Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,6,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.0671684673\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.6.b.a.99.1 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.0000i | 1.76777i | 0.467707 | + | 0.883883i | \(0.345080\pi\) | ||||
−0.467707 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(3\) | − 14.0000i | − 0.898100i | −0.893507 | − | 0.449050i | \(-0.851762\pi\) | ||||
0.893507 | − | 0.449050i | \(-0.148238\pi\) | |||||||
\(4\) | −68.0000 | −2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 140.000 | 1.58763 | ||||||||
\(7\) | 49.0000i | 0.377964i | ||||||||
\(8\) | − 360.000i | − 1.98874i | ||||||||
\(9\) | 47.0000 | 0.193416 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 232.000 | 0.578104 | 0.289052 | − | 0.957313i | \(-0.406660\pi\) | ||||
0.289052 | + | 0.957313i | \(0.406660\pi\) | |||||||
\(12\) | 952.000i | 1.90846i | ||||||||
\(13\) | − 140.000i | − 0.229757i | −0.993380 | − | 0.114879i | \(-0.963352\pi\) | ||||
0.993380 | − | 0.114879i | \(-0.0366479\pi\) | |||||||
\(14\) | −490.000 | −0.668153 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1424.00 | 1.39062 | ||||||||
\(17\) | 1722.00i | 1.44514i | 0.691296 | + | 0.722572i | \(0.257040\pi\) | ||||
−0.691296 | + | 0.722572i | \(0.742960\pi\) | |||||||
\(18\) | 470.000i | 0.341914i | ||||||||
\(19\) | 98.0000 | 0.0622791 | 0.0311395 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311395 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 686.000 | 0.339450 | ||||||||
\(22\) | 2320.00i | 1.02195i | ||||||||
\(23\) | 1824.00i | 0.718961i | 0.933153 | + | 0.359480i | \(0.117046\pi\) | ||||
−0.933153 | + | 0.359480i | \(0.882954\pi\) | |||||||
\(24\) | −5040.00 | −1.78609 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1400.00 | 0.406158 | ||||||||
\(27\) | − 4060.00i | − 1.07181i | ||||||||
\(28\) | − 3332.00i | − 0.803175i | ||||||||
\(29\) | −3418.00 | −0.754705 | −0.377352 | − | 0.926070i | \(-0.623165\pi\) | ||||
−0.377352 | + | 0.926070i | \(0.623165\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7644.00 | −1.42862 | −0.714310 | − | 0.699830i | \(-0.753259\pi\) | ||||
−0.714310 | + | 0.699830i | \(0.753259\pi\) | |||||||
\(32\) | 2720.00i | 0.469563i | ||||||||
\(33\) | − 3248.00i | − 0.519196i | ||||||||
\(34\) | −17220.0 | −2.55468 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3196.00 | −0.411008 | ||||||||
\(37\) | 10398.0i | 1.24866i | 0.781159 | + | 0.624332i | \(0.214629\pi\) | ||||
−0.781159 | + | 0.624332i | \(0.785371\pi\) | |||||||
\(38\) | 980.000i | 0.110095i | ||||||||
\(39\) | −1960.00 | −0.206345 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17962.0 | −1.66876 | −0.834382 | − | 0.551186i | \(-0.814175\pi\) | ||||
−0.834382 | + | 0.551186i | \(0.814175\pi\) | |||||||
\(42\) | 6860.00i | 0.600069i | ||||||||
\(43\) | 10880.0i | 0.897342i | 0.893697 | + | 0.448671i | \(0.148102\pi\) | ||||
−0.893697 | + | 0.448671i | \(0.851898\pi\) | |||||||
\(44\) | −15776.0 | −1.22847 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −18240.0 | −1.27096 | ||||||||
\(47\) | − 9324.00i | − 0.615684i | −0.951438 | − | 0.307842i | \(-0.900393\pi\) | ||||
0.951438 | − | 0.307842i | \(-0.0996068\pi\) | |||||||
\(48\) | − 19936.0i | − 1.24892i | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24108.0 | 1.29788 | ||||||||
\(52\) | 9520.00i | 0.488235i | ||||||||
\(53\) | 2262.00i | 0.110612i | 0.998469 | + | 0.0553061i | \(0.0176135\pi\) | ||||
−0.998469 | + | 0.0553061i | \(0.982387\pi\) | |||||||
\(54\) | 40600.0 | 1.89471 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17640.0 | 0.751672 | ||||||||
\(57\) | − 1372.00i | − 0.0559329i | ||||||||
\(58\) | − 34180.0i | − 1.33414i | ||||||||
\(59\) | 2730.00 | 0.102102 | 0.0510508 | − | 0.998696i | \(-0.483743\pi\) | ||||
0.0510508 | + | 0.998696i | \(0.483743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25648.0 | 0.882529 | 0.441264 | − | 0.897377i | \(-0.354530\pi\) | ||||
0.441264 | + | 0.897377i | \(0.354530\pi\) | |||||||
\(62\) | − 76440.0i | − 2.52547i | ||||||||
\(63\) | 2303.00i | 0.0731042i | ||||||||
\(64\) | 18368.0 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 32480.0 | 0.917817 | ||||||||
\(67\) | 48404.0i | 1.31733i | 0.752437 | + | 0.658664i | \(0.228878\pi\) | ||||
−0.752437 | + | 0.658664i | \(0.771122\pi\) | |||||||
\(68\) | − 117096.i | − 3.07093i | ||||||||
\(69\) | 25536.0 | 0.645699 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −58560.0 | −1.37865 | −0.689327 | − | 0.724450i | \(-0.742094\pi\) | ||||
−0.689327 | + | 0.724450i | \(0.742094\pi\) | |||||||
\(72\) | − 16920.0i | − 0.384653i | ||||||||
\(73\) | 68082.0i | 1.49529i | 0.664099 | + | 0.747645i | \(0.268815\pi\) | ||||
−0.664099 | + | 0.747645i | \(0.731185\pi\) | |||||||
\(74\) | −103980. | −2.20735 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6664.00 | −0.132343 | ||||||||
\(77\) | 11368.0i | 0.218503i | ||||||||
\(78\) | − 19600.0i | − 0.364770i | ||||||||
\(79\) | −31784.0 | −0.572982 | −0.286491 | − | 0.958083i | \(-0.592489\pi\) | ||||
−0.286491 | + | 0.958083i | \(0.592489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −45419.0 | −0.769175 | ||||||||
\(82\) | − 179620.i | − 2.94999i | ||||||||
\(83\) | − 20538.0i | − 0.327237i | −0.986524 | − | 0.163619i | \(-0.947683\pi\) | ||||
0.986524 | − | 0.163619i | \(-0.0523167\pi\) | |||||||
\(84\) | −46648.0 | −0.721331 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −108800. | −1.58629 | ||||||||
\(87\) | 47852.0i | 0.677801i | ||||||||
\(88\) | − 83520.0i | − 1.14970i | ||||||||
\(89\) | 50582.0 | 0.676894 | 0.338447 | − | 0.940985i | \(-0.390098\pi\) | ||||
0.338447 | + | 0.940985i | \(0.390098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6860.00 | 0.0868402 | ||||||||
\(92\) | − 124032.i | − 1.52779i | ||||||||
\(93\) | 107016.i | 1.28304i | ||||||||
\(94\) | 93240.0 | 1.08839 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 38080.0 | 0.421715 | ||||||||
\(97\) | 58506.0i | 0.631351i | 0.948867 | + | 0.315676i | \(0.102231\pi\) | ||||
−0.948867 | + | 0.315676i | \(0.897769\pi\) | |||||||
\(98\) | − 24010.0i | − 0.252538i | ||||||||
\(99\) | 10904.0 | 0.111814 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 38696.0 | 0.377453 | 0.188726 | − | 0.982030i | \(-0.439564\pi\) | ||||
0.188726 | + | 0.982030i | \(0.439564\pi\) | |||||||
\(102\) | 241080.i | 2.29436i | ||||||||
\(103\) | 53060.0i | 0.492804i | 0.969168 | + | 0.246402i | \(0.0792483\pi\) | ||||
−0.969168 | + | 0.246402i | \(0.920752\pi\) | |||||||
\(104\) | −50400.0 | −0.456927 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22620.0 | −0.195537 | ||||||||
\(107\) | 146324.i | 1.23554i | 0.786360 | + | 0.617769i | \(0.211963\pi\) | ||||
−0.786360 | + | 0.617769i | \(0.788037\pi\) | |||||||
\(108\) | 276080.i | 2.27759i | ||||||||
\(109\) | −92898.0 | −0.748928 | −0.374464 | − | 0.927241i | \(-0.622173\pi\) | ||||
−0.374464 | + | 0.927241i | \(0.622173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 145572. | 1.12143 | ||||||||
\(112\) | 69776.0i | 0.525607i | ||||||||
\(113\) | − 83354.0i | − 0.614088i | −0.951695 | − | 0.307044i | \(-0.900660\pi\) | ||||
0.951695 | − | 0.307044i | \(-0.0993398\pi\) | |||||||
\(114\) | 13720.0 | 0.0988762 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 232424. | 1.60375 | ||||||||
\(117\) | − 6580.00i | − 0.0444387i | ||||||||
\(118\) | 27300.0i | 0.180492i | ||||||||
\(119\) | −84378.0 | −0.546213 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −107227. | −0.665795 | ||||||||
\(122\) | 256480.i | 1.56011i | ||||||||
\(123\) | 251468.i | 1.49872i | ||||||||
\(124\) | 519792. | 3.03582 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23030.0 | −0.129231 | ||||||||
\(127\) | − 60384.0i | − 0.332210i | −0.986108 | − | 0.166105i | \(-0.946881\pi\) | ||||
0.986108 | − | 0.166105i | \(-0.0531191\pi\) | |||||||
\(128\) | 270720.i | 1.46048i | ||||||||
\(129\) | 152320. | 0.805903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −61586.0 | −0.313548 | −0.156774 | − | 0.987635i | \(-0.550109\pi\) | ||||
−0.156774 | + | 0.987635i | \(0.550109\pi\) | |||||||
\(132\) | 220864.i | 1.10329i | ||||||||
\(133\) | 4802.00i | 0.0235393i | ||||||||
\(134\) | −484040. | −2.32873 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 619920. | 2.87401 | ||||||||
\(137\) | 204462.i | 0.930703i | 0.885126 | + | 0.465352i | \(0.154072\pi\) | ||||
−0.885126 | + | 0.465352i | \(0.845928\pi\) | |||||||
\(138\) | 255360.i | 1.14145i | ||||||||
\(139\) | 35406.0 | 0.155432 | 0.0777159 | − | 0.996976i | \(-0.475237\pi\) | ||||
0.0777159 | + | 0.996976i | \(0.475237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −130536. | −0.552946 | ||||||||
\(142\) | − 585600.i | − 2.43714i | ||||||||
\(143\) | − 32480.0i | − 0.132824i | ||||||||
\(144\) | 66928.0 | 0.268969 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −680820. | −2.64332 | ||||||||
\(147\) | 33614.0i | 0.128300i | ||||||||
\(148\) | − 707064.i | − 2.65341i | ||||||||
\(149\) | 20226.0 | 0.0746353 | 0.0373177 | − | 0.999303i | \(-0.488119\pi\) | ||||
0.0373177 | + | 0.999303i | \(0.488119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 70904.0 | 0.253063 | 0.126531 | − | 0.991963i | \(-0.459616\pi\) | ||||
0.126531 | + | 0.991963i | \(0.459616\pi\) | |||||||
\(152\) | − 35280.0i | − 0.123857i | ||||||||
\(153\) | 80934.0i | 0.279513i | ||||||||
\(154\) | −113680. | −0.386262 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 133280. | 0.438484 | ||||||||
\(157\) | − 293524.i | − 0.950374i | −0.879885 | − | 0.475187i | \(-0.842380\pi\) | ||||
0.879885 | − | 0.475187i | \(-0.157620\pi\) | |||||||
\(158\) | − 317840.i | − 1.01290i | ||||||||
\(159\) | 31668.0 | 0.0993408 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −89376.0 | −0.271742 | ||||||||
\(162\) | − 454190.i | − 1.35972i | ||||||||
\(163\) | 13192.0i | 0.0388903i | 0.999811 | + | 0.0194452i | \(0.00618998\pi\) | ||||
−0.999811 | + | 0.0194452i | \(0.993810\pi\) | |||||||
\(164\) | 1.22142e6 | 3.54612 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 205380. | 0.578479 | ||||||||
\(167\) | − 493612.i | − 1.36960i | −0.728730 | − | 0.684801i | \(-0.759889\pi\) | ||||
0.728730 | − | 0.684801i | \(-0.240111\pi\) | |||||||
\(168\) | − 246960.i | − 0.675077i | ||||||||
\(169\) | 351693. | 0.947212 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4606.00 | 0.0120457 | ||||||||
\(172\) | − 739840.i | − 1.90685i | ||||||||
\(173\) | 240716.i | 0.611490i | 0.952113 | + | 0.305745i | \(0.0989056\pi\) | ||||
−0.952113 | + | 0.305745i | \(0.901094\pi\) | |||||||
\(174\) | −478520. | −1.19819 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 330368. | 0.803926 | ||||||||
\(177\) | − 38220.0i | − 0.0916975i | ||||||||
\(178\) | 505820.i | 1.19659i | ||||||||
\(179\) | −294932. | −0.688001 | −0.344001 | − | 0.938969i | \(-0.611782\pi\) | ||||
−0.344001 | + | 0.938969i | \(0.611782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −336980. | −0.764553 | −0.382277 | − | 0.924048i | \(-0.624860\pi\) | ||||
−0.382277 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(182\) | 68600.0i | 0.153513i | ||||||||
\(183\) | − 359072.i | − 0.792600i | ||||||||
\(184\) | 656640. | 1.42982 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.07016e6 | −2.26812 | ||||||||
\(187\) | 399504.i | 0.835444i | ||||||||
\(188\) | 634032.i | 1.30833i | ||||||||
\(189\) | 198940. | 0.405105 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 358264. | 0.710591 | 0.355296 | − | 0.934754i | \(-0.384380\pi\) | ||||
0.355296 | + | 0.934754i | \(0.384380\pi\) | |||||||
\(192\) | − 257152.i | − 0.503427i | ||||||||
\(193\) | − 989554.i | − 1.91226i | −0.292948 | − | 0.956128i | \(-0.594636\pi\) | ||||
0.292948 | − | 0.956128i | \(-0.405364\pi\) | |||||||
\(194\) | −585060. | −1.11608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 163268. | 0.303571 | ||||||||
\(197\) | 990050.i | 1.81757i | 0.417263 | + | 0.908786i | \(0.362989\pi\) | ||||
−0.417263 | + | 0.908786i | \(0.637011\pi\) | |||||||
\(198\) | 109040.i | 0.197662i | ||||||||
\(199\) | 840756. | 1.50500 | 0.752501 | − | 0.658591i | \(-0.228847\pi\) | ||||
0.752501 | + | 0.658591i | \(0.228847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 677656. | 1.18309 | ||||||||
\(202\) | 386960.i | 0.667249i | ||||||||
\(203\) | − 167482.i | − 0.285252i | ||||||||
\(204\) | −1.63934e6 | −2.75800 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −530600. | −0.871163 | ||||||||
\(207\) | 85728.0i | 0.139058i | ||||||||
\(208\) | − 199360.i | − 0.319506i | ||||||||
\(209\) | 22736.0 | 0.0360038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.15073e6 | 1.77938 | 0.889689 | − | 0.456568i | \(-0.150921\pi\) | ||||
0.889689 | + | 0.456568i | \(0.150921\pi\) | |||||||
\(212\) | − 153816.i | − 0.235051i | ||||||||
\(213\) | 819840.i | 1.23817i | ||||||||
\(214\) | −1.46324e6 | −2.18414 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.46160e6 | −2.13154 | ||||||||
\(217\) | − 374556.i | − 0.539967i | ||||||||
\(218\) | − 928980.i | − 1.32393i | ||||||||
\(219\) | 953148. | 1.34292 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 241080. | 0.332032 | ||||||||
\(222\) | 1.45572e6i | 1.98242i | ||||||||
\(223\) | − 824264.i | − 1.10995i | −0.831866 | − | 0.554976i | \(-0.812727\pi\) | ||||
0.831866 | − | 0.554976i | \(-0.187273\pi\) | |||||||
\(224\) | −133280. | −0.177478 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 833540. | 1.08556 | ||||||||
\(227\) | − 74382.0i | − 0.0958083i | −0.998852 | − | 0.0479042i | \(-0.984746\pi\) | ||||
0.998852 | − | 0.0479042i | \(-0.0152542\pi\) | |||||||
\(228\) | 93296.0i | 0.118857i | ||||||||
\(229\) | −1.13196e6 | −1.42640 | −0.713199 | − | 0.700961i | \(-0.752755\pi\) | ||||
−0.713199 | + | 0.700961i | \(0.752755\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 159152. | 0.196238 | ||||||||
\(232\) | 1.23048e6i | 1.50091i | ||||||||
\(233\) | − 198726.i | − 0.239809i | −0.992785 | − | 0.119904i | \(-0.961741\pi\) | ||||
0.992785 | − | 0.119904i | \(-0.0382588\pi\) | |||||||
\(234\) | 65800.0 | 0.0785572 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −185640. | −0.216966 | ||||||||
\(237\) | 444976.i | 0.514595i | ||||||||
\(238\) | − 843780.i | − 0.965577i | ||||||||
\(239\) | −482904. | −0.546847 | −0.273424 | − | 0.961894i | \(-0.588156\pi\) | ||||
−0.273424 | + | 0.961894i | \(0.588156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 805910. | 0.893807 | 0.446904 | − | 0.894582i | \(-0.352527\pi\) | ||||
0.446904 | + | 0.894582i | \(0.352527\pi\) | |||||||
\(242\) | − 1.07227e6i | − 1.17697i | ||||||||
\(243\) | − 350714.i | − 0.381011i | ||||||||
\(244\) | −1.74406e6 | −1.87537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.51468e6 | −2.64938 | ||||||||
\(247\) | − 13720.0i | − 0.0143091i | ||||||||
\(248\) | 2.75184e6i | 2.84115i | ||||||||
\(249\) | −287532. | −0.293892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 430738. | 0.431548 | 0.215774 | − | 0.976443i | \(-0.430773\pi\) | ||||
0.215774 | + | 0.976443i | \(0.430773\pi\) | |||||||
\(252\) | − 156604.i | − 0.155347i | ||||||||
\(253\) | 423168.i | 0.415634i | ||||||||
\(254\) | 603840. | 0.587270 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.11942e6 | −2.02124 | ||||||||
\(257\) | 1.17691e6i | 1.11150i | 0.831349 | + | 0.555751i | \(0.187569\pi\) | ||||
−0.831349 | + | 0.555751i | \(0.812431\pi\) | |||||||
\(258\) | 1.52320e6i | 1.42465i | ||||||||
\(259\) | −509502. | −0.471951 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −160646. | −0.145972 | ||||||||
\(262\) | − 615860.i | − 0.554279i | ||||||||
\(263\) | 1.29098e6i | 1.15088i | 0.817845 | + | 0.575438i | \(0.195169\pi\) | ||||
−0.817845 | + | 0.575438i | \(0.804831\pi\) | |||||||
\(264\) | −1.16928e6 | −1.03254 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −48020.0 | −0.0416119 | ||||||||
\(267\) | − 708148.i | − 0.607919i | ||||||||
\(268\) | − 3.29147e6i | − 2.79932i | ||||||||
\(269\) | 1.27756e6 | 1.07646 | 0.538232 | − | 0.842797i | \(-0.319093\pi\) | ||||
0.538232 | + | 0.842797i | \(0.319093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65054e6 | 1.36522 | 0.682612 | − | 0.730781i | \(-0.260844\pi\) | ||||
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(272\) | 2.45213e6i | 2.00965i | ||||||||
\(273\) | − 96040.0i | − 0.0779912i | ||||||||
\(274\) | −2.04462e6 | −1.64527 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.73645e6 | −1.37211 | ||||||||
\(277\) | 1.06409e6i | 0.833257i | 0.909077 | + | 0.416628i | \(0.136788\pi\) | ||||
−0.909077 | + | 0.416628i | \(0.863212\pi\) | |||||||
\(278\) | 354060.i | 0.274767i | ||||||||
\(279\) | −359268. | −0.276317 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22342.0 | −0.0168794 | −0.00843969 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843969 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(282\) | − 1.30536e6i | − 0.977479i | ||||||||
\(283\) | − 2.49574e6i | − 1.85239i | −0.377042 | − | 0.926196i | \(-0.623059\pi\) | ||||
0.377042 | − | 0.926196i | \(-0.376941\pi\) | |||||||
\(284\) | 3.98208e6 | 2.92964 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 324800. | 0.234802 | ||||||||
\(287\) | − 880138.i | − 0.630734i | ||||||||
\(288\) | 127840.i | 0.0908208i | ||||||||
\(289\) | −1.54543e6 | −1.08844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 819084. | 0.567017 | ||||||||
\(292\) | − 4.62958e6i | − 3.17749i | ||||||||
\(293\) | − 1.93178e6i | − 1.31458i | −0.753637 | − | 0.657291i | \(-0.771702\pi\) | ||||
0.753637 | − | 0.657291i | \(-0.228298\pi\) | |||||||
\(294\) | −336140. | −0.226805 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.74328e6 | 2.48326 | ||||||||
\(297\) | − 941920.i | − 0.619616i | ||||||||
\(298\) | 202260.i | 0.131938i | ||||||||
\(299\) | 255360. | 0.165187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −533120. | −0.339163 | ||||||||
\(302\) | 709040.i | 0.447356i | ||||||||
\(303\) | − 541744.i | − 0.338991i | ||||||||
\(304\) | 139552. | 0.0866068 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −809340. | −0.494114 | ||||||||
\(307\) | 459074.i | 0.277995i | 0.990293 | + | 0.138997i | \(0.0443880\pi\) | ||||
−0.990293 | + | 0.138997i | \(0.955612\pi\) | |||||||
\(308\) | − 773024.i | − 0.464319i | ||||||||
\(309\) | 742840. | 0.442587 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 667128. | 0.391118 | 0.195559 | − | 0.980692i | \(-0.437348\pi\) | ||||
0.195559 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(312\) | 705600.i | 0.410367i | ||||||||
\(313\) | − 111034.i | − 0.0640612i | −0.999487 | − | 0.0320306i | \(-0.989803\pi\) | ||||
0.999487 | − | 0.0320306i | \(-0.0101974\pi\) | |||||||
\(314\) | 2.93524e6 | 1.68004 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.16131e6 | 1.21759 | ||||||||
\(317\) | 68778.0i | 0.0384416i | 0.999815 | + | 0.0192208i | \(0.00611855\pi\) | ||||
−0.999815 | + | 0.0192208i | \(0.993881\pi\) | |||||||
\(318\) | 316680.i | 0.175611i | ||||||||
\(319\) | −792976. | −0.436298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.04854e6 | 1.10964 | ||||||||
\(322\) | − 893760.i | − 0.480376i | ||||||||
\(323\) | 168756.i | 0.0900022i | ||||||||
\(324\) | 3.08849e6 | 1.63450 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −131920. | −0.0687490 | ||||||||
\(327\) | 1.30057e6i | 0.672613i | ||||||||
\(328\) | 6.46632e6i | 3.31874i | ||||||||
\(329\) | 456876. | 0.232707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −564448. | −0.283174 | −0.141587 | − | 0.989926i | \(-0.545221\pi\) | ||||
−0.141587 | + | 0.989926i | \(0.545221\pi\) | |||||||
\(332\) | 1.39658e6i | 0.695379i | ||||||||
\(333\) | 488706.i | 0.241511i | ||||||||
\(334\) | 4.93612e6 | 2.42114 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 976864. | 0.472048 | ||||||||
\(337\) | − 2.07729e6i | − 0.996376i | −0.867069 | − | 0.498188i | \(-0.833999\pi\) | ||||
0.867069 | − | 0.498188i | \(-0.166001\pi\) | |||||||
\(338\) | 3.51693e6i | 1.67445i | ||||||||
\(339\) | −1.16696e6 | −0.551512 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.77341e6 | −0.825891 | ||||||||
\(342\) | 46060.0i | 0.0212941i | ||||||||
\(343\) | − 117649.i | − 0.0539949i | ||||||||
\(344\) | 3.91680e6 | 1.78458 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.40716e6 | −1.08097 | ||||||||
\(347\) | 53248.0i | 0.0237399i | 0.999930 | + | 0.0118700i | \(0.00377842\pi\) | ||||
−0.999930 | + | 0.0118700i | \(0.996222\pi\) | |||||||
\(348\) | − 3.25394e6i | − 1.44033i | ||||||||
\(349\) | 2.27200e6 | 0.998494 | 0.499247 | − | 0.866460i | \(-0.333610\pi\) | ||||
0.499247 | + | 0.866460i | \(0.333610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −568400. | −0.246256 | ||||||||
\(352\) | 631040.i | 0.271456i | ||||||||
\(353\) | 4.00645e6i | 1.71129i | 0.517565 | + | 0.855644i | \(0.326838\pi\) | ||||
−0.517565 | + | 0.855644i | \(0.673162\pi\) | |||||||
\(354\) | 382200. | 0.162100 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.43958e6 | −1.43840 | ||||||||
\(357\) | 1.18129e6i | 0.490554i | ||||||||
\(358\) | − 2.94932e6i | − 1.21623i | ||||||||
\(359\) | −73784.0 | −0.0302152 | −0.0151076 | − | 0.999886i | \(-0.504809\pi\) | ||||
−0.0151076 | + | 0.999886i | \(0.504809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46650e6 | −0.996121 | ||||||||
\(362\) | − 3.36980e6i | − 1.35155i | ||||||||
\(363\) | 1.50118e6i | 0.597951i | ||||||||
\(364\) | −466480. | −0.184535 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.59072e6 | 1.40113 | ||||||||
\(367\) | − 1.40431e6i | − 0.544250i | −0.962262 | − | 0.272125i | \(-0.912274\pi\) | ||||
0.962262 | − | 0.272125i | \(-0.0877264\pi\) | |||||||
\(368\) | 2.59738e6i | 0.999805i | ||||||||
\(369\) | −844214. | −0.322765 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −110838. | −0.0418075 | ||||||||
\(372\) | − 7.27709e6i | − 2.72647i | ||||||||
\(373\) | − 1.60323e6i | − 0.596657i | −0.954463 | − | 0.298329i | \(-0.903571\pi\) | ||||
0.954463 | − | 0.298329i | \(-0.0964291\pi\) | |||||||
\(374\) | −3.99504e6 | −1.47687 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.35664e6 | −1.22443 | ||||||||
\(377\) | 478520.i | 0.173399i | ||||||||
\(378\) | 1.98940e6i | 0.716131i | ||||||||
\(379\) | 4.77012e6 | 1.70581 | 0.852906 | − | 0.522064i | \(-0.174838\pi\) | ||||
0.852906 | + | 0.522064i | \(0.174838\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −845376. | −0.298358 | ||||||||
\(382\) | 3.58264e6i | 1.25616i | ||||||||
\(383\) | − 2.23079e6i | − 0.777072i | −0.921434 | − | 0.388536i | \(-0.872981\pi\) | ||||
0.921434 | − | 0.388536i | \(-0.127019\pi\) | |||||||
\(384\) | 3.79008e6 | 1.31166 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.89554e6 | 3.38042 | ||||||||
\(387\) | 511360.i | 0.173560i | ||||||||
\(388\) | − 3.97841e6i | − 1.34162i | ||||||||
\(389\) | −4.84024e6 | −1.62178 | −0.810892 | − | 0.585196i | \(-0.801018\pi\) | ||||
−0.810892 | + | 0.585196i | \(0.801018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.14093e6 | −1.03900 | ||||||||
\(392\) | 864360.i | 0.284105i | ||||||||
\(393\) | 862204.i | 0.281597i | ||||||||
\(394\) | −9.90050e6 | −3.21304 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −741472. | −0.237606 | ||||||||
\(397\) | − 995820.i | − 0.317106i | −0.987350 | − | 0.158553i | \(-0.949317\pi\) | ||||
0.987350 | − | 0.158553i | \(-0.0506829\pi\) | |||||||
\(398\) | 8.40756e6i | 2.66049i | ||||||||
\(399\) | 67228.0 | 0.0211406 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.31605e6 | −1.02982 | −0.514909 | − | 0.857245i | \(-0.672174\pi\) | ||||
−0.514909 | + | 0.857245i | \(0.672174\pi\) | |||||||
\(402\) | 6.77656e6i | 2.09143i | ||||||||
\(403\) | 1.07016e6i | 0.328236i | ||||||||
\(404\) | −2.63133e6 | −0.802087 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.67482e6 | 0.504258 | ||||||||
\(407\) | 2.41234e6i | 0.721858i | ||||||||
\(408\) | − 8.67888e6i | − 2.58115i | ||||||||
\(409\) | −3.07273e6 | −0.908274 | −0.454137 | − | 0.890932i | \(-0.650052\pi\) | ||||
−0.454137 | + | 0.890932i | \(0.650052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.86247e6 | 0.835865 | ||||||||
\(412\) | − 3.60808e6i | − 1.04721i | ||||||||
\(413\) | 133770.i | 0.0385908i | ||||||||
\(414\) | −857280. | −0.245823 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 380800. | 0.107886 | ||||||||
\(417\) | − 495684.i | − 0.139593i | ||||||||
\(418\) | 227360.i | 0.0636463i | ||||||||
\(419\) | −2.81438e6 | −0.783154 | −0.391577 | − | 0.920145i | \(-0.628070\pi\) | ||||
−0.391577 | + | 0.920145i | \(0.628070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.05802e6 | 0.840883 | 0.420441 | − | 0.907320i | \(-0.361875\pi\) | ||||
0.420441 | + | 0.907320i | \(0.361875\pi\) | |||||||
\(422\) | 1.15073e7i | 3.14552i | ||||||||
\(423\) | − 438228.i | − 0.119083i | ||||||||
\(424\) | 814320. | 0.219979 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.19840e6 | −2.18880 | ||||||||
\(427\) | 1.25675e6i | 0.333565i | ||||||||
\(428\) | − 9.95003e6i | − 2.62552i | ||||||||
\(429\) | −454720. | −0.119289 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.93750e6 | 0.502398 | 0.251199 | − | 0.967936i | \(-0.419175\pi\) | ||||
0.251199 | + | 0.967936i | \(0.419175\pi\) | |||||||
\(432\) | − 5.78144e6i | − 1.49048i | ||||||||
\(433\) | 3.94790e6i | 1.01192i | 0.862557 | + | 0.505961i | \(0.168862\pi\) | ||||
−0.862557 | + | 0.505961i | \(0.831138\pi\) | |||||||
\(434\) | 3.74556e6 | 0.954536 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.31706e6 | 1.59147 | ||||||||
\(437\) | 178752.i | 0.0447762i | ||||||||
\(438\) | 9.53148e6i | 2.37397i | ||||||||
\(439\) | 7.41770e6 | 1.83700 | 0.918498 | − | 0.395426i | \(-0.129403\pi\) | ||||
0.918498 | + | 0.395426i | \(0.129403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −112847. | −0.0276308 | ||||||||
\(442\) | 2.41080e6i | 0.586956i | ||||||||
\(443\) | 1.40269e6i | 0.339589i | 0.985480 | + | 0.169794i | \(0.0543103\pi\) | ||||
−0.985480 | + | 0.169794i | \(0.945690\pi\) | |||||||
\(444\) | −9.89890e6 | −2.38303 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.24264e6 | 1.96214 | ||||||||
\(447\) | − 283164.i | − 0.0670300i | ||||||||
\(448\) | 900032.i | 0.211867i | ||||||||
\(449\) | 590574. | 0.138248 | 0.0691239 | − | 0.997608i | \(-0.477980\pi\) | ||||
0.0691239 | + | 0.997608i | \(0.477980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.16718e6 | −0.964720 | ||||||||
\(452\) | 5.66807e6i | 1.30494i | ||||||||
\(453\) | − 992656.i | − 0.227276i | ||||||||
\(454\) | 743820. | 0.169367 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −493920. | −0.111236 | ||||||||
\(457\) | 2.90484e6i | 0.650627i | 0.945606 | + | 0.325313i | \(0.105470\pi\) | ||||
−0.945606 | + | 0.325313i | \(0.894530\pi\) | |||||||
\(458\) | − 1.13196e7i | − 2.52154i | ||||||||
\(459\) | 6.99132e6 | 1.54891 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −922684. | −0.202209 | −0.101105 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101105 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(462\) | 1.59152e6i | 0.346902i | ||||||||
\(463\) | 7.18235e6i | 1.55709i | 0.627588 | + | 0.778546i | \(0.284042\pi\) | ||||
−0.627588 | + | 0.778546i | \(0.715958\pi\) | |||||||
\(464\) | −4.86723e6 | −1.04951 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.98726e6 | 0.423926 | ||||||||
\(467\) | 612570.i | 0.129976i | 0.997886 | + | 0.0649881i | \(0.0207009\pi\) | ||||
−0.997886 | + | 0.0649881i | \(0.979299\pi\) | |||||||
\(468\) | 447440.i | 0.0944322i | ||||||||
\(469\) | −2.37180e6 | −0.497904 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.10934e6 | −0.853531 | ||||||||
\(472\) | − 982800.i | − 0.203053i | ||||||||
\(473\) | 2.52416e6i | 0.518757i | ||||||||
\(474\) | −4.44976e6 | −0.909684 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.73770e6 | 1.16070 | ||||||||
\(477\) | 106314.i | 0.0213941i | ||||||||
\(478\) | − 4.82904e6i | − 0.966699i | ||||||||
\(479\) | −2.60330e6 | −0.518424 | −0.259212 | − | 0.965820i | \(-0.583463\pi\) | ||||
−0.259212 | + | 0.965820i | \(0.583463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.45572e6 | 0.286890 | ||||||||
\(482\) | 8.05910e6i | 1.58004i | ||||||||
\(483\) | 1.25126e6i | 0.244051i | ||||||||
\(484\) | 7.29144e6 | 1.41482 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.50714e6 | 0.673539 | ||||||||
\(487\) | − 5.46309e6i | − 1.04380i | −0.853008 | − | 0.521898i | \(-0.825224\pi\) | ||||
0.853008 | − | 0.521898i | \(-0.174776\pi\) | |||||||
\(488\) | − 9.23328e6i | − 1.75512i | ||||||||
\(489\) | 184688. | 0.0349274 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.64090e6 | 0.307170 | 0.153585 | − | 0.988135i | \(-0.450918\pi\) | ||||
0.153585 | + | 0.988135i | \(0.450918\pi\) | |||||||
\(492\) | − 1.70998e7i | − 3.18478i | ||||||||
\(493\) | − 5.88580e6i | − 1.09066i | ||||||||
\(494\) | 137200. | 0.0252951 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.08851e7 | −1.98667 | ||||||||
\(497\) | − 2.86944e6i | − 0.521082i | ||||||||
\(498\) | − 2.87532e6i | − 0.519533i | ||||||||
\(499\) | −2.99796e6 | −0.538983 | −0.269491 | − | 0.963003i | \(-0.586856\pi\) | ||||
−0.269491 | + | 0.963003i | \(0.586856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.91057e6 | −1.23004 | ||||||||
\(502\) | 4.30738e6i | 0.762876i | ||||||||
\(503\) | − 6.89405e6i | − 1.21494i | −0.794343 | − | 0.607469i | \(-0.792185\pi\) | ||||
0.794343 | − | 0.607469i | \(-0.207815\pi\) | |||||||
\(504\) | 829080. | 0.145385 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.23168e6 | −0.734745 | ||||||||
\(507\) | − 4.92370e6i | − 0.850691i | ||||||||
\(508\) | 4.10611e6i | 0.705946i | ||||||||
\(509\) | −2.30476e6 | −0.394305 | −0.197152 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197152 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.33602e6 | −0.565166 | ||||||||
\(512\) | − 1.25312e7i | − 2.11260i | ||||||||
\(513\) | − 397880.i | − 0.0667511i | ||||||||
\(514\) | −1.17691e7 | −1.96488 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.03578e7 | −1.71254 | ||||||||
\(517\) | − 2.16317e6i | − 0.355929i | ||||||||
\(518\) | − 5.09502e6i | − 0.834299i | ||||||||
\(519\) | 3.37002e6 | 0.549180 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.20960e7 | −1.95231 | −0.976155 | − | 0.217073i | \(-0.930349\pi\) | ||||
−0.976155 | + | 0.217073i | \(0.930349\pi\) | |||||||
\(522\) | − 1.60646e6i | − 0.258044i | ||||||||
\(523\) | 5.48443e6i | 0.876753i | 0.898791 | + | 0.438377i | \(0.144446\pi\) | ||||
−0.898791 | + | 0.438377i | \(0.855554\pi\) | |||||||
\(524\) | 4.18785e6 | 0.666289 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.29098e7 | −2.03448 | ||||||||
\(527\) | − 1.31630e7i | − 2.06456i | ||||||||
\(528\) | − 4.62515e6i | − 0.722007i | ||||||||
\(529\) | 3.10937e6 | 0.483095 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 128310. | 0.0197480 | ||||||||
\(532\) | − 326536.i | − 0.0500210i | ||||||||
\(533\) | 2.51468e6i | 0.383411i | ||||||||
\(534\) | 7.08148e6 | 1.07466 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.74254e7 | 2.61982 | ||||||||
\(537\) | 4.12905e6i | 0.617894i | ||||||||
\(538\) | 1.27756e7i | 1.90294i | ||||||||
\(539\) | −557032. | −0.0825863 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.71799e6 | −0.986839 | −0.493420 | − | 0.869791i | \(-0.664253\pi\) | ||||
−0.493420 | + | 0.869791i | \(0.664253\pi\) | |||||||
\(542\) | 1.65054e7i | 2.41340i | ||||||||
\(543\) | 4.71772e6i | 0.686646i | ||||||||
\(544\) | −4.68384e6 | −0.678586 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 960400. | 0.137870 | ||||||||
\(547\) | 5.00235e6i | 0.714835i | 0.933945 | + | 0.357418i | \(0.116343\pi\) | ||||
−0.933945 | + | 0.357418i | \(0.883657\pi\) | |||||||
\(548\) | − 1.39034e7i | − 1.97774i | ||||||||
\(549\) | 1.20546e6 | 0.170695 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −334964. | −0.0470023 | ||||||||
\(552\) | − 9.19296e6i | − 1.28413i | ||||||||
\(553\) | − 1.55742e6i | − 0.216567i | ||||||||
\(554\) | −1.06409e7 | −1.47300 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.40761e6 | −0.330293 | ||||||||
\(557\) | − 9.01961e6i | − 1.23183i | −0.787814 | − | 0.615913i | \(-0.788787\pi\) | ||||
0.787814 | − | 0.615913i | \(-0.211213\pi\) | |||||||
\(558\) | − 3.59268e6i | − 0.488465i | ||||||||
\(559\) | 1.52320e6 | 0.206171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.59306e6 | 0.750312 | ||||||||
\(562\) | − 223420.i | − 0.0298388i | ||||||||
\(563\) | 1.24051e7i | 1.64941i | 0.565561 | + | 0.824707i | \(0.308660\pi\) | ||||
−0.565561 | + | 0.824707i | \(0.691340\pi\) | |||||||
\(564\) | 8.87645e6 | 1.17501 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.49574e7 | 3.27460 | ||||||||
\(567\) | − 2.22553e6i | − 0.290721i | ||||||||
\(568\) | 2.10816e7i | 2.74178i | ||||||||
\(569\) | −6.48804e6 | −0.840103 | −0.420052 | − | 0.907500i | \(-0.637988\pi\) | ||||
−0.420052 | + | 0.907500i | \(0.637988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.02285e7 | −1.31287 | −0.656435 | − | 0.754382i | \(-0.727936\pi\) | ||||
−0.656435 | + | 0.754382i | \(0.727936\pi\) | |||||||
\(572\) | 2.20864e6i | 0.282251i | ||||||||
\(573\) | − 5.01570e6i | − 0.638182i | ||||||||
\(574\) | 8.80138e6 | 1.11499 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 863296. | 0.108419 | ||||||||
\(577\) | − 2.65338e6i | − 0.331787i | −0.986144 | − | 0.165894i | \(-0.946949\pi\) | ||||
0.986144 | − | 0.165894i | \(-0.0530508\pi\) | |||||||
\(578\) | − 1.54543e7i | − 1.92411i | ||||||||
\(579\) | −1.38538e7 | −1.71740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00636e6 | 0.123684 | ||||||||
\(582\) | 8.19084e6i | 1.00235i | ||||||||
\(583\) | 524784.i | 0.0639454i | ||||||||
\(584\) | 2.45095e7 | 2.97374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.93178e7 | 2.32387 | ||||||||
\(587\) | 1.43044e7i | 1.71346i | 0.515766 | + | 0.856729i | \(0.327507\pi\) | ||||
−0.515766 | + | 0.856729i | \(0.672493\pi\) | |||||||
\(588\) | − 2.28575e6i | − 0.272638i | ||||||||
\(589\) | −749112. | −0.0889731 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.38607e7 | 1.63236 | ||||||||
\(592\) | 1.48068e7i | 1.73642i | ||||||||
\(593\) | − 1.00265e7i | − 1.17088i | −0.810714 | − | 0.585442i | \(-0.800921\pi\) | ||||
0.810714 | − | 0.585442i | \(-0.199079\pi\) | |||||||
\(594\) | 9.41920e6 | 1.09534 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.37537e6 | −0.158600 | ||||||||
\(597\) | − 1.17706e7i | − 1.35164i | ||||||||
\(598\) | 2.55360e6i | 0.292011i | ||||||||
\(599\) | 7.52292e6 | 0.856681 | 0.428341 | − | 0.903617i | \(-0.359098\pi\) | ||||
0.428341 | + | 0.903617i | \(0.359098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.38625e6 | 0.382413 | 0.191207 | − | 0.981550i | \(-0.438760\pi\) | ||||
0.191207 | + | 0.981550i | \(0.438760\pi\) | |||||||
\(602\) | − 5.33120e6i | − 0.599562i | ||||||||
\(603\) | 2.27499e6i | 0.254792i | ||||||||
\(604\) | −4.82147e6 | −0.537759 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.41744e6 | 0.599256 | ||||||||
\(607\) | 6.90861e6i | 0.761060i | 0.924769 | + | 0.380530i | \(0.124258\pi\) | ||||
−0.924769 | + | 0.380530i | \(0.875742\pi\) | |||||||
\(608\) | 266560.i | 0.0292439i | ||||||||
\(609\) | −2.34475e6 | −0.256185 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.30536e6 | −0.141458 | ||||||||
\(612\) | − 5.50351e6i | − 0.593966i | ||||||||
\(613\) | − 9.68896e6i | − 1.04142i | −0.853734 | − | 0.520710i | \(-0.825667\pi\) | ||||
0.853734 | − | 0.520710i | \(-0.174333\pi\) | |||||||
\(614\) | −4.59074e6 | −0.491430 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.09248e6 | 0.434545 | ||||||||
\(617\) | 7.84742e6i | 0.829877i | 0.909849 | + | 0.414939i | \(0.136197\pi\) | ||||
−0.909849 | + | 0.414939i | \(0.863803\pi\) | |||||||
\(618\) | 7.42840e6i | 0.782391i | ||||||||
\(619\) | 1.01972e7 | 1.06968 | 0.534840 | − | 0.844953i | \(-0.320372\pi\) | ||||
0.534840 | + | 0.844953i | \(0.320372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.40544e6 | 0.770587 | ||||||||
\(622\) | 6.67128e6i | 0.691406i | ||||||||
\(623\) | 2.47852e6i | 0.255842i | ||||||||
\(624\) | −2.79104e6 | −0.286949 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.11034e6 | 0.113245 | ||||||||
\(627\) | − 318304.i | − 0.0323350i | ||||||||
\(628\) | 1.99596e7i | 2.01954i | ||||||||
\(629\) | −1.79054e7 | −1.80450 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.36258e6 | −0.836116 | −0.418058 | − | 0.908420i | \(-0.637289\pi\) | ||||
−0.418058 | + | 0.908420i | \(0.637289\pi\) | |||||||
\(632\) | 1.14422e7i | 1.13951i | ||||||||
\(633\) | − 1.61102e7i | − 1.59806i | ||||||||
\(634\) | −687780. | −0.0679558 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.15342e6 | −0.211099 | ||||||||
\(637\) | 336140.i | 0.0328225i | ||||||||
\(638\) | − 7.92976e6i | − 0.771273i | ||||||||
\(639\) | −2.75232e6 | −0.266653 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.10283e6 | 0.106014 | 0.0530070 | − | 0.998594i | \(-0.483119\pi\) | ||||
0.0530070 | + | 0.998594i | \(0.483119\pi\) | |||||||
\(642\) | 2.04854e7i | 1.96158i | ||||||||
\(643\) | 1.71354e7i | 1.63443i | 0.576330 | + | 0.817217i | \(0.304484\pi\) | ||||
−0.576330 | + | 0.817217i | \(0.695516\pi\) | |||||||
\(644\) | 6.07757e6 | 0.577451 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.68756e6 | −0.159103 | ||||||||
\(647\) | 54964.0i | 0.00516200i | 0.999997 | + | 0.00258100i | \(0.000821558\pi\) | ||||
−0.999997 | + | 0.00258100i | \(0.999178\pi\) | |||||||
\(648\) | 1.63508e7i | 1.52969i | ||||||||
\(649\) | 633360. | 0.0590254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.24378e6 | −0.484945 | ||||||||
\(652\) | − 897056.i | − 0.0826420i | ||||||||
\(653\) | − 485166.i | − 0.0445254i | −0.999752 | − | 0.0222627i | \(-0.992913\pi\) | ||||
0.999752 | − | 0.0222627i | \(-0.00708702\pi\) | |||||||
\(654\) | −1.30057e7 | −1.18902 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.55779e7 | −2.32063 | ||||||||
\(657\) | 3.19985e6i | 0.289212i | ||||||||
\(658\) | 4.56876e6i | 0.411371i | ||||||||
\(659\) | 2.72136e6 | 0.244103 | 0.122051 | − | 0.992524i | \(-0.461053\pi\) | ||||
0.122051 | + | 0.992524i | \(0.461053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.14525e6 | −0.190974 | −0.0954869 | − | 0.995431i | \(-0.530441\pi\) | ||||
−0.0954869 | + | 0.995431i | \(0.530441\pi\) | |||||||
\(662\) | − 5.64448e6i | − 0.500586i | ||||||||
\(663\) | − 3.37512e6i | − 0.298198i | ||||||||
\(664\) | −7.39368e6 | −0.650789 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.88706e6 | −0.426935 | ||||||||
\(667\) | − 6.23443e6i | − 0.542603i | ||||||||
\(668\) | 3.35656e7i | 2.91041i | ||||||||
\(669\) | −1.15397e7 | −0.996848 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.95034e6 | 0.510194 | ||||||||
\(672\) | 1.86592e6i | 0.159393i | ||||||||
\(673\) | 2.92796e6i | 0.249188i | 0.992208 | + | 0.124594i | \(0.0397629\pi\) | ||||
−0.992208 | + | 0.124594i | \(0.960237\pi\) | |||||||
\(674\) | 2.07729e7 | 1.76136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39151e7 | −2.01282 | ||||||||
\(677\) | 1.34992e7i | 1.13198i | 0.824414 | + | 0.565988i | \(0.191505\pi\) | ||||
−0.824414 | + | 0.565988i | \(0.808495\pi\) | |||||||
\(678\) | − 1.16696e7i | − 0.974945i | ||||||||
\(679\) | −2.86679e6 | −0.238628 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.04135e6 | −0.0860455 | ||||||||
\(682\) | − 1.77341e7i | − 1.45998i | ||||||||
\(683\) | − 5.42972e6i | − 0.445375i | −0.974890 | − | 0.222688i | \(-0.928517\pi\) | ||||
0.974890 | − | 0.222688i | \(-0.0714830\pi\) | |||||||
\(684\) | −313208. | −0.0255972 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.17649e6 | 0.0954504 | ||||||||
\(687\) | 1.58474e7i | 1.28105i | ||||||||
\(688\) | 1.54931e7i | 1.24787i | ||||||||
\(689\) | 316680. | 0.0254140 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.08280e7 | 1.65940 | 0.829702 | − | 0.558207i | \(-0.188510\pi\) | ||||
0.829702 | + | 0.558207i | \(0.188510\pi\) | |||||||
\(692\) | − 1.63687e7i | − 1.29942i | ||||||||
\(693\) | 534296.i | 0.0422619i | ||||||||
\(694\) | −532480. | −0.0419667 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.72267e7 | 1.34797 | ||||||||
\(697\) | − 3.09306e7i | − 2.41160i | ||||||||
\(698\) | 2.27200e7i | 1.76510i | ||||||||
\(699\) | −2.78216e6 | −0.215372 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.35141e7 | 1.80731 | 0.903655 | − | 0.428261i | \(-0.140874\pi\) | ||||
0.903655 | + | 0.428261i | \(0.140874\pi\) | |||||||
\(702\) | − 5.68400e6i | − 0.435323i | ||||||||
\(703\) | 1.01900e6i | 0.0777656i | ||||||||
\(704\) | 4.26138e6 | 0.324055 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00645e7 | −3.02516 | ||||||||
\(707\) | 1.89610e6i | 0.142664i | ||||||||
\(708\) | 2.59896e6i | 0.194857i | ||||||||
\(709\) | 1.95747e7 | 1.46244 | 0.731221 | − | 0.682140i | \(-0.238951\pi\) | ||||
0.731221 | + | 0.682140i | \(0.238951\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.49385e6 | −0.110824 | ||||||||
\(712\) | − 1.82095e7i | − 1.34617i | ||||||||
\(713\) | − 1.39427e7i | − 1.02712i | ||||||||
\(714\) | −1.18129e7 | −0.867185 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.00554e7 | 1.46200 | ||||||||
\(717\) | 6.76066e6i | 0.491124i | ||||||||
\(718\) | − 737840.i | − 0.0534135i | ||||||||
\(719\) | 2.61152e7 | 1.88396 | 0.941978 | − | 0.335674i | \(-0.108964\pi\) | ||||
0.941978 | + | 0.335674i | \(0.108964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.59994e6 | −0.186262 | ||||||||
\(722\) | − 2.46650e7i | − 1.76091i | ||||||||
\(723\) | − 1.12827e7i | − 0.802729i | ||||||||
\(724\) | 2.29146e7 | 1.62468 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.50118e7 | −1.05704 | ||||||||
\(727\) | − 1.54126e7i | − 1.08154i | −0.841172 | − | 0.540768i | \(-0.818134\pi\) | ||||
0.841172 | − | 0.540768i | \(-0.181866\pi\) | |||||||
\(728\) | − 2.46960e6i | − 0.172702i | ||||||||
\(729\) | −1.59468e7 | −1.11136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.87354e7 | −1.29679 | ||||||||
\(732\) | 2.44169e7i | 1.68427i | ||||||||
\(733\) | − 1.69868e7i | − 1.16776i | −0.811841 | − | 0.583878i | \(-0.801535\pi\) | ||||
0.811841 | − | 0.583878i | \(-0.198465\pi\) | |||||||
\(734\) | 1.40431e7 | 0.962107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.96128e6 | −0.337597 | ||||||||
\(737\) | 1.12297e7i | 0.761554i | ||||||||
\(738\) | − 8.44214e6i | − 0.570574i | ||||||||
\(739\) | −2.01511e6 | −0.135734 | −0.0678669 | − | 0.997694i | \(-0.521619\pi\) | ||||
−0.0678669 | + | 0.997694i | \(0.521619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −192080. | −0.0128510 | ||||||||
\(742\) | − 1.10838e6i | − 0.0739059i | ||||||||
\(743\) | − 1.51381e7i | − 1.00600i | −0.864286 | − | 0.503001i | \(-0.832229\pi\) | ||||
0.864286 | − | 0.503001i | \(-0.167771\pi\) | |||||||
\(744\) | 3.85258e7 | 2.55164 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.60323e7 | 1.05475 | ||||||||
\(747\) | − 965286.i | − 0.0632928i | ||||||||
\(748\) | − 2.71663e7i | − 1.77532i | ||||||||
\(749\) | −7.16988e6 | −0.466989 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.21401e6 | 0.466742 | 0.233371 | − | 0.972388i | \(-0.425024\pi\) | ||||
0.233371 | + | 0.972388i | \(0.425024\pi\) | |||||||
\(752\) | − 1.32774e7i | − 0.856185i | ||||||||
\(753\) | − 6.03033e6i | − 0.387573i | ||||||||
\(754\) | −4.78520e6 | −0.306529 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.35279e7 | −0.860848 | ||||||||
\(757\) | 1.09697e7i | 0.695755i | 0.937540 | + | 0.347877i | \(0.113097\pi\) | ||||
−0.937540 | + | 0.347877i | \(0.886903\pi\) | |||||||
\(758\) | 4.77012e7i | 3.01548i | ||||||||
\(759\) | 5.92435e6 | 0.373281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.92442e7 | 1.20459 | 0.602293 | − | 0.798275i | \(-0.294254\pi\) | ||||
0.602293 | + | 0.798275i | \(0.294254\pi\) | |||||||
\(762\) | − 8.45376e6i | − 0.527427i | ||||||||
\(763\) | − 4.55200e6i | − 0.283068i | ||||||||
\(764\) | −2.43620e7 | −1.51001 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.23079e7 | 1.37368 | ||||||||
\(767\) | − 382200.i | − 0.0234586i | ||||||||
\(768\) | 2.96719e7i | 1.81528i | ||||||||
\(769\) | −8.21185e6 | −0.500755 | −0.250378 | − | 0.968148i | \(-0.580555\pi\) | ||||
−0.250378 | + | 0.968148i | \(0.580555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.64767e7 | 0.998241 | ||||||||
\(772\) | 6.72897e7i | 4.06355i | ||||||||
\(773\) | 1.86187e7i | 1.12073i | 0.828247 | + | 0.560363i | \(0.189338\pi\) | ||||
−0.828247 | + | 0.560363i | \(0.810662\pi\) | |||||||
\(774\) | −5.11360e6 | −0.306813 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.10622e7 | 1.25559 | ||||||||
\(777\) | 7.13303e6i | 0.423859i | ||||||||
\(778\) | − 4.84024e7i | − 2.86694i | ||||||||
\(779\) | −1.76028e6 | −0.103929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.35859e7 | −0.797006 | ||||||||
\(782\) | − 3.14093e7i | − 1.83671i | ||||||||
\(783\) | 1.38771e7i | 0.808898i | ||||||||
\(784\) | −3.41902e6 | −0.198661 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.62204e6 | −0.497799 | ||||||||
\(787\) | − 2.62501e7i | − 1.51075i | −0.655291 | − | 0.755377i | \(-0.727454\pi\) | ||||
0.655291 | − | 0.755377i | \(-0.272546\pi\) | |||||||
\(788\) | − 6.73234e7i | − 3.86234i | ||||||||
\(789\) | 1.80737e7 | 1.03360 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.08435e6 | 0.232103 | ||||||||
\(792\) | − 3.92544e6i | − 0.222370i | ||||||||
\(793\) | − 3.59072e6i | − 0.202768i | ||||||||
\(794\) | 9.95820e6 | 0.560570 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.71714e7 | −3.19813 | ||||||||
\(797\) | 1.00373e7i | 0.559720i | 0.960041 | + | 0.279860i | \(0.0902881\pi\) | ||||
−0.960041 | + | 0.279860i | \(0.909712\pi\) | |||||||
\(798\) | 672280.i | 0.0373717i | ||||||||
\(799\) | 1.60559e7 | 0.889751 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.37735e6 | 0.130922 | ||||||||
\(802\) | − 3.31605e7i | − 1.82048i | ||||||||
\(803\) | 1.57950e7i | 0.864433i | ||||||||
\(804\) | −4.60806e7 | −2.51407 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.07016e7 | −0.580245 | ||||||||
\(807\) | − 1.78858e7i | − 0.966772i | ||||||||
\(808\) | − 1.39306e7i | − 0.750655i | ||||||||
\(809\) | −1.40884e7 | −0.756816 | −0.378408 | − | 0.925639i | \(-0.623528\pi\) | ||||
−0.378408 | + | 0.925639i | \(0.623528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.81433e7 | 0.968646 | 0.484323 | − | 0.874889i | \(-0.339066\pi\) | ||||
0.484323 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(812\) | 1.13888e7i | 0.606160i | ||||||||
\(813\) | − 2.31076e7i | − 1.22611i | ||||||||
\(814\) | −2.41234e7 | −1.27608 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.43298e7 | 1.80487 | ||||||||
\(817\) | 1.06624e6i | 0.0558856i | ||||||||
\(818\) | − 3.07273e7i | − 1.60562i | ||||||||
\(819\) | 322420. | 0.0167962 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.13669e7 | −1.10633 | −0.553164 | − | 0.833072i | \(-0.686580\pi\) | ||||
−0.553164 | + | 0.833072i | \(0.686580\pi\) | |||||||
\(822\) | 2.86247e7i | 1.47761i | ||||||||
\(823\) | 1.78017e7i | 0.916142i | 0.888916 | + | 0.458071i | \(0.151459\pi\) | ||||
−0.888916 | + | 0.458071i | \(0.848541\pi\) | |||||||
\(824\) | 1.91016e7 | 0.980058 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.33770e6 | −0.0682195 | ||||||||
\(827\) | − 1.62921e7i | − 0.828350i | −0.910197 | − | 0.414175i | \(-0.864070\pi\) | ||||
0.910197 | − | 0.414175i | \(-0.135930\pi\) | |||||||
\(828\) | − 5.82950e6i | − 0.295499i | ||||||||
\(829\) | 2.08499e6 | 0.105370 | 0.0526851 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526851 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.48973e7 | 0.748348 | ||||||||
\(832\) | − 2.57152e6i | − 0.128790i | ||||||||
\(833\) | − 4.13452e6i | − 0.206449i | ||||||||
\(834\) | 4.95684e6 | 0.246769 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.54605e6 | −0.0765081 | ||||||||
\(837\) | 3.10346e7i | 1.53120i | ||||||||
\(838\) | − 2.81438e7i | − 1.38443i | ||||||||
\(839\) | 2.27850e7 | 1.11749 | 0.558745 | − | 0.829340i | \(-0.311283\pi\) | ||||
0.558745 | + | 0.829340i | \(0.311283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.82842e6 | −0.430421 | ||||||||
\(842\) | 3.05802e7i | 1.48648i | ||||||||
\(843\) | 312788.i | 0.0151594i | ||||||||
\(844\) | −7.82498e7 | −3.78118 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.38228e6 | 0.210511 | ||||||||
\(847\) | − 5.25412e6i | − 0.251647i | ||||||||
\(848\) | 3.22109e6i | 0.153820i | ||||||||
\(849\) | −3.49403e7 | −1.66363 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.89660e7 | −0.897740 | ||||||||
\(852\) | − 5.57491e7i | − 2.63111i | ||||||||
\(853\) | − 2.26975e7i | − 1.06808i | −0.845458 | − | 0.534042i | \(-0.820672\pi\) | ||||
0.845458 | − | 0.534042i | \(-0.179328\pi\) | |||||||
\(854\) | −1.25675e7 | −0.589664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.26766e7 | 2.45716 | ||||||||
\(857\) | − 2.52900e7i | − 1.17624i | −0.808774 | − | 0.588120i | \(-0.799868\pi\) | ||||
0.808774 | − | 0.588120i | \(-0.200132\pi\) | |||||||
\(858\) | − 4.54720e6i | − 0.210875i | ||||||||
\(859\) | 1.03947e7 | 0.480652 | 0.240326 | − | 0.970692i | \(-0.422746\pi\) | ||||
0.240326 | + | 0.970692i | \(0.422746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.23219e7 | −0.566462 | ||||||||
\(862\) | 1.93750e7i | 0.888122i | ||||||||
\(863\) | 4.33399e7i | 1.98089i | 0.137892 | + | 0.990447i | \(0.455967\pi\) | ||||
−0.137892 | + | 0.990447i | \(0.544033\pi\) | |||||||
\(864\) | 1.10432e7 | 0.503281 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.94790e7 | −1.78884 | ||||||||
\(867\) | 2.16360e7i | 0.977527i | ||||||||
\(868\) | 2.54698e7i | 1.14743i | ||||||||
\(869\) | −7.37389e6 | −0.331243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.77656e6 | 0.302666 | ||||||||
\(872\) | 3.34433e7i | 1.48942i | ||||||||
\(873\) | 2.74978e6i | 0.122113i | ||||||||
\(874\) | −1.78752e6 | −0.0791539 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.48141e7 | −2.85370 | ||||||||
\(877\) | − 3.71659e7i | − 1.63172i | −0.578248 | − | 0.815861i | \(-0.696264\pi\) | ||||
0.578248 | − | 0.815861i | \(-0.303736\pi\) | |||||||
\(878\) | 7.41770e7i | 3.24738i | ||||||||
\(879\) | −2.70449e7 | −1.18063 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.04785e6 | 0.392740 | 0.196370 | − | 0.980530i | \(-0.437085\pi\) | ||||
0.196370 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(882\) | − 1.12847e6i | − 0.0488448i | ||||||||
\(883\) | 3.29679e7i | 1.42295i | 0.702712 | + | 0.711474i | \(0.251972\pi\) | ||||
−0.702712 | + | 0.711474i | \(0.748028\pi\) | |||||||
\(884\) | −1.63934e7 | −0.705569 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.40269e7 | −0.600313 | ||||||||
\(887\) | 1.61099e7i | 0.687517i | 0.939058 | + | 0.343758i | \(0.111700\pi\) | ||||
−0.939058 | + | 0.343758i | \(0.888300\pi\) | |||||||
\(888\) | − 5.24059e7i | − 2.23022i | ||||||||
\(889\) | 2.95882e6 | 0.125564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.05372e7 | −0.444663 | ||||||||
\(892\) | 5.60500e7i | 2.35865i | ||||||||
\(893\) | − 913752.i | − 0.0383442i | ||||||||
\(894\) | 2.83164e6 | 0.118493 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.32653e7 | −0.552009 | ||||||||
\(897\) | − 3.57504e6i | − 0.148354i | ||||||||
\(898\) | 5.90574e6i | 0.244390i | ||||||||
\(899\) | 2.61272e7 | 1.07819 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.89516e6 | −0.159850 | ||||||||
\(902\) | − 4.16718e7i | − 1.70540i | ||||||||
\(903\) | 7.46368e6i | 0.304603i | ||||||||
\(904\) | −3.00074e7 | −1.22126 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.92656e6 | 0.401771 | ||||||||
\(907\) | 4.47286e7i | 1.80537i | 0.430300 | + | 0.902686i | \(0.358408\pi\) | ||||
−0.430300 | + | 0.902686i | \(0.641592\pi\) | |||||||
\(908\) | 5.05798e6i | 0.203593i | ||||||||
\(909\) | 1.81871e6 | 0.0730053 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.60518e6 | −0.263687 | −0.131844 | − | 0.991271i | \(-0.542090\pi\) | ||||
−0.131844 | + | 0.991271i | \(0.542090\pi\) | |||||||
\(912\) | − 1.95373e6i | − 0.0777816i | ||||||||
\(913\) | − 4.76482e6i | − 0.189177i | ||||||||
\(914\) | −2.90484e7 | −1.15016 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.69730e7 | 3.03110 | ||||||||
\(917\) | − 3.01771e6i | − 0.118510i | ||||||||
\(918\) | 6.99132e7i | 2.73812i | ||||||||
\(919\) | 3.08930e7 | 1.20662 | 0.603311 | − | 0.797506i | \(-0.293848\pi\) | ||||
0.603311 | + | 0.797506i | \(0.293848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.42704e6 | 0.249667 | ||||||||
\(922\) | − 9.22684e6i | − 0.357459i | ||||||||
\(923\) | 8.19840e6i | 0.316756i | ||||||||
\(924\) | −1.08223e7 | −0.417005 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.18235e7 | −2.75258 | ||||||||
\(927\) | 2.49382e6i | 0.0953160i | ||||||||
\(928\) | − 9.29696e6i | − 0.354381i | ||||||||
\(929\) | 4.87215e6 | 0.185217 | 0.0926087 | − | 0.995703i | \(-0.470479\pi\) | ||||
0.0926087 | + | 0.995703i | \(0.470479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −235298. | −0.00889701 | ||||||||
\(932\) | 1.35134e7i | 0.509593i | ||||||||
\(933\) | − 9.33979e6i | − 0.351264i | ||||||||
\(934\) | −6.12570e6 | −0.229767 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.36880e6 | −0.0883769 | ||||||||
\(937\) | 3.25004e7i | 1.20932i | 0.796485 | + | 0.604658i | \(0.206690\pi\) | ||||
−0.796485 | + | 0.604658i | \(0.793310\pi\) | |||||||
\(938\) | − 2.37180e7i | − 0.880177i | ||||||||
\(939\) | −1.55448e6 | −0.0575334 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.64040e6 | −0.0972066 | −0.0486033 | − | 0.998818i | \(-0.515477\pi\) | ||||
−0.0486033 | + | 0.998818i | \(0.515477\pi\) | |||||||
\(942\) | − 4.10934e7i | − 1.50884i | ||||||||
\(943\) | − 3.27627e7i | − 1.19978i | ||||||||
\(944\) | 3.88752e6 | 0.141985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.52416e7 | −0.917042 | ||||||||
\(947\) | 4.08179e7i | 1.47903i | 0.673142 | + | 0.739513i | \(0.264944\pi\) | ||||
−0.673142 | + | 0.739513i | \(0.735056\pi\) | |||||||
\(948\) | − 3.02584e7i | − 1.09351i | ||||||||
\(949\) | 9.53148e6 | 0.343554 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 962892. | 0.0345244 | ||||||||
\(952\) | 3.03761e7i | 1.08627i | ||||||||
\(953\) | − 6.71983e6i | − 0.239677i | −0.992793 | − | 0.119838i | \(-0.961762\pi\) | ||||
0.992793 | − | 0.119838i | \(-0.0382376\pi\) | |||||||
\(954\) | −1.06314e6 | −0.0378198 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.28375e7 | 1.16205 | ||||||||
\(957\) | 1.11017e7i | 0.391840i | ||||||||
\(958\) | − 2.60330e7i | − 0.916454i | ||||||||
\(959\) | −1.00186e7 | −0.351773 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.98016e7 | 1.04095 | ||||||||
\(962\) | 1.45572e7i | 0.507154i | ||||||||
\(963\) | 6.87723e6i | 0.238972i | ||||||||
\(964\) | −5.48019e7 | −1.89934 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.25126e7 | −0.431426 | ||||||||
\(967\) | 2.78979e6i | 0.0959413i | 0.998849 | + | 0.0479707i | \(0.0152754\pi\) | ||||
−0.998849 | + | 0.0479707i | \(0.984725\pi\) | |||||||
\(968\) | 3.86017e7i | 1.32409i | ||||||||
\(969\) | 2.36258e6 | 0.0808310 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.33594e7 | 1.13545 | 0.567727 | − | 0.823217i | \(-0.307823\pi\) | ||||
0.567727 | + | 0.823217i | \(0.307823\pi\) | |||||||
\(972\) | 2.38486e7i | 0.809648i | ||||||||
\(973\) | 1.73489e6i | 0.0587477i | ||||||||
\(974\) | 5.46309e7 | 1.84519 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.65228e7 | 1.22727 | ||||||||
\(977\) | 7.60033e6i | 0.254739i | 0.991855 | + | 0.127370i | \(0.0406534\pi\) | ||||
−0.991855 | + | 0.127370i | \(0.959347\pi\) | |||||||
\(978\) | 1.84688e6i | 0.0617435i | ||||||||
\(979\) | 1.17350e7 | 0.391316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.36621e6 | −0.144854 | ||||||||
\(982\) | 1.64090e7i | 0.543004i | ||||||||
\(983\) | − 5.79760e6i | − 0.191366i | −0.995412 | − | 0.0956829i | \(-0.969497\pi\) | ||||
0.995412 | − | 0.0956829i | \(-0.0305035\pi\) | |||||||
\(984\) | 9.05285e7 | 2.98056 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.88580e7 | 1.92803 | ||||||||
\(987\) | − 6.39626e6i | − 0.208994i | ||||||||
\(988\) | 932960.i | 0.0304068i | ||||||||
\(989\) | −1.98451e7 | −0.645153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.26825e7 | 0.410224 | 0.205112 | − | 0.978739i | \(-0.434244\pi\) | ||||
0.205112 | + | 0.978739i | \(0.434244\pi\) | |||||||
\(992\) | − 2.07917e7i | − 0.670827i | ||||||||
\(993\) | 7.90227e6i | 0.254319i | ||||||||
\(994\) | 2.86944e7 | 0.921152 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.95522e7 | 0.624521 | ||||||||
\(997\) | − 1.44400e7i | − 0.460077i | −0.973182 | − | 0.230039i | \(-0.926115\pi\) | ||||
0.973182 | − | 0.230039i | \(-0.0738853\pi\) | |||||||
\(998\) | − 2.99796e7i | − 0.952796i | ||||||||
\(999\) | 4.22159e7 | 1.33833 |
(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 | 175.6.b.a.99.2 | 2 | ||
5.2 | odd | 4 | 7.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 175.6.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 175.6.b.a.99.1 | 2 | ||
15.2 | even | 4 | 63.6.a.e.1.1 | 1 | |||
20.7 | even | 4 | 112.6.a.g.1.1 | 1 | |||
35.2 | odd | 12 | 49.6.c.c.18.1 | 2 | |||
35.12 | even | 12 | 49.6.c.b.18.1 | 2 | |||
35.17 | even | 12 | 49.6.c.b.30.1 | 2 | |||
35.27 | even | 4 | 49.6.a.a.1.1 | 1 | |||
35.32 | odd | 12 | 49.6.c.c.30.1 | 2 | |||
40.27 | even | 4 | 448.6.a.c.1.1 | 1 | |||
40.37 | odd | 4 | 448.6.a.m.1.1 | 1 | |||
55.32 | even | 4 | 847.6.a.b.1.1 | 1 | |||
60.47 | odd | 4 | 1008.6.a.y.1.1 | 1 | |||
105.62 | odd | 4 | 441.6.a.k.1.1 | 1 | |||
140.27 | odd | 4 | 784.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
49.6.a.a.1.1 | 1 | 35.27 | even | 4 | |||
49.6.c.b.18.1 | 2 | 35.12 | even | 12 | |||
49.6.c.b.30.1 | 2 | 35.17 | even | 12 | |||
49.6.c.c.18.1 | 2 | 35.2 | odd | 12 | |||
49.6.c.c.30.1 | 2 | 35.32 | odd | 12 | |||
63.6.a.e.1.1 | 1 | 15.2 | even | 4 | |||
112.6.a.g.1.1 | 1 | 20.7 | even | 4 | |||
175.6.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
175.6.b.a.99.1 | 2 | 5.4 | even | 2 | inner | ||
175.6.b.a.99.2 | 2 | 1.1 | even | 1 | trivial | ||
441.6.a.k.1.1 | 1 | 105.62 | odd | 4 | |||
448.6.a.c.1.1 | 1 | 40.27 | even | 4 | |||
448.6.a.m.1.1 | 1 | 40.37 | odd | 4 | |||
784.6.a.c.1.1 | 1 | 140.27 | odd | 4 | |||
847.6.a.b.1.1 | 1 | 55.32 | even | 4 | |||
1008.6.a.y.1.1 | 1 | 60.47 | odd | 4 |