Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,12,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (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: | \(19.2085795140\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{151})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 75x^{2} + 1444 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(6.14410 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.12.b.c.24.3 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 63.7292i | − 1.40823i | −0.710086 | − | 0.704115i | \(-0.751344\pi\) | ||||
0.710086 | − | 0.704115i | \(-0.248656\pi\) | |||||||
\(3\) | 283.223i | 0.672916i | 0.941698 | + | 0.336458i | \(0.109229\pi\) | ||||
−0.941698 | + | 0.336458i | \(0.890771\pi\) | |||||||
\(4\) | −2013.42 | −0.983113 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 18049.6 | 0.947621 | ||||||||
\(7\) | − 41926.3i | − 0.942861i | −0.881903 | − | 0.471431i | \(-0.843738\pi\) | ||||
0.881903 | − | 0.471431i | \(-0.156262\pi\) | |||||||
\(8\) | − 2204.06i | − 0.0237809i | ||||||||
\(9\) | 96932.0 | 0.547184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −957905. | −1.79334 | −0.896670 | − | 0.442699i | \(-0.854021\pi\) | ||||
−0.896670 | + | 0.442699i | \(0.854021\pi\) | |||||||
\(12\) | − 570245.i | − 0.661553i | ||||||||
\(13\) | 1.39098e6i | 1.03904i | 0.854458 | + | 0.519520i | \(0.173889\pi\) | ||||
−0.854458 | + | 0.519520i | \(0.826111\pi\) | |||||||
\(14\) | −2.67193e6 | −1.32777 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.26394e6 | −1.01660 | ||||||||
\(17\) | − 3.76857e6i | − 0.643736i | −0.946785 | − | 0.321868i | \(-0.895689\pi\) | ||||
0.946785 | − | 0.321868i | \(-0.104311\pi\) | |||||||
\(18\) | − 6.17740e6i | − 0.770561i | ||||||||
\(19\) | −9.41036e6 | −0.871889 | −0.435945 | − | 0.899973i | \(-0.643586\pi\) | ||||
−0.435945 | + | 0.899973i | \(0.643586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18745e7 | 0.634467 | ||||||||
\(22\) | 6.10466e7i | 2.52544i | ||||||||
\(23\) | 3.02942e7i | 0.981423i | 0.871322 | + | 0.490712i | \(0.163263\pi\) | ||||
−0.871322 | + | 0.490712i | \(0.836737\pi\) | |||||||
\(24\) | 624238. | 0.0160025 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.86460e7 | 1.46321 | ||||||||
\(27\) | 7.76254e7i | 1.04113i | ||||||||
\(28\) | 8.44151e7i | 0.926939i | ||||||||
\(29\) | −1.03553e8 | −0.937502 | −0.468751 | − | 0.883330i | \(-0.655296\pi\) | ||||
−0.468751 | + | 0.883330i | \(0.655296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48554e7 | −0.344136 | −0.172068 | − | 0.985085i | \(-0.555045\pi\) | ||||
−0.172068 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(32\) | 2.67224e8i | 1.40783i | ||||||||
\(33\) | − 2.71300e8i | − 1.20677i | ||||||||
\(34\) | −2.40168e8 | −0.906529 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.95164e8 | −0.537943 | ||||||||
\(37\) | − 4.78282e8i | − 1.13390i | −0.823752 | − | 0.566950i | \(-0.808123\pi\) | ||||
0.823752 | − | 0.566950i | \(-0.191877\pi\) | |||||||
\(38\) | 5.99715e8i | 1.22782i | ||||||||
\(39\) | −3.93957e8 | −0.699187 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.29557e8 | −1.25304 | −0.626520 | − | 0.779406i | \(-0.715521\pi\) | ||||
−0.626520 | + | 0.779406i | \(0.715521\pi\) | |||||||
\(42\) | − 7.56752e8i | − 0.893475i | ||||||||
\(43\) | − 2.68608e7i | − 0.0278639i | −0.999903 | − | 0.0139320i | \(-0.995565\pi\) | ||||
0.999903 | − | 0.0139320i | \(-0.00443483\pi\) | |||||||
\(44\) | 1.92866e9 | 1.76306 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.93063e9 | 1.38207 | ||||||||
\(47\) | 1.20497e9i | 0.766370i | 0.923672 | + | 0.383185i | \(0.125173\pi\) | ||||
−0.923672 | + | 0.383185i | \(0.874827\pi\) | |||||||
\(48\) | − 1.20764e9i | − 0.684088i | ||||||||
\(49\) | 2.19508e8 | 0.111013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.06735e9 | 0.433181 | ||||||||
\(52\) | − 2.80062e9i | − 1.02149i | ||||||||
\(53\) | − 4.02058e9i | − 1.32060i | −0.751001 | − | 0.660301i | \(-0.770429\pi\) | ||||
0.751001 | − | 0.660301i | \(-0.229571\pi\) | |||||||
\(54\) | 4.94700e9 | 1.46614 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.24080e7 | −0.0224221 | ||||||||
\(57\) | − 2.66523e9i | − 0.586709i | ||||||||
\(58\) | 6.59933e9i | 1.32022i | ||||||||
\(59\) | −7.97972e9 | −1.45312 | −0.726560 | − | 0.687103i | \(-0.758882\pi\) | ||||
−0.726560 | + | 0.687103i | \(0.758882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.07472e9 | −0.314518 | −0.157259 | − | 0.987557i | \(-0.550266\pi\) | ||||
−0.157259 | + | 0.987557i | \(0.550266\pi\) | |||||||
\(62\) | 3.49589e9i | 0.484623i | ||||||||
\(63\) | − 4.06400e9i | − 0.515918i | ||||||||
\(64\) | 8.29741e9 | 0.965946 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.72898e10 | −1.69941 | ||||||||
\(67\) | − 5.61370e9i | − 0.507969i | −0.967208 | − | 0.253985i | \(-0.918259\pi\) | ||||
0.967208 | − | 0.253985i | \(-0.0817413\pi\) | |||||||
\(68\) | 7.58770e9i | 0.632865i | ||||||||
\(69\) | −8.58000e9 | −0.660416 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.51224e10 | 0.994714 | 0.497357 | − | 0.867546i | \(-0.334304\pi\) | ||||
0.497357 | + | 0.867546i | \(0.334304\pi\) | |||||||
\(72\) | − 2.13643e8i | − 0.0130125i | ||||||||
\(73\) | − 6.64484e9i | − 0.375153i | −0.982250 | − | 0.187577i | \(-0.939937\pi\) | ||||
0.982250 | − | 0.187577i | \(-0.0600633\pi\) | |||||||
\(74\) | −3.04806e10 | −1.59679 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.89470e10 | 0.857166 | ||||||||
\(77\) | 4.01615e10i | 1.69087i | ||||||||
\(78\) | 2.51066e10i | 0.984616i | ||||||||
\(79\) | 1.57985e10 | 0.577652 | 0.288826 | − | 0.957382i | \(-0.406735\pi\) | ||||
0.288826 | + | 0.957382i | \(0.406735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.81405e9 | −0.153406 | ||||||||
\(82\) | 5.92399e10i | 1.76457i | ||||||||
\(83\) | − 2.04046e10i | − 0.568589i | −0.958737 | − | 0.284295i | \(-0.908241\pi\) | ||||
0.958737 | − | 0.284295i | \(-0.0917594\pi\) | |||||||
\(84\) | −2.39083e10 | −0.623752 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.71182e9 | −0.0392389 | ||||||||
\(87\) | − 2.93285e10i | − 0.630861i | ||||||||
\(88\) | 2.11128e9i | 0.0426472i | ||||||||
\(89\) | 4.21030e10 | 0.799223 | 0.399611 | − | 0.916685i | \(-0.369145\pi\) | ||||
0.399611 | + | 0.916685i | \(0.369145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.83187e10 | 0.979670 | ||||||||
\(92\) | − 6.09948e10i | − 0.964850i | ||||||||
\(93\) | − 1.55363e10i | − 0.231575i | ||||||||
\(94\) | 7.67919e10 | 1.07923 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.56837e10 | −0.947351 | ||||||||
\(97\) | − 1.10181e11i | − 1.30275i | −0.758755 | − | 0.651376i | \(-0.774192\pi\) | ||||
0.758755 | − | 0.651376i | \(-0.225808\pi\) | |||||||
\(98\) | − 1.39891e10i | − 0.156331i | ||||||||
\(99\) | −9.28516e10 | −0.981287 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.33271e10 | −0.315522 | −0.157761 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157761 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(102\) | − 6.80211e10i | − 0.610018i | ||||||||
\(103\) | 8.49419e10i | 0.721966i | 0.932572 | + | 0.360983i | \(0.117559\pi\) | ||||
−0.932572 | + | 0.360983i | \(0.882441\pi\) | |||||||
\(104\) | 3.06580e9 | 0.0247093 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56229e11 | −1.85971 | ||||||||
\(107\) | − 1.43774e11i | − 0.990989i | −0.868611 | − | 0.495494i | \(-0.834987\pi\) | ||||
0.868611 | − | 0.495494i | \(-0.165013\pi\) | |||||||
\(108\) | − 1.56292e11i | − 1.02354i | ||||||||
\(109\) | 3.01296e11 | 1.87563 | 0.937816 | − | 0.347134i | \(-0.112845\pi\) | ||||
0.937816 | + | 0.347134i | \(0.112845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.35460e11 | 0.763020 | ||||||||
\(112\) | 1.78771e11i | 0.958515i | ||||||||
\(113\) | − 2.22891e11i | − 1.13805i | −0.822320 | − | 0.569026i | \(-0.807320\pi\) | ||||
0.822320 | − | 0.569026i | \(-0.192680\pi\) | |||||||
\(114\) | −1.69853e11 | −0.826221 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.08495e11 | 0.921671 | ||||||||
\(117\) | 1.34830e11i | 0.568546i | ||||||||
\(118\) | 5.08541e11i | 2.04633i | ||||||||
\(119\) | −1.58003e11 | −0.606954 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32271e11 | 2.21607 | ||||||||
\(122\) | 1.32220e11i | 0.442914i | ||||||||
\(123\) | − 2.63271e11i | − 0.843191i | ||||||||
\(124\) | 1.10447e11 | 0.338324 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.58996e11 | −0.726532 | ||||||||
\(127\) | 1.79939e11i | 0.483287i | 0.970365 | + | 0.241644i | \(0.0776865\pi\) | ||||
−0.970365 | + | 0.241644i | \(0.922313\pi\) | |||||||
\(128\) | 1.84863e10i | 0.0475549i | ||||||||
\(129\) | 7.60759e9 | 0.0187501 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.65153e11 | −1.27989 | −0.639946 | − | 0.768420i | \(-0.721043\pi\) | ||||
−0.639946 | + | 0.768420i | \(0.721043\pi\) | |||||||
\(132\) | 5.46240e11i | 1.18639i | ||||||||
\(133\) | 3.94542e11i | 0.822071i | ||||||||
\(134\) | −3.57757e11 | −0.715338 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.30615e9 | −0.0153086 | ||||||||
\(137\) | − 1.24499e9i | − 0.00220396i | −0.999999 | − | 0.00110198i | \(-0.999649\pi\) | ||||
0.999999 | − | 0.00110198i | \(-0.000350771\pi\) | |||||||
\(138\) | 5.46797e11i | 0.930017i | ||||||||
\(139\) | −4.68084e11 | −0.765142 | −0.382571 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382571 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41275e11 | −0.515703 | ||||||||
\(142\) | − 9.63736e11i | − 1.40079i | ||||||||
\(143\) | − 1.33243e12i | − 1.86335i | ||||||||
\(144\) | −4.13312e11 | −0.556268 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.23470e11 | −0.528302 | ||||||||
\(147\) | 6.21697e10i | 0.0747022i | ||||||||
\(148\) | 9.62981e11i | 1.11475i | ||||||||
\(149\) | −1.05439e12 | −1.17619 | −0.588096 | − | 0.808791i | \(-0.700122\pi\) | ||||
−0.588096 | + | 0.808791i | \(0.700122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91301e11 | 0.509301 | 0.254651 | − | 0.967033i | \(-0.418040\pi\) | ||||
0.254651 | + | 0.967033i | \(0.418040\pi\) | |||||||
\(152\) | 2.07410e10i | 0.0207343i | ||||||||
\(153\) | − 3.65295e11i | − 0.352242i | ||||||||
\(154\) | 2.55946e12 | 2.38114 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.93198e11 | 0.687379 | ||||||||
\(157\) | − 6.17375e11i | − 0.516536i | −0.966073 | − | 0.258268i | \(-0.916848\pi\) | ||||
0.966073 | − | 0.258268i | \(-0.0831518\pi\) | |||||||
\(158\) | − 1.00683e12i | − 0.813467i | ||||||||
\(159\) | 1.13872e12 | 0.888654 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.27013e12 | 0.925346 | ||||||||
\(162\) | 3.06795e11i | 0.216031i | ||||||||
\(163\) | 2.97234e11i | 0.202333i | 0.994870 | + | 0.101166i | \(0.0322574\pi\) | ||||
−0.994870 | + | 0.101166i | \(0.967743\pi\) | |||||||
\(164\) | 1.87158e12 | 1.23188 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.30037e12 | −0.800705 | ||||||||
\(167\) | 2.53524e11i | 0.151035i | 0.997144 | + | 0.0755177i | \(0.0240609\pi\) | ||||
−0.997144 | + | 0.0755177i | \(0.975939\pi\) | |||||||
\(168\) | − 2.61720e10i | − 0.0150882i | ||||||||
\(169\) | −1.42662e11 | −0.0796035 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.12165e11 | −0.477084 | ||||||||
\(172\) | 5.40820e10i | 0.0273934i | ||||||||
\(173\) | 1.80555e12i | 0.885843i | 0.896560 | + | 0.442922i | \(0.146058\pi\) | ||||
−0.896560 | + | 0.442922i | \(0.853942\pi\) | |||||||
\(174\) | −1.86908e12 | −0.888397 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.08445e12 | 1.82311 | ||||||||
\(177\) | − 2.26004e12i | − 0.977828i | ||||||||
\(178\) | − 2.68319e12i | − 1.12549i | ||||||||
\(179\) | −1.63020e12 | −0.663054 | −0.331527 | − | 0.943446i | \(-0.607564\pi\) | ||||
−0.331527 | + | 0.943446i | \(0.607564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16028e12 | −1.59181 | −0.795904 | − | 0.605423i | \(-0.793004\pi\) | ||||
−0.795904 | + | 0.605423i | \(0.793004\pi\) | |||||||
\(182\) | − 3.71660e12i | − 1.37960i | ||||||||
\(183\) | − 5.87608e11i | − 0.211644i | ||||||||
\(184\) | 6.67701e10 | 0.0233391 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.90115e11 | −0.326110 | ||||||||
\(187\) | 3.60994e12i | 1.15444i | ||||||||
\(188\) | − 2.42611e12i | − 0.753429i | ||||||||
\(189\) | 3.25455e12 | 0.981636 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.03600e12 | −0.864208 | −0.432104 | − | 0.901824i | \(-0.642229\pi\) | ||||
−0.432104 | + | 0.901824i | \(0.642229\pi\) | |||||||
\(192\) | 2.35001e12i | 0.650000i | ||||||||
\(193\) | 3.77397e12i | 1.01445i | 0.861812 | + | 0.507227i | \(0.169330\pi\) | ||||
−0.861812 | + | 0.507227i | \(0.830670\pi\) | |||||||
\(194\) | −7.02174e12 | −1.83457 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.41961e11 | −0.109138 | ||||||||
\(197\) | 1.03079e12i | 0.247518i | 0.992312 | + | 0.123759i | \(0.0394950\pi\) | ||||
−0.992312 | + | 0.123759i | \(0.960505\pi\) | |||||||
\(198\) | 5.91736e12i | 1.38188i | ||||||||
\(199\) | −1.14293e12 | −0.259614 | −0.129807 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129807 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58993e12 | 0.341821 | ||||||||
\(202\) | 2.12391e12i | 0.444328i | ||||||||
\(203\) | 4.34159e12i | 0.883935i | ||||||||
\(204\) | −2.14901e12 | −0.425865 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.41328e12 | 1.01670 | ||||||||
\(207\) | 2.93648e12i | 0.537019i | ||||||||
\(208\) | − 5.93105e12i | − 1.05629i | ||||||||
\(209\) | 9.01423e12 | 1.56359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.96492e12 | 1.14647 | 0.573235 | − | 0.819391i | \(-0.305688\pi\) | ||||
0.573235 | + | 0.819391i | \(0.305688\pi\) | |||||||
\(212\) | 8.09510e12i | 1.29830i | ||||||||
\(213\) | 4.28299e12i | 0.669359i | ||||||||
\(214\) | −9.16259e12 | −1.39554 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.71091e11 | 0.0247589 | ||||||||
\(217\) | 2.29989e12i | 0.324472i | ||||||||
\(218\) | − 1.92014e13i | − 2.64132i | ||||||||
\(219\) | 1.88197e12 | 0.252447 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.24201e12 | 0.668868 | ||||||||
\(222\) | − 8.63279e12i | − 1.07451i | ||||||||
\(223\) | 6.80403e12i | 0.826208i | 0.910684 | + | 0.413104i | \(0.135555\pi\) | ||||
−0.910684 | + | 0.413104i | \(0.864445\pi\) | |||||||
\(224\) | 1.12037e13 | 1.32739 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.42047e13 | −1.60264 | ||||||||
\(227\) | − 8.00368e12i | − 0.881348i | −0.897667 | − | 0.440674i | \(-0.854739\pi\) | ||||
0.897667 | − | 0.440674i | \(-0.145261\pi\) | |||||||
\(228\) | 5.36621e12i | 0.576801i | ||||||||
\(229\) | −1.20624e13 | −1.26572 | −0.632862 | − | 0.774265i | \(-0.718120\pi\) | ||||
−0.632862 | + | 0.774265i | \(0.718120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.13746e13 | −1.13781 | ||||||||
\(232\) | 2.28236e11i | 0.0222946i | ||||||||
\(233\) | − 1.05744e13i | − 1.00878i | −0.863476 | − | 0.504390i | \(-0.831717\pi\) | ||||
0.863476 | − | 0.504390i | \(-0.168283\pi\) | |||||||
\(234\) | 8.59263e12 | 0.800643 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.60665e13 | 1.42858 | ||||||||
\(237\) | 4.47449e12i | 0.388711i | ||||||||
\(238\) | 1.00694e13i | 0.854731i | ||||||||
\(239\) | 4.81329e12 | 0.399258 | 0.199629 | − | 0.979872i | \(-0.436026\pi\) | ||||
0.199629 | + | 0.979872i | \(0.436026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29674e13 | −1.02745 | −0.513724 | − | 0.857956i | \(-0.671734\pi\) | ||||
−0.513724 | + | 0.857956i | \(0.671734\pi\) | |||||||
\(242\) | − 4.02941e13i | − 3.12074i | ||||||||
\(243\) | 1.23877e13i | 0.937896i | ||||||||
\(244\) | 4.17728e12 | 0.309207 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.67781e13 | −1.18741 | ||||||||
\(247\) | − 1.30896e13i | − 0.905928i | ||||||||
\(248\) | 1.20904e11i | 0.00818385i | ||||||||
\(249\) | 5.77905e12 | 0.382613 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.10147e12 | 0.323214 | 0.161607 | − | 0.986855i | \(-0.448332\pi\) | ||||
0.161607 | + | 0.986855i | \(0.448332\pi\) | |||||||
\(252\) | 8.18253e12i | 0.507206i | ||||||||
\(253\) | − 2.90190e13i | − 1.76003i | ||||||||
\(254\) | 1.14674e13 | 0.680580 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.81712e13 | 1.03291 | ||||||||
\(257\) | 1.20976e13i | 0.673079i | 0.941669 | + | 0.336539i | \(0.109256\pi\) | ||||
−0.941669 | + | 0.336539i | \(0.890744\pi\) | |||||||
\(258\) | − 4.84826e11i | − 0.0264045i | ||||||||
\(259\) | −2.00526e13 | −1.06911 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00376e13 | −0.512986 | ||||||||
\(262\) | 3.60167e13i | 1.80238i | ||||||||
\(263\) | − 1.09431e13i | − 0.536271i | −0.963381 | − | 0.268135i | \(-0.913593\pi\) | ||||
0.963381 | − | 0.268135i | \(-0.0864074\pi\) | |||||||
\(264\) | −5.97961e11 | −0.0286980 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.51439e13 | 1.15767 | ||||||||
\(267\) | 1.19245e13i | 0.537810i | ||||||||
\(268\) | 1.13027e13i | 0.499391i | ||||||||
\(269\) | −1.23621e13 | −0.535125 | −0.267562 | − | 0.963541i | \(-0.586218\pi\) | ||||
−0.267562 | + | 0.963541i | \(0.586218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.34683e13 | 0.559734 | 0.279867 | − | 0.960039i | \(-0.409710\pi\) | ||||
0.279867 | + | 0.960039i | \(0.409710\pi\) | |||||||
\(272\) | 1.60690e13i | 0.654424i | ||||||||
\(273\) | 1.65172e13i | 0.659236i | ||||||||
\(274\) | −7.93424e10 | −0.00310368 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.72751e13 | 0.649263 | ||||||||
\(277\) | − 2.20976e13i | − 0.814153i | −0.913394 | − | 0.407077i | \(-0.866548\pi\) | ||||
0.913394 | − | 0.407077i | \(-0.133452\pi\) | |||||||
\(278\) | 2.98306e13i | 1.07750i | ||||||||
\(279\) | −5.31724e12 | −0.188306 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.15247e12 | 0.243541 | 0.121770 | − | 0.992558i | \(-0.461143\pi\) | ||||
0.121770 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(282\) | 2.17492e13i | 0.726229i | ||||||||
\(283\) | − 9.90996e12i | − 0.324524i | −0.986748 | − | 0.162262i | \(-0.948121\pi\) | ||||
0.986748 | − | 0.162262i | \(-0.0518789\pi\) | |||||||
\(284\) | −3.04476e13 | −0.977917 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.49145e13 | −2.62403 | ||||||||
\(287\) | 3.89729e13i | 1.18144i | ||||||||
\(288\) | 2.59025e13i | 0.770341i | ||||||||
\(289\) | 2.00697e13 | 0.585604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.12057e13 | 0.876642 | ||||||||
\(292\) | 1.33788e13i | 0.368818i | ||||||||
\(293\) | − 6.76585e13i | − 1.83042i | −0.402980 | − | 0.915209i | \(-0.632026\pi\) | ||||
0.402980 | − | 0.915209i | \(-0.367974\pi\) | |||||||
\(294\) | 3.96203e12 | 0.105198 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.05416e12 | −0.0269651 | ||||||||
\(297\) | − 7.43577e13i | − 1.86709i | ||||||||
\(298\) | 6.71957e13i | 1.65635i | ||||||||
\(299\) | −4.21386e13 | −1.01974 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12618e12 | −0.0262718 | ||||||||
\(302\) | − 3.13103e13i | − 0.717213i | ||||||||
\(303\) | − 9.43898e12i | − 0.212320i | ||||||||
\(304\) | 4.01252e13 | 0.886364 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.32800e13 | −0.496038 | ||||||||
\(307\) | 2.76335e13i | 0.578328i | 0.957280 | + | 0.289164i | \(0.0933773\pi\) | ||||
−0.957280 | + | 0.289164i | \(0.906623\pi\) | |||||||
\(308\) | − 8.08617e13i | − 1.66232i | ||||||||
\(309\) | −2.40575e13 | −0.485823 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.21728e13 | −0.237251 | −0.118626 | − | 0.992939i | \(-0.537849\pi\) | ||||
−0.118626 | + | 0.992939i | \(0.537849\pi\) | |||||||
\(312\) | 8.68302e11i | 0.0166273i | ||||||||
\(313\) | 8.17271e13i | 1.53770i | 0.639428 | + | 0.768851i | \(0.279171\pi\) | ||||
−0.639428 | + | 0.768851i | \(0.720829\pi\) | |||||||
\(314\) | −3.93448e13 | −0.727402 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.18089e13 | −0.567897 | ||||||||
\(317\) | − 7.61714e13i | − 1.33649i | −0.743941 | − | 0.668246i | \(-0.767045\pi\) | ||||
0.743941 | − | 0.668246i | \(-0.232955\pi\) | |||||||
\(318\) | − 7.25697e13i | − 1.25143i | ||||||||
\(319\) | 9.91937e13 | 1.68126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.07200e13 | 0.666852 | ||||||||
\(322\) | − 8.09441e13i | − 1.30310i | ||||||||
\(323\) | 3.54636e13i | 0.561267i | ||||||||
\(324\) | 9.69267e12 | 0.150816 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.89425e13 | 0.284931 | ||||||||
\(327\) | 8.53338e13i | 1.26214i | ||||||||
\(328\) | 2.04880e12i | 0.0297984i | ||||||||
\(329\) | 5.05201e13 | 0.722581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.05093e13 | 1.11376 | 0.556881 | − | 0.830592i | \(-0.311998\pi\) | ||||
0.556881 | + | 0.830592i | \(0.311998\pi\) | |||||||
\(332\) | 4.10830e13i | 0.558988i | ||||||||
\(333\) | − 4.63608e13i | − 0.620452i | ||||||||
\(334\) | 1.61569e13 | 0.212693 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.06321e13 | −0.645000 | ||||||||
\(337\) | 7.90669e13i | 0.990901i | 0.868636 | + | 0.495451i | \(0.164997\pi\) | ||||
−0.868636 | + | 0.495451i | \(0.835003\pi\) | |||||||
\(338\) | 9.09176e12i | 0.112100i | ||||||||
\(339\) | 6.31279e13 | 0.765813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.25463e13 | 0.617153 | ||||||||
\(342\) | 5.81316e13i | 0.671844i | ||||||||
\(343\) | − 9.21053e13i | − 1.04753i | ||||||||
\(344\) | −5.92027e10 | −0.000662629 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.15067e14 | 1.24747 | ||||||||
\(347\) | − 1.40156e14i | − 1.49554i | −0.663956 | − | 0.747772i | \(-0.731124\pi\) | ||||
0.663956 | − | 0.747772i | \(-0.268876\pi\) | |||||||
\(348\) | 5.90504e13i | 0.620207i | ||||||||
\(349\) | 9.88347e13 | 1.02181 | 0.510905 | − | 0.859637i | \(-0.329311\pi\) | ||||
0.510905 | + | 0.859637i | \(0.329311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.07975e14 | −1.08177 | ||||||||
\(352\) | − 2.55975e14i | − 2.52472i | ||||||||
\(353\) | − 2.74254e13i | − 0.266313i | −0.991095 | − | 0.133156i | \(-0.957489\pi\) | ||||
0.991095 | − | 0.133156i | \(-0.0425113\pi\) | |||||||
\(354\) | −1.44030e14 | −1.37701 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.47708e13 | −0.785726 | ||||||||
\(357\) | − 4.47499e13i | − 0.408429i | ||||||||
\(358\) | 1.03891e14i | 0.933733i | ||||||||
\(359\) | −1.57856e14 | −1.39715 | −0.698574 | − | 0.715538i | \(-0.746182\pi\) | ||||
−0.698574 | + | 0.715538i | \(0.746182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.79354e13 | −0.239809 | ||||||||
\(362\) | 2.65132e14i | 2.24163i | ||||||||
\(363\) | 1.79073e14i | 1.49123i | ||||||||
\(364\) | −1.17420e14 | −0.963127 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.74478e13 | −0.298044 | ||||||||
\(367\) | 1.95534e14i | 1.53306i | 0.642210 | + | 0.766529i | \(0.278018\pi\) | ||||
−0.642210 | + | 0.766529i | \(0.721982\pi\) | |||||||
\(368\) | − 1.29173e14i | − 0.997717i | ||||||||
\(369\) | −9.01038e13 | −0.685643 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68568e14 | −1.24514 | ||||||||
\(372\) | 3.12810e13i | 0.227664i | ||||||||
\(373\) | 8.35940e13i | 0.599482i | 0.954021 | + | 0.299741i | \(0.0969003\pi\) | ||||
−0.954021 | + | 0.299741i | \(0.903100\pi\) | |||||||
\(374\) | 2.30059e14 | 1.62572 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.65583e12 | 0.0182249 | ||||||||
\(377\) | − 1.44040e14i | − 0.974102i | ||||||||
\(378\) | − 2.07410e14i | − 1.38237i | ||||||||
\(379\) | −2.81905e14 | −1.85177 | −0.925887 | − | 0.377802i | \(-0.876680\pi\) | ||||
−0.925887 | + | 0.377802i | \(0.876680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.09629e13 | −0.325212 | ||||||||
\(382\) | 1.93482e14i | 1.21700i | ||||||||
\(383\) | 2.51689e13i | 0.156053i | 0.996951 | + | 0.0780264i | \(0.0248618\pi\) | ||||
−0.996951 | + | 0.0780264i | \(0.975138\pi\) | |||||||
\(384\) | −5.23574e12 | −0.0320005 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.40512e14 | 1.42859 | ||||||||
\(387\) | − 2.60367e12i | − 0.0152467i | ||||||||
\(388\) | 2.21840e14i | 1.28075i | ||||||||
\(389\) | 1.44036e14 | 0.819879 | 0.409939 | − | 0.912113i | \(-0.365550\pi\) | ||||
0.409939 | + | 0.912113i | \(0.365550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.14166e14 | 0.631778 | ||||||||
\(392\) | − 4.83809e11i | − 0.00263998i | ||||||||
\(393\) | − 1.60064e14i | − 0.861261i | ||||||||
\(394\) | 6.56916e13 | 0.348563 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.86949e14 | 0.964716 | ||||||||
\(397\) | − 3.78848e13i | − 0.192804i | −0.995342 | − | 0.0964021i | \(-0.969267\pi\) | ||||
0.995342 | − | 0.0964021i | \(-0.0307335\pi\) | |||||||
\(398\) | 7.28380e13i | 0.365596i | ||||||||
\(399\) | −1.11743e14 | −0.553185 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.24111e13 | 0.0597747 | 0.0298874 | − | 0.999553i | \(-0.490485\pi\) | ||||
0.0298874 | + | 0.999553i | \(0.490485\pi\) | |||||||
\(402\) | − 1.01325e14i | − 0.481363i | ||||||||
\(403\) | − 7.63027e13i | − 0.357571i | ||||||||
\(404\) | 6.71012e13 | 0.310194 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.76686e14 | 1.24478 | ||||||||
\(407\) | 4.58149e14i | 2.03347i | ||||||||
\(408\) | − 2.35249e12i | − 0.0103014i | ||||||||
\(409\) | 4.37138e14 | 1.88860 | 0.944301 | − | 0.329082i | \(-0.106739\pi\) | ||||
0.944301 | + | 0.329082i | \(0.106739\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.52610e11 | 0.00148308 | ||||||||
\(412\) | − 1.71023e14i | − 0.709775i | ||||||||
\(413\) | 3.34560e14i | 1.37009i | ||||||||
\(414\) | 1.87139e14 | 0.756246 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.71702e14 | −1.46279 | ||||||||
\(417\) | − 1.32572e14i | − 0.514877i | ||||||||
\(418\) | − 5.74470e14i | − 2.20190i | ||||||||
\(419\) | −5.14822e14 | −1.94751 | −0.973755 | − | 0.227598i | \(-0.926913\pi\) | ||||
−0.973755 | + | 0.227598i | \(0.926913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.90682e14 | −1.43970 | −0.719850 | − | 0.694130i | \(-0.755789\pi\) | ||||
−0.719850 | + | 0.694130i | \(0.755789\pi\) | |||||||
\(422\) | − 4.43869e14i | − 1.61449i | ||||||||
\(423\) | 1.16800e14i | 0.419345i | ||||||||
\(424\) | −8.86159e12 | −0.0314050 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.72952e14 | 0.942612 | ||||||||
\(427\) | 8.69855e13i | 0.296547i | ||||||||
\(428\) | 2.89476e14i | 0.974254i | ||||||||
\(429\) | 3.77373e14 | 1.25388 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.29050e14 | −1.06571 | −0.532853 | − | 0.846208i | \(-0.678880\pi\) | ||||
−0.532853 | + | 0.846208i | \(0.678880\pi\) | |||||||
\(432\) | − 3.30990e14i | − 1.05841i | ||||||||
\(433\) | − 5.59793e14i | − 1.76744i | −0.468019 | − | 0.883718i | \(-0.655032\pi\) | ||||
0.468019 | − | 0.883718i | \(-0.344968\pi\) | |||||||
\(434\) | 1.46570e14 | 0.456932 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.06634e14 | −1.84396 | ||||||||
\(437\) | − 2.85079e14i | − 0.855693i | ||||||||
\(438\) | − 1.19936e14i | − 0.355503i | ||||||||
\(439\) | −1.25752e14 | −0.368095 | −0.184047 | − | 0.982917i | \(-0.558920\pi\) | ||||
−0.184047 | + | 0.982917i | \(0.558920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.12774e13 | 0.0607443 | ||||||||
\(442\) | − 3.34069e14i | − 0.941920i | ||||||||
\(443\) | 3.33211e14i | 0.927894i | 0.885863 | + | 0.463947i | \(0.153567\pi\) | ||||
−0.885863 | + | 0.463947i | \(0.846433\pi\) | |||||||
\(444\) | −2.72738e14 | −0.750135 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.33616e14 | 1.16349 | ||||||||
\(447\) | − 2.98628e14i | − 0.791479i | ||||||||
\(448\) | − 3.47880e14i | − 0.910753i | ||||||||
\(449\) | 1.08196e14 | 0.279804 | 0.139902 | − | 0.990165i | \(-0.455321\pi\) | ||||
0.139902 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.90427e14 | 2.24713 | ||||||||
\(452\) | 4.48773e14i | 1.11883i | ||||||||
\(453\) | 1.39148e14i | 0.342717i | ||||||||
\(454\) | −5.10068e14 | −1.24114 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.87431e12 | −0.0139524 | ||||||||
\(457\) | 1.81057e14i | 0.424890i | 0.977173 | + | 0.212445i | \(0.0681426\pi\) | ||||
−0.977173 | + | 0.212445i | \(0.931857\pi\) | |||||||
\(458\) | 7.68728e14i | 1.78243i | ||||||||
\(459\) | 2.92537e14 | 0.670210 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.74610e14 | −0.837962 | −0.418981 | − | 0.907995i | \(-0.637613\pi\) | ||||
−0.418981 | + | 0.907995i | \(0.637613\pi\) | |||||||
\(462\) | 7.24897e14i | 1.60231i | ||||||||
\(463\) | 2.33341e13i | 0.0509678i | 0.999675 | + | 0.0254839i | \(0.00811266\pi\) | ||||
−0.999675 | + | 0.0254839i | \(0.991887\pi\) | |||||||
\(464\) | 4.41542e14 | 0.953067 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.73896e14 | −1.42060 | ||||||||
\(467\) | 7.37382e14i | 1.53621i | 0.640326 | + | 0.768103i | \(0.278799\pi\) | ||||
−0.640326 | + | 0.768103i | \(0.721201\pi\) | |||||||
\(468\) | − 2.71469e14i | − 0.558945i | ||||||||
\(469\) | −2.35362e14 | −0.478945 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.74854e14 | 0.347586 | ||||||||
\(472\) | 1.75877e13i | 0.0345564i | ||||||||
\(473\) | 2.57301e13i | 0.0499695i | ||||||||
\(474\) | 2.85156e14 | 0.547395 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.18125e14 | 0.596704 | ||||||||
\(477\) | − 3.89723e14i | − 0.722612i | ||||||||
\(478\) | − 3.06747e14i | − 0.562247i | ||||||||
\(479\) | 3.39424e14 | 0.615030 | 0.307515 | − | 0.951543i | \(-0.400503\pi\) | ||||
0.307515 | + | 0.951543i | \(0.400503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.65281e14 | 1.17817 | ||||||||
\(482\) | 8.26404e14i | 1.44688i | ||||||||
\(483\) | 3.59728e14i | 0.622680i | ||||||||
\(484\) | −1.27302e15 | −2.17865 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.89456e14 | 1.32077 | ||||||||
\(487\) | 3.27468e14i | 0.541700i | 0.962622 | + | 0.270850i | \(0.0873048\pi\) | ||||
−0.962622 | + | 0.270850i | \(0.912695\pi\) | |||||||
\(488\) | 4.57280e12i | 0.00747952i | ||||||||
\(489\) | −8.41833e13 | −0.136153 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.28187e14 | −0.519006 | −0.259503 | − | 0.965742i | \(-0.583559\pi\) | ||||
−0.259503 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(492\) | 5.30075e14i | 0.828952i | ||||||||
\(493\) | 3.90246e14i | 0.603504i | ||||||||
\(494\) | −8.34191e14 | −1.27576 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.33900e14 | 0.349849 | ||||||||
\(497\) | − 6.34025e14i | − 0.937878i | ||||||||
\(498\) | − 3.68294e14i | − 0.538807i | ||||||||
\(499\) | −2.84812e14 | −0.412103 | −0.206052 | − | 0.978541i | \(-0.566061\pi\) | ||||
−0.206052 | + | 0.978541i | \(0.566061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.18038e13 | −0.101634 | ||||||||
\(502\) | − 3.25112e14i | − 0.455159i | ||||||||
\(503\) | − 2.01563e13i | − 0.0279117i | −0.999903 | − | 0.0139559i | \(-0.995558\pi\) | ||||
0.999903 | − | 0.0139559i | \(-0.00444243\pi\) | |||||||
\(504\) | −8.95729e12 | −0.0122690 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.84936e15 | −2.47852 | ||||||||
\(507\) | − 4.04052e13i | − 0.0535665i | ||||||||
\(508\) | − 3.62292e14i | − 0.475126i | ||||||||
\(509\) | 6.91697e14 | 0.897362 | 0.448681 | − | 0.893692i | \(-0.351894\pi\) | ||||
0.448681 | + | 0.893692i | \(0.351894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.78594e14 | −0.353717 | ||||||||
\(512\) | − 1.12018e15i | − 1.40703i | ||||||||
\(513\) | − 7.30482e14i | − 0.907746i | ||||||||
\(514\) | 7.70969e14 | 0.947850 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.53172e13 | −0.0184335 | ||||||||
\(517\) | − 1.15425e15i | − 1.37436i | ||||||||
\(518\) | 1.27794e15i | 1.50555i | ||||||||
\(519\) | −5.11374e14 | −0.596098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.00013e14 | 0.570656 | 0.285328 | − | 0.958430i | \(-0.407898\pi\) | ||||
0.285328 | + | 0.958430i | \(0.407898\pi\) | |||||||
\(522\) | 6.39686e14i | 0.722403i | ||||||||
\(523\) | − 2.89272e14i | − 0.323256i | −0.986852 | − | 0.161628i | \(-0.948326\pi\) | ||||
0.986852 | − | 0.161628i | \(-0.0516745\pi\) | |||||||
\(524\) | 1.13789e15 | 1.25828 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.97396e14 | −0.755193 | ||||||||
\(527\) | 2.06727e14i | 0.221533i | ||||||||
\(528\) | 1.15681e15i | 1.22680i | ||||||||
\(529\) | 3.50713e13 | 0.0368083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.73490e14 | −0.795123 | ||||||||
\(532\) | − 7.94377e14i | − 0.808188i | ||||||||
\(533\) | − 1.29299e15i | − 1.30196i | ||||||||
\(534\) | 7.59940e14 | 0.757360 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.23729e13 | −0.0120800 | ||||||||
\(537\) | − 4.61709e14i | − 0.446180i | ||||||||
\(538\) | 7.87828e14i | 0.753579i | ||||||||
\(539\) | −2.10268e14 | −0.199084 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20798e15 | 1.12066 | 0.560331 | − | 0.828269i | \(-0.310674\pi\) | ||||
0.560331 | + | 0.828269i | \(0.310674\pi\) | |||||||
\(542\) | − 8.58325e14i | − 0.788235i | ||||||||
\(543\) | − 1.17829e15i | − 1.07115i | ||||||||
\(544\) | 1.00705e15 | 0.906271 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.05263e15 | 0.928356 | ||||||||
\(547\) | 1.74686e15i | 1.52521i | 0.646867 | + | 0.762603i | \(0.276079\pi\) | ||||
−0.646867 | + | 0.762603i | \(0.723921\pi\) | |||||||
\(548\) | 2.50668e12i | 0.00216674i | ||||||||
\(549\) | −2.01107e14 | −0.172099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.74468e14 | 0.817398 | ||||||||
\(552\) | 1.89108e13i | 0.0157053i | ||||||||
\(553\) | − 6.62373e14i | − 0.544646i | ||||||||
\(554\) | −1.40826e15 | −1.14652 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.42447e14 | 0.752221 | ||||||||
\(557\) | − 8.14516e14i | − 0.643719i | −0.946787 | − | 0.321859i | \(-0.895692\pi\) | ||||
0.946787 | − | 0.321859i | \(-0.104308\pi\) | |||||||
\(558\) | 3.38864e14i | 0.265178i | ||||||||
\(559\) | 3.73628e13 | 0.0289517 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.02242e15 | −0.776840 | ||||||||
\(562\) | − 4.55821e14i | − 0.342961i | ||||||||
\(563\) | − 8.94179e14i | − 0.666237i | −0.942885 | − | 0.333118i | \(-0.891899\pi\) | ||||
0.942885 | − | 0.333118i | \(-0.108101\pi\) | |||||||
\(564\) | 6.87129e14 | 0.506994 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.31554e14 | −0.457004 | ||||||||
\(567\) | 2.01835e14i | 0.144641i | ||||||||
\(568\) | − 3.33305e13i | − 0.0236552i | ||||||||
\(569\) | −5.58478e14 | −0.392544 | −0.196272 | − | 0.980549i | \(-0.562884\pi\) | ||||
−0.196272 | + | 0.980549i | \(0.562884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.19826e15 | 0.826136 | 0.413068 | − | 0.910700i | \(-0.364457\pi\) | ||||
0.413068 | + | 0.910700i | \(0.364457\pi\) | |||||||
\(572\) | 2.68273e15i | 1.83189i | ||||||||
\(573\) | − 8.59863e14i | − 0.581539i | ||||||||
\(574\) | 2.48371e15 | 1.66374 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.04284e14 | 0.528550 | ||||||||
\(577\) | 1.70453e15i | 1.10953i | 0.832008 | + | 0.554764i | \(0.187192\pi\) | ||||
−0.832008 | + | 0.554764i | \(0.812808\pi\) | |||||||
\(578\) | − 1.27903e15i | − 0.824665i | ||||||||
\(579\) | −1.06887e15 | −0.682643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.55491e14 | −0.536101 | ||||||||
\(582\) | − 1.98872e15i | − 1.23451i | ||||||||
\(583\) | 3.85134e15i | 2.36829i | ||||||||
\(584\) | −1.46456e13 | −0.00892147 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.31182e15 | −2.57765 | ||||||||
\(587\) | − 8.77553e14i | − 0.519713i | −0.965647 | − | 0.259857i | \(-0.916325\pi\) | ||||
0.965647 | − | 0.259857i | \(-0.0836753\pi\) | |||||||
\(588\) | − 1.25173e14i | − 0.0734407i | ||||||||
\(589\) | 5.16209e14 | 0.300048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.91944e14 | −0.166559 | ||||||||
\(592\) | 2.03937e15i | 1.15273i | ||||||||
\(593\) | 3.16216e15i | 1.77086i | 0.464776 | + | 0.885428i | \(0.346135\pi\) | ||||
−0.464776 | + | 0.885428i | \(0.653865\pi\) | |||||||
\(594\) | −4.73876e15 | −2.62930 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.12293e15 | 1.15633 | ||||||||
\(597\) | − 3.23704e14i | − 0.174698i | ||||||||
\(598\) | 2.68546e15i | 1.43603i | ||||||||
\(599\) | −1.86633e15 | −0.988873 | −0.494437 | − | 0.869214i | \(-0.664626\pi\) | ||||
−0.494437 | + | 0.869214i | \(0.664626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.57728e14 | 0.446211 | 0.223105 | − | 0.974794i | \(-0.428381\pi\) | ||||
0.223105 | + | 0.974794i | \(0.428381\pi\) | |||||||
\(602\) | 7.17703e13i | 0.0369968i | ||||||||
\(603\) | − 5.44147e14i | − 0.277953i | ||||||||
\(604\) | −9.89193e14 | −0.500701 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.01539e14 | −0.298995 | ||||||||
\(607\) | − 2.90938e15i | − 1.43306i | −0.697558 | − | 0.716528i | \(-0.745730\pi\) | ||||
0.697558 | − | 0.716528i | \(-0.254270\pi\) | |||||||
\(608\) | − 2.51467e15i | − 1.22747i | ||||||||
\(609\) | −1.22964e15 | −0.594814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.67609e15 | −0.796289 | ||||||||
\(612\) | 7.35491e14i | 0.346294i | ||||||||
\(613\) | − 3.95415e15i | − 1.84510i | −0.385875 | − | 0.922551i | \(-0.626100\pi\) | ||||
0.385875 | − | 0.922551i | \(-0.373900\pi\) | |||||||
\(614\) | 1.76106e15 | 0.814419 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.85181e13 | 0.0402104 | ||||||||
\(617\) | 1.44545e15i | 0.650778i | 0.945580 | + | 0.325389i | \(0.105495\pi\) | ||||
−0.945580 | + | 0.325389i | \(0.894505\pi\) | |||||||
\(618\) | 1.53316e15i | 0.684151i | ||||||||
\(619\) | 4.27132e15 | 1.88914 | 0.944569 | − | 0.328314i | \(-0.106481\pi\) | ||||
0.944569 | + | 0.328314i | \(0.106481\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35160e15 | −1.02178 | ||||||||
\(622\) | 7.75764e14i | 0.334105i | ||||||||
\(623\) | − 1.76522e15i | − 0.753556i | ||||||||
\(624\) | 1.67981e15 | 0.710794 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.20840e15 | 2.16544 | ||||||||
\(627\) | 2.55303e15i | 1.05217i | ||||||||
\(628\) | 1.24303e15i | 0.507813i | ||||||||
\(629\) | −1.80244e15 | −0.729933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.19799e15 | 0.874711 | 0.437355 | − | 0.899289i | \(-0.355915\pi\) | ||||
0.437355 | + | 0.899289i | \(0.355915\pi\) | |||||||
\(632\) | − 3.48207e13i | − 0.0137371i | ||||||||
\(633\) | 1.97262e15i | 0.771478i | ||||||||
\(634\) | −4.85435e15 | −1.88209 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.29272e15 | −0.873647 | ||||||||
\(637\) | 3.05331e14i | 0.115347i | ||||||||
\(638\) | − 6.32154e15i | − 2.36760i | ||||||||
\(639\) | 1.46584e15 | 0.544292 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.69744e14 | −0.244450 | −0.122225 | − | 0.992502i | \(-0.539003\pi\) | ||||
−0.122225 | + | 0.992502i | \(0.539003\pi\) | |||||||
\(642\) | − 2.59505e15i | − 0.939082i | ||||||||
\(643\) | 3.43086e15i | 1.23096i | 0.788154 | + | 0.615478i | \(0.211037\pi\) | ||||
−0.788154 | + | 0.615478i | \(0.788963\pi\) | |||||||
\(644\) | −2.55729e15 | −0.909720 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.26007e15 | 0.790393 | ||||||||
\(647\) | 2.12502e15i | 0.736869i | 0.929654 | + | 0.368435i | \(0.120106\pi\) | ||||
−0.929654 | + | 0.368435i | \(0.879894\pi\) | |||||||
\(648\) | 1.06104e13i | 0.00364813i | ||||||||
\(649\) | 7.64381e15 | 2.60594 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.51380e14 | −0.218343 | ||||||||
\(652\) | − 5.98455e14i | − 0.198916i | ||||||||
\(653\) | 4.76025e15i | 1.56894i | 0.620166 | + | 0.784471i | \(0.287065\pi\) | ||||
−0.620166 | + | 0.784471i | \(0.712935\pi\) | |||||||
\(654\) | 5.43826e15 | 1.77739 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.96357e15 | 1.27384 | ||||||||
\(657\) | − 6.44097e14i | − 0.205278i | ||||||||
\(658\) | − 3.21961e15i | − 1.01756i | ||||||||
\(659\) | −1.31734e15 | −0.412886 | −0.206443 | − | 0.978459i | \(-0.566189\pi\) | ||||
−0.206443 | + | 0.978459i | \(0.566189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.45528e15 | −0.756822 | −0.378411 | − | 0.925638i | \(-0.623529\pi\) | ||||
−0.378411 | + | 0.925638i | \(0.623529\pi\) | |||||||
\(662\) | − 5.13080e15i | − 1.56843i | ||||||||
\(663\) | 1.48465e15i | 0.450092i | ||||||||
\(664\) | −4.49729e13 | −0.0135215 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.95454e15 | −0.873739 | ||||||||
\(667\) | − 3.13705e15i | − 0.920087i | ||||||||
\(668\) | − 5.10449e14i | − 0.148485i | ||||||||
\(669\) | −1.92706e15 | −0.555969 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.98739e15 | 0.564038 | ||||||||
\(672\) | 3.17314e15i | 0.893220i | ||||||||
\(673\) | − 8.60705e14i | − 0.240310i | −0.992755 | − | 0.120155i | \(-0.961661\pi\) | ||||
0.992755 | − | 0.120155i | \(-0.0383391\pi\) | |||||||
\(674\) | 5.03888e15 | 1.39542 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.87238e14 | 0.0782593 | ||||||||
\(677\) | − 1.90003e15i | − 0.513479i | −0.966481 | − | 0.256739i | \(-0.917352\pi\) | ||||
0.966481 | − | 0.256739i | \(-0.0826482\pi\) | |||||||
\(678\) | − 4.02309e15i | − 1.07844i | ||||||||
\(679\) | −4.61948e15 | −1.22831 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.26682e15 | 0.593073 | ||||||||
\(682\) | − 3.34873e15i | − 0.869093i | ||||||||
\(683\) | − 2.35084e15i | − 0.605214i | −0.953115 | − | 0.302607i | \(-0.902143\pi\) | ||||
0.953115 | − | 0.302607i | \(-0.0978570\pi\) | |||||||
\(684\) | 1.83657e15 | 0.469027 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.86980e15 | −1.47516 | ||||||||
\(687\) | − 3.41635e15i | − 0.851726i | ||||||||
\(688\) | 1.14533e14i | 0.0283265i | ||||||||
\(689\) | 5.59255e15 | 1.37216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.60668e15 | −1.59534 | −0.797672 | − | 0.603092i | \(-0.793935\pi\) | ||||
−0.797672 | + | 0.603092i | \(0.793935\pi\) | |||||||
\(692\) | − 3.63533e15i | − 0.870884i | ||||||||
\(693\) | 3.89293e15i | 0.925217i | ||||||||
\(694\) | −8.93203e15 | −2.10607 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.46416e13 | −0.0150024 | ||||||||
\(697\) | 3.50310e15i | 0.806627i | ||||||||
\(698\) | − 6.29866e15i | − 1.43894i | ||||||||
\(699\) | 2.99490e15 | 0.678825 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.01300e14 | −0.178791 | −0.0893956 | − | 0.995996i | \(-0.528494\pi\) | ||||
−0.0893956 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(702\) | 6.88118e15i | 1.52338i | ||||||||
\(703\) | 4.50081e15i | 0.988636i | ||||||||
\(704\) | −7.94813e15 | −1.73227 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.74780e15 | −0.375030 | ||||||||
\(707\) | 1.39728e15i | 0.297493i | ||||||||
\(708\) | 4.55039e15i | 0.961315i | ||||||||
\(709\) | −4.10789e15 | −0.861121 | −0.430560 | − | 0.902562i | \(-0.641684\pi\) | ||||
−0.430560 | + | 0.902562i | \(0.641684\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53138e15 | 0.316082 | ||||||||
\(712\) | − 9.27973e13i | − 0.0190062i | ||||||||
\(713\) | − 1.66180e15i | − 0.337743i | ||||||||
\(714\) | −2.85188e15 | −0.575162 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.28227e15 | 0.651857 | ||||||||
\(717\) | 1.36323e15i | 0.268667i | ||||||||
\(718\) | 1.00601e16i | 1.96751i | ||||||||
\(719\) | −2.12875e15 | −0.413157 | −0.206578 | − | 0.978430i | \(-0.566233\pi\) | ||||
−0.206578 | + | 0.978430i | \(0.566233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.56130e15 | 0.680714 | ||||||||
\(722\) | 1.78030e15i | 0.337706i | ||||||||
\(723\) | − 3.67267e15i | − 0.691386i | ||||||||
\(724\) | 8.37637e15 | 1.56493 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.14122e16 | 2.10000 | ||||||||
\(727\) | 4.60450e15i | 0.840898i | 0.907316 | + | 0.420449i | \(0.138127\pi\) | ||||
−0.907316 | + | 0.420449i | \(0.861873\pi\) | |||||||
\(728\) | − 1.28538e14i | − 0.0232974i | ||||||||
\(729\) | −4.36126e15 | −0.784531 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.01227e14 | −0.0179370 | ||||||||
\(732\) | 1.18310e15i | 0.208070i | ||||||||
\(733\) | − 3.94830e15i | − 0.689190i | −0.938752 | − | 0.344595i | \(-0.888016\pi\) | ||||
0.938752 | − | 0.344595i | \(-0.111984\pi\) | |||||||
\(734\) | 1.24612e16 | 2.15890 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.09532e15 | −1.38168 | ||||||||
\(737\) | 5.37739e15i | 0.910962i | ||||||||
\(738\) | 5.74224e15i | 0.965543i | ||||||||
\(739\) | −2.01640e15 | −0.336537 | −0.168269 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168269 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.70727e15 | 0.609613 | ||||||||
\(742\) | 1.07427e16i | 1.75345i | ||||||||
\(743\) | − 7.15627e15i | − 1.15944i | −0.814816 | − | 0.579720i | \(-0.803162\pi\) | ||||
0.814816 | − | 0.579720i | \(-0.196838\pi\) | |||||||
\(744\) | −3.42428e13 | −0.00550704 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.32738e15 | 0.844209 | ||||||||
\(747\) | − 1.97786e15i | − 0.311123i | ||||||||
\(748\) | − 7.26830e15i | − 1.13494i | ||||||||
\(749\) | −6.02791e15 | −0.934365 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.55257e14 | −0.0389904 | −0.0194952 | − | 0.999810i | \(-0.506206\pi\) | ||||
−0.0194952 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(752\) | − 5.13792e15i | − 0.779094i | ||||||||
\(753\) | 1.44485e15i | 0.217496i | ||||||||
\(754\) | −9.17953e15 | −1.37176 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.55276e15 | −0.965059 | ||||||||
\(757\) | 5.67357e15i | 0.829524i | 0.909930 | + | 0.414762i | \(0.136135\pi\) | ||||
−0.909930 | + | 0.414762i | \(0.863865\pi\) | |||||||
\(758\) | 1.79656e16i | 2.60772i | ||||||||
\(759\) | 8.21883e15 | 1.18435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.59220e15 | 1.22036 | 0.610181 | − | 0.792262i | \(-0.291097\pi\) | ||||
0.610181 | + | 0.792262i | \(0.291097\pi\) | |||||||
\(762\) | 3.24782e15i | 0.457973i | ||||||||
\(763\) | − 1.26322e16i | − 1.76846i | ||||||||
\(764\) | 6.11273e15 | 0.849614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.60400e15 | 0.219758 | ||||||||
\(767\) | − 1.10996e16i | − 1.50985i | ||||||||
\(768\) | 5.14650e15i | 0.695064i | ||||||||
\(769\) | −1.23682e16 | −1.65849 | −0.829243 | − | 0.558888i | \(-0.811228\pi\) | ||||
−0.829243 | + | 0.558888i | \(0.811228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.42630e15 | −0.452925 | ||||||||
\(772\) | − 7.59856e15i | − 0.997324i | ||||||||
\(773\) | 8.62674e15i | 1.12424i | 0.827055 | + | 0.562120i | \(0.190014\pi\) | ||||
−0.827055 | + | 0.562120i | \(0.809986\pi\) | |||||||
\(774\) | −1.65930e14 | −0.0214709 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.42845e14 | −0.0309806 | ||||||||
\(777\) | − 5.67936e15i | − 0.719422i | ||||||||
\(778\) | − 9.17933e15i | − 1.15458i | ||||||||
\(779\) | 8.74746e15 | 1.09251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.44858e16 | −1.78386 | ||||||||
\(782\) | − 7.27571e15i | − 0.889689i | ||||||||
\(783\) | − 8.03831e15i | − 0.976057i | ||||||||
\(784\) | −9.35970e14 | −0.112856 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.02008e16 | −1.21285 | ||||||||
\(787\) | − 1.18931e16i | − 1.40421i | −0.712073 | − | 0.702106i | \(-0.752243\pi\) | ||||
0.712073 | − | 0.702106i | \(-0.247757\pi\) | |||||||
\(788\) | − 2.07541e15i | − 0.243338i | ||||||||
\(789\) | 3.09933e15 | 0.360865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.34502e15 | −1.07302 | ||||||||
\(792\) | 2.04650e14i | 0.0233359i | ||||||||
\(793\) | − 2.88589e15i | − 0.326797i | ||||||||
\(794\) | −2.41437e15 | −0.271513 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.30119e15 | 0.255230 | ||||||||
\(797\) | 6.33100e15i | 0.697351i | 0.937243 | + | 0.348676i | \(0.113369\pi\) | ||||
−0.937243 | + | 0.348676i | \(0.886631\pi\) | |||||||
\(798\) | 7.12131e15i | 0.779012i | ||||||||
\(799\) | 4.54103e15 | 0.493340 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.08112e15 | 0.437322 | ||||||||
\(802\) | − 7.90952e14i | − 0.0841766i | ||||||||
\(803\) | 6.36512e15i | 0.672777i | ||||||||
\(804\) | −3.20118e15 | −0.336049 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.86271e15 | −0.503542 | ||||||||
\(807\) | − 3.50123e15i | − 0.360094i | ||||||||
\(808\) | 7.34547e13i | 0.00750339i | ||||||||
\(809\) | −1.06496e16 | −1.08048 | −0.540238 | − | 0.841512i | \(-0.681666\pi\) | ||||
−0.540238 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.79444e15 | 0.680047 | 0.340024 | − | 0.940417i | \(-0.389565\pi\) | ||||
0.340024 | + | 0.940417i | \(0.389565\pi\) | |||||||
\(812\) | − 8.74141e15i | − 0.869008i | ||||||||
\(813\) | 3.81453e15i | 0.376654i | ||||||||
\(814\) | 2.91975e16 | 2.86359 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.55109e15 | −0.440372 | ||||||||
\(817\) | 2.52770e14i | 0.0242943i | ||||||||
\(818\) | − 2.78585e16i | − 2.65959i | ||||||||
\(819\) | 5.65294e15 | 0.536060 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.03099e16 | 1.90029 | 0.950145 | − | 0.311807i | \(-0.100934\pi\) | ||||
0.950145 | + | 0.311807i | \(0.100934\pi\) | |||||||
\(822\) | − 2.24715e13i | − 0.00208852i | ||||||||
\(823\) | − 1.88821e15i | − 0.174322i | −0.996194 | − | 0.0871609i | \(-0.972221\pi\) | ||||
0.996194 | − | 0.0871609i | \(-0.0277794\pi\) | |||||||
\(824\) | 1.87217e14 | 0.0171690 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.13213e16 | 1.92940 | ||||||||
\(827\) | 1.10204e16i | 0.990644i | 0.868710 | + | 0.495322i | \(0.164950\pi\) | ||||
−0.868710 | + | 0.495322i | \(0.835050\pi\) | |||||||
\(828\) | − 5.91235e15i | − 0.527950i | ||||||||
\(829\) | 8.45180e15 | 0.749720 | 0.374860 | − | 0.927081i | \(-0.377691\pi\) | ||||
0.374860 | + | 0.927081i | \(0.377691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.25854e15 | 0.547857 | ||||||||
\(832\) | 1.15415e16i | 1.00366i | ||||||||
\(833\) | − 8.27233e14i | − 0.0714629i | ||||||||
\(834\) | −8.44870e15 | −0.725065 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.81494e16 | −1.53719 | ||||||||
\(837\) | − 4.25817e15i | − 0.358288i | ||||||||
\(838\) | 3.28092e16i | 2.74254i | ||||||||
\(839\) | −5.30367e15 | −0.440439 | −0.220219 | − | 0.975450i | \(-0.570677\pi\) | ||||
−0.220219 | + | 0.975450i | \(0.570677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47735e15 | −0.121089 | ||||||||
\(842\) | 2.48979e16i | 2.02743i | ||||||||
\(843\) | 2.02574e15i | 0.163882i | ||||||||
\(844\) | −1.40233e16 | −1.12711 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.44359e15 | 0.590535 | ||||||||
\(847\) | − 2.65088e16i | − 2.08945i | ||||||||
\(848\) | 1.71435e16i | 1.34253i | ||||||||
\(849\) | 2.80672e15 | 0.218377 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.44892e16 | 1.11284 | ||||||||
\(852\) | − 8.62344e15i | − 0.658056i | ||||||||
\(853\) | − 4.43767e15i | − 0.336462i | −0.985748 | − | 0.168231i | \(-0.946195\pi\) | ||||
0.985748 | − | 0.168231i | \(-0.0538054\pi\) | |||||||
\(854\) | 5.54352e15 | 0.417607 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.16885e14 | −0.0235666 | ||||||||
\(857\) | 2.12803e16i | 1.57247i | 0.617926 | + | 0.786236i | \(0.287973\pi\) | ||||
−0.617926 | + | 0.786236i | \(0.712027\pi\) | |||||||
\(858\) | − 2.40497e16i | − 1.76575i | ||||||||
\(859\) | 4.61602e15 | 0.336748 | 0.168374 | − | 0.985723i | \(-0.446148\pi\) | ||||
0.168374 | + | 0.985723i | \(0.446148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.10380e16 | −0.795012 | ||||||||
\(862\) | 2.09701e16i | 1.50076i | ||||||||
\(863\) | 6.10081e15i | 0.433839i | 0.976190 | + | 0.216919i | \(0.0696009\pi\) | ||||
−0.976190 | + | 0.216919i | \(0.930399\pi\) | |||||||
\(864\) | −2.07433e16 | −1.46573 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.56752e16 | −2.48896 | ||||||||
\(867\) | 5.68420e15i | 0.394062i | ||||||||
\(868\) | − 4.63062e15i | − 0.318993i | ||||||||
\(869\) | −1.51334e16 | −1.03593 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.80854e15 | 0.527800 | ||||||||
\(872\) | − 6.64073e14i | − 0.0446041i | ||||||||
\(873\) | − 1.06800e16i | − 0.712844i | ||||||||
\(874\) | −1.81679e16 | −1.20501 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.78918e15 | −0.248184 | ||||||||
\(877\) | − 9.32501e14i | − 0.0606948i | −0.999539 | − | 0.0303474i | \(-0.990339\pi\) | ||||
0.999539 | − | 0.0303474i | \(-0.00966137\pi\) | |||||||
\(878\) | 8.01407e15i | 0.518362i | ||||||||
\(879\) | 1.91624e16 | 1.23172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.26049e16 | −0.800150 | −0.400075 | − | 0.916482i | \(-0.631016\pi\) | ||||
−0.400075 | + | 0.916482i | \(0.631016\pi\) | |||||||
\(882\) | − 1.35599e15i | − 0.0855420i | ||||||||
\(883\) | 2.18236e16i | 1.36818i | 0.729397 | + | 0.684090i | \(0.239801\pi\) | ||||
−0.729397 | + | 0.684090i | \(0.760199\pi\) | |||||||
\(884\) | −1.05543e16 | −0.657572 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.12353e16 | 1.30669 | ||||||||
\(887\) | 2.71175e16i | 1.65832i | 0.559008 | + | 0.829162i | \(0.311182\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(888\) | − 2.98562e14i | − 0.0181453i | ||||||||
\(889\) | 7.54420e15 | 0.455673 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.61140e15 | 0.275109 | ||||||||
\(892\) | − 1.36993e16i | − 0.812256i | ||||||||
\(893\) | − 1.13392e16i | − 0.668190i | ||||||||
\(894\) | −1.90313e16 | −1.11458 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.75064e14 | 0.0448377 | ||||||||
\(897\) | − 1.19346e16i | − 0.686198i | ||||||||
\(898\) | − 6.89522e15i | − 0.394029i | ||||||||
\(899\) | 5.68042e15 | 0.322628 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51519e16 | −0.850119 | ||||||||
\(902\) | − 5.67463e16i | − 3.16447i | ||||||||
\(903\) | − 3.18958e14i | − 0.0176787i | ||||||||
\(904\) | −4.91265e14 | −0.0270638 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.86777e15 | 0.482624 | ||||||||
\(907\) | − 2.41689e16i | − 1.30742i | −0.756744 | − | 0.653712i | \(-0.773211\pi\) | ||||
0.756744 | − | 0.653712i | \(-0.226789\pi\) | |||||||
\(908\) | 1.61147e16i | 0.866465i | ||||||||
\(909\) | −3.23046e15 | −0.172649 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.08024e16 | −1.09841 | −0.549203 | − | 0.835689i | \(-0.685069\pi\) | ||||
−0.549203 | + | 0.835689i | \(0.685069\pi\) | |||||||
\(912\) | 1.13644e16i | 0.596449i | ||||||||
\(913\) | 1.95457e16i | 1.01967i | ||||||||
\(914\) | 1.15386e16 | 0.598342 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.42866e16 | 1.24435 | ||||||||
\(917\) | 2.36948e16i | 1.20676i | ||||||||
\(918\) | − 1.86432e16i | − 0.943810i | ||||||||
\(919\) | 1.27606e16 | 0.642151 | 0.321076 | − | 0.947054i | \(-0.395956\pi\) | ||||
0.321076 | + | 0.947054i | \(0.395956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.82642e15 | −0.389166 | ||||||||
\(922\) | 2.38736e16i | 1.18004i | ||||||||
\(923\) | 2.10349e16i | 1.03355i | ||||||||
\(924\) | 2.29019e16 | 1.11860 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.48707e15 | 0.0717744 | ||||||||
\(927\) | 8.23358e15i | 0.395048i | ||||||||
\(928\) | − 2.76717e16i | − 1.31984i | ||||||||
\(929\) | −2.66057e16 | −1.26150 | −0.630751 | − | 0.775985i | \(-0.717253\pi\) | ||||
−0.630751 | + | 0.775985i | \(0.717253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06565e15 | −0.0967908 | ||||||||
\(932\) | 2.12906e16i | 0.991745i | ||||||||
\(933\) | − 3.44761e15i | − 0.159650i | ||||||||
\(934\) | 4.69928e16 | 2.16333 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.97174e14 | 0.0135205 | ||||||||
\(937\) | 1.35312e16i | 0.612023i | 0.952028 | + | 0.306012i | \(0.0989946\pi\) | ||||
−0.952028 | + | 0.306012i | \(0.901005\pi\) | |||||||
\(938\) | 1.49994e16i | 0.674465i | ||||||||
\(939\) | −2.31470e16 | −1.03474 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.75735e16 | 1.21829 | 0.609143 | − | 0.793061i | \(-0.291514\pi\) | ||||
0.609143 | + | 0.793061i | \(0.291514\pi\) | |||||||
\(942\) | − 1.11433e16i | − 0.489481i | ||||||||
\(943\) | − 2.81602e16i | − 1.22976i | ||||||||
\(944\) | 3.40250e16 | 1.47724 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.63976e15 | 0.0703686 | ||||||||
\(947\) | − 4.64018e16i | − 1.97975i | −0.141955 | − | 0.989873i | \(-0.545339\pi\) | ||||
0.141955 | − | 0.989873i | \(-0.454661\pi\) | |||||||
\(948\) | − 9.00900e15i | − 0.382147i | ||||||||
\(949\) | 9.24283e15 | 0.389799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.15735e16 | 0.899347 | ||||||||
\(952\) | 3.48246e14i | 0.0144339i | ||||||||
\(953\) | 5.27189e15i | 0.217248i | 0.994083 | + | 0.108624i | \(0.0346444\pi\) | ||||
−0.994083 | + | 0.108624i | \(0.965356\pi\) | |||||||
\(954\) | −2.48367e16 | −1.01760 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.69115e15 | −0.392516 | ||||||||
\(957\) | 2.80939e16i | 1.13135i | ||||||||
\(958\) | − 2.16312e16i | − 0.866105i | ||||||||
\(959\) | −5.21979e13 | −0.00207803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.23994e16 | −0.881571 | ||||||||
\(962\) | − 4.23978e16i | − 1.65913i | ||||||||
\(963\) | − 1.39363e16i | − 0.542253i | ||||||||
\(964\) | 2.61088e16 | 1.01010 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.29252e16 | 0.876877 | ||||||||
\(967\) | − 3.13722e16i | − 1.19316i | −0.802553 | − | 0.596581i | \(-0.796526\pi\) | ||||
0.802553 | − | 0.596581i | \(-0.203474\pi\) | |||||||
\(968\) | − 1.39356e15i | − 0.0527001i | ||||||||
\(969\) | −1.00441e16 | −0.377686 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.02261e16 | −1.49555 | −0.747776 | − | 0.663951i | \(-0.768878\pi\) | ||||
−0.747776 | + | 0.663951i | \(0.768878\pi\) | |||||||
\(972\) | − 2.49415e16i | − 0.922057i | ||||||||
\(973\) | 1.96250e16i | 0.721423i | ||||||||
\(974\) | 2.08693e16 | 0.762839 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.84648e15 | 0.319740 | ||||||||
\(977\) | 1.61108e16i | 0.579025i | 0.957174 | + | 0.289513i | \(0.0934932\pi\) | ||||
−0.957174 | + | 0.289513i | \(0.906507\pi\) | |||||||
\(978\) | 5.36494e15i | 0.191735i | ||||||||
\(979\) | −4.03307e16 | −1.43328 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.92052e16 | 1.02631 | ||||||||
\(982\) | 2.09151e16i | 0.730880i | ||||||||
\(983\) | − 3.39027e16i | − 1.17812i | −0.808089 | − | 0.589060i | \(-0.799498\pi\) | ||||
0.808089 | − | 0.589060i | \(-0.200502\pi\) | |||||||
\(984\) | −5.80265e14 | −0.0200518 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.48701e16 | 0.849873 | ||||||||
\(987\) | 1.43084e16i | 0.486236i | ||||||||
\(988\) | 2.63548e16i | 0.890629i | ||||||||
\(989\) | 8.13727e14 | 0.0273463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.18340e16 | −1.39035 | −0.695174 | − | 0.718841i | \(-0.744673\pi\) | ||||
−0.695174 | + | 0.718841i | \(0.744673\pi\) | |||||||
\(992\) | − 1.46586e16i | − 0.484484i | ||||||||
\(993\) | 2.28021e16i | 0.749468i | ||||||||
\(994\) | −4.04059e16 | −1.32075 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.16356e16 | −0.376152 | ||||||||
\(997\) | − 3.94947e16i | − 1.26974i | −0.772618 | − | 0.634871i | \(-0.781053\pi\) | ||||
0.772618 | − | 0.634871i | \(-0.218947\pi\) | |||||||
\(998\) | 1.81509e16i | 0.580336i | ||||||||
\(999\) | 3.71268e16 | 1.18053 |
(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 | 25.12.b.c.24.2 | 4 | ||
3.2 | odd | 2 | 225.12.b.f.199.3 | 4 | |||
5.2 | odd | 4 | 5.12.a.b.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 25.12.a.c.1.1 | 2 | |||
5.4 | even | 2 | inner | 25.12.b.c.24.3 | 4 | ||
15.2 | even | 4 | 45.12.a.d.1.1 | 2 | |||
15.8 | even | 4 | 225.12.a.h.1.2 | 2 | |||
15.14 | odd | 2 | 225.12.b.f.199.2 | 4 | |||
20.7 | even | 4 | 80.12.a.j.1.1 | 2 | |||
35.27 | even | 4 | 245.12.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.12.a.b.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
25.12.a.c.1.1 | 2 | 5.3 | odd | 4 | |||
25.12.b.c.24.2 | 4 | 1.1 | even | 1 | trivial | ||
25.12.b.c.24.3 | 4 | 5.4 | even | 2 | inner | ||
45.12.a.d.1.1 | 2 | 15.2 | even | 4 | |||
80.12.a.j.1.1 | 2 | 20.7 | even | 4 | |||
225.12.a.h.1.2 | 2 | 15.8 | even | 4 | |||
225.12.b.f.199.2 | 4 | 15.14 | odd | 2 | |||
225.12.b.f.199.3 | 4 | 3.2 | odd | 2 | |||
245.12.a.b.1.2 | 2 | 35.27 | even | 4 |