 0.271900 | ||||||||
\(995\) | −7332.53 | −0.233625 | ||||||||
\(996\) | 18551.6 | 0.590190 | ||||||||
\(997\) | 19624.6 | 0.623388 | 0.311694 | − | 0.950182i | \(-0.399104\pi\) | ||||
0.311694 | + | 0.950182i | \(0.399104\pi\) | |||||||
\(998\) | −48296.3 | −1.53186 | ||||||||
\(999\) | −8844.33 | −0.280102 |
(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 | 507.4.a.k.1.1 | 4 | ||
3.2 | odd | 2 | 1521.4.a.z.1.4 | 4 | |||
13.5 | odd | 4 | 507.4.b.e.337.4 | 4 | |||
13.6 | odd | 12 | 39.4.j.b.10.2 | yes | 4 | ||
13.8 | odd | 4 | 507.4.b.e.337.1 | 4 | |||
13.11 | odd | 12 | 39.4.j.b.4.2 | ✓ | 4 | ||
13.12 | even | 2 | inner | 507.4.a.k.1.4 | 4 | ||
39.11 | even | 12 | 117.4.q.d.82.1 | 4 | |||
39.32 | even | 12 | 117.4.q.d.10.1 | 4 | |||
39.38 | odd | 2 | 1521.4.a.z.1.1 | 4 | |||
52.11 | even | 12 | 624.4.bv.c.433.2 | 4 | |||
52.19 | even | 12 | 624.4.bv.c.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.b.4.2 | ✓ | 4 | 13.11 | odd | 12 | ||
39.4.j.b.10.2 | yes | 4 | 13.6 | odd | 12 | ||
117.4.q.d.10.1 | 4 | 39.32 | even | 12 | |||
117.4.q.d.82.1 | 4 | 39.11 | even | 12 | |||
507.4.a.k.1.1 | 4 | 1.1 | even | 1 | trivial | ||
507.4.a.k.1.4 | 4 | 13.12 | even | 2 | inner | ||
507.4.b.e.337.1 | 4 | 13.8 | odd | 4 | |||
507.4.b.e.337.4 | 4 | 13.5 | odd | 4 | |||
624.4.bv.c.49.1 | 4 | 52.19 | even | 12 | |||
624.4.bv.c.433.2 | 4 | 52.11 | even | 12 | |||
1521.4.a.z.1.1 | 4 | 39.38 | odd | 2 | |||
1521.4.a.z.1.4 | 4 | 3.2 | odd | 2 |