Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.5 | ||
Root | \(1.57646 + 0.910170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.4.c.a.440.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.82034i | − 0.643587i | −0.946810 | − | 0.321794i | \(-0.895714\pi\) | ||||
0.946810 | − | 0.321794i | \(-0.104286\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.68636 | 0.585795 | ||||||||
\(5\) | −15.0874 | −1.34946 | −0.674731 | − | 0.738064i | \(-0.735740\pi\) | ||||
−0.674731 | + | 0.738064i | \(0.735740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 23.0935i | − 1.02060i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.4643i | 0.868497i | ||||||||
\(11\) | 9.89034i | 0.271096i | 0.990771 | + | 0.135548i | \(0.0432794\pi\) | ||||
−0.990771 | + | 0.135548i | \(0.956721\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 67.8891i | 1.44839i | 0.689596 | + | 0.724194i | \(0.257788\pi\) | ||||
−0.689596 | + | 0.724194i | \(0.742212\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.54712 | −0.0710487 | ||||||||
\(17\) | 70.1373 | 1.00064 | 0.500318 | − | 0.865842i | \(-0.333217\pi\) | ||||
0.500318 | + | 0.865842i | \(0.333217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61.4580i | 0.742075i | 0.928618 | + | 0.371038i | \(0.120998\pi\) | ||||
−0.928618 | + | 0.371038i | \(0.879002\pi\) | |||||||
\(20\) | −70.7052 | −0.790508 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0038 | 0.174474 | ||||||||
\(23\) | − 131.515i | − 1.19229i | −0.802875 | − | 0.596147i | \(-0.796697\pi\) | ||||
0.802875 | − | 0.596147i | \(-0.203303\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 102.631 | 0.821047 | ||||||||
\(26\) | 123.581 | 0.932165 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.738i | 1.01645i | 0.861225 | + | 0.508223i | \(0.169698\pi\) | ||||
−0.861225 | + | 0.508223i | \(0.830302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 76.4814i | − 0.443112i | −0.975148 | − | 0.221556i | \(-0.928886\pi\) | ||||
0.975148 | − | 0.221556i | \(-0.0711136\pi\) | |||||||
\(32\) | − 176.471i | − 0.974872i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 127.674i | − 0.643996i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 348.682 | 1.54927 | 0.774634 | − | 0.632410i | \(-0.217934\pi\) | ||||
0.774634 | + | 0.632410i | \(0.217934\pi\) | |||||||
\(38\) | 111.874 | 0.477590 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 348.422i | 1.37726i | ||||||||
\(41\) | −138.909 | −0.529120 | −0.264560 | − | 0.964369i | \(-0.585227\pi\) | ||||
−0.264560 | + | 0.964369i | \(0.585227\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 539.651 | 1.91386 | 0.956931 | − | 0.290316i | \(-0.0937604\pi\) | ||||
0.956931 | + | 0.290316i | \(0.0937604\pi\) | |||||||
\(44\) | 46.3497i | 0.158806i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −239.402 | −0.767346 | ||||||||
\(47\) | 223.643 | 0.694078 | 0.347039 | − | 0.937851i | \(-0.387187\pi\) | ||||
0.347039 | + | 0.937851i | \(0.387187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 186.823i | − 0.528415i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 318.153i | 0.848459i | ||||||||
\(53\) | 530.011i | 1.37363i | 0.726830 | + | 0.686817i | \(0.240993\pi\) | ||||
−0.726830 | + | 0.686817i | \(0.759007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 149.220i | − 0.365833i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 288.958 | 0.654172 | ||||||||
\(59\) | 542.876 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295583\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 134.197i | 0.281674i | 0.990033 | + | 0.140837i | \(0.0449793\pi\) | ||||
−0.990033 | + | 0.140837i | \(0.955021\pi\) | |||||||
\(62\) | −139.222 | −0.285181 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −357.614 | −0.698464 | ||||||||
\(65\) | − 1024.27i | − 1.95454i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 320.580 | 0.584553 | 0.292276 | − | 0.956334i | \(-0.405587\pi\) | ||||
0.292276 | + | 0.956334i | \(0.405587\pi\) | |||||||
\(68\) | 328.689 | 0.586167 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 416.958i | − 0.696955i | −0.937317 | − | 0.348478i | \(-0.886699\pi\) | ||||
0.937317 | − | 0.348478i | \(-0.113301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 545.607i | 0.874774i | 0.899273 | + | 0.437387i | \(0.144096\pi\) | ||||
−0.899273 | + | 0.437387i | \(0.855904\pi\) | |||||||
\(74\) | − 634.719i | − 0.997089i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 288.014i | 0.434704i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −322.737 | −0.459630 | −0.229815 | − | 0.973234i | \(-0.573812\pi\) | ||||
−0.229815 | + | 0.973234i | \(0.573812\pi\) | |||||||
\(80\) | 68.6044 | 0.0958776 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 252.861i | 0.340535i | ||||||||
\(83\) | −885.170 | −1.17060 | −0.585301 | − | 0.810816i | \(-0.699024\pi\) | ||||
−0.585301 | + | 0.810816i | \(0.699024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1058.19 | −1.35032 | ||||||||
\(86\) | − 982.349i | − 1.23174i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 228.403 | 0.276680 | ||||||||
\(89\) | 1624.62 | 1.93494 | 0.967471 | − | 0.252984i | \(-0.0814119\pi\) | ||||
0.967471 | + | 0.252984i | \(0.0814119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 616.327i | − 0.698441i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 407.106i | − 0.446700i | ||||||||
\(95\) | − 927.244i | − 1.00140i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 739.155i | − 0.773710i | −0.922141 | − | 0.386855i | \(-0.873561\pi\) | ||||
0.922141 | − | 0.386855i | \(-0.126439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 480.965 | 0.480965 | ||||||||
\(101\) | 239.516 | 0.235967 | 0.117984 | − | 0.993016i | \(-0.462357\pi\) | ||||
0.117984 | + | 0.993016i | \(0.462357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 51.1361i | 0.0489184i | 0.999701 | + | 0.0244592i | \(0.00778637\pi\) | ||||
−0.999701 | + | 0.0244592i | \(0.992214\pi\) | |||||||
\(104\) | 1567.80 | 1.47822 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 964.800 | 0.884054 | ||||||||
\(107\) | 1190.99i | 1.07605i | 0.842929 | + | 0.538025i | \(0.180829\pi\) | ||||
−0.842929 | + | 0.538025i | \(0.819171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 389.170 | 0.341979 | 0.170989 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170989 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(110\) | −271.631 | −0.235446 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 718.545i | 0.598186i | 0.954224 | + | 0.299093i | \(0.0966841\pi\) | ||||
−0.954224 | + | 0.299093i | \(0.903316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1984.23i | 1.60896i | ||||||||
\(116\) | 743.905i | 0.595430i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 988.220i | − 0.770958i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1233.18 | 0.926507 | ||||||||
\(122\) | 244.283 | 0.181282 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 358.420i | − 0.259573i | ||||||||
\(125\) | 337.493 | 0.241490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −179.456 | −0.125387 | −0.0626934 | − | 0.998033i | \(-0.519969\pi\) | ||||
−0.0626934 | + | 0.998033i | \(0.519969\pi\) | |||||||
\(128\) | − 760.787i | − 0.525349i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1864.53 | −1.25792 | ||||||||
\(131\) | −2446.87 | −1.63194 | −0.815968 | − | 0.578096i | \(-0.803796\pi\) | ||||
−0.815968 | + | 0.578096i | \(0.803796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 583.564i | − 0.376211i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 1619.72i | − 1.02125i | ||||||||
\(137\) | 511.557i | 0.319016i | 0.987197 | + | 0.159508i | \(0.0509908\pi\) | ||||
−0.987197 | + | 0.159508i | \(0.949009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 599.427i | − 0.365775i | −0.983134 | − | 0.182888i | \(-0.941456\pi\) | ||||
0.983134 | − | 0.182888i | \(-0.0585444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −759.006 | −0.448552 | ||||||||
\(143\) | −671.447 | −0.392652 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 2394.95i | − 1.37166i | ||||||||
\(146\) | 993.191 | 0.562994 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1634.05 | 0.907554 | ||||||||
\(149\) | 2193.50i | 1.20603i | 0.797729 | + | 0.603016i | \(0.206034\pi\) | ||||
−0.797729 | + | 0.603016i | \(0.793966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −717.366 | −0.386612 | −0.193306 | − | 0.981139i | \(-0.561921\pi\) | ||||
−0.193306 | + | 0.981139i | \(0.561921\pi\) | |||||||
\(152\) | 1419.28 | 0.757360 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1153.91i | 0.597963i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1802.94i | − 0.916500i | −0.888823 | − | 0.458250i | \(-0.848476\pi\) | ||||
0.888823 | − | 0.458250i | \(-0.151524\pi\) | |||||||
\(158\) | 587.492i | 0.295812i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2662.49i | 1.31555i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2907.81 | −1.39728 | −0.698642 | − | 0.715472i | \(-0.746212\pi\) | ||||
−0.698642 | + | 0.715472i | \(0.746212\pi\) | |||||||
\(164\) | −650.977 | −0.309956 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1611.31i | 0.753385i | ||||||||
\(167\) | −3491.37 | −1.61779 | −0.808893 | − | 0.587956i | \(-0.799933\pi\) | ||||
−0.808893 | + | 0.587956i | \(0.799933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2411.93 | −1.09783 | ||||||||
\(170\) | 1926.27i | 0.869048i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2529.00 | 1.12113 | ||||||||
\(173\) | −1754.75 | −0.771165 | −0.385583 | − | 0.922673i | \(-0.625999\pi\) | ||||
−0.385583 | + | 0.922673i | \(0.625999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 44.9726i | − 0.0192610i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2957.37i | − 1.24530i | ||||||||
\(179\) | 791.707i | 0.330586i | 0.986244 | + | 0.165293i | \(0.0528571\pi\) | ||||
−0.986244 | + | 0.165293i | \(0.947143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2522.19i | 1.03576i | 0.855452 | + | 0.517882i | \(0.173279\pi\) | ||||
−0.855452 | + | 0.517882i | \(0.826721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3037.14 | −1.21685 | ||||||||
\(185\) | −5260.71 | −2.09068 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 693.682i | 0.271268i | ||||||||
\(188\) | 1048.07 | 0.406588 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1687.90 | −0.644490 | ||||||||
\(191\) | − 903.283i | − 0.342195i | −0.985254 | − | 0.171098i | \(-0.945269\pi\) | ||||
0.985254 | − | 0.171098i | \(-0.0547313\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −198.875 | −0.0741727 | −0.0370863 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370863 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(194\) | −1345.51 | −0.497950 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3220.69i | 1.16480i | 0.812904 | + | 0.582398i | \(0.197886\pi\) | ||||
−0.812904 | + | 0.582398i | \(0.802114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2849.92i | 1.01520i | 0.861592 | + | 0.507601i | \(0.169468\pi\) | ||||
−0.861592 | + | 0.507601i | \(0.830532\pi\) | |||||||
\(200\) | − 2370.11i | − 0.837959i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 436.000i | − 0.151866i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2095.78 | 0.714027 | ||||||||
\(206\) | 93.0851 | 0.0314832 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 308.700i | − 0.102906i | ||||||||
\(209\) | −607.841 | −0.201173 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1204.50 | 0.392993 | 0.196496 | − | 0.980505i | \(-0.437044\pi\) | ||||
0.196496 | + | 0.980505i | \(0.437044\pi\) | |||||||
\(212\) | 2483.82i | 0.804668i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2168.01 | 0.692532 | ||||||||
\(215\) | −8141.96 | −2.58268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 708.421i | − 0.220093i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 699.299i | − 0.214303i | ||||||||
\(221\) | 4761.56i | 1.44931i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3377.73i | 1.01430i | 0.861857 | + | 0.507151i | \(0.169301\pi\) | ||||
−0.861857 | + | 0.507151i | \(0.830699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1308.00 | 0.384985 | ||||||||
\(227\) | 4523.96 | 1.32276 | 0.661378 | − | 0.750052i | \(-0.269972\pi\) | ||||
0.661378 | + | 0.750052i | \(0.269972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3913.99i | − 1.12945i | −0.825280 | − | 0.564724i | \(-0.808983\pi\) | ||||
0.825280 | − | 0.564724i | \(-0.191017\pi\) | |||||||
\(230\) | 3611.96 | 1.03550 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3665.82 | 1.03738 | ||||||||
\(233\) | 4369.16i | 1.22847i | 0.789124 | + | 0.614234i | \(0.210535\pi\) | ||||
−0.789124 | + | 0.614234i | \(0.789465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3374.20 | −0.936632 | ||||||||
\(236\) | 2544.12 | 0.701728 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1945.23i | 0.526471i | 0.964732 | + | 0.263235i | \(0.0847896\pi\) | ||||
−0.964732 | + | 0.263235i | \(0.915210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 4041.23i | − 1.08016i | −0.841614 | − | 0.540080i | \(-0.818394\pi\) | ||||
0.841614 | − | 0.540080i | \(-0.181606\pi\) | |||||||
\(242\) | − 2244.81i | − 0.596288i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 628.894i | 0.165003i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4172.33 | −1.07481 | ||||||||
\(248\) | −1766.22 | −0.452239 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 614.352i | − 0.155420i | ||||||||
\(251\) | 4415.70 | 1.11042 | 0.555212 | − | 0.831709i | \(-0.312637\pi\) | ||||
0.555212 | + | 0.831709i | \(0.312637\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1300.73 | 0.323226 | ||||||||
\(254\) | 326.671i | 0.0806974i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4245.80 | −1.03657 | ||||||||
\(257\) | −697.600 | −0.169319 | −0.0846597 | − | 0.996410i | \(-0.526980\pi\) | ||||
−0.0846597 | + | 0.996410i | \(0.526980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 4800.11i | − 1.14496i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4454.13i | 1.05029i | ||||||||
\(263\) | − 797.510i | − 0.186983i | −0.995620 | − | 0.0934915i | \(-0.970197\pi\) | ||||
0.995620 | − | 0.0934915i | \(-0.0298028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 7996.51i | − 1.85367i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1502.35 | 0.342428 | ||||||||
\(269\) | 410.703 | 0.0930892 | 0.0465446 | − | 0.998916i | \(-0.485179\pi\) | ||||
0.0465446 | + | 0.998916i | \(0.485179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 3791.37i | − 0.849850i | −0.905228 | − | 0.424925i | \(-0.860300\pi\) | ||||
0.905228 | − | 0.424925i | \(-0.139700\pi\) | |||||||
\(272\) | −318.923 | −0.0710939 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 931.207 | 0.205315 | ||||||||
\(275\) | 1015.05i | 0.222582i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3246.62 | 0.704226 | 0.352113 | − | 0.935958i | \(-0.385463\pi\) | ||||
0.352113 | + | 0.935958i | \(0.385463\pi\) | |||||||
\(278\) | −1091.16 | −0.235408 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1599.58i | 0.339583i | 0.985480 | + | 0.169791i | \(0.0543094\pi\) | ||||
−0.985480 | + | 0.169791i | \(0.945691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4266.27i | − 0.896125i | −0.894002 | − | 0.448062i | \(-0.852114\pi\) | ||||
0.894002 | − | 0.448062i | \(-0.147886\pi\) | |||||||
\(284\) | − 1954.02i | − 0.408273i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1222.26i | 0.252706i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.24157 | 0.00127042 | ||||||||
\(290\) | −4359.63 | −0.882780 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2556.91i | 0.512438i | ||||||||
\(293\) | −2926.77 | −0.583562 | −0.291781 | − | 0.956485i | \(-0.594248\pi\) | ||||
−0.291781 | + | 0.956485i | \(0.594248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8190.62 | −1.61653 | ||||||||
\(296\) | − 8052.28i | − 1.58118i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3992.92 | 0.776187 | ||||||||
\(299\) | 8928.44 | 1.72691 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1305.85i | 0.248819i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 279.457i | − 0.0527235i | ||||||||
\(305\) | − 2024.68i | − 0.380108i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3571.36i | − 0.663935i | −0.943291 | − | 0.331968i | \(-0.892288\pi\) | ||||
0.943291 | − | 0.331968i | \(-0.107712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2100.51 | 0.384841 | ||||||||
\(311\) | 2573.41 | 0.469212 | 0.234606 | − | 0.972091i | \(-0.424620\pi\) | ||||
0.234606 | + | 0.972091i | \(0.424620\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1476.35i | 0.266608i | 0.991075 | + | 0.133304i | \(0.0425587\pi\) | ||||
−0.991075 | + | 0.133304i | \(0.957441\pi\) | |||||||
\(314\) | −3281.97 | −0.589848 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1512.46 | −0.269249 | ||||||||
\(317\) | − 2526.90i | − 0.447712i | −0.974622 | − | 0.223856i | \(-0.928136\pi\) | ||||
0.974622 | − | 0.223856i | \(-0.0718645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1569.98 | −0.275554 | ||||||||
\(320\) | 5395.47 | 0.942550 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4310.50i | 0.742546i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6967.52i | 1.18919i | ||||||||
\(326\) | 5293.20i | 0.899274i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3207.89i | 0.540019i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1475.56 | 0.245027 | 0.122513 | − | 0.992467i | \(-0.460905\pi\) | ||||
0.122513 | + | 0.992467i | \(0.460905\pi\) | |||||||
\(332\) | −4148.23 | −0.685733 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6355.48i | 1.04119i | ||||||||
\(335\) | −4836.73 | −0.788832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6727.28 | −1.08741 | −0.543706 | − | 0.839275i | \(-0.682979\pi\) | ||||
−0.543706 | + | 0.839275i | \(0.682979\pi\) | |||||||
\(338\) | 4390.54i | 0.706549i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4959.07 | −0.791010 | ||||||||
\(341\) | 756.428 | 0.120126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 12462.4i | − 1.95328i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3194.25i | 0.496312i | ||||||||
\(347\) | − 538.160i | − 0.0832563i | −0.999133 | − | 0.0416281i | \(-0.986746\pi\) | ||||
0.999133 | − | 0.0416281i | \(-0.0132545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 6975.93i | − 1.06995i | −0.844867 | − | 0.534976i | \(-0.820321\pi\) | ||||
0.844867 | − | 0.534976i | \(-0.179679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1745.36 | 0.264283 | ||||||||
\(353\) | 8876.80 | 1.33843 | 0.669213 | − | 0.743071i | \(-0.266631\pi\) | ||||
0.669213 | + | 0.743071i | \(0.266631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6290.83i | 0.940514i | ||||||||
\(356\) | 7613.57 | 1.13348 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1441.18 | 0.212761 | ||||||||
\(359\) | − 11045.8i | − 1.62389i | −0.583735 | − | 0.811944i | \(-0.698409\pi\) | ||||
0.583735 | − | 0.811944i | \(-0.301591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3081.92 | 0.449324 | ||||||||
\(362\) | 4591.25 | 0.666604 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 8231.82i | − 1.18047i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8326.07i | 1.18424i | 0.805848 | + | 0.592122i | \(0.201710\pi\) | ||||
−0.805848 | + | 0.592122i | \(0.798290\pi\) | |||||||
\(368\) | 598.015i | 0.0847110i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9576.29i | 1.34553i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4545.32 | −0.630959 | −0.315479 | − | 0.948932i | \(-0.602165\pi\) | ||||
−0.315479 | + | 0.948932i | \(0.602165\pi\) | |||||||
\(374\) | 1262.74 | 0.174584 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 5164.70i | − 0.708375i | ||||||||
\(377\) | −10776.6 | −1.47221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11527.2 | 1.56230 | 0.781151 | − | 0.624343i | \(-0.214633\pi\) | ||||
0.781151 | + | 0.624343i | \(0.214633\pi\) | |||||||
\(380\) | − 4345.40i | − 0.586617i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1644.28 | −0.220233 | ||||||||
\(383\) | −3920.46 | −0.523044 | −0.261522 | − | 0.965197i | \(-0.584224\pi\) | ||||
−0.261522 | + | 0.965197i | \(0.584224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 362.020i | 0.0477366i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 3463.95i | − 0.453235i | ||||||||
\(389\) | 796.437i | 0.103807i | 0.998652 | + | 0.0519035i | \(0.0165288\pi\) | ||||
−0.998652 | + | 0.0519035i | \(0.983471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9224.11i | − 1.19305i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5862.76 | 0.749648 | ||||||||
\(395\) | 4869.28 | 0.620254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3855.07i | − 0.487357i | −0.969856 | − | 0.243678i | \(-0.921646\pi\) | ||||
0.969856 | − | 0.243678i | \(-0.0783541\pi\) | |||||||
\(398\) | 5187.82 | 0.653371 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −466.675 | −0.0583344 | ||||||||
\(401\) | − 4655.35i | − 0.579744i | −0.957065 | − | 0.289872i | \(-0.906387\pi\) | ||||
0.957065 | − | 0.289872i | \(-0.0936127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5192.26 | 0.641798 | ||||||||
\(404\) | 1122.46 | 0.138229 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3448.58i | 0.420000i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 9790.50i | − 1.18364i | −0.806070 | − | 0.591821i | \(-0.798409\pi\) | ||||
0.806070 | − | 0.591821i | \(-0.201591\pi\) | |||||||
\(410\) | − 3815.03i | − 0.459539i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 239.642i | 0.0286561i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13354.9 | 1.57968 | ||||||||
\(416\) | 11980.4 | 1.41199 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1106.48i | 0.129473i | ||||||||
\(419\) | 3007.46 | 0.350654 | 0.175327 | − | 0.984510i | \(-0.443902\pi\) | ||||
0.175327 | + | 0.984510i | \(0.443902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7646.06 | 0.885145 | 0.442573 | − | 0.896733i | \(-0.354066\pi\) | ||||
0.442573 | + | 0.896733i | \(0.354066\pi\) | |||||||
\(422\) | − 2192.61i | − 0.252925i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12239.8 | 1.40193 | ||||||||
\(425\) | 7198.25 | 0.821568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5581.41i | 0.630345i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14821.1i | 1.66218i | ||||||||
\(431\) | − 14991.6i | − 1.67545i | −0.546090 | − | 0.837727i | \(-0.683884\pi\) | ||||
0.546090 | − | 0.837727i | \(-0.316116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5666.63i | 0.628916i | 0.949271 | + | 0.314458i | \(0.101823\pi\) | ||||
−0.949271 | + | 0.314458i | \(0.898177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1823.79 | 0.200330 | ||||||||
\(437\) | 8082.65 | 0.884772 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5531.10i | 0.601332i | 0.953729 | + | 0.300666i | \(0.0972090\pi\) | ||||
−0.953729 | + | 0.300666i | \(0.902791\pi\) | |||||||
\(440\) | −3446.01 | −0.373368 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8667.66 | 0.932757 | ||||||||
\(443\) | 403.222i | 0.0432452i | 0.999766 | + | 0.0216226i | \(0.00688323\pi\) | ||||
−0.999766 | + | 0.0216226i | \(0.993117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24511.4 | −2.61113 | ||||||||
\(446\) | 6148.61 | 0.652792 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8429.03i | 0.885948i | 0.896534 | + | 0.442974i | \(0.146077\pi\) | ||||
−0.896534 | + | 0.442974i | \(0.853923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1373.86i | − 0.143442i | ||||||||
\(452\) | 3367.36i | 0.350415i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 8235.15i | − 0.851310i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 685.661 | 0.0701835 | 0.0350917 | − | 0.999384i | \(-0.488828\pi\) | ||||
0.0350917 | + | 0.999384i | \(0.488828\pi\) | |||||||
\(458\) | −7124.79 | −0.726899 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9298.80i | 0.942519i | ||||||||
\(461\) | −4864.48 | −0.491456 | −0.245728 | − | 0.969339i | \(-0.579027\pi\) | ||||
−0.245728 | + | 0.969339i | \(0.579027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8354.23 | −0.838562 | −0.419281 | − | 0.907857i | \(-0.637718\pi\) | ||||
−0.419281 | + | 0.907857i | \(0.637718\pi\) | |||||||
\(464\) | − 721.802i | − 0.0722173i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7953.36 | 0.790627 | ||||||||
\(467\) | 1002.94 | 0.0993800 | 0.0496900 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496900 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6142.19i | 0.602804i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 12536.9i | − 1.22258i | ||||||||
\(473\) | 5337.34i | 0.518839i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6307.49i | 0.609279i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3540.98 | 0.338830 | ||||||||
\(479\) | −6052.76 | −0.577364 | −0.288682 | − | 0.957425i | \(-0.593217\pi\) | ||||
−0.288682 | + | 0.957425i | \(0.593217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23671.7i | 2.24394i | ||||||||
\(482\) | −7356.41 | −0.695177 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5779.13 | 0.542743 | ||||||||
\(485\) | 11152.0i | 1.04409i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15309.4 | 1.42451 | 0.712255 | − | 0.701920i | \(-0.247674\pi\) | ||||
0.712255 | + | 0.701920i | \(0.247674\pi\) | |||||||
\(488\) | 3099.07 | 0.287476 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4291.01i | − 0.394400i | −0.980363 | − | 0.197200i | \(-0.936815\pi\) | ||||
0.980363 | − | 0.197200i | \(-0.0631848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11133.5i | 1.01709i | ||||||||
\(494\) | 7595.06i | 0.691736i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 347.770i | 0.0314826i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6891.53 | 0.618251 | 0.309126 | − | 0.951021i | \(-0.399964\pi\) | ||||
0.309126 | + | 0.951021i | \(0.399964\pi\) | |||||||
\(500\) | 1581.61 | 0.141464 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 8038.07i | − 0.714655i | ||||||||
\(503\) | 13534.6 | 1.19975 | 0.599877 | − | 0.800092i | \(-0.295216\pi\) | ||||
0.599877 | + | 0.800092i | \(0.295216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3613.68 | −0.318429 | ||||||||
\(506\) | − 2367.77i | − 0.208024i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −840.995 | −0.0734510 | ||||||||
\(509\) | −12087.8 | −1.05262 | −0.526310 | − | 0.850293i | \(-0.676425\pi\) | ||||
−0.526310 | + | 0.850293i | \(0.676425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1642.50i | 0.141776i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1269.87i | 0.108972i | ||||||||
\(515\) | − 771.513i | − 0.0660134i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2211.91i | 0.188161i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −23654.0 | −1.99480 | ||||||||
\(521\) | −7625.87 | −0.641258 | −0.320629 | − | 0.947205i | \(-0.603894\pi\) | ||||
−0.320629 | + | 0.947205i | \(0.603894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15390.7i | − 1.28678i | −0.765537 | − | 0.643392i | \(-0.777527\pi\) | ||||
0.765537 | − | 0.643392i | \(-0.222473\pi\) | |||||||
\(524\) | −11466.9 | −0.955981 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1451.74 | −0.120340 | ||||||||
\(527\) | − 5364.20i | − 0.443393i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5129.20 | −0.421567 | ||||||||
\(530\) | −14556.4 | −1.19300 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9430.40i | − 0.766371i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 17969.0i | − 1.45209i | ||||||||
\(536\) | − 7403.30i | − 0.596593i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 747.619i | − 0.0599110i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13700.9 | −1.08881 | −0.544406 | − | 0.838822i | \(-0.683245\pi\) | ||||
−0.544406 | + | 0.838822i | \(0.683245\pi\) | |||||||
\(542\) | −6901.59 | −0.546953 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 12377.2i | − 0.975491i | ||||||||
\(545\) | −5871.58 | −0.461487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6139.00 | −0.479863 | −0.239931 | − | 0.970790i | \(-0.577125\pi\) | ||||
−0.239931 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(548\) | 2397.34i | 0.186878i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1847.74 | 0.143251 | ||||||||
\(551\) | −9755.73 | −0.754280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 5909.95i | − 0.453231i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 2809.13i | − 0.214269i | ||||||||
\(557\) | 22732.7i | 1.72929i | 0.502382 | + | 0.864646i | \(0.332457\pi\) | ||||
−0.502382 | + | 0.864646i | \(0.667543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36636.4i | 2.77202i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2911.78 | 0.218551 | ||||||||
\(563\) | −9917.61 | −0.742411 | −0.371206 | − | 0.928551i | \(-0.621055\pi\) | ||||
−0.371206 | + | 0.928551i | \(0.621055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10841.0i | − 0.807230i | ||||||||
\(566\) | −7766.06 | −0.576735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9629.02 | −0.711311 | ||||||||
\(569\) | 5137.02i | 0.378480i | 0.981931 | + | 0.189240i | \(0.0606024\pi\) | ||||
−0.981931 | + | 0.189240i | \(0.939398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18186.0 | −1.33286 | −0.666429 | − | 0.745568i | \(-0.732178\pi\) | ||||
−0.666429 | + | 0.745568i | \(0.732178\pi\) | |||||||
\(572\) | −3146.64 | −0.230014 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 13497.5i | − 0.978930i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12398.6i | 0.894562i | 0.894394 | + | 0.447281i | \(0.147608\pi\) | ||||
−0.894394 | + | 0.447281i | \(0.852392\pi\) | |||||||
\(578\) | − 11.3618i | 0 0.000817626i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 11223.6i | − 0.803509i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5241.99 | −0.372386 | ||||||||
\(584\) | 12600.0 | 0.892793 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5327.72i | 0.375573i | ||||||||
\(587\) | 18977.6 | 1.33439 | 0.667195 | − | 0.744883i | \(-0.267495\pi\) | ||||
0.667195 | + | 0.744883i | \(0.267495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4700.40 | 0.328822 | ||||||||
\(590\) | 14909.7i | 1.04038i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1585.50 | −0.110074 | ||||||||
\(593\) | 10728.9 | 0.742972 | 0.371486 | − | 0.928439i | \(-0.378848\pi\) | ||||
0.371486 | + | 0.928439i | \(0.378848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10279.5i | 0.706488i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 16252.8i | − 1.11142i | ||||||||
\(599\) | 1821.37i | 0.124239i | 0.998069 | + | 0.0621196i | \(0.0197860\pi\) | ||||
−0.998069 | + | 0.0621196i | \(0.980214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 18933.3i | − 1.28503i | −0.766273 | − | 0.642516i | \(-0.777891\pi\) | ||||
0.766273 | − | 0.642516i | \(-0.222109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3361.84 | −0.226475 | ||||||||
\(605\) | −18605.5 | −1.25029 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 15384.4i | − 1.02872i | −0.857574 | − | 0.514360i | \(-0.828029\pi\) | ||||
0.857574 | − | 0.514360i | \(-0.171971\pi\) | |||||||
\(608\) | 10845.5 | 0.723428 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3685.61 | −0.244633 | ||||||||
\(611\) | 15182.9i | 1.00529i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5507.20 | −0.362861 | −0.181431 | − | 0.983404i | \(-0.558073\pi\) | ||||
−0.181431 | + | 0.983404i | \(0.558073\pi\) | |||||||
\(614\) | −6501.08 | −0.427300 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18134.0i | 1.18322i | 0.806224 | + | 0.591610i | \(0.201507\pi\) | ||||
−0.806224 | + | 0.591610i | \(0.798493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3635.84i | 0.236085i | 0.993009 | + | 0.118043i | \(0.0376619\pi\) | ||||
−0.993009 | + | 0.118043i | \(0.962338\pi\) | |||||||
\(620\) | 5407.64i | 0.350284i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 4684.49i | − 0.301979i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17920.8 | −1.14693 | ||||||||
\(626\) | 2687.46 | 0.171586 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 8449.24i | − 0.536881i | ||||||||
\(629\) | 24455.6 | 1.55025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5912.59 | −0.373021 | −0.186511 | − | 0.982453i | \(-0.559718\pi\) | ||||
−0.186511 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(632\) | 7453.13i | 0.469098i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4599.81 | −0.288142 | ||||||||
\(635\) | 2707.53 | 0.169205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2857.89i | 0.177343i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11478.3i | 0.708939i | ||||||||
\(641\) | − 27466.6i | − 1.69245i | −0.532822 | − | 0.846227i | \(-0.678868\pi\) | ||||
0.532822 | − | 0.846227i | \(-0.321132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 28474.0i | − 1.74635i | −0.487403 | − | 0.873177i | \(-0.662056\pi\) | ||||
0.487403 | − | 0.873177i | \(-0.337944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7846.57 | 0.477894 | ||||||||
\(647\) | 1323.36 | 0.0804122 | 0.0402061 | − | 0.999191i | \(-0.487199\pi\) | ||||
0.0402061 | + | 0.999191i | \(0.487199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5369.24i | 0.324747i | ||||||||
\(650\) | 12683.3 | 0.765351 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13627.0 | −0.818522 | ||||||||
\(653\) | − 3846.75i | − 0.230528i | −0.993335 | − | 0.115264i | \(-0.963229\pi\) | ||||
0.993335 | − | 0.115264i | \(-0.0367714\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36917.0 | 2.20224 | ||||||||
\(656\) | 631.635 | 0.0375933 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6796.84i | 0.401771i | 0.979615 | + | 0.200886i | \(0.0643819\pi\) | ||||
−0.979615 | + | 0.200886i | \(0.935618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 31064.4i | − 1.82793i | −0.405790 | − | 0.913966i | \(-0.633004\pi\) | ||||
0.405790 | − | 0.913966i | \(-0.366996\pi\) | |||||||
\(662\) | − 2686.02i | − 0.157696i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20441.7i | 1.19471i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20876.5 | 1.21190 | ||||||||
\(668\) | −16361.8 | −0.947691 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8804.49i | 0.507682i | ||||||||
\(671\) | −1327.25 | −0.0763605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15508.2 | 0.888259 | 0.444129 | − | 0.895963i | \(-0.353513\pi\) | ||||
0.444129 | + | 0.895963i | \(0.353513\pi\) | |||||||
\(674\) | 12245.9i | 0.699845i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11303.2 | −0.643103 | ||||||||
\(677\) | −30674.8 | −1.74140 | −0.870701 | − | 0.491813i | \(-0.836334\pi\) | ||||
−0.870701 | + | 0.491813i | \(0.836334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 24437.4i | 1.37813i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 1376.96i | − 0.0773114i | ||||||||
\(683\) | − 17658.7i | − 0.989296i | −0.869093 | − | 0.494648i | \(-0.835297\pi\) | ||||
0.869093 | − | 0.494648i | \(-0.164703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 7718.08i | − 0.430500i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2453.86 | −0.135977 | ||||||||
\(689\) | −35982.0 | −1.98956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13166.2i | − 0.724843i | −0.932014 | − | 0.362422i | \(-0.881950\pi\) | ||||
0.932014 | − | 0.362422i | \(-0.118050\pi\) | |||||||
\(692\) | −8223.42 | −0.451745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −979.634 | −0.0535827 | ||||||||
\(695\) | 9043.82i | 0.493599i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9742.69 | −0.529456 | ||||||||
\(698\) | −12698.6 | −0.688607 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 25910.0i | − 1.39602i | −0.716090 | − | 0.698008i | \(-0.754070\pi\) | ||||
0.716090 | − | 0.698008i | \(-0.245930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21429.3i | 1.14967i | ||||||||
\(704\) | − 3536.92i | − 0.189350i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 16158.8i | − 0.861394i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6208.49 | 0.328864 | 0.164432 | − | 0.986388i | \(-0.447421\pi\) | ||||
0.164432 | + | 0.986388i | \(0.447421\pi\) | |||||||
\(710\) | 11451.5 | 0.605303 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 37518.2i | − 1.97480i | ||||||||
\(713\) | −10058.5 | −0.528320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10130.4 | 0.529868 | ||||||||
\(716\) | 3710.23i | 0.193656i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20107.1 | −1.04511 | ||||||||
\(719\) | 28758.8 | 1.49169 | 0.745843 | − | 0.666122i | \(-0.232047\pi\) | ||||
0.745843 | + | 0.666122i | \(0.232047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 5610.13i | − 0.289180i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11819.9i | 0.606745i | ||||||||
\(725\) | 16291.4i | 0.834550i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35275.7i | 1.79959i | 0.436312 | + | 0.899795i | \(0.356284\pi\) | ||||
−0.436312 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14984.7 | −0.759738 | ||||||||
\(731\) | 37849.7 | 1.91508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7950.28i | 0.400615i | 0.979733 | + | 0.200307i | \(0.0641940\pi\) | ||||
−0.979733 | + | 0.200307i | \(0.935806\pi\) | |||||||
\(734\) | 15156.3 | 0.762164 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23208.5 | −1.16233 | ||||||||
\(737\) | 3170.64i | 0.158470i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33353.6 | 1.66026 | 0.830130 | − | 0.557570i | \(-0.188266\pi\) | ||||
0.830130 | + | 0.557570i | \(0.188266\pi\) | |||||||
\(740\) | −24653.6 | −1.22471 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32933.6i | − 1.62613i | −0.582171 | − | 0.813066i | \(-0.697797\pi\) | ||||
0.582171 | − | 0.813066i | \(-0.302203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 33094.3i | − 1.62749i | ||||||||
\(746\) | 8274.02i | 0.406077i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3250.85i | 0.158907i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39636.6 | −1.92591 | −0.962956 | − | 0.269660i | \(-0.913089\pi\) | ||||
−0.962956 | + | 0.269660i | \(0.913089\pi\) | |||||||
\(752\) | −1016.93 | −0.0493134 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19617.1i | 0.947496i | ||||||||
\(755\) | 10823.2 | 0.521718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3996.51 | −0.191883 | −0.0959417 | − | 0.995387i | \(-0.530586\pi\) | ||||
−0.0959417 | + | 0.995387i | \(0.530586\pi\) | |||||||
\(758\) | − 20983.4i | − 1.00548i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21413.3 | −1.02203 | ||||||||
\(761\) | 26235.7 | 1.24973 | 0.624863 | − | 0.780734i | \(-0.285155\pi\) | ||||
0.624863 | + | 0.780734i | \(0.285155\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 4233.11i | − 0.200456i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7136.57i | 0.336625i | ||||||||
\(767\) | 36855.4i | 1.73503i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36456.9i | 1.70958i | 0.518971 | + | 0.854792i | \(0.326315\pi\) | ||||
−0.518971 | + | 0.854792i | \(0.673685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −932.000 | −0.0434500 | ||||||||
\(773\) | −9465.47 | −0.440426 | −0.220213 | − | 0.975452i | \(-0.570675\pi\) | ||||
−0.220213 | + | 0.975452i | \(0.570675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 7849.36i | − 0.363816i | ||||||||
\(776\) | −17069.7 | −0.789646 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1449.79 | 0.0668089 | ||||||||
\(779\) | − 8537.06i | − 0.392647i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4123.86 | 0.188941 | ||||||||
\(782\) | −16791.0 | −0.767833 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27201.8i | 1.23678i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25017.6i | 1.13314i | 0.824013 | + | 0.566571i | \(0.191730\pi\) | ||||
−0.824013 | + | 0.566571i | \(0.808270\pi\) | |||||||
\(788\) | 15093.3i | 0.682332i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 8863.75i | − 0.399187i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9110.48 | −0.407973 | ||||||||
\(794\) | −7017.54 | −0.313657 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13355.7i | 0.594701i | ||||||||
\(797\) | −38893.5 | −1.72858 | −0.864290 | − | 0.502994i | \(-0.832232\pi\) | ||||
−0.864290 | + | 0.502994i | \(0.832232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15685.7 | 0.694519 | ||||||||
\(800\) | − 18111.3i | − 0.800415i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8474.32 | −0.373116 | ||||||||
\(803\) | −5396.24 | −0.237147 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 9451.67i | − 0.413053i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 5531.26i | − 0.240828i | ||||||||
\(809\) | 7011.64i | 0.304717i | 0.988325 | + | 0.152359i | \(0.0486869\pi\) | ||||
−0.988325 | + | 0.152359i | \(0.951313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5013.82i | − 0.217089i | −0.994092 | − | 0.108544i | \(-0.965381\pi\) | ||||
0.994092 | − | 0.108544i | \(-0.0346189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6277.59 | 0.270306 | ||||||||
\(815\) | 43871.4 | 1.88558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33165.9i | 1.42023i | ||||||||
\(818\) | −17822.0 | −0.761776 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9821.58 | 0.418274 | ||||||||
\(821\) | − 696.609i | − 0.0296124i | −0.999890 | − | 0.0148062i | \(-0.995287\pi\) | ||||
0.999890 | − | 0.0148062i | \(-0.00471314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6413.15 | 0.271626 | 0.135813 | − | 0.990734i | \(-0.456635\pi\) | ||||
0.135813 | + | 0.990734i | \(0.456635\pi\) | |||||||
\(824\) | 1180.91 | 0.0499260 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16718.9i | 0.702989i | 0.936190 | + | 0.351494i | \(0.114326\pi\) | ||||
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 14557.2i | − 0.609882i | −0.952371 | − | 0.304941i | \(-0.901363\pi\) | ||||
0.952371 | − | 0.304941i | \(-0.0986367\pi\) | |||||||
\(830\) | − 24310.5i | − 1.01666i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 24278.1i | − 1.01165i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52675.8 | 2.18314 | ||||||||
\(836\) | −2848.56 | −0.117846 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 5474.61i | − 0.225677i | ||||||||
\(839\) | 19467.0 | 0.801045 | 0.400523 | − | 0.916287i | \(-0.368829\pi\) | ||||
0.400523 | + | 0.916287i | \(0.368829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −808.829 | −0.0331637 | ||||||||
\(842\) | − 13918.4i | − 0.569668i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5644.74 | 0.230213 | ||||||||
\(845\) | 36389.9 | 1.48148 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 2410.02i | − 0.0975950i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 13103.3i | − 0.528751i | ||||||||
\(851\) | − 45856.9i | − 1.84718i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22345.3i | 0.896938i | 0.893798 | + | 0.448469i | \(0.148031\pi\) | ||||
−0.893798 | + | 0.448469i | \(0.851969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27504.1 | 1.09821 | ||||||||
\(857\) | −48079.7 | −1.91642 | −0.958209 | − | 0.286068i | \(-0.907652\pi\) | ||||
−0.958209 | + | 0.286068i | \(0.907652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26110.7i | 1.03712i | 0.855041 | + | 0.518560i | \(0.173532\pi\) | ||||
−0.855041 | + | 0.518560i | \(0.826468\pi\) | |||||||
\(860\) | −38156.2 | −1.51292 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27289.8 | −1.07830 | ||||||||
\(863\) | 2928.55i | 0.115514i | 0.998331 | + | 0.0577572i | \(0.0183949\pi\) | ||||
−0.998331 | + | 0.0577572i | \(0.981605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26474.8 | 1.04066 | ||||||||
\(866\) | 10315.2 | 0.404763 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3191.98i | − 0.124604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21763.9i | 0.846660i | ||||||||
\(872\) | − 8987.29i | − 0.349023i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 14713.2i | − 0.569428i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13090.6 | 0.504033 | 0.252016 | − | 0.967723i | \(-0.418906\pi\) | ||||
0.252016 | + | 0.967723i | \(0.418906\pi\) | |||||||
\(878\) | 10068.5 | 0.387010 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 678.521i | 0.0259920i | ||||||||
\(881\) | 7888.79 | 0.301680 | 0.150840 | − | 0.988558i | \(-0.451802\pi\) | ||||
0.150840 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45061.9 | 1.71739 | 0.858694 | − | 0.512489i | \(-0.171276\pi\) | ||||
0.858694 | + | 0.512489i | \(0.171276\pi\) | |||||||
\(884\) | 22314.4i | 0.848998i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 734.000 | 0.0278321 | ||||||||
\(887\) | 3546.58 | 0.134253 | 0.0671266 | − | 0.997744i | \(-0.478617\pi\) | ||||
0.0671266 | + | 0.997744i | \(0.478617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 44619.1i | 1.68049i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15829.2i | 0.594173i | ||||||||
\(893\) | 13744.6i | 0.515058i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11944.8i | − 0.446114i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15343.7 | 0.570185 | ||||||||
\(899\) | 12140.5 | 0.450400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37173.5i | 1.37451i | ||||||||
\(902\) | −2500.89 | −0.0923175 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16593.7 | 0.610508 | ||||||||
\(905\) | − 38053.4i | − 1.39772i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14679.5 | −0.537405 | −0.268703 | − | 0.963223i | \(-0.586595\pi\) | ||||
−0.268703 | + | 0.963223i | \(0.586595\pi\) | |||||||
\(908\) | 21200.9 | 0.774864 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 12355.2i | − 0.449336i | −0.974435 | − | 0.224668i | \(-0.927870\pi\) | ||||
0.974435 | − | 0.224668i | \(-0.0721297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 8754.64i | − 0.317345i | ||||||||
\(914\) | − 1248.14i | − 0.0451692i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 18342.4i | − 0.661626i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3070.36 | −0.110209 | −0.0551044 | − | 0.998481i | \(-0.517549\pi\) | ||||
−0.0551044 | + | 0.998481i | \(0.517549\pi\) | |||||||
\(920\) | 45822.7 | 1.64210 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8855.01i | 0.316295i | ||||||||
\(923\) | 28306.9 | 1.00946 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35785.5 | 1.27202 | ||||||||
\(926\) | 15207.5i | 0.539688i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28012.6 | 0.990905 | ||||||||
\(929\) | 30528.7 | 1.07816 | 0.539082 | − | 0.842254i | \(-0.318771\pi\) | ||||
0.539082 | + | 0.842254i | \(0.318771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20475.5i | 0.719631i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 1825.69i | − 0.0639597i | ||||||||
\(935\) | − 10465.9i | − 0.366065i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 18235.1i | − 0.635769i | −0.948129 | − | 0.317885i | \(-0.897028\pi\) | ||||
0.948129 | − | 0.317885i | \(-0.102972\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15812.7 | −0.548674 | ||||||||
\(941\) | 13372.3 | 0.463258 | 0.231629 | − | 0.972804i | \(-0.425594\pi\) | ||||
0.231629 | + | 0.972804i | \(0.425594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18268.6i | 0.630867i | ||||||||
\(944\) | −2468.52 | −0.0851098 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9715.77 | 0.333919 | ||||||||
\(947\) | − 5117.10i | − 0.175590i | −0.996139 | − | 0.0877948i | \(-0.972018\pi\) | ||||
0.996139 | − | 0.0877948i | \(-0.0279820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37040.8 | −1.26701 | ||||||||
\(950\) | 11481.8 | 0.392124 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 35456.7i | − 1.20520i | −0.798044 | − | 0.602599i | \(-0.794132\pi\) | ||||
0.798044 | − | 0.602599i | \(-0.205868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13628.2i | 0.461779i | ||||||||
\(956\) | 9116.05i | 0.308404i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11018.1i | 0.371584i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23941.6 | 0.803652 | ||||||||
\(962\) | 43090.5 | 1.44417 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 18938.7i | − 0.632752i | ||||||||
\(965\) | 3000.51 | 0.100093 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2804.92 | −0.0932784 | −0.0466392 | − | 0.998912i | \(-0.514851\pi\) | ||||
−0.0466392 | + | 0.998912i | \(0.514851\pi\) | |||||||
\(968\) | − 28478.5i | − 0.945591i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20300.4 | 0.671964 | ||||||||
\(971\) | −27367.5 | −0.904496 | −0.452248 | − | 0.891892i | \(-0.649378\pi\) | ||||
−0.452248 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 27868.4i | − 0.916797i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 610.208i | − 0.0200126i | ||||||||
\(977\) | 24096.8i | 0.789075i | 0.918880 | + | 0.394537i | \(0.129095\pi\) | ||||
−0.918880 | + | 0.394537i | \(0.870905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16068.1i | 0.524554i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7811.09 | −0.253831 | ||||||||
\(983\) | 9310.72 | 0.302102 | 0.151051 | − | 0.988526i | \(-0.451734\pi\) | ||||
0.151051 | + | 0.988526i | \(0.451734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 48592.0i | − 1.57185i | ||||||||
\(986\) | 20266.7 | 0.654588 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19553.0 | −0.629621 | ||||||||
\(989\) | − 70972.3i | − 2.28189i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24190.5 | −0.775414 | −0.387707 | − | 0.921783i | \(-0.626733\pi\) | ||||
−0.387707 | + | 0.921783i | \(0.626733\pi\) | |||||||
\(992\) | −13496.7 | −0.431977 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 42998.0i | − 1.36998i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48866.7i | 1.55228i | 0.630560 | + | 0.776140i | \(0.282825\pi\) | ||||
−0.630560 | + | 0.776140i | \(0.717175\pi\) | |||||||
\(998\) | − 12544.9i | − 0.397899i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.c.a.440.5 | 16 | ||
3.2 | odd | 2 | inner | 441.4.c.a.440.12 | 16 | ||
7.2 | even | 3 | 441.4.p.c.80.3 | 16 | |||
7.3 | odd | 6 | 441.4.p.c.215.6 | 16 | |||
7.4 | even | 3 | 63.4.p.a.26.6 | yes | 16 | ||
7.5 | odd | 6 | 63.4.p.a.17.3 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 441.4.c.a.440.6 | 16 | ||
21.2 | odd | 6 | 441.4.p.c.80.6 | 16 | |||
21.5 | even | 6 | 63.4.p.a.17.6 | yes | 16 | ||
21.11 | odd | 6 | 63.4.p.a.26.3 | yes | 16 | ||
21.17 | even | 6 | 441.4.p.c.215.3 | 16 | |||
21.20 | even | 2 | inner | 441.4.c.a.440.11 | 16 | ||
28.11 | odd | 6 | 1008.4.bt.a.593.8 | 16 | |||
28.19 | even | 6 | 1008.4.bt.a.17.1 | 16 | |||
84.11 | even | 6 | 1008.4.bt.a.593.1 | 16 | |||
84.47 | odd | 6 | 1008.4.bt.a.17.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.3 | ✓ | 16 | 7.5 | odd | 6 | ||
63.4.p.a.17.6 | yes | 16 | 21.5 | even | 6 | ||
63.4.p.a.26.3 | yes | 16 | 21.11 | odd | 6 | ||
63.4.p.a.26.6 | yes | 16 | 7.4 | even | 3 | ||
441.4.c.a.440.5 | 16 | 1.1 | even | 1 | trivial | ||
441.4.c.a.440.6 | 16 | 7.6 | odd | 2 | inner | ||
441.4.c.a.440.11 | 16 | 21.20 | even | 2 | inner | ||
441.4.c.a.440.12 | 16 | 3.2 | odd | 2 | inner | ||
441.4.p.c.80.3 | 16 | 7.2 | even | 3 | |||
441.4.p.c.80.6 | 16 | 21.2 | odd | 6 | |||
441.4.p.c.215.3 | 16 | 21.17 | even | 6 | |||
441.4.p.c.215.6 | 16 | 7.3 | odd | 6 | |||
1008.4.bt.a.17.1 | 16 | 28.19 | even | 6 | |||
1008.4.bt.a.17.8 | 16 | 84.47 | odd | 6 | |||
1008.4.bt.a.593.1 | 16 | 84.11 | even | 6 | |||
1008.4.bt.a.593.8 | 16 | 28.11 | odd | 6 |