Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,7,Mod(97,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.97");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.8179502921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.6 | ||
Root | \(2.26350 + 3.92050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.97 |
Dual form | 147.7.d.b.97.5 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.52700 | 0.690875 | 0.345438 | − | 0.938442i | \(-0.387730\pi\) | ||||
0.345438 | + | 0.938442i | \(0.387730\pi\) | |||||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | −33.4522 | −0.522691 | ||||||||
\(5\) | − 66.9661i | − 0.535729i | −0.963457 | − | 0.267864i | \(-0.913682\pi\) | ||||
0.963457 | − | 0.267864i | \(-0.0863179\pi\) | |||||||
\(6\) | 86.1574i | 0.398877i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −538.619 | −1.05199 | ||||||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | − 370.122i | − 0.370122i | ||||||||
\(11\) | 1725.74 | 1.29657 | 0.648285 | − | 0.761397i | \(-0.275486\pi\) | ||||
0.648285 | + | 0.761397i | \(0.275486\pi\) | |||||||
\(12\) | − 521.469i | − 0.301776i | ||||||||
\(13\) | − 2807.43i | − 1.27785i | −0.769271 | − | 0.638923i | \(-0.779380\pi\) | ||||
0.769271 | − | 0.638923i | \(-0.220620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1043.90 | 0.309303 | ||||||||
\(16\) | −836.004 | −0.204102 | ||||||||
\(17\) | 6147.14i | 1.25120i | 0.780145 | + | 0.625599i | \(0.215145\pi\) | ||||
−0.780145 | + | 0.625599i | \(0.784855\pi\) | |||||||
\(18\) | −1343.06 | −0.230292 | ||||||||
\(19\) | 8934.27i | 1.30256i | 0.758837 | + | 0.651281i | \(0.225768\pi\) | ||||
−0.758837 | + | 0.651281i | \(0.774232\pi\) | |||||||
\(20\) | 2240.17i | 0.280021i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9538.15 | 0.895769 | ||||||||
\(23\) | 9901.28 | 0.813781 | 0.406891 | − | 0.913477i | \(-0.366613\pi\) | ||||
0.406891 | + | 0.913477i | \(0.366613\pi\) | |||||||
\(24\) | − 8396.24i | − 0.607367i | ||||||||
\(25\) | 11140.5 | 0.712995 | ||||||||
\(26\) | − 15516.6i | − 0.882832i | ||||||||
\(27\) | − 3788.00i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13610.4 | −0.558054 | −0.279027 | − | 0.960283i | \(-0.590012\pi\) | ||||
−0.279027 | + | 0.960283i | \(0.590012\pi\) | |||||||
\(30\) | 5769.62 | 0.213690 | ||||||||
\(31\) | 25210.5i | 0.846246i | 0.906072 | + | 0.423123i | \(0.139066\pi\) | ||||
−0.906072 | + | 0.423123i | \(0.860934\pi\) | |||||||
\(32\) | 29851.0 | 0.910980 | ||||||||
\(33\) | 26901.6i | 0.748576i | ||||||||
\(34\) | 33975.2i | 0.864422i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8128.90 | 0.174230 | ||||||||
\(37\) | 22732.7 | 0.448793 | 0.224397 | − | 0.974498i | \(-0.427959\pi\) | ||||
0.224397 | + | 0.974498i | \(0.427959\pi\) | |||||||
\(38\) | 49379.7i | 0.899907i | ||||||||
\(39\) | 43763.4 | 0.737764 | ||||||||
\(40\) | 36069.2i | 0.563581i | ||||||||
\(41\) | 37897.2i | 0.549865i | 0.961464 | + | 0.274932i | \(0.0886554\pi\) | ||||
−0.961464 | + | 0.274932i | \(0.911345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 73646.2 | 0.926286 | 0.463143 | − | 0.886284i | \(-0.346722\pi\) | ||||
0.463143 | + | 0.886284i | \(0.346722\pi\) | |||||||
\(44\) | −57729.7 | −0.677706 | ||||||||
\(45\) | 16272.8i | 0.178576i | ||||||||
\(46\) | 54724.4 | 0.562221 | ||||||||
\(47\) | 139168.i | 1.34043i | 0.742166 | + | 0.670216i | \(0.233799\pi\) | ||||
−0.742166 | + | 0.670216i | \(0.766201\pi\) | |||||||
\(48\) | − 13032.0i | − 0.117839i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 61573.8 | 0.492591 | ||||||||
\(51\) | −95824.4 | −0.722379 | ||||||||
\(52\) | 93914.7i | 0.667919i | ||||||||
\(53\) | −16517.6 | −0.110948 | −0.0554739 | − | 0.998460i | \(-0.517667\pi\) | ||||
−0.0554739 | + | 0.998460i | \(0.517667\pi\) | |||||||
\(54\) | − 20936.3i | − 0.132959i | ||||||||
\(55\) | − 115566.i | − 0.694610i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −139271. | −0.752034 | ||||||||
\(58\) | −75224.5 | −0.385545 | ||||||||
\(59\) | 71579.5i | 0.348524i | 0.984699 | + | 0.174262i | \(0.0557540\pi\) | ||||
−0.984699 | + | 0.174262i | \(0.944246\pi\) | |||||||
\(60\) | −34920.7 | −0.161670 | ||||||||
\(61\) | − 263915.i | − 1.16272i | −0.813646 | − | 0.581360i | \(-0.802521\pi\) | ||||
0.813646 | − | 0.581360i | \(-0.197479\pi\) | |||||||
\(62\) | 139339.i | 0.584651i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 218491. | 0.833476 | ||||||||
\(65\) | −188002. | −0.684578 | ||||||||
\(66\) | 148685.i | 0.517172i | ||||||||
\(67\) | 548667. | 1.82425 | 0.912125 | − | 0.409912i | \(-0.134441\pi\) | ||||
0.912125 | + | 0.409912i | \(0.134441\pi\) | |||||||
\(68\) | − 205635.i | − 0.653990i | ||||||||
\(69\) | 154346.i | 0.469837i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 465655. | 1.30103 | 0.650517 | − | 0.759491i | \(-0.274552\pi\) | ||||
0.650517 | + | 0.759491i | \(0.274552\pi\) | |||||||
\(72\) | 130884. | 0.350663 | ||||||||
\(73\) | 333732.i | 0.857885i | 0.903332 | + | 0.428942i | \(0.141114\pi\) | ||||
−0.903332 | + | 0.428942i | \(0.858886\pi\) | |||||||
\(74\) | 125644. | 0.310060 | ||||||||
\(75\) | 173664.i | 0.411648i | ||||||||
\(76\) | − 298871.i | − 0.680837i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 241881. | 0.509703 | ||||||||
\(79\) | −410024. | −0.831626 | −0.415813 | − | 0.909450i | \(-0.636503\pi\) | ||||
−0.415813 | + | 0.909450i | \(0.636503\pi\) | |||||||
\(80\) | 55983.9i | 0.109343i | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 209458.i | 0.379888i | ||||||||
\(83\) | − 71948.9i | − 0.125832i | −0.998019 | − | 0.0629158i | \(-0.979960\pi\) | ||||
0.998019 | − | 0.0629158i | \(-0.0200400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 411649. | 0.670302 | ||||||||
\(86\) | 407043. | 0.639948 | ||||||||
\(87\) | − 212165.i | − 0.322192i | ||||||||
\(88\) | −929514. | −1.36398 | ||||||||
\(89\) | − 163396.i | − 0.231777i | −0.993262 | − | 0.115889i | \(-0.963028\pi\) | ||||
0.993262 | − | 0.115889i | \(-0.0369716\pi\) | |||||||
\(90\) | 89939.6i | 0.123374i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −331220. | −0.425357 | ||||||||
\(93\) | −392993. | −0.488581 | ||||||||
\(94\) | 769180.i | 0.926072i | ||||||||
\(95\) | 598293. | 0.697819 | ||||||||
\(96\) | 465331.i | 0.525955i | ||||||||
\(97\) | − 651914.i | − 0.714291i | −0.934049 | − | 0.357146i | \(-0.883750\pi\) | ||||
0.934049 | − | 0.357146i | \(-0.116250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −419354. | −0.432190 | ||||||||
\(100\) | −372676. | −0.372676 | ||||||||
\(101\) | − 1.02058e6i | − 0.990567i | −0.868731 | − | 0.495283i | \(-0.835064\pi\) | ||||
0.868731 | − | 0.495283i | \(-0.164936\pi\) | |||||||
\(102\) | −529621. | −0.499074 | ||||||||
\(103\) | 419326.i | 0.383742i | 0.981420 | + | 0.191871i | \(0.0614556\pi\) | ||||
−0.981420 | + | 0.191871i | \(0.938544\pi\) | |||||||
\(104\) | 1.51213e6i | 1.34428i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −91292.8 | −0.0766512 | ||||||||
\(107\) | 2.21241e6 | 1.80599 | 0.902993 | − | 0.429655i | \(-0.141365\pi\) | ||||
0.902993 | + | 0.429655i | \(0.141365\pi\) | |||||||
\(108\) | 126717.i | 0.100592i | ||||||||
\(109\) | 765910. | 0.591423 | 0.295711 | − | 0.955277i | \(-0.404443\pi\) | ||||
0.295711 | + | 0.955277i | \(0.404443\pi\) | |||||||
\(110\) | − 638732.i | − 0.479889i | ||||||||
\(111\) | 354368.i | 0.259111i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.66096e6 | −1.84418 | −0.922090 | − | 0.386976i | \(-0.873520\pi\) | ||||
−0.922090 | + | 0.386976i | \(0.873520\pi\) | |||||||
\(114\) | −769754. | −0.519562 | ||||||||
\(115\) | − 663050.i | − 0.435966i | ||||||||
\(116\) | 455297. | 0.291690 | ||||||||
\(117\) | 682204.i | 0.425948i | ||||||||
\(118\) | 395620.i | 0.240787i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −562263. | −0.325384 | ||||||||
\(121\) | 1.20660e6 | 0.681096 | ||||||||
\(122\) | − 1.45866e6i | − 0.803295i | ||||||||
\(123\) | −590759. | −0.317464 | ||||||||
\(124\) | − 843349.i | − 0.442326i | ||||||||
\(125\) | − 1.79238e6i | − 0.917700i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11648e6 | −0.545055 | −0.272527 | − | 0.962148i | \(-0.587859\pi\) | ||||
−0.272527 | + | 0.962148i | \(0.587859\pi\) | |||||||
\(128\) | −702865. | −0.335152 | ||||||||
\(129\) | 1.14803e6i | 0.534791i | ||||||||
\(130\) | −1.03909e6 | −0.472958 | ||||||||
\(131\) | 286165.i | 0.127293i | 0.997973 | + | 0.0636463i | \(0.0202730\pi\) | ||||
−0.997973 | + | 0.0636463i | \(0.979727\pi\) | |||||||
\(132\) | − 899918.i | − 0.391274i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.03248e6 | 1.26033 | ||||||||
\(135\) | −253667. | −0.103101 | ||||||||
\(136\) | − 3.31096e6i | − 1.31625i | ||||||||
\(137\) | −3.73393e6 | −1.45213 | −0.726063 | − | 0.687628i | \(-0.758652\pi\) | ||||
−0.726063 | + | 0.687628i | \(0.758652\pi\) | |||||||
\(138\) | 853069.i | 0.324599i | ||||||||
\(139\) | − 618216.i | − 0.230195i | −0.993354 | − | 0.115097i | \(-0.963282\pi\) | ||||
0.993354 | − | 0.115097i | \(-0.0367180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.16941e6 | −0.773899 | ||||||||
\(142\) | 2.57367e6 | 0.898853 | ||||||||
\(143\) | − 4.84488e6i | − 1.65682i | ||||||||
\(144\) | 203149. | 0.0680341 | ||||||||
\(145\) | 911433.i | 0.298965i | ||||||||
\(146\) | 1.84454e6i | 0.592691i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −760461. | −0.234580 | ||||||||
\(149\) | 3.72319e6 | 1.12553 | 0.562765 | − | 0.826617i | \(-0.309738\pi\) | ||||
0.562765 | + | 0.826617i | \(0.309738\pi\) | |||||||
\(150\) | 959841.i | 0.284397i | ||||||||
\(151\) | −2.55199e6 | −0.741221 | −0.370611 | − | 0.928788i | \(-0.620852\pi\) | ||||
−0.370611 | + | 0.928788i | \(0.620852\pi\) | |||||||
\(152\) | − 4.81216e6i | − 1.37028i | ||||||||
\(153\) | − 1.49375e6i | − 0.417066i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.68825e6 | 0.453358 | ||||||||
\(156\) | −1.46399e6 | −0.385623 | ||||||||
\(157\) | 6.77876e6i | 1.75166i | 0.482615 | + | 0.875832i | \(0.339687\pi\) | ||||
−0.482615 | + | 0.875832i | \(0.660313\pi\) | |||||||
\(158\) | −2.26620e6 | −0.574550 | ||||||||
\(159\) | − 257484.i | − 0.0640558i | ||||||||
\(160\) | − 1.99900e6i | − 0.488038i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 326364. | 0.0767639 | ||||||||
\(163\) | −8.27141e6 | −1.90993 | −0.954964 | − | 0.296722i | \(-0.904106\pi\) | ||||
−0.954964 | + | 0.296722i | \(0.904106\pi\) | |||||||
\(164\) | − 1.26775e6i | − 0.287409i | ||||||||
\(165\) | 1.80149e6 | 0.401033 | ||||||||
\(166\) | − 397662.i | − 0.0869340i | ||||||||
\(167\) | 2.59960e6i | 0.558158i | 0.960268 | + | 0.279079i | \(0.0900291\pi\) | ||||
−0.960268 | + | 0.279079i | \(0.909971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05483e6 | −0.632888 | ||||||||
\(170\) | 2.27519e6 | 0.463095 | ||||||||
\(171\) | − 2.17103e6i | − 0.434187i | ||||||||
\(172\) | −2.46363e6 | −0.484162 | ||||||||
\(173\) | − 8.20544e6i | − 1.58476i | −0.610027 | − | 0.792380i | \(-0.708842\pi\) | ||||
0.610027 | − | 0.792380i | \(-0.291158\pi\) | |||||||
\(174\) | − 1.17263e6i | − 0.222595i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.44272e6 | −0.264633 | ||||||||
\(177\) | −1.11581e6 | −0.201221 | ||||||||
\(178\) | − 903090.i | − 0.160129i | ||||||||
\(179\) | 8.18803e6 | 1.42764 | 0.713822 | − | 0.700327i | \(-0.246962\pi\) | ||||
0.713822 | + | 0.700327i | \(0.246962\pi\) | |||||||
\(180\) | − 544360.i | − 0.0933402i | ||||||||
\(181\) | 3.25606e6i | 0.549106i | 0.961572 | + | 0.274553i | \(0.0885298\pi\) | ||||
−0.961572 | + | 0.274553i | \(0.911470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.11403e6 | 0.671297 | ||||||||
\(184\) | −5.33301e6 | −0.856090 | ||||||||
\(185\) | − 1.52232e6i | − 0.240431i | ||||||||
\(186\) | −2.17207e6 | −0.337548 | ||||||||
\(187\) | 1.06083e7i | 1.62227i | ||||||||
\(188\) | − 4.65547e6i | − 0.700633i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.30677e6 | 0.482106 | ||||||||
\(191\) | 8.60850e6 | 1.23546 | 0.617728 | − | 0.786392i | \(-0.288053\pi\) | ||||
0.617728 | + | 0.786392i | \(0.288053\pi\) | |||||||
\(192\) | 3.40593e6i | 0.481208i | ||||||||
\(193\) | −179886. | −0.0250222 | −0.0125111 | − | 0.999922i | \(-0.503983\pi\) | ||||
−0.0125111 | + | 0.999922i | \(0.503983\pi\) | |||||||
\(194\) | − 3.60313e6i | − 0.493486i | ||||||||
\(195\) | − 2.93067e6i | − 0.395241i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.69333e6 | 0.352283 | 0.176141 | − | 0.984365i | \(-0.443638\pi\) | ||||
0.176141 | + | 0.984365i | \(0.443638\pi\) | |||||||
\(198\) | −2.31777e6 | −0.298590 | ||||||||
\(199\) | − 6.04221e6i | − 0.766720i | −0.923599 | − | 0.383360i | \(-0.874767\pi\) | ||||
0.923599 | − | 0.383360i | \(-0.125233\pi\) | |||||||
\(200\) | −6.00051e6 | −0.750063 | ||||||||
\(201\) | 8.55287e6i | 1.05323i | ||||||||
\(202\) | − 5.64076e6i | − 0.684358i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.20554e6 | 0.377581 | ||||||||
\(205\) | 2.53783e6 | 0.294578 | ||||||||
\(206\) | 2.31761e6i | 0.265118i | ||||||||
\(207\) | −2.40601e6 | −0.271260 | ||||||||
\(208\) | 2.34702e6i | 0.260811i | ||||||||
\(209\) | 1.54182e7i | 1.68886i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.38113e7 | −1.47024 | −0.735118 | − | 0.677939i | \(-0.762873\pi\) | ||||
−0.735118 | + | 0.677939i | \(0.762873\pi\) | |||||||
\(212\) | 552550. | 0.0579915 | ||||||||
\(213\) | 7.25884e6i | 0.751153i | ||||||||
\(214\) | 1.22280e7 | 1.24771 | ||||||||
\(215\) | − 4.93180e6i | − 0.496238i | ||||||||
\(216\) | 2.04029e6i | 0.202456i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.23318e6 | 0.408599 | ||||||||
\(219\) | −5.20236e6 | −0.495300 | ||||||||
\(220\) | 3.86593e6i | 0.363067i | ||||||||
\(221\) | 1.72576e7 | 1.59884 | ||||||||
\(222\) | 1.95859e6i | 0.179013i | ||||||||
\(223\) | 9.81400e6i | 0.884976i | 0.896774 | + | 0.442488i | \(0.145904\pi\) | ||||
−0.896774 | + | 0.442488i | \(0.854096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70715e6 | −0.237665 | ||||||||
\(226\) | −1.47071e7 | −1.27410 | ||||||||
\(227\) | 1.45743e7i | 1.24598i | 0.782231 | + | 0.622989i | \(0.214082\pi\) | ||||
−0.782231 | + | 0.622989i | \(0.785918\pi\) | |||||||
\(228\) | 4.65894e6 | 0.393082 | ||||||||
\(229\) | 1.46985e7i | 1.22396i | 0.790875 | + | 0.611978i | \(0.209626\pi\) | ||||
−0.790875 | + | 0.611978i | \(0.790374\pi\) | |||||||
\(230\) | − 3.66468e6i | − 0.301198i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.33080e6 | 0.587067 | ||||||||
\(233\) | 5.75195e6 | 0.454723 | 0.227362 | − | 0.973810i | \(-0.426990\pi\) | ||||
0.227362 | + | 0.973810i | \(0.426990\pi\) | |||||||
\(234\) | 3.77055e6i | 0.294277i | ||||||||
\(235\) | 9.31952e6 | 0.718108 | ||||||||
\(236\) | − 2.39450e6i | − 0.182171i | ||||||||
\(237\) | − 6.39164e6i | − 0.480140i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.60167e7 | 1.17322 | 0.586610 | − | 0.809869i | \(-0.300462\pi\) | ||||
0.586610 | + | 0.809869i | \(0.300462\pi\) | |||||||
\(240\) | −872702. | −0.0631295 | ||||||||
\(241\) | 2.58206e7i | 1.84465i | 0.386410 | + | 0.922327i | \(0.373715\pi\) | ||||
−0.386410 | + | 0.922327i | \(0.626285\pi\) | |||||||
\(242\) | 6.66890e6 | 0.470553 | ||||||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | 8.82856e6i | 0.607744i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.26513e6 | −0.219328 | ||||||||
\(247\) | 2.50823e7 | 1.66447 | ||||||||
\(248\) | − 1.35789e7i | − 0.890243i | ||||||||
\(249\) | 1.12157e6 | 0.0726490 | ||||||||
\(250\) | − 9.90651e6i | − 0.634016i | ||||||||
\(251\) | − 9.51912e6i | − 0.601971i | −0.953629 | − | 0.300985i | \(-0.902684\pi\) | ||||
0.953629 | − | 0.300985i | \(-0.0973156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.70870e7 | 1.05513 | ||||||||
\(254\) | −6.17079e6 | −0.376565 | ||||||||
\(255\) | 6.41698e6i | 0.386999i | ||||||||
\(256\) | −1.78682e7 | −1.06502 | ||||||||
\(257\) | 2.23864e7i | 1.31882i | 0.751785 | + | 0.659408i | \(0.229193\pi\) | ||||
−0.751785 | + | 0.659408i | \(0.770807\pi\) | |||||||
\(258\) | 6.34517e6i | 0.369474i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.28910e6 | 0.357823 | ||||||||
\(261\) | 3.30732e6 | 0.186018 | ||||||||
\(262\) | 1.58164e6i | 0.0879433i | ||||||||
\(263\) | 1.04932e7 | 0.576819 | 0.288410 | − | 0.957507i | \(-0.406874\pi\) | ||||
0.288410 | + | 0.957507i | \(0.406874\pi\) | |||||||
\(264\) | − 1.44897e7i | − 0.787494i | ||||||||
\(265\) | 1.10612e6i | 0.0594380i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.54709e6 | 0.133817 | ||||||||
\(268\) | −1.83541e7 | −0.953520 | ||||||||
\(269\) | − 2.69811e7i | − 1.38613i | −0.720877 | − | 0.693063i | \(-0.756261\pi\) | ||||
0.720877 | − | 0.693063i | \(-0.243739\pi\) | |||||||
\(270\) | −1.40202e6 | −0.0712299 | ||||||||
\(271\) | − 1.26965e6i | − 0.0637935i | −0.999491 | − | 0.0318968i | \(-0.989845\pi\) | ||||
0.999491 | − | 0.0318968i | \(-0.0101548\pi\) | |||||||
\(272\) | − 5.13903e6i | − 0.255373i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.06374e7 | −1.00324 | ||||||||
\(275\) | 1.92256e7 | 0.924449 | ||||||||
\(276\) | − 5.16321e6i | − 0.245580i | ||||||||
\(277\) | −6.70033e6 | −0.315251 | −0.157626 | − | 0.987499i | \(-0.550384\pi\) | ||||
−0.157626 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(278\) | − 3.41688e6i | − 0.159036i | ||||||||
\(279\) | − 6.12616e6i | − 0.282082i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −321000. | −0.0144673 | −0.00723363 | − | 0.999974i | \(-0.502303\pi\) | ||||
−0.00723363 | + | 0.999974i | \(0.502303\pi\) | |||||||
\(282\) | −1.19903e7 | −0.534668 | ||||||||
\(283\) | − 3.20211e6i | − 0.141279i | −0.997502 | − | 0.0706394i | \(-0.977496\pi\) | ||||
0.997502 | − | 0.0706394i | \(-0.0225040\pi\) | |||||||
\(284\) | −1.55772e7 | −0.680039 | ||||||||
\(285\) | 9.32646e6i | 0.402886i | ||||||||
\(286\) | − 2.67776e7i | − 1.14465i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.25380e6 | −0.303660 | ||||||||
\(289\) | −1.36497e7 | −0.565496 | ||||||||
\(290\) | 5.03749e6i | 0.206548i | ||||||||
\(291\) | 1.01623e7 | 0.412396 | ||||||||
\(292\) | − 1.11641e7i | − 0.448409i | ||||||||
\(293\) | − 2.67440e6i | − 0.106322i | −0.998586 | − | 0.0531610i | \(-0.983070\pi\) | ||||
0.998586 | − | 0.0531610i | \(-0.0169297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.79340e6 | 0.186714 | ||||||||
\(296\) | −1.22443e7 | −0.472126 | ||||||||
\(297\) | − 6.53708e6i | − 0.249525i | ||||||||
\(298\) | 2.05781e7 | 0.777601 | ||||||||
\(299\) | − 2.77971e7i | − 1.03989i | ||||||||
\(300\) | − 5.80945e6i | − 0.215165i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.41048e7 | −0.512092 | ||||||||
\(303\) | 1.59093e7 | 0.571904 | ||||||||
\(304\) | − 7.46908e6i | − 0.265856i | ||||||||
\(305\) | −1.76734e7 | −0.622903 | ||||||||
\(306\) | − 8.25598e6i | − 0.288141i | ||||||||
\(307\) | 1.98765e7i | 0.686950i | 0.939162 | + | 0.343475i | \(0.111604\pi\) | ||||
−0.939162 | + | 0.343475i | \(0.888396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.53664e6 | −0.221554 | ||||||||
\(310\) | 9.33096e6 | 0.313214 | ||||||||
\(311\) | 1.57710e7i | 0.524296i | 0.965028 | + | 0.262148i | \(0.0844309\pi\) | ||||
−0.965028 | + | 0.262148i | \(0.915569\pi\) | |||||||
\(312\) | −2.35718e7 | −0.776120 | ||||||||
\(313\) | − 1.05533e7i | − 0.344154i | −0.985083 | − | 0.172077i | \(-0.944952\pi\) | ||||
0.985083 | − | 0.172077i | \(-0.0550479\pi\) | |||||||
\(314\) | 3.74662e7i | 1.21018i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.37162e7 | 0.434684 | ||||||||
\(317\) | −3.23227e7 | −1.01468 | −0.507341 | − | 0.861745i | \(-0.669371\pi\) | ||||
−0.507341 | + | 0.861745i | \(0.669371\pi\) | |||||||
\(318\) | − 1.42311e6i | − 0.0442546i | ||||||||
\(319\) | −2.34879e7 | −0.723556 | ||||||||
\(320\) | − 1.46315e7i | − 0.446517i | ||||||||
\(321\) | 3.44881e7i | 1.04269i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.49201e7 | −1.62976 | ||||||||
\(324\) | −1.97532e6 | −0.0580768 | ||||||||
\(325\) | − 3.12763e7i | − 0.911097i | ||||||||
\(326\) | −4.57161e7 | −1.31952 | ||||||||
\(327\) | 1.19394e7i | 0.341458i | ||||||||
\(328\) | − 2.04122e7i | − 0.578452i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.95685e6 | 0.277064 | ||||||||
\(331\) | 2.00329e7 | 0.552409 | 0.276205 | − | 0.961099i | \(-0.410923\pi\) | ||||
0.276205 | + | 0.961099i | \(0.410923\pi\) | |||||||
\(332\) | 2.40685e6i | 0.0657711i | ||||||||
\(333\) | −5.52405e6 | −0.149598 | ||||||||
\(334\) | 1.43680e7i | 0.385618i | ||||||||
\(335\) | − 3.67421e7i | − 0.977303i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.66702e6 | −0.0958128 | −0.0479064 | − | 0.998852i | \(-0.515255\pi\) | ||||
−0.0479064 | + | 0.998852i | \(0.515255\pi\) | |||||||
\(338\) | −1.68841e7 | −0.437247 | ||||||||
\(339\) | − 4.14803e7i | − 1.06474i | ||||||||
\(340\) | −1.37706e7 | −0.350361 | ||||||||
\(341\) | 4.35067e7i | 1.09722i | ||||||||
\(342\) | − 1.19993e7i | − 0.299969i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.96672e7 | −0.974443 | ||||||||
\(345\) | 1.03359e7 | 0.251705 | ||||||||
\(346\) | − 4.53515e7i | − 1.09487i | ||||||||
\(347\) | 6.45603e6 | 0.154517 | 0.0772587 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772587 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(348\) | 7.09738e6i | 0.168407i | ||||||||
\(349\) | − 4.01536e7i | − 0.944600i | −0.881438 | − | 0.472300i | \(-0.843424\pi\) | ||||
0.881438 | − | 0.472300i | \(-0.156576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.06345e7 | −0.245921 | ||||||||
\(352\) | 5.15150e7 | 1.18115 | ||||||||
\(353\) | − 8.11656e6i | − 0.184522i | −0.995735 | − | 0.0922610i | \(-0.970591\pi\) | ||||
0.995735 | − | 0.0922610i | \(-0.0294094\pi\) | |||||||
\(354\) | −6.16711e6 | −0.139018 | ||||||||
\(355\) | − 3.11831e7i | − 0.697001i | ||||||||
\(356\) | 5.46596e6i | 0.121148i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.52552e7 | 0.986324 | ||||||||
\(359\) | 3.69171e7 | 0.797893 | 0.398946 | − | 0.916974i | \(-0.369376\pi\) | ||||
0.398946 | + | 0.916974i | \(0.369376\pi\) | |||||||
\(360\) | − 8.76481e6i | − 0.187860i | ||||||||
\(361\) | −3.27752e7 | −0.696665 | ||||||||
\(362\) | 1.79962e7i | 0.379364i | ||||||||
\(363\) | 1.88091e7i | 0.393231i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.23487e7 | 0.459593 | ||||||||
\(366\) | 2.27383e7 | 0.463782 | ||||||||
\(367\) | − 1.97155e7i | − 0.398851i | −0.979913 | − | 0.199425i | \(-0.936092\pi\) | ||||
0.979913 | − | 0.199425i | \(-0.0639076\pi\) | |||||||
\(368\) | −8.27750e6 | −0.166095 | ||||||||
\(369\) | − 9.20902e6i | − 0.183288i | ||||||||
\(370\) | − 8.41387e6i | − 0.166108i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.31465e7 | 0.255377 | ||||||||
\(373\) | 1.04331e7 | 0.201041 | 0.100521 | − | 0.994935i | \(-0.467949\pi\) | ||||
0.100521 | + | 0.994935i | \(0.467949\pi\) | |||||||
\(374\) | 5.86323e7i | 1.12078i | ||||||||
\(375\) | 2.79405e7 | 0.529835 | ||||||||
\(376\) | − 7.49584e7i | − 1.41012i | ||||||||
\(377\) | 3.82101e7i | 0.713106i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.26018e7 | −0.966235 | −0.483118 | − | 0.875556i | \(-0.660496\pi\) | ||||
−0.483118 | + | 0.875556i | \(0.660496\pi\) | |||||||
\(380\) | −2.00142e7 | −0.364744 | ||||||||
\(381\) | − 1.74042e7i | − 0.314687i | ||||||||
\(382\) | 4.75792e7 | 0.853547 | ||||||||
\(383\) | 7.35366e7i | 1.30890i | 0.756104 | + | 0.654451i | \(0.227100\pi\) | ||||
−0.756104 | + | 0.654451i | \(0.772900\pi\) | |||||||
\(384\) | − 1.09566e7i | − 0.193500i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −994230. | −0.0172872 | ||||||||
\(387\) | −1.78960e7 | −0.308762 | ||||||||
\(388\) | 2.18080e7i | 0.373354i | ||||||||
\(389\) | 1.72139e7 | 0.292436 | 0.146218 | − | 0.989252i | \(-0.453290\pi\) | ||||
0.146218 | + | 0.989252i | \(0.453290\pi\) | |||||||
\(390\) | − 1.61978e7i | − 0.273062i | ||||||||
\(391\) | 6.08645e7i | 1.01820i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.46088e6 | −0.0734924 | ||||||||
\(394\) | 1.48861e7 | 0.243384 | ||||||||
\(395\) | 2.74577e7i | 0.445526i | ||||||||
\(396\) | 1.40283e7 | 0.225902 | ||||||||
\(397\) | − 6.13174e7i | − 0.979969i | −0.871731 | − | 0.489984i | \(-0.837002\pi\) | ||||
0.871731 | − | 0.489984i | \(-0.162998\pi\) | |||||||
\(398\) | − 3.33953e7i | − 0.529708i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.31354e6 | −0.145524 | ||||||||
\(401\) | −4.61470e7 | −0.715667 | −0.357833 | − | 0.933785i | \(-0.616484\pi\) | ||||
−0.357833 | + | 0.933785i | \(0.616484\pi\) | |||||||
\(402\) | 4.72717e7i | 0.727651i | ||||||||
\(403\) | 7.07767e7 | 1.08137 | ||||||||
\(404\) | 3.41408e7i | 0.517761i | ||||||||
\(405\) | − 3.95428e6i | − 0.0595254i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.92307e7 | 0.581892 | ||||||||
\(408\) | 5.16128e7 | 0.759936 | ||||||||
\(409\) | 6.06926e7i | 0.887086i | 0.896253 | + | 0.443543i | \(0.146279\pi\) | ||||
−0.896253 | + | 0.443543i | \(0.853721\pi\) | |||||||
\(410\) | 1.40266e7 | 0.203517 | ||||||||
\(411\) | − 5.82062e7i | − 0.838386i | ||||||||
\(412\) | − 1.40274e7i | − 0.200579i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.32980e7 | −0.187407 | ||||||||
\(415\) | −4.81814e6 | −0.0674116 | ||||||||
\(416\) | − 8.38045e7i | − 1.16409i | ||||||||
\(417\) | 9.63703e6 | 0.132903 | ||||||||
\(418\) | 8.52163e7i | 1.16679i | ||||||||
\(419\) | − 1.17371e8i | − 1.59558i | −0.602939 | − | 0.797788i | \(-0.706004\pi\) | ||||
0.602939 | − | 0.797788i | \(-0.293996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28510e7 | −0.172222 | −0.0861111 | − | 0.996286i | \(-0.527444\pi\) | ||||
−0.0861111 | + | 0.996286i | \(0.527444\pi\) | |||||||
\(422\) | −7.63351e7 | −1.01575 | ||||||||
\(423\) | − 3.38178e7i | − 0.446811i | ||||||||
\(424\) | 8.89668e6 | 0.116716 | ||||||||
\(425\) | 6.84824e7i | 0.892098i | ||||||||
\(426\) | 4.01196e7i | 0.518953i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.40101e7 | −0.943973 | ||||||||
\(429\) | 7.55241e7 | 0.956564 | ||||||||
\(430\) | − 2.72581e7i | − 0.342838i | ||||||||
\(431\) | −1.13856e8 | −1.42209 | −0.711043 | − | 0.703149i | \(-0.751777\pi\) | ||||
−0.711043 | + | 0.703149i | \(0.751777\pi\) | |||||||
\(432\) | 3.16678e6i | 0.0392795i | ||||||||
\(433\) | − 2.76112e7i | − 0.340111i | −0.985434 | − | 0.170056i | \(-0.945605\pi\) | ||||
0.985434 | − | 0.170056i | \(-0.0543947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.42078e7 | −0.172608 | ||||||||
\(436\) | −2.56214e7 | −0.309132 | ||||||||
\(437\) | 8.84607e7i | 1.06000i | ||||||||
\(438\) | −2.87535e7 | −0.342190 | ||||||||
\(439\) | 7.18746e7i | 0.849536i | 0.905302 | + | 0.424768i | \(0.139644\pi\) | ||||
−0.905302 | + | 0.424768i | \(0.860356\pi\) | |||||||
\(440\) | 6.22459e7i | 0.730723i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.53829e7 | 1.10460 | ||||||||
\(443\) | −9.50290e7 | −1.09306 | −0.546531 | − | 0.837439i | \(-0.684052\pi\) | ||||
−0.546531 | + | 0.837439i | \(0.684052\pi\) | |||||||
\(444\) | − 1.18544e7i | − 0.135435i | ||||||||
\(445\) | −1.09420e7 | −0.124170 | ||||||||
\(446\) | 5.42420e7i | 0.611408i | ||||||||
\(447\) | 5.80389e7i | 0.649825i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.15401e8 | 1.27488 | 0.637440 | − | 0.770500i | \(-0.279993\pi\) | ||||
0.637440 | + | 0.770500i | \(0.279993\pi\) | |||||||
\(450\) | −1.49624e7 | −0.164197 | ||||||||
\(451\) | 6.54006e7i | 0.712938i | ||||||||
\(452\) | 8.90151e7 | 0.963937 | ||||||||
\(453\) | − 3.97816e7i | − 0.427944i | ||||||||
\(454\) | 8.05522e7i | 0.860815i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.50142e7 | 0.791132 | ||||||||
\(457\) | 9.17526e6 | 0.0961324 | 0.0480662 | − | 0.998844i | \(-0.484694\pi\) | ||||
0.0480662 | + | 0.998844i | \(0.484694\pi\) | |||||||
\(458\) | 8.12384e7i | 0.845600i | ||||||||
\(459\) | 2.32853e7 | 0.240793 | ||||||||
\(460\) | 2.21805e7i | 0.227876i | ||||||||
\(461\) | − 5.79354e7i | − 0.591346i | −0.955289 | − | 0.295673i | \(-0.904456\pi\) | ||||
0.955289 | − | 0.295673i | \(-0.0955438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51781e7 | 0.656687 | 0.328344 | − | 0.944558i | \(-0.393510\pi\) | ||||
0.328344 | + | 0.944558i | \(0.393510\pi\) | |||||||
\(464\) | 1.13783e7 | 0.113900 | ||||||||
\(465\) | 2.63172e7i | 0.261747i | ||||||||
\(466\) | 3.17910e7 | 0.314157 | ||||||||
\(467\) | − 1.69452e8i | − 1.66378i | −0.554943 | − | 0.831888i | \(-0.687260\pi\) | ||||
0.554943 | − | 0.831888i | \(-0.312740\pi\) | |||||||
\(468\) | − 2.28213e7i | − 0.222640i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.15090e7 | 0.496123 | ||||||||
\(471\) | −1.05670e8 | −1.01132 | ||||||||
\(472\) | − 3.85541e7i | − 0.366644i | ||||||||
\(473\) | 1.27094e8 | 1.20100 | ||||||||
\(474\) | − 3.53266e7i | − 0.331717i | ||||||||
\(475\) | 9.95326e7i | 0.928719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.01377e6 | 0.0369826 | ||||||||
\(478\) | 8.85244e7 | 0.810549 | ||||||||
\(479\) | 9.15319e7i | 0.832848i | 0.909171 | + | 0.416424i | \(0.136717\pi\) | ||||
−0.909171 | + | 0.416424i | \(0.863283\pi\) | |||||||
\(480\) | 3.11614e7 | 0.281769 | ||||||||
\(481\) | − 6.38205e7i | − 0.573488i | ||||||||
\(482\) | 1.42710e8i | 1.27443i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.03636e7 | −0.356003 | ||||||||
\(485\) | −4.36561e7 | −0.382666 | ||||||||
\(486\) | 5.08751e6i | 0.0443197i | ||||||||
\(487\) | −1.31240e8 | −1.13626 | −0.568131 | − | 0.822938i | \(-0.692333\pi\) | ||||
−0.568131 | + | 0.822938i | \(0.692333\pi\) | |||||||
\(488\) | 1.42150e8i | 1.22317i | ||||||||
\(489\) | − 1.28939e8i | − 1.10270i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.81776e7 | −0.744927 | −0.372463 | − | 0.928047i | \(-0.621487\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621487\pi\) | |||||||
\(492\) | 1.97622e7 | 0.165936 | ||||||||
\(493\) | − 8.36648e7i | − 0.698235i | ||||||||
\(494\) | 1.38630e8 | 1.14994 | ||||||||
\(495\) | 2.80825e7i | 0.231537i | ||||||||
\(496\) | − 2.10761e7i | − 0.172721i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.19894e6 | 0.0501914 | ||||||||
\(499\) | −2.28471e8 | −1.83878 | −0.919389 | − | 0.393350i | \(-0.871316\pi\) | ||||
−0.919389 | + | 0.393350i | \(0.871316\pi\) | |||||||
\(500\) | 5.99592e7i | 0.479674i | ||||||||
\(501\) | −4.05238e7 | −0.322253 | ||||||||
\(502\) | − 5.26122e7i | − 0.415887i | ||||||||
\(503\) | − 2.07735e8i | − 1.63232i | −0.577824 | − | 0.816161i | \(-0.696098\pi\) | ||||
0.577824 | − | 0.816161i | \(-0.303902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.83444e7 | −0.530675 | ||||||||
\(506\) | 9.44398e7 | 0.728960 | ||||||||
\(507\) | − 4.76201e7i | − 0.365398i | ||||||||
\(508\) | 3.73488e7 | 0.284895 | ||||||||
\(509\) | − 5.48436e7i | − 0.415885i | −0.978141 | − | 0.207942i | \(-0.933323\pi\) | ||||
0.978141 | − | 0.207942i | \(-0.0666767\pi\) | |||||||
\(510\) | 3.54667e7i | 0.267368i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.37739e7 | −0.400647 | ||||||||
\(513\) | 3.38430e7 | 0.250678 | ||||||||
\(514\) | 1.23729e8i | 0.911137i | ||||||||
\(515\) | 2.80806e7 | 0.205582 | ||||||||
\(516\) | − 3.84042e7i | − 0.279531i | ||||||||
\(517\) | 2.40167e8i | 1.73797i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.27910e8 | 0.914962 | ||||||||
\(520\) | 1.01262e8 | 0.720169 | ||||||||
\(521\) | 2.85252e7i | 0.201704i | 0.994901 | + | 0.100852i | \(0.0321569\pi\) | ||||
−0.994901 | + | 0.100852i | \(0.967843\pi\) | |||||||
\(522\) | 1.82796e7 | 0.128515 | ||||||||
\(523\) | − 1.07664e8i | − 0.752599i | −0.926498 | − | 0.376300i | \(-0.877196\pi\) | ||||
0.926498 | − | 0.376300i | \(-0.122804\pi\) | |||||||
\(524\) | − 9.57287e6i | − 0.0665347i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.79958e7 | 0.398510 | ||||||||
\(527\) | −1.54973e8 | −1.05882 | ||||||||
\(528\) | − 2.24898e7i | − 0.152786i | ||||||||
\(529\) | −5.00006e7 | −0.337760 | ||||||||
\(530\) | 6.11352e6i | 0.0410642i | ||||||||
\(531\) | − 1.73938e7i | − 0.116175i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06394e8 | 0.702642 | ||||||||
\(534\) | 1.40778e7 | 0.0924507 | ||||||||
\(535\) | − 1.48156e8i | − 0.967518i | ||||||||
\(536\) | −2.95522e8 | −1.91909 | ||||||||
\(537\) | 1.27639e8i | 0.824251i | ||||||||
\(538\) | − 1.49125e8i | − 0.957640i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.48574e6 | 0.0538900 | ||||||||
\(541\) | 5.55754e7 | 0.350987 | 0.175493 | − | 0.984481i | \(-0.443848\pi\) | ||||
0.175493 | + | 0.984481i | \(0.443848\pi\) | |||||||
\(542\) | − 7.01736e6i | − 0.0440734i | ||||||||
\(543\) | −5.07569e7 | −0.317026 | ||||||||
\(544\) | 1.83498e8i | 1.13982i | ||||||||
\(545\) | − 5.12900e7i | − 0.316842i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.44170e7 | 0.332485 | 0.166243 | − | 0.986085i | \(-0.446837\pi\) | ||||
0.166243 | + | 0.986085i | \(0.446837\pi\) | |||||||
\(548\) | 1.24908e8 | 0.759014 | ||||||||
\(549\) | 6.41315e7i | 0.387573i | ||||||||
\(550\) | 1.06260e8 | 0.638679 | ||||||||
\(551\) | − 1.21599e8i | − 0.726899i | ||||||||
\(552\) | − 8.31335e7i | − 0.494264i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.70327e7 | −0.217799 | ||||||||
\(555\) | 2.37306e7 | 0.138813 | ||||||||
\(556\) | 2.06807e7i | 0.120321i | ||||||||
\(557\) | 1.25227e7 | 0.0724657 | 0.0362329 | − | 0.999343i | \(-0.488464\pi\) | ||||
0.0362329 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(558\) | − 3.38593e7i | − 0.194884i | ||||||||
\(559\) | − 2.06756e8i | − 1.18365i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65368e8 | −0.936616 | ||||||||
\(562\) | −1.77417e6 | −0.00999508 | ||||||||
\(563\) | − 1.74062e8i | − 0.975391i | −0.873014 | − | 0.487695i | \(-0.837838\pi\) | ||||
0.873014 | − | 0.487695i | \(-0.162162\pi\) | |||||||
\(564\) | 7.25717e7 | 0.404510 | ||||||||
\(565\) | 1.78194e8i | 0.987980i | ||||||||
\(566\) | − 1.76981e7i | − 0.0976060i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.50810e8 | −1.36868 | ||||||||
\(569\) | 4.75605e7 | 0.258172 | 0.129086 | − | 0.991633i | \(-0.458796\pi\) | ||||
0.129086 | + | 0.991633i | \(0.458796\pi\) | |||||||
\(570\) | 5.15474e7i | 0.278344i | ||||||||
\(571\) | 1.65541e8 | 0.889198 | 0.444599 | − | 0.895730i | \(-0.353346\pi\) | ||||
0.444599 | + | 0.895730i | \(0.353346\pi\) | |||||||
\(572\) | 1.62072e8i | 0.866004i | ||||||||
\(573\) | 1.34193e8i | 0.713291i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.10306e8 | 0.580222 | ||||||||
\(576\) | −5.30933e7 | −0.277825 | ||||||||
\(577\) | 5.13486e7i | 0.267301i | 0.991029 | + | 0.133651i | \(0.0426700\pi\) | ||||
−0.991029 | + | 0.133651i | \(0.957330\pi\) | |||||||
\(578\) | −7.54419e7 | −0.390687 | ||||||||
\(579\) | − 2.80414e6i | − 0.0144466i | ||||||||
\(580\) | − 3.04895e7i | − 0.156267i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.61673e7 | 0.284914 | ||||||||
\(583\) | −2.85050e7 | −0.143852 | ||||||||
\(584\) | − 1.79754e8i | − 0.902486i | ||||||||
\(585\) | 4.56845e7 | 0.228193 | ||||||||
\(586\) | − 1.47814e7i | − 0.0734552i | ||||||||
\(587\) | 2.37624e8i | 1.17483i | 0.809285 | + | 0.587416i | \(0.199855\pi\) | ||||
−0.809285 | + | 0.587416i | \(0.800145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.25238e8 | −1.10229 | ||||||||
\(590\) | 2.64931e7 | 0.128996 | ||||||||
\(591\) | 4.19849e7i | 0.203391i | ||||||||
\(592\) | −1.90046e7 | −0.0915998 | ||||||||
\(593\) | − 3.70225e8i | − 1.77542i | −0.460401 | − | 0.887711i | \(-0.652295\pi\) | ||||
0.460401 | − | 0.887711i | \(-0.347705\pi\) | |||||||
\(594\) | − 3.61305e7i | − 0.172391i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.24549e8 | −0.588305 | ||||||||
\(597\) | 9.41888e7 | 0.442666 | ||||||||
\(598\) | − 1.53635e8i | − 0.718432i | ||||||||
\(599\) | −3.75877e7 | −0.174890 | −0.0874451 | − | 0.996169i | \(-0.527870\pi\) | ||||
−0.0874451 | + | 0.996169i | \(0.527870\pi\) | |||||||
\(600\) | − 9.35387e7i | − 0.433049i | ||||||||
\(601\) | 2.67605e7i | 0.123274i | 0.998099 | + | 0.0616369i | \(0.0196321\pi\) | ||||
−0.998099 | + | 0.0616369i | \(0.980368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.33326e8 | −0.608083 | ||||||||
\(604\) | 8.53698e7 | 0.387430 | ||||||||
\(605\) | − 8.08015e7i | − 0.364883i | ||||||||
\(606\) | 8.79307e7 | 0.395114 | ||||||||
\(607\) | 7.72576e7i | 0.345442i | 0.984971 | + | 0.172721i | \(0.0552559\pi\) | ||||
−0.984971 | + | 0.172721i | \(0.944744\pi\) | |||||||
\(608\) | 2.66697e8i | 1.18661i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.76808e7 | −0.430348 | ||||||||
\(611\) | 3.90703e8 | 1.71287 | ||||||||
\(612\) | 4.99694e7i | 0.217997i | ||||||||
\(613\) | −3.52971e8 | −1.53235 | −0.766174 | − | 0.642633i | \(-0.777842\pi\) | ||||
−0.766174 | + | 0.642633i | \(0.777842\pi\) | |||||||
\(614\) | 1.09858e8i | 0.474597i | ||||||||
\(615\) | 3.95608e7i | 0.170075i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.82109e8 | 0.775310 | 0.387655 | − | 0.921805i | \(-0.373285\pi\) | ||||
0.387655 | + | 0.921805i | \(0.373285\pi\) | |||||||
\(618\) | −3.61280e7 | −0.153066 | ||||||||
\(619\) | − 9.73800e7i | − 0.410580i | −0.978701 | − | 0.205290i | \(-0.934186\pi\) | ||||
0.978701 | − | 0.205290i | \(-0.0658137\pi\) | |||||||
\(620\) | −5.64757e7 | −0.236966 | ||||||||
\(621\) | − 3.75060e7i | − 0.156612i | ||||||||
\(622\) | 8.71661e7i | 0.362223i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.65864e7 | −0.150579 | ||||||||
\(625\) | 5.40422e7 | 0.221357 | ||||||||
\(626\) | − 5.83279e7i | − 0.237768i | ||||||||
\(627\) | −2.40346e8 | −0.975065 | ||||||||
\(628\) | − 2.26765e8i | − 0.915580i | ||||||||
\(629\) | 1.39741e8i | 0.561529i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.37285e8 | −0.546430 | −0.273215 | − | 0.961953i | \(-0.588087\pi\) | ||||
−0.273215 | + | 0.961953i | \(0.588087\pi\) | |||||||
\(632\) | 2.20847e8 | 0.874862 | ||||||||
\(633\) | − 2.15297e8i | − 0.848842i | ||||||||
\(634\) | −1.78648e8 | −0.701019 | ||||||||
\(635\) | 7.47663e7i | 0.292001i | ||||||||
\(636\) | 8.61341e6i | 0.0334814i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.29818e8 | −0.499887 | ||||||||
\(639\) | −1.13154e8 | −0.433678 | ||||||||
\(640\) | 4.70681e7i | 0.179551i | ||||||||
\(641\) | −2.09345e8 | −0.794857 | −0.397428 | − | 0.917633i | \(-0.630097\pi\) | ||||
−0.397428 | + | 0.917633i | \(0.630097\pi\) | |||||||
\(642\) | 1.90616e8i | 0.720366i | ||||||||
\(643\) | − 3.49818e8i | − 1.31586i | −0.753079 | − | 0.657930i | \(-0.771432\pi\) | ||||
0.753079 | − | 0.657930i | \(-0.228568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.68791e7 | 0.286503 | ||||||||
\(646\) | −3.03544e8 | −1.12596 | ||||||||
\(647\) | − 3.69732e8i | − 1.36513i | −0.730824 | − | 0.682566i | \(-0.760864\pi\) | ||||
0.730824 | − | 0.682566i | \(-0.239136\pi\) | |||||||
\(648\) | −3.18049e7 | −0.116888 | ||||||||
\(649\) | 1.23527e8i | 0.451886i | ||||||||
\(650\) | − 1.72864e8i | − 0.629454i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.76697e8 | 0.998303 | ||||||||
\(653\) | −3.95246e7 | −0.141947 | −0.0709737 | − | 0.997478i | \(-0.522611\pi\) | ||||
−0.0709737 | + | 0.997478i | \(0.522611\pi\) | |||||||
\(654\) | 6.59888e7i | 0.235905i | ||||||||
\(655\) | 1.91634e7 | 0.0681943 | ||||||||
\(656\) | − 3.16822e7i | − 0.112229i | ||||||||
\(657\) | − 8.10968e7i | − 0.285962i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.29124e8 | −1.15002 | −0.575008 | − | 0.818148i | \(-0.695001\pi\) | ||||
−0.575008 | + | 0.818148i | \(0.695001\pi\) | |||||||
\(660\) | −6.02639e7 | −0.209617 | ||||||||
\(661\) | 1.60841e8i | 0.556919i | 0.960448 | + | 0.278460i | \(0.0898238\pi\) | ||||
−0.960448 | + | 0.278460i | \(0.910176\pi\) | |||||||
\(662\) | 1.10722e8 | 0.381646 | ||||||||
\(663\) | 2.69020e8i | 0.923089i | ||||||||
\(664\) | 3.87530e7i | 0.132374i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.05315e7 | −0.103353 | ||||||||
\(667\) | −1.34760e8 | −0.454134 | ||||||||
\(668\) | − 8.69625e7i | − 0.291744i | ||||||||
\(669\) | −1.52985e8 | −0.510941 | ||||||||
\(670\) | − 2.03073e8i | − 0.675194i | ||||||||
\(671\) | − 4.55448e8i | − 1.50755i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.32162e8 | 1.74582 | 0.872908 | − | 0.487886i | \(-0.162232\pi\) | ||||
0.872908 | + | 0.487886i | \(0.162232\pi\) | |||||||
\(674\) | −2.02676e7 | −0.0661947 | ||||||||
\(675\) | − 4.22003e7i | − 0.137216i | ||||||||
\(676\) | 1.02191e8 | 0.330805 | ||||||||
\(677\) | − 5.41413e8i | − 1.74487i | −0.488730 | − | 0.872435i | \(-0.662540\pi\) | ||||
0.488730 | − | 0.872435i | \(-0.337460\pi\) | |||||||
\(678\) | − 2.29262e8i | − 0.735601i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.21722e8 | −0.705151 | ||||||||
\(681\) | −2.27191e8 | −0.719365 | ||||||||
\(682\) | 2.40462e8i | 0.758041i | ||||||||
\(683\) | 2.48939e8 | 0.781323 | 0.390662 | − | 0.920534i | \(-0.372246\pi\) | ||||
0.390662 | + | 0.920534i | \(0.372246\pi\) | |||||||
\(684\) | 7.26257e7i | 0.226946i | ||||||||
\(685\) | 2.50047e8i | 0.777946i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.29126e8 | −0.706651 | ||||||||
\(688\) | −6.15685e7 | −0.189057 | ||||||||
\(689\) | 4.63719e7i | 0.141774i | ||||||||
\(690\) | 5.71267e7 | 0.173897 | ||||||||
\(691\) | 9.24413e7i | 0.280177i | 0.990139 | + | 0.140088i | \(0.0447386\pi\) | ||||
−0.990139 | + | 0.140088i | \(0.955261\pi\) | |||||||
\(692\) | 2.74491e8i | 0.828341i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.56825e7 | 0.106752 | ||||||||
\(695\) | −4.13995e7 | −0.123322 | ||||||||
\(696\) | 1.14276e8i | 0.338943i | ||||||||
\(697\) | −2.32959e8 | −0.687989 | ||||||||
\(698\) | − 2.21929e8i | − 0.652601i | ||||||||
\(699\) | 8.96640e7i | 0.262535i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.38435e8 | 1.56307 | 0.781537 | − | 0.623859i | \(-0.214436\pi\) | ||||
0.781537 | + | 0.623859i | \(0.214436\pi\) | |||||||
\(702\) | −5.87770e7 | −0.169901 | ||||||||
\(703\) | 2.03100e8i | 0.584581i | ||||||||
\(704\) | 3.77057e8 | 1.08066 | ||||||||
\(705\) | 1.45277e8i | 0.414600i | ||||||||
\(706\) | − 4.48603e7i | − 0.127482i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.73265e7 | 0.105176 | ||||||||
\(709\) | 7.06910e7 | 0.198347 | 0.0991735 | − | 0.995070i | \(-0.468380\pi\) | ||||
0.0991735 | + | 0.995070i | \(0.468380\pi\) | |||||||
\(710\) | − 1.72349e8i | − 0.481541i | ||||||||
\(711\) | 9.96359e7 | 0.277209 | ||||||||
\(712\) | 8.80081e7i | 0.243828i | ||||||||
\(713\) | 2.49616e8i | 0.688660i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.24442e8 | −0.887604 | ||||||||
\(716\) | −2.73908e8 | −0.746217 | ||||||||
\(717\) | 2.49676e8i | 0.677359i | ||||||||
\(718\) | 2.04041e8 | 0.551245 | ||||||||
\(719\) | − 3.91374e8i | − 1.05294i | −0.850193 | − | 0.526472i | \(-0.823515\pi\) | ||||
0.850193 | − | 0.526472i | \(-0.176485\pi\) | |||||||
\(720\) | − 1.36041e7i | − 0.0364478i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.81149e8 | −0.481309 | ||||||||
\(723\) | −4.02503e8 | −1.06501 | ||||||||
\(724\) | − 1.08922e8i | − 0.287013i | ||||||||
\(725\) | −1.51627e8 | −0.397889 | ||||||||
\(726\) | 1.03958e8i | 0.271674i | ||||||||
\(727\) | − 4.83550e8i | − 1.25846i | −0.777221 | − | 0.629228i | \(-0.783371\pi\) | ||||
0.777221 | − | 0.629228i | \(-0.216629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 1.23521e8 | 0.317522 | ||||||||
\(731\) | 4.52713e8i | 1.15897i | ||||||||
\(732\) | −1.37624e8 | −0.350881 | ||||||||
\(733\) | − 3.19519e8i | − 0.811305i | −0.914027 | − | 0.405653i | \(-0.867044\pi\) | ||||
0.914027 | − | 0.405653i | \(-0.132956\pi\) | |||||||
\(734\) | − 1.08968e8i | − 0.275556i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.95563e8 | 0.741339 | ||||||||
\(737\) | 9.46854e8 | 2.36527 | ||||||||
\(738\) | − 5.08983e7i | − 0.126629i | ||||||||
\(739\) | 3.53513e8 | 0.875935 | 0.437968 | − | 0.898991i | \(-0.355698\pi\) | ||||
0.437968 | + | 0.898991i | \(0.355698\pi\) | |||||||
\(740\) | 5.09251e7i | 0.125671i | ||||||||
\(741\) | 3.90994e8i | 0.960983i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.63396e8 | 1.12976 | 0.564880 | − | 0.825173i | \(-0.308923\pi\) | ||||
0.564880 | + | 0.825173i | \(0.308923\pi\) | |||||||
\(744\) | 2.11674e8 | 0.513982 | ||||||||
\(745\) | − 2.49328e8i | − 0.602978i | ||||||||
\(746\) | 5.76636e7 | 0.138894 | ||||||||
\(747\) | 1.74836e7i | 0.0419439i | ||||||||
\(748\) | − 3.54873e8i | − 0.847945i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.54427e8 | 0.366050 | ||||||||
\(751\) | −2.97019e7 | −0.0701237 | −0.0350618 | − | 0.999385i | \(-0.511163\pi\) | ||||
−0.0350618 | + | 0.999385i | \(0.511163\pi\) | |||||||
\(752\) | − 1.16345e8i | − 0.273586i | ||||||||
\(753\) | 1.48388e8 | 0.347548 | ||||||||
\(754\) | 2.11187e8i | 0.492667i | ||||||||
\(755\) | 1.70897e8i | 0.397093i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.11235e8 | 1.63955 | 0.819776 | − | 0.572684i | \(-0.194098\pi\) | ||||
0.819776 | + | 0.572684i | \(0.194098\pi\) | |||||||
\(758\) | −2.90730e8 | −0.667548 | ||||||||
\(759\) | 2.66360e8i | 0.609177i | ||||||||
\(760\) | −3.22252e8 | −0.734099 | ||||||||
\(761\) | 3.67489e8i | 0.833856i | 0.908940 | + | 0.416928i | \(0.136893\pi\) | ||||
−0.908940 | + | 0.416928i | \(0.863107\pi\) | |||||||
\(762\) | − 9.61931e7i | − 0.217410i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87974e8 | −0.645763 | ||||||||
\(765\) | −1.00031e8 | −0.223434 | ||||||||
\(766\) | 4.06437e8i | 0.904288i | ||||||||
\(767\) | 2.00954e8 | 0.445360 | ||||||||
\(768\) | − 2.78537e8i | − 0.614892i | ||||||||
\(769\) | 3.18891e8i | 0.701235i | 0.936519 | + | 0.350617i | \(0.114028\pi\) | ||||
−0.936519 | + | 0.350617i | \(0.885972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.48969e8 | −0.761419 | ||||||||
\(772\) | 6.01759e6 | 0.0130789 | ||||||||
\(773\) | − 1.56061e8i | − 0.337876i | −0.985627 | − | 0.168938i | \(-0.945966\pi\) | ||||
0.985627 | − | 0.168938i | \(-0.0540337\pi\) | |||||||
\(774\) | −9.89114e7 | −0.213316 | ||||||||
\(775\) | 2.80859e8i | 0.603369i | ||||||||
\(776\) | 3.51133e8i | 0.751427i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.51413e7 | 0.202037 | ||||||||
\(779\) | −3.38584e8 | −0.716232 | ||||||||
\(780\) | 9.80373e7i | 0.206589i | ||||||||
\(781\) | 8.03597e8 | 1.68688 | ||||||||
\(782\) | 3.36398e8i | 0.703450i | ||||||||
\(783\) | 5.15560e7i | 0.107397i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.53947e8 | 0.938417 | ||||||||
\(786\) | −2.46553e7 | −0.0507741 | ||||||||
\(787\) | 7.50607e8i | 1.53988i | 0.638114 | + | 0.769942i | \(0.279715\pi\) | ||||
−0.638114 | + | 0.769942i | \(0.720285\pi\) | |||||||
\(788\) | −9.00981e7 | −0.184135 | ||||||||
\(789\) | 1.63572e8i | 0.333027i | ||||||||
\(790\) | 1.51759e8i | 0.307803i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.25872e8 | 0.454660 | ||||||||
\(793\) | −7.40923e8 | −1.48578 | ||||||||
\(794\) | − 3.38901e8i | − 0.677036i | ||||||||
\(795\) | −1.72427e7 | −0.0343165 | ||||||||
\(796\) | 2.02126e8i | 0.400758i | ||||||||
\(797\) | − 1.08408e6i | − 0.00214134i | −0.999999 | − | 0.00107067i | \(-0.999659\pi\) | ||||
0.999999 | − | 0.00107067i | \(-0.000340806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.55483e8 | −1.67715 | ||||||||
\(800\) | 3.32557e8 | 0.649524 | ||||||||
\(801\) | 3.97052e7i | 0.0772591i | ||||||||
\(802\) | −2.55055e8 | −0.494436 | ||||||||
\(803\) | 5.75933e8i | 1.11231i | ||||||||
\(804\) | − 2.86113e8i | − 0.550515i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.91183e8 | 0.747093 | ||||||||
\(807\) | 4.20594e8 | 0.800280 | ||||||||
\(808\) | 5.49705e8i | 1.04207i | ||||||||
\(809\) | 4.47774e8 | 0.845694 | 0.422847 | − | 0.906201i | \(-0.361031\pi\) | ||||
0.422847 | + | 0.906201i | \(0.361031\pi\) | |||||||
\(810\) | − 2.18553e7i | − 0.0411246i | ||||||||
\(811\) | 7.02416e8i | 1.31684i | 0.752652 | + | 0.658418i | \(0.228774\pi\) | ||||
−0.752652 | + | 0.658418i | \(0.771226\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.97919e7 | 0.0368312 | ||||||||
\(814\) | 2.16828e8 | 0.402015 | ||||||||
\(815\) | 5.53904e8i | 1.02320i | ||||||||
\(816\) | 8.01095e7 | 0.147439 | ||||||||
\(817\) | 6.57975e8i | 1.20654i | ||||||||
\(818\) | 3.35448e8i | 0.612866i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.48960e7 | −0.153973 | ||||||||
\(821\) | 6.63875e8 | 1.19966 | 0.599828 | − | 0.800129i | \(-0.295236\pi\) | ||||
0.599828 | + | 0.800129i | \(0.295236\pi\) | |||||||
\(822\) | − 3.21706e8i | − 0.579220i | ||||||||
\(823\) | 4.16855e8 | 0.747800 | 0.373900 | − | 0.927469i | \(-0.378020\pi\) | ||||
0.373900 | + | 0.927469i | \(0.378020\pi\) | |||||||
\(824\) | − 2.25857e8i | − 0.403693i | ||||||||
\(825\) | 2.99698e8i | 0.533731i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.14598e8 | 0.202609 | 0.101305 | − | 0.994855i | \(-0.467698\pi\) | ||||
0.101305 | + | 0.994855i | \(0.467698\pi\) | |||||||
\(828\) | 8.04865e7 | 0.141786 | ||||||||
\(829\) | − 4.68094e8i | − 0.821617i | −0.911722 | − | 0.410808i | \(-0.865246\pi\) | ||||
0.911722 | − | 0.410808i | \(-0.134754\pi\) | |||||||
\(830\) | −2.66299e7 | −0.0465730 | ||||||||
\(831\) | − 1.04448e8i | − 0.182010i | ||||||||
\(832\) | − 6.13397e8i | − 1.06505i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.32639e7 | 0.0918195 | ||||||||
\(835\) | 1.74085e8 | 0.299021 | ||||||||
\(836\) | − 5.15773e8i | − 0.882754i | ||||||||
\(837\) | 9.54973e7 | 0.162860 | ||||||||
\(838\) | − 6.48708e8i | − 1.10234i | ||||||||
\(839\) | − 6.49855e8i | − 1.10035i | −0.835050 | − | 0.550174i | \(-0.814561\pi\) | ||||
0.835050 | − | 0.550174i | \(-0.185439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.09581e8 | −0.688576 | ||||||||
\(842\) | −7.10272e7 | −0.118984 | ||||||||
\(843\) | − 5.00390e6i | − 0.00835268i | ||||||||
\(844\) | 4.62019e8 | 0.768480 | ||||||||
\(845\) | 2.04570e8i | 0.339056i | ||||||||
\(846\) | − 1.86911e8i | − 0.308691i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.38088e7 | 0.0226447 | ||||||||
\(849\) | 4.99160e7 | 0.0815673 | ||||||||
\(850\) | 3.78503e8i | 0.616328i | ||||||||
\(851\) | 2.25083e8 | 0.365220 | ||||||||
\(852\) | − 2.42824e8i | − 0.392621i | ||||||||
\(853\) | 7.47082e7i | 0.120371i | 0.998187 | + | 0.0601854i | \(0.0191692\pi\) | ||||
−0.998187 | + | 0.0601854i | \(0.980831\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.45385e8 | −0.232606 | ||||||||
\(856\) | −1.19165e9 | −1.89988 | ||||||||
\(857\) | 8.66704e8i | 1.37698i | 0.725245 | + | 0.688491i | \(0.241727\pi\) | ||||
−0.725245 | + | 0.688491i | \(0.758273\pi\) | |||||||
\(858\) | 4.17422e8 | 0.660866 | ||||||||
\(859\) | − 1.74675e7i | − 0.0275583i | −0.999905 | − | 0.0137791i | \(-0.995614\pi\) | ||||
0.999905 | − | 0.0137791i | \(-0.00438617\pi\) | |||||||
\(860\) | 1.64980e8i | 0.259379i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.29285e8 | −0.982484 | ||||||||
\(863\) | −1.11908e9 | −1.74113 | −0.870563 | − | 0.492056i | \(-0.836245\pi\) | ||||
−0.870563 | + | 0.492056i | \(0.836245\pi\) | |||||||
\(864\) | − 1.13075e8i | − 0.175318i | ||||||||
\(865\) | −5.49486e8 | −0.849002 | ||||||||
\(866\) | − 1.52607e8i | − 0.234974i | ||||||||
\(867\) | − 2.12778e8i | − 0.326489i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.07593e8 | −1.07826 | ||||||||
\(870\) | −7.85267e7 | −0.119250 | ||||||||
\(871\) | − 1.54034e9i | − 2.33111i | ||||||||
\(872\) | −4.12533e8 | −0.622171 | ||||||||
\(873\) | 1.58415e8i | 0.238097i | ||||||||
\(874\) | 4.88922e8i | 0.732328i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.74031e8 | 0.258889 | ||||||||
\(877\) | 1.16546e9 | 1.72782 | 0.863910 | − | 0.503646i | \(-0.168008\pi\) | ||||
0.863910 | + | 0.503646i | \(0.168008\pi\) | |||||||
\(878\) | 3.97251e8i | 0.586923i | ||||||||
\(879\) | 4.16897e7 | 0.0613850 | ||||||||
\(880\) | 9.66134e7i | 0.141772i | ||||||||
\(881\) | − 2.07806e8i | − 0.303900i | −0.988388 | − | 0.151950i | \(-0.951445\pi\) | ||||
0.988388 | − | 0.151950i | \(-0.0485553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.48816e8 | −0.506657 | −0.253329 | − | 0.967380i | \(-0.581525\pi\) | ||||
−0.253329 | + | 0.967380i | \(0.581525\pi\) | |||||||
\(884\) | −5.77306e8 | −0.835698 | ||||||||
\(885\) | 7.47217e7i | 0.107800i | ||||||||
\(886\) | −5.25225e8 | −0.755170 | ||||||||
\(887\) | − 8.44527e8i | − 1.21016i | −0.796165 | − | 0.605080i | \(-0.793141\pi\) | ||||
0.796165 | − | 0.605080i | \(-0.206859\pi\) | |||||||
\(888\) | − 1.90869e8i | − 0.272582i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.04764e7 | −0.0857858 | ||||||||
\(891\) | 1.01903e8 | 0.144063 | ||||||||
\(892\) | − 3.28300e8i | − 0.462569i | ||||||||
\(893\) | −1.24336e9 | −1.74600 | ||||||||
\(894\) | 3.20781e8i | 0.448948i | ||||||||
\(895\) | − 5.48320e8i | − 0.764830i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.33314e8 | 0.600379 | ||||||||
\(898\) | 6.37820e8 | 0.880783 | ||||||||
\(899\) | − 3.43125e8i | − 0.472251i | ||||||||
\(900\) | 9.05603e7 | 0.124225 | ||||||||
\(901\) | − 1.01536e8i | − 0.138818i | ||||||||
\(902\) | 3.61469e8i | 0.492552i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.43324e9 | 1.94006 | ||||||||
\(905\) | 2.18045e8 | 0.294172 | ||||||||
\(906\) | − 2.19873e8i | − 0.295656i | ||||||||
\(907\) | −7.99849e8 | −1.07198 | −0.535989 | − | 0.844225i | \(-0.680061\pi\) | ||||
−0.535989 | + | 0.844225i | \(0.680061\pi\) | |||||||
\(908\) | − 4.87543e8i | − 0.651261i | ||||||||
\(909\) | 2.48001e8i | 0.330189i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.54047e8 | 0.203750 | 0.101875 | − | 0.994797i | \(-0.467516\pi\) | ||||
0.101875 | + | 0.994797i | \(0.467516\pi\) | |||||||
\(912\) | 1.16431e8 | 0.153492 | ||||||||
\(913\) | − 1.24165e8i | − 0.163150i | ||||||||
\(914\) | 5.07117e7 | 0.0664155 | ||||||||
\(915\) | − 2.75501e8i | − 0.359633i | ||||||||
\(916\) | − 4.91697e8i | − 0.639751i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.28698e8 | 0.166358 | ||||||||
\(919\) | 6.87088e8 | 0.885250 | 0.442625 | − | 0.896707i | \(-0.354047\pi\) | ||||
0.442625 | + | 0.896707i | \(0.354047\pi\) | |||||||
\(920\) | 3.57131e8i | 0.458632i | ||||||||
\(921\) | −3.09844e8 | −0.396611 | ||||||||
\(922\) | − 3.20209e8i | − 0.408546i | ||||||||
\(923\) | − 1.30729e9i | − 1.66252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53255e8 | 0.319987 | ||||||||
\(926\) | 3.60239e8 | 0.453689 | ||||||||
\(927\) | − 1.01896e8i | − 0.127914i | ||||||||
\(928\) | −4.06283e8 | −0.508376 | ||||||||
\(929\) | 3.78043e8i | 0.471513i | 0.971812 | + | 0.235757i | \(0.0757568\pi\) | ||||
−0.971812 | + | 0.235757i | \(0.924243\pi\) | |||||||
\(930\) | 1.45455e8i | 0.180834i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.92416e8 | −0.237680 | ||||||||
\(933\) | −2.45845e8 | −0.302703 | ||||||||
\(934\) | − 9.36559e8i | − 1.14946i | ||||||||
\(935\) | 7.10398e8 | 0.869095 | ||||||||
\(936\) | − 3.67448e8i | − 0.448093i | ||||||||
\(937\) | 1.27190e9i | 1.54609i | 0.634351 | + | 0.773045i | \(0.281268\pi\) | ||||
−0.634351 | + | 0.773045i | \(0.718732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.64509e8 | 0.198698 | ||||||||
\(940\) | −3.11759e8 | −0.375349 | ||||||||
\(941\) | 6.98803e8i | 0.838660i | 0.907834 | + | 0.419330i | \(0.137735\pi\) | ||||
−0.907834 | + | 0.419330i | \(0.862265\pi\) | |||||||
\(942\) | −5.84040e8 | −0.698699 | ||||||||
\(943\) | 3.75231e8i | 0.447470i | ||||||||
\(944\) | − 5.98408e7i | − 0.0711346i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.02448e8 | 0.829738 | ||||||||
\(947\) | −3.91438e8 | −0.460907 | −0.230453 | − | 0.973083i | \(-0.574021\pi\) | ||||
−0.230453 | + | 0.973083i | \(0.574021\pi\) | |||||||
\(948\) | 2.13815e8i | 0.250965i | ||||||||
\(949\) | 9.36927e8 | 1.09624 | ||||||||
\(950\) | 5.50117e8i | 0.641629i | ||||||||
\(951\) | − 5.03861e8i | − 0.585827i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.05418e8 | −1.04609 | −0.523047 | − | 0.852304i | \(-0.675205\pi\) | ||||
−0.523047 | + | 0.852304i | \(0.675205\pi\) | |||||||
\(954\) | 2.21841e7 | 0.0255504 | ||||||||
\(955\) | − 5.76478e8i | − 0.661869i | ||||||||
\(956\) | −5.35795e8 | −0.613232 | ||||||||
\(957\) | − 3.66140e8i | − 0.417745i | ||||||||
\(958\) | 5.05897e8i | 0.575394i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.28082e8 | 0.257797 | ||||||||
\(961\) | 2.51933e8 | 0.283867 | ||||||||
\(962\) | − 3.52736e8i | − 0.396209i | ||||||||
\(963\) | −5.37616e8 | −0.601995 | ||||||||
\(964\) | − 8.63756e8i | − 0.964185i | ||||||||
\(965\) | 1.20463e7i | 0.0134051i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.33523e9 | −1.47665 | −0.738323 | − | 0.674448i | \(-0.764382\pi\) | ||||
−0.738323 | + | 0.674448i | \(0.764382\pi\) | |||||||
\(968\) | −6.49899e8 | −0.716506 | ||||||||
\(969\) | − 8.56120e8i | − 0.940943i | ||||||||
\(970\) | −2.41288e8 | −0.264375 | ||||||||
\(971\) | − 6.30242e8i | − 0.688414i | −0.938894 | − | 0.344207i | \(-0.888148\pi\) | ||||
0.938894 | − | 0.344207i | \(-0.111852\pi\) | |||||||
\(972\) | − 3.07922e7i | − 0.0335307i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.25362e8 | −0.785015 | ||||||||
\(975\) | 4.87549e8 | 0.526022 | ||||||||
\(976\) | 2.20634e8i | 0.237314i | ||||||||
\(977\) | −4.09104e8 | −0.438682 | −0.219341 | − | 0.975648i | \(-0.570391\pi\) | ||||
−0.219341 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(978\) | − 7.12644e8i | − 0.761826i | ||||||||
\(979\) | − 2.81978e8i | − 0.300516i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.86116e8 | −0.197141 | ||||||||
\(982\) | −4.87358e8 | −0.514652 | ||||||||
\(983\) | − 9.18323e8i | − 0.966796i | −0.875401 | − | 0.483398i | \(-0.839402\pi\) | ||||
0.875401 | − | 0.483398i | \(-0.160598\pi\) | |||||||
\(984\) | 3.18194e8 | 0.333969 | ||||||||
\(985\) | − 1.80362e8i | − 0.188728i | ||||||||
\(986\) | − 4.62415e8i | − 0.482394i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39059e8 | −0.870005 | ||||||||
\(989\) | 7.29192e8 | 0.753794 | ||||||||
\(990\) | 1.55212e8i | 0.159963i | ||||||||
\(991\) | −5.18738e8 | −0.533000 | −0.266500 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266500 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(992\) | 7.52560e8i | 0.770914i | ||||||||
\(993\) | 3.12283e8i | 0.318934i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.04623e8 | −0.410754 | ||||||||
\(996\) | −3.75191e7 | −0.0379730 | ||||||||
\(997\) | − 3.60955e8i | − 0.364223i | −0.983278 | − | 0.182111i | \(-0.941707\pi\) | ||||
0.983278 | − | 0.182111i | \(-0.0582931\pi\) | |||||||
\(998\) | −1.26276e9 | −1.27037 | ||||||||
\(999\) | − 8.61115e7i | − 0.0863703i |
(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 | 147.7.d.b.97.6 | 8 | ||
3.2 | odd | 2 | 441.7.d.c.244.4 | 8 | |||
7.2 | even | 3 | 21.7.f.a.10.2 | ✓ | 8 | ||
7.3 | odd | 6 | 21.7.f.a.19.2 | yes | 8 | ||
7.4 | even | 3 | 147.7.f.d.19.2 | 8 | |||
7.5 | odd | 6 | 147.7.f.d.31.2 | 8 | |||
7.6 | odd | 2 | inner | 147.7.d.b.97.5 | 8 | ||
21.2 | odd | 6 | 63.7.m.d.10.3 | 8 | |||
21.17 | even | 6 | 63.7.m.d.19.3 | 8 | |||
21.20 | even | 2 | 441.7.d.c.244.3 | 8 | |||
28.3 | even | 6 | 336.7.bh.d.145.2 | 8 | |||
28.23 | odd | 6 | 336.7.bh.d.241.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.a.10.2 | ✓ | 8 | 7.2 | even | 3 | ||
21.7.f.a.19.2 | yes | 8 | 7.3 | odd | 6 | ||
63.7.m.d.10.3 | 8 | 21.2 | odd | 6 | |||
63.7.m.d.19.3 | 8 | 21.17 | even | 6 | |||
147.7.d.b.97.5 | 8 | 7.6 | odd | 2 | inner | ||
147.7.d.b.97.6 | 8 | 1.1 | even | 1 | trivial | ||
147.7.f.d.19.2 | 8 | 7.4 | even | 3 | |||
147.7.f.d.31.2 | 8 | 7.5 | odd | 6 | |||
336.7.bh.d.145.2 | 8 | 28.3 | even | 6 | |||
336.7.bh.d.241.2 | 8 | 28.23 | odd | 6 | |||
441.7.d.c.244.3 | 8 | 21.20 | even | 2 | |||
441.7.d.c.244.4 | 8 | 3.2 | odd | 2 |