Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.24 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.17 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15560i | 0.538899i | 0.963014 | + | 0.269450i | \(0.0868418\pi\) | ||||
−0.963014 | + | 0.269450i | \(0.913158\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.3534 | 0.709588 | ||||||||
\(5\) | −30.9385 | −1.23754 | −0.618770 | − | 0.785573i | \(-0.712369\pi\) | ||||
−0.618770 | + | 0.785573i | \(0.712369\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 73.3307 | 1.49655 | 0.748273 | − | 0.663391i | \(-0.230883\pi\) | ||||
0.748273 | + | 0.663391i | \(0.230883\pi\) | |||||||
\(8\) | 58.9629i | 0.921295i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 66.6909i | − | 0.666909i | ||||||
\(11\) | − | 203.451i | − | 1.68141i | −0.541494 | − | 0.840705i | \(-0.682141\pi\) | ||
0.541494 | − | 0.840705i | \(-0.317859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 115.092i | 0.681018i | 0.940241 | + | 0.340509i | \(0.110599\pi\) | ||||
−0.940241 | + | 0.340509i | \(0.889401\pi\) | |||||||
\(14\) | 158.071i | 0.806487i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 54.5542 | 0.213102 | ||||||||
\(17\) | 149.563 | 0.517520 | 0.258760 | − | 0.965942i | \(-0.416686\pi\) | ||||
0.258760 | + | 0.965942i | \(0.416686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −97.5337 | −0.270177 | −0.135088 | − | 0.990834i | \(-0.543132\pi\) | ||||
−0.135088 | + | 0.990834i | \(0.543132\pi\) | |||||||
\(20\) | −351.257 | −0.878143 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 438.557 | 0.906110 | ||||||||
\(23\) | − | 785.535i | − | 1.48494i | −0.669878 | − | 0.742472i | \(-0.733653\pi\) | ||
0.669878 | − | 0.742472i | \(-0.266347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 332.189 | 0.531503 | ||||||||
\(26\) | −248.092 | −0.367000 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 832.553 | 1.06193 | ||||||||
\(29\) | −279.591 | −0.332451 | −0.166226 | − | 0.986088i | \(-0.553158\pi\) | ||||
−0.166226 | + | 0.986088i | \(0.553158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 520.224i | − | 0.541336i | −0.962673 | − | 0.270668i | \(-0.912755\pi\) | ||
0.962673 | − | 0.270668i | \(-0.0872445\pi\) | |||||||
\(32\) | 1061.00i | 1.03614i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 322.398i | 0.278891i | ||||||||
\(35\) | −2268.74 | −1.85203 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 737.478i | − | 0.538699i | −0.963043 | − | 0.269349i | \(-0.913191\pi\) | ||
0.963043 | − | 0.269349i | \(-0.0868086\pi\) | |||||||
\(38\) | − | 210.243i | − | 0.145598i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1824.22i | − | 1.14014i | ||||||
\(41\) | −540.849 | −0.321743 | −0.160871 | − | 0.986975i | \(-0.551430\pi\) | ||||
−0.160871 | + | 0.986975i | \(0.551430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1171.64i | − | 0.633660i | −0.948482 | − | 0.316830i | \(-0.897382\pi\) | ||
0.948482 | − | 0.316830i | \(-0.102618\pi\) | |||||||
\(44\) | − | 2309.86i | − | 1.19311i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1693.30 | 0.800235 | ||||||||
\(47\) | 1505.45i | 0.681509i | 0.940152 | + | 0.340755i | \(0.110682\pi\) | ||||
−0.940152 | + | 0.340755i | \(0.889318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2976.40 | 1.23965 | ||||||||
\(50\) | 716.067i | 0.286427i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1306.69i | 0.483242i | ||||||||
\(53\) | 3630.24 | 1.29236 | 0.646179 | − | 0.763185i | \(-0.276366\pi\) | ||||
0.646179 | + | 0.763185i | \(0.276366\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6294.45i | 2.08081i | ||||||||
\(56\) | 4323.79i | 1.37876i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 602.686i | − | 0.179158i | ||||||
\(59\) | −3344.70 | − | 964.542i | −0.960845 | − | 0.277088i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5340.44i | − | 1.43522i | −0.696447 | − | 0.717608i | \(-0.745237\pi\) | ||
0.696447 | − | 0.717608i | \(-0.254763\pi\) | |||||||
\(62\) | 1121.39 | 0.291725 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1414.23 | −0.345270 | ||||||||
\(65\) | − | 3560.77i | − | 0.842786i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1694.69i | − | 0.377520i | −0.982023 | − | 0.188760i | \(-0.939553\pi\) | ||
0.982023 | − | 0.188760i | \(-0.0604469\pi\) | |||||||
\(68\) | 1698.05 | 0.367226 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 4890.49i | − | 0.998059i | ||||||
\(71\) | 9066.29 | 1.79851 | 0.899255 | − | 0.437425i | \(-0.144109\pi\) | ||||
0.899255 | + | 0.437425i | \(0.144109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 876.744i | 0.164523i | 0.996611 | + | 0.0822616i | \(0.0262143\pi\) | ||||
−0.996611 | + | 0.0822616i | \(0.973786\pi\) | |||||||
\(74\) | 1589.71 | 0.290304 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1107.34 | −0.191714 | ||||||||
\(77\) | − | 14919.2i | − | 2.51631i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7895.46 | 1.26509 | 0.632547 | − | 0.774522i | \(-0.282009\pi\) | ||||
0.632547 | + | 0.774522i | \(0.282009\pi\) | |||||||
\(80\) | −1687.82 | −0.263723 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1165.85i | − | 0.173387i | ||||||
\(83\) | 3535.87i | 0.513264i | 0.966509 | + | 0.256632i | \(0.0826128\pi\) | ||||
−0.966509 | + | 0.256632i | \(0.917387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4627.26 | −0.640451 | ||||||||
\(86\) | 2525.58 | 0.341479 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11996.0 | 1.54907 | ||||||||
\(89\) | − | 11418.1i | − | 1.44150i | −0.693195 | − | 0.720750i | \(-0.743797\pi\) | ||
0.693195 | − | 0.720750i | \(-0.256203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8439.78i | 1.01917i | ||||||||
\(92\) | − | 8918.49i | − | 1.05370i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3245.15 | −0.367265 | ||||||||
\(95\) | 3017.55 | 0.334354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15153.6i | − | 1.61054i | −0.592909 | − | 0.805269i | \(-0.702021\pi\) | ||
0.592909 | − | 0.805269i | \(-0.297979\pi\) | |||||||
\(98\) | 6415.91i | 0.668046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3771.48 | 0.377148 | ||||||||
\(101\) | 10320.2i | 1.01168i | 0.862626 | + | 0.505842i | \(0.168818\pi\) | ||||
−0.862626 | + | 0.505842i | \(0.831182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13724.8i | − | 1.29369i | −0.762620 | − | 0.646847i | \(-0.776087\pi\) | ||
0.762620 | − | 0.646847i | \(-0.223913\pi\) | |||||||
\(104\) | −6786.16 | −0.627419 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7825.33i | 0.696451i | ||||||||
\(107\) | 9382.60 | 0.819513 | 0.409756 | − | 0.912195i | \(-0.365614\pi\) | ||||
0.409756 | + | 0.912195i | \(0.365614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15647.4i | 1.31701i | 0.752575 | + | 0.658507i | \(0.228812\pi\) | ||||
−0.752575 | + | 0.658507i | \(0.771188\pi\) | |||||||
\(110\) | −13568.3 | −1.12135 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4000.50 | 0.318917 | ||||||||
\(113\) | 16451.0i | 1.28836i | 0.764875 | + | 0.644179i | \(0.222801\pi\) | ||||
−0.764875 | + | 0.644179i | \(0.777199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24303.3i | 1.83768i | ||||||||
\(116\) | −3174.31 | −0.235903 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2079.16 | − | 7209.82i | 0.149322 | − | 0.517798i | ||||
\(119\) | 10967.6 | 0.774492 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26751.1 | −1.82714 | ||||||||
\(122\) | 11511.8 | 0.773437 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5906.31i | − | 0.384125i | ||||||
\(125\) | 9059.11 | 0.579783 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15007.8 | 0.930484 | 0.465242 | − | 0.885183i | \(-0.345967\pi\) | ||||
0.465242 | + | 0.885183i | \(0.345967\pi\) | |||||||
\(128\) | 13927.5i | 0.850070i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7675.59 | 0.454177 | ||||||||
\(131\) | − | 521.489i | − | 0.0303880i | −0.999885 | − | 0.0151940i | \(-0.995163\pi\) | ||
0.999885 | − | 0.0151940i | \(-0.00483659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7152.22 | −0.404332 | ||||||||
\(134\) | 3653.07 | 0.203445 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8818.68i | 0.476789i | ||||||||
\(137\) | 29732.3 | 1.58411 | 0.792057 | − | 0.610447i | \(-0.209010\pi\) | ||||
0.792057 | + | 0.610447i | \(0.209010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5711.68 | −0.295620 | −0.147810 | − | 0.989016i | \(-0.547222\pi\) | ||||
−0.147810 | + | 0.989016i | \(0.547222\pi\) | |||||||
\(140\) | −25757.9 | −1.31418 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19543.3i | 0.969216i | ||||||||
\(143\) | 23415.5 | 1.14507 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8650.13 | 0.411421 | ||||||||
\(146\) | −1889.91 | −0.0886614 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8372.89i | − | 0.382254i | ||||||
\(149\) | − | 6283.15i | − | 0.283012i | −0.989937 | − | 0.141506i | \(-0.954806\pi\) | ||
0.989937 | − | 0.141506i | \(-0.0451944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 39803.8i | − | 1.74571i | −0.487983 | − | 0.872853i | \(-0.662267\pi\) | ||
0.487983 | − | 0.872853i | \(-0.337733\pi\) | |||||||
\(152\) | − | 5750.87i | − | 0.248912i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 32159.7 | 1.35604 | ||||||||
\(155\) | 16094.9i | 0.669924i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2933.82i | 0.119024i | 0.998228 | + | 0.0595119i | \(0.0189544\pi\) | ||||
−0.998228 | + | 0.0595119i | \(0.981046\pi\) | |||||||
\(158\) | 17019.4i | 0.681758i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 32825.8i | − | 1.28226i | ||||||
\(161\) | − | 57603.8i | − | 2.22228i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 44939.2 | 1.69142 | 0.845708 | − | 0.533645i | \(-0.179178\pi\) | ||||
0.845708 | + | 0.533645i | \(0.179178\pi\) | |||||||
\(164\) | −6140.48 | −0.228305 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7621.92 | −0.276597 | ||||||||
\(167\) | −5237.32 | −0.187791 | −0.0938957 | − | 0.995582i | \(-0.529932\pi\) | ||||
−0.0938957 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15314.8 | 0.536215 | ||||||||
\(170\) | − | 9974.50i | − | 0.345138i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 13302.1i | − | 0.449637i | ||||||
\(173\) | − | 23988.2i | − | 0.801503i | −0.916187 | − | 0.400751i | \(-0.868749\pi\) | ||
0.916187 | − | 0.400751i | \(-0.131251\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24359.7 | 0.795419 | ||||||||
\(176\) | − | 11099.1i | − | 0.358312i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24612.9 | 0.776824 | ||||||||
\(179\) | 48379.7i | 1.50993i | 0.655765 | + | 0.754965i | \(0.272346\pi\) | ||||
−0.655765 | + | 0.754965i | \(0.727654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9403.26 | −0.287026 | −0.143513 | − | 0.989648i | \(-0.545840\pi\) | ||||
−0.143513 | + | 0.989648i | \(0.545840\pi\) | |||||||
\(182\) | −18192.8 | −0.549232 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 46317.4 | 1.36807 | ||||||||
\(185\) | 22816.5i | 0.666661i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 30428.7i | − | 0.870163i | ||||||
\(188\) | 17092.0i | 0.483590i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6504.61i | 0.180183i | ||||||||
\(191\) | − | 26293.8i | − | 0.720754i | −0.932807 | − | 0.360377i | \(-0.882648\pi\) | ||
0.932807 | − | 0.360377i | \(-0.117352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35955.0 | −0.965260 | −0.482630 | − | 0.875824i | \(-0.660318\pi\) | ||||
−0.482630 | + | 0.875824i | \(0.660318\pi\) | |||||||
\(194\) | 32665.0 | 0.867918 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 33792.2 | 0.879639 | ||||||||
\(197\) | −16157.0 | −0.416321 | −0.208160 | − | 0.978095i | \(-0.566748\pi\) | ||||
−0.208160 | + | 0.978095i | \(0.566748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8326.75 | −0.210266 | −0.105133 | − | 0.994458i | \(-0.533527\pi\) | ||||
−0.105133 | + | 0.994458i | \(0.533527\pi\) | |||||||
\(200\) | 19586.9i | 0.489671i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22246.2 | −0.545195 | ||||||||
\(203\) | −20502.6 | −0.497528 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16733.1 | 0.398169 | ||||||||
\(206\) | 29585.1 | 0.697171 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6278.75i | 0.145127i | ||||||||
\(209\) | 19843.3i | 0.454277i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 75444.4i | 1.69458i | 0.531130 | + | 0.847290i | \(0.321768\pi\) | ||||
−0.531130 | + | 0.847290i | \(0.678232\pi\) | |||||||
\(212\) | 41215.5 | 0.917042 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20225.1i | 0.441635i | ||||||||
\(215\) | 36248.7i | 0.784179i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 38148.4i | − | 0.810134i | ||||||
\(218\) | −33729.6 | −0.709738 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 71463.4i | 1.47652i | ||||||||
\(221\) | 17213.5i | 0.352440i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 80926.3 | 1.62735 | 0.813673 | − | 0.581322i | \(-0.197464\pi\) | ||||
0.813673 | + | 0.581322i | \(0.197464\pi\) | |||||||
\(224\) | 77804.2i | 1.55062i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −35461.8 | −0.694295 | ||||||||
\(227\) | − | 50468.1i | − | 0.979411i | −0.871888 | − | 0.489706i | \(-0.837104\pi\) | ||
0.871888 | − | 0.489706i | \(-0.162896\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 88590.6i | 1.68934i | 0.535288 | + | 0.844669i | \(0.320203\pi\) | ||||
−0.535288 | + | 0.844669i | \(0.679797\pi\) | |||||||
\(230\) | −52388.0 | −0.990322 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 16485.5i | − | 0.306286i | ||||||
\(233\) | − | 21367.1i | − | 0.393580i | −0.980446 | − | 0.196790i | \(-0.936948\pi\) | ||
0.980446 | − | 0.196790i | \(-0.0630518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 46576.4i | − | 0.843394i | ||||||
\(236\) | −37973.7 | − | 10950.8i | −0.681804 | − | 0.196618i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23641.7i | 0.417373i | ||||||||
\(239\) | −27789.3 | −0.486498 | −0.243249 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243249 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −114284. | −1.96767 | −0.983836 | − | 0.179071i | \(-0.942691\pi\) | ||||
−0.983836 | + | 0.179071i | \(0.942691\pi\) | |||||||
\(242\) | − | 57664.6i | − | 0.984643i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 60632.1i | − | 1.01841i | ||||||
\(245\) | −92085.2 | −1.53411 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11225.4i | − | 0.183995i | ||||||
\(248\) | 30673.9 | 0.498730 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19527.8i | 0.312445i | ||||||||
\(251\) | −76189.7 | −1.20934 | −0.604671 | − | 0.796475i | \(-0.706695\pi\) | ||||
−0.604671 | + | 0.796475i | \(0.706695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −159818. | −2.49680 | ||||||||
\(254\) | 32350.7i | 0.501437i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −52649.8 | −0.803373 | ||||||||
\(257\) | 9932.87 | 0.150386 | 0.0751932 | − | 0.997169i | \(-0.476043\pi\) | ||||
0.0751932 | + | 0.997169i | \(0.476043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 54079.8i | − | 0.806187i | ||||||
\(260\) | − | 40426.9i | − | 0.598031i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1124.12 | 0.0163761 | ||||||||
\(263\) | −34983.1 | −0.505762 | −0.252881 | − | 0.967497i | \(-0.581378\pi\) | ||||
−0.252881 | + | 0.967497i | \(0.581378\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −112314. | −1.59934 | ||||||||
\(266\) | − | 15417.3i | − | 0.217894i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 19240.5i | − | 0.267884i | ||||||
\(269\) | − | 61848.8i | − | 0.854725i | −0.904080 | − | 0.427363i | \(-0.859443\pi\) | ||
0.904080 | − | 0.427363i | \(-0.140557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −91570.5 | −1.24686 | −0.623429 | − | 0.781880i | \(-0.714261\pi\) | ||||
−0.623429 | + | 0.781880i | \(0.714261\pi\) | |||||||
\(272\) | 8159.30 | 0.110285 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 64090.7i | 0.853678i | ||||||||
\(275\) | − | 67584.1i | − | 0.893675i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −88687.7 | −1.15586 | −0.577928 | − | 0.816088i | \(-0.696139\pi\) | ||||
−0.577928 | + | 0.816088i | \(0.696139\pi\) | |||||||
\(278\) | − | 12312.1i | − | 0.159309i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 133772.i | − | 1.70627i | ||||||
\(281\) | 54231.2 | 0.686809 | 0.343405 | − | 0.939188i | \(-0.388420\pi\) | ||||
0.343405 | + | 0.939188i | \(0.388420\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19900.8i | 0.248483i | 0.992252 | + | 0.124242i | \(0.0396498\pi\) | ||||
−0.992252 | + | 0.124242i | \(0.960350\pi\) | |||||||
\(284\) | 102933. | 1.27620 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 50474.5i | 0.617077i | ||||||||
\(287\) | −39660.9 | −0.481503 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −61151.9 | −0.732173 | ||||||||
\(290\) | 18646.2i | 0.221715i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9954.03i | 0.116744i | ||||||||
\(293\) | −88852.6 | −1.03499 | −0.517494 | − | 0.855687i | \(-0.673135\pi\) | ||||
−0.517494 | + | 0.855687i | \(0.673135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 103480. | + | 29841.5i | 1.18908 | + | 0.342907i | ||||
\(296\) | 43483.9 | 0.496301 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13543.9 | 0.152515 | ||||||||
\(299\) | 90408.8 | 1.01127 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 85917.0i | − | 0.948301i | ||||||
\(302\) | 85801.0 | 0.940760 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5320.88 | −0.0575753 | ||||||||
\(305\) | 165225.i | 1.77614i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5886.60 | −0.0624579 | −0.0312290 | − | 0.999512i | \(-0.509942\pi\) | ||||
−0.0312290 | + | 0.999512i | \(0.509942\pi\) | |||||||
\(308\) | − | 169383.i | − | 1.78554i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −34694.2 | −0.361022 | ||||||||
\(311\) | 94490.4 | 0.976938 | 0.488469 | − | 0.872581i | \(-0.337556\pi\) | ||||
0.488469 | + | 0.872581i | \(0.337556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 90255.1i | 0.921262i | 0.887592 | + | 0.460631i | \(0.152377\pi\) | ||||
−0.887592 | + | 0.460631i | \(0.847623\pi\) | |||||||
\(314\) | −6324.13 | −0.0641418 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 89640.3 | 0.897696 | ||||||||
\(317\) | −159546. | −1.58770 | −0.793849 | − | 0.608115i | \(-0.791926\pi\) | ||||
−0.793849 | + | 0.608115i | \(0.791926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56883.0i | 0.558987i | ||||||||
\(320\) | 43754.1 | 0.427286 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 124171. | 1.19759 | ||||||||
\(323\) | −14587.5 | −0.139822 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38232.4i | 0.361963i | ||||||||
\(326\) | 96870.9i | 0.911503i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 31890.1i | − | 0.296420i | ||||||
\(329\) | 110396.i | 1.01991i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20831.2 | 0.190134 | 0.0950669 | − | 0.995471i | \(-0.469694\pi\) | ||||
0.0950669 | + | 0.995471i | \(0.469694\pi\) | |||||||
\(332\) | 40144.2i | 0.364206i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 11289.5i | − | 0.101201i | ||||||
\(335\) | 52431.1i | 0.467196i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 189217.i | − | 1.66610i | −0.553199 | − | 0.833049i | \(-0.686593\pi\) | ||
0.553199 | − | 0.833049i | \(-0.313407\pi\) | |||||||
\(338\) | 33012.6i | 0.288966i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −52535.1 | −0.454456 | ||||||||
\(341\) | −105840. | −0.910207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 42194.2 | 0.358645 | ||||||||
\(344\) | 69083.1 | 0.583788 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 51708.8 | 0.431929 | ||||||||
\(347\) | − | 150636.i | − | 1.25104i | −0.780209 | − | 0.625519i | \(-0.784887\pi\) | ||
0.780209 | − | 0.625519i | \(-0.215113\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 80454.6i | 0.660541i | 0.943886 | + | 0.330271i | \(0.107140\pi\) | ||||
−0.943886 | + | 0.330271i | \(0.892860\pi\) | |||||||
\(350\) | 52509.7i | 0.428651i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 215862. | 1.74217 | ||||||||
\(353\) | − | 93087.5i | − | 0.747037i | −0.927623 | − | 0.373518i | \(-0.878151\pi\) | ||
0.927623 | − | 0.373518i | \(-0.121849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −280497. | −2.22573 | ||||||||
\(356\) | − | 129635.i | − | 1.02287i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −104287. | −0.813700 | ||||||||
\(359\) | 36181.0 | 0.280732 | 0.140366 | − | 0.990100i | \(-0.455172\pi\) | ||||
0.140366 | + | 0.990100i | \(0.455172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −120808. | −0.927005 | ||||||||
\(362\) | − | 20269.6i | − | 0.154678i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 95820.3i | 0.723194i | ||||||||
\(365\) | − | 27125.1i | − | 0.203604i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 147497.i | 1.09509i | 0.836775 | + | 0.547547i | \(0.184438\pi\) | ||||
−0.836775 | + | 0.547547i | \(0.815562\pi\) | |||||||
\(368\) | − | 42854.2i | − | 0.316445i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −49183.1 | −0.359263 | ||||||||
\(371\) | 266208. | 1.93407 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 93006.2 | 0.668489 | 0.334244 | − | 0.942486i | \(-0.391519\pi\) | ||||
0.334244 | + | 0.942486i | \(0.391519\pi\) | |||||||
\(374\) | 65592.0 | 0.468930 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −88765.9 | −0.627871 | ||||||||
\(377\) | − | 32178.7i | − | 0.226405i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −197981. | −1.37831 | −0.689153 | − | 0.724615i | \(-0.742017\pi\) | ||||
−0.689153 | + | 0.724615i | \(0.742017\pi\) | |||||||
\(380\) | 34259.4 | 0.237254 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 56678.9 | 0.388414 | ||||||||
\(383\) | −130011. | −0.886307 | −0.443153 | − | 0.896446i | \(-0.646140\pi\) | ||||
−0.443153 | + | 0.896446i | \(0.646140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 461577.i | 3.11403i | ||||||||
\(386\) | − | 77504.4i | − | 0.520178i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 172044.i | − | 1.14282i | ||||||
\(389\) | 97356.2 | 0.643375 | 0.321688 | − | 0.946846i | \(-0.395750\pi\) | ||||
0.321688 | + | 0.946846i | \(0.395750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 117487.i | − | 0.768487i | ||||||
\(392\) | 175497.i | 1.14208i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 34827.9i | − | 0.224355i | ||||||
\(395\) | −244273. | −1.56560 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21590.6i | − | 0.136988i | −0.997652 | − | 0.0684942i | \(-0.978181\pi\) | ||
0.997652 | − | 0.0684942i | \(-0.0218195\pi\) | |||||||
\(398\) | − | 17949.1i | − | 0.113312i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18122.3 | 0.113265 | ||||||||
\(401\) | 14919.3i | 0.0927809i | 0.998923 | + | 0.0463905i | \(0.0147718\pi\) | ||||
−0.998923 | + | 0.0463905i | \(0.985228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59873.6 | 0.368659 | ||||||||
\(404\) | 117169.i | 0.717878i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 44195.4i | − | 0.268118i | ||||||
\(407\) | −150040. | −0.905773 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 90196.9i | 0.539194i | 0.962973 | + | 0.269597i | \(0.0868905\pi\) | ||||
−0.962973 | + | 0.269597i | \(0.913110\pi\) | |||||||
\(410\) | 36069.7i | 0.214573i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 155823.i | − | 0.917989i | ||||||
\(413\) | −245269. | − | 70730.5i | −1.43795 | − | 0.414674i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 109395.i | − | 0.635184i | ||||||
\(416\) | −122113. | −0.705627 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −42774.1 | −0.244810 | ||||||||
\(419\) | − | 141820.i | − | 0.807808i | −0.914801 | − | 0.403904i | \(-0.867653\pi\) | ||
0.914801 | − | 0.403904i | \(-0.132347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 328314.i | − | 1.85236i | −0.377084 | − | 0.926179i | \(-0.623073\pi\) | ||
0.377084 | − | 0.926179i | \(-0.376927\pi\) | |||||||
\(422\) | −162628. | −0.913208 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 214049.i | 1.19064i | ||||||||
\(425\) | 49683.3 | 0.275063 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 391618.i | − | 2.14787i | ||||||
\(428\) | 106524. | 0.581516 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −78137.5 | −0.422593 | ||||||||
\(431\) | 256724.i | 1.38201i | 0.722849 | + | 0.691006i | \(0.242832\pi\) | ||||
−0.722849 | + | 0.691006i | \(0.757168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 63696.1 | 0.339733 | 0.169866 | − | 0.985467i | \(-0.445666\pi\) | ||||
0.169866 | + | 0.985467i | \(0.445666\pi\) | |||||||
\(434\) | 82232.5 | 0.436580 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 177652.i | 0.934537i | ||||||||
\(437\) | 76616.2i | 0.401197i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 301024. | 1.56197 | 0.780985 | − | 0.624550i | \(-0.214717\pi\) | ||||
0.780985 | + | 0.624550i | \(0.214717\pi\) | |||||||
\(440\) | −371139. | −1.91704 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −37105.4 | −0.189930 | ||||||||
\(443\) | 214549.i | 1.09325i | 0.837378 | + | 0.546625i | \(0.184088\pi\) | ||||
−0.837378 | + | 0.546625i | \(0.815912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 353260.i | 1.78391i | ||||||||
\(446\) | 174445.i | 0.876976i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −103706. | −0.516713 | ||||||||
\(449\) | −20938.9 | −0.103863 | −0.0519315 | − | 0.998651i | \(-0.516538\pi\) | ||||
−0.0519315 | + | 0.998651i | \(0.516538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 110036.i | 0.540981i | ||||||||
\(452\) | 186775.i | 0.914203i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 108789. | 0.527804 | ||||||||
\(455\) | − | 261114.i | − | 1.26127i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 155521.i | 0.744659i | 0.928101 | + | 0.372330i | \(0.121441\pi\) | ||||
−0.928101 | + | 0.372330i | \(0.878559\pi\) | |||||||
\(458\) | −190966. | −0.910383 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 275925.i | 1.30399i | ||||||||
\(461\) | −424691. | −1.99835 | −0.999175 | − | 0.0406056i | \(-0.987071\pi\) | ||||
−0.999175 | + | 0.0406056i | \(0.987071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 51304.1i | 0.239326i | 0.992815 | + | 0.119663i | \(0.0381814\pi\) | ||||
−0.992815 | + | 0.119663i | \(0.961819\pi\) | |||||||
\(464\) | −15252.9 | −0.0708461 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 46058.8 | 0.212100 | ||||||||
\(467\) | − | 18311.1i | − | 0.0839614i | −0.999118 | − | 0.0419807i | \(-0.986633\pi\) | ||
0.999118 | − | 0.0419807i | \(-0.0133668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 124273.i | − | 0.564976i | ||||||
\(470\) | 100400. | 0.454504 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 56872.2 | − | 197213.i | 0.255279 | − | 0.885222i | ||||
\(473\) | −238370. | −1.06544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32399.7 | −0.143600 | ||||||||
\(476\) | 124519. | 0.549570 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 59902.4i | − | 0.262173i | ||||||
\(479\) | 117396. | 0.511659 | 0.255830 | − | 0.966722i | \(-0.417651\pi\) | ||||
0.255830 | + | 0.966722i | \(0.417651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 84877.9 | 0.366863 | ||||||||
\(482\) | − | 246351.i | − | 1.06038i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −303716. | −1.29651 | ||||||||
\(485\) | 468828.i | 1.99310i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 276423. | 1.16551 | 0.582756 | − | 0.812647i | \(-0.301974\pi\) | ||||
0.582756 | + | 0.812647i | \(0.301974\pi\) | |||||||
\(488\) | 314888. | 1.32226 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 198499.i | − | 0.826733i | ||||||
\(491\) | 95438.0 | 0.395875 | 0.197938 | − | 0.980215i | \(-0.436576\pi\) | ||||
0.197938 | + | 0.980215i | \(0.436576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41816.6 | −0.172050 | ||||||||
\(494\) | 24197.3 | 0.0991548 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 28380.4i | − | 0.115360i | ||||||
\(497\) | 664838. | 2.69155 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 296293. | 1.18993 | 0.594964 | − | 0.803752i | \(-0.297166\pi\) | ||||
0.594964 | + | 0.803752i | \(0.297166\pi\) | |||||||
\(500\) | 102852. | 0.411407 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 164234.i | − | 0.651713i | ||||||
\(503\) | − | 38668.3i | − | 0.152834i | −0.997076 | − | 0.0764169i | \(-0.975652\pi\) | ||
0.997076 | − | 0.0764169i | \(-0.0243480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 319291.i | − | 1.25200i | ||||||
\(506\) | − | 344502.i | − | 1.34552i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 170389. | 0.660260 | ||||||||
\(509\) | 382145.i | 1.47500i | 0.675347 | + | 0.737500i | \(0.263994\pi\) | ||||
−0.675347 | + | 0.737500i | \(0.736006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64292.3i | 0.246217i | ||||||||
\(512\) | 109349.i | 0.417133i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21411.3i | 0.0810431i | ||||||||
\(515\) | 424624.i | 1.60100i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 306285. | 1.14590 | ||||||||
\(518\) | 116574. | 0.434454 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 209953. | 0.776455 | ||||||||
\(521\) | 193927. | 0.714437 | 0.357218 | − | 0.934021i | \(-0.383725\pi\) | ||||
0.357218 | + | 0.934021i | \(0.383725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 242685. | 0.887238 | 0.443619 | − | 0.896216i | \(-0.353694\pi\) | ||||
0.443619 | + | 0.896216i | \(0.353694\pi\) | |||||||
\(524\) | − | 5920.68i | − | 0.0215630i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 75409.4i | − | 0.272555i | ||||||
\(527\) | − | 77806.3i | − | 0.280152i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −337224. | −1.20506 | ||||||||
\(530\) | − | 242104.i | − | 0.861886i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −81202.0 | −0.286909 | ||||||||
\(533\) | − | 62247.5i | − | 0.219113i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −290283. | −1.01418 | ||||||||
\(536\) | 99923.8 | 0.347808 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 133321. | 0.460611 | ||||||||
\(539\) | − | 605550.i | − | 2.08436i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 87558.4i | 0.299160i | 0.988750 | + | 0.149580i | \(0.0477922\pi\) | ||||
−0.988750 | + | 0.149580i | \(0.952208\pi\) | |||||||
\(542\) | − | 197389.i | − | 0.671931i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 158687.i | 0.536221i | ||||||||
\(545\) | − | 484108.i | − | 1.62986i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −169774. | −0.567411 | −0.283705 | − | 0.958912i | \(-0.591564\pi\) | ||||
−0.283705 | + | 0.958912i | \(0.591564\pi\) | |||||||
\(548\) | 337562. | 1.12407 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 145684. | 0.481600 | ||||||||
\(551\) | 27269.6 | 0.0898205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 578980. | 1.89327 | ||||||||
\(554\) | − | 191175.i | − | 0.622890i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −64847.0 | −0.209768 | ||||||||
\(557\) | 76223.9 | 0.245686 | 0.122843 | − | 0.992426i | \(-0.460799\pi\) | ||||
0.122843 | + | 0.992426i | \(0.460799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 134846. | 0.431534 | ||||||||
\(560\) | −123769. | −0.394673 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 116900.i | 0.370121i | ||||||||
\(563\) | 589979.i | 1.86131i | 0.365892 | + | 0.930657i | \(0.380764\pi\) | ||||
−0.365892 | + | 0.930657i | \(0.619236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 508970.i | − | 1.59439i | ||||||
\(566\) | −42898.0 | −0.133907 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 534575.i | 1.65696i | ||||||||
\(569\) | − | 312707.i | − | 0.965856i | −0.875660 | − | 0.482928i | \(-0.839573\pi\) | ||
0.875660 | − | 0.482928i | \(-0.160427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 614610.i | 1.88507i | 0.334110 | + | 0.942534i | \(0.391564\pi\) | ||||
−0.334110 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(572\) | 265846. | 0.812528 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 85492.9i | − | 0.259481i | ||||||
\(575\) | − | 260946.i | − | 0.789252i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −170463. | −0.512010 | −0.256005 | − | 0.966675i | \(-0.582406\pi\) | ||||
−0.256005 | + | 0.966675i | \(0.582406\pi\) | |||||||
\(578\) | − | 131819.i | − | 0.394568i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 98208.5 | 0.291940 | ||||||||
\(581\) | 259288.i | 0.768123i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 738574.i | − | 2.17298i | ||||||
\(584\) | −51695.4 | −0.151575 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 191530.i | − | 0.557754i | ||||||
\(587\) | 315184.i | 0.914721i | 0.889281 | + | 0.457360i | \(0.151205\pi\) | ||||
−0.889281 | + | 0.457360i | \(0.848795\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50739.4i | 0.146256i | ||||||||
\(590\) | −64326.1 | + | 223061.i | −0.184792 | + | 0.640796i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 40232.6i | − | 0.114798i | ||||||
\(593\) | 93311.9 | 0.265355 | 0.132678 | − | 0.991159i | \(-0.457643\pi\) | ||||
0.132678 | + | 0.991159i | \(0.457643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −339320. | −0.958464 | ||||||||
\(596\) | − | 71335.1i | − | 0.200822i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 194885.i | 0.544974i | ||||||||
\(599\) | 70659.2 | 0.196932 | 0.0984658 | − | 0.995140i | \(-0.468607\pi\) | ||||
0.0984658 | + | 0.995140i | \(0.468607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 624282.i | 1.72835i | 0.503190 | + | 0.864176i | \(0.332159\pi\) | ||||
−0.503190 | + | 0.864176i | \(0.667841\pi\) | |||||||
\(602\) | 185202. | 0.511039 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 451909.i | − | 1.23873i | ||||||
\(605\) | 827639. | 2.26115 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 72992.7 | 0.198108 | 0.0990540 | − | 0.995082i | \(-0.468418\pi\) | ||||
0.0990540 | + | 0.995082i | \(0.468418\pi\) | |||||||
\(608\) | − | 103484.i | − | 0.279940i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −356158. | −0.957158 | ||||||||
\(611\) | −173266. | −0.464120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 446331.i | − | 1.18778i | −0.804546 | − | 0.593890i | \(-0.797591\pi\) | ||
0.804546 | − | 0.593890i | \(-0.202409\pi\) | |||||||
\(614\) | − | 12689.1i | − | 0.0336585i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 879678. | 2.31826 | ||||||||
\(617\) | 676732. | 1.77765 | 0.888825 | − | 0.458246i | \(-0.151522\pi\) | ||||
0.888825 | + | 0.458246i | \(0.151522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 217204. | 0.566874 | 0.283437 | − | 0.958991i | \(-0.408525\pi\) | ||||
0.283437 | + | 0.958991i | \(0.408525\pi\) | |||||||
\(620\) | 182732.i | 0.475370i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 203683.i | 0.526471i | ||||||||
\(623\) | − | 837300.i | − | 2.15727i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −487894. | −1.24901 | ||||||||
\(626\) | −194554. | −0.496467 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 33308.8i | 0.0844578i | ||||||||
\(629\) | − | 110300.i | − | 0.278787i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 74809.2 | 0.187887 | 0.0939434 | − | 0.995578i | \(-0.470053\pi\) | ||||
0.0939434 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(632\) | 465539.i | 1.16553i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 343917.i | − | 0.855609i | ||||||
\(635\) | −464318. | −1.15151 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 342559.i | 0.844223i | ||||||||
\(638\) | −122617. | −0.301237 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 430897.i | − | 1.05200i | ||||||
\(641\) | 461489. | 1.12317 | 0.561585 | − | 0.827419i | \(-0.310192\pi\) | ||||
0.561585 | + | 0.827419i | \(0.310192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −363629. | −0.879501 | −0.439751 | − | 0.898120i | \(-0.644933\pi\) | ||||
−0.439751 | + | 0.898120i | \(0.644933\pi\) | |||||||
\(644\) | − | 654000.i | − | 1.57691i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 31444.7i | − | 0.0753498i | ||||||
\(647\) | −641950. | −1.53353 | −0.766766 | − | 0.641926i | \(-0.778135\pi\) | ||||
−0.766766 | + | 0.641926i | \(0.778135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −196237. | + | 680481.i | −0.465898 | + | 1.61557i | ||||
\(650\) | −82413.6 | −0.195062 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 510213. | 1.20021 | ||||||||
\(653\) | −426122. | −0.999327 | −0.499664 | − | 0.866220i | \(-0.666543\pi\) | ||||
−0.499664 | + | 0.866220i | \(0.666543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16134.1i | 0.0376064i | ||||||||
\(656\) | −29505.6 | −0.0685641 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −237969. | −0.549628 | ||||||||
\(659\) | − | 468334.i | − | 1.07841i | −0.842174 | − | 0.539206i | \(-0.818724\pi\) | ||
0.842174 | − | 0.539206i | \(-0.181276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 485472. | 1.11112 | 0.555561 | − | 0.831476i | \(-0.312504\pi\) | ||||
0.555561 | + | 0.831476i | \(0.312504\pi\) | |||||||
\(662\) | 44903.8i | 0.102463i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −208485. | −0.472868 | ||||||||
\(665\) | 221279. | 0.500376 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 219629.i | 0.493671i | ||||||||
\(668\) | −59461.4 | −0.133255 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −113020. | −0.251772 | ||||||||
\(671\) | −1.08651e6 | −2.41319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 153856.i | − | 0.339692i | −0.985471 | − | 0.169846i | \(-0.945673\pi\) | ||
0.985471 | − | 0.169846i | \(-0.0543270\pi\) | |||||||
\(674\) | 407876. | 0.897859 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 173875. | 0.380491 | ||||||||
\(677\) | 624029. | 1.36153 | 0.680766 | − | 0.732501i | \(-0.261647\pi\) | ||||
0.680766 | + | 0.732501i | \(0.261647\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.11122e6i | − | 2.41024i | ||||||
\(680\) | − | 272837.i | − | 0.590044i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 228148.i | − | 0.490510i | ||||||
\(683\) | 717942.i | 1.53903i | 0.638627 | + | 0.769516i | \(0.279503\pi\) | ||||
−0.638627 | + | 0.769516i | \(0.720497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −919871. | −1.96040 | ||||||||
\(686\) | 90953.8i | 0.193274i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 63917.7i | − | 0.135034i | ||||||
\(689\) | 417811.i | 0.880120i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 647155.i | 1.35535i | 0.735361 | + | 0.677676i | \(0.237013\pi\) | ||||
−0.735361 | + | 0.677676i | \(0.762987\pi\) | |||||||
\(692\) | − | 272347.i | − | 0.568737i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 324711. | 0.674184 | ||||||||
\(695\) | 176711. | 0.365841 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −80891.2 | −0.166508 | ||||||||
\(698\) | −173428. | −0.355965 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 276565. | 0.564419 | ||||||||
\(701\) | − | 394820.i | − | 0.803457i | −0.915759 | − | 0.401729i | \(-0.868409\pi\) | ||
0.915759 | − | 0.401729i | \(-0.131591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 71929.0i | 0.145544i | ||||||||
\(704\) | 287725.i | 0.580541i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 200659. | 0.402578 | ||||||||
\(707\) | 756787.i | 1.51403i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −404978. | −0.805637 | −0.402818 | − | 0.915280i | \(-0.631969\pi\) | ||||
−0.402818 | + | 0.915280i | \(0.631969\pi\) | |||||||
\(710\) | − | 604639.i | − | 1.19944i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 673246. | 1.32805 | ||||||||
\(713\) | −408654. | −0.803853 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −724441. | −1.41707 | ||||||||
\(716\) | 549274.i | 1.07143i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 77991.6i | 0.151286i | ||||||||
\(719\) | 54443.6i | 0.105315i | 0.998613 | + | 0.0526574i | \(0.0167691\pi\) | ||||
−0.998613 | + | 0.0526574i | \(0.983231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.00645e6i | − | 1.93607i | ||||||
\(722\) | − | 260414.i | − | 0.499562i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −106759. | −0.203670 | ||||||||
\(725\) | −92877.3 | −0.176699 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 611738. | 1.15743 | 0.578717 | − | 0.815528i | \(-0.303553\pi\) | ||||
0.578717 | + | 0.815528i | \(0.303553\pi\) | |||||||
\(728\) | −497634. | −0.938961 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 58470.9 | 0.109722 | ||||||||
\(731\) | − | 175234.i | − | 0.327931i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 523681. | 0.974674 | 0.487337 | − | 0.873214i | \(-0.337968\pi\) | ||||
0.487337 | + | 0.873214i | \(0.337968\pi\) | |||||||
\(734\) | −317944. | −0.590146 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 833455. | 1.53860 | ||||||||
\(737\) | −344785. | −0.634766 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 304017.i | − | 0.556684i | −0.960482 | − | 0.278342i | \(-0.910215\pi\) | ||
0.960482 | − | 0.278342i | \(-0.0897848\pi\) | |||||||
\(740\) | 259044.i | 0.473054i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 573837.i | 1.04227i | ||||||||
\(743\) | −678235. | −1.22858 | −0.614289 | − | 0.789081i | \(-0.710557\pi\) | ||||
−0.614289 | + | 0.789081i | \(0.710557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 194391.i | 0.350238i | ||||||||
\(746\) | 200484.i | 0.360248i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 345469.i | − | 0.617457i | ||||||
\(749\) | 688033. | 1.22644 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 908208.i | 1.61030i | 0.593074 | + | 0.805148i | \(0.297914\pi\) | ||||
−0.593074 | + | 0.805148i | \(0.702086\pi\) | |||||||
\(752\) | 82128.8i | 0.145231i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 69364.4 | 0.122010 | ||||||||
\(755\) | 1.23147e6i | 2.16038i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −761493. | −1.32885 | −0.664423 | − | 0.747357i | \(-0.731322\pi\) | ||||
−0.664423 | + | 0.747357i | \(0.731322\pi\) | |||||||
\(758\) | − | 426768.i | − | 0.742768i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 177923.i | 0.308039i | ||||||||
\(761\) | −631628. | −1.09067 | −0.545334 | − | 0.838219i | \(-0.683597\pi\) | ||||
−0.545334 | + | 0.838219i | \(0.683597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.14744e6i | 1.97097i | ||||||||
\(764\) | − | 298525.i | − | 0.511438i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 280252.i | − | 0.477630i | ||||||
\(767\) | 111011. | − | 384948.i | 0.188702 | − | 0.654352i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 361776.i | − | 0.611769i | −0.952069 | − | 0.305885i | \(-0.901048\pi\) | ||
0.952069 | − | 0.305885i | \(-0.0989521\pi\) | |||||||
\(770\) | −994973. | −1.67815 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −408211. | −0.684937 | ||||||||
\(773\) | 300146.i | 0.502312i | 0.967947 | + | 0.251156i | \(0.0808108\pi\) | ||||
−0.967947 | + | 0.251156i | \(0.919189\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 172813.i | − | 0.287722i | ||||||
\(776\) | 893498. | 1.48378 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 209861.i | 0.346714i | ||||||||
\(779\) | 52751.1 | 0.0869273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.84454e6i | − | 3.02403i | ||||||
\(782\) | 253255. | 0.414137 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 162375. | 0.264172 | ||||||||
\(785\) | − | 90767.8i | − | 0.147297i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −174818. | −0.282253 | −0.141126 | − | 0.989992i | \(-0.545072\pi\) | ||||
−0.141126 | + | 0.989992i | \(0.545072\pi\) | |||||||
\(788\) | −183437. | −0.295416 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 526555.i | − | 0.843703i | ||||||
\(791\) | 1.20637e6i | 1.92809i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 614642. | 0.977408 | ||||||||
\(794\) | 46540.6 | 0.0738229 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −94537.0 | −0.149202 | ||||||||
\(797\) | − | 142726.i | − | 0.224691i | −0.993669 | − | 0.112345i | \(-0.964164\pi\) | ||
0.993669 | − | 0.112345i | \(-0.0358363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 225160.i | 0.352694i | ||||||||
\(800\) | 352454.i | 0.550710i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32159.9 | −0.0499996 | ||||||||
\(803\) | 178374. | 0.276631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.78218e6i | 2.75016i | ||||||||
\(806\) | 129063.i | 0.198670i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −608508. | −0.932059 | ||||||||
\(809\) | − | 1.05340e6i | − | 1.60952i | −0.593600 | − | 0.804760i | \(-0.702294\pi\) | ||
0.593600 | − | 0.804760i | \(-0.297706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 231482.i | − | 0.351945i | −0.984395 | − | 0.175972i | \(-0.943693\pi\) | ||
0.984395 | − | 0.175972i | \(-0.0563070\pi\) | |||||||
\(812\) | −232775. | −0.353040 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 323427.i | − | 0.488120i | ||||||
\(815\) | −1.39035e6 | −2.09319 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 114274.i | 0.171200i | ||||||||
\(818\) | −194428. | −0.290571 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 189977. | 0.282536 | ||||||||
\(821\) | − | 832114.i | − | 1.23451i | −0.786761 | − | 0.617257i | \(-0.788244\pi\) | ||
0.786761 | − | 0.617257i | \(-0.211756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 771617.i | 1.13921i | 0.821920 | + | 0.569603i | \(0.192903\pi\) | ||||
−0.821920 | + | 0.569603i | \(0.807097\pi\) | |||||||
\(824\) | 809254. | 1.19187 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 152467. | − | 528702.i | 0.223468 | − | 0.774909i | ||||
\(827\) | 605496. | 0.885320 | 0.442660 | − | 0.896690i | \(-0.354035\pi\) | ||||
0.442660 | + | 0.896690i | \(0.354035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 230768. | 0.335789 | 0.167895 | − | 0.985805i | \(-0.446303\pi\) | ||||
0.167895 | + | 0.985805i | \(0.446303\pi\) | |||||||
\(830\) | 235811. | 0.342300 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 162766.i | − | 0.235135i | ||||||
\(833\) | 445159. | 0.641543 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 162035. | 0.232399 | ||||||||
\(836\) | 225289.i | 0.322350i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 305706. | 0.435327 | ||||||||
\(839\) | − | 321881.i | − | 0.457269i | −0.973512 | − | 0.228634i | \(-0.926574\pi\) | ||
0.973512 | − | 0.228634i | \(-0.0734260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −629110. | −0.889476 | ||||||||
\(842\) | 707712. | 0.998234 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 856551.i | 1.20245i | ||||||||
\(845\) | −473817. | −0.663587 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.96168e6 | −2.73440 | ||||||||
\(848\) | 198045. | 0.275405 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 107097.i | 0.148231i | ||||||||
\(851\) | −579315. | −0.799937 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −937941. | −1.28907 | −0.644536 | − | 0.764574i | \(-0.722949\pi\) | ||||
−0.644536 | + | 0.764574i | \(0.722949\pi\) | |||||||
\(854\) | 844171. | 1.15748 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 553225.i | 0.755013i | ||||||||
\(857\) | 1.06976e6i | 1.45655i | 0.685285 | + | 0.728275i | \(0.259678\pi\) | ||||
−0.685285 | + | 0.728275i | \(0.740322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 483593.i | 0.655381i | 0.944785 | + | 0.327690i | \(0.106270\pi\) | ||||
−0.944785 | + | 0.327690i | \(0.893730\pi\) | |||||||
\(860\) | 411546.i | 0.556444i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −553394. | −0.744766 | ||||||||
\(863\) | − | 955910.i | − | 1.28350i | −0.766914 | − | 0.641749i | \(-0.778209\pi\) | ||
0.766914 | − | 0.641749i | \(-0.221791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 742158.i | 0.991891i | ||||||||
\(866\) | 137303.i | 0.183082i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 433114.i | − | 0.574861i | ||||||
\(869\) | − | 1.60633e6i | − | 2.12714i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 195045. | 0.257098 | ||||||||
\(872\) | −922619. | −1.21336 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −165154. | −0.216205 | ||||||||
\(875\) | 664311. | 0.867672 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −593572. | −0.771745 | −0.385873 | − | 0.922552i | \(-0.626100\pi\) | ||||
−0.385873 | + | 0.922552i | \(0.626100\pi\) | |||||||
\(878\) | 648887.i | 0.841744i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 343389.i | 0.443426i | ||||||||
\(881\) | 194695.i | 0.250844i | 0.992103 | + | 0.125422i | \(0.0400285\pi\) | ||||
−0.992103 | + | 0.125422i | \(0.959972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51348.5 | −0.0658577 | −0.0329288 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329288 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(884\) | 195432.i | 0.250087i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −462481. | −0.589151 | ||||||||
\(887\) | − | 15142.4i | − | 0.0192463i | −0.999954 | − | 0.00962314i | \(-0.996937\pi\) | ||
0.999954 | − | 0.00962314i | \(-0.00306319\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.10053e6 | 1.39251 | ||||||||
\(890\) | −761485. | −0.961350 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 918789. | 1.15475 | ||||||||
\(893\) | − | 146833.i | − | 0.184128i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.49679e6i | − | 1.86860i | ||||||
\(896\) | 1.02132e6i | 1.27217i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 45135.8i | − | 0.0559717i | ||||||
\(899\) | 145450.i | 0.179968i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 542950. | 0.668821 | ||||||||
\(902\) | −237193. | −0.291534 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −970002. | −1.18696 | ||||||||
\(905\) | 290922. | 0.355206 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −183053. | −0.222517 | −0.111258 | − | 0.993792i | \(-0.535488\pi\) | ||||
−0.111258 | + | 0.993792i | \(0.535488\pi\) | |||||||
\(908\) | − | 572984.i | − | 0.694978i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 562857. | 0.679696 | ||||||||
\(911\) | 1.37793e6 | 1.66032 | 0.830159 | − | 0.557527i | \(-0.188250\pi\) | ||||
0.830159 | + | 0.557527i | \(0.188250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 719376. | 0.863007 | ||||||||
\(914\) | −335241. | −0.401296 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.00580e6i | 1.19873i | ||||||||
\(917\) | − | 38241.2i | − | 0.0454771i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 276141.i | − | 0.326964i | −0.986546 | − | 0.163482i | \(-0.947727\pi\) | ||
0.986546 | − | 0.163482i | \(-0.0522726\pi\) | |||||||
\(920\) | −1.43299e6 | −1.69304 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 915463.i | − | 1.07691i | ||||||
\(923\) | 1.04346e6i | 1.22482i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 244983.i | − | 0.286320i | ||||||
\(926\) | −110591. | −0.128973 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 296647.i | − | 0.344465i | ||||||
\(929\) | − | 160509.i | − | 0.185981i | −0.995667 | − | 0.0929904i | \(-0.970357\pi\) | ||
0.995667 | − | 0.0929904i | \(-0.0296426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −290299. | −0.334924 | ||||||||
\(932\) | − | 242589.i | − | 0.279280i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39471.3 | 0.0452467 | ||||||||
\(935\) | 941418.i | 1.07686i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 90776.5i | 0.103394i | 0.998663 | + | 0.0516969i | \(0.0164630\pi\) | ||||
−0.998663 | + | 0.0516969i | \(0.983537\pi\) | |||||||
\(938\) | 267882. | 0.304465 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 528801.i | − | 0.598462i | ||||||
\(941\) | − | 1.24928e6i | − | 1.41085i | −0.708785 | − | 0.705424i | \(-0.750757\pi\) | ||
0.708785 | − | 0.705424i | \(-0.249243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 424856.i | 0.477770i | ||||||||
\(944\) | −182467. | − | 52619.8i | −0.204758 | − | 0.0590480i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 513830.i | − | 0.574166i | ||||||
\(947\) | −620940. | −0.692388 | −0.346194 | − | 0.938163i | \(-0.612526\pi\) | ||||
−0.346194 | + | 0.938163i | \(0.612526\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −100906. | −0.112043 | ||||||||
\(950\) | − | 69840.7i | − | 0.0773858i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 646680.i | 0.713536i | ||||||||
\(953\) | 1.35262e6 | 1.48932 | 0.744661 | − | 0.667443i | \(-0.232611\pi\) | ||||
0.744661 | + | 0.667443i | \(0.232611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 813491.i | 0.891962i | ||||||||
\(956\) | −315503. | −0.345213 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 253058.i | 0.275733i | ||||||||
\(959\) | 2.18029e6 | 2.37070 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 652888. | 0.706956 | ||||||||
\(962\) | 182963.i | 0.197702i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.29752e6 | −1.39624 | ||||||||
\(965\) | 1.11239e6 | 1.19455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 328428.i | 0.351226i | 0.984459 | + | 0.175613i | \(0.0561908\pi\) | ||||
−0.984459 | + | 0.175613i | \(0.943809\pi\) | |||||||
\(968\) | − | 1.57732e6i | − | 1.68333i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.01060e6 | −1.07408 | ||||||||
\(971\) | −1.82403e6 | −1.93461 | −0.967306 | − | 0.253614i | \(-0.918381\pi\) | ||||
−0.967306 | + | 0.253614i | \(0.918381\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −418841. | −0.442409 | ||||||||
\(974\) | 595857.i | 0.628093i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 291343.i | − | 0.305848i | ||||||
\(977\) | − | 260498.i | − | 0.272907i | −0.990646 | − | 0.136454i | \(-0.956430\pi\) | ||
0.990646 | − | 0.136454i | \(-0.0435705\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.32302e6 | −2.42375 | ||||||||
\(980\) | −1.04548e6 | −1.08859 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 205726.i | 0.213337i | ||||||||
\(983\) | 1.55845e6i | 1.61282i | 0.591360 | + | 0.806408i | \(0.298591\pi\) | ||||
−0.591360 | + | 0.806408i | \(0.701409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 499873. | 0.515213 | ||||||||
\(986\) | − | 90139.7i | − | 0.0927176i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 127446.i | − | 0.130561i | ||||||
\(989\) | −920362. | −0.940949 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.21576e6i | − | 1.23794i | −0.785416 | − | 0.618969i | \(-0.787551\pi\) | ||
0.785416 | − | 0.618969i | \(-0.212449\pi\) | |||||||
\(992\) | 551959. | 0.560898 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.43312e6i | 1.45048i | ||||||||
\(995\) | 257617. | 0.260213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 994803. | 1.00080 | 0.500399 | − | 0.865795i | \(-0.333187\pi\) | ||||
0.500399 | + | 0.865795i | \(0.333187\pi\) | |||||||
\(998\) | 638689.i | 0.641252i | ||||||||
\(999\) | 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 | 531.5.c.d.235.24 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.17 | ✓ | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.17 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.24 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.17 | ✓ | 40 | 3.2 | odd | 2 | ||
177.5.c.a.58.24 | yes | 40 | 177.176 | even | 2 | ||
531.5.c.d.235.17 | 40 | 59.58 | odd | 2 | inner | ||
531.5.c.d.235.24 | 40 | 1.1 | even | 1 | trivial |