Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,6,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(8.01919099065\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.6.b.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 26.0000i | 1.66790i | 0.551839 | + | 0.833950i | \(0.313926\pi\) | ||||
−0.551839 | + | 0.833950i | \(0.686074\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 104.000 | 1.17938 | ||||||||
\(7\) | − 22.0000i | − 0.169698i | −0.996394 | − | 0.0848492i | \(-0.972959\pi\) | ||||
0.996394 | − | 0.0848492i | \(-0.0270408\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −433.000 | −1.78189 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −768.000 | −1.91372 | −0.956862 | − | 0.290541i | \(-0.906165\pi\) | ||||
−0.956862 | + | 0.290541i | \(0.906165\pi\) | |||||||
\(12\) | − 416.000i | − 0.833950i | ||||||||
\(13\) | 46.0000i | 0.0754917i | 0.999287 | + | 0.0377459i | \(0.0120177\pi\) | ||||
−0.999287 | + | 0.0377459i | \(0.987982\pi\) | |||||||
\(14\) | −88.0000 | −0.119995 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 378.000i | 0.317227i | 0.987341 | + | 0.158613i | \(0.0507023\pi\) | ||||
−0.987341 | + | 0.158613i | \(0.949298\pi\) | |||||||
\(18\) | 1732.00i | 1.25999i | ||||||||
\(19\) | −1100.00 | −0.699051 | −0.349525 | − | 0.936927i | \(-0.613657\pi\) | ||||
−0.349525 | + | 0.936927i | \(0.613657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 572.000 | 0.283040 | ||||||||
\(22\) | 3072.00i | 1.35321i | ||||||||
\(23\) | 1986.00i | 0.782816i | 0.920217 | + | 0.391408i | \(0.128012\pi\) | ||||
−0.920217 | + | 0.391408i | \(0.871988\pi\) | |||||||
\(24\) | −1664.00 | −0.589692 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 184.000 | 0.0533807 | ||||||||
\(27\) | − 4940.00i | − 1.30412i | ||||||||
\(28\) | 352.000i | 0.0848492i | ||||||||
\(29\) | 5610.00 | 1.23870 | 0.619352 | − | 0.785113i | \(-0.287395\pi\) | ||||
0.619352 | + | 0.785113i | \(0.287395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3988.00 | −0.745334 | −0.372667 | − | 0.927965i | \(-0.621557\pi\) | ||||
−0.372667 | + | 0.927965i | \(0.621557\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | − 19968.0i | − 3.19190i | ||||||||
\(34\) | 1512.00 | 0.224313 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6928.00 | 0.890947 | ||||||||
\(37\) | − 142.000i | − 0.0170523i | −0.999964 | − | 0.00852617i | \(-0.997286\pi\) | ||||
0.999964 | − | 0.00852617i | \(-0.00271400\pi\) | |||||||
\(38\) | 4400.00i | 0.494303i | ||||||||
\(39\) | −1196.00 | −0.125913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1542.00 | 0.143260 | 0.0716300 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716300 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(42\) | − 2288.00i | − 0.200139i | ||||||||
\(43\) | 5026.00i | 0.414526i | 0.978285 | + | 0.207263i | \(0.0664555\pi\) | ||||
−0.978285 | + | 0.207263i | \(0.933544\pi\) | |||||||
\(44\) | 12288.0 | 0.956862 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7944.00 | 0.553534 | ||||||||
\(47\) | 24738.0i | 1.63350i | 0.576990 | + | 0.816752i | \(0.304227\pi\) | ||||
−0.576990 | + | 0.816752i | \(0.695773\pi\) | |||||||
\(48\) | 6656.00i | 0.416975i | ||||||||
\(49\) | 16323.0 | 0.971202 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9828.00 | −0.529102 | ||||||||
\(52\) | − 736.000i | − 0.0377459i | ||||||||
\(53\) | 14166.0i | 0.692720i | 0.938102 | + | 0.346360i | \(0.112582\pi\) | ||||
−0.938102 | + | 0.346360i | \(0.887418\pi\) | |||||||
\(54\) | −19760.0 | −0.922152 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1408.00 | 0.0599974 | ||||||||
\(57\) | − 28600.0i | − 1.16595i | ||||||||
\(58\) | − 22440.0i | − 0.875897i | ||||||||
\(59\) | −28380.0 | −1.06141 | −0.530704 | − | 0.847557i | \(-0.678072\pi\) | ||||
−0.530704 | + | 0.847557i | \(0.678072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5522.00 | 0.190008 | 0.0950040 | − | 0.995477i | \(-0.469714\pi\) | ||||
0.0950040 | + | 0.995477i | \(0.469714\pi\) | |||||||
\(62\) | 15952.0i | 0.527031i | ||||||||
\(63\) | 9526.00i | 0.302384i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −79872.0 | −2.25702 | ||||||||
\(67\) | − 24742.0i | − 0.673361i | −0.941619 | − | 0.336680i | \(-0.890696\pi\) | ||||
0.941619 | − | 0.336680i | \(-0.109304\pi\) | |||||||
\(68\) | − 6048.00i | − 0.158613i | ||||||||
\(69\) | −51636.0 | −1.30566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42372.0 | 0.997546 | 0.498773 | − | 0.866733i | \(-0.333784\pi\) | ||||
0.498773 | + | 0.866733i | \(0.333784\pi\) | |||||||
\(72\) | − 27712.0i | − 0.629994i | ||||||||
\(73\) | 52126.0i | 1.14485i | 0.819958 | + | 0.572423i | \(0.193997\pi\) | ||||
−0.819958 | + | 0.572423i | \(0.806003\pi\) | |||||||
\(74\) | −568.000 | −0.0120578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17600.0 | 0.349525 | ||||||||
\(77\) | 16896.0i | 0.324756i | ||||||||
\(78\) | 4784.00i | 0.0890337i | ||||||||
\(79\) | 39640.0 | 0.714605 | 0.357302 | − | 0.933989i | \(-0.383697\pi\) | ||||
0.357302 | + | 0.933989i | \(0.383697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23221.0 | 0.393250 | ||||||||
\(82\) | − 6168.00i | − 0.101300i | ||||||||
\(83\) | 59826.0i | 0.953223i | 0.879114 | + | 0.476612i | \(0.158135\pi\) | ||||
−0.879114 | + | 0.476612i | \(0.841865\pi\) | |||||||
\(84\) | −9152.00 | −0.141520 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20104.0 | 0.293114 | ||||||||
\(87\) | 145860.i | 2.06604i | ||||||||
\(88\) | − 49152.0i | − 0.676604i | ||||||||
\(89\) | −57690.0 | −0.772015 | −0.386007 | − | 0.922496i | \(-0.626146\pi\) | ||||
−0.386007 | + | 0.922496i | \(0.626146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1012.00 | 0.0128108 | ||||||||
\(92\) | − 31776.0i | − 0.391408i | ||||||||
\(93\) | − 103688.i | − 1.24314i | ||||||||
\(94\) | 98952.0 | 1.15506 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 26624.0 | 0.294846 | ||||||||
\(97\) | − 144382.i | − 1.55806i | −0.626988 | − | 0.779029i | \(-0.715712\pi\) | ||||
0.626988 | − | 0.779029i | \(-0.284288\pi\) | |||||||
\(98\) | − 65292.0i | − 0.686744i | ||||||||
\(99\) | 332544. | 3.41005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −141258. | −1.37787 | −0.688937 | − | 0.724821i | \(-0.741922\pi\) | ||||
−0.688937 | + | 0.724821i | \(0.741922\pi\) | |||||||
\(102\) | 39312.0i | 0.374132i | ||||||||
\(103\) | − 139814.i | − 1.29855i | −0.760555 | − | 0.649273i | \(-0.775073\pi\) | ||||
0.760555 | − | 0.649273i | \(-0.224927\pi\) | |||||||
\(104\) | −2944.00 | −0.0266904 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 56664.0 | 0.489827 | ||||||||
\(107\) | 86418.0i | 0.729701i | 0.931066 | + | 0.364850i | \(0.118880\pi\) | ||||
−0.931066 | + | 0.364850i | \(0.881120\pi\) | |||||||
\(108\) | 79040.0i | 0.652060i | ||||||||
\(109\) | −218450. | −1.76111 | −0.880554 | − | 0.473947i | \(-0.842829\pi\) | ||||
−0.880554 | + | 0.473947i | \(0.842829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3692.00 | 0.0284416 | ||||||||
\(112\) | − 5632.00i | − 0.0424246i | ||||||||
\(113\) | 28806.0i | 0.212220i | 0.994354 | + | 0.106110i | \(0.0338396\pi\) | ||||
−0.994354 | + | 0.106110i | \(0.966160\pi\) | |||||||
\(114\) | −114400. | −0.824449 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −89760.0 | −0.619352 | ||||||||
\(117\) | − 19918.0i | − 0.134518i | ||||||||
\(118\) | 113520.i | 0.750529i | ||||||||
\(119\) | 8316.00 | 0.0538328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 428773. | 2.66234 | ||||||||
\(122\) | − 22088.0i | − 0.134356i | ||||||||
\(123\) | 40092.0i | 0.238943i | ||||||||
\(124\) | 63808.0 | 0.372667 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 38104.0 | 0.213818 | ||||||||
\(127\) | − 216502.i | − 1.19111i | −0.803314 | − | 0.595556i | \(-0.796932\pi\) | ||||
0.803314 | − | 0.595556i | \(-0.203068\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −130676. | −0.691388 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −244608. | −1.24535 | −0.622676 | − | 0.782479i | \(-0.713955\pi\) | ||||
−0.622676 | + | 0.782479i | \(0.713955\pi\) | |||||||
\(132\) | 319488.i | 1.59595i | ||||||||
\(133\) | 24200.0i | 0.118628i | ||||||||
\(134\) | −98968.0 | −0.476138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24192.0 | −0.112157 | ||||||||
\(137\) | − 239502.i | − 1.09020i | −0.838370 | − | 0.545102i | \(-0.816491\pi\) | ||||
0.838370 | − | 0.545102i | \(-0.183509\pi\) | |||||||
\(138\) | 206544.i | 0.923241i | ||||||||
\(139\) | −30860.0 | −0.135475 | −0.0677375 | − | 0.997703i | \(-0.521578\pi\) | ||||
−0.0677375 | + | 0.997703i | \(0.521578\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −643188. | −2.72452 | ||||||||
\(142\) | − 169488.i | − 0.705372i | ||||||||
\(143\) | − 35328.0i | − 0.144470i | ||||||||
\(144\) | −110848. | −0.445473 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 208504. | 0.809529 | ||||||||
\(147\) | 424398.i | 1.61987i | ||||||||
\(148\) | 2272.00i | 0.00852617i | ||||||||
\(149\) | 100950. | 0.372512 | 0.186256 | − | 0.982501i | \(-0.440365\pi\) | ||||
0.186256 | + | 0.982501i | \(0.440365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12452.0 | 0.0444423 | 0.0222212 | − | 0.999753i | \(-0.492926\pi\) | ||||
0.0222212 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(152\) | − 70400.0i | − 0.247152i | ||||||||
\(153\) | − 163674.i | − 0.565264i | ||||||||
\(154\) | 67584.0 | 0.229637 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 19136.0 | 0.0629564 | ||||||||
\(157\) | − 6022.00i | − 0.0194981i | −0.999952 | − | 0.00974903i | \(-0.996897\pi\) | ||||
0.999952 | − | 0.00974903i | \(-0.00310326\pi\) | |||||||
\(158\) | − 158560.i | − 0.505302i | ||||||||
\(159\) | −368316. | −1.15539 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 43692.0 | 0.132843 | ||||||||
\(162\) | − 92884.0i | − 0.278070i | ||||||||
\(163\) | 500866.i | 1.47656i | 0.674492 | + | 0.738282i | \(0.264363\pi\) | ||||
−0.674492 | + | 0.738282i | \(0.735637\pi\) | |||||||
\(164\) | −24672.0 | −0.0716300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 239304. | 0.674031 | ||||||||
\(167\) | 555258.i | 1.54065i | 0.637652 | + | 0.770324i | \(0.279906\pi\) | ||||
−0.637652 | + | 0.770324i | \(0.720094\pi\) | |||||||
\(168\) | 36608.0i | 0.100070i | ||||||||
\(169\) | 369177. | 0.994301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 476300. | 1.24563 | ||||||||
\(172\) | − 80416.0i | − 0.207263i | ||||||||
\(173\) | − 417354.i | − 1.06020i | −0.847934 | − | 0.530102i | \(-0.822154\pi\) | ||||
0.847934 | − | 0.530102i | \(-0.177846\pi\) | |||||||
\(174\) | 583440. | 1.46091 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −196608. | −0.478431 | ||||||||
\(177\) | − 737880.i | − 1.77032i | ||||||||
\(178\) | 230760.i | 0.545897i | ||||||||
\(179\) | 52380.0 | 0.122189 | 0.0610946 | − | 0.998132i | \(-0.480541\pi\) | ||||
0.0610946 | + | 0.998132i | \(0.480541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 546662. | 1.24029 | 0.620144 | − | 0.784488i | \(-0.287074\pi\) | ||||
0.620144 | + | 0.784488i | \(0.287074\pi\) | |||||||
\(182\) | − 4048.00i | − 0.00905862i | ||||||||
\(183\) | 143572.i | 0.316914i | ||||||||
\(184\) | −127104. | −0.276767 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −414752. | −0.879035 | ||||||||
\(187\) | − 290304.i | − 0.607084i | ||||||||
\(188\) | − 395808.i | − 0.816752i | ||||||||
\(189\) | −108680. | −0.221307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −452028. | −0.896565 | −0.448283 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448283 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(192\) | − 106496.i | − 0.208488i | ||||||||
\(193\) | − 485594.i | − 0.938383i | −0.883097 | − | 0.469191i | \(-0.844545\pi\) | ||||
0.883097 | − | 0.469191i | \(-0.155455\pi\) | |||||||
\(194\) | −577528. | −1.10171 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −261168. | −0.485601 | ||||||||
\(197\) | 1.01018e6i | 1.85452i | 0.374414 | + | 0.927262i | \(0.377844\pi\) | ||||
−0.374414 | + | 0.927262i | \(0.622156\pi\) | |||||||
\(198\) | − 1.33018e6i | − 2.41127i | ||||||||
\(199\) | 807640. | 1.44572 | 0.722862 | − | 0.690993i | \(-0.242826\pi\) | ||||
0.722862 | + | 0.690993i | \(0.242826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 643292. | 1.12310 | ||||||||
\(202\) | 565032.i | 0.974304i | ||||||||
\(203\) | − 123420.i | − 0.210206i | ||||||||
\(204\) | 157248. | 0.264551 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −559256. | −0.918211 | ||||||||
\(207\) | − 859938.i | − 1.39489i | ||||||||
\(208\) | 11776.0i | 0.0188729i | ||||||||
\(209\) | 844800. | 1.33779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 149552. | 0.231252 | 0.115626 | − | 0.993293i | \(-0.463113\pi\) | ||||
0.115626 | + | 0.993293i | \(0.463113\pi\) | |||||||
\(212\) | − 226656.i | − 0.346360i | ||||||||
\(213\) | 1.10167e6i | 1.66381i | ||||||||
\(214\) | 345672. | 0.515976 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 316160. | 0.461076 | ||||||||
\(217\) | 87736.0i | 0.126482i | ||||||||
\(218\) | 873800.i | 1.24529i | ||||||||
\(219\) | −1.35528e6 | −1.90949 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17388.0 | −0.0239480 | ||||||||
\(222\) | − 14768.0i | − 0.0201113i | ||||||||
\(223\) | 443506.i | 0.597224i | 0.954375 | + | 0.298612i | \(0.0965237\pi\) | ||||
−0.954375 | + | 0.298612i | \(0.903476\pi\) | |||||||
\(224\) | −22528.0 | −0.0299987 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 115224. | 0.150062 | ||||||||
\(227\) | 420018.i | 0.541007i | 0.962719 | + | 0.270504i | \(0.0871902\pi\) | ||||
−0.962719 | + | 0.270504i | \(0.912810\pi\) | |||||||
\(228\) | 457600.i | 0.582974i | ||||||||
\(229\) | −1.05875e6 | −1.33415 | −0.667075 | − | 0.744990i | \(-0.732454\pi\) | ||||
−0.667075 | + | 0.744990i | \(0.732454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −439296. | −0.541661 | ||||||||
\(232\) | 359040.i | 0.437948i | ||||||||
\(233\) | 1.27345e6i | 1.53671i | 0.640026 | + | 0.768353i | \(0.278923\pi\) | ||||
−0.640026 | + | 0.768353i | \(0.721077\pi\) | |||||||
\(234\) | −79672.0 | −0.0951187 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 454080. | 0.530704 | ||||||||
\(237\) | 1.03064e6i | 1.19189i | ||||||||
\(238\) | − 33264.0i | − 0.0380655i | ||||||||
\(239\) | 370680. | 0.419763 | 0.209882 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209882 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −561298. | −0.622517 | −0.311258 | − | 0.950325i | \(-0.600750\pi\) | ||||
−0.311258 | + | 0.950325i | \(0.600750\pi\) | |||||||
\(242\) | − 1.71509e6i | − 1.88256i | ||||||||
\(243\) | − 596674.i | − 0.648219i | ||||||||
\(244\) | −88352.0 | −0.0950040 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 160368. | 0.168958 | ||||||||
\(247\) | − 50600.0i | − 0.0527726i | ||||||||
\(248\) | − 255232.i | − 0.263515i | ||||||||
\(249\) | −1.55548e6 | −1.58988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 577152. | 0.578237 | 0.289119 | − | 0.957293i | \(-0.406638\pi\) | ||||
0.289119 | + | 0.957293i | \(0.406638\pi\) | |||||||
\(252\) | − 152416.i | − 0.151192i | ||||||||
\(253\) | − 1.52525e6i | − 1.49809i | ||||||||
\(254\) | −866008. | −0.842243 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − 651462.i | − 0.615257i | −0.951507 | − | 0.307628i | \(-0.900465\pi\) | ||||
0.951507 | − | 0.307628i | \(-0.0995353\pi\) | |||||||
\(258\) | 522704.i | 0.488885i | ||||||||
\(259\) | −3124.00 | −0.00289375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.42913e6 | −2.20724 | ||||||||
\(262\) | 978432.i | 0.880597i | ||||||||
\(263\) | − 917574.i | − 0.817997i | −0.912535 | − | 0.408999i | \(-0.865878\pi\) | ||||
0.912535 | − | 0.408999i | \(-0.134122\pi\) | |||||||
\(264\) | 1.27795e6 | 1.12851 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 96800.0 | 0.0838825 | ||||||||
\(267\) | − 1.49994e6i | − 1.28764i | ||||||||
\(268\) | 395872.i | 0.336680i | ||||||||
\(269\) | 735390. | 0.619637 | 0.309818 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309818 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12131e6 | −0.927474 | −0.463737 | − | 0.885973i | \(-0.653492\pi\) | ||||
−0.463737 | + | 0.885973i | \(0.653492\pi\) | |||||||
\(272\) | 96768.0i | 0.0793066i | ||||||||
\(273\) | 26312.0i | 0.0213672i | ||||||||
\(274\) | −958008. | −0.770891 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 826176. | 0.652830 | ||||||||
\(277\) | − 1.66034e6i | − 1.30016i | −0.759864 | − | 0.650082i | \(-0.774735\pi\) | ||||
0.759864 | − | 0.650082i | \(-0.225265\pi\) | |||||||
\(278\) | 123440.i | 0.0957952i | ||||||||
\(279\) | 1.72680e6 | 1.32811 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.45210e6 | 1.09706 | 0.548531 | − | 0.836130i | \(-0.315187\pi\) | ||||
0.548531 | + | 0.836130i | \(0.315187\pi\) | |||||||
\(282\) | 2.57275e6i | 1.92653i | ||||||||
\(283\) | − 309014.i | − 0.229357i | −0.993403 | − | 0.114679i | \(-0.963416\pi\) | ||||
0.993403 | − | 0.114679i | \(-0.0365838\pi\) | |||||||
\(284\) | −677952. | −0.498773 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −141312. | −0.102156 | ||||||||
\(287\) | − 33924.0i | − 0.0243110i | ||||||||
\(288\) | 443392.i | 0.314997i | ||||||||
\(289\) | 1.27697e6 | 0.899367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.75393e6 | 2.59869 | ||||||||
\(292\) | − 834016.i | − 0.572423i | ||||||||
\(293\) | 1.59301e6i | 1.08405i | 0.840363 | + | 0.542024i | \(0.182342\pi\) | ||||
−0.840363 | + | 0.542024i | \(0.817658\pi\) | |||||||
\(294\) | 1.69759e6 | 1.14542 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9088.00 | 0.00602891 | ||||||||
\(297\) | 3.79392e6i | 2.49573i | ||||||||
\(298\) | − 403800.i | − 0.263406i | ||||||||
\(299\) | −91356.0 | −0.0590961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110572. | 0.0703443 | ||||||||
\(302\) | − 49808.0i | − 0.0314255i | ||||||||
\(303\) | − 3.67271e6i | − 2.29816i | ||||||||
\(304\) | −281600. | −0.174763 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −654696. | −0.399702 | ||||||||
\(307\) | 1.24726e6i | 0.755284i | 0.925952 | + | 0.377642i | \(0.123265\pi\) | ||||
−0.925952 | + | 0.377642i | \(0.876735\pi\) | |||||||
\(308\) | − 270336.i | − 0.162378i | ||||||||
\(309\) | 3.63516e6 | 2.16585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −665988. | −0.390450 | −0.195225 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195225 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(312\) | − 76544.0i | − 0.0445169i | ||||||||
\(313\) | 591286.i | 0.341143i | 0.985345 | + | 0.170572i | \(0.0545614\pi\) | ||||
−0.985345 | + | 0.170572i | \(0.945439\pi\) | |||||||
\(314\) | −24088.0 | −0.0137872 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −634240. | −0.357302 | ||||||||
\(317\) | − 516342.i | − 0.288595i | −0.989534 | − | 0.144298i | \(-0.953908\pi\) | ||||
0.989534 | − | 0.144298i | \(-0.0460923\pi\) | |||||||
\(318\) | 1.47326e6i | 0.816983i | ||||||||
\(319\) | −4.30848e6 | −2.37054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.24687e6 | −1.21707 | ||||||||
\(322\) | − 174768.i | − 0.0939339i | ||||||||
\(323\) | − 415800.i | − 0.221757i | ||||||||
\(324\) | −371536. | −0.196625 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00346e6 | 1.04409 | ||||||||
\(327\) | − 5.67970e6i | − 2.93735i | ||||||||
\(328\) | 98688.0i | 0.0506500i | ||||||||
\(329\) | 544236. | 0.277203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.29577e6 | −1.65343 | −0.826717 | − | 0.562619i | \(-0.809794\pi\) | ||||
−0.826717 | + | 0.562619i | \(0.809794\pi\) | |||||||
\(332\) | − 957216.i | − 0.476612i | ||||||||
\(333\) | 61486.0i | 0.0303854i | ||||||||
\(334\) | 2.22103e6 | 1.08940 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 146432. | 0.0707600 | ||||||||
\(337\) | 1.91098e6i | 0.916602i | 0.888797 | + | 0.458301i | \(0.151542\pi\) | ||||
−0.888797 | + | 0.458301i | \(0.848458\pi\) | |||||||
\(338\) | − 1.47671e6i | − 0.703077i | ||||||||
\(339\) | −748956. | −0.353962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.06278e6 | 1.42636 | ||||||||
\(342\) | − 1.90520e6i | − 0.880796i | ||||||||
\(343\) | − 728860.i | − 0.334510i | ||||||||
\(344\) | −321664. | −0.146557 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.66942e6 | −0.749677 | ||||||||
\(347\) | 2.42006e6i | 1.07895i | 0.842001 | + | 0.539476i | \(0.181378\pi\) | ||||
−0.842001 | + | 0.539476i | \(0.818622\pi\) | |||||||
\(348\) | − 2.33376e6i | − 1.03302i | ||||||||
\(349\) | −2.50727e6 | −1.10189 | −0.550944 | − | 0.834542i | \(-0.685732\pi\) | ||||
−0.550944 | + | 0.834542i | \(0.685732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 227240. | 0.0984503 | ||||||||
\(352\) | 786432.i | 0.338302i | ||||||||
\(353\) | 413166.i | 0.176477i | 0.996099 | + | 0.0882384i | \(0.0281237\pi\) | ||||
−0.996099 | + | 0.0882384i | \(0.971876\pi\) | |||||||
\(354\) | −2.95152e6 | −1.25181 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 923040. | 0.386007 | ||||||||
\(357\) | 216216.i | 0.0897878i | ||||||||
\(358\) | − 209520.i | − 0.0864008i | ||||||||
\(359\) | −1.73772e6 | −0.711613 | −0.355806 | − | 0.934560i | \(-0.615794\pi\) | ||||
−0.355806 | + | 0.934560i | \(0.615794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26610e6 | −0.511328 | ||||||||
\(362\) | − 2.18665e6i | − 0.877016i | ||||||||
\(363\) | 1.11481e7i | 4.44052i | ||||||||
\(364\) | −16192.0 | −0.00640541 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 574288. | 0.224092 | ||||||||
\(367\) | 1.16098e6i | 0.449944i | 0.974365 | + | 0.224972i | \(0.0722291\pi\) | ||||
−0.974365 | + | 0.224972i | \(0.927771\pi\) | |||||||
\(368\) | 508416.i | 0.195704i | ||||||||
\(369\) | −667686. | −0.255274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 311652. | 0.117553 | ||||||||
\(372\) | 1.65901e6i | 0.621572i | ||||||||
\(373\) | − 343754.i | − 0.127931i | −0.997952 | − | 0.0639655i | \(-0.979625\pi\) | ||||
0.997952 | − | 0.0639655i | \(-0.0203748\pi\) | |||||||
\(374\) | −1.16122e6 | −0.429273 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.58323e6 | −0.577531 | ||||||||
\(377\) | 258060.i | 0.0935120i | ||||||||
\(378\) | 434720.i | 0.156488i | ||||||||
\(379\) | −573140. | −0.204957 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.62905e6 | 1.98666 | ||||||||
\(382\) | 1.80811e6i | 0.633967i | ||||||||
\(383\) | 2.88055e6i | 1.00341i | 0.865039 | + | 0.501704i | \(0.167293\pi\) | ||||
−0.865039 | + | 0.501704i | \(0.832707\pi\) | |||||||
\(384\) | −425984. | −0.147423 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.94238e6 | −0.663537 | ||||||||
\(387\) | − 2.17626e6i | − 0.738640i | ||||||||
\(388\) | 2.31011e6i | 0.779029i | ||||||||
\(389\) | 3.08559e6 | 1.03387 | 0.516933 | − | 0.856026i | \(-0.327074\pi\) | ||||
0.516933 | + | 0.856026i | \(0.327074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −750708. | −0.248330 | ||||||||
\(392\) | 1.04467e6i | 0.343372i | ||||||||
\(393\) | − 6.35981e6i | − 2.07712i | ||||||||
\(394\) | 4.04071e6 | 1.31135 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.32070e6 | −1.70503 | ||||||||
\(397\) | 885458.i | 0.281963i | 0.990012 | + | 0.140981i | \(0.0450258\pi\) | ||||
−0.990012 | + | 0.140981i | \(0.954974\pi\) | |||||||
\(398\) | − 3.23056e6i | − 1.02228i | ||||||||
\(399\) | −629200. | −0.197859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.75344e6 | −1.16565 | −0.582825 | − | 0.812598i | \(-0.698053\pi\) | ||||
−0.582825 | + | 0.812598i | \(0.698053\pi\) | |||||||
\(402\) | − 2.57317e6i | − 0.794151i | ||||||||
\(403\) | − 183448.i | − 0.0562666i | ||||||||
\(404\) | 2.26013e6 | 0.688937 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −493680. | −0.148638 | ||||||||
\(407\) | 109056.i | 0.0326335i | ||||||||
\(408\) | − 628992.i | − 0.187066i | ||||||||
\(409\) | 1.94653e6 | 0.575377 | 0.287689 | − | 0.957724i | \(-0.407113\pi\) | ||||
0.287689 | + | 0.957724i | \(0.407113\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.22705e6 | 1.81835 | ||||||||
\(412\) | 2.23702e6i | 0.649273i | ||||||||
\(413\) | 624360.i | 0.180119i | ||||||||
\(414\) | −3.43975e6 | −0.986339 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 47104.0 | 0.0133452 | ||||||||
\(417\) | − 802360.i | − 0.225959i | ||||||||
\(418\) | − 3.37920e6i | − 0.945961i | ||||||||
\(419\) | 2.99166e6 | 0.832486 | 0.416243 | − | 0.909253i | \(-0.363346\pi\) | ||||
0.416243 | + | 0.909253i | \(0.363346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.96660e6 | 1.09072 | 0.545360 | − | 0.838202i | \(-0.316393\pi\) | ||||
0.545360 | + | 0.838202i | \(0.316393\pi\) | |||||||
\(422\) | − 598208.i | − 0.163520i | ||||||||
\(423\) | − 1.07116e7i | − 2.91073i | ||||||||
\(424\) | −906624. | −0.244913 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.40669e6 | 1.17649 | ||||||||
\(427\) | − 121484.i | − 0.0322440i | ||||||||
\(428\) | − 1.38269e6i | − 0.364850i | ||||||||
\(429\) | 918528. | 0.240962 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.17115e6 | −1.34089 | −0.670446 | − | 0.741958i | \(-0.733897\pi\) | ||||
−0.670446 | + | 0.741958i | \(0.733897\pi\) | |||||||
\(432\) | − 1.26464e6i | − 0.326030i | ||||||||
\(433\) | 4.53485e6i | 1.16237i | 0.813773 | + | 0.581183i | \(0.197410\pi\) | ||||
−0.813773 | + | 0.581183i | \(0.802590\pi\) | |||||||
\(434\) | 350944. | 0.0894362 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.49520e6 | 0.880554 | ||||||||
\(437\) | − 2.18460e6i | − 0.547228i | ||||||||
\(438\) | 5.42110e6i | 1.35021i | ||||||||
\(439\) | 1.08220e6 | 0.268007 | 0.134004 | − | 0.990981i | \(-0.457217\pi\) | ||||
0.134004 | + | 0.990981i | \(0.457217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.06786e6 | −1.73058 | ||||||||
\(442\) | 69552.0i | 0.0169338i | ||||||||
\(443\) | 1.08079e6i | 0.261656i | 0.991405 | + | 0.130828i | \(0.0417635\pi\) | ||||
−0.991405 | + | 0.130828i | \(0.958236\pi\) | |||||||
\(444\) | −59072.0 | −0.0142208 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.77402e6 | 0.422301 | ||||||||
\(447\) | 2.62470e6i | 0.621314i | ||||||||
\(448\) | 90112.0i | 0.0212123i | ||||||||
\(449\) | −2.61783e6 | −0.612810 | −0.306405 | − | 0.951901i | \(-0.599126\pi\) | ||||
−0.306405 | + | 0.951901i | \(0.599126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18426e6 | −0.274160 | ||||||||
\(452\) | − 460896.i | − 0.106110i | ||||||||
\(453\) | 323752.i | 0.0741254i | ||||||||
\(454\) | 1.68007e6 | 0.382550 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.83040e6 | 0.412225 | ||||||||
\(457\) | 1.59046e6i | 0.356231i | 0.984010 | + | 0.178115i | \(0.0570001\pi\) | ||||
−0.984010 | + | 0.178115i | \(0.943000\pi\) | |||||||
\(458\) | 4.23500e6i | 0.943387i | ||||||||
\(459\) | 1.86732e6 | 0.413701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.25470e6 | 0.932431 | 0.466216 | − | 0.884671i | \(-0.345617\pi\) | ||||
0.466216 | + | 0.884671i | \(0.345617\pi\) | |||||||
\(462\) | 1.75718e6i | 0.383012i | ||||||||
\(463\) | − 3.26605e6i | − 0.708061i | −0.935234 | − | 0.354031i | \(-0.884811\pi\) | ||||
0.935234 | − | 0.354031i | \(-0.115189\pi\) | |||||||
\(464\) | 1.43616e6 | 0.309676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.09378e6 | 1.08662 | ||||||||
\(467\) | − 601542.i | − 0.127636i | −0.997962 | − | 0.0638181i | \(-0.979672\pi\) | ||||
0.997962 | − | 0.0638181i | \(-0.0203277\pi\) | |||||||
\(468\) | 318688.i | 0.0672591i | ||||||||
\(469\) | −544324. | −0.114268 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 156572. | 0.0325208 | ||||||||
\(472\) | − 1.81632e6i | − 0.375264i | ||||||||
\(473\) | − 3.85997e6i | − 0.793288i | ||||||||
\(474\) | 4.12256e6 | 0.842793 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −133056. | −0.0269164 | ||||||||
\(477\) | − 6.13388e6i | − 1.23435i | ||||||||
\(478\) | − 1.48272e6i | − 0.296817i | ||||||||
\(479\) | 4.57932e6 | 0.911931 | 0.455966 | − | 0.889997i | \(-0.349294\pi\) | ||||
0.455966 | + | 0.889997i | \(0.349294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6532.00 | 0.00128731 | ||||||||
\(482\) | 2.24519e6i | 0.440186i | ||||||||
\(483\) | 1.13599e6i | 0.221568i | ||||||||
\(484\) | −6.86037e6 | −1.33117 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.38670e6 | −0.458360 | ||||||||
\(487\) | 7.05226e6i | 1.34743i | 0.738992 | + | 0.673714i | \(0.235302\pi\) | ||||
−0.738992 | + | 0.673714i | \(0.764698\pi\) | |||||||
\(488\) | 353408.i | 0.0671780i | ||||||||
\(489\) | −1.30225e7 | −2.46276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.62349e6 | −0.491106 | −0.245553 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245553 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(492\) | − 641472.i | − 0.119472i | ||||||||
\(493\) | 2.12058e6i | 0.392950i | ||||||||
\(494\) | −202400. | −0.0373158 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.02093e6 | −0.186333 | ||||||||
\(497\) | − 932184.i | − 0.169282i | ||||||||
\(498\) | 6.22190e6i | 1.12422i | ||||||||
\(499\) | 3.61234e6 | 0.649437 | 0.324719 | − | 0.945811i | \(-0.394730\pi\) | ||||
0.324719 | + | 0.945811i | \(0.394730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.44367e7 | −2.56965 | ||||||||
\(502\) | − 2.30861e6i | − 0.408875i | ||||||||
\(503\) | − 9.15629e6i | − 1.61361i | −0.590815 | − | 0.806807i | \(-0.701194\pi\) | ||||
0.590815 | − | 0.806807i | \(-0.298806\pi\) | |||||||
\(504\) | −609664. | −0.106909 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.10099e6 | −1.05931 | ||||||||
\(507\) | 9.59860e6i | 1.65840i | ||||||||
\(508\) | 3.46403e6i | 0.595556i | ||||||||
\(509\) | −7.26159e6 | −1.24233 | −0.621165 | − | 0.783679i | \(-0.713340\pi\) | ||||
−0.621165 | + | 0.783679i | \(0.713340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.14677e6 | 0.194279 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 5.43400e6i | 0.911646i | ||||||||
\(514\) | −2.60585e6 | −0.435052 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.09082e6 | 0.345694 | ||||||||
\(517\) | − 1.89988e7i | − 3.12608i | ||||||||
\(518\) | 12496.0i | 0.00204619i | ||||||||
\(519\) | 1.08512e7 | 1.76831 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.81020e6 | 0.937771 | 0.468886 | − | 0.883259i | \(-0.344656\pi\) | ||||
0.468886 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(522\) | 9.71652e6i | 1.56075i | ||||||||
\(523\) | 8.17067e6i | 1.30618i | 0.757280 | + | 0.653090i | \(0.226528\pi\) | ||||
−0.757280 | + | 0.653090i | \(0.773472\pi\) | |||||||
\(524\) | 3.91373e6 | 0.622676 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.67030e6 | −0.578411 | ||||||||
\(527\) | − 1.50746e6i | − 0.236440i | ||||||||
\(528\) | − 5.11181e6i | − 0.797976i | ||||||||
\(529\) | 2.49215e6 | 0.387199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22885e7 | 1.89132 | ||||||||
\(532\) | − 387200.i | − 0.0593139i | ||||||||
\(533\) | 70932.0i | 0.0108149i | ||||||||
\(534\) | −5.99976e6 | −0.910502 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.58349e6 | 0.238069 | ||||||||
\(537\) | 1.36188e6i | 0.203800i | ||||||||
\(538\) | − 2.94156e6i | − 0.438149i | ||||||||
\(539\) | −1.25361e7 | −1.85861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −817378. | −0.120069 | −0.0600343 | − | 0.998196i | \(-0.519121\pi\) | ||||
−0.0600343 | + | 0.998196i | \(0.519121\pi\) | |||||||
\(542\) | 4.48523e6i | 0.655823i | ||||||||
\(543\) | 1.42132e7i | 2.06868i | ||||||||
\(544\) | 387072. | 0.0560783 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 105248. | 0.0151089 | ||||||||
\(547\) | − 3.50750e6i | − 0.501221i | −0.968088 | − | 0.250611i | \(-0.919369\pi\) | ||||
0.968088 | − | 0.250611i | \(-0.0806314\pi\) | |||||||
\(548\) | 3.83203e6i | 0.545102i | ||||||||
\(549\) | −2.39103e6 | −0.338574 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.17100e6 | −0.865918 | ||||||||
\(552\) | − 3.30470e6i | − 0.461620i | ||||||||
\(553\) | − 872080.i | − 0.121267i | ||||||||
\(554\) | −6.64137e6 | −0.919355 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 493760. | 0.0677375 | ||||||||
\(557\) | 9.61490e6i | 1.31313i | 0.754271 | + | 0.656563i | \(0.227991\pi\) | ||||
−0.754271 | + | 0.656563i | \(0.772009\pi\) | |||||||
\(558\) | − 6.90722e6i | − 0.939112i | ||||||||
\(559\) | −231196. | −0.0312933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.54790e6 | 1.01256 | ||||||||
\(562\) | − 5.80841e6i | − 0.775740i | ||||||||
\(563\) | − 2.01941e6i | − 0.268506i | −0.990947 | − | 0.134253i | \(-0.957136\pi\) | ||||
0.990947 | − | 0.134253i | \(-0.0428635\pi\) | |||||||
\(564\) | 1.02910e7 | 1.36226 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.23606e6 | −0.162180 | ||||||||
\(567\) | − 510862.i | − 0.0667338i | ||||||||
\(568\) | 2.71181e6i | 0.352686i | ||||||||
\(569\) | −1.37859e6 | −0.178507 | −0.0892533 | − | 0.996009i | \(-0.528448\pi\) | ||||
−0.0892533 | + | 0.996009i | \(0.528448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.54295e6 | 1.09652 | 0.548261 | − | 0.836307i | \(-0.315290\pi\) | ||||
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(572\) | 565248.i | 0.0722352i | ||||||||
\(573\) | − 1.17527e7i | − 1.49538i | ||||||||
\(574\) | −135696. | −0.0171905 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.77357e6 | 0.222737 | ||||||||
\(577\) | − 2.31458e6i | − 0.289423i | −0.989474 | − | 0.144711i | \(-0.953775\pi\) | ||||
0.989474 | − | 0.144711i | \(-0.0462254\pi\) | |||||||
\(578\) | − 5.10789e6i | − 0.635949i | ||||||||
\(579\) | 1.26254e7 | 1.56513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.31617e6 | 0.161760 | ||||||||
\(582\) | − 1.50157e7i | − 1.83755i | ||||||||
\(583\) | − 1.08795e7i | − 1.32568i | ||||||||
\(584\) | −3.33606e6 | −0.404764 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.37202e6 | 0.766537 | ||||||||
\(587\) | 928338.i | 0.111202i | 0.998453 | + | 0.0556008i | \(0.0177074\pi\) | ||||
−0.998453 | + | 0.0556008i | \(0.982293\pi\) | |||||||
\(588\) | − 6.79037e6i | − 0.809935i | ||||||||
\(589\) | 4.38680e6 | 0.521026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.62646e7 | −3.09316 | ||||||||
\(592\) | − 36352.0i | − 0.00426309i | ||||||||
\(593\) | 909486.i | 0.106209i | 0.998589 | + | 0.0531043i | \(0.0169116\pi\) | ||||
−0.998589 | + | 0.0531043i | \(0.983088\pi\) | |||||||
\(594\) | 1.51757e7 | 1.76475 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.61520e6 | −0.186256 | ||||||||
\(597\) | 2.09986e7i | 2.41132i | ||||||||
\(598\) | 365424.i | 0.0417873i | ||||||||
\(599\) | 8.51136e6 | 0.969241 | 0.484621 | − | 0.874724i | \(-0.338958\pi\) | ||||
0.484621 | + | 0.874724i | \(0.338958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.12498e6 | 0.691701 | 0.345851 | − | 0.938290i | \(-0.387590\pi\) | ||||
0.345851 | + | 0.938290i | \(0.387590\pi\) | |||||||
\(602\) | − 442288.i | − 0.0497409i | ||||||||
\(603\) | 1.07133e7i | 1.19986i | ||||||||
\(604\) | −199232. | −0.0222212 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.46908e7 | −1.62504 | ||||||||
\(607\) | − 4.51646e6i | − 0.497538i | −0.968563 | − | 0.248769i | \(-0.919974\pi\) | ||||
0.968563 | − | 0.248769i | \(-0.0800261\pi\) | |||||||
\(608\) | 1.12640e6i | 0.123576i | ||||||||
\(609\) | 3.20892e6 | 0.350603 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13795e6 | −0.123316 | ||||||||
\(612\) | 2.61878e6i | 0.282632i | ||||||||
\(613\) | − 9.63979e6i | − 1.03614i | −0.855340 | − | 0.518068i | \(-0.826651\pi\) | ||||
0.855340 | − | 0.518068i | \(-0.173349\pi\) | |||||||
\(614\) | 4.98903e6 | 0.534067 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.08134e6 | −0.114819 | ||||||||
\(617\) | − 9.92650e6i | − 1.04974i | −0.851181 | − | 0.524872i | \(-0.824113\pi\) | ||||
0.851181 | − | 0.524872i | \(-0.175887\pi\) | |||||||
\(618\) | − 1.45407e7i | − 1.53149i | ||||||||
\(619\) | −7.63322e6 | −0.800721 | −0.400360 | − | 0.916358i | \(-0.631115\pi\) | ||||
−0.400360 | + | 0.916358i | \(0.631115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.81084e6 | 1.02089 | ||||||||
\(622\) | 2.66395e6i | 0.276090i | ||||||||
\(623\) | 1.26918e6i | 0.131010i | ||||||||
\(624\) | −306176. | −0.0314782 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36514e6 | 0.241225 | ||||||||
\(627\) | 2.19648e7i | 2.23130i | ||||||||
\(628\) | 96352.0i | 0.00974903i | ||||||||
\(629\) | 53676.0 | 0.00540946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.80314e7 | 1.80284 | 0.901418 | − | 0.432949i | \(-0.142527\pi\) | ||||
0.901418 | + | 0.432949i | \(0.142527\pi\) | |||||||
\(632\) | 2.53696e6i | 0.252651i | ||||||||
\(633\) | 3.88835e6i | 0.385706i | ||||||||
\(634\) | −2.06537e6 | −0.204068 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.89306e6 | 0.577694 | ||||||||
\(637\) | 750858.i | 0.0733178i | ||||||||
\(638\) | 1.72339e7i | 1.67623i | ||||||||
\(639\) | −1.83471e7 | −1.77752 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.30190e6 | 0.894184 | 0.447092 | − | 0.894488i | \(-0.352460\pi\) | ||||
0.447092 | + | 0.894488i | \(0.352460\pi\) | |||||||
\(642\) | 8.98747e6i | 0.860597i | ||||||||
\(643\) | 1.38332e7i | 1.31946i | 0.751503 | + | 0.659730i | \(0.229329\pi\) | ||||
−0.751503 | + | 0.659730i | \(0.770671\pi\) | |||||||
\(644\) | −699072. | −0.0664213 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66320e6 | −0.156806 | ||||||||
\(647\) | − 1.48997e7i | − 1.39932i | −0.714478 | − | 0.699658i | \(-0.753336\pi\) | ||||
0.714478 | − | 0.699658i | \(-0.246664\pi\) | |||||||
\(648\) | 1.48614e6i | 0.139035i | ||||||||
\(649\) | 2.17958e7 | 2.03124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.28114e6 | −0.210959 | ||||||||
\(652\) | − 8.01386e6i | − 0.738282i | ||||||||
\(653\) | 1.93306e7i | 1.77403i | 0.461738 | + | 0.887016i | \(0.347226\pi\) | ||||
−0.461738 | + | 0.887016i | \(0.652774\pi\) | |||||||
\(654\) | −2.27188e7 | −2.07702 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 394752. | 0.0358150 | ||||||||
\(657\) | − 2.25706e7i | − 2.03999i | ||||||||
\(658\) | − 2.17694e6i | − 0.196012i | ||||||||
\(659\) | 4.06110e6 | 0.364276 | 0.182138 | − | 0.983273i | \(-0.441698\pi\) | ||||
0.182138 | + | 0.983273i | \(0.441698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.35152e7 | −1.20315 | −0.601575 | − | 0.798816i | \(-0.705460\pi\) | ||||
−0.601575 | + | 0.798816i | \(0.705460\pi\) | |||||||
\(662\) | 1.31831e7i | 1.16915i | ||||||||
\(663\) | − 452088.i | − 0.0399429i | ||||||||
\(664\) | −3.82886e6 | −0.337015 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 245944. | 0.0214858 | ||||||||
\(667\) | 1.11415e7i | 0.969678i | ||||||||
\(668\) | − 8.88413e6i | − 0.770324i | ||||||||
\(669\) | −1.15312e7 | −0.996111 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.24090e6 | −0.363623 | ||||||||
\(672\) | − 585728.i | − 0.0500349i | ||||||||
\(673\) | − 1.43520e7i | − 1.22144i | −0.791845 | − | 0.610722i | \(-0.790879\pi\) | ||||
0.791845 | − | 0.610722i | \(-0.209121\pi\) | |||||||
\(674\) | 7.64391e6 | 0.648136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90683e6 | −0.497150 | ||||||||
\(677\) | 1.89530e6i | 0.158930i | 0.996838 | + | 0.0794650i | \(0.0253212\pi\) | ||||
−0.996838 | + | 0.0794650i | \(0.974679\pi\) | |||||||
\(678\) | 2.99582e6i | 0.250289i | ||||||||
\(679\) | −3.17640e6 | −0.264400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09205e7 | −0.902347 | ||||||||
\(682\) | − 1.22511e7i | − 1.00859i | ||||||||
\(683\) | − 2.91641e6i | − 0.239220i | −0.992821 | − | 0.119610i | \(-0.961836\pi\) | ||||
0.992821 | − | 0.119610i | \(-0.0381644\pi\) | |||||||
\(684\) | −7.62080e6 | −0.622817 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.91544e6 | −0.236534 | ||||||||
\(687\) | − 2.75275e7i | − 2.22523i | ||||||||
\(688\) | 1.28666e6i | 0.103631i | ||||||||
\(689\) | −651636. | −0.0522946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.44278e7 | 1.14949 | 0.574743 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574743 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(692\) | 6.67766e6i | 0.530102i | ||||||||
\(693\) | − 7.31597e6i | − 0.578680i | ||||||||
\(694\) | 9.68023e6 | 0.762934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.33504e6 | −0.730454 | ||||||||
\(697\) | 582876.i | 0.0454458i | ||||||||
\(698\) | 1.00291e7i | 0.779153i | ||||||||
\(699\) | −3.31096e7 | −2.56307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.58679e7 | −1.21962 | −0.609811 | − | 0.792547i | \(-0.708754\pi\) | ||||
−0.609811 | + | 0.792547i | \(0.708754\pi\) | |||||||
\(702\) | − 908960.i | − 0.0696149i | ||||||||
\(703\) | 156200.i | 0.0119205i | ||||||||
\(704\) | 3.14573e6 | 0.239216 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.65266e6 | 0.124788 | ||||||||
\(707\) | 3.10768e6i | 0.233823i | ||||||||
\(708\) | 1.18061e7i | 0.885162i | ||||||||
\(709\) | 301810. | 0.0225485 | 0.0112743 | − | 0.999936i | \(-0.496411\pi\) | ||||
0.0112743 | + | 0.999936i | \(0.496411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.71641e7 | −1.27335 | ||||||||
\(712\) | − 3.69216e6i | − 0.272948i | ||||||||
\(713\) | − 7.92017e6i | − 0.583459i | ||||||||
\(714\) | 864864. | 0.0634896 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −838080. | −0.0610946 | ||||||||
\(717\) | 9.63768e6i | 0.700123i | ||||||||
\(718\) | 6.95088e6i | 0.503186i | ||||||||
\(719\) | −2.12677e7 | −1.53426 | −0.767130 | − | 0.641492i | \(-0.778316\pi\) | ||||
−0.767130 | + | 0.641492i | \(0.778316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.07591e6 | −0.220361 | ||||||||
\(722\) | 5.06440e6i | 0.361564i | ||||||||
\(723\) | − 1.45937e7i | − 1.03830i | ||||||||
\(724\) | −8.74659e6 | −0.620144 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.45924e7 | 3.13992 | ||||||||
\(727\) | 1.55009e7i | 1.08773i | 0.839174 | + | 0.543863i | \(0.183039\pi\) | ||||
−0.839174 | + | 0.543863i | \(0.816961\pi\) | |||||||
\(728\) | 64768.0i | 0.00452931i | ||||||||
\(729\) | 2.11562e7 | 1.47441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.89983e6 | −0.131499 | ||||||||
\(732\) | − 2.29715e6i | − 0.158457i | ||||||||
\(733\) | 1.21850e7i | 0.837653i | 0.908066 | + | 0.418827i | \(0.137559\pi\) | ||||
−0.908066 | + | 0.418827i | \(0.862441\pi\) | |||||||
\(734\) | 4.64391e6 | 0.318159 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.03366e6 | 0.138384 | ||||||||
\(737\) | 1.90019e7i | 1.28863i | ||||||||
\(738\) | 2.67074e6i | 0.180506i | ||||||||
\(739\) | 2.90282e7 | 1.95528 | 0.977641 | − | 0.210282i | \(-0.0674382\pi\) | ||||
0.977641 | + | 0.210282i | \(0.0674382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31560e6 | 0.0880194 | ||||||||
\(742\) | − 1.24661e6i | − 0.0831228i | ||||||||
\(743\) | − 1.61145e7i | − 1.07089i | −0.844570 | − | 0.535445i | \(-0.820144\pi\) | ||||
0.844570 | − | 0.535445i | \(-0.179856\pi\) | |||||||
\(744\) | 6.63603e6 | 0.439517 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.37502e6 | −0.0904609 | ||||||||
\(747\) | − 2.59047e7i | − 1.69854i | ||||||||
\(748\) | 4.64486e6i | 0.303542i | ||||||||
\(749\) | 1.90120e6 | 0.123829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.92431e6 | −0.189201 | −0.0946005 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946005 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(752\) | 6.33293e6i | 0.408376i | ||||||||
\(753\) | 1.50060e7i | 0.964442i | ||||||||
\(754\) | 1.03224e6 | 0.0661230 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.73888e6 | 0.110653 | ||||||||
\(757\) | 2.60325e7i | 1.65111i | 0.564319 | + | 0.825557i | \(0.309139\pi\) | ||||
−0.564319 | + | 0.825557i | \(0.690861\pi\) | |||||||
\(758\) | 2.29256e6i | 0.144926i | ||||||||
\(759\) | 3.96564e7 | 2.49867 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63263e7 | 1.02194 | 0.510970 | − | 0.859598i | \(-0.329286\pi\) | ||||
0.510970 | + | 0.859598i | \(0.329286\pi\) | |||||||
\(762\) | − 2.25162e7i | − 1.40478i | ||||||||
\(763\) | 4.80590e6i | 0.298857i | ||||||||
\(764\) | 7.23245e6 | 0.448283 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.15222e7 | 0.709517 | ||||||||
\(767\) | − 1.30548e6i | − 0.0801275i | ||||||||
\(768\) | 1.70394e6i | 0.104244i | ||||||||
\(769\) | −2.58132e7 | −1.57408 | −0.787040 | − | 0.616902i | \(-0.788388\pi\) | ||||
−0.787040 | + | 0.616902i | \(0.788388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69380e7 | 1.02619 | ||||||||
\(772\) | 7.76950e6i | 0.469191i | ||||||||
\(773\) | 1.90592e7i | 1.14725i | 0.819119 | + | 0.573624i | \(0.194463\pi\) | ||||
−0.819119 | + | 0.573624i | \(0.805537\pi\) | |||||||
\(774\) | −8.70503e6 | −0.522298 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.24045e6 | 0.550857 | ||||||||
\(777\) | − 81224.0i | − 0.00482649i | ||||||||
\(778\) | − 1.23424e7i | − 0.731054i | ||||||||
\(779\) | −1.69620e6 | −0.100146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.25417e7 | −1.90903 | ||||||||
\(782\) | 3.00283e6i | 0.175596i | ||||||||
\(783\) | − 2.77134e7i | − 1.61542i | ||||||||
\(784\) | 4.17869e6 | 0.242801 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.54392e7 | −1.46875 | ||||||||
\(787\) | − 1.73411e7i | − 0.998021i | −0.866596 | − | 0.499011i | \(-0.833697\pi\) | ||||
0.866596 | − | 0.499011i | \(-0.166303\pi\) | |||||||
\(788\) | − 1.61628e7i | − 0.927262i | ||||||||
\(789\) | 2.38569e7 | 1.36434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 633732. | 0.0360134 | ||||||||
\(792\) | 2.12828e7i | 1.20564i | ||||||||
\(793\) | 254012.i | 0.0143440i | ||||||||
\(794\) | 3.54183e6 | 0.199378 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.29222e7 | −0.722862 | ||||||||
\(797\) | − 2.58169e7i | − 1.43965i | −0.694153 | − | 0.719827i | \(-0.744221\pi\) | ||||
0.694153 | − | 0.719827i | \(-0.255779\pi\) | |||||||
\(798\) | 2.51680e6i | 0.139908i | ||||||||
\(799\) | −9.35096e6 | −0.518190 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.49798e7 | 1.37565 | ||||||||
\(802\) | 1.50138e7i | 0.824239i | ||||||||
\(803\) | − 4.00328e7i | − 2.19092i | ||||||||
\(804\) | −1.02927e7 | −0.561549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −733792. | −0.0397865 | ||||||||
\(807\) | 1.91201e7i | 1.03349i | ||||||||
\(808\) | − 9.04051e6i | − 0.487152i | ||||||||
\(809\) | −8.88489e6 | −0.477288 | −0.238644 | − | 0.971107i | \(-0.576703\pi\) | ||||
−0.238644 | + | 0.971107i | \(0.576703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.46396e7 | −1.31547 | −0.657735 | − | 0.753249i | \(-0.728485\pi\) | ||||
−0.657735 | + | 0.753249i | \(0.728485\pi\) | |||||||
\(812\) | 1.97472e6i | 0.105103i | ||||||||
\(813\) | − 2.91540e7i | − 1.54693i | ||||||||
\(814\) | 436224. | 0.0230754 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.51597e6 | −0.132276 | ||||||||
\(817\) | − 5.52860e6i | − 0.289774i | ||||||||
\(818\) | − 7.78612e6i | − 0.406853i | ||||||||
\(819\) | −438196. | −0.0228275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.13768e7 | 0.589062 | 0.294531 | − | 0.955642i | \(-0.404837\pi\) | ||||
0.294531 | + | 0.955642i | \(0.404837\pi\) | |||||||
\(822\) | − 2.49082e7i | − 1.28577i | ||||||||
\(823\) | 1.30783e7i | 0.673057i | 0.941673 | + | 0.336529i | \(0.109253\pi\) | ||||
−0.941673 | + | 0.336529i | \(0.890747\pi\) | |||||||
\(824\) | 8.94810e6 | 0.459106 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.49744e6 | 0.127363 | ||||||||
\(827\) | − 3.57188e7i | − 1.81607i | −0.418891 | − | 0.908037i | \(-0.637581\pi\) | ||||
0.418891 | − | 0.908037i | \(-0.362419\pi\) | |||||||
\(828\) | 1.37590e7i | 0.697447i | ||||||||
\(829\) | −1.61880e7 | −0.818103 | −0.409052 | − | 0.912511i | \(-0.634140\pi\) | ||||
−0.409052 | + | 0.912511i | \(0.634140\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.31689e7 | 2.16854 | ||||||||
\(832\) | − 188416.i | − 0.00943647i | ||||||||
\(833\) | 6.17009e6i | 0.308091i | ||||||||
\(834\) | −3.20944e6 | −0.159777 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.35168e7 | −0.668895 | ||||||||
\(837\) | 1.97007e7i | 0.972005i | ||||||||
\(838\) | − 1.19666e7i | − 0.588657i | ||||||||
\(839\) | 2.55497e7 | 1.25309 | 0.626543 | − | 0.779387i | \(-0.284469\pi\) | ||||
0.626543 | + | 0.779387i | \(0.284469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09610e7 | 0.534390 | ||||||||
\(842\) | − 1.58664e7i | − 0.771256i | ||||||||
\(843\) | 3.77547e7i | 1.82979i | ||||||||
\(844\) | −2.39283e6 | −0.115626 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.28462e7 | −2.05820 | ||||||||
\(847\) | − 9.43301e6i | − 0.451795i | ||||||||
\(848\) | 3.62650e6i | 0.173180i | ||||||||
\(849\) | 8.03436e6 | 0.382545 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 282012. | 0.0133488 | ||||||||
\(852\) | − 1.76268e7i | − 0.831904i | ||||||||
\(853\) | 2.22953e7i | 1.04916i | 0.851362 | + | 0.524579i | \(0.175777\pi\) | ||||
−0.851362 | + | 0.524579i | \(0.824223\pi\) | |||||||
\(854\) | −485936. | −0.0228000 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.53075e6 | −0.257988 | ||||||||
\(857\) | 1.96872e7i | 0.915656i | 0.889041 | + | 0.457828i | \(0.151372\pi\) | ||||
−0.889041 | + | 0.457828i | \(0.848628\pi\) | |||||||
\(858\) | − 3.67411e6i | − 0.170386i | ||||||||
\(859\) | −6.77582e6 | −0.313313 | −0.156657 | − | 0.987653i | \(-0.550072\pi\) | ||||
−0.156657 | + | 0.987653i | \(0.550072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 882024. | 0.0405483 | ||||||||
\(862\) | 2.06846e7i | 0.948154i | ||||||||
\(863\) | 2.63804e7i | 1.20574i | 0.797839 | + | 0.602871i | \(0.205977\pi\) | ||||
−0.797839 | + | 0.602871i | \(0.794023\pi\) | |||||||
\(864\) | −5.05856e6 | −0.230538 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.81394e7 | 0.821917 | ||||||||
\(867\) | 3.32013e7i | 1.50006i | ||||||||
\(868\) | − 1.40378e6i | − 0.0632410i | ||||||||
\(869\) | −3.04435e7 | −1.36756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.13813e6 | 0.0508332 | ||||||||
\(872\) | − 1.39808e7i | − 0.622645i | ||||||||
\(873\) | 6.25174e7i | 2.77629i | ||||||||
\(874\) | −8.73840e6 | −0.386949 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.16844e7 | 0.954745 | ||||||||
\(877\) | 2.95161e7i | 1.29587i | 0.761697 | + | 0.647934i | \(0.224367\pi\) | ||||
−0.761697 | + | 0.647934i | \(0.775633\pi\) | |||||||
\(878\) | − 4.32880e6i | − 0.189510i | ||||||||
\(879\) | −4.14182e7 | −1.80808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.48565e7 | −0.644877 | −0.322438 | − | 0.946590i | \(-0.604502\pi\) | ||||
−0.322438 | + | 0.946590i | \(0.604502\pi\) | |||||||
\(882\) | 2.82714e7i | 1.22370i | ||||||||
\(883\) | 1.45340e7i | 0.627313i | 0.949537 | + | 0.313656i | \(0.101554\pi\) | ||||
−0.949537 | + | 0.313656i | \(0.898446\pi\) | |||||||
\(884\) | 278208. | 0.0119740 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.32314e6 | 0.185019 | ||||||||
\(887\) | − 1.72028e7i | − 0.734160i | −0.930189 | − | 0.367080i | \(-0.880358\pi\) | ||||
0.930189 | − | 0.367080i | \(-0.119642\pi\) | |||||||
\(888\) | 236288.i | 0.0100556i | ||||||||
\(889\) | −4.76304e6 | −0.202130 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78337e7 | −0.752572 | ||||||||
\(892\) | − 7.09610e6i | − 0.298612i | ||||||||
\(893\) | − 2.72118e7i | − 1.14190i | ||||||||
\(894\) | 1.04988e7 | 0.439335 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 360448. | 0.0149994 | ||||||||
\(897\) | − 2.37526e6i | − 0.0985665i | ||||||||
\(898\) | 1.04713e7i | 0.433322i | ||||||||
\(899\) | −2.23727e7 | −0.923249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.35475e6 | −0.219749 | ||||||||
\(902\) | 4.73702e6i | 0.193860i | ||||||||
\(903\) | 2.87487e6i | 0.117327i | ||||||||
\(904\) | −1.84358e6 | −0.0750312 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.29501e6 | 0.0524146 | ||||||||
\(907\) | − 3.44434e7i | − 1.39023i | −0.718897 | − | 0.695116i | \(-0.755353\pi\) | ||||
0.718897 | − | 0.695116i | \(-0.244647\pi\) | |||||||
\(908\) | − 6.72029e6i | − 0.270504i | ||||||||
\(909\) | 6.11647e7 | 2.45522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −983748. | −0.0392724 | −0.0196362 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196362 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(912\) | − 7.32160e6i | − 0.291487i | ||||||||
\(913\) | − 4.59464e7i | − 1.82421i | ||||||||
\(914\) | 6.36183e6 | 0.251893 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.69400e7 | 0.667075 | ||||||||
\(917\) | 5.38138e6i | 0.211334i | ||||||||
\(918\) | − 7.46928e6i | − 0.292531i | ||||||||
\(919\) | −3.08857e7 | −1.20634 | −0.603168 | − | 0.797614i | \(-0.706095\pi\) | ||||
−0.603168 | + | 0.797614i | \(0.706095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.24287e7 | −1.25974 | ||||||||
\(922\) | − 1.70188e7i | − 0.659328i | ||||||||
\(923\) | 1.94911e6i | 0.0753065i | ||||||||
\(924\) | 7.02874e6 | 0.270830 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.30642e7 | −0.500675 | ||||||||
\(927\) | 6.05395e7i | 2.31387i | ||||||||
\(928\) | − 5.74464e6i | − 0.218974i | ||||||||
\(929\) | 3.20874e7 | 1.21982 | 0.609909 | − | 0.792472i | \(-0.291206\pi\) | ||||
0.609909 | + | 0.792472i | \(0.291206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.79553e7 | −0.678920 | ||||||||
\(932\) | − 2.03751e7i | − 0.768353i | ||||||||
\(933\) | − 1.73157e7i | − 0.651232i | ||||||||
\(934\) | −2.40617e6 | −0.0902524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.27475e6 | 0.0475594 | ||||||||
\(937\) | 1.52520e7i | 0.567515i | 0.958896 | + | 0.283757i | \(0.0915810\pi\) | ||||
−0.958896 | + | 0.283757i | \(0.908419\pi\) | |||||||
\(938\) | 2.17730e6i | 0.0807998i | ||||||||
\(939\) | −1.53734e7 | −0.568993 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.48166e6 | 0.128178 | 0.0640889 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640889 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(942\) | − 626288.i | − 0.0229957i | ||||||||
\(943\) | 3.06241e6i | 0.112146i | ||||||||
\(944\) | −7.26528e6 | −0.265352 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.54399e7 | −0.560939 | ||||||||
\(947\) | − 2.54010e7i | − 0.920398i | −0.887816 | − | 0.460199i | \(-0.847778\pi\) | ||||
0.887816 | − | 0.460199i | \(-0.152222\pi\) | |||||||
\(948\) | − 1.64902e7i | − 0.595945i | ||||||||
\(949\) | −2.39780e6 | −0.0864265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.34249e7 | 0.481348 | ||||||||
\(952\) | 532224.i | 0.0190328i | ||||||||
\(953\) | 4.97352e7i | 1.77391i | 0.461856 | + | 0.886955i | \(0.347184\pi\) | ||||
−0.461856 | + | 0.886955i | \(0.652816\pi\) | |||||||
\(954\) | −2.45355e7 | −0.872819 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.93088e6 | −0.209882 | ||||||||
\(957\) | − 1.12020e8i | − 3.95383i | ||||||||
\(958\) | − 1.83173e7i | − 0.644833i | ||||||||
\(959\) | −5.26904e6 | −0.185006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.27250e7 | −0.444477 | ||||||||
\(962\) | − 26128.0i | 0 0.000910266i | ||||||||
\(963\) | − 3.74190e7i | − 1.30025i | ||||||||
\(964\) | 8.98077e6 | 0.311258 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.54397e6 | 0.156672 | ||||||||
\(967\) | 3.05173e7i | 1.04949i | 0.851258 | + | 0.524747i | \(0.175840\pi\) | ||||
−0.851258 | + | 0.524747i | \(0.824160\pi\) | |||||||
\(968\) | 2.74415e7i | 0.941280i | ||||||||
\(969\) | 1.08108e7 | 0.369869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.19854e7 | 1.08869 | 0.544344 | − | 0.838862i | \(-0.316779\pi\) | ||||
0.544344 | + | 0.838862i | \(0.316779\pi\) | |||||||
\(972\) | 9.54678e6i | 0.324109i | ||||||||
\(973\) | 678920.i | 0.0229899i | ||||||||
\(974\) | 2.82090e7 | 0.952776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.41363e6 | 0.0475020 | ||||||||
\(977\) | 2.90786e6i | 0.0974623i | 0.998812 | + | 0.0487312i | \(0.0155178\pi\) | ||||
−0.998812 | + | 0.0487312i | \(0.984482\pi\) | |||||||
\(978\) | 5.20901e7i | 1.74144i | ||||||||
\(979\) | 4.43059e7 | 1.47742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.45888e7 | 3.13810 | ||||||||
\(982\) | 1.04940e7i | 0.347264i | ||||||||
\(983\) | − 3.49621e7i | − 1.15402i | −0.816737 | − | 0.577010i | \(-0.804219\pi\) | ||||
0.816737 | − | 0.577010i | \(-0.195781\pi\) | |||||||
\(984\) | −2.56589e6 | −0.0844792 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.48232e6 | 0.277858 | ||||||||
\(987\) | 1.41501e7i | 0.462347i | ||||||||
\(988\) | 809600.i | 0.0263863i | ||||||||
\(989\) | −9.98164e6 | −0.324497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.00465e6 | 0.0971874 | 0.0485937 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485937 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(992\) | 4.08371e6i | 0.131758i | ||||||||
\(993\) | − 8.56900e7i | − 2.75776i | ||||||||
\(994\) | −3.72874e6 | −0.119700 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.48876e7 | 0.794941 | ||||||||
\(997\) | 3.20789e7i | 1.02207i | 0.859560 | + | 0.511035i | \(0.170738\pi\) | ||||
−0.859560 | + | 0.511035i | \(0.829262\pi\) | |||||||
\(998\) | − 1.44494e7i | − 0.459222i | ||||||||
\(999\) | −701480. | −0.0222383 |
(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 | 50.6.b.d.49.1 | 2 | ||
3.2 | odd | 2 | 450.6.c.o.199.2 | 2 | |||
4.3 | odd | 2 | 400.6.c.a.49.1 | 2 | |||
5.2 | odd | 4 | 50.6.a.g.1.1 | 1 | |||
5.3 | odd | 4 | 10.6.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 50.6.b.d.49.2 | 2 | ||
15.2 | even | 4 | 450.6.a.h.1.1 | 1 | |||
15.8 | even | 4 | 90.6.a.f.1.1 | 1 | |||
15.14 | odd | 2 | 450.6.c.o.199.1 | 2 | |||
20.3 | even | 4 | 80.6.a.h.1.1 | 1 | |||
20.7 | even | 4 | 400.6.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.a.49.2 | 2 | |||
35.13 | even | 4 | 490.6.a.j.1.1 | 1 | |||
40.3 | even | 4 | 320.6.a.a.1.1 | 1 | |||
40.13 | odd | 4 | 320.6.a.p.1.1 | 1 | |||
60.23 | odd | 4 | 720.6.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
50.6.a.g.1.1 | 1 | 5.2 | odd | 4 | |||
50.6.b.d.49.1 | 2 | 1.1 | even | 1 | trivial | ||
50.6.b.d.49.2 | 2 | 5.4 | even | 2 | inner | ||
80.6.a.h.1.1 | 1 | 20.3 | even | 4 | |||
90.6.a.f.1.1 | 1 | 15.8 | even | 4 | |||
320.6.a.a.1.1 | 1 | 40.3 | even | 4 | |||
320.6.a.p.1.1 | 1 | 40.13 | odd | 4 | |||
400.6.a.a.1.1 | 1 | 20.7 | even | 4 | |||
400.6.c.a.49.1 | 2 | 4.3 | odd | 2 | |||
400.6.c.a.49.2 | 2 | 20.19 | odd | 2 | |||
450.6.a.h.1.1 | 1 | 15.2 | even | 4 | |||
450.6.c.o.199.1 | 2 | 15.14 | odd | 2 | |||
450.6.c.o.199.2 | 2 | 3.2 | odd | 2 | |||
490.6.a.j.1.1 | 1 | 35.13 | even | 4 | |||
720.6.a.r.1.1 | 1 | 60.23 | odd | 4 |