Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.0765073\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0765073 | 0.0270494 | 0.0135247 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135247 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.99415 | −0.999268 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.229522 | −0.0156170 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −1.22367 | −0.0540790 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.8947 | 0.298624 | 0.149312 | − | 0.988790i | \(-0.452294\pi\) | ||||
0.149312 | + | 0.988790i | \(0.452294\pi\) | |||||||
\(12\) | 23.9824 | 0.576928 | ||||||||
\(13\) | 26.5468 | 0.566366 | 0.283183 | − | 0.959066i | \(-0.408610\pi\) | ||||
0.283183 | + | 0.959066i | \(0.408610\pi\) | |||||||
\(14\) | −0.535551 | −0.0102237 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 63.8596 | 0.997806 | ||||||||
\(17\) | 95.1237 | 1.35711 | 0.678556 | − | 0.734549i | \(-0.262606\pi\) | ||||
0.678556 | + | 0.734549i | \(0.262606\pi\) | |||||||
\(18\) | 0.688565 | 0.00901647 | ||||||||
\(19\) | −35.4649 | −0.428221 | −0.214111 | − | 0.976809i | \(-0.568685\pi\) | ||||
−0.214111 | + | 0.976809i | \(0.568685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0.833522 | 0.00807761 | ||||||||
\(23\) | −62.8303 | −0.569610 | −0.284805 | − | 0.958585i | \(-0.591929\pi\) | ||||
−0.284805 | + | 0.958585i | \(0.591929\pi\) | |||||||
\(24\) | 3.67101 | 0.0312225 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.03102 | 0.0153199 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 55.9590 | 0.377688 | ||||||||
\(29\) | 117.823 | 0.754452 | 0.377226 | − | 0.926121i | \(-0.376878\pi\) | ||||
0.377226 | + | 0.926121i | \(0.376878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −171.090 | −0.991250 | −0.495625 | − | 0.868537i | \(-0.665061\pi\) | ||||
−0.495625 | + | 0.868537i | \(0.665061\pi\) | |||||||
\(32\) | 14.6751 | 0.0810691 | ||||||||
\(33\) | −32.6840 | −0.172411 | ||||||||
\(34\) | 7.27766 | 0.0367091 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −71.9473 | −0.333089 | ||||||||
\(37\) | −203.813 | −0.905584 | −0.452792 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452792 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(38\) | −2.71332 | −0.0115831 | ||||||||
\(39\) | −79.6404 | −0.326992 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −428.705 | −1.63299 | −0.816494 | − | 0.577354i | \(-0.804085\pi\) | ||||
−0.816494 | + | 0.577354i | \(0.804085\pi\) | |||||||
\(42\) | 1.60665 | 0.00590266 | ||||||||
\(43\) | 96.5851 | 0.342537 | 0.171268 | − | 0.985224i | \(-0.445213\pi\) | ||||
0.171268 | + | 0.985224i | \(0.445213\pi\) | |||||||
\(44\) | −87.0936 | −0.298406 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.80698 | −0.0154076 | ||||||||
\(47\) | 407.806 | 1.26563 | 0.632816 | − | 0.774303i | \(-0.281899\pi\) | ||||
0.632816 | + | 0.774303i | \(0.281899\pi\) | |||||||
\(48\) | −191.579 | −0.576083 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −285.371 | −0.783529 | ||||||||
\(52\) | −212.219 | −0.565952 | ||||||||
\(53\) | 380.874 | 0.987115 | 0.493558 | − | 0.869713i | \(-0.335696\pi\) | ||||
0.493558 | + | 0.869713i | \(0.335696\pi\) | |||||||
\(54\) | −2.06570 | −0.00520566 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.56568 | 0.0204399 | ||||||||
\(57\) | 106.395 | 0.247234 | ||||||||
\(58\) | 9.01429 | 0.0204075 | ||||||||
\(59\) | −287.149 | −0.633620 | −0.316810 | − | 0.948489i | \(-0.602612\pi\) | ||||
−0.316810 | + | 0.948489i | \(0.602612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −823.988 | −1.72952 | −0.864761 | − | 0.502183i | \(-0.832530\pi\) | ||||
−0.864761 | + | 0.502183i | \(0.832530\pi\) | |||||||
\(62\) | −13.0897 | −0.0268127 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −509.754 | −0.995613 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.50057 | −0.00466361 | ||||||||
\(67\) | −585.549 | −1.06770 | −0.533852 | − | 0.845578i | \(-0.679256\pi\) | ||||
−0.533852 | + | 0.845578i | \(0.679256\pi\) | |||||||
\(68\) | −760.433 | −1.35612 | ||||||||
\(69\) | 188.491 | 0.328864 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −653.856 | −1.09294 | −0.546468 | − | 0.837480i | \(-0.684028\pi\) | ||||
−0.546468 | + | 0.837480i | \(0.684028\pi\) | |||||||
\(72\) | −11.0130 | −0.0180263 | ||||||||
\(73\) | 1051.77 | 1.68630 | 0.843152 | − | 0.537676i | \(-0.180698\pi\) | ||||
0.843152 | + | 0.537676i | \(0.180698\pi\) | |||||||
\(74\) | −15.5932 | −0.0244955 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 283.512 | 0.427908 | ||||||||
\(77\) | −76.2627 | −0.112869 | ||||||||
\(78\) | −6.09307 | −0.00884493 | ||||||||
\(79\) | −751.268 | −1.06993 | −0.534964 | − | 0.844875i | \(-0.679675\pi\) | ||||
−0.534964 | + | 0.844875i | \(0.679675\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −32.7991 | −0.0441713 | ||||||||
\(83\) | −844.677 | −1.11705 | −0.558526 | − | 0.829487i | \(-0.688633\pi\) | ||||
−0.558526 | + | 0.829487i | \(0.688633\pi\) | |||||||
\(84\) | −167.877 | −0.218058 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.38946 | 0.00926542 | ||||||||
\(87\) | −353.468 | −0.435583 | ||||||||
\(88\) | −13.3315 | −0.0161493 | ||||||||
\(89\) | −262.334 | −0.312442 | −0.156221 | − | 0.987722i | \(-0.549931\pi\) | ||||
−0.156221 | + | 0.987722i | \(0.549931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −185.828 | −0.214066 | ||||||||
\(92\) | 502.275 | 0.569193 | ||||||||
\(93\) | 513.271 | 0.572298 | ||||||||
\(94\) | 31.2001 | 0.0342346 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −44.0252 | −0.0468052 | ||||||||
\(97\) | 814.908 | 0.853004 | 0.426502 | − | 0.904487i | \(-0.359746\pi\) | ||||
0.426502 | + | 0.904487i | \(0.359746\pi\) | |||||||
\(98\) | 3.74886 | 0.00386420 | ||||||||
\(99\) | 98.0521 | 0.0995414 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 315.660 | 0.310984 | 0.155492 | − | 0.987837i | \(-0.450304\pi\) | ||||
0.155492 | + | 0.987837i | \(0.450304\pi\) | |||||||
\(102\) | −21.8330 | −0.0211940 | ||||||||
\(103\) | −1858.26 | −1.77767 | −0.888835 | − | 0.458228i | \(-0.848484\pi\) | ||||
−0.888835 | + | 0.458228i | \(0.848484\pi\) | |||||||
\(104\) | −32.4845 | −0.0306285 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.1397 | 0.0267009 | ||||||||
\(107\) | −1202.75 | −1.08668 | −0.543338 | − | 0.839514i | \(-0.682840\pi\) | ||||
−0.543338 | + | 0.839514i | \(0.682840\pi\) | |||||||
\(108\) | 215.842 | 0.192309 | ||||||||
\(109\) | 262.450 | 0.230625 | 0.115313 | − | 0.993329i | \(-0.463213\pi\) | ||||
0.115313 | + | 0.993329i | \(0.463213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 611.438 | 0.522839 | ||||||||
\(112\) | −447.017 | −0.377135 | ||||||||
\(113\) | 138.803 | 0.115553 | 0.0577765 | − | 0.998330i | \(-0.481599\pi\) | ||||
0.0577765 | + | 0.998330i | \(0.481599\pi\) | |||||||
\(114\) | 8.13997 | 0.00668752 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −941.892 | −0.753900 | ||||||||
\(117\) | 238.921 | 0.188789 | ||||||||
\(118\) | −21.9690 | −0.0171390 | ||||||||
\(119\) | −665.866 | −0.512940 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1212.31 | −0.910824 | ||||||||
\(122\) | −63.0411 | −0.0467826 | ||||||||
\(123\) | 1286.12 | 0.942806 | ||||||||
\(124\) | 1367.72 | 0.990525 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.81996 | −0.00340790 | ||||||||
\(127\) | 2632.46 | 1.83931 | 0.919657 | − | 0.392722i | \(-0.128466\pi\) | ||||
0.919657 | + | 0.392722i | \(0.128466\pi\) | |||||||
\(128\) | −156.400 | −0.108000 | ||||||||
\(129\) | −289.755 | −0.197764 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −301.676 | −0.201203 | −0.100601 | − | 0.994927i | \(-0.532077\pi\) | ||||
−0.100601 | + | 0.994927i | \(0.532077\pi\) | |||||||
\(132\) | 261.281 | 0.172285 | ||||||||
\(133\) | 248.254 | 0.161852 | ||||||||
\(134\) | −44.7987 | −0.0288808 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −116.400 | −0.0733913 | ||||||||
\(137\) | −2131.17 | −1.32904 | −0.664520 | − | 0.747271i | \(-0.731364\pi\) | ||||
−0.664520 | + | 0.747271i | \(0.731364\pi\) | |||||||
\(138\) | 14.4209 | 0.00889559 | ||||||||
\(139\) | 1691.63 | 1.03225 | 0.516123 | − | 0.856515i | \(-0.327375\pi\) | ||||
0.516123 | + | 0.856515i | \(0.327375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1223.42 | −0.730712 | ||||||||
\(142\) | −50.0247 | −0.0295633 | ||||||||
\(143\) | 289.219 | 0.169131 | ||||||||
\(144\) | 574.736 | 0.332602 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 80.4679 | 0.0456135 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 1629.31 | 0.904921 | ||||||||
\(149\) | −80.4827 | −0.0442510 | −0.0221255 | − | 0.999755i | \(-0.507043\pi\) | ||||
−0.0221255 | + | 0.999755i | \(0.507043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 833.698 | 0.449307 | 0.224654 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224654 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(152\) | 43.3973 | 0.0231578 | ||||||||
\(153\) | 856.114 | 0.452371 | ||||||||
\(154\) | −5.83465 | −0.00305305 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 636.657 | 0.326752 | ||||||||
\(157\) | 2108.68 | 1.07192 | 0.535960 | − | 0.844244i | \(-0.319950\pi\) | ||||
0.535960 | + | 0.844244i | \(0.319950\pi\) | |||||||
\(158\) | −57.4775 | −0.0289409 | ||||||||
\(159\) | −1142.62 | −0.569911 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 439.812 | 0.215292 | ||||||||
\(162\) | 6.19709 | 0.00300549 | ||||||||
\(163\) | 174.223 | 0.0837189 | 0.0418594 | − | 0.999124i | \(-0.486672\pi\) | ||||
0.0418594 | + | 0.999124i | \(0.486672\pi\) | |||||||
\(164\) | 3427.13 | 1.63179 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −64.6239 | −0.0302156 | ||||||||
\(167\) | −1009.94 | −0.467972 | −0.233986 | − | 0.972240i | \(-0.575177\pi\) | ||||
−0.233986 | + | 0.972240i | \(0.575177\pi\) | |||||||
\(168\) | −25.6970 | −0.0118010 | ||||||||
\(169\) | −1492.27 | −0.679229 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −319.184 | −0.142740 | ||||||||
\(172\) | −772.115 | −0.342286 | ||||||||
\(173\) | −3404.03 | −1.49598 | −0.747988 | − | 0.663712i | \(-0.768980\pi\) | ||||
−0.747988 | + | 0.663712i | \(0.768980\pi\) | |||||||
\(174\) | −27.0429 | −0.0117823 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 695.729 | 0.297969 | ||||||||
\(177\) | 861.446 | 0.365820 | ||||||||
\(178\) | −20.0704 | −0.00845136 | ||||||||
\(179\) | −1493.22 | −0.623509 | −0.311755 | − | 0.950163i | \(-0.600917\pi\) | ||||
−0.311755 | + | 0.950163i | \(0.600917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1293.52 | −0.531196 | −0.265598 | − | 0.964084i | \(-0.585569\pi\) | ||||
−0.265598 | + | 0.964084i | \(0.585569\pi\) | |||||||
\(182\) | −14.2172 | −0.00579037 | ||||||||
\(183\) | 2471.96 | 0.998540 | ||||||||
\(184\) | 76.8835 | 0.0308039 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 39.2690 | 0.0154803 | ||||||||
\(187\) | 1036.34 | 0.405267 | ||||||||
\(188\) | −3260.06 | −1.26471 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2004.86 | 0.759510 | 0.379755 | − | 0.925087i | \(-0.376008\pi\) | ||||
0.379755 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(192\) | 1529.26 | 0.574817 | ||||||||
\(193\) | 446.924 | 0.166686 | 0.0833428 | − | 0.996521i | \(-0.473440\pi\) | ||||
0.0833428 | + | 0.996521i | \(0.473440\pi\) | |||||||
\(194\) | 62.3464 | 0.0230733 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −391.713 | −0.142753 | ||||||||
\(197\) | −713.335 | −0.257985 | −0.128992 | − | 0.991646i | \(-0.541174\pi\) | ||||
−0.128992 | + | 0.991646i | \(0.541174\pi\) | |||||||
\(198\) | 7.50170 | 0.00269254 | ||||||||
\(199\) | −4073.28 | −1.45099 | −0.725496 | − | 0.688227i | \(-0.758389\pi\) | ||||
−0.725496 | + | 0.688227i | \(0.758389\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1756.65 | 0.616439 | ||||||||
\(202\) | 24.1503 | 0.00841192 | ||||||||
\(203\) | −824.759 | −0.285156 | ||||||||
\(204\) | 2281.30 | 0.782955 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −142.170 | −0.0480849 | ||||||||
\(207\) | −565.473 | −0.189870 | ||||||||
\(208\) | 1695.27 | 0.565123 | ||||||||
\(209\) | −386.378 | −0.127877 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4996.44 | 1.63018 | 0.815092 | − | 0.579331i | \(-0.196686\pi\) | ||||
0.815092 | + | 0.579331i | \(0.196686\pi\) | |||||||
\(212\) | −3044.77 | −0.986393 | ||||||||
\(213\) | 1961.57 | 0.631007 | ||||||||
\(214\) | −92.0192 | −0.0293939 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 33.0390 | 0.0104075 | ||||||||
\(217\) | 1197.63 | 0.374657 | ||||||||
\(218\) | 20.0793 | 0.00623827 | ||||||||
\(219\) | −3155.30 | −0.973588 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2525.23 | 0.768622 | ||||||||
\(222\) | 46.7795 | 0.0141425 | ||||||||
\(223\) | 2326.57 | 0.698650 | 0.349325 | − | 0.937002i | \(-0.386411\pi\) | ||||
0.349325 | + | 0.937002i | \(0.386411\pi\) | |||||||
\(224\) | −102.725 | −0.0306412 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.6194 | 0.00312564 | ||||||||
\(227\) | −731.574 | −0.213904 | −0.106952 | − | 0.994264i | \(-0.534109\pi\) | ||||
−0.106952 | + | 0.994264i | \(0.534109\pi\) | |||||||
\(228\) | −850.535 | −0.247053 | ||||||||
\(229\) | −913.230 | −0.263528 | −0.131764 | − | 0.991281i | \(-0.542064\pi\) | ||||
−0.131764 | + | 0.991281i | \(0.542064\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 228.788 | 0.0651652 | ||||||||
\(232\) | −144.176 | −0.0408000 | ||||||||
\(233\) | −5301.18 | −1.49052 | −0.745262 | − | 0.666772i | \(-0.767675\pi\) | ||||
−0.745262 | + | 0.666772i | \(0.767675\pi\) | |||||||
\(234\) | 18.2792 | 0.00510662 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2295.51 | 0.633156 | ||||||||
\(237\) | 2253.80 | 0.617723 | ||||||||
\(238\) | −50.9436 | −0.0138747 | ||||||||
\(239\) | −2696.95 | −0.729920 | −0.364960 | − | 0.931023i | \(-0.618917\pi\) | ||||
−0.364960 | + | 0.931023i | \(0.618917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4299.38 | 1.14916 | 0.574579 | − | 0.818449i | \(-0.305166\pi\) | ||||
0.574579 | + | 0.818449i | \(0.305166\pi\) | |||||||
\(242\) | −92.7502 | −0.0246372 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 6587.08 | 1.72826 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 98.3972 | 0.0255023 | ||||||||
\(247\) | −941.480 | −0.242530 | ||||||||
\(248\) | 209.358 | 0.0536058 | ||||||||
\(249\) | 2534.03 | 0.644930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4712.81 | 1.18514 | 0.592570 | − | 0.805519i | \(-0.298113\pi\) | ||||
0.592570 | + | 0.805519i | \(0.298113\pi\) | |||||||
\(252\) | 503.631 | 0.125896 | ||||||||
\(253\) | −684.516 | −0.170099 | ||||||||
\(254\) | 201.402 | 0.0497524 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4066.06 | 0.992691 | ||||||||
\(257\) | −6833.53 | −1.65861 | −0.829307 | − | 0.558793i | \(-0.811265\pi\) | ||||
−0.829307 | + | 0.558793i | \(0.811265\pi\) | |||||||
\(258\) | −22.1684 | −0.00534939 | ||||||||
\(259\) | 1426.69 | 0.342278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1060.40 | 0.251484 | ||||||||
\(262\) | −23.0804 | −0.00544242 | ||||||||
\(263\) | −8221.38 | −1.92757 | −0.963787 | − | 0.266674i | \(-0.914075\pi\) | ||||
−0.963787 | + | 0.266674i | \(0.914075\pi\) | |||||||
\(264\) | 39.9944 | 0.00932381 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 18.9933 | 0.00437801 | ||||||||
\(267\) | 787.001 | 0.180388 | ||||||||
\(268\) | 4680.96 | 1.06692 | ||||||||
\(269\) | 6319.20 | 1.43230 | 0.716149 | − | 0.697947i | \(-0.245903\pi\) | ||||
0.716149 | + | 0.697947i | \(0.245903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1127.67 | −0.252771 | −0.126386 | − | 0.991981i | \(-0.540338\pi\) | ||||
−0.126386 | + | 0.991981i | \(0.540338\pi\) | |||||||
\(272\) | 6074.56 | 1.35413 | ||||||||
\(273\) | 557.483 | 0.123591 | ||||||||
\(274\) | −163.050 | −0.0359497 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1506.82 | −0.328624 | ||||||||
\(277\) | −2522.90 | −0.547243 | −0.273622 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273622 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(278\) | 129.422 | 0.0279216 | ||||||||
\(279\) | −1539.81 | −0.330417 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9070.33 | −1.92559 | −0.962794 | − | 0.270235i | \(-0.912898\pi\) | ||||
−0.962794 | + | 0.270235i | \(0.912898\pi\) | |||||||
\(282\) | −93.6004 | −0.0197653 | ||||||||
\(283\) | −145.080 | −0.0304739 | −0.0152369 | − | 0.999884i | \(-0.504850\pi\) | ||||
−0.0152369 | + | 0.999884i | \(0.504850\pi\) | |||||||
\(284\) | 5227.02 | 1.09214 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22.1273 | 0.00457489 | ||||||||
\(287\) | 3000.94 | 0.617211 | ||||||||
\(288\) | 132.076 | 0.0270230 | ||||||||
\(289\) | 4135.53 | 0.841752 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2444.73 | −0.492482 | ||||||||
\(292\) | −8407.99 | −1.68507 | ||||||||
\(293\) | 5876.23 | 1.17165 | 0.585824 | − | 0.810438i | \(-0.300771\pi\) | ||||
0.585824 | + | 0.810438i | \(0.300771\pi\) | |||||||
\(294\) | −11.2466 | −0.00223100 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 249.399 | 0.0489731 | ||||||||
\(297\) | −294.156 | −0.0574703 | ||||||||
\(298\) | −6.15751 | −0.00119696 | ||||||||
\(299\) | −1667.94 | −0.322608 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −676.095 | −0.129467 | ||||||||
\(302\) | 63.7839 | 0.0121535 | ||||||||
\(303\) | −946.980 | −0.179547 | ||||||||
\(304\) | −2264.77 | −0.427282 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 65.4989 | 0.0122364 | ||||||||
\(307\) | −2894.45 | −0.538094 | −0.269047 | − | 0.963127i | \(-0.586709\pi\) | ||||
−0.269047 | + | 0.963127i | \(0.586709\pi\) | |||||||
\(308\) | 609.655 | 0.112787 | ||||||||
\(309\) | 5574.78 | 1.02634 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3009.61 | 0.548744 | 0.274372 | − | 0.961624i | \(-0.411530\pi\) | ||||
0.274372 | + | 0.961624i | \(0.411530\pi\) | |||||||
\(312\) | 97.4535 | 0.0176834 | ||||||||
\(313\) | 10064.0 | 1.81741 | 0.908706 | − | 0.417436i | \(-0.137071\pi\) | ||||
0.908706 | + | 0.417436i | \(0.137071\pi\) | |||||||
\(314\) | 161.330 | 0.0289948 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6005.75 | 1.06914 | ||||||||
\(317\) | 8304.18 | 1.47132 | 0.735661 | − | 0.677349i | \(-0.236871\pi\) | ||||
0.735661 | + | 0.677349i | \(0.236871\pi\) | |||||||
\(318\) | −87.4190 | −0.0154158 | ||||||||
\(319\) | 1283.64 | 0.225298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3608.25 | 0.627393 | ||||||||
\(322\) | 33.6488 | 0.00582353 | ||||||||
\(323\) | −3373.55 | −0.581144 | ||||||||
\(324\) | −647.526 | −0.111030 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3293 | 0.00226455 | ||||||||
\(327\) | −787.349 | −0.133151 | ||||||||
\(328\) | 524.593 | 0.0883103 | ||||||||
\(329\) | −2854.64 | −0.478364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7066.25 | −1.17340 | −0.586702 | − | 0.809803i | \(-0.699574\pi\) | ||||
−0.586702 | + | 0.809803i | \(0.699574\pi\) | |||||||
\(332\) | 6752.47 | 1.11623 | ||||||||
\(333\) | −1834.31 | −0.301861 | ||||||||
\(334\) | −77.2677 | −0.0126584 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1341.05 | 0.217739 | ||||||||
\(337\) | 1510.59 | 0.244175 | 0.122087 | − | 0.992519i | \(-0.461041\pi\) | ||||
0.122087 | + | 0.992519i | \(0.461041\pi\) | |||||||
\(338\) | −114.169 | −0.0183727 | ||||||||
\(339\) | −416.409 | −0.0667145 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1863.97 | −0.296011 | ||||||||
\(342\) | −24.4199 | −0.00386104 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −118.188 | −0.0185241 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −260.433 | −0.0404653 | ||||||||
\(347\) | −11921.4 | −1.84431 | −0.922154 | − | 0.386822i | \(-0.873573\pi\) | ||||
−0.922154 | + | 0.386822i | \(0.873573\pi\) | |||||||
\(348\) | 2825.68 | 0.435265 | ||||||||
\(349\) | −3329.00 | −0.510594 | −0.255297 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255297 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −716.764 | −0.108997 | ||||||||
\(352\) | 159.880 | 0.0242092 | ||||||||
\(353\) | −5883.87 | −0.887158 | −0.443579 | − | 0.896235i | \(-0.646291\pi\) | ||||
−0.443579 | + | 0.896235i | \(0.646291\pi\) | |||||||
\(354\) | 65.9069 | 0.00989523 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2097.13 | 0.312213 | ||||||||
\(357\) | 1997.60 | 0.296146 | ||||||||
\(358\) | −114.242 | −0.0168656 | ||||||||
\(359\) | 822.114 | 0.120862 | 0.0604311 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604311 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5601.24 | −0.816626 | ||||||||
\(362\) | −98.9636 | −0.0143685 | ||||||||
\(363\) | 3636.92 | 0.525864 | ||||||||
\(364\) | 1485.53 | 0.213910 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 189.123 | 0.0270099 | ||||||||
\(367\) | 9873.06 | 1.40428 | 0.702139 | − | 0.712040i | \(-0.252229\pi\) | ||||
0.702139 | + | 0.712040i | \(0.252229\pi\) | |||||||
\(368\) | −4012.32 | −0.568360 | ||||||||
\(369\) | −3858.35 | −0.544329 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2666.12 | −0.373095 | ||||||||
\(372\) | −4103.17 | −0.571880 | ||||||||
\(373\) | −7152.24 | −0.992840 | −0.496420 | − | 0.868083i | \(-0.665352\pi\) | ||||
−0.496420 | + | 0.868083i | \(0.665352\pi\) | |||||||
\(374\) | 79.2877 | 0.0109622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −499.020 | −0.0684441 | ||||||||
\(377\) | 3127.82 | 0.427296 | ||||||||
\(378\) | 14.4599 | 0.00196755 | ||||||||
\(379\) | −14117.4 | −1.91336 | −0.956680 | − | 0.291140i | \(-0.905965\pi\) | ||||
−0.956680 | + | 0.291140i | \(0.905965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7897.38 | −1.06193 | ||||||||
\(382\) | 153.386 | 0.0205443 | ||||||||
\(383\) | 5293.18 | 0.706185 | 0.353093 | − | 0.935588i | \(-0.385130\pi\) | ||||
0.353093 | + | 0.935588i | \(0.385130\pi\) | |||||||
\(384\) | 469.201 | 0.0623537 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.1930 | 0.00450875 | ||||||||
\(387\) | 869.266 | 0.114179 | ||||||||
\(388\) | −6514.50 | −0.852380 | ||||||||
\(389\) | −8910.01 | −1.16132 | −0.580662 | − | 0.814144i | \(-0.697206\pi\) | ||||
−0.580662 | + | 0.814144i | \(0.697206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5976.66 | −0.773024 | ||||||||
\(392\) | −59.9598 | −0.00772557 | ||||||||
\(393\) | 905.029 | 0.116165 | ||||||||
\(394\) | −54.5753 | −0.00697834 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −783.843 | −0.0994686 | ||||||||
\(397\) | −3986.11 | −0.503922 | −0.251961 | − | 0.967737i | \(-0.581075\pi\) | ||||
−0.251961 | + | 0.967737i | \(0.581075\pi\) | |||||||
\(398\) | −311.636 | −0.0392485 | ||||||||
\(399\) | −744.763 | −0.0934456 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3119.10 | 0.388429 | 0.194215 | − | 0.980959i | \(-0.437784\pi\) | ||||
0.194215 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(402\) | 134.396 | 0.0166743 | ||||||||
\(403\) | −4541.90 | −0.561410 | ||||||||
\(404\) | −2523.43 | −0.310756 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −63.1000 | −0.00771331 | ||||||||
\(407\) | −2220.47 | −0.270429 | ||||||||
\(408\) | 349.200 | 0.0423725 | ||||||||
\(409\) | −4125.99 | −0.498819 | −0.249410 | − | 0.968398i | \(-0.580237\pi\) | ||||
−0.249410 | + | 0.968398i | \(0.580237\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6393.52 | 0.767321 | ||||||||
\(412\) | 14855.2 | 1.77637 | ||||||||
\(413\) | 2010.04 | 0.239486 | ||||||||
\(414\) | −43.2628 | −0.00513587 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 389.576 | 0.0459148 | ||||||||
\(417\) | −5074.89 | −0.595967 | ||||||||
\(418\) | −29.5608 | −0.00345901 | ||||||||
\(419\) | −13550.2 | −1.57988 | −0.789939 | − | 0.613185i | \(-0.789888\pi\) | ||||
−0.789939 | + | 0.613185i | \(0.789888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6464.49 | 0.748361 | 0.374180 | − | 0.927356i | \(-0.377924\pi\) | ||||
0.374180 | + | 0.927356i | \(0.377924\pi\) | |||||||
\(422\) | 382.264 | 0.0440955 | ||||||||
\(423\) | 3670.26 | 0.421877 | ||||||||
\(424\) | −466.064 | −0.0533822 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 150.074 | 0.0170684 | ||||||||
\(427\) | 5767.92 | 0.653698 | ||||||||
\(428\) | 9614.97 | 1.08588 | ||||||||
\(429\) | −867.656 | −0.0976477 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8652.70 | −0.967020 | −0.483510 | − | 0.875339i | \(-0.660638\pi\) | ||||
−0.483510 | + | 0.875339i | \(0.660638\pi\) | |||||||
\(432\) | −1724.21 | −0.192028 | ||||||||
\(433\) | 10201.3 | 1.13221 | 0.566103 | − | 0.824334i | \(-0.308450\pi\) | ||||
0.566103 | + | 0.824334i | \(0.308450\pi\) | |||||||
\(434\) | 91.6276 | 0.0101343 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2098.06 | −0.230456 | ||||||||
\(437\) | 2228.27 | 0.243919 | ||||||||
\(438\) | −241.404 | −0.0263350 | ||||||||
\(439\) | 13063.9 | 1.42029 | 0.710143 | − | 0.704057i | \(-0.248630\pi\) | ||||
0.710143 | + | 0.704057i | \(0.248630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 193.199 | 0.0207908 | ||||||||
\(443\) | −2032.27 | −0.217959 | −0.108980 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108980 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(444\) | −4887.93 | −0.522456 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 178.000 | 0.0188981 | ||||||||
\(447\) | 241.448 | 0.0255483 | ||||||||
\(448\) | 3568.28 | 0.376306 | ||||||||
\(449\) | 1640.75 | 0.172454 | 0.0862271 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862271 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4670.60 | −0.487650 | ||||||||
\(452\) | −1109.61 | −0.115468 | ||||||||
\(453\) | −2501.09 | −0.259408 | ||||||||
\(454\) | −55.9707 | −0.00578598 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −130.192 | −0.0133702 | ||||||||
\(457\) | −5578.74 | −0.571033 | −0.285517 | − | 0.958374i | \(-0.592165\pi\) | ||||
−0.285517 | + | 0.958374i | \(0.592165\pi\) | |||||||
\(458\) | −69.8687 | −0.00712828 | ||||||||
\(459\) | −2568.34 | −0.261176 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15124.5 | −1.52803 | −0.764013 | − | 0.645201i | \(-0.776773\pi\) | ||||
−0.764013 | + | 0.645201i | \(0.776773\pi\) | |||||||
\(462\) | 17.5040 | 0.00176268 | ||||||||
\(463\) | −14882.8 | −1.49387 | −0.746934 | − | 0.664898i | \(-0.768475\pi\) | ||||
−0.746934 | + | 0.664898i | \(0.768475\pi\) | |||||||
\(464\) | 7524.10 | 0.752797 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −405.579 | −0.0403178 | ||||||||
\(467\) | −5926.96 | −0.587296 | −0.293648 | − | 0.955914i | \(-0.594869\pi\) | ||||
−0.293648 | + | 0.955914i | \(0.594869\pi\) | |||||||
\(468\) | −1909.97 | −0.188651 | ||||||||
\(469\) | 4098.84 | 0.403554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6326.05 | −0.618873 | ||||||||
\(472\) | 351.375 | 0.0342655 | ||||||||
\(473\) | 1052.26 | 0.102290 | ||||||||
\(474\) | 172.432 | 0.0167090 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5323.03 | 0.512565 | ||||||||
\(477\) | 3427.87 | 0.329038 | ||||||||
\(478\) | −206.336 | −0.0197439 | ||||||||
\(479\) | 13214.0 | 1.26046 | 0.630231 | − | 0.776407i | \(-0.282960\pi\) | ||||
0.630231 | + | 0.776407i | \(0.282960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5410.58 | −0.512892 | ||||||||
\(482\) | 328.933 | 0.0310840 | ||||||||
\(483\) | −1319.44 | −0.124299 | ||||||||
\(484\) | 9691.35 | 0.910157 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.5913 | −0.00173522 | ||||||||
\(487\) | −17646.0 | −1.64192 | −0.820961 | − | 0.570984i | \(-0.806562\pi\) | ||||
−0.820961 | + | 0.570984i | \(0.806562\pi\) | |||||||
\(488\) | 1008.29 | 0.0935309 | ||||||||
\(489\) | −522.668 | −0.0483351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11540.7 | −1.06074 | −0.530371 | − | 0.847766i | \(-0.677947\pi\) | ||||
−0.530371 | + | 0.847766i | \(0.677947\pi\) | |||||||
\(492\) | −10281.4 | −0.942116 | ||||||||
\(493\) | 11207.7 | 1.02388 | ||||||||
\(494\) | −72.0301 | −0.00656029 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10925.8 | −0.989075 | ||||||||
\(497\) | 4576.99 | 0.413091 | ||||||||
\(498\) | 193.872 | 0.0174450 | ||||||||
\(499\) | −6820.43 | −0.611873 | −0.305936 | − | 0.952052i | \(-0.598969\pi\) | ||||
−0.305936 | + | 0.952052i | \(0.598969\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3029.82 | 0.270184 | ||||||||
\(502\) | 360.564 | 0.0320573 | ||||||||
\(503\) | 7174.71 | 0.635993 | 0.317996 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317996 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(504\) | 77.0911 | 0.00681332 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −52.3704 | −0.00460109 | ||||||||
\(507\) | 4476.80 | 0.392153 | ||||||||
\(508\) | −21044.3 | −1.83797 | ||||||||
\(509\) | −3889.82 | −0.338729 | −0.169365 | − | 0.985553i | \(-0.554172\pi\) | ||||
−0.169365 | + | 0.985553i | \(0.554172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7362.38 | −0.637363 | ||||||||
\(512\) | 1562.29 | 0.134851 | ||||||||
\(513\) | 957.552 | 0.0824112 | ||||||||
\(514\) | −522.815 | −0.0448645 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2316.35 | 0.197619 | ||||||||
\(517\) | 4442.92 | 0.377948 | ||||||||
\(518\) | 109.152 | 0.00925843 | ||||||||
\(519\) | 10212.1 | 0.863702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3687.49 | 0.310080 | 0.155040 | − | 0.987908i | \(-0.450449\pi\) | ||||
0.155040 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(522\) | 81.1286 | 0.00680250 | ||||||||
\(523\) | −8280.56 | −0.692320 | −0.346160 | − | 0.938175i | \(-0.612515\pi\) | ||||
−0.346160 | + | 0.938175i | \(0.612515\pi\) | |||||||
\(524\) | 2411.65 | 0.201056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −628.995 | −0.0521397 | ||||||||
\(527\) | −16274.8 | −1.34524 | ||||||||
\(528\) | −2087.19 | −0.172032 | ||||||||
\(529\) | −8219.35 | −0.675545 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2584.34 | −0.211207 | ||||||||
\(532\) | −1984.58 | −0.161734 | ||||||||
\(533\) | −11380.8 | −0.924869 | ||||||||
\(534\) | 60.2113 | 0.00487940 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 716.518 | 0.0577404 | ||||||||
\(537\) | 4479.65 | 0.359983 | ||||||||
\(538\) | 483.465 | 0.0387428 | ||||||||
\(539\) | 533.839 | 0.0426606 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9002.84 | 0.715457 | 0.357728 | − | 0.933826i | \(-0.383551\pi\) | ||||
0.357728 | + | 0.933826i | \(0.383551\pi\) | |||||||
\(542\) | −86.2748 | −0.00683731 | ||||||||
\(543\) | 3880.56 | 0.306686 | ||||||||
\(544\) | 1395.95 | 0.110020 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 42.6515 | 0.00334307 | ||||||||
\(547\) | 17066.3 | 1.33401 | 0.667005 | − | 0.745053i | \(-0.267576\pi\) | ||||
0.667005 | + | 0.745053i | \(0.267576\pi\) | |||||||
\(548\) | 17036.9 | 1.32807 | ||||||||
\(549\) | −7415.89 | −0.576508 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4178.57 | −0.323073 | ||||||||
\(552\) | −230.650 | −0.0177847 | ||||||||
\(553\) | 5258.88 | 0.404395 | ||||||||
\(554\) | −193.020 | −0.0148026 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13523.1 | −1.03149 | ||||||||
\(557\) | −23487.4 | −1.78670 | −0.893351 | − | 0.449360i | \(-0.851652\pi\) | ||||
−0.893351 | + | 0.449360i | \(0.851652\pi\) | |||||||
\(558\) | −117.807 | −0.00893757 | ||||||||
\(559\) | 2564.03 | 0.194001 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3109.03 | −0.233981 | ||||||||
\(562\) | −693.946 | −0.0520860 | ||||||||
\(563\) | 15357.7 | 1.14964 | 0.574821 | − | 0.818279i | \(-0.305072\pi\) | ||||
0.574821 | + | 0.818279i | \(0.305072\pi\) | |||||||
\(564\) | 9780.19 | 0.730178 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.0997 | −0.000824300 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 800.103 | 0.0591049 | ||||||||
\(569\) | 8871.22 | 0.653604 | 0.326802 | − | 0.945093i | \(-0.394029\pi\) | ||||
0.326802 | + | 0.945093i | \(0.394029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6428.16 | −0.471121 | −0.235561 | − | 0.971860i | \(-0.575693\pi\) | ||||
−0.235561 | + | 0.971860i | \(0.575693\pi\) | |||||||
\(572\) | −2312.06 | −0.169007 | ||||||||
\(573\) | −6014.57 | −0.438503 | ||||||||
\(574\) | 229.593 | 0.0166952 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4587.78 | −0.331871 | ||||||||
\(577\) | 8519.56 | 0.614686 | 0.307343 | − | 0.951599i | \(-0.400560\pi\) | ||||
0.307343 | + | 0.951599i | \(0.400560\pi\) | |||||||
\(578\) | 316.398 | 0.0227689 | ||||||||
\(579\) | −1340.77 | −0.0962360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5912.74 | 0.422206 | ||||||||
\(582\) | −187.039 | −0.0133214 | ||||||||
\(583\) | 4149.50 | 0.294777 | ||||||||
\(584\) | −1287.02 | −0.0911936 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 449.574 | 0.0316924 | ||||||||
\(587\) | 13458.2 | 0.946300 | 0.473150 | − | 0.880982i | \(-0.343117\pi\) | ||||
0.473150 | + | 0.880982i | \(0.343117\pi\) | |||||||
\(588\) | 1175.14 | 0.0824183 | ||||||||
\(589\) | 6067.70 | 0.424474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2140.01 | 0.148948 | ||||||||
\(592\) | −13015.4 | −0.903597 | ||||||||
\(593\) | −15744.8 | −1.09032 | −0.545162 | − | 0.838331i | \(-0.683532\pi\) | ||||
−0.545162 | + | 0.838331i | \(0.683532\pi\) | |||||||
\(594\) | −22.5051 | −0.00155454 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 643.390 | 0.0442186 | ||||||||
\(597\) | 12219.8 | 0.837730 | ||||||||
\(598\) | −127.610 | −0.00872635 | ||||||||
\(599\) | −9108.67 | −0.621319 | −0.310660 | − | 0.950521i | \(-0.600550\pi\) | ||||
−0.310660 | + | 0.950521i | \(0.600550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25596.1 | 1.73725 | 0.868625 | − | 0.495470i | \(-0.165004\pi\) | ||||
0.868625 | + | 0.495470i | \(0.165004\pi\) | |||||||
\(602\) | −51.7262 | −0.00350200 | ||||||||
\(603\) | −5269.94 | −0.355901 | ||||||||
\(604\) | −6664.70 | −0.448978 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −72.4509 | −0.00485663 | ||||||||
\(607\) | −4719.62 | −0.315590 | −0.157795 | − | 0.987472i | \(-0.550439\pi\) | ||||
−0.157795 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(608\) | −520.450 | −0.0347155 | ||||||||
\(609\) | 2474.28 | 0.164635 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10826.0 | 0.716811 | ||||||||
\(612\) | −6843.90 | −0.452040 | ||||||||
\(613\) | 8663.56 | 0.570829 | 0.285414 | − | 0.958404i | \(-0.407869\pi\) | ||||
0.285414 | + | 0.958404i | \(0.407869\pi\) | |||||||
\(614\) | −221.446 | −0.0145551 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 93.3203 | 0.00610387 | ||||||||
\(617\) | 22393.6 | 1.46115 | 0.730577 | − | 0.682830i | \(-0.239251\pi\) | ||||
0.730577 | + | 0.682830i | \(0.239251\pi\) | |||||||
\(618\) | 426.511 | 0.0277618 | ||||||||
\(619\) | −22053.3 | −1.43198 | −0.715991 | − | 0.698109i | \(-0.754025\pi\) | ||||
−0.715991 | + | 0.698109i | \(0.754025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1696.42 | 0.109621 | ||||||||
\(622\) | 230.257 | 0.0148432 | ||||||||
\(623\) | 1836.34 | 0.118092 | ||||||||
\(624\) | −5085.80 | −0.326274 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 769.968 | 0.0491599 | ||||||||
\(627\) | 1159.14 | 0.0738300 | ||||||||
\(628\) | −16857.1 | −1.07114 | ||||||||
\(629\) | −19387.4 | −1.22898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1637.02 | −0.103278 | −0.0516392 | − | 0.998666i | \(-0.516445\pi\) | ||||
−0.0516392 | + | 0.998666i | \(0.516445\pi\) | |||||||
\(632\) | 919.303 | 0.0578606 | ||||||||
\(633\) | −14989.3 | −0.941187 | ||||||||
\(634\) | 635.330 | 0.0397984 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9134.30 | 0.569494 | ||||||||
\(637\) | 1300.79 | 0.0809095 | ||||||||
\(638\) | 98.2078 | 0.00609417 | ||||||||
\(639\) | −5884.70 | −0.364312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25331.3 | 1.56089 | 0.780443 | − | 0.625227i | \(-0.214994\pi\) | ||||
0.780443 | + | 0.625227i | \(0.214994\pi\) | |||||||
\(642\) | 276.058 | 0.0169706 | ||||||||
\(643\) | −2162.69 | −0.132641 | −0.0663205 | − | 0.997798i | \(-0.521126\pi\) | ||||
−0.0663205 | + | 0.997798i | \(0.521126\pi\) | |||||||
\(644\) | −3515.92 | −0.215135 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −258.101 | −0.0157196 | ||||||||
\(647\) | −247.980 | −0.0150682 | −0.00753408 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753408 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(648\) | −99.1171 | −0.00600878 | ||||||||
\(649\) | −3128.39 | −0.189214 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3592.90 | −0.216308 | ||||||||
\(652\) | −1392.76 | −0.0836576 | ||||||||
\(653\) | −1225.37 | −0.0734339 | −0.0367169 | − | 0.999326i | \(-0.511690\pi\) | ||||
−0.0367169 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(654\) | −60.2380 | −0.00360167 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27376.9 | −1.62940 | ||||||||
\(657\) | 9465.91 | 0.562101 | ||||||||
\(658\) | −218.401 | −0.0129394 | ||||||||
\(659\) | −2284.95 | −0.135067 | −0.0675335 | − | 0.997717i | \(-0.521513\pi\) | ||||
−0.0675335 | + | 0.997717i | \(0.521513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24079.0 | 1.41689 | 0.708445 | − | 0.705766i | \(-0.249397\pi\) | ||||
0.708445 | + | 0.705766i | \(0.249397\pi\) | |||||||
\(662\) | −540.620 | −0.0317399 | ||||||||
\(663\) | −7575.70 | −0.443764 | ||||||||
\(664\) | 1033.60 | 0.0604091 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −140.338 | −0.00816517 | ||||||||
\(667\) | −7402.84 | −0.429744 | ||||||||
\(668\) | 8073.60 | 0.467630 | ||||||||
\(669\) | −6979.72 | −0.403366 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8977.08 | −0.516478 | ||||||||
\(672\) | 308.176 | 0.0176907 | ||||||||
\(673\) | 31756.3 | 1.81889 | 0.909447 | − | 0.415819i | \(-0.136505\pi\) | ||||
0.909447 | + | 0.415819i | \(0.136505\pi\) | |||||||
\(674\) | 115.571 | 0.00660479 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11929.4 | 0.678732 | ||||||||
\(677\) | 19214.7 | 1.09081 | 0.545406 | − | 0.838172i | \(-0.316375\pi\) | ||||
0.545406 | + | 0.838172i | \(0.316375\pi\) | |||||||
\(678\) | −31.8583 | −0.00180459 | ||||||||
\(679\) | −5704.36 | −0.322405 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2194.72 | 0.123498 | ||||||||
\(682\) | −142.608 | −0.00800693 | ||||||||
\(683\) | 16969.5 | 0.950688 | 0.475344 | − | 0.879800i | \(-0.342324\pi\) | ||||
0.475344 | + | 0.879800i | \(0.342324\pi\) | |||||||
\(684\) | 2551.60 | 0.142636 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.2420 | −0.00146053 | ||||||||
\(687\) | 2739.69 | 0.152148 | ||||||||
\(688\) | 6167.88 | 0.341785 | ||||||||
\(689\) | 10111.0 | 0.559069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9412.73 | 0.518202 | 0.259101 | − | 0.965850i | \(-0.416574\pi\) | ||||
0.259101 | + | 0.965850i | \(0.416574\pi\) | |||||||
\(692\) | 27212.3 | 1.49488 | ||||||||
\(693\) | −686.364 | −0.0376231 | ||||||||
\(694\) | −912.075 | −0.0498875 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 432.528 | 0.0235559 | ||||||||
\(697\) | −40780.0 | −2.21615 | ||||||||
\(698\) | −254.693 | −0.0138113 | ||||||||
\(699\) | 15903.5 | 0.860554 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14947.9 | 0.805384 | 0.402692 | − | 0.915335i | \(-0.368075\pi\) | ||||
0.402692 | + | 0.915335i | \(0.368075\pi\) | |||||||
\(702\) | −54.8376 | −0.00294831 | ||||||||
\(703\) | 7228.20 | 0.387790 | ||||||||
\(704\) | −5553.60 | −0.297314 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −450.159 | −0.0239971 | ||||||||
\(707\) | −2209.62 | −0.117541 | ||||||||
\(708\) | −6886.52 | −0.365553 | ||||||||
\(709\) | 14067.4 | 0.745152 | 0.372576 | − | 0.928002i | \(-0.378475\pi\) | ||||
0.372576 | + | 0.928002i | \(0.378475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6761.41 | −0.356642 | ||||||||
\(712\) | 321.009 | 0.0168965 | ||||||||
\(713\) | 10749.7 | 0.564626 | ||||||||
\(714\) | 152.831 | 0.00801057 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11937.0 | 0.623053 | ||||||||
\(717\) | 8090.84 | 0.421420 | ||||||||
\(718\) | 62.8977 | 0.00326925 | ||||||||
\(719\) | 20536.2 | 1.06519 | 0.532595 | − | 0.846370i | \(-0.321217\pi\) | ||||
0.532595 | + | 0.846370i | \(0.321217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13007.8 | 0.671896 | ||||||||
\(722\) | −428.536 | −0.0220893 | ||||||||
\(723\) | −12898.1 | −0.663467 | ||||||||
\(724\) | 10340.6 | 0.530807 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 278.251 | 0.0142243 | ||||||||
\(727\) | 15008.2 | 0.765643 | 0.382821 | − | 0.923822i | \(-0.374953\pi\) | ||||
0.382821 | + | 0.923822i | \(0.374953\pi\) | |||||||
\(728\) | 227.391 | 0.0115765 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9187.53 | 0.464861 | ||||||||
\(732\) | −19761.2 | −0.997810 | ||||||||
\(733\) | −26461.7 | −1.33340 | −0.666701 | − | 0.745325i | \(-0.732294\pi\) | ||||
−0.666701 | + | 0.745325i | \(0.732294\pi\) | |||||||
\(734\) | 755.361 | 0.0379849 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −922.039 | −0.0461777 | ||||||||
\(737\) | −6379.36 | −0.318842 | ||||||||
\(738\) | −295.191 | −0.0147238 | ||||||||
\(739\) | 21868.2 | 1.08854 | 0.544272 | − | 0.838909i | \(-0.316806\pi\) | ||||
0.544272 | + | 0.838909i | \(0.316806\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2824.44 | 0.140025 | ||||||||
\(742\) | −203.978 | −0.0100920 | ||||||||
\(743\) | 23832.7 | 1.17677 | 0.588383 | − | 0.808582i | \(-0.299765\pi\) | ||||
0.588383 | + | 0.808582i | \(0.299765\pi\) | |||||||
\(744\) | −628.074 | −0.0309493 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −547.199 | −0.0268557 | ||||||||
\(747\) | −7602.09 | −0.372351 | ||||||||
\(748\) | −8284.67 | −0.404970 | ||||||||
\(749\) | 8419.26 | 0.410725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17221.2 | −0.836763 | −0.418381 | − | 0.908271i | \(-0.637402\pi\) | ||||
−0.418381 | + | 0.908271i | \(0.637402\pi\) | |||||||
\(752\) | 26042.3 | 1.26285 | ||||||||
\(753\) | −14138.4 | −0.684241 | ||||||||
\(754\) | 239.301 | 0.0115581 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1510.89 | −0.0726861 | ||||||||
\(757\) | 1461.19 | 0.0701557 | 0.0350779 | − | 0.999385i | \(-0.488832\pi\) | ||||
0.0350779 | + | 0.999385i | \(0.488832\pi\) | |||||||
\(758\) | −1080.09 | −0.0517553 | ||||||||
\(759\) | 2053.55 | 0.0982069 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6949.62 | −0.331043 | −0.165521 | − | 0.986206i | \(-0.552931\pi\) | ||||
−0.165521 | + | 0.986206i | \(0.552931\pi\) | |||||||
\(762\) | −604.207 | −0.0287245 | ||||||||
\(763\) | −1837.15 | −0.0871681 | ||||||||
\(764\) | −16027.1 | −0.758954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 404.967 | 0.0191019 | ||||||||
\(767\) | −7622.88 | −0.358861 | ||||||||
\(768\) | −12198.2 | −0.573131 | ||||||||
\(769\) | −12778.2 | −0.599209 | −0.299605 | − | 0.954063i | \(-0.596855\pi\) | ||||
−0.299605 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20500.6 | 0.957602 | ||||||||
\(772\) | −3572.78 | −0.166564 | ||||||||
\(773\) | 20178.8 | 0.938915 | 0.469458 | − | 0.882955i | \(-0.344449\pi\) | ||||
0.469458 | + | 0.882955i | \(0.344449\pi\) | |||||||
\(774\) | 66.5051 | 0.00308847 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −997.178 | −0.0461296 | ||||||||
\(777\) | −4280.07 | −0.197615 | ||||||||
\(778\) | −681.680 | −0.0314131 | ||||||||
\(779\) | 15204.0 | 0.699280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7123.55 | −0.326377 | ||||||||
\(782\) | −457.258 | −0.0209098 | ||||||||
\(783\) | −3181.21 | −0.145194 | ||||||||
\(784\) | 3129.12 | 0.142544 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 69.2413 | 0.00314218 | ||||||||
\(787\) | −782.952 | −0.0354628 | −0.0177314 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177314 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(788\) | 5702.51 | 0.257796 | ||||||||
\(789\) | 24664.1 | 1.11289 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −971.620 | −0.0436749 | ||||||||
\(792\) | −119.983 | −0.00538310 | ||||||||
\(793\) | −21874.3 | −0.979543 | ||||||||
\(794\) | −304.966 | −0.0136308 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32562.4 | 1.44993 | ||||||||
\(797\) | −18184.7 | −0.808200 | −0.404100 | − | 0.914715i | \(-0.632415\pi\) | ||||
−0.404100 | + | 0.914715i | \(0.632415\pi\) | |||||||
\(798\) | −56.9798 | −0.00252765 | ||||||||
\(799\) | 38792.1 | 1.71760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2361.00 | −0.104147 | ||||||||
\(802\) | 238.634 | 0.0105068 | ||||||||
\(803\) | 11458.7 | 0.503571 | ||||||||
\(804\) | −14042.9 | −0.615988 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −347.489 | −0.0151858 | ||||||||
\(807\) | −18957.6 | −0.826938 | ||||||||
\(808\) | −386.263 | −0.0168177 | ||||||||
\(809\) | 33601.8 | 1.46029 | 0.730146 | − | 0.683291i | \(-0.239452\pi\) | ||||
0.730146 | + | 0.683291i | \(0.239452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4640.05 | −0.200905 | −0.100453 | − | 0.994942i | \(-0.532029\pi\) | ||||
−0.100453 | + | 0.994942i | \(0.532029\pi\) | |||||||
\(812\) | 6593.24 | 0.284948 | ||||||||
\(813\) | 3383.01 | 0.145937 | ||||||||
\(814\) | −169.882 | −0.00731495 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −18223.7 | −0.781809 | ||||||||
\(817\) | −3425.38 | −0.146682 | ||||||||
\(818\) | −315.668 | −0.0134928 | ||||||||
\(819\) | −1672.45 | −0.0713554 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34248.4 | 1.45588 | 0.727939 | − | 0.685641i | \(-0.240478\pi\) | ||||
0.727939 | + | 0.685641i | \(0.240478\pi\) | |||||||
\(822\) | 489.151 | 0.0207556 | ||||||||
\(823\) | −5076.24 | −0.215002 | −0.107501 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107501 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(824\) | 2273.90 | 0.0961346 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 153.783 | 0.00647795 | ||||||||
\(827\) | 10769.6 | 0.452835 | 0.226418 | − | 0.974030i | \(-0.427299\pi\) | ||||
0.226418 | + | 0.974030i | \(0.427299\pi\) | |||||||
\(828\) | 4520.47 | 0.189731 | ||||||||
\(829\) | 25104.1 | 1.05175 | 0.525876 | − | 0.850561i | \(-0.323738\pi\) | ||||
0.525876 | + | 0.850561i | \(0.323738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7568.70 | 0.315951 | ||||||||
\(832\) | −13532.3 | −0.563881 | ||||||||
\(833\) | 4661.06 | 0.193873 | ||||||||
\(834\) | −388.266 | −0.0161206 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3088.77 | 0.127784 | ||||||||
\(837\) | 4619.44 | 0.190766 | ||||||||
\(838\) | −1036.69 | −0.0427348 | ||||||||
\(839\) | 37028.0 | 1.52366 | 0.761829 | − | 0.647778i | \(-0.224301\pi\) | ||||
0.761829 | + | 0.647778i | \(0.224301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10506.8 | −0.430801 | ||||||||
\(842\) | 494.580 | 0.0202427 | ||||||||
\(843\) | 27211.0 | 1.11174 | ||||||||
\(844\) | −39942.3 | −1.62899 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 280.801 | 0.0114115 | ||||||||
\(847\) | 8486.14 | 0.344259 | ||||||||
\(848\) | 24322.5 | 0.984949 | ||||||||
\(849\) | 435.240 | 0.0175941 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12805.6 | 0.515829 | ||||||||
\(852\) | −15681.1 | −0.630545 | ||||||||
\(853\) | −22334.8 | −0.896518 | −0.448259 | − | 0.893904i | \(-0.647956\pi\) | ||||
−0.448259 | + | 0.893904i | \(0.647956\pi\) | |||||||
\(854\) | 441.288 | 0.0176821 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1471.77 | 0.0587664 | ||||||||
\(857\) | 18241.5 | 0.727090 | 0.363545 | − | 0.931577i | \(-0.381566\pi\) | ||||
0.363545 | + | 0.931577i | \(0.381566\pi\) | |||||||
\(858\) | −66.3820 | −0.00264131 | ||||||||
\(859\) | −12413.0 | −0.493045 | −0.246523 | − | 0.969137i | \(-0.579288\pi\) | ||||
−0.246523 | + | 0.969137i | \(0.579288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9002.81 | −0.356347 | ||||||||
\(862\) | −661.994 | −0.0261573 | ||||||||
\(863\) | −4676.16 | −0.184448 | −0.0922238 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922238 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(864\) | −396.227 | −0.0156017 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 780.477 | 0.0306255 | ||||||||
\(867\) | −12406.6 | −0.485986 | ||||||||
\(868\) | −9574.05 | −0.374383 | ||||||||
\(869\) | −8184.82 | −0.319506 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15544.5 | −0.604711 | ||||||||
\(872\) | −321.152 | −0.0124720 | ||||||||
\(873\) | 7334.18 | 0.284335 | ||||||||
\(874\) | 170.479 | 0.00659787 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25224.0 | 0.972875 | ||||||||
\(877\) | −7649.96 | −0.294551 | −0.147275 | − | 0.989096i | \(-0.547050\pi\) | ||||
−0.147275 | + | 0.989096i | \(0.547050\pi\) | |||||||
\(878\) | 999.483 | 0.0384179 | ||||||||
\(879\) | −17628.7 | −0.676451 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6816.13 | 0.260660 | 0.130330 | − | 0.991471i | \(-0.458396\pi\) | ||||
0.130330 | + | 0.991471i | \(0.458396\pi\) | |||||||
\(882\) | 33.7397 | 0.00128807 | ||||||||
\(883\) | −22141.7 | −0.843860 | −0.421930 | − | 0.906628i | \(-0.638647\pi\) | ||||
−0.421930 | + | 0.906628i | \(0.638647\pi\) | |||||||
\(884\) | −20187.1 | −0.768060 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −155.483 | −0.00589566 | ||||||||
\(887\) | −28729.2 | −1.08752 | −0.543762 | − | 0.839240i | \(-0.683001\pi\) | ||||
−0.543762 | + | 0.839240i | \(0.683001\pi\) | |||||||
\(888\) | −748.197 | −0.0282746 | ||||||||
\(889\) | −18427.2 | −0.695196 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 882.469 | 0.0331805 | ||||||||
\(892\) | −18599.0 | −0.698139 | ||||||||
\(893\) | −14462.8 | −0.541970 | ||||||||
\(894\) | 18.4725 | 0.000691067 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1094.80 | 0.0408201 | ||||||||
\(897\) | 5003.83 | 0.186258 | ||||||||
\(898\) | 125.530 | 0.00466478 | ||||||||
\(899\) | −20158.3 | −0.747851 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36230.2 | 1.33963 | ||||||||
\(902\) | −357.335 | −0.0131906 | ||||||||
\(903\) | 2028.29 | 0.0747477 | ||||||||
\(904\) | −169.849 | −0.00624899 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −191.352 | −0.00701682 | ||||||||
\(907\) | 47268.0 | 1.73044 | 0.865219 | − | 0.501395i | \(-0.167180\pi\) | ||||
0.865219 | + | 0.501395i | \(0.167180\pi\) | |||||||
\(908\) | 5848.31 | 0.213748 | ||||||||
\(909\) | 2840.94 | 0.103661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32904.1 | −1.19666 | −0.598332 | − | 0.801248i | \(-0.704170\pi\) | ||||
−0.598332 | + | 0.801248i | \(0.704170\pi\) | |||||||
\(912\) | 6794.32 | 0.246691 | ||||||||
\(913\) | −9202.48 | −0.333579 | ||||||||
\(914\) | −426.814 | −0.0154461 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7300.49 | 0.263335 | ||||||||
\(917\) | 2111.73 | 0.0760476 | ||||||||
\(918\) | −196.497 | −0.00706466 | ||||||||
\(919\) | −2561.48 | −0.0919426 | −0.0459713 | − | 0.998943i | \(-0.514638\pi\) | ||||
−0.0459713 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8683.34 | 0.310669 | ||||||||
\(922\) | −1157.14 | −0.0413322 | ||||||||
\(923\) | −17357.8 | −0.619002 | ||||||||
\(924\) | −1828.97 | −0.0651175 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1138.64 | −0.0404082 | ||||||||
\(927\) | −16724.4 | −0.592556 | ||||||||
\(928\) | 1729.06 | 0.0611628 | ||||||||
\(929\) | −44532.6 | −1.57273 | −0.786365 | − | 0.617762i | \(-0.788040\pi\) | ||||
−0.786365 | + | 0.617762i | \(0.788040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1737.78 | −0.0611745 | ||||||||
\(932\) | 42378.4 | 1.48943 | ||||||||
\(933\) | −9028.83 | −0.316817 | ||||||||
\(934\) | −453.456 | −0.0158860 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −292.360 | −0.0102095 | ||||||||
\(937\) | 6891.28 | 0.240265 | 0.120133 | − | 0.992758i | \(-0.461668\pi\) | ||||
0.120133 | + | 0.992758i | \(0.461668\pi\) | |||||||
\(938\) | 313.591 | 0.0109159 | ||||||||
\(939\) | −30192.0 | −1.04928 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36509.6 | 1.26480 | 0.632401 | − | 0.774641i | \(-0.282069\pi\) | ||||
0.632401 | + | 0.774641i | \(0.282069\pi\) | |||||||
\(942\) | −483.989 | −0.0167401 | ||||||||
\(943\) | 26935.7 | 0.930166 | ||||||||
\(944\) | −18337.2 | −0.632229 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 80.5057 | 0.00276688 | ||||||||
\(947\) | −23454.7 | −0.804830 | −0.402415 | − | 0.915457i | \(-0.631829\pi\) | ||||
−0.402415 | + | 0.915457i | \(0.631829\pi\) | |||||||
\(948\) | −18017.2 | −0.617271 | ||||||||
\(949\) | 27921.1 | 0.955065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24912.5 | −0.849469 | ||||||||
\(952\) | 814.799 | 0.0277393 | ||||||||
\(953\) | 8009.19 | 0.272238 | 0.136119 | − | 0.990692i | \(-0.456537\pi\) | ||||
0.136119 | + | 0.990692i | \(0.456537\pi\) | |||||||
\(954\) | 262.257 | 0.00890030 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21559.8 | 0.729386 | ||||||||
\(957\) | −3850.92 | −0.130076 | ||||||||
\(958\) | 1010.96 | 0.0340948 | ||||||||
\(959\) | 14918.2 | 0.502330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −519.069 | −0.0174237 | ||||||||
\(962\) | −413.948 | −0.0138734 | ||||||||
\(963\) | −10824.8 | −0.362225 | ||||||||
\(964\) | −34369.8 | −1.14832 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −100.946 | −0.00336222 | ||||||||
\(967\) | −1962.54 | −0.0652648 | −0.0326324 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326324 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(968\) | 1483.46 | 0.0492564 | ||||||||
\(969\) | 10120.7 | 0.335524 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52109.6 | −1.72222 | −0.861110 | − | 0.508419i | \(-0.830230\pi\) | ||||
−0.861110 | + | 0.508419i | \(0.830230\pi\) | |||||||
\(972\) | 1942.58 | 0.0641031 | ||||||||
\(973\) | −11841.4 | −0.390152 | ||||||||
\(974\) | −1350.05 | −0.0444130 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52619.5 | −1.72573 | ||||||||
\(977\) | 10104.1 | 0.330868 | 0.165434 | − | 0.986221i | \(-0.447097\pi\) | ||||
0.165434 | + | 0.986221i | \(0.447097\pi\) | |||||||
\(978\) | −39.9879 | −0.00130744 | ||||||||
\(979\) | −2858.04 | −0.0933027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2362.05 | 0.0768750 | ||||||||
\(982\) | −882.947 | −0.0286924 | ||||||||
\(983\) | 18109.7 | 0.587599 | 0.293799 | − | 0.955867i | \(-0.405080\pi\) | ||||
0.293799 | + | 0.955867i | \(0.405080\pi\) | |||||||
\(984\) | −1573.78 | −0.0509860 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 857.473 | 0.0276952 | ||||||||
\(987\) | 8563.93 | 0.276183 | ||||||||
\(988\) | 7526.33 | 0.242353 | ||||||||
\(989\) | −6068.47 | −0.195112 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48982.5 | −1.57011 | −0.785055 | − | 0.619426i | \(-0.787366\pi\) | ||||
−0.785055 | + | 0.619426i | \(0.787366\pi\) | |||||||
\(992\) | −2510.76 | −0.0803597 | ||||||||
\(993\) | 21198.8 | 0.677465 | ||||||||
\(994\) | 350.173 | 0.0111739 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −20257.4 | −0.644458 | ||||||||
\(997\) | 41760.0 | 1.32653 | 0.663265 | − | 0.748384i | \(-0.269170\pi\) | ||||
0.663265 | + | 0.748384i | \(0.269170\pi\) | |||||||
\(998\) | −521.813 | −0.0165508 | ||||||||
\(999\) | 5502.94 | 0.174280 |
(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 | 525.4.a.r.1.2 | 3 | ||
3.2 | odd | 2 | 1575.4.a.bc.1.2 | 3 | |||
5.2 | odd | 4 | 105.4.d.a.64.4 | yes | 6 | ||
5.3 | odd | 4 | 105.4.d.a.64.3 | ✓ | 6 | ||
5.4 | even | 2 | 525.4.a.q.1.2 | 3 | |||
15.2 | even | 4 | 315.4.d.a.64.3 | 6 | |||
15.8 | even | 4 | 315.4.d.a.64.4 | 6 | |||
15.14 | odd | 2 | 1575.4.a.bd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.a.64.3 | ✓ | 6 | 5.3 | odd | 4 | ||
105.4.d.a.64.4 | yes | 6 | 5.2 | odd | 4 | ||
315.4.d.a.64.3 | 6 | 15.2 | even | 4 | |||
315.4.d.a.64.4 | 6 | 15.8 | even | 4 | |||
525.4.a.q.1.2 | 3 | 5.4 | even | 2 | |||
525.4.a.r.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1575.4.a.bc.1.2 | 3 | 3.2 | odd | 2 | |||
1575.4.a.bd.1.2 | 3 | 15.14 | odd | 2 |