Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.a (trivial) |
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: | yes |
Analytic conductor: | \(38.6276877123\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.176777 | 0.0883883 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883883 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −496.000 | −0.968750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −324.000 | −0.102062 | ||||||||
\(7\) | 7680.00 | 1.20898 | 0.604491 | − | 0.796612i | \(-0.293376\pi\) | ||||
0.604491 | + | 0.796612i | \(0.293376\pi\) | |||||||
\(8\) | −4032.00 | −0.348029 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −86404.0 | −1.77937 | −0.889686 | − | 0.456573i | \(-0.849077\pi\) | ||||
−0.889686 | + | 0.456573i | \(0.849077\pi\) | |||||||
\(12\) | 40176.0 | 0.559308 | ||||||||
\(13\) | 149978. | 1.45641 | 0.728203 | − | 0.685361i | \(-0.240356\pi\) | ||||
0.728203 | + | 0.685361i | \(0.240356\pi\) | |||||||
\(14\) | 30720.0 | 0.213720 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 237824. | 0.907227 | ||||||||
\(17\) | 207622. | 0.602911 | 0.301456 | − | 0.953480i | \(-0.402528\pi\) | ||||
0.301456 | + | 0.953480i | \(0.402528\pi\) | |||||||
\(18\) | 26244.0 | 0.0589256 | ||||||||
\(19\) | 716284. | 1.26094 | 0.630469 | − | 0.776214i | \(-0.282862\pi\) | ||||
0.630469 | + | 0.776214i | \(0.282862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −622080. | −0.698006 | ||||||||
\(22\) | −345616. | −0.314552 | ||||||||
\(23\) | −1.36992e6 | −1.02075 | −0.510376 | − | 0.859952i | \(-0.670494\pi\) | ||||
−0.510376 | + | 0.859952i | \(0.670494\pi\) | |||||||
\(24\) | 326592. | 0.200935 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 599912. | 0.257459 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −3.80928e6 | −1.17120 | ||||||||
\(29\) | −3.19440e6 | −0.838684 | −0.419342 | − | 0.907828i | \(-0.637739\pi\) | ||||
−0.419342 | + | 0.907828i | \(0.637739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.34900e6 | −0.456831 | −0.228415 | − | 0.973564i | \(-0.573354\pi\) | ||||
−0.228415 | + | 0.973564i | \(0.573354\pi\) | |||||||
\(32\) | 3.01568e6 | 0.508406 | ||||||||
\(33\) | 6.99872e6 | 1.02732 | ||||||||
\(34\) | 830488. | 0.106581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.25426e6 | −0.322917 | ||||||||
\(37\) | −1.87357e7 | −1.64347 | −0.821736 | − | 0.569868i | \(-0.806994\pi\) | ||||
−0.821736 | + | 0.569868i | \(0.806994\pi\) | |||||||
\(38\) | 2.86514e6 | 0.222905 | ||||||||
\(39\) | −1.21482e7 | −0.840856 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92826e7 | −1.61839 | −0.809194 | − | 0.587541i | \(-0.800096\pi\) | ||||
−0.809194 | + | 0.587541i | \(0.800096\pi\) | |||||||
\(42\) | −2.48832e6 | −0.123391 | ||||||||
\(43\) | 1.51672e6 | 0.0676548 | 0.0338274 | − | 0.999428i | \(-0.489230\pi\) | ||||
0.0338274 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(44\) | 4.28564e7 | 1.72377 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.47968e6 | −0.180445 | ||||||||
\(47\) | −615752. | −0.0184063 | −0.00920313 | − | 0.999958i | \(-0.502929\pi\) | ||||
−0.00920313 | + | 0.999958i | \(0.502929\pi\) | |||||||
\(48\) | −1.92637e7 | −0.523788 | ||||||||
\(49\) | 1.86288e7 | 0.461639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68174e7 | −0.348091 | ||||||||
\(52\) | −7.43891e7 | −1.41089 | ||||||||
\(53\) | −4.74743e6 | −0.0826451 | −0.0413226 | − | 0.999146i | \(-0.513157\pi\) | ||||
−0.0413226 | + | 0.999146i | \(0.513157\pi\) | |||||||
\(54\) | −2.12576e6 | −0.0340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.09658e7 | −0.420761 | ||||||||
\(57\) | −5.80190e7 | −0.728003 | ||||||||
\(58\) | −1.27776e7 | −0.148260 | ||||||||
\(59\) | 6.06161e7 | 0.651259 | 0.325630 | − | 0.945497i | \(-0.394424\pi\) | ||||
0.325630 | + | 0.945497i | \(0.394424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26746e8 | −1.17206 | −0.586029 | − | 0.810290i | \(-0.699309\pi\) | ||||
−0.586029 | + | 0.810290i | \(0.699309\pi\) | |||||||
\(62\) | −9.39600e6 | −0.0807570 | ||||||||
\(63\) | 5.03885e7 | 0.402994 | ||||||||
\(64\) | −1.09703e8 | −0.817352 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.79949e7 | 0.181606 | ||||||||
\(67\) | 1.11183e8 | 0.674063 | 0.337031 | − | 0.941493i | \(-0.390577\pi\) | ||||
0.337031 | + | 0.941493i | \(0.390577\pi\) | |||||||
\(68\) | −1.02981e8 | −0.584070 | ||||||||
\(69\) | 1.10964e8 | 0.589331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.75552e8 | −0.819865 | −0.409932 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409932 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(72\) | −2.64540e7 | −0.116010 | ||||||||
\(73\) | 6.12334e7 | 0.252369 | 0.126184 | − | 0.992007i | \(-0.459727\pi\) | ||||
0.126184 | + | 0.992007i | \(0.459727\pi\) | |||||||
\(74\) | −7.49428e7 | −0.290528 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.55277e8 | −1.22153 | ||||||||
\(77\) | −6.63583e8 | −2.15123 | ||||||||
\(78\) | −4.85929e7 | −0.148644 | ||||||||
\(79\) | 2.34431e8 | 0.677163 | 0.338582 | − | 0.940937i | \(-0.390053\pi\) | ||||
0.338582 | + | 0.940937i | \(0.390053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.17131e8 | −0.286093 | ||||||||
\(83\) | −1.18910e8 | −0.275023 | −0.137511 | − | 0.990500i | \(-0.543910\pi\) | ||||
−0.137511 | + | 0.990500i | \(0.543910\pi\) | |||||||
\(84\) | 3.08552e8 | 0.676194 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.06690e6 | 0.0119598 | ||||||||
\(87\) | 2.58747e8 | 0.484215 | ||||||||
\(88\) | 3.48381e8 | 0.619273 | ||||||||
\(89\) | −3.16534e8 | −0.534768 | −0.267384 | − | 0.963590i | \(-0.586159\pi\) | ||||
−0.267384 | + | 0.963590i | \(0.586159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15183e9 | 1.76077 | ||||||||
\(92\) | 6.79480e8 | 0.988853 | ||||||||
\(93\) | 1.90269e8 | 0.263751 | ||||||||
\(94\) | −2.46301e6 | −0.00325380 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.44270e8 | −0.293528 | ||||||||
\(97\) | −2.42912e8 | −0.278597 | −0.139299 | − | 0.990250i | \(-0.544485\pi\) | ||||
−0.139299 | + | 0.990250i | \(0.544485\pi\) | |||||||
\(98\) | 7.45152e7 | 0.0816070 | ||||||||
\(99\) | −5.66897e8 | −0.593124 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.53803e8 | −0.625173 | −0.312587 | − | 0.949889i | \(-0.601195\pi\) | ||||
−0.312587 | + | 0.949889i | \(0.601195\pi\) | |||||||
\(102\) | −6.72695e7 | −0.0615343 | ||||||||
\(103\) | −1.40420e9 | −1.22931 | −0.614656 | − | 0.788795i | \(-0.710705\pi\) | ||||
−0.614656 | + | 0.788795i | \(0.710705\pi\) | |||||||
\(104\) | −6.04711e8 | −0.506872 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.89897e7 | −0.0146097 | ||||||||
\(107\) | 1.83854e9 | 1.35595 | 0.677977 | − | 0.735083i | \(-0.262857\pi\) | ||||
0.677977 | + | 0.735083i | \(0.262857\pi\) | |||||||
\(108\) | 2.63595e8 | 0.186436 | ||||||||
\(109\) | −9.33452e8 | −0.633392 | −0.316696 | − | 0.948527i | \(-0.602574\pi\) | ||||
−0.316696 | + | 0.948527i | \(0.602574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51759e9 | 0.948859 | ||||||||
\(112\) | 1.82649e9 | 1.09682 | ||||||||
\(113\) | 9.28534e7 | 0.0535728 | 0.0267864 | − | 0.999641i | \(-0.491473\pi\) | ||||
0.0267864 | + | 0.999641i | \(0.491473\pi\) | |||||||
\(114\) | −2.32076e8 | −0.128694 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.58442e9 | 0.812476 | ||||||||
\(117\) | 9.84006e8 | 0.485469 | ||||||||
\(118\) | 2.42464e8 | 0.115127 | ||||||||
\(119\) | 1.59454e9 | 0.728909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.10770e9 | 2.16616 | ||||||||
\(122\) | −5.06983e8 | −0.207192 | ||||||||
\(123\) | 2.37189e9 | 0.934377 | ||||||||
\(124\) | 1.16510e9 | 0.442555 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.01554e8 | 0.0712400 | ||||||||
\(127\) | −1.73819e9 | −0.592900 | −0.296450 | − | 0.955048i | \(-0.595803\pi\) | ||||
−0.296450 | + | 0.955048i | \(0.595803\pi\) | |||||||
\(128\) | −1.98284e9 | −0.652894 | ||||||||
\(129\) | −1.22855e8 | −0.0390605 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.49730e9 | −0.740882 | −0.370441 | − | 0.928856i | \(-0.620793\pi\) | ||||
−0.370441 | + | 0.928856i | \(0.620793\pi\) | |||||||
\(132\) | −3.47137e9 | −0.995217 | ||||||||
\(133\) | 5.50106e9 | 1.52445 | ||||||||
\(134\) | 4.44731e8 | 0.119159 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.37132e8 | −0.209831 | ||||||||
\(137\) | 7.96226e9 | 1.93105 | 0.965526 | − | 0.260306i | \(-0.0838234\pi\) | ||||
0.965526 | + | 0.260306i | \(0.0838234\pi\) | |||||||
\(138\) | 4.43854e8 | 0.104180 | ||||||||
\(139\) | −2.85565e9 | −0.648842 | −0.324421 | − | 0.945913i | \(-0.605169\pi\) | ||||
−0.324421 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.98759e7 | 0.0106269 | ||||||||
\(142\) | −7.02206e8 | −0.144933 | ||||||||
\(143\) | −1.29587e10 | −2.59149 | ||||||||
\(144\) | 1.56036e9 | 0.302409 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.44933e8 | 0.0446129 | ||||||||
\(147\) | −1.50893e9 | −0.266527 | ||||||||
\(148\) | 9.29291e9 | 1.59211 | ||||||||
\(149\) | −9.63383e9 | −1.60126 | −0.800628 | − | 0.599161i | \(-0.795501\pi\) | ||||
−0.800628 | + | 0.599161i | \(0.795501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.38292e9 | −0.842601 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(152\) | −2.88806e9 | −0.438843 | ||||||||
\(153\) | 1.36221e9 | 0.200970 | ||||||||
\(154\) | −2.65433e9 | −0.380287 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.02552e9 | 0.814580 | ||||||||
\(157\) | −5.19434e8 | −0.0682310 | −0.0341155 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341155 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(158\) | 9.37725e8 | 0.119707 | ||||||||
\(159\) | 3.84542e8 | 0.0477152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.05210e10 | −1.23407 | ||||||||
\(162\) | 1.72187e8 | 0.0196419 | ||||||||
\(163\) | −9.41239e9 | −1.04437 | −0.522187 | − | 0.852831i | \(-0.674884\pi\) | ||||
−0.522187 | + | 0.852831i | \(0.674884\pi\) | |||||||
\(164\) | 1.45242e10 | 1.56781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.75642e8 | −0.0486176 | ||||||||
\(167\) | −9.37241e9 | −0.932453 | −0.466227 | − | 0.884665i | \(-0.654387\pi\) | ||||
−0.466227 | + | 0.884665i | \(0.654387\pi\) | |||||||
\(168\) | 2.50823e9 | 0.242927 | ||||||||
\(169\) | 1.18889e10 | 1.12112 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.69954e9 | 0.420313 | ||||||||
\(172\) | −7.52295e8 | −0.0655406 | ||||||||
\(173\) | −1.23573e10 | −1.04886 | −0.524428 | − | 0.851455i | \(-0.675721\pi\) | ||||
−0.524428 | + | 0.851455i | \(0.675721\pi\) | |||||||
\(174\) | 1.03499e9 | 0.0855979 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.05489e10 | −1.61429 | ||||||||
\(177\) | −4.90990e9 | −0.376005 | ||||||||
\(178\) | −1.26614e9 | −0.0945346 | ||||||||
\(179\) | −6.66040e8 | −0.0484910 | −0.0242455 | − | 0.999706i | \(-0.507718\pi\) | ||||
−0.0242455 | + | 0.999706i | \(0.507718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.27207e9 | 0.365113 | 0.182557 | − | 0.983195i | \(-0.441563\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441563\pi\) | |||||||
\(182\) | 4.60732e9 | 0.311263 | ||||||||
\(183\) | 1.02664e10 | 0.676688 | ||||||||
\(184\) | 5.52352e9 | 0.355251 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.61076e8 | 0.0466251 | ||||||||
\(187\) | −1.79394e10 | −1.07280 | ||||||||
\(188\) | 3.05413e8 | 0.0178311 | ||||||||
\(189\) | −4.08147e9 | −0.232669 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.93896e10 | −1.59788 | −0.798939 | − | 0.601412i | \(-0.794605\pi\) | ||||
−0.798939 | + | 0.601412i | \(0.794605\pi\) | |||||||
\(192\) | 8.88596e9 | 0.471899 | ||||||||
\(193\) | 1.48746e10 | 0.771681 | 0.385841 | − | 0.922565i | \(-0.373911\pi\) | ||||
0.385841 | + | 0.922565i | \(0.373911\pi\) | |||||||
\(194\) | −9.71649e8 | −0.0492495 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.23988e9 | −0.447213 | ||||||||
\(197\) | −4.98675e9 | −0.235895 | −0.117948 | − | 0.993020i | \(-0.537632\pi\) | ||||
−0.117948 | + | 0.993020i | \(0.537632\pi\) | |||||||
\(198\) | −2.26759e9 | −0.104851 | ||||||||
\(199\) | 1.45527e10 | 0.657816 | 0.328908 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328908 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.00579e9 | −0.389170 | ||||||||
\(202\) | −2.61521e9 | −0.110516 | ||||||||
\(203\) | −2.45330e10 | −1.01395 | ||||||||
\(204\) | 8.34142e9 | 0.337213 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.61681e9 | −0.217314 | ||||||||
\(207\) | −8.98805e9 | −0.340250 | ||||||||
\(208\) | 3.56684e10 | 1.32129 | ||||||||
\(209\) | −6.18898e10 | −2.24368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.15407e10 | 1.79011 | 0.895054 | − | 0.445959i | \(-0.147137\pi\) | ||||
0.895054 | + | 0.445959i | \(0.147137\pi\) | |||||||
\(212\) | 2.35473e9 | 0.0800624 | ||||||||
\(213\) | 1.42197e10 | 0.473349 | ||||||||
\(214\) | 7.35414e9 | 0.239701 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.14277e9 | 0.0669782 | ||||||||
\(217\) | −1.80403e10 | −0.552300 | ||||||||
\(218\) | −3.73381e9 | −0.111969 | ||||||||
\(219\) | −4.95990e9 | −0.145705 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.11387e10 | 0.878083 | ||||||||
\(222\) | 6.07037e9 | 0.167736 | ||||||||
\(223\) | −4.61272e10 | −1.24907 | −0.624533 | − | 0.780998i | \(-0.714711\pi\) | ||||
−0.624533 | + | 0.780998i | \(0.714711\pi\) | |||||||
\(224\) | 2.31604e10 | 0.614654 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.71414e8 | 0.00947043 | ||||||||
\(227\) | 3.75833e10 | 0.939460 | 0.469730 | − | 0.882810i | \(-0.344351\pi\) | ||||
0.469730 | + | 0.882810i | \(0.344351\pi\) | |||||||
\(228\) | 2.87774e10 | 0.705253 | ||||||||
\(229\) | −6.41082e10 | −1.54047 | −0.770236 | − | 0.637759i | \(-0.779862\pi\) | ||||
−0.770236 | + | 0.637759i | \(0.779862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.37502e10 | 1.24201 | ||||||||
\(232\) | 1.28798e10 | 0.291887 | ||||||||
\(233\) | −6.96578e10 | −1.54835 | −0.774174 | − | 0.632973i | \(-0.781834\pi\) | ||||
−0.774174 | + | 0.632973i | \(0.781834\pi\) | |||||||
\(234\) | 3.93602e9 | 0.0858195 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00656e10 | −0.630907 | ||||||||
\(237\) | −1.89889e10 | −0.390960 | ||||||||
\(238\) | 6.37815e9 | 0.128854 | ||||||||
\(239\) | 6.65825e10 | 1.31999 | 0.659993 | − | 0.751272i | \(-0.270559\pi\) | ||||
0.659993 | + | 0.751272i | \(0.270559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.41659e10 | −0.843354 | −0.421677 | − | 0.906746i | \(-0.638558\pi\) | ||||
−0.421677 | + | 0.906746i | \(0.638558\pi\) | |||||||
\(242\) | 2.04308e10 | 0.382927 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 6.28659e10 | 1.13543 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.48757e9 | 0.165176 | ||||||||
\(247\) | 1.07427e11 | 1.83644 | ||||||||
\(248\) | 9.47117e9 | 0.158990 | ||||||||
\(249\) | 9.63174e9 | 0.158784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.36236e10 | 1.32983 | 0.664916 | − | 0.746918i | \(-0.268467\pi\) | ||||
0.664916 | + | 0.746918i | \(0.268467\pi\) | |||||||
\(252\) | −2.49927e10 | −0.390401 | ||||||||
\(253\) | 1.18367e11 | 1.81630 | ||||||||
\(254\) | −6.95277e9 | −0.104811 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.82367e10 | 0.701936 | ||||||||
\(257\) | 8.65274e10 | 1.23724 | 0.618621 | − | 0.785690i | \(-0.287692\pi\) | ||||
0.618621 | + | 0.785690i | \(0.287692\pi\) | |||||||
\(258\) | −4.91419e8 | −0.00690499 | ||||||||
\(259\) | −1.43890e11 | −1.98693 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.09585e10 | −0.279561 | ||||||||
\(262\) | −9.98919e9 | −0.130971 | ||||||||
\(263\) | 9.61535e10 | 1.23927 | 0.619633 | − | 0.784892i | \(-0.287282\pi\) | ||||
0.619633 | + | 0.784892i | \(0.287282\pi\) | |||||||
\(264\) | −2.82189e10 | −0.357538 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.20042e10 | 0.269488 | ||||||||
\(267\) | 2.56393e10 | 0.308749 | ||||||||
\(268\) | −5.51466e10 | −0.652998 | ||||||||
\(269\) | −1.09505e10 | −0.127511 | −0.0637557 | − | 0.997966i | \(-0.520308\pi\) | ||||
−0.0637557 | + | 0.997966i | \(0.520308\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.80287e10 | 0.878805 | 0.439403 | − | 0.898290i | \(-0.355190\pi\) | ||||
0.439403 | + | 0.898290i | \(0.355190\pi\) | |||||||
\(272\) | 4.93775e10 | 0.546977 | ||||||||
\(273\) | −9.32983e10 | −1.01658 | ||||||||
\(274\) | 3.18491e10 | 0.341365 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.50379e10 | −0.570914 | ||||||||
\(277\) | −6.56840e10 | −0.670349 | −0.335174 | − | 0.942156i | \(-0.608795\pi\) | ||||
−0.335174 | + | 0.942156i | \(0.608795\pi\) | |||||||
\(278\) | −1.14226e10 | −0.114700 | ||||||||
\(279\) | −1.54118e10 | −0.152277 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.44906e10 | −0.617046 | −0.308523 | − | 0.951217i | \(-0.599835\pi\) | ||||
−0.308523 | + | 0.951217i | \(0.599835\pi\) | |||||||
\(282\) | 1.99504e8 | 0.00187858 | ||||||||
\(283\) | −9.63133e10 | −0.892580 | −0.446290 | − | 0.894888i | \(-0.647255\pi\) | ||||
−0.446290 | + | 0.894888i | \(0.647255\pi\) | |||||||
\(284\) | 8.70736e10 | 0.794244 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.18348e10 | −0.458115 | ||||||||
\(287\) | −2.24891e11 | −1.95660 | ||||||||
\(288\) | 1.97859e10 | 0.169469 | ||||||||
\(289\) | −7.54810e10 | −0.636498 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96759e10 | 0.160848 | ||||||||
\(292\) | −3.03717e10 | −0.244482 | ||||||||
\(293\) | −8.16308e10 | −0.647068 | −0.323534 | − | 0.946217i | \(-0.604871\pi\) | ||||
−0.323534 | + | 0.946217i | \(0.604871\pi\) | |||||||
\(294\) | −6.03573e9 | −0.0471158 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.55424e10 | 0.571976 | ||||||||
\(297\) | 4.59186e10 | 0.342440 | ||||||||
\(298\) | −3.85353e10 | −0.283065 | ||||||||
\(299\) | −2.05458e11 | −1.48663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.16484e10 | 0.0817935 | ||||||||
\(302\) | −2.15317e10 | −0.148952 | ||||||||
\(303\) | 5.29580e10 | 0.360944 | ||||||||
\(304\) | 1.70350e11 | 1.14396 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.44883e9 | 0.0355269 | ||||||||
\(307\) | 2.95582e10 | 0.189914 | 0.0949568 | − | 0.995481i | \(-0.469729\pi\) | ||||
0.0949568 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(308\) | 3.29137e11 | 2.08400 | ||||||||
\(309\) | 1.13740e11 | 0.709744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.99071e10 | −0.241896 | −0.120948 | − | 0.992659i | \(-0.538593\pi\) | ||||
−0.120948 | + | 0.992659i | \(0.538593\pi\) | |||||||
\(312\) | 4.89816e10 | 0.292643 | ||||||||
\(313\) | −1.85371e11 | −1.09167 | −0.545836 | − | 0.837892i | \(-0.683788\pi\) | ||||
−0.545836 | + | 0.837892i | \(0.683788\pi\) | |||||||
\(314\) | −2.07774e9 | −0.0120617 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.16278e11 | −0.656002 | ||||||||
\(317\) | −2.68895e11 | −1.49560 | −0.747800 | − | 0.663924i | \(-0.768890\pi\) | ||||
−0.747800 | + | 0.663924i | \(0.768890\pi\) | |||||||
\(318\) | 1.53817e9 | 0.00843493 | ||||||||
\(319\) | 2.76009e11 | 1.49233 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.48921e11 | −0.782860 | ||||||||
\(322\) | −4.20839e10 | −0.218155 | ||||||||
\(323\) | 1.48716e11 | 0.760234 | ||||||||
\(324\) | −2.13512e10 | −0.107639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.76496e10 | −0.184621 | ||||||||
\(327\) | 7.56096e10 | 0.365689 | ||||||||
\(328\) | 1.18068e11 | 0.563246 | ||||||||
\(329\) | −4.72898e9 | −0.0222528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.29099e11 | −1.96486 | −0.982430 | − | 0.186629i | \(-0.940244\pi\) | ||||
−0.982430 | + | 0.186629i | \(0.940244\pi\) | |||||||
\(332\) | 5.89796e10 | 0.266428 | ||||||||
\(333\) | −1.22925e11 | −0.547824 | ||||||||
\(334\) | −3.74896e10 | −0.164836 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.47946e11 | −0.633250 | ||||||||
\(337\) | 2.02598e10 | 0.0855657 | 0.0427828 | − | 0.999084i | \(-0.486378\pi\) | ||||
0.0427828 | + | 0.999084i | \(0.486378\pi\) | |||||||
\(338\) | 4.75556e10 | 0.198188 | ||||||||
\(339\) | −7.52112e9 | −0.0309303 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.02963e11 | 0.812872 | ||||||||
\(342\) | 1.87982e10 | 0.0743015 | ||||||||
\(343\) | −1.66847e11 | −0.650869 | ||||||||
\(344\) | −6.11543e9 | −0.0235458 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.94292e10 | −0.185413 | ||||||||
\(347\) | −2.92783e10 | −0.108409 | −0.0542043 | − | 0.998530i | \(-0.517262\pi\) | ||||
−0.0542043 | + | 0.998530i | \(0.517262\pi\) | |||||||
\(348\) | −1.28338e11 | −0.469083 | ||||||||
\(349\) | 7.05132e10 | 0.254423 | 0.127211 | − | 0.991876i | \(-0.459397\pi\) | ||||
0.127211 | + | 0.991876i | \(0.459397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.97045e10 | −0.280285 | ||||||||
\(352\) | −2.60567e11 | −0.904643 | ||||||||
\(353\) | 6.57350e10 | 0.225325 | 0.112663 | − | 0.993633i | \(-0.464062\pi\) | ||||
0.112663 | + | 0.993633i | \(0.464062\pi\) | |||||||
\(354\) | −1.96396e10 | −0.0664688 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.57001e11 | 0.518057 | ||||||||
\(357\) | −1.29157e11 | −0.420836 | ||||||||
\(358\) | −2.66416e9 | −0.00857209 | ||||||||
\(359\) | 5.81702e11 | 1.84831 | 0.924157 | − | 0.382013i | \(-0.124769\pi\) | ||||
0.924157 | + | 0.382013i | \(0.124769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.90375e11 | 0.589967 | ||||||||
\(362\) | 2.10883e10 | 0.0645435 | ||||||||
\(363\) | −4.13724e11 | −1.25064 | ||||||||
\(364\) | −5.71308e11 | −1.70575 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.10656e10 | 0.119623 | ||||||||
\(367\) | 4.17070e11 | 1.20008 | 0.600042 | − | 0.799969i | \(-0.295151\pi\) | ||||
0.600042 | + | 0.799969i | \(0.295151\pi\) | |||||||
\(368\) | −3.25800e11 | −0.926053 | ||||||||
\(369\) | −1.92123e11 | −0.539463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.64603e10 | −0.0999165 | ||||||||
\(372\) | −9.43734e10 | −0.255509 | ||||||||
\(373\) | 7.60417e10 | 0.203405 | 0.101703 | − | 0.994815i | \(-0.467571\pi\) | ||||
0.101703 | + | 0.994815i | \(0.467571\pi\) | |||||||
\(374\) | −7.17575e10 | −0.189647 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.48271e9 | 0.00640591 | ||||||||
\(377\) | −4.79090e11 | −1.22147 | ||||||||
\(378\) | −1.63259e10 | −0.0411304 | ||||||||
\(379\) | −1.79180e11 | −0.446080 | −0.223040 | − | 0.974809i | \(-0.571598\pi\) | ||||
−0.223040 | + | 0.974809i | \(0.571598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.40794e11 | 0.342311 | ||||||||
\(382\) | −1.17558e11 | −0.282467 | ||||||||
\(383\) | 7.95018e11 | 1.88792 | 0.943958 | − | 0.330066i | \(-0.107071\pi\) | ||||
0.943958 | + | 0.330066i | \(0.107071\pi\) | |||||||
\(384\) | 1.60610e11 | 0.376949 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.94985e10 | 0.136415 | ||||||||
\(387\) | 9.95123e9 | 0.0225516 | ||||||||
\(388\) | 1.20484e11 | 0.269891 | ||||||||
\(389\) | −1.79533e11 | −0.397532 | −0.198766 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.84426e11 | −0.615422 | ||||||||
\(392\) | −7.51113e10 | −0.160664 | ||||||||
\(393\) | 2.02281e11 | 0.427749 | ||||||||
\(394\) | −1.99470e10 | −0.0417008 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.81181e11 | 0.574589 | ||||||||
\(397\) | 3.43730e11 | 0.694480 | 0.347240 | − | 0.937776i | \(-0.387119\pi\) | ||||
0.347240 | + | 0.937776i | \(0.387119\pi\) | |||||||
\(398\) | 5.82108e10 | 0.116287 | ||||||||
\(399\) | −4.45586e11 | −0.880143 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.72080e11 | 1.49112 | 0.745560 | − | 0.666438i | \(-0.232182\pi\) | ||||
0.745560 | + | 0.666438i | \(0.232182\pi\) | |||||||
\(402\) | −3.60232e10 | −0.0687963 | ||||||||
\(403\) | −3.52298e11 | −0.665331 | ||||||||
\(404\) | 3.24286e11 | 0.605637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.81320e10 | −0.179244 | ||||||||
\(407\) | 1.61884e12 | 2.92435 | ||||||||
\(408\) | 6.78077e10 | 0.121146 | ||||||||
\(409\) | 2.60632e11 | 0.460546 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.44943e11 | −1.11489 | ||||||||
\(412\) | 6.96484e11 | 1.19090 | ||||||||
\(413\) | 4.65531e11 | 0.787361 | ||||||||
\(414\) | −3.59522e10 | −0.0601483 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.52286e11 | 0.740445 | ||||||||
\(417\) | 2.31308e11 | 0.374609 | ||||||||
\(418\) | −2.47559e11 | −0.396630 | ||||||||
\(419\) | −5.60166e11 | −0.887879 | −0.443939 | − | 0.896057i | \(-0.646419\pi\) | ||||
−0.443939 | + | 0.896057i | \(0.646419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68321e11 | 0.261137 | 0.130569 | − | 0.991439i | \(-0.458320\pi\) | ||||
0.130569 | + | 0.991439i | \(0.458320\pi\) | |||||||
\(422\) | 2.06163e11 | 0.316449 | ||||||||
\(423\) | −4.03995e9 | −0.00613542 | ||||||||
\(424\) | 1.91416e10 | 0.0287629 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68787e10 | 0.0836771 | ||||||||
\(427\) | −9.73407e11 | −1.41700 | ||||||||
\(428\) | −9.11913e11 | −1.31358 | ||||||||
\(429\) | 1.04965e12 | 1.49620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.48383e11 | 0.625895 | 0.312948 | − | 0.949770i | \(-0.398684\pi\) | ||||
0.312948 | + | 0.949770i | \(0.398684\pi\) | |||||||
\(432\) | −1.26389e11 | −0.174596 | ||||||||
\(433\) | 1.08485e12 | 1.48311 | 0.741556 | − | 0.670891i | \(-0.234088\pi\) | ||||
0.741556 | + | 0.670891i | \(0.234088\pi\) | |||||||
\(434\) | −7.21613e10 | −0.0976339 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.62992e11 | 0.613599 | ||||||||
\(437\) | −9.81252e11 | −1.28711 | ||||||||
\(438\) | −1.98396e10 | −0.0257573 | ||||||||
\(439\) | 4.60548e11 | 0.591814 | 0.295907 | − | 0.955217i | \(-0.404378\pi\) | ||||
0.295907 | + | 0.955217i | \(0.404378\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.22224e11 | 0.153880 | ||||||||
\(442\) | 1.24555e11 | 0.155225 | ||||||||
\(443\) | 1.32095e10 | 0.0162956 | 0.00814779 | − | 0.999967i | \(-0.497406\pi\) | ||||
0.00814779 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(444\) | −7.52726e11 | −0.919207 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.84509e11 | −0.220806 | ||||||||
\(447\) | 7.80341e11 | 0.924486 | ||||||||
\(448\) | −8.42520e11 | −0.988165 | ||||||||
\(449\) | −6.91889e11 | −0.803393 | −0.401696 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401696 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.53014e12 | 2.87971 | ||||||||
\(452\) | −4.60553e10 | −0.0518987 | ||||||||
\(453\) | 4.36017e11 | 0.486476 | ||||||||
\(454\) | 1.50333e11 | 0.166075 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.33933e11 | 0.253366 | ||||||||
\(457\) | 3.73135e11 | 0.400168 | 0.200084 | − | 0.979779i | \(-0.435878\pi\) | ||||
0.200084 | + | 0.979779i | \(0.435878\pi\) | |||||||
\(458\) | −2.56433e11 | −0.272320 | ||||||||
\(459\) | −1.10339e11 | −0.116030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.45940e12 | −1.50494 | −0.752470 | − | 0.658627i | \(-0.771138\pi\) | ||||
−0.752470 | + | 0.658627i | \(0.771138\pi\) | |||||||
\(462\) | 2.15001e11 | 0.219559 | ||||||||
\(463\) | −1.34213e11 | −0.135732 | −0.0678658 | − | 0.997694i | \(-0.521619\pi\) | ||||
−0.0678658 | + | 0.997694i | \(0.521619\pi\) | |||||||
\(464\) | −7.59705e11 | −0.760877 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.78631e11 | −0.273712 | ||||||||
\(467\) | 3.64531e10 | 0.0354657 | 0.0177329 | − | 0.999843i | \(-0.494355\pi\) | ||||
0.0177329 | + | 0.999843i | \(0.494355\pi\) | |||||||
\(468\) | −4.88067e11 | −0.470298 | ||||||||
\(469\) | 8.53883e11 | 0.814930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.20741e10 | 0.0393932 | ||||||||
\(472\) | −2.44404e11 | −0.226657 | ||||||||
\(473\) | −1.31051e11 | −0.120383 | ||||||||
\(474\) | −7.59557e10 | −0.0691127 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.90890e11 | −0.706131 | ||||||||
\(477\) | −3.11479e10 | −0.0275484 | ||||||||
\(478\) | 2.66330e11 | 0.233343 | ||||||||
\(479\) | 8.82280e11 | 0.765767 | 0.382883 | − | 0.923797i | \(-0.374931\pi\) | ||||
0.382883 | + | 0.923797i | \(0.374931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.80994e12 | −2.39356 | ||||||||
\(482\) | −1.76663e11 | −0.149085 | ||||||||
\(483\) | 8.52200e11 | 0.712491 | ||||||||
\(484\) | −2.53342e12 | −2.09847 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.39471e10 | −0.0113402 | ||||||||
\(487\) | −5.09840e11 | −0.410727 | −0.205364 | − | 0.978686i | \(-0.565838\pi\) | ||||
−0.205364 | + | 0.978686i | \(0.565838\pi\) | |||||||
\(488\) | 5.11039e11 | 0.407910 | ||||||||
\(489\) | 7.62404e11 | 0.602969 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.52131e12 | −1.18128 | −0.590638 | − | 0.806937i | \(-0.701124\pi\) | ||||
−0.590638 | + | 0.806937i | \(0.701124\pi\) | |||||||
\(492\) | −1.17646e12 | −0.905178 | ||||||||
\(493\) | −6.63228e11 | −0.505652 | ||||||||
\(494\) | 4.29707e11 | 0.324640 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.58649e11 | −0.414449 | ||||||||
\(497\) | −1.34824e12 | −0.991202 | ||||||||
\(498\) | 3.85270e10 | 0.0280694 | ||||||||
\(499\) | 7.03413e11 | 0.507876 | 0.253938 | − | 0.967220i | \(-0.418274\pi\) | ||||
0.253938 | + | 0.967220i | \(0.418274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.59165e11 | 0.538352 | ||||||||
\(502\) | 3.34494e11 | 0.235083 | ||||||||
\(503\) | −3.78018e8 | −0.000263304 0 | −0.000131652 | − | 1.00000i | \(-0.500042\pi\) | ||||
−0.000131652 | 1.00000i | \(0.500042\pi\) | ||||||||
\(504\) | −2.03166e11 | −0.140254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.73466e11 | 0.321079 | ||||||||
\(507\) | −9.63001e11 | −0.647278 | ||||||||
\(508\) | 8.62144e11 | 0.574372 | ||||||||
\(509\) | 1.32057e12 | 0.872027 | 0.436013 | − | 0.899940i | \(-0.356390\pi\) | ||||
0.436013 | + | 0.899940i | \(0.356390\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.70272e11 | 0.305109 | ||||||||
\(512\) | 1.20816e12 | 0.776980 | ||||||||
\(513\) | −3.80663e11 | −0.242668 | ||||||||
\(514\) | 3.46110e11 | 0.218715 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.09359e10 | 0.0378399 | ||||||||
\(517\) | 5.32034e10 | 0.0327516 | ||||||||
\(518\) | −5.75561e11 | −0.351243 | ||||||||
\(519\) | 1.00094e12 | 0.605558 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.31853e12 | −0.784009 | −0.392005 | − | 0.919963i | \(-0.628218\pi\) | ||||
−0.392005 | + | 0.919963i | \(0.628218\pi\) | |||||||
\(522\) | −8.38339e10 | −0.0494200 | ||||||||
\(523\) | 1.69211e12 | 0.988945 | 0.494472 | − | 0.869193i | \(-0.335361\pi\) | ||||
0.494472 | + | 0.869193i | \(0.335361\pi\) | |||||||
\(524\) | 1.23866e12 | 0.717730 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.84614e11 | 0.219073 | ||||||||
\(527\) | −4.87704e11 | −0.275428 | ||||||||
\(528\) | 1.66446e12 | 0.932013 | ||||||||
\(529\) | 7.55281e10 | 0.0419332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.97702e11 | 0.217086 | ||||||||
\(532\) | −2.72853e12 | −1.47681 | ||||||||
\(533\) | −4.39175e12 | −2.35703 | ||||||||
\(534\) | 1.02557e11 | 0.0545796 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.48288e11 | −0.234594 | ||||||||
\(537\) | 5.39492e10 | 0.0279963 | ||||||||
\(538\) | −4.38021e10 | −0.0225411 | ||||||||
\(539\) | −1.60960e12 | −0.821427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.86369e12 | −0.935373 | −0.467687 | − | 0.883894i | \(-0.654912\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654912\pi\) | |||||||
\(542\) | 3.12115e11 | 0.155352 | ||||||||
\(543\) | −4.27037e11 | −0.210798 | ||||||||
\(544\) | 6.26122e11 | 0.306523 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.73193e11 | −0.179708 | ||||||||
\(547\) | −4.37242e11 | −0.208823 | −0.104412 | − | 0.994534i | \(-0.533296\pi\) | ||||
−0.104412 | + | 0.994534i | \(0.533296\pi\) | |||||||
\(548\) | −3.94928e12 | −1.87071 | ||||||||
\(549\) | −8.31578e11 | −0.390686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.28810e12 | −1.05753 | ||||||||
\(552\) | −4.47405e11 | −0.205104 | ||||||||
\(553\) | 1.80043e12 | 0.818679 | ||||||||
\(554\) | −2.62736e11 | −0.118502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.41640e12 | 0.628565 | ||||||||
\(557\) | 7.09146e11 | 0.312167 | 0.156084 | − | 0.987744i | \(-0.450113\pi\) | ||||
0.156084 | + | 0.987744i | \(0.450113\pi\) | |||||||
\(558\) | −6.16472e10 | −0.0269190 | ||||||||
\(559\) | 2.27475e11 | 0.0985328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.45309e12 | 0.619383 | ||||||||
\(562\) | −2.57962e11 | −0.109079 | ||||||||
\(563\) | −3.77472e10 | −0.0158342 | −0.00791711 | − | 0.999969i | \(-0.502520\pi\) | ||||
−0.00791711 | + | 0.999969i | \(0.502520\pi\) | |||||||
\(564\) | −2.47385e10 | −0.0102948 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.85253e11 | −0.157787 | ||||||||
\(567\) | 3.30599e11 | 0.134331 | ||||||||
\(568\) | 7.07824e11 | 0.285337 | ||||||||
\(569\) | −3.56270e11 | −0.142487 | −0.0712433 | − | 0.997459i | \(-0.522697\pi\) | ||||
−0.0712433 | + | 0.997459i | \(0.522697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.87932e12 | 1.52719 | 0.763596 | − | 0.645694i | \(-0.223432\pi\) | ||||
0.763596 | + | 0.645694i | \(0.223432\pi\) | |||||||
\(572\) | 6.42751e12 | 2.51050 | ||||||||
\(573\) | 2.38056e12 | 0.922535 | ||||||||
\(574\) | −8.99562e11 | −0.345882 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.19762e11 | −0.272451 | ||||||||
\(577\) | 4.28876e12 | 1.61080 | 0.805399 | − | 0.592734i | \(-0.201951\pi\) | ||||
0.805399 | + | 0.592734i | \(0.201951\pi\) | |||||||
\(578\) | −3.01924e11 | −0.112518 | ||||||||
\(579\) | −1.20484e12 | −0.445530 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.13232e11 | −0.332498 | ||||||||
\(582\) | 7.87036e10 | 0.0284342 | ||||||||
\(583\) | 4.10197e11 | 0.147056 | ||||||||
\(584\) | −2.46893e11 | −0.0878316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26523e11 | −0.114387 | ||||||||
\(587\) | −4.43245e12 | −1.54089 | −0.770447 | − | 0.637504i | \(-0.779967\pi\) | ||||
−0.770447 | + | 0.637504i | \(0.779967\pi\) | |||||||
\(588\) | 7.48430e11 | 0.258198 | ||||||||
\(589\) | −1.68255e12 | −0.576036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.03927e11 | 0.136194 | ||||||||
\(592\) | −4.45580e12 | −1.49100 | ||||||||
\(593\) | 5.10104e12 | 1.69400 | 0.846998 | − | 0.531596i | \(-0.178407\pi\) | ||||
0.846998 | + | 0.531596i | \(0.178407\pi\) | |||||||
\(594\) | 1.83675e11 | 0.0605355 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.77838e12 | 1.55122 | ||||||||
\(597\) | −1.17877e12 | −0.379790 | ||||||||
\(598\) | −8.21831e11 | −0.262801 | ||||||||
\(599\) | −7.04599e11 | −0.223626 | −0.111813 | − | 0.993729i | \(-0.535666\pi\) | ||||
−0.111813 | + | 0.993729i | \(0.535666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.73879e12 | −0.543641 | −0.271821 | − | 0.962348i | \(-0.587626\pi\) | ||||
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(602\) | 4.65938e10 | 0.0144592 | ||||||||
\(603\) | 7.29469e11 | 0.224688 | ||||||||
\(604\) | 2.66993e12 | 0.816269 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.11832e11 | 0.0638065 | ||||||||
\(607\) | 5.78292e11 | 0.172901 | 0.0864507 | − | 0.996256i | \(-0.472447\pi\) | ||||
0.0864507 | + | 0.996256i | \(0.472447\pi\) | |||||||
\(608\) | 2.16008e12 | 0.641068 | ||||||||
\(609\) | 1.98717e12 | 0.585407 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.23493e10 | −0.0268070 | ||||||||
\(612\) | −6.75655e11 | −0.194690 | ||||||||
\(613\) | −3.74595e12 | −1.07150 | −0.535748 | − | 0.844378i | \(-0.679970\pi\) | ||||
−0.535748 | + | 0.844378i | \(0.679970\pi\) | |||||||
\(614\) | 1.18233e11 | 0.0335723 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.67557e12 | 0.748691 | ||||||||
\(617\) | 3.94875e12 | 1.09692 | 0.548461 | − | 0.836176i | \(-0.315214\pi\) | ||||
0.548461 | + | 0.836176i | \(0.315214\pi\) | |||||||
\(618\) | 4.54962e11 | 0.125466 | ||||||||
\(619\) | 3.42253e12 | 0.937000 | 0.468500 | − | 0.883463i | \(-0.344795\pi\) | ||||
0.468500 | + | 0.883463i | \(0.344795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.28032e11 | 0.196444 | ||||||||
\(622\) | −1.59628e11 | −0.0427615 | ||||||||
\(623\) | −2.43098e12 | −0.646526 | ||||||||
\(624\) | −2.88914e12 | −0.762847 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.41484e11 | −0.192982 | ||||||||
\(627\) | 5.01307e12 | 1.29539 | ||||||||
\(628\) | 2.57639e11 | 0.0660988 | ||||||||
\(629\) | −3.88995e12 | −0.990868 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.84755e12 | 1.46839 | 0.734196 | − | 0.678938i | \(-0.237560\pi\) | ||||
0.734196 | + | 0.678938i | \(0.237560\pi\) | |||||||
\(632\) | −9.45226e11 | −0.235673 | ||||||||
\(633\) | −4.17479e12 | −1.03352 | ||||||||
\(634\) | −1.07558e12 | −0.264387 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.90733e11 | −0.0462241 | ||||||||
\(637\) | 2.79391e12 | 0.672334 | ||||||||
\(638\) | 1.10404e12 | 0.263809 | ||||||||
\(639\) | −1.15179e12 | −0.273288 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.66671e12 | 0.623899 | 0.311950 | − | 0.950099i | \(-0.399018\pi\) | ||||
0.311950 | + | 0.950099i | \(0.399018\pi\) | |||||||
\(642\) | −5.95685e11 | −0.138391 | ||||||||
\(643\) | −9.68716e10 | −0.0223484 | −0.0111742 | − | 0.999938i | \(-0.503557\pi\) | ||||
−0.0111742 | + | 0.999938i | \(0.503557\pi\) | |||||||
\(644\) | 5.21841e12 | 1.19551 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.94865e11 | 0.134392 | ||||||||
\(647\) | −4.47368e10 | −0.0100368 | −0.00501840 | − | 0.999987i | \(-0.501597\pi\) | ||||
−0.00501840 | + | 0.999987i | \(0.501597\pi\) | |||||||
\(648\) | −1.73564e11 | −0.0386699 | ||||||||
\(649\) | −5.23747e12 | −1.15883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.46127e12 | 0.318871 | ||||||||
\(652\) | 4.66855e12 | 1.01174 | ||||||||
\(653\) | −4.95385e12 | −1.06619 | −0.533094 | − | 0.846056i | \(-0.678971\pi\) | ||||
−0.533094 | + | 0.846056i | \(0.678971\pi\) | |||||||
\(654\) | 3.02438e11 | 0.0646453 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.96411e12 | −1.46824 | ||||||||
\(657\) | 4.01752e11 | 0.0841228 | ||||||||
\(658\) | −1.89159e10 | −0.00393378 | ||||||||
\(659\) | −5.85077e12 | −1.20845 | −0.604225 | − | 0.796814i | \(-0.706517\pi\) | ||||
−0.604225 | + | 0.796814i | \(0.706517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.81007e11 | −0.179503 | −0.0897517 | − | 0.995964i | \(-0.528607\pi\) | ||||
−0.0897517 | + | 0.995964i | \(0.528607\pi\) | |||||||
\(662\) | −1.71640e12 | −0.347342 | ||||||||
\(663\) | −2.52224e12 | −0.506962 | ||||||||
\(664\) | 4.79447e11 | 0.0957159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.91700e11 | −0.0968425 | ||||||||
\(667\) | 4.37608e12 | 0.856088 | ||||||||
\(668\) | 4.64872e12 | 0.903314 | ||||||||
\(669\) | 3.73630e12 | 0.721149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09513e13 | 2.08553 | ||||||||
\(672\) | −1.87599e12 | −0.354870 | ||||||||
\(673\) | 8.66521e12 | 1.62821 | 0.814107 | − | 0.580715i | \(-0.197227\pi\) | ||||
0.814107 | + | 0.580715i | \(0.197227\pi\) | |||||||
\(674\) | 8.10390e10 | 0.0151260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.89689e12 | −1.08608 | ||||||||
\(677\) | −8.98549e12 | −1.64397 | −0.821983 | − | 0.569512i | \(-0.807132\pi\) | ||||
−0.821983 | + | 0.569512i | \(0.807132\pi\) | |||||||
\(678\) | −3.00845e10 | −0.00546776 | ||||||||
\(679\) | −1.86557e12 | −0.336819 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.04425e12 | −0.542397 | ||||||||
\(682\) | 8.11852e11 | 0.143697 | ||||||||
\(683\) | 3.86477e12 | 0.679564 | 0.339782 | − | 0.940504i | \(-0.389647\pi\) | ||||
0.339782 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(684\) | −2.33097e12 | −0.407178 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.67386e11 | −0.115059 | ||||||||
\(687\) | 5.19276e12 | 0.889392 | ||||||||
\(688\) | 3.60713e11 | 0.0613782 | ||||||||
\(689\) | −7.12010e11 | −0.120365 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.08564e12 | −1.18230 | −0.591150 | − | 0.806561i | \(-0.701326\pi\) | ||||
−0.591150 | + | 0.806561i | \(0.701326\pi\) | |||||||
\(692\) | 6.12922e12 | 1.01608 | ||||||||
\(693\) | −4.35377e12 | −0.717077 | ||||||||
\(694\) | −1.17113e11 | −0.0191641 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.04327e12 | −0.168521 | ||||||||
\(697\) | −6.07972e12 | −0.975744 | ||||||||
\(698\) | 2.82053e11 | 0.0449760 | ||||||||
\(699\) | 5.64229e12 | 0.893939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.69380e12 | 0.734165 | 0.367083 | − | 0.930188i | \(-0.380357\pi\) | ||||
0.367083 | + | 0.930188i | \(0.380357\pi\) | |||||||
\(702\) | −3.18818e11 | −0.0495479 | ||||||||
\(703\) | −1.34201e13 | −2.07232 | ||||||||
\(704\) | 9.47879e12 | 1.45437 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.62940e11 | 0.0398323 | ||||||||
\(707\) | −5.02120e12 | −0.755824 | ||||||||
\(708\) | 2.43531e12 | 0.364254 | ||||||||
\(709\) | 1.06645e13 | 1.58501 | 0.792503 | − | 0.609868i | \(-0.208777\pi\) | ||||
0.792503 | + | 0.609868i | \(0.208777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53810e12 | 0.225721 | ||||||||
\(712\) | 1.27627e12 | 0.186115 | ||||||||
\(713\) | 3.21794e12 | 0.466311 | ||||||||
\(714\) | −5.16630e11 | −0.0743940 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.30356e11 | 0.0469757 | ||||||||
\(717\) | −5.39318e12 | −0.762095 | ||||||||
\(718\) | 2.32681e12 | 0.326739 | ||||||||
\(719\) | −8.15663e12 | −1.13823 | −0.569116 | − | 0.822257i | \(-0.692715\pi\) | ||||
−0.569116 | + | 0.822257i | \(0.692715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.07843e13 | −1.48622 | ||||||||
\(722\) | 7.61500e11 | 0.104292 | ||||||||
\(723\) | 3.57743e12 | 0.486911 | ||||||||
\(724\) | −2.61495e12 | −0.353703 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.65490e12 | −0.221083 | ||||||||
\(727\) | −6.64771e12 | −0.882606 | −0.441303 | − | 0.897358i | \(-0.645484\pi\) | ||||
−0.441303 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(728\) | −4.64418e12 | −0.612799 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.14905e11 | 0.0407898 | ||||||||
\(732\) | −5.09213e12 | −0.655541 | ||||||||
\(733\) | −7.07821e12 | −0.905640 | −0.452820 | − | 0.891602i | \(-0.649582\pi\) | ||||
−0.452820 | + | 0.891602i | \(0.649582\pi\) | |||||||
\(734\) | 1.66828e12 | 0.212147 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.13124e12 | −0.518956 | ||||||||
\(737\) | −9.60663e12 | −1.19941 | ||||||||
\(738\) | −7.68493e11 | −0.0953644 | ||||||||
\(739\) | −2.61052e12 | −0.321979 | −0.160989 | − | 0.986956i | \(-0.551468\pi\) | ||||
−0.160989 | + | 0.986956i | \(0.551468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.70157e12 | −1.06027 | ||||||||
\(742\) | −1.45841e11 | −0.0176629 | ||||||||
\(743\) | 1.41841e13 | 1.70747 | 0.853734 | − | 0.520709i | \(-0.174333\pi\) | ||||
0.853734 | + | 0.520709i | \(0.174333\pi\) | |||||||
\(744\) | −7.67165e11 | −0.0917932 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.04167e11 | 0.0359573 | ||||||||
\(747\) | −7.80171e11 | −0.0916742 | ||||||||
\(748\) | 8.89793e12 | 1.03928 | ||||||||
\(749\) | 1.41199e13 | 1.63932 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44355e11 | 0.0968603 | 0.0484301 | − | 0.998827i | \(-0.484578\pi\) | ||||
0.0484301 | + | 0.998827i | \(0.484578\pi\) | |||||||
\(752\) | −1.46441e11 | −0.0166986 | ||||||||
\(753\) | −6.77351e12 | −0.767779 | ||||||||
\(754\) | −1.91636e12 | −0.215927 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.02441e12 | 0.225398 | ||||||||
\(757\) | −9.05305e12 | −1.00199 | −0.500995 | − | 0.865450i | \(-0.667032\pi\) | ||||
−0.500995 | + | 0.865450i | \(0.667032\pi\) | |||||||
\(758\) | −7.16719e11 | −0.0788565 | ||||||||
\(759\) | −9.58769e12 | −1.04864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.97701e12 | −0.754116 | −0.377058 | − | 0.926190i | \(-0.623064\pi\) | ||||
−0.377058 | + | 0.926190i | \(0.623064\pi\) | |||||||
\(762\) | 5.63174e11 | 0.0605126 | ||||||||
\(763\) | −7.16891e12 | −0.765760 | ||||||||
\(764\) | 1.45772e13 | 1.54794 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.18007e12 | 0.333739 | ||||||||
\(767\) | 9.09108e12 | 0.948498 | ||||||||
\(768\) | −3.90717e12 | −0.405263 | ||||||||
\(769\) | −1.07233e13 | −1.10576 | −0.552879 | − | 0.833261i | \(-0.686471\pi\) | ||||
−0.552879 | + | 0.833261i | \(0.686471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.00872e12 | −0.714322 | ||||||||
\(772\) | −7.37781e12 | −0.747566 | ||||||||
\(773\) | 1.37568e13 | 1.38583 | 0.692916 | − | 0.721019i | \(-0.256326\pi\) | ||||
0.692916 | + | 0.721019i | \(0.256326\pi\) | |||||||
\(774\) | 3.98049e10 | 0.00398660 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.79422e11 | 0.0969599 | ||||||||
\(777\) | 1.16551e13 | 1.14715 | ||||||||
\(778\) | −7.18134e11 | −0.0702744 | ||||||||
\(779\) | −2.09747e13 | −2.04069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.51684e13 | 1.45884 | ||||||||
\(782\) | −1.13770e12 | −0.108792 | ||||||||
\(783\) | 1.69764e12 | 0.161405 | ||||||||
\(784\) | 4.43037e12 | 0.418811 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.09124e11 | 0.0756160 | ||||||||
\(787\) | 1.27539e13 | 1.18510 | 0.592551 | − | 0.805533i | \(-0.298121\pi\) | ||||
0.592551 | + | 0.805533i | \(0.298121\pi\) | |||||||
\(788\) | 2.47343e12 | 0.228524 | ||||||||
\(789\) | −7.78843e12 | −0.715490 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.13114e11 | 0.0647686 | ||||||||
\(792\) | 2.28573e12 | 0.206424 | ||||||||
\(793\) | −1.90091e13 | −1.70699 | ||||||||
\(794\) | 1.37492e12 | 0.122768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.21814e12 | −0.637260 | ||||||||
\(797\) | −1.27845e13 | −1.12233 | −0.561164 | − | 0.827704i | \(-0.689646\pi\) | ||||
−0.561164 | + | 0.827704i | \(0.689646\pi\) | |||||||
\(798\) | −1.78234e12 | −0.155589 | ||||||||
\(799\) | −1.27844e11 | −0.0110973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.07678e12 | −0.178256 | ||||||||
\(802\) | 3.08832e12 | 0.263595 | ||||||||
\(803\) | −5.29081e12 | −0.449057 | ||||||||
\(804\) | 4.46687e12 | 0.377009 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.40919e12 | −0.117615 | ||||||||
\(807\) | 8.86992e11 | 0.0736188 | ||||||||
\(808\) | 2.63613e12 | 0.217579 | ||||||||
\(809\) | 6.03746e12 | 0.495548 | 0.247774 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247774 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.50043e12 | −0.202965 | −0.101482 | − | 0.994837i | \(-0.532359\pi\) | ||||
−0.101482 | + | 0.994837i | \(0.532359\pi\) | |||||||
\(812\) | 1.21684e13 | 0.982269 | ||||||||
\(813\) | −6.32033e12 | −0.507379 | ||||||||
\(814\) | 6.47536e12 | 0.516957 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.99958e12 | −0.315797 | ||||||||
\(817\) | 1.08641e12 | 0.0853085 | ||||||||
\(818\) | 1.04253e12 | 0.0814138 | ||||||||
\(819\) | 7.55716e12 | 0.586923 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.21082e12 | −0.323461 | −0.161731 | − | 0.986835i | \(-0.551708\pi\) | ||||
−0.161731 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(822\) | −2.57977e12 | −0.197087 | ||||||||
\(823\) | −2.08206e11 | −0.0158196 | −0.00790978 | − | 0.999969i | \(-0.502518\pi\) | ||||
−0.00790978 | + | 0.999969i | \(0.502518\pi\) | |||||||
\(824\) | 5.66174e12 | 0.427836 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.86213e12 | 0.139187 | ||||||||
\(827\) | 9.26106e12 | 0.688472 | 0.344236 | − | 0.938883i | \(-0.388138\pi\) | ||||
0.344236 | + | 0.938883i | \(0.388138\pi\) | |||||||
\(828\) | 4.45807e12 | 0.329618 | ||||||||
\(829\) | 2.42762e13 | 1.78519 | 0.892597 | − | 0.450856i | \(-0.148881\pi\) | ||||
0.892597 | + | 0.450856i | \(0.148881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.32041e12 | 0.387026 | ||||||||
\(832\) | −1.64531e13 | −1.19040 | ||||||||
\(833\) | 3.86775e12 | 0.278327 | ||||||||
\(834\) | 9.25231e11 | 0.0662221 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.06973e13 | 2.17356 | ||||||||
\(837\) | 1.24835e12 | 0.0879171 | ||||||||
\(838\) | −2.24066e12 | −0.156956 | ||||||||
\(839\) | −1.25546e13 | −0.874728 | −0.437364 | − | 0.899285i | \(-0.644088\pi\) | ||||
−0.437364 | + | 0.899285i | \(0.644088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.30294e12 | −0.296608 | ||||||||
\(842\) | 6.73284e11 | 0.0461630 | ||||||||
\(843\) | 5.22374e12 | 0.356252 | ||||||||
\(844\) | −2.55642e13 | −1.73417 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.61598e10 | −0.00108460 | ||||||||
\(847\) | 3.92272e13 | 2.61886 | ||||||||
\(848\) | −1.12905e12 | −0.0749778 | ||||||||
\(849\) | 7.80137e12 | 0.515331 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.56664e13 | 1.67758 | ||||||||
\(852\) | −7.05296e12 | −0.458557 | ||||||||
\(853\) | 1.36320e13 | 0.881632 | 0.440816 | − | 0.897597i | \(-0.354689\pi\) | ||||
0.440816 | + | 0.897597i | \(0.354689\pi\) | |||||||
\(854\) | −3.89363e12 | −0.250492 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.41297e12 | −0.471911 | ||||||||
\(857\) | −1.73987e13 | −1.10180 | −0.550901 | − | 0.834570i | \(-0.685716\pi\) | ||||
−0.550901 | + | 0.834570i | \(0.685716\pi\) | |||||||
\(858\) | 4.19862e12 | 0.264493 | ||||||||
\(859\) | −6.43355e10 | −0.00403163 | −0.00201582 | − | 0.999998i | \(-0.500642\pi\) | ||||
−0.00201582 | + | 0.999998i | \(0.500642\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.82161e13 | 1.12965 | ||||||||
\(862\) | 1.79353e12 | 0.110644 | ||||||||
\(863\) | −3.32120e12 | −0.203820 | −0.101910 | − | 0.994794i | \(-0.532495\pi\) | ||||
−0.101910 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(864\) | −1.60266e12 | −0.0978427 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.33940e12 | 0.262180 | ||||||||
\(867\) | 6.11396e12 | 0.367482 | ||||||||
\(868\) | 8.94800e12 | 0.535041 | ||||||||
\(869\) | −2.02558e13 | −1.20493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.66750e13 | 0.981709 | ||||||||
\(872\) | 3.76368e12 | 0.220439 | ||||||||
\(873\) | −1.59375e12 | −0.0928657 | ||||||||
\(874\) | −3.92501e12 | −0.227530 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.46011e12 | 0.141152 | ||||||||
\(877\) | −1.95832e12 | −0.111786 | −0.0558928 | − | 0.998437i | \(-0.517800\pi\) | ||||
−0.0558928 | + | 0.998437i | \(0.517800\pi\) | |||||||
\(878\) | 1.84219e12 | 0.104619 | ||||||||
\(879\) | 6.61210e12 | 0.373585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.02253e13 | −1.69036 | −0.845179 | − | 0.534483i | \(-0.820506\pi\) | ||||
−0.845179 | + | 0.534483i | \(0.820506\pi\) | |||||||
\(882\) | 4.88894e11 | 0.0272023 | ||||||||
\(883\) | 9.30097e12 | 0.514879 | 0.257439 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257439 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(884\) | −1.54448e13 | −0.850643 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.28380e10 | 0.00288068 | ||||||||
\(887\) | −9.27171e12 | −0.502925 | −0.251463 | − | 0.967867i | \(-0.580912\pi\) | ||||
−0.251463 | + | 0.967867i | \(0.580912\pi\) | |||||||
\(888\) | −6.11893e12 | −0.330231 | ||||||||
\(889\) | −1.33493e13 | −0.716805 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.71941e12 | −0.197708 | ||||||||
\(892\) | 2.28791e13 | 1.21003 | ||||||||
\(893\) | −4.41053e11 | −0.0232092 | ||||||||
\(894\) | 3.12136e12 | 0.163428 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.52282e13 | −0.789338 | ||||||||
\(897\) | 1.66421e13 | 0.858305 | ||||||||
\(898\) | −2.76756e12 | −0.142021 | ||||||||
\(899\) | 7.50365e12 | 0.383137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.85671e11 | −0.0498276 | ||||||||
\(902\) | 1.01205e13 | 0.509066 | ||||||||
\(903\) | −9.43524e11 | −0.0472235 | ||||||||
\(904\) | −3.74385e11 | −0.0186449 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.74407e12 | 0.0859976 | ||||||||
\(907\) | −1.32868e12 | −0.0651908 | −0.0325954 | − | 0.999469i | \(-0.510377\pi\) | ||||
−0.0325954 | + | 0.999469i | \(0.510377\pi\) | |||||||
\(908\) | −1.86413e13 | −0.910102 | ||||||||
\(909\) | −4.28960e12 | −0.208391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71297e12 | 0.130501 | 0.0652503 | − | 0.997869i | \(-0.479215\pi\) | ||||
0.0652503 | + | 0.997869i | \(0.479215\pi\) | |||||||
\(912\) | −1.37983e13 | −0.660464 | ||||||||
\(913\) | 1.02743e13 | 0.489368 | ||||||||
\(914\) | 1.49254e12 | 0.0707404 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.17977e13 | 1.49233 | ||||||||
\(917\) | −1.91792e13 | −0.895714 | ||||||||
\(918\) | −4.41355e11 | −0.0205114 | ||||||||
\(919\) | 1.32139e12 | 0.0611100 | 0.0305550 | − | 0.999533i | \(-0.490273\pi\) | ||||
0.0305550 | + | 0.999533i | \(0.490273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.39422e12 | −0.109647 | ||||||||
\(922\) | −5.83758e12 | −0.266038 | ||||||||
\(923\) | −2.63289e13 | −1.19406 | ||||||||
\(924\) | −2.66601e13 | −1.20320 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.36853e11 | −0.0239942 | ||||||||
\(927\) | −9.21297e12 | −0.409771 | ||||||||
\(928\) | −9.63329e12 | −0.426392 | ||||||||
\(929\) | 1.16124e12 | 0.0511507 | 0.0255754 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255754 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.33435e13 | 0.582098 | ||||||||
\(932\) | 3.45503e13 | 1.49996 | ||||||||
\(933\) | 3.23247e12 | 0.139659 | ||||||||
\(934\) | 1.45813e11 | 0.00626952 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.96751e12 | −0.168957 | ||||||||
\(937\) | −3.40914e13 | −1.44483 | −0.722415 | − | 0.691460i | \(-0.756968\pi\) | ||||
−0.722415 | + | 0.691460i | \(0.756968\pi\) | |||||||
\(938\) | 3.41553e12 | 0.144061 | ||||||||
\(939\) | 1.50151e13 | 0.630277 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.60215e12 | −0.0666114 | −0.0333057 | − | 0.999445i | \(-0.510603\pi\) | ||||
−0.0333057 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(942\) | 1.68297e11 | 0.00696380 | ||||||||
\(943\) | 4.01149e13 | 1.65197 | ||||||||
\(944\) | 1.44160e13 | 0.590840 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.24204e11 | −0.0212809 | ||||||||
\(947\) | 3.38850e13 | 1.36909 | 0.684546 | − | 0.728969i | \(-0.260000\pi\) | ||||
0.684546 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(948\) | 9.41851e12 | 0.378743 | ||||||||
\(949\) | 9.18366e12 | 0.367551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.17805e13 | 0.863485 | ||||||||
\(952\) | −6.42917e12 | −0.253682 | ||||||||
\(953\) | −2.15757e13 | −0.847320 | −0.423660 | − | 0.905821i | \(-0.639255\pi\) | ||||
−0.423660 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(954\) | −1.24592e11 | −0.00486991 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.30249e13 | −1.27874 | ||||||||
\(957\) | −2.23567e13 | −0.861598 | ||||||||
\(958\) | 3.52912e12 | 0.135370 | ||||||||
\(959\) | 6.11502e13 | 2.33461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09218e13 | −0.791306 | ||||||||
\(962\) | −1.12398e13 | −0.423126 | ||||||||
\(963\) | 1.20626e13 | 0.451985 | ||||||||
\(964\) | 2.19063e13 | 0.816999 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.40880e12 | 0.125952 | ||||||||
\(967\) | −3.06249e13 | −1.12630 | −0.563152 | − | 0.826353i | \(-0.690411\pi\) | ||||
−0.563152 | + | 0.826353i | \(0.690411\pi\) | |||||||
\(968\) | −2.05943e13 | −0.753888 | ||||||||
\(969\) | −1.20460e13 | −0.438921 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.92365e12 | 0.0694447 | 0.0347224 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347224 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(972\) | 1.72945e12 | 0.0621453 | ||||||||
\(973\) | −2.19314e13 | −0.784438 | ||||||||
\(974\) | −2.03936e12 | −0.0726070 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.01432e13 | −1.06332 | ||||||||
\(977\) | 1.83893e13 | 0.645714 | 0.322857 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322857 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(978\) | 3.04962e12 | 0.106591 | ||||||||
\(979\) | 2.73498e13 | 0.951552 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.12438e12 | −0.211131 | ||||||||
\(982\) | −6.08524e12 | −0.208822 | ||||||||
\(983\) | 4.63273e13 | 1.58251 | 0.791254 | − | 0.611488i | \(-0.209429\pi\) | ||||
0.791254 | + | 0.611488i | \(0.209429\pi\) | |||||||
\(984\) | −9.56347e12 | −0.325190 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.65291e12 | −0.0893875 | ||||||||
\(987\) | 3.83047e11 | 0.0128477 | ||||||||
\(988\) | −5.32837e13 | −1.77905 | ||||||||
\(989\) | −2.07779e12 | −0.0690587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.76252e12 | 0.0909857 | 0.0454929 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454929 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(992\) | −7.08383e12 | −0.232255 | ||||||||
\(993\) | 3.47570e13 | 1.13441 | ||||||||
\(994\) | −5.39295e12 | −0.175221 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.77734e12 | −0.153822 | ||||||||
\(997\) | 1.74502e13 | 0.559337 | 0.279668 | − | 0.960097i | \(-0.409776\pi\) | ||||
0.279668 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(998\) | 2.81365e12 | 0.0897807 | ||||||||
\(999\) | 9.95692e12 | 0.316286 |
(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 | 75.10.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 225.10.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 75.10.b.d.49.2 | 2 | |||
5.3 | odd | 4 | 75.10.b.d.49.1 | 2 | |||
5.4 | even | 2 | 15.10.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 225.10.b.e.199.1 | 2 | |||
15.8 | even | 4 | 225.10.b.e.199.2 | 2 | |||
15.14 | odd | 2 | 45.10.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 240.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
45.10.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
75.10.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.10.b.d.49.1 | 2 | 5.3 | odd | 4 | |||
75.10.b.d.49.2 | 2 | 5.2 | odd | 4 | |||
225.10.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
225.10.b.e.199.1 | 2 | 15.2 | even | 4 | |||
225.10.b.e.199.2 | 2 | 15.8 | even | 4 | |||
240.10.a.c.1.1 | 1 | 20.19 | odd | 2 |