Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.4 | ||
Character | \(\chi\) | \(=\) | 252.53 |
Dual form | 252.9.bk.a.233.4 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −700.103 | + | 404.204i | −1.12016 | + | 0.646727i | −0.941443 | − | 0.337173i | \(-0.890529\pi\) |
−0.178721 | + | 0.983900i | \(0.557196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −641.390 | + | 2313.75i | −0.267135 | + | 0.963659i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5978.45 | + | 3451.66i | 0.408336 | + | 0.235753i | 0.690075 | − | 0.723738i | \(-0.257578\pi\) |
−0.281738 | + | 0.959491i | \(0.590911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −33154.5 | −1.16083 | −0.580415 | − | 0.814321i | \(-0.697110\pi\) | ||||
−0.580415 | + | 0.814321i | \(0.697110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 61631.2 | + | 35582.8i | 0.737913 | + | 0.426034i | 0.821310 | − | 0.570482i | \(-0.193244\pi\) |
−0.0833972 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 91181.6 | + | 157931.i | 0.699669 | + | 1.21186i | 0.968581 | + | 0.248698i | \(0.0800025\pi\) |
−0.268912 | + | 0.963165i | \(0.586664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −439230. | + | 253590.i | −1.56957 | + | 0.906192i | −0.573351 | + | 0.819310i | \(0.694357\pi\) |
−0.996219 | + | 0.0868819i | \(0.972310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 131450. | − | 227678.i | 0.336512 | − | 0.582856i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.28004e6i | 1.80981i | 0.425615 | + | 0.904904i | \(0.360058\pi\) | ||||
−0.425615 | + | 0.904904i | \(0.639942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220600. | + | 382090.i | −0.238868 | + | 0.413731i | −0.960390 | − | 0.278660i | \(-0.910110\pi\) |
0.721522 | + | 0.692392i | \(0.243443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −486187. | − | 1.87911e6i | −0.323990 | − | 1.25222i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.41122e6 | + | 2.44431e6i | 0.752989 | + | 1.30421i | 0.946368 | + | 0.323090i | \(0.104722\pi\) |
−0.193380 | + | 0.981124i | \(0.561945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.61027e6i | 0.923739i | 0.886948 | + | 0.461870i | \(0.152821\pi\) | ||||
−0.886948 | + | 0.461870i | \(0.847179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.88701e6 | 1.72195 | 0.860976 | − | 0.508645i | \(-0.169854\pi\) | ||||
0.860976 | + | 0.508645i | \(0.169854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.57507e6 | − | 2.06406e6i | 0.732643 | − | 0.422992i | −0.0867452 | − | 0.996231i | \(-0.527647\pi\) |
0.819388 | + | 0.573239i | \(0.194313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.94204e6 | − | 2.96803e6i | −0.857278 | − | 0.514853i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19334e7 | − | 6.88974e6i | −1.51238 | − | 0.873171i | −0.999895 | − | 0.0144717i | \(-0.995393\pi\) |
−0.512480 | − | 0.858699i | \(-0.671273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.58070e6 | −0.609871 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.24676e6 | − | 1.29717e6i | −0.185416 | − | 0.107050i | 0.404419 | − | 0.914574i | \(-0.367474\pi\) |
−0.589835 | + | 0.807524i | \(0.700807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.73438e6 | − | 1.16643e7i | −0.486383 | − | 0.842440i | 0.513495 | − | 0.858093i | \(-0.328351\pi\) |
−0.999877 | + | 0.0156529i | \(0.995017\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.32115e7 | − | 1.34012e7i | 1.30032 | − | 0.750740i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.29779e7 | − | 2.24784e7i | 0.644030 | − | 1.11549i | −0.340494 | − | 0.940247i | \(-0.610594\pi\) |
0.984525 | − | 0.175247i | \(-0.0560723\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.46905e7i | 0.971622i | 0.874064 | + | 0.485811i | \(0.161476\pi\) | ||||
−0.874064 | + | 0.485811i | \(0.838524\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.86854e7 | + | 3.23641e7i | −0.657979 | + | 1.13965i | 0.323159 | + | 0.946345i | \(0.395255\pi\) |
−0.981138 | + | 0.193308i | \(0.938078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.18208e7 | + | 1.16187e7i | −0.336266 | + | 0.330519i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.45367e7 | − | 2.51783e7i | −0.373214 | − | 0.646426i | 0.616844 | − | 0.787086i | \(-0.288411\pi\) |
−0.990058 | + | 0.140660i | \(0.955078\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.80101e6i | − | 0.101163i | −0.998720 | − | 0.0505813i | \(-0.983893\pi\) | ||
0.998720 | − | 0.0505813i | \(-0.0161074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.75309e7 | −1.10211 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.67403e7 | + | 9.66503e6i | −0.266811 | + | 0.154043i | −0.627438 | − | 0.778667i | \(-0.715896\pi\) |
0.360626 | + | 0.932710i | \(0.382563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.12649e7 | − | 7.67110e7i | 0.310098 | − | 1.11864i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.27673e8 | − | 7.37120e7i | −1.56749 | − | 0.904990i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.62373e8 | 1.83412 | 0.917060 | − | 0.398749i | \(-0.130556\pi\) | ||||
0.917060 | + | 0.398749i | \(0.130556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50788e7 | − | 2.60263e7i | −0.433199 | − | 0.250107i | 0.267510 | − | 0.963555i | \(-0.413799\pi\) |
−0.700708 | + | 0.713448i | \(0.747133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.26371e7 | + | 1.43132e8i | 0.734220 | + | 1.27171i | 0.955065 | + | 0.296397i | \(0.0957851\pi\) |
−0.220845 | + | 0.975309i | \(0.570882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.34074e8 | + | 7.74076e7i | −1.02284 | + | 0.590539i | −0.914926 | − | 0.403621i | \(-0.867752\pi\) |
−0.107917 | + | 0.994160i | \(0.534418\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.41466e7 | + | 7.64642e7i | −0.312746 | + | 0.541692i | −0.978956 | − | 0.204072i | \(-0.934582\pi\) |
0.666210 | + | 0.745764i | \(0.267916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.87851e7i | − | 0.421872i | −0.977500 | − | 0.210936i | \(-0.932349\pi\) | ||
0.977500 | − | 0.210936i | \(-0.0676511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.05004e8 | − | 3.55077e8i | 1.17212 | − | 2.03017i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.21859e8 | + | 1.19777e8i | −0.607674 | + | 0.597288i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.33515e7 | − | 1.44369e8i | −0.388841 | − | 0.673493i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.03254e8i | − | 0.422929i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.10140e8 | 0.423380 | 0.211690 | − | 0.977337i | \(-0.432103\pi\) | ||||
0.211690 | + | 0.977337i | \(0.432103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.29909e8 | + | 7.50031e7i | −0.441118 | + | 0.254680i | −0.704072 | − | 0.710129i | \(-0.748637\pi\) |
0.262954 | + | 0.964808i | \(0.415303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.23895e8 | + | 1.09676e8i | −1.35473 | + | 0.350512i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.52727e8 | − | 2.03647e8i | −1.00128 | − | 0.578090i | −0.0926542 | − | 0.995698i | \(-0.529535\pi\) |
−0.908627 | + | 0.417608i | \(0.862868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.95491e7 | 0.186308 | 0.0931542 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931542 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.98212e8 | − | 1.14438e8i | −0.474009 | − | 0.273669i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.17399e8 | − | 8.96162e8i | −1.17045 | − | 2.02728i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.52070e8 | + | 2.61003e8i | −0.917193 | + | 0.529541i | −0.882738 | − | 0.469865i | \(-0.844303\pi\) |
−0.0344543 | + | 0.999406i | \(0.510969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.08313e8 | − | 3.60808e8i | 0.400690 | − | 0.694015i | −0.593120 | − | 0.805114i | \(-0.702104\pi\) |
0.993809 | + | 0.111099i | \(0.0354372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.56669e8i | − | 0.617930i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.54864e8 | − | 2.68232e8i | 0.254889 | − | 0.441481i | −0.709976 | − | 0.704226i | \(-0.751294\pi\) |
0.964865 | + | 0.262745i | \(0.0846277\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.05024e8 | − | 1.17892e9i | −0.453973 | − | 1.75461i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.76515e8 | − | 1.17176e9i | −0.958356 | − | 1.65992i | −0.726494 | − | 0.687173i | \(-0.758852\pi\) |
−0.231862 | − | 0.972749i | \(-0.574482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00867e9i | 1.29683i | 0.761288 | + | 0.648414i | \(0.224568\pi\) | ||||
−0.761288 | + | 0.648414i | \(0.775432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.83488e8 | 0.347526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.04404e9 | + | 6.02778e8i | −1.16556 | + | 0.672935i | −0.952630 | − | 0.304133i | \(-0.901633\pi\) |
−0.212928 | + | 0.977068i | \(0.568300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.42478e8 | + | 4.50172e8i | 0.471780 | + | 0.479984i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.75263e8 | − | 3.89863e8i | −0.657750 | − | 0.379752i | 0.133669 | − | 0.991026i | \(-0.457324\pi\) |
−0.791419 | + | 0.611274i | \(0.790657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.78614e9 | 1.66418 | 0.832091 | − | 0.554639i | \(-0.187144\pi\) | ||||
0.832091 | + | 0.554639i | \(0.187144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.97600e9 | − | 1.14084e9i | −1.68694 | − | 0.973956i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.45639e8 | + | 4.25460e8i | 0.200878 | + | 0.347930i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.65713e9 | − | 9.56742e8i | 1.24515 | − | 0.718888i | 0.275012 | − | 0.961441i | \(-0.411318\pi\) |
0.970138 | + | 0.242553i | \(0.0779847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.74296e8 | + | 4.75094e8i | −0.197692 | + | 0.342413i | −0.947780 | − | 0.318925i | \(-0.896678\pi\) |
0.750087 | + | 0.661339i | \(0.230011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.76800e8i | 0.582151i | 0.956700 | + | 0.291076i | \(0.0940131\pi\) | ||||
−0.956700 | + | 0.291076i | \(0.905987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.36157e8 | − | 1.27506e9i | 0.469416 | − | 0.813052i | −0.529973 | − | 0.848015i | \(-0.677798\pi\) |
0.999389 | + | 0.0349623i | \(0.0111311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.96170e9 | − | 8.21007e8i | −1.74404 | − | 0.483463i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.05508e9 | − | 1.82745e9i | −0.597407 | − | 1.03474i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.25891e9i | 0.659796i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.46116e9 | 1.24168 | 0.620840 | − | 0.783937i | \(-0.286792\pi\) | ||||
0.620840 | + | 0.783937i | \(0.286792\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.12151e9 | + | 2.37956e9i | −1.92887 | + | 1.11363i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.42568e8 | − | 7.55480e8i | −0.334886 | − | 0.340709i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.04335e9 | − | 1.17973e9i | −0.856591 | − | 0.494553i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.61371e9 | −1.05691 | −0.528454 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528454 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.08436e9 | + | 2.35810e9i | 1.53823 | + | 0.888095i | 0.998943 | + | 0.0459712i | \(0.0146382\pi\) |
0.539284 | + | 0.842124i | \(0.318695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.41923e9 | + | 2.45818e9i | 0.516074 | + | 0.893866i | 0.999826 | + | 0.0186609i | \(0.00594029\pi\) |
−0.483752 | + | 0.875205i | \(0.660726\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.01012e9 | − | 5.83193e8i | 0.342728 | − | 0.197874i | −0.318750 | − | 0.947839i | \(-0.603263\pi\) |
0.661478 | + | 0.749965i | \(0.269930\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.66861e9 | + | 2.89011e9i | −0.547120 | + | 0.947640i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.74981e8i | − | 0.298816i | −0.988776 | − | 0.149408i | \(-0.952263\pi\) | ||
0.988776 | − | 0.149408i | \(-0.0477369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.87499e9 | − | 3.24757e9i | 0.555814 | − | 0.962699i | −0.442025 | − | 0.897003i | \(-0.645740\pi\) |
0.997840 | − | 0.0656961i | \(-0.0209268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.65962e9 | + | 8.03300e7i | 1.29326 | + | 0.0222953i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.02308e9 | − | 5.23612e9i | −0.812197 | − | 1.40677i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.11453e9i | − | 0.784689i | −0.919818 | − | 0.392345i | \(-0.871664\pi\) | ||
0.919818 | − | 0.392345i | \(-0.128336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.50122e9 | −0.854549 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.73155e9 | − | 2.15441e9i | 0.855377 | − | 0.493852i | −0.00708477 | − | 0.999975i | \(-0.502255\pi\) |
0.862461 | + | 0.506123i | \(0.168922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.56065e9 | + | 1.69745e9i | −1.45797 | + | 0.377224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.97787e9 | − | 1.71927e9i | −0.622419 | − | 0.359354i | 0.155391 | − | 0.987853i | \(-0.450336\pi\) |
−0.777810 | + | 0.628499i | \(0.783669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.11394e10 | 2.25881 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.04971e9 | + | 6.06049e8i | 0.200474 | + | 0.115744i | 0.596877 | − | 0.802333i | \(-0.296408\pi\) |
−0.396402 | + | 0.918077i | \(0.629741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.97273e8 | + | 1.03451e9i | 0.110738 | + | 0.191804i | 0.916068 | − | 0.401023i | \(-0.131345\pi\) |
−0.805330 | + | 0.592827i | \(0.798012\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.57173e9 | − | 9.07441e8i | 0.274820 | − | 0.158667i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.27297e8 | − | 1.08651e9i | 0.106550 | − | 0.184550i | −0.807820 | − | 0.589429i | \(-0.799353\pi\) |
0.914370 | + | 0.404878i | \(0.132686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.32808e9i | 0.533788i | 0.963726 | + | 0.266894i | \(0.0859974\pi\) | ||||
−0.963726 | + | 0.266894i | \(0.914003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.33297e9 | + | 4.04082e9i | −0.363717 | + | 0.629976i | −0.988569 | − | 0.150767i | \(-0.951826\pi\) |
0.624852 | + | 0.780743i | \(0.285159\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.03949e9 | − | 1.67420e9i | −0.890170 | − | 0.246763i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.55608e8 | − | 1.65516e9i | −0.136990 | − | 0.237273i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.20087e9i | 0.705676i | 0.935684 | + | 0.352838i | \(0.114783\pi\) | ||||
−0.935684 | + | 0.352838i | \(0.885217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09728e9 | 0.276929 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.45624e10 | − | 8.40763e9i | 1.82200 | − | 1.05193i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.77587e9 | + | 1.36211e10i | −0.459993 | + | 1.65938i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.42951e9 | + | 5.44413e9i | 1.08966 | + | 0.629114i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.89434e9 | 0.438410 | 0.219205 | − | 0.975679i | \(-0.429654\pi\) | ||||
0.219205 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.39232e9 | + | 8.03858e8i | 0.148833 | + | 0.0859286i | 0.572567 | − | 0.819858i | \(-0.305948\pi\) |
−0.423734 | + | 0.905787i | \(0.639281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.77134e9 | + | 8.26421e9i | 0.497123 | + | 0.861041i | 0.999994 | − | 0.00331945i | \(-0.00105662\pi\) |
−0.502872 | + | 0.864361i | \(0.667723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.22083e9 | − | 4.74630e9i | 0.814101 | − | 0.470022i | −0.0342769 | − | 0.999412i | \(-0.510913\pi\) |
0.848378 | + | 0.529391i | \(0.177579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.41827e9 | + | 7.65267e9i | −0.426668 | + | 0.739010i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.29780e10i | 1.19233i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.35815e9 | + | 7.54854e9i | −0.390633 | + | 0.676596i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.48271e9 | + | 9.59566e9i | 0.211906 | + | 0.819014i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.22096e9 | + | 1.59712e10i | 0.768182 | + | 1.33053i | 0.938548 | + | 0.345149i | \(0.112172\pi\) |
−0.170366 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.09830e10i | 1.66605i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.09585e9 | −0.472623 | −0.236311 | − | 0.971677i | \(-0.575939\pi\) | ||||
−0.236311 | + | 0.971677i | \(0.575939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.63769e9 | + | 1.52287e9i | −0.195077 | + | 0.112628i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00370e10 | − | 9.53096e9i | 0.725152 | − | 0.688589i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.20375e9 | − | 6.94985e8i | −0.0830267 | − | 0.0479355i | 0.457912 | − | 0.888998i | \(-0.348598\pi\) |
−0.540939 | + | 0.841062i | \(0.681931\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.89927e7 | 0.00532458 | 0.00266229 | − | 0.999996i | \(-0.499153\pi\) | ||||
0.00266229 | + | 0.999996i | \(0.499153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.44156e10 | + | 1.40964e10i | 1.57242 | + | 0.907838i | 0.995871 | + | 0.0907756i | \(0.0289346\pi\) |
0.576550 | + | 0.817062i | \(0.304399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.98002e9 | − | 1.72859e10i | −0.628374 | − | 1.08838i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.10750e9 | − | 2.37147e9i | 0.247286 | − | 0.142771i | −0.371235 | − | 0.928539i | \(-0.621066\pi\) |
0.618521 | + | 0.785768i | \(0.287732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.13637e9 | + | 1.40926e10i | −0.479073 | + | 0.829779i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.02110e10i | − | 1.70213i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.29244e9 | + | 1.08988e10i | −0.346860 | + | 0.600780i | −0.985690 | − | 0.168569i | \(-0.946086\pi\) |
0.638830 | + | 0.769348i | \(0.279419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.35950e10 | − | 2.31918e10i | 1.24545 | − | 1.22416i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.91240e9 | + | 5.04442e9i | 0.150458 | + | 0.260601i | 0.931396 | − | 0.364008i | \(-0.118592\pi\) |
−0.780938 | + | 0.624609i | \(0.785258\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.24392e10i | − | 2.10088i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.27413e9 | −0.255619 | −0.127810 | − | 0.991799i | \(-0.540795\pi\) | ||||
−0.127810 | + | 0.991799i | \(0.540795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.79667e10 | + | 1.03731e10i | −0.834975 | + | 0.482073i | −0.855553 | − | 0.517715i | \(-0.826783\pi\) |
0.0205779 | + | 0.999788i | \(0.493449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.57941e9 | − | 1.29123e10i | 0.162918 | − | 0.587708i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.88921e10 | + | 1.09074e10i | 0.825053 | + | 0.476345i | 0.852156 | − | 0.523288i | \(-0.175295\pi\) |
−0.0271026 | + | 0.999633i | \(0.508628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.60937e10 | −1.54427 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.03544e10 | + | 1.17516e10i | 0.836122 | + | 0.482735i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.25903e10 | + | 2.18071e10i | 0.506844 | + | 0.877880i | 0.999969 | + | 0.00792086i | \(0.00252131\pi\) |
−0.493125 | + | 0.869959i | \(0.664145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.80415e9 | − | 3.92838e9i | 0.263146 | − | 0.151927i | −0.362623 | − | 0.931936i | \(-0.618119\pi\) |
0.625769 | + | 0.780009i | \(0.284785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.31386e9 | − | 1.26680e10i | 0.277285 | − | 0.480272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.94842e10i | 0.710077i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.66718e9 | − | 9.81584e9i | 0.202523 | − | 0.350780i | −0.746818 | − | 0.665029i | \(-0.768419\pi\) |
0.949341 | + | 0.314249i | \(0.101753\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.44236e9 | − | 4.36643e9i | 0.152691 | − | 0.150081i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.94059e9 | + | 3.36120e9i | 0.0654246 | + | 0.113319i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.52508e10i | 0.819254i | 0.912253 | + | 0.409627i | \(0.134341\pi\) | ||||
−0.912253 | + | 0.409627i | \(0.865659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.17703e10 | 0.374679 | 0.187339 | − | 0.982295i | \(-0.440014\pi\) | ||||
0.187339 | + | 0.982295i | \(0.440014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.62028e10 | − | 9.35472e9i | 0.496633 | − | 0.286731i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.13076e10 | − | 8.10028e9i | 0.941755 | − | 0.243663i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.91524e9 | + | 5.14722e9i | 0.258359 | + | 0.149164i | 0.623586 | − | 0.781755i | \(-0.285675\pi\) |
−0.365227 | + | 0.930919i | \(0.619008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.82082e10 | −1.08694 | −0.543469 | − | 0.839429i | \(-0.682889\pi\) | ||||
−0.543469 | + | 0.839429i | \(0.682889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00994e10 | − | 4.62454e10i | −2.19636 | − | 1.26807i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.98026e9 | − | 3.42990e9i | −0.0533167 | − | 0.0923472i | 0.838135 | − | 0.545462i | \(-0.183646\pi\) |
−0.891452 | + | 0.453115i | \(0.850313\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.51740e10 | + | 3.18547e10i | −1.43258 | + | 0.827102i | −0.997317 | − | 0.0731995i | \(-0.976679\pi\) |
−0.435266 | + | 0.900302i | \(0.643346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.81330e9 | − | 1.35330e10i | 0.199248 | − | 0.345108i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.62898e9i | − | 0.0892893i | −0.999003 | − | 0.0446446i | \(-0.985784\pi\) | ||
0.999003 | − | 0.0446446i | \(-0.0142156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00975e9 | + | 1.56053e10i | −0.217774 | + | 0.377196i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.61193e10 | + | 6.23010e10i | 0.376097 | + | 1.45361i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.40813e9 | + | 5.90306e9i | 0.0781361 | + | 0.135336i | 0.902446 | − | 0.430804i | \(-0.141770\pi\) |
−0.824310 | + | 0.566139i | \(0.808436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.72817e10i | − | 0.825452i | −0.910855 | − | 0.412726i | \(-0.864577\pi\) | ||
0.910855 | − | 0.412726i | \(-0.135423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.90344e9 | −0.106703 | −0.0533516 | − | 0.998576i | \(-0.516990\pi\) | ||||
−0.0533516 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.47483e10 | + | 1.42884e10i | −0.520328 | + | 0.300412i | −0.737069 | − | 0.675817i | \(-0.763791\pi\) |
0.216741 | + | 0.976229i | \(0.430457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.36855e10 | + | 4.44451e10i | 0.902913 | + | 0.918613i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.51952e10 | + | 2.03200e10i | 0.703135 | + | 0.405955i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.79433e10 | 0.941788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.25993e10 | − | 2.45947e10i | −0.809208 | − | 0.467197i | 0.0374726 | − | 0.999298i | \(-0.488069\pi\) |
−0.846681 | + | 0.532101i | \(0.821403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.67883e10 | − | 8.10397e10i | −0.874092 | − | 1.51397i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13678e11 | + | 6.56320e10i | −2.05452 | + | 1.18618i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.22069e10 | − | 7.31045e10i | 0.750357 | − | 1.29966i | −0.197293 | − | 0.980345i | \(-0.563215\pi\) |
0.947650 | − | 0.319311i | \(-0.103452\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.47411e10i | 0.425690i | 0.977086 | + | 0.212845i | \(0.0682730\pi\) | ||||
−0.977086 | + | 0.212845i | \(0.931727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.55475e10 | + | 7.88906e10i | −0.771040 | + | 1.33548i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.71276e10 | − | 1.58363e10i | −0.936312 | − | 0.259554i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.13363e9 | + | 1.06238e10i | 0.0989271 | + | 0.171347i | 0.911241 | − | 0.411874i | \(-0.135126\pi\) |
−0.812314 | + | 0.583221i | \(0.801792\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.16195e11i | − | 1.81517i | −0.419871 | − | 0.907584i | \(-0.637925\pi\) | ||
0.419871 | − | 0.907584i | \(-0.362075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.20797e10 | 0.647005 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.92103e10 | − | 5.15056e10i | 1.32906 | − | 0.767332i | 0.343903 | − | 0.939005i | \(-0.388251\pi\) |
0.985154 | + | 0.171673i | \(0.0549174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.28977e10 | − | 6.39914e10i | −0.922468 | − | 0.938508i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.15709e11 | − | 6.68045e10i | −1.64489 | − | 0.949680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.84978e10 | 0.398886 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00487e11 | + | 5.80160e10i | 1.36382 | + | 0.787403i | 0.990130 | − | 0.140150i | \(-0.0447584\pi\) |
0.373692 | + | 0.927553i | \(0.378092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.86272e10 | − | 3.22633e10i | −0.248967 | − | 0.431224i | 0.714272 | − | 0.699868i | \(-0.246758\pi\) |
−0.963239 | + | 0.268644i | \(0.913424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.71916e10 | + | 1.56991e10i | −0.352527 | + | 0.203532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.94598e10 | − | 1.54949e11i | 1.14237 | − | 1.97864i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.65420e10i | − | 1.07230i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.25770e10 | − | 1.08387e11i | 0.763835 | − | 1.32300i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.93011e10 | − | 3.48024e10i | −0.228679 | − | 0.412339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.13051e10 | + | 1.95811e10i | 0.131974 | + | 0.228585i | 0.924437 | − | 0.381334i | \(-0.124535\pi\) |
−0.792464 | + | 0.609919i | \(0.791202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.13771e10i | − | 0.809045i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.58562e11 | −1.77113 | −0.885563 | − | 0.464519i | \(-0.846227\pi\) | ||||
−0.885563 | + | 0.464519i | \(0.846227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.02159e11 | + | 1.16716e11i | −2.19324 | + | 1.26627i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.75800e10 | − | 1.74851e10i | 0.722633 | − | 0.186969i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00309e10 | − | 5.19793e10i | −0.935342 | − | 0.540020i | −0.0468452 | − | 0.998902i | \(-0.514917\pi\) |
−0.888497 | + | 0.458882i | \(0.848250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.95181e11 | −1.99889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.42375e10 | − | 2.55405e10i | −0.440308 | − | 0.254212i | 0.263420 | − | 0.964681i | \(-0.415149\pi\) |
−0.703728 | + | 0.710469i | \(0.748483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.78032e10 | + | 4.81566e10i | 0.272836 | + | 0.472566i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.62604e10 | − | 2.09350e10i | 0.345926 | − | 0.199721i | −0.316963 | − | 0.948438i | \(-0.602663\pi\) |
0.662890 | + | 0.748717i | \(0.269330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.83659e10 | + | 3.18106e10i | −0.172769 | + | 0.299245i | −0.939387 | − | 0.342859i | \(-0.888605\pi\) |
0.766618 | + | 0.642104i | \(0.221938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.33337e11i | 1.21978i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.04732e10 | − | 7.01016e10i | 0.365144 | − | 0.632448i | −0.623655 | − | 0.781700i | \(-0.714353\pi\) |
0.988799 | + | 0.149252i | \(0.0476864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.11083e10 | + | 3.07932e9i | 0.0974863 | + | 0.0270240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.75620e10 | − | 8.23799e10i | −0.411705 | − | 0.713094i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.69569e10i | 0.395500i | 0.980252 | + | 0.197750i | \(0.0633635\pi\) | ||||
−0.980252 | + | 0.197750i | \(0.936637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.04585e10 | −0.668514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.02621e11 | − | 5.92484e10i | 0.829886 | − | 0.479135i | −0.0239277 | − | 0.999714i | \(-0.507617\pi\) |
0.853814 | + | 0.520579i | \(0.174284\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.68998e10 | − | 1.33112e11i | 0.294412 | − | 1.06206i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.19459e10 | + | 6.89700e9i | 0.0927926 | + | 0.0535738i | 0.545678 | − | 0.837995i | \(-0.316272\pi\) |
−0.452886 | + | 0.891569i | \(0.649605\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.06073e11 | 1.57951 | 0.789757 | − | 0.613420i | \(-0.210207\pi\) | ||||
0.789757 | + | 0.613420i | \(0.210207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.16709e11 | + | 6.73821e10i | 0.871132 | + | 0.502948i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.39703e9 | + | 1.45441e10i | 0.0618544 | + | 0.107135i | 0.895294 | − | 0.445475i | \(-0.146965\pi\) |
−0.833440 | + | 0.552610i | \(0.813632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18529e11 | + | 6.84330e10i | −0.850474 | + | 0.491021i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.06152e11 | + | 1.83861e11i | −0.751776 | + | 1.30211i | 0.195186 | + | 0.980766i | \(0.437469\pi\) |
−0.946961 | + | 0.321347i | \(0.895864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.48225e10i | − | 0.102278i | −0.998692 | − | 0.0511388i | \(-0.983715\pi\) | ||
0.998692 | − | 0.0511388i | \(-0.0162851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.02885e11 | + | 1.78203e11i | −0.700795 | + | 1.21381i | 0.267393 | + | 0.963588i | \(0.413838\pi\) |
−0.968188 | + | 0.250225i | \(0.919495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.16253e10 | − | 4.49319e10i | −0.0771709 | − | 0.298265i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.30834e10 | + | 1.61225e11i | 0.610031 | + | 1.05661i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00861e11i | 1.28320i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.67614e11 | 1.05729 | 0.528643 | − | 0.848844i | \(-0.322701\pi\) | ||||
0.528643 | + | 0.848844i | \(0.322701\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.71093e10 | + | 4.45191e10i | −0.474255 | + | 0.273811i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.63851e11 | + | 9.84034e10i | 0.995154 | + | 0.597657i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.04139e11 | − | 1.17860e11i | −1.20919 | − | 0.698125i | −0.246606 | − | 0.969116i | \(-0.579315\pi\) |
−0.962582 | + | 0.270991i | \(0.912649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.02507e11 | 0.599666 | 0.299833 | − | 0.953992i | \(-0.403069\pi\) | ||||
0.299833 | + | 0.953992i | \(0.403069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.26048e11 | − | 7.27741e10i | −0.719317 | − | 0.415298i | 0.0951843 | − | 0.995460i | \(-0.469656\pi\) |
−0.814501 | + | 0.580162i | \(0.802989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.95475e9 | − | 1.55101e10i | −0.0504748 | − | 0.0874249i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.29084e11 | − | 7.45267e10i | 0.709937 | − | 0.409882i | −0.101101 | − | 0.994876i | \(-0.532236\pi\) |
0.811038 | + | 0.584994i | \(0.198903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.06332e10 | − | 1.05020e11i | 0.329416 | − | 0.570566i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.29763e11i | 0.688034i | 0.938963 | + | 0.344017i | \(0.111788\pi\) | ||||
−0.938963 | + | 0.344017i | \(0.888212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.68060e10 | + | 6.37498e10i | −0.192802 | + | 0.333943i | −0.946178 | − | 0.323647i | \(-0.895091\pi\) |
0.753376 | + | 0.657591i | \(0.228424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.52439e11 | − | 2.48124e11i | 1.29083 | − | 1.26877i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.24606e11 | − | 5.62234e11i | −1.64003 | − | 2.84062i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.29791e10i | − | 0.458665i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.98570e10 | 0.340525 | 0.170263 | − | 0.985399i | \(-0.445538\pi\) | ||||
0.170263 | + | 0.985399i | \(0.445538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.08476e11 | + | 6.26284e10i | −0.516389 | + | 0.298138i | −0.735456 | − | 0.677572i | \(-0.763032\pi\) |
0.219067 | + | 0.975710i | \(0.429699\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.04145e11 | + | 3.75691e11i | −0.489957 | + | 1.76747i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.80457e11 | + | 1.61922e11i | 1.28880 | + | 0.744086i | 0.978439 | − | 0.206534i | \(-0.0662185\pi\) |
0.310356 | + | 0.950620i | \(0.399552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.29260e11 | 1.49547 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.95645e11 | + | 2.28425e11i | 1.75561 | + | 1.01360i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.73309e10 | + | 3.00180e10i | 0.0760167 | + | 0.131665i | 0.901528 | − | 0.432721i | \(-0.142446\pi\) |
−0.825511 | + | 0.564386i | \(0.809113\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.86915e10 | + | 2.81121e10i | −0.208696 | + | 0.120491i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.28806e10 | + | 1.60874e11i | −0.393545 | + | 0.681639i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.09479e11i | − | 0.867497i | −0.901034 | − | 0.433748i | \(-0.857191\pi\) | ||
0.901034 | − | 0.433748i | \(-0.142809\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.57355e11 | + | 4.45752e11i | −1.05369 | + | 1.82504i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.91313e10 | − | 8.76079e10i | 0.356741 | − | 0.350644i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.29890e10 | − | 1.09100e11i | −0.249275 | − | 0.431758i | 0.714049 | − | 0.700095i | \(-0.246859\pi\) |
−0.963325 | + | 0.268337i | \(0.913526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.23767e11i | − | 0.865841i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.85025e11 | 0.707957 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.21606e11 | − | 1.27944e11i | 0.829212 | − | 0.478746i | −0.0243706 | − | 0.999703i | \(-0.507758\pi\) |
0.853583 | + | 0.520957i | \(0.174425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.84173e11 | + | 9.93980e10i | −1.42163 | + | 0.367821i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.91438e11 | + | 1.68262e11i | 1.05486 | + | 0.609022i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.28182e10 | −0.0816851 | −0.0408426 | − | 0.999166i | \(-0.513004\pi\) | ||||
−0.0408426 | + | 0.999166i | \(0.513004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.62824e11 | + | 2.09476e11i | 1.27065 | + | 0.733610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.38696e10 | − | 1.10625e11i | −0.221247 | − | 0.383212i | 0.733940 | − | 0.679215i | \(-0.237679\pi\) |
−0.955187 | + | 0.296003i | \(0.904346\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.55176e11 | − | 8.95908e10i | 0.525962 | − | 0.303664i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.93903e11 | + | 5.09056e11i | −0.985432 | + | 1.70682i | −0.345434 | + | 0.938443i | \(0.612268\pi\) |
−0.639999 | + | 0.768376i | \(0.721065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.81454e11i | 1.25166i | 0.779959 | + | 0.625830i | \(0.215240\pi\) | ||||
−0.779959 | + | 0.625830i | \(0.784760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.10997e11 | − | 3.65457e11i | 0.684938 | − | 1.18635i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.31079e10 | − | 3.59862e11i | −0.295842 | − | 1.14343i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.92521e10 | − | 1.37269e11i | −0.249144 | − | 0.431531i | 0.714144 | − | 0.699999i | \(-0.246816\pi\) |
−0.963289 | + | 0.268468i | \(0.913483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.36804e11i | 1.03655i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.23086e11 | −1.59290 | −0.796452 | − | 0.604702i | \(-0.793292\pi\) | ||||
−0.796452 | + | 0.604702i | \(0.793292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.89734e11 | − | 1.09543e11i | 0.565727 | − | 0.326623i | −0.189714 | − | 0.981839i | \(-0.560756\pi\) |
0.755441 | + | 0.655217i | \(0.227423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.48604e11 | − | 1.51188e11i | −0.438461 | − | 0.446085i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.44900e10 | + | 4.30068e10i | 0.215237 | + | 0.124267i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.67374e11 | 0.478610 | 0.239305 | − | 0.970944i | \(-0.423080\pi\) | ||||
0.239305 | + | 0.970944i | \(0.423080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.36157e11 | + | 1.36345e11i | 0.661428 | + | 0.381876i | 0.792821 | − | 0.609455i | \(-0.208612\pi\) |
−0.131393 | + | 0.991330i | \(0.541945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.79956e10 | + | 1.00451e11i | 0.160764 | + | 0.278451i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.12242e11 | + | 2.38008e11i | −1.11944 | + | 0.646312i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.52233e10 | + | 1.47611e11i | −0.229063 | + | 0.396748i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.50387e11i | 0.659375i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.07075e11 | − | 1.85459e11i | 0.279119 | − | 0.483447i | −0.692047 | − | 0.721852i | \(-0.743291\pi\) |
0.971166 | + | 0.238405i | \(0.0766244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.59151e11 | + | 4.41181e10i | 0.406541 | + | 0.112697i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.23275e11 | + | 3.86723e11i | 0.564608 | + | 0.977929i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.97596e11i | − | 1.23323i | −0.787265 | − | 0.616614i | \(-0.788504\pi\) | ||
0.787265 | − | 0.616614i | \(-0.211496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.93781e11 | 0.720836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.23420e11 | + | 1.28992e11i | −0.537353 | + | 0.310241i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.90071e11 | + | 7.02070e11i | 1.64328 | + | 1.67185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.50290e11 | − | 2.59975e11i | −1.05123 | − | 0.606929i | −0.128238 | − | 0.991743i | \(-0.540932\pi\) |
−0.922994 | + | 0.384814i | \(0.874265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.02055e11 | 0.698237 | 0.349118 | − | 0.937079i | \(-0.386481\pi\) | ||||
0.349118 | + | 0.937079i | \(0.386481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.47260e11 | + | 5.46901e11i | 2.14703 | + | 1.23959i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.36787e11 | + | 9.29742e11i | 1.20480 | + | 2.08677i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.46145e11 | − | 3.73052e11i | 1.42219 | − | 0.821101i | 0.425703 | − | 0.904863i | \(-0.360027\pi\) |
0.996486 | + | 0.0837617i | \(0.0266934\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.22067e11 | − | 3.84632e11i | 0.484045 | − | 0.838390i | −0.515787 | − | 0.856717i | \(-0.672501\pi\) |
0.999832 | + | 0.0183266i | \(0.00583385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.64292e11i | 0.778802i | 0.921068 | + | 0.389401i | \(0.127318\pi\) | ||||
−0.921068 | + | 0.389401i | \(0.872682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.65493e11 | + | 6.33053e11i | −0.773858 | + | 1.34036i | 0.161576 | + | 0.986860i | \(0.448342\pi\) |
−0.935434 | + | 0.353502i | \(0.884991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.98973e11 | − | 3.58775e11i | −0.413251 | − | 0.745147i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.07708e11 | − | 7.06172e11i | −0.838694 | − | 1.45266i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.01006e11i | − | 0.203845i | −0.994792 | − | 0.101923i | \(-0.967501\pi\) | ||
0.994792 | − | 0.101923i | \(-0.0324994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.13826e12 | −2.27541 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.98470e11 | + | 1.14587e11i | −0.389286 | + | 0.224755i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.87494e11 | − | 1.00257e11i | 0.752890 | − | 0.194797i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.23970e12 | − | 7.15742e11i | −2.36374 | − | 1.36470i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.84535e11 | 0.348564 | 0.174282 | − | 0.984696i | \(-0.444240\pi\) | ||||
0.174282 | + | 0.984696i | \(0.444240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.69695e11 | + | 3.86649e11i | 1.24152 | + | 0.716792i | 0.969404 | − | 0.245472i | \(-0.0789431\pi\) |
0.272117 | + | 0.962264i | \(0.412276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.57615e10 | + | 2.72998e10i | 0.0289485 | + | 0.0501403i | 0.880137 | − | 0.474720i | \(-0.157451\pi\) |
−0.851188 | + | 0.524861i | \(0.824117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.68796e10 | + | 3.86129e10i | −0.120573 | + | 0.0696129i | −0.559074 | − | 0.829118i | \(-0.688843\pi\) |
0.438501 | + | 0.898731i | \(0.355510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.87291e11 | − | 8.44014e11i | 0.870411 | − | 1.50760i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.00703e11i | − | 0.351945i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.30276e11 | + | 7.45261e11i | −0.747610 | + | 1.29490i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.38904e11 | + | 6.62261e10i | 0.407559 | + | 0.112979i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.42310e11 | − | 2.46488e11i | −0.240568 | − | 0.416676i | 0.720308 | − | 0.693654i | \(-0.244000\pi\) |
−0.960876 | + | 0.276978i | \(0.910667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.54602e10i | − | 0.0588624i | −0.999567 | − | 0.0294312i | \(-0.990630\pi\) | ||
0.999567 | − | 0.0294312i | \(-0.00936959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.80065e10 | 0.144768 | 0.0723839 | − | 0.997377i | \(-0.476939\pi\) | ||||
0.0723839 | + | 0.997377i | \(0.476939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.11155e11 | + | 3.52851e11i | −0.987318 | + | 0.570028i | −0.904472 | − | 0.426534i | \(-0.859734\pi\) |
−0.0828466 | + | 0.996562i | \(0.526401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.06427e10 | + | 2.54836e11i | −0.113099 | + | 0.407994i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.51960e11 | + | 3.76409e11i | 1.02522 | + | 0.591908i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.30338e11 | 0.982384 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.89091e11 | − | 2.82377e11i | −0.748775 | − | 0.432305i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.90312e11 | − | 8.49246e11i | −0.744001 | − | 1.28865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.25048e12 | + | 7.21965e11i | −1.86416 | + | 1.07627i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.90256e9 | + | 1.02235e10i | −0.00872190 | + | 0.0151068i | −0.870353 | − | 0.492428i | \(-0.836110\pi\) |
0.861632 | + | 0.507534i | \(0.169443\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.42842e11i | 0.497761i | 0.968534 | + | 0.248880i | \(0.0800626\pi\) | ||||
−0.968534 | + | 0.248880i | \(0.919937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65714e10 | − | 2.87026e10i | 0.0238494 | − | 0.0413083i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.02157e10 | − | 3.48683e11i | −0.127587 | − | 0.493121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.28433e11 | − | 7.42068e11i | −0.600649 | − | 1.04036i | −0.992723 | − | 0.120421i | \(-0.961575\pi\) |
0.392074 | − | 0.919934i | \(-0.371758\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.18601e11i | − | 1.12789i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.42020e11 | 1.01356 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.99296e11 | − | 5.19209e11i | 1.20737 | − | 0.697074i | 0.245185 | − | 0.969476i | \(-0.421151\pi\) |
0.962184 | + | 0.272402i | \(0.0878180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.81211e10 | − | 1.05113e12i | 0.0241204 | − | 1.39913i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.43945e11 | − | 1.98577e11i | −0.450032 | − | 0.259826i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.49832e11 | −1.23222 | −0.616110 | − | 0.787660i | \(-0.711292\pi\) | ||||
−0.616110 | + | 0.787660i | \(0.711292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.29832e11 | + | 1.32694e11i | 0.293125 | + | 0.169236i | 0.639350 | − | 0.768916i | \(-0.279203\pi\) |
−0.346226 | + | 0.938151i | \(0.612537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.61936e11 | − | 1.14651e12i | −0.837085 | − | 1.44987i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.46887e11 | + | 3.15745e11i | −0.679982 | + | 0.392588i | −0.799848 | − | 0.600202i | \(-0.795087\pi\) |
0.119866 | + | 0.992790i | \(0.461753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.19506e11 | − | 1.07302e12i | 0.763802 | − | 1.32294i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.74996e11i | 0.333391i | 0.986008 | + | 0.166696i | \(0.0533097\pi\) | ||||
−0.986008 | + | 0.166696i | \(0.946690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.73439e11 | + | 1.33964e12i | −0.929849 | + | 1.61055i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.97423e11 | − | 6.85503e11i | 0.824559 | − | 0.810466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.29117e11 | + | 5.70048e11i | 0.385884 | + | 0.668371i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.43486e11i | − | 0.511412i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.42625e11 | −0.849305 | −0.424652 | − | 0.905356i | \(-0.639604\pi\) | ||||
−0.424652 | + | 0.905356i | \(0.639604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.98214e10 | − | 1.14439e10i | 0.0222976 | − | 0.0128735i | −0.488810 | − | 0.872390i | \(-0.662569\pi\) |
0.511107 | + | 0.859517i | \(0.329235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.46081e10 | + | 1.60919e11i | −0.0497694 | + | 0.179538i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.25487e11 | − | 4.76595e11i | −0.906007 | − | 0.523084i | −0.0268630 | − | 0.999639i | \(-0.508552\pi\) |
−0.879144 | + | 0.476556i | \(0.841885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.33442e11 | −0.145265 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.00006e11 | − | 5.19619e11i | −0.963898 | − | 0.556507i | −0.0665277 | − | 0.997785i | \(-0.521192\pi\) |
−0.897371 | + | 0.441278i | \(0.854525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.54407e11 | − | 6.13850e11i | −0.376493 | − | 0.652105i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.58575e12 | + | 1.49288e12i | −2.70272 | + | 1.56042i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.06924e11 | + | 5.31608e11i | −0.318227 | + | 0.551185i | −0.980118 | − | 0.198415i | \(-0.936421\pi\) |
0.661891 | + | 0.749600i | \(0.269754\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.19023e12i | 1.21434i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.94291e11 | − | 1.20255e12i | 0.702685 | − | 1.21709i | −0.264835 | − | 0.964294i | \(-0.585318\pi\) |
0.967520 | − | 0.252793i | \(-0.0813491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.9.bk.a.53.4 | ✓ | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.53.19 | yes | 44 | |
7.2 | even | 3 | inner | 252.9.bk.a.233.19 | yes | 44 | |
21.2 | odd | 6 | inner | 252.9.bk.a.233.4 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.4 | ✓ | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.53.19 | yes | 44 | 3.2 | odd | 2 | inner | |
252.9.bk.a.233.4 | yes | 44 | 21.2 | odd | 6 | inner | |
252.9.bk.a.233.19 | yes | 44 | 7.2 | even | 3 | inner |