Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not 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: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.6 | ||
Root | \(6.38941i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.e.113.3 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.80363i | 0.867070i | 0.901137 | + | 0.433535i | \(0.142734\pi\) | ||||
−0.901137 | + | 0.433535i | \(0.857266\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −33.0971 | −1.32388 | −0.661941 | − | 0.749556i | \(-0.730267\pi\) | ||||
−0.661941 | + | 0.749556i | \(0.730267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.0783 | −0.328129 | −0.164064 | − | 0.986450i | \(-0.552461\pi\) | ||||
−0.164064 | + | 0.986450i | \(0.552461\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 20.1034 | 0.248190 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 215.592 | 1.78175 | 0.890875 | − | 0.454248i | \(-0.150092\pi\) | ||||
0.890875 | + | 0.454248i | \(0.150092\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 281.497i | − | 1.66567i | −0.553525 | − | 0.832833i | \(-0.686718\pi\) | ||
0.553525 | − | 0.832833i | \(-0.313282\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 258.277i | − | 1.14790i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 226.582 | 0.784022 | 0.392011 | − | 0.919961i | \(-0.371780\pi\) | ||||
0.392011 | + | 0.919961i | \(0.371780\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.9969 | + | 360.729i | −0.0387726 | + | 0.999248i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 125.469i | − | 0.284511i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −414.609 | −0.783760 | −0.391880 | − | 0.920016i | \(-0.628175\pi\) | ||||
−0.391880 | + | 0.920016i | \(0.628175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 470.416 | 0.752666 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 788.973i | 1.08227i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 606.612i | 0.721298i | 0.932702 | + | 0.360649i | \(0.117445\pi\) | ||||
−0.932702 | + | 0.360649i | \(0.882555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 478.655i | 0.498080i | 0.968493 | + | 0.249040i | \(0.0801151\pi\) | ||||
−0.968493 | + | 0.249040i | \(0.919885\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1682.40i | 1.54490i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 532.145 | 0.434404 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 104.604i | − | 0.0764094i | −0.999270 | − | 0.0382047i | \(-0.987836\pi\) | ||
0.999270 | − | 0.0382047i | \(-0.0121639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2196.70 | 1.44425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1891.12i | 1.12500i | 0.826799 | + | 0.562498i | \(0.190159\pi\) | ||||
−0.826799 | + | 0.562498i | \(0.809841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −315.912 | −0.170855 | −0.0854277 | − | 0.996344i | \(-0.527226\pi\) | ||||
−0.0854277 | + | 0.996344i | \(0.527226\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −665.364 | −0.328575 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 474.327 | 0.214725 | 0.107362 | − | 0.994220i | \(-0.465759\pi\) | ||||
0.107362 | + | 0.994220i | \(0.465759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2142.49 | −0.892331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1768.16i | 0.679801i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 774.381i | − | 0.275679i | −0.990455 | − | 0.137839i | \(-0.955984\pi\) | ||
0.990455 | − | 0.137839i | \(-0.0440158\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7135.46 | −2.35883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2814.99 | − | 109.227i | −0.866418 | − | 0.0336186i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 567.212i | − | 0.162945i | −0.996676 | − | 0.0814725i | \(-0.974038\pi\) | ||
0.996676 | − | 0.0814725i | \(-0.0259623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4799.51 | 1.28984 | 0.644922 | − | 0.764248i | \(-0.276890\pi\) | ||||
0.644922 | + | 0.764248i | \(0.276890\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −323.229 | −0.0814384 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9316.74i | 2.20515i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4464.01i | − | 0.994433i | −0.867627 | − | 0.497216i | \(-0.834356\pi\) | ||
0.867627 | − | 0.497216i | \(-0.165644\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3235.45i | − | 0.679575i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7636.34i | 1.51485i | 0.652924 | + | 0.757423i | \(0.273542\pi\) | ||||
−0.652924 | + | 0.757423i | \(0.726458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8396.65 | 1.57565 | 0.787826 | − | 0.615898i | \(-0.211207\pi\) | ||||
0.787826 | + | 0.615898i | \(0.211207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3670.95i | 0.652614i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3466.35 | −0.584644 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9706.71i | 1.55531i | 0.628689 | + | 0.777657i | \(0.283592\pi\) | ||||
−0.628689 | + | 0.777657i | \(0.716408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4528.48 | −0.690212 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10589.4 | 1.53715 | 0.768575 | − | 0.639760i | \(-0.220966\pi\) | ||||
0.768575 | + | 0.639760i | \(0.220966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7499.21 | −1.03795 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4733.77 | −0.625416 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10281.7i | − | 1.29804i | −0.760773 | − | 0.649018i | \(-0.775180\pi\) | ||
0.760773 | − | 0.649018i | \(-0.224820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4526.01i | 0.546553i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3735.24 | −0.431870 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 463.257 | − | 11939.1i | 0.0513304 | − | 1.32289i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15477.3i | 1.64494i | 0.568806 | + | 0.822472i | \(0.307406\pi\) | ||||
−0.568806 | + | 0.822472i | \(0.692594\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4334.13 | 0.442213 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10464.5 | 1.02583 | 0.512914 | − | 0.858440i | \(-0.328566\pi\) | ||||
0.512914 | + | 0.858440i | \(0.328566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3224.53i | 0.303943i | 0.988385 | + | 0.151972i | \(0.0485622\pi\) | ||||
−0.988385 | + | 0.151972i | \(0.951438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4152.66i | 0.376659i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7740.93i | 0.676123i | 0.941124 | + | 0.338061i | \(0.109771\pi\) | ||||
−0.941124 | + | 0.338061i | \(0.890229\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12613.1i | 1.06162i | 0.847492 | + | 0.530809i | \(0.178112\pi\) | ||||
−0.847492 | + | 0.530809i | \(0.821888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 816.294 | 0.0662523 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 900.876i | − | 0.0705518i | −0.999378 | − | 0.0352759i | \(-0.988769\pi\) | ||
0.999378 | − | 0.0352759i | \(-0.0112310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13722.3 | 1.03761 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5659.06i | − | 0.413402i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3643.06 | −0.257260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31838.8 | 2.17464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14757.6 | −0.975449 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5116.28 | 0.327442 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16688.1i | 1.03467i | 0.855784 | + | 0.517334i | \(0.173075\pi\) | ||||
−0.855784 | + | 0.517334i | \(0.826925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2465.26i | − | 0.148144i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9365.24 | −0.545728 | −0.272864 | − | 0.962053i | \(-0.587971\pi\) | ||||
−0.272864 | + | 0.962053i | \(0.587971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 225.047 | − | 5799.91i | 0.0127224 | − | 0.327882i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 26112.7i | − | 1.43280i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −36021.1 | −1.91918 | −0.959591 | − | 0.281399i | \(-0.909201\pi\) | ||||
−0.959591 | + | 0.281399i | \(0.909201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10371.8 | 0.536813 | 0.268406 | − | 0.963306i | \(-0.413503\pi\) | ||||
0.268406 | + | 0.963306i | \(0.413503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3701.47i | 0.186181i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 60688.6i | − | 2.96780i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20077.1i | − | 0.954914i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 16719.2i | − | 0.773714i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1353.29 | 0.0609562 | 0.0304781 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304781 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29132.7i | 1.27769i | 0.769334 | + | 0.638847i | \(0.220588\pi\) | ||||
−0.769334 | + | 0.638847i | \(0.779412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4555.07 | 0.194586 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 15842.1i | − | 0.659399i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11934.0 | −0.484156 | −0.242078 | − | 0.970257i | \(-0.577829\pi\) | ||||
−0.242078 | + | 0.970257i | \(0.577829\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6042.98 | 0.239033 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6666.22 | 0.257174 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13818.7 | −0.520108 | −0.260054 | − | 0.965594i | \(-0.583740\pi\) | ||||
−0.260054 | + | 0.965594i | \(0.583740\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 55682.5i | − | 2.04527i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10267.5i | 0.368157i | 0.982912 | + | 0.184079i | \(0.0589301\pi\) | ||||
−0.982912 | + | 0.184079i | \(0.941070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −50679.8 | −1.77444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −281.386 | + | 7251.87i | −0.00962298 | + | 0.248003i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 29001.7i | − | 0.969015i | −0.874787 | − | 0.484508i | \(-0.838999\pi\) | ||
0.874787 | − | 0.484508i | \(-0.161001\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7563.50 | −0.246971 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4426.31 | 0.141285 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 25479.5i | − | 0.795217i | −0.917555 | − | 0.397608i | \(-0.869840\pi\) | ||
0.917555 | − | 0.397608i | \(-0.130160\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 31158.1i | 0.951073i | 0.879696 | + | 0.475536i | \(0.157746\pi\) | ||||
−0.879696 | + | 0.475536i | \(0.842254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 37453.6i | 1.11839i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3462.10i | 0.101157i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 48849.3 | 1.39693 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 12685.4i | − | 0.355123i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17888.8 | −0.490359 | −0.245179 | − | 0.969478i | \(-0.578847\pi\) | ||||
−0.245179 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 784.195i | 0.0210528i | 0.999945 | + | 0.0105264i | \(0.00335071\pi\) | ||||
−0.999945 | + | 0.0105264i | \(0.996649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −72704.4 | −1.91202 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 42272.4 | 1.08924 | 0.544621 | − | 0.838682i | \(-0.316673\pi\) | ||||
0.544621 | + | 0.838682i | \(0.316673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15361.7 | 0.387911 | 0.193955 | − | 0.981010i | \(-0.437868\pi\) | ||||
0.193955 | + | 0.981010i | \(0.437868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34835.5 | 0.862243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9753.30i | − | 0.236679i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 62590.4i | − | 1.48936i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8335.05 | −0.194521 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3017.62 | + | 77770.1i | −0.0690831 | + | 1.78041i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 36036.6i | − | 0.809429i | −0.914443 | − | 0.404714i | \(-0.867371\pi\) | ||
0.914443 | − | 0.404714i | \(-0.132629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −59591.2 | −1.31348 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10455.8 | 0.226193 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7695.96i | − | 0.163434i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 65524.3i | 1.36620i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 63782.3i | − | 1.30592i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 44099.4i | − | 0.886795i | −0.896325 | − | 0.443398i | \(-0.853773\pi\) | ||
0.896325 | − | 0.443398i | \(-0.146227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9456.96 | 0.186804 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 34866.5i | − | 0.676638i | −0.941032 | − | 0.338319i | \(-0.890142\pi\) | ||
0.941032 | − | 0.338319i | \(-0.109858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26085.5 | 0.497425 | 0.248712 | − | 0.968577i | \(-0.419993\pi\) | ||||
0.248712 | + | 0.968577i | \(0.419993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 27050.1i | − | 0.506927i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 75466.8 | 1.39009 | 0.695047 | − | 0.718964i | \(-0.255383\pi\) | ||||
0.695047 | + | 0.718964i | \(0.255383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15698.8 | −0.284271 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −75747.5 | −1.34856 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 42891.8 | 0.750895 | 0.375447 | − | 0.926844i | \(-0.377489\pi\) | ||||
0.375447 | + | 0.926844i | \(0.377489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15629.3i | 0.269095i | 0.990907 | + | 0.134547i | \(0.0429580\pi\) | ||||
−0.990907 | + | 0.134547i | \(0.957042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 28568.3i | 0.483806i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 70910.1 | 1.18134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 101544. | + | 3940.10i | 1.66441 | + | 0.0645822i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 82635.9i | 1.33282i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −76998.8 | −1.22218 | −0.611092 | − | 0.791560i | \(-0.709269\pi\) | ||||
−0.611092 | + | 0.791560i | \(0.709269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −89386.3 | −1.39646 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 58521.0i | − | 0.899977i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8903.45i | 0.134801i | 0.997726 | + | 0.0674003i | \(0.0214705\pi\) | ||||
−0.997726 | + | 0.0674003i | \(0.978530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1681.86i | 0.0250721i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12195.0i | 0.179019i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 79232.7 | 1.14549 | 0.572747 | − | 0.819732i | \(-0.305878\pi\) | ||||
0.572747 | + | 0.819732i | \(0.305878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25629.8i | 0.364966i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 80234.9 | 1.12549 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 132817.i | − | 1.83548i | −0.397177 | − | 0.917742i | \(-0.630010\pi\) | ||
0.397177 | − | 0.917742i | \(-0.369990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73016.0 | −0.994213 | −0.497106 | − | 0.867690i | \(-0.665604\pi\) | ||||
−0.497106 | + | 0.867690i | \(0.665604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −35319.3 | −0.473900 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 101418. | 1.34106 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 66280.9 | 0.863831 | 0.431916 | − | 0.901914i | \(-0.357838\pi\) | ||||
0.431916 | + | 0.901914i | \(0.357838\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9622.59i | 0.123619i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 112860.i | 1.42932i | 0.699473 | + | 0.714659i | \(0.253418\pi\) | ||||
−0.699473 | + | 0.714659i | \(0.746582\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −80766.6 | −1.00846 | −0.504230 | − | 0.863569i | \(-0.668224\pi\) | ||||
−0.504230 | + | 0.863569i | \(0.668224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 93168.0 | + | 3615.08i | 1.14704 | + | 0.0445070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 30406.0i | − | 0.369144i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −32181.5 | −0.385310 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −120779. | −1.42628 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 133666.i | − | 1.55699i | −0.627653 | − | 0.778493i | \(-0.715984\pi\) | ||
0.627653 | − | 0.778493i | \(-0.284016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18773.0i | 0.215720i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 170096.i | 1.92833i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 116711.i | 1.30548i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5079.33 | 0.0560626 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 81660.8i | 0.889464i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −158850. | −1.70760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 100857.i | − | 1.07011i | −0.844816 | − | 0.535057i | \(-0.820290\pi\) | ||
0.844816 | − | 0.535057i | \(-0.179710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25163.1 | −0.263540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −121531. | −1.25651 | −0.628254 | − | 0.778009i | \(-0.716230\pi\) | ||||
−0.628254 | + | 0.778009i | \(0.716230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 189932. | 1.93869 | 0.969346 | − | 0.245700i | \(-0.0790180\pi\) | ||||
0.969346 | + | 0.245700i | \(0.0790180\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10697.9 | 0.107815 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 67336.1i | 0.670085i | 0.942203 | + | 0.335042i | \(0.108751\pi\) | ||||
−0.942203 | + | 0.335042i | \(0.891249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 130781.i | 1.28517i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −60407.3 | −0.586246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3171.45 | + | 81734.7i | −0.0303986 | + | 0.783432i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 132421.i | − | 1.25369i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −98427.7 | −0.920496 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7626.38 | −0.0704574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 154310.i | 1.40844i | 0.709984 | + | 0.704218i | \(0.248702\pi\) | ||||
−0.709984 | + | 0.704218i | \(0.751298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2102.90i | − | 0.0189640i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 147746.i | 1.31651i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 127543.i | 1.12304i | 0.827463 | + | 0.561521i | \(0.189783\pi\) | ||||
−0.827463 | + | 0.561521i | \(0.810217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7030.10 | 0.0611733 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 103194.i | 0.887454i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 73051.6 | 0.620929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 107084.i | 0.899677i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 71084.5 | 0.590359 | 0.295179 | − | 0.955442i | \(-0.404621\pi\) | ||||
0.295179 | + | 0.955442i | \(0.404621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 83601.6 | 0.686378 | 0.343189 | − | 0.939266i | \(-0.388493\pi\) | ||||
0.343189 | + | 0.939266i | \(0.388493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 222094. | 1.80270 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −40368.7 | −0.323963 | −0.161981 | − | 0.986794i | \(-0.551788\pi\) | ||||
−0.161981 | + | 0.986794i | \(0.551788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 252740.i | − | 2.00548i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 28429.1i | − | 0.223063i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −143079. | −1.11016 | −0.555081 | − | 0.831796i | \(-0.687313\pi\) | ||||
−0.555081 | + | 0.831796i | \(0.687313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −129929. | − | 10098.2i | −0.996993 | − | 0.0774869i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 248458.i | 1.88556i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −277904. | −2.08598 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30831.7 | 0.228910 | 0.114455 | − | 0.993428i | \(-0.463488\pi\) | ||||
0.114455 | + | 0.993428i | \(0.463488\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38017.9i | 0.279213i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12450.8i | 0.0904582i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 199882.i | 1.43666i | 0.695701 | + | 0.718332i | \(0.255094\pi\) | ||||
−0.695701 | + | 0.718332i | \(0.744906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 39925.5i | 0.283915i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 170760. | 1.20144 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 49499.6i | 0.344606i | 0.985044 | + | 0.172303i | \(0.0551209\pi\) | ||||
−0.985044 | + | 0.172303i | \(0.944879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −130228. | −0.897129 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 49593.2i | − | 0.338084i | −0.985609 | − | 0.169042i | \(-0.945933\pi\) | ||
0.985609 | − | 0.169042i | \(-0.0540674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 114726. | 0.774000 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6350.90 | −0.0424046 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15826.9 | −0.104592 | −0.0522958 | − | 0.998632i | \(-0.516654\pi\) | ||||
−0.0522958 | + | 0.998632i | \(0.516654\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −93943.1 | −0.614485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 73082.8i | − | 0.473184i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 321264.i | − | 2.05905i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2861.99 | −0.0181588 | −0.00907939 | − | 0.999959i | \(-0.502890\pi\) | ||||
−0.00907939 | + | 0.999959i | \(0.502890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 45260.3 | + | 1756.18i | 0.284297 | + | 0.0110312i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 226034.i | − | 1.40567i | −0.711351 | − | 0.702837i | \(-0.751916\pi\) | ||
0.711351 | − | 0.702837i | \(-0.248084\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 134740. | 0.829634 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 149879. | 0.913759 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 22551.9i | − | 0.136142i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 300321.i | − | 1.79531i | −0.440700 | − | 0.897655i | \(-0.645270\pi\) | ||
0.440700 | − | 0.897655i | \(-0.354730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 281095.i | − | 1.66406i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9119.81i | 0.0534670i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −350479. | −2.03501 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 80937.4i | 0.465454i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 88915.8 | 0.506467 | 0.253233 | − | 0.967405i | \(-0.418506\pi\) | ||||
0.253233 | + | 0.967405i | \(0.418506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 52919.8i | − | 0.298575i | −0.988794 | − | 0.149288i | \(-0.952302\pi\) | ||
0.988794 | − | 0.149288i | \(-0.0476980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9535.59 | 0.0532926 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 106588. | 0.590106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −77168.1 | −0.423235 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 473591. | 2.57329 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18064.2i | − | 0.0972442i | −0.998817 | − | 0.0486221i | \(-0.984517\pi\) | ||
0.998817 | − | 0.0486221i | \(-0.0154830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 188974.i | 1.00792i | 0.863726 | + | 0.503961i | \(0.168125\pi\) | ||||
−0.863726 | + | 0.503961i | \(0.831875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 156674. | 0.827977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5803.25 | − | 149561.i | 0.0303884 | − | 0.783171i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 249410.i | − | 1.29415i | −0.762427 | − | 0.647074i | \(-0.775992\pi\) | ||
0.762427 | − | 0.647074i | \(-0.224008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43071.3 | −0.221468 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −43050.1 | −0.219365 | −0.109682 | − | 0.993967i | \(-0.534983\pi\) | ||||
−0.109682 | + | 0.993967i | \(0.534983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 340296.i | 1.71845i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10560.6i | 0.0528533i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19223.8i | 0.0953556i | 0.998863 | + | 0.0476778i | \(0.0151821\pi\) | ||||
−0.998863 | + | 0.0476778i | \(0.984818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 407709.i | 2.00446i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −227341. | −1.10785 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 149798.i | − | 0.723572i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38484.7 | 0.184271 | 0.0921353 | − | 0.995747i | \(-0.470631\pi\) | ||||
0.0921353 | + | 0.995747i | \(0.470631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 178767.i | 0.848521i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −203940. | −0.959623 | −0.479812 | − | 0.877371i | \(-0.659295\pi\) | ||||
−0.479812 | + | 0.877371i | \(0.659295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 203200. | 0.947900 | 0.473950 | − | 0.880552i | \(-0.342828\pi\) | ||||
0.473950 | + | 0.880552i | \(0.342828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 123626. | 0.571745 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 121674. | 0.557912 | 0.278956 | − | 0.960304i | \(-0.410012\pi\) | ||||
0.278956 | + | 0.960304i | \(0.410012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 71773.8i | 0.326302i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 93128.2i | − | 0.419797i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −68108.0 | −0.304422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6584.37 | + | 169693.i | −0.0291828 | + | 0.752100i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 15567.7i | − | 0.0684207i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 208037. | 0.906711 | 0.453355 | − | 0.891330i | \(-0.350227\pi\) | ||||
0.453355 | + | 0.891330i | \(0.350227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29445.9 | −0.127272 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 52020.7i | 0.222988i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 512253.i | − | 2.17771i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 47417.7i | 0.199932i | 0.994991 | + | 0.0999660i | \(0.0318734\pi\) | ||||
−0.994991 | + | 0.0999660i | \(0.968127\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 107836.i | − | 0.450970i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 218823. | 0.907676 | 0.453838 | − | 0.891084i | \(-0.350054\pi\) | ||||
0.453838 | + | 0.891084i | \(0.350054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 137447.i | 0.565513i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −143447. | −0.585438 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 122780.i | − | 0.497065i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −147213. | −0.591214 | −0.295607 | − | 0.955310i | \(-0.595522\pi\) | ||||
−0.295607 | + | 0.955310i | \(0.595522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −80124.1 | −0.319218 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −189477. | −0.748895 | −0.374448 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374448 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −346343. | −1.35807 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 395486.i | − | 1.53856i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 117829.i | − | 0.454797i | −0.973802 | − | 0.227398i | \(-0.926978\pi\) | ||
0.973802 | − | 0.227398i | \(-0.0730220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −135004. | −0.517017 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −284605. | − | 11043.2i | −1.08145 | − | 0.0419624i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 106723.i | − | 0.402385i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 102261. | 0.382586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 226318. | 0.840204 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 254449.i | − | 0.937402i | −0.883357 | − | 0.468701i | \(-0.844722\pi\) | ||
0.883357 | − | 0.468701i | \(-0.155278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33047.5i | 0.120819i | 0.998174 | + | 0.0604094i | \(0.0192406\pi\) | ||||
−0.998174 | + | 0.0604094i | \(0.980759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 59022.7i | − | 0.214141i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 108455.i | 0.390505i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −107940. | −0.385720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 11402.9i | − | 0.0404414i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 532345. | 1.87387 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 256202.i | − | 0.895107i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 198833. | 0.689508 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −461903. | −1.58991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −363239. | −1.24108 | −0.620538 | − | 0.784176i | \(-0.713086\pi\) | ||||
−0.620538 | + | 0.784176i | \(0.713086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −243146. | −0.824647 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 417456.i | − | 1.40546i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 899.921i | − | 0.00300767i | −0.999999 | − | 0.00150383i | \(-0.999521\pi\) | ||
0.999999 | − | 0.00150383i | \(-0.000478685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 96486.5 | 0.320127 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −218822. | − | 8490.69i | −0.720756 | − | 0.0279666i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 156068.i | − | 0.510343i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27016.9 | −0.0877102 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 340311. | 1.09690 | 0.548448 | − | 0.836184i | \(-0.315219\pi\) | ||||
0.548448 | + | 0.836184i | \(0.315219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 88928.3i | 0.284588i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 381202.i | 1.21124i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 631686.i | − | 1.99289i | −0.0842180 | − | 0.996447i | \(-0.526839\pi\) | ||
0.0842180 | − | 0.996447i | \(-0.473161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29816.3i | 0.0934023i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 72810.3 | 0.226478 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5519.19i | 0.0170471i | 0.999964 | + | 0.00852356i | \(0.00271317\pi\) | ||||
−0.999964 | + | 0.00852356i | \(0.997287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 478673. | 1.46814 | 0.734068 | − | 0.679076i | \(-0.237619\pi\) | ||||
0.734068 | + | 0.679076i | \(0.237619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 139597.i | − | 0.425175i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −195039. | −0.589909 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 65914.9 | 0.197985 | 0.0989925 | − | 0.995088i | \(-0.468438\pi\) | ||||
0.0989925 | + | 0.995088i | \(0.468438\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6119.56 | −0.0182542 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −170260. | −0.504383 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 166950.i | − | 0.491191i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 187298.i | 0.547295i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −289436. | −0.839994 | −0.419997 | − | 0.907526i | \(-0.637969\pi\) | ||||
−0.419997 | + | 0.907526i | \(0.637969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −172664. | − | 6699.69i | −0.497705 | − | 0.0193119i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 329878.i | 0.944449i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 388285. | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 120575. | 0.340582 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 119877.i | 0.336346i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 601872.i | − | 1.67745i | −0.544553 | − | 0.838727i | \(-0.683301\pi\) | ||
0.544553 | − | 0.838727i | \(-0.316699\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 176095.i | − | 0.487527i | −0.969835 | − | 0.243764i | \(-0.921618\pi\) | ||
0.969835 | − | 0.243764i | \(-0.0783821\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 89741.7i | − | 0.246808i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.05377e6 | −2.87896 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 607939.i | 1.64999i | 0.565137 | + | 0.824997i | \(0.308823\pi\) | ||||
−0.565137 | + | 0.824997i | \(0.691177\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 76111.1 | 0.205217 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 133522.i | − | 0.357660i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 194933. | 0.518757 | 0.259379 | − | 0.965776i | \(-0.416482\pi\) | ||||
0.259379 | + | 0.965776i | \(0.416482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 488432. | 1.29138 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 148271. | 0.389480 | 0.194740 | − | 0.980855i | \(-0.437614\pi\) | ||||
0.194740 | + | 0.980855i | \(0.437614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 572353. | 1.49377 | 0.746884 | − | 0.664955i | \(-0.231549\pi\) | ||||
0.746884 | + | 0.664955i | \(0.231549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 327115.i | − | 0.848238i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 165313.i | 0.425923i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −463344. | −1.18616 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −606889. | − | 23548.4i | −1.54374 | − | 0.0598999i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 23701.5i | − | 0.0599066i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −236439. | −0.593829 | −0.296914 | − | 0.954904i | \(-0.595958\pi\) | ||||
−0.296914 | + | 0.954904i | \(0.595958\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 281216. | 0.701831 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 552329.i | − | 1.36978i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 603105.i | 1.48633i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 153516.i | 0.375970i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 247053.i | 0.601275i | 0.953738 | + | 0.300638i | \(0.0971995\pi\) | ||||
−0.953738 | + | 0.300638i | \(0.902801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −543389. | −1.31428 | −0.657142 | − | 0.753767i | \(-0.728235\pi\) | ||||
−0.657142 | + | 0.753767i | \(0.728235\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 81592.8i | 0.196125i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 263444. | 0.629332 | 0.314666 | − | 0.949202i | \(-0.398107\pi\) | ||||
0.314666 | + | 0.949202i | \(0.398107\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 122286.i | − | 0.290327i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60056.4 | 0.141709 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −261207. | −0.612574 | −0.306287 | − | 0.951939i | \(-0.599087\pi\) | ||||
−0.306287 | + | 0.951939i | \(0.599087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 309962. | 0.722480 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 168801. | 0.391061 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 532996.i | 1.22731i | 0.789576 | + | 0.613653i | \(0.210301\pi\) | ||||
−0.789576 | + | 0.613653i | \(0.789699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495346.i | 1.13372i | 0.823814 | + | 0.566860i | \(0.191842\pi\) | ||||
−0.823814 | + | 0.566860i | \(0.808158\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 497734. | 1.13232 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7448.39 | + | 191960.i | −0.0168430 | + | 0.434078i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 251507.i | − | 0.565325i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 344136. | 0.768913 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.03474e6 | 2.29818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 425648.i | − | 0.939768i | −0.882728 | − | 0.469884i | \(-0.844296\pi\) | ||
0.882728 | − | 0.469884i | \(-0.155704\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 371146.i | 0.814586i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 423249.i | 0.923461i | 0.887020 | + | 0.461730i | \(0.152771\pi\) | ||||
−0.887020 | + | 0.461730i | \(0.847229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 248849.i | − | 0.539754i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 272085. | 0.586692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 310900.i | 0.666467i | 0.942844 | + | 0.333233i | \(0.108140\pi\) | ||||
−0.942844 | + | 0.333233i | \(0.891860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.19219e6 | 2.54077 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 203561.i | 0.431302i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −217986. | −0.459188 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −314072. | −0.657769 | −0.328885 | − | 0.944370i | \(-0.606673\pi\) | ||||
−0.328885 | + | 0.944370i | \(0.606673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −69685.5 | −0.145103 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −343275. | −0.710677 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 428494.i | 0.882021i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 588915.i | 1.20531i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 607472. | 1.23620 | 0.618102 | − | 0.786098i | \(-0.287902\pi\) | ||||
0.618102 | + | 0.786098i | \(0.287902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37733.8 | + | 1464.14i | 0.0763519 | + | 0.00296259i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 122508.i | − | 0.246482i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −168251. | −0.336604 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −293984. | −0.584833 | −0.292416 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292416 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 195138.i | 0.386013i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 198455.i | − | 0.390375i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00861e6i | 3.92902i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 334712.i | 0.651078i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −911462. | −1.76312 | −0.881558 | − | 0.472075i | \(-0.843505\pi\) | ||||
−0.881558 | + | 0.472075i | \(0.843505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 51845.1i | − | 0.0997326i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −121965. | −0.233324 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 285360.i | 0.542896i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 174790. | 0.330710 | 0.165355 | − | 0.986234i | \(-0.447123\pi\) | ||||
0.165355 | + | 0.986234i | \(0.447123\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −589743. | −1.10971 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −71580.0 | −0.133954 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −401715. | −0.747671 | −0.373835 | − | 0.927495i | \(-0.621958\pi\) | ||||
−0.373835 | + | 0.927495i | \(0.621958\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 553356.i | 1.02431i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 962404.i | − | 1.77183i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 302531. | 0.553963 | 0.276982 | − | 0.960875i | \(-0.410666\pi\) | ||||
0.276982 | + | 0.960875i | \(0.410666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30747.0 | + | 792413.i | −0.0559973 | + | 1.44316i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 909052.i | − | 1.64669i | −0.567543 | − | 0.823344i | \(-0.692106\pi\) | ||
0.567543 | − | 0.823344i | \(-0.307894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44789.9 | −0.0806989 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 212883. | 0.381505 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 124461.i | − | 0.221855i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 370317.i | 0.656589i | 0.944575 | + | 0.328295i | \(0.106474\pi\) | ||||
−0.944575 | + | 0.328295i | \(0.893526\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 600870.i | − | 1.05972i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 964208.i | − | 1.69152i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 154581. | 0.269751 | 0.134876 | − | 0.990863i | \(-0.456937\pi\) | ||||
0.134876 | + | 0.990863i | \(0.456937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 697538.i | − | 1.21083i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −722058. | −1.24682 | −0.623409 | − | 0.781896i | \(-0.714253\pi\) | ||||
−0.623409 | + | 0.781896i | \(0.714253\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 202797.i | − | 0.348347i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −150760. | −0.257610 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −159669. | −0.271412 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 496131. | 0.838965 | 0.419482 | − | 0.907763i | \(-0.362212\pi\) | ||||
0.419482 | + | 0.907763i | \(0.362212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −69479.2 | −0.116882 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 317854.i | 0.531948i | 0.963980 | + | 0.265974i | \(0.0856935\pi\) | ||||
−0.963980 | + | 0.265974i | \(0.914306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 225167.i | 0.374888i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13124.6 | −0.0217393 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −682180. | − | 26469.8i | −1.12415 | − | 0.0436190i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.64633e6i | 2.69908i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −478601. | −0.780638 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 394979. | 0.640966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 206097.i | − | 0.332752i | −0.986062 | − | 0.166376i | \(-0.946793\pi\) | ||
0.986062 | − | 0.166376i | \(-0.0532066\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 618302.i | 0.993223i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14484.6i | 0.0231501i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.35105e6i | − | 2.14845i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −200005. | −0.316451 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 406943.i | − | 0.640644i | −0.947309 | − | 0.320322i | \(-0.896209\pi\) | ||
0.947309 | − | 0.320322i | \(-0.103791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 107474. | 0.168349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 206698.i | − | 0.322160i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.81025e6 | 2.80742 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −220632. | −0.340469 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.03646e6 | 1.59149 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −301170. | −0.460166 | −0.230083 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230083 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 454953.i | 0.691711i | 0.938288 | + | 0.345855i | \(0.112411\pi\) | ||||
−0.938288 | + | 0.345855i | \(0.887589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 569789.i | − | 0.862052i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 457360. | 0.688562 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4421.79 | − | 113958.i | 0.00662451 | − | 0.170727i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 90988.1i | 0.135649i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −833823. | −1.23705 | −0.618526 | − | 0.785764i | \(-0.712270\pi\) | ||||
−0.618526 | + | 0.785764i | \(0.712270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −903550. | −1.33399 | −0.666995 | − | 0.745063i | \(-0.732420\pi\) | ||||
−0.666995 | + | 0.745063i | \(0.732420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 791427.i | 1.16279i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 273012.i | − | 0.399182i | −0.979879 | − | 0.199591i | \(-0.936039\pi\) | ||
0.979879 | − | 0.199591i | \(-0.0639613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29206.8i | 0.0424986i | 0.999774 | + | 0.0212493i | \(0.00676438\pi\) | ||||
−0.999774 | + | 0.0212493i | \(0.993236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 517232.i | 0.749002i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −485450. | −0.699607 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 339826.i | − | 0.487397i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −377646. | −0.539056 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 563481.i | 0.800488i | 0.916409 | + | 0.400244i | \(0.131075\pi\) | ||||
−0.916409 | + | 0.400244i | \(0.868925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 339303. | 0.479729 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −880720. | −1.23932 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.67735e6 | 2.34915 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −511915. | −0.713561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 630272.i | − | 0.874405i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43369.9i | 0.0598866i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −852435. | −1.17156 | −0.585778 | − | 0.810472i | \(-0.699211\pi\) | ||||
−0.585778 | + | 0.810472i | \(0.699211\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9313.04 | − | 240016.i | 0.0127397 | − | 0.328328i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 103865.i | 0.141419i | 0.997497 | + | 0.0707097i | \(0.0225264\pi\) | ||||
−0.997497 | + | 0.0707097i | \(0.977474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 74101.6 | 0.100425 | 0.0502125 | − | 0.998739i | \(-0.484010\pi\) | ||||
0.0502125 | + | 0.998739i | \(0.484010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 237277. | 0.320073 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 434232.i | − | 0.583042i | −0.956564 | − | 0.291521i | \(-0.905839\pi\) | ||
0.956564 | − | 0.291521i | \(-0.0941613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 959870.i | 1.28286i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 251132.i | − | 0.334091i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.09269e6i | 2.77118i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.25661e6 | −1.65639 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 311146.i | 0.408259i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −82261.1 | −0.107443 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 493156.i | 0.641188i | 0.947217 | + | 0.320594i | \(0.103883\pi\) | ||||
−0.947217 | + | 0.320594i | \(0.896117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.04308e6 | 1.35002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −699253. | −0.900913 | −0.450456 | − | 0.892798i | \(-0.648739\pi\) | ||||
−0.450456 | + | 0.892798i | \(0.648739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −657183. | −0.842878 | −0.421439 | − | 0.906857i | \(-0.638475\pi\) | ||||
−0.421439 | + | 0.906857i | \(0.638475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −146498. | −0.187044 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 123664.i | 0.157179i | 0.996907 | + | 0.0785895i | \(0.0250416\pi\) | ||||
−0.996907 | + | 0.0785895i | \(0.974958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 268317.i | − | 0.339504i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −976303. | −1.22978 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6639.12 | + | 171103.i | −0.00832545 | + | 0.214563i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 843298.i | 1.05277i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −910772. | −1.13194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −290358. | −0.359264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 175461.i | − | 0.216138i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39637.2i | 0.0486102i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.03124e6i | − | 1.25911i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 30174.9i | − | 0.0366801i | −0.999832 | − | 0.0183401i | \(-0.994162\pi\) | ||
0.999832 | − | 0.0183401i | \(-0.00583815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 210371. | 0.254600 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 198609.i | 0.239311i | 0.992815 | + | 0.119655i | \(0.0381790\pi\) | ||||
−0.992815 | + | 0.119655i | \(0.961821\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.28299e6 | 2.73882 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.23960e6i | − | 1.48061i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 150577. | 0.179069 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.20577e6 | 1.42769 | 0.713845 | − | 0.700304i | \(-0.246952\pi\) | ||||
0.713845 | + | 0.700304i | \(0.246952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 787052. | 0.927863 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.14961e6 | 2.52323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 49207.6i | − | 0.0575107i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 64824.1i | 0.0754357i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.04643e6 | 1.21249 | 0.606246 | − | 0.795277i | \(-0.292675\pi\) | ||||
0.606246 | + | 0.795277i | \(0.292675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29988.2 | − | 772856.i | 0.0345980 | − | 0.891660i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 948380.i | − | 1.08948i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.61677e6 | −1.84937 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 251416. | 0.286361 | 0.143181 | − | 0.989697i | \(-0.454267\pi\) | ||||
0.143181 | + | 0.989697i | \(0.454267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.48216e6i | 1.68098i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.26323e6i | − | 1.42660i | −0.700858 | − | 0.713301i | \(-0.747199\pi\) | ||
0.700858 | − | 0.713301i | \(-0.252801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 784074.i | − | 0.881726i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 419848.i | 0.470142i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04458e6 | 1.16477 | 0.582386 | − | 0.812913i | \(-0.302119\pi\) | ||||
0.582386 | + | 0.812913i | \(0.302119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.36363e6i | − | 2.62451i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −525466. | −0.581010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 928965.i | − | 1.02285i | −0.859327 | − | 0.511427i | \(-0.829117\pi\) | ||
0.859327 | − | 0.511427i | \(-0.170883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 592066. | 0.649178 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.02056e6 | −1.11434 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 579159. | 0.629739 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 694411. | 0.751916 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 155619.i | 0.167807i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 25954.5i | − | 0.0278714i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 72252.5 | 0.0772680 | 0.0386340 | − | 0.999253i | \(-0.487699\pi\) | ||||
0.0386340 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −637827. | − | 24748.8i | −0.679290 | − | 0.0263577i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 217697.i | 0.230895i | 0.993314 | + | 0.115447i | \(0.0368302\pi\) | ||||
−0.993314 | + | 0.115447i | \(0.963170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −166761. | −0.176144 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03336e6 | 1.08704 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.19511e6i | − | 1.25204i | −0.779805 | − | 0.626022i | \(-0.784682\pi\) | ||
0.779805 | − | 0.626022i | \(-0.215318\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.21666e6i | − | 2.31278i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 253566.i | 0.263483i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 743610.i | − | 0.769552i | −0.923010 | − | 0.384776i | \(-0.874279\pi\) | ||
0.923010 | − | 0.384776i | \(-0.125721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.39909e6 | −1.44203 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 59513.5i | − | 0.0610915i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 130980. | 0.133910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 213907.i | − | 0.217810i | −0.994052 | − | 0.108905i | \(-0.965266\pi\) | ||
0.994052 | − | 0.108905i | \(-0.0347345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.20418e6 | −1.22121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −508426. | −0.513549 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 563076. | 0.566470 | 0.283235 | − | 0.959051i | \(-0.408592\pi\) | ||||
0.283235 | + | 0.959051i | \(0.408592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 82530.1 | 0.0826954 |
(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 | 304.5.e.e.113.6 | 8 | ||
4.3 | odd | 2 | 38.5.b.a.37.2 | ✓ | 8 | ||
12.11 | even | 2 | 342.5.d.a.37.8 | 8 | |||
19.18 | odd | 2 | inner | 304.5.e.e.113.3 | 8 | ||
76.75 | even | 2 | 38.5.b.a.37.7 | yes | 8 | ||
228.227 | odd | 2 | 342.5.d.a.37.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.2 | ✓ | 8 | 4.3 | odd | 2 | ||
38.5.b.a.37.7 | yes | 8 | 76.75 | even | 2 | ||
304.5.e.e.113.3 | 8 | 19.18 | odd | 2 | inner | ||
304.5.e.e.113.6 | 8 | 1.1 | even | 1 | trivial | ||
342.5.d.a.37.4 | 8 | 228.227 | odd | 2 | |||
342.5.d.a.37.8 | 8 | 12.11 | even | 2 |