Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(41,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.41");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 202x^{6} + 620x^{5} + 12167x^{4} - 25372x^{3} - 177926x^{2} + 190716x + 977814 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{7}\cdot 5^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Root | \(-2.67163 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.41 |
Dual form | 60.7.g.a.41.1 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −24.1542 | + | 12.0655i | −0.894599 | + | 0.446870i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 55.9017i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −436.815 | −1.27351 | −0.636757 | − | 0.771065i | \(-0.719724\pi\) | ||||
−0.636757 | + | 0.771065i | \(0.719724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 437.848 | − | 582.864i | 0.600614 | − | 0.799539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1100.06i | 0.826494i | 0.910619 | + | 0.413247i | \(0.135605\pi\) | ||||
−0.910619 | + | 0.413247i | \(0.864395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 908.083 | 0.413329 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −674.482 | − | 1350.26i | −0.199846 | − | 0.400077i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 9747.84i | − | 1.98409i | −0.125882 | − | 0.992045i | \(-0.540176\pi\) | ||
0.125882 | − | 0.992045i | \(-0.459824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7704.75 | 1.12331 | 0.561653 | − | 0.827373i | \(-0.310166\pi\) | ||||
0.561653 | + | 0.827373i | \(0.310166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10550.9 | − | 5270.39i | 1.13928 | − | 0.569095i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 19320.0i | − | 1.58790i | −0.607982 | − | 0.793951i | \(-0.708021\pi\) | ||
0.607982 | − | 0.793951i | \(-0.291979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3125.00 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3543.30 | + | 19361.4i | −0.180018 | + | 0.983663i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8106.42i | − | 0.332380i | −0.986094 | − | 0.166190i | \(-0.946853\pi\) | ||
0.986094 | − | 0.166190i | \(-0.0531465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −768.733 | −0.0258042 | −0.0129021 | − | 0.999917i | \(-0.504107\pi\) | ||||
−0.0129021 | + | 0.999917i | \(0.504107\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13272.8 | − | 26571.1i | −0.369335 | − | 0.739380i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 24418.7i | − | 0.569533i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 72219.1 | 1.42576 | 0.712881 | − | 0.701285i | \(-0.247390\pi\) | ||||
0.712881 | + | 0.701285i | \(0.247390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21934.0 | + | 10956.5i | −0.369763 | + | 0.184704i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14041.3i | 0.203731i | 0.994798 | + | 0.101865i | \(0.0324811\pi\) | ||||
−0.994798 | + | 0.101865i | \(0.967519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −121342. | −1.52618 | −0.763092 | − | 0.646289i | \(-0.776320\pi\) | ||||
−0.763092 | + | 0.646289i | \(0.776320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32583.1 | + | 24476.4i | 0.357565 | + | 0.268603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37066.0i | 0.357011i | 0.983939 | + | 0.178506i | \(0.0571263\pi\) | ||||
−0.983939 | + | 0.178506i | \(0.942874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 73158.5 | 0.621837 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 117612. | + | 235451.i | 0.886631 | + | 1.77496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 173405.i | − | 1.16476i | −0.812918 | − | 0.582378i | \(-0.802122\pi\) | ||
0.812918 | − | 0.582378i | \(-0.197878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −61495.4 | −0.369619 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −186102. | + | 92961.6i | −1.00491 | + | 0.501972i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 138336.i | 0.673563i | 0.941583 | + | 0.336782i | \(0.109338\pi\) | ||||
−0.941583 | + | 0.336782i | \(0.890662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −278669. | −1.22772 | −0.613861 | − | 0.789414i | \(-0.710384\pi\) | ||||
−0.613861 | + | 0.789414i | \(0.710384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −191258. | + | 254604.i | −0.764890 | + | 1.01822i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 50763.4i | 0.184846i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −96214.3 | −0.319901 | −0.159950 | − | 0.987125i | \(-0.551133\pi\) | ||||
−0.159950 | + | 0.987125i | \(0.551133\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 233105. | + | 466658.i | 0.709586 | + | 1.42053i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 338334.i | − | 0.945302i | −0.881250 | − | 0.472651i | \(-0.843297\pi\) | ||
0.881250 | − | 0.472651i | \(-0.156703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37504.8 | 0.0964093 | 0.0482046 | − | 0.998837i | \(-0.484650\pi\) | ||||
0.0482046 | + | 0.998837i | \(0.484650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75481.8 | − | 37704.7i | 0.178920 | − | 0.0893740i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 480524.i | − | 1.05255i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 721768. | 1.46392 | 0.731958 | − | 0.681350i | \(-0.238607\pi\) | ||||
0.731958 | + | 0.681350i | \(0.238607\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −148020. | − | 510411.i | −0.278526 | − | 0.960429i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 310971.i | − | 0.543858i | −0.962317 | − | 0.271929i | \(-0.912338\pi\) | ||
0.962317 | − | 0.271929i | \(-0.0876615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 544921. | 0.887312 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 97808.0 | + | 195804.i | 0.148531 | + | 0.297347i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.11509e6i | − | 1.58176i | −0.611969 | − | 0.790882i | \(-0.709622\pi\) | ||
0.611969 | − | 0.790882i | \(-0.290378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −396665. | −0.526380 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18568.1 | − | 9275.14i | 0.0230844 | − | 0.0115311i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 430709.i | 0.502357i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 306615. | 0.335952 | 0.167976 | − | 0.985791i | \(-0.446277\pi\) | ||||
0.167976 | + | 0.985791i | \(0.446277\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 641187. | + | 481660.i | 0.660814 | + | 0.496404i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.43599e6i | − | 1.39376i | −0.717189 | − | 0.696879i | \(-0.754571\pi\) | ||
0.717189 | − | 0.696879i | \(-0.245429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.55067e6 | −1.41908 | −0.709540 | − | 0.704665i | \(-0.751097\pi\) | ||||
−0.709540 | + | 0.704665i | \(0.751097\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 294624. | + | 589814.i | 0.254507 | + | 0.509503i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.02996e6i | − | 0.840756i | −0.907349 | − | 0.420378i | \(-0.861897\pi\) | ||
0.907349 | − | 0.420378i | \(-0.138103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 906603. | 0.700064 | 0.350032 | − | 0.936738i | \(-0.386171\pi\) | ||||
0.350032 | + | 0.936738i | \(0.386171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.74439e6 | + | 871359.i | −1.27548 | + | 0.637131i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 889378.i | − | 0.616383i | −0.951324 | − | 0.308192i | \(-0.900276\pi\) | ||
0.951324 | − | 0.308192i | \(-0.0997238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.08002e6 | 0.710131 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 397602. | − | 529289.i | 0.248251 | − | 0.330473i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.25800e6i | 2.52677i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 561422. | 0.316908 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −169415. | − | 339156.i | −0.0910411 | − | 0.182257i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 174693.i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.88160e6 | −1.40677 | −0.703383 | − | 0.710811i | \(-0.748328\pi\) | ||||
−0.703383 | + | 0.710811i | \(0.748328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.93092e6 | − | 1.46406e6i | 1.36532 | − | 0.682007i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 627919.i | 0.279312i | 0.990200 | + | 0.139656i | \(0.0445997\pi\) | ||||
−0.990200 | + | 0.139656i | \(0.955400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.36555e6 | −1.43054 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.08234e6 | − | 198077.i | −0.439908 | − | 0.0805066i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00040e6i | 1.55576i | 0.628415 | + | 0.777878i | \(0.283704\pi\) | ||||
−0.628415 | + | 0.777878i | \(0.716296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.05700e6 | 1.51064 | 0.755319 | − | 0.655357i | \(-0.227482\pi\) | ||||
0.755319 | + | 0.655357i | \(0.227482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −447219. | − | 895298.i | −0.159538 | − | 0.319382i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 998949.i | 0.341614i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 453163. | 0.148645 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.76708e6 | + | 882694.i | −0.556295 | + | 0.277880i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.19253e6i | 0.965110i | 0.875866 | + | 0.482555i | \(0.160291\pi\) | ||||
−0.875866 | + | 0.482555i | \(0.839709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.95081e6 | −0.566610 | −0.283305 | − | 0.959030i | \(-0.591431\pi\) | ||||
−0.283305 | + | 0.959030i | \(0.591431\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.68166e6 | − | 4.26807e6i | −1.58636 | − | 1.19167i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 42973.5i | − | 0.0115400i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.91636e6 | 1.01201 | 0.506003 | − | 0.862532i | \(-0.331122\pi\) | ||||
0.506003 | + | 0.862532i | \(0.331122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.09222e6 | + | 4.18847e6i | 0.520495 | + | 1.04199i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.43927e6i | 2.02221i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66984e6 | −0.847392 | −0.423696 | − | 0.905804i | \(-0.639268\pi\) | ||||
−0.423696 | + | 0.905804i | \(0.639268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.48537e6 | − | 741973.i | 0.330661 | − | 0.165172i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.16638e6i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00219e6 | −0.829159 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.37351e6 | − | 4.49082e6i | 0.674673 | − | 0.898126i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 5.80835e6i | − | 1.12180i | −0.827884 | − | 0.560899i | \(-0.810456\pi\) | ||
0.827884 | − | 0.560899i | \(-0.189544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.36505e6 | 0.254703 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.66909e6 | − | 3.34139e6i | −0.300995 | − | 0.602569i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.27743e6i | − | 1.09452i | −0.836963 | − | 0.547259i | \(-0.815671\pi\) | ||
0.836963 | − | 0.547259i | \(-0.184329\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.24869e6 | 0.210581 | 0.105291 | − | 0.994442i | \(-0.466423\pi\) | ||||
0.105291 | + | 0.994442i | \(0.466423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.73103e6 | − | 3.36228e6i | 1.09832 | − | 0.548632i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.03717e6i | 0.637620i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.07232e7 | 1.63984 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.54777e6 | − | 8.45737e6i | 0.229256 | − | 1.25271i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.38849e6i | − | 1.06037i | −0.847883 | − | 0.530183i | \(-0.822123\pi\) | ||
0.847883 | − | 0.530183i | \(-0.177877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −901327. | −0.125375 | −0.0626874 | − | 0.998033i | \(-0.519967\pi\) | ||||
−0.0626874 | + | 0.998033i | \(0.519967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −612486. | − | 1.22615e6i | −0.0826023 | − | 0.165363i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.82439e6i | 1.02341i | 0.859160 | + | 0.511707i | \(0.170987\pi\) | ||||
−0.859160 | + | 0.511707i | \(0.829013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.89870e6 | 0.621615 | 0.310808 | − | 0.950473i | \(-0.399401\pi\) | ||||
0.310808 | + | 0.950473i | \(0.399401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.32398e6 | − | 1.16087e6i | 0.286183 | − | 0.142954i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.54101e6i | 0.423291i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −784933. | −0.0911111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.12609e7 | − | 8.45921e6i | −1.26959 | − | 0.953716i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.47571e6i | 0.928405i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.05764e7 | −1.12587 | −0.562935 | − | 0.826501i | \(-0.690328\pi\) | ||||
−0.562935 | + | 0.826501i | \(0.690328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.08217e6 | + | 8.17218e6i | 0.422427 | + | 0.845666i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.78325e6i | − | 0.682531i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 335794. | 0.0328620 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −905898. | + | 452515.i | −0.0862476 | + | 0.0430824i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.85185e6i | − | 0.820082i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.73263e6 | 0.877639 | 0.438819 | − | 0.898575i | \(-0.355397\pi\) | ||||
0.438819 | + | 0.898575i | \(0.355397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.36827e6 | + | 1.82145e6i | −0.120123 | + | 0.159908i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5.26593e6i | − | 0.450192i | −0.974337 | − | 0.225096i | \(-0.927730\pi\) | ||
0.974337 | − | 0.225096i | \(-0.0722696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.98690e7 | −1.65451 | −0.827255 | − | 0.561827i | \(-0.810099\pi\) | ||||
−0.827255 | + | 0.561827i | \(0.810099\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.79776e6 | + | 1.16067e7i | 0.470354 | + | 0.941611i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.42512e7i | 1.91719i | 0.284774 | + | 0.958595i | \(0.408081\pi\) | ||||
−0.284774 | + | 0.958595i | \(0.591919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.07205e6 | −0.159660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.74337e7 | + | 8.70849e6i | −1.30962 | + | 0.654181i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.38393e6i | − | 0.687371i | −0.939085 | − | 0.343685i | \(-0.888325\pi\) | ||
0.939085 | − | 0.343685i | \(-0.111675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 239568. | 0.0171151 | 0.00855753 | − | 0.999963i | \(-0.497276\pi\) | ||||
0.00855753 | + | 0.999963i | \(0.497276\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.73366e6 | + | 1.05426e7i | 0.678356 | + | 0.734734i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.08968e6i | 0.278094i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.99656e6 | 0.464294 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.75202e6 | + | 7.51124e6i | 0.243034 | + | 0.486534i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.51087e6i | 0.158783i | 0.996844 | + | 0.0793913i | \(0.0252977\pi\) | ||||
−0.996844 | + | 0.0793913i | \(0.974702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.12532e7 | 1.31239 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.31621e7 | + | 6.57474e6i | −0.793788 | + | 0.396513i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.15026e7i | − | 0.677634i | −0.940852 | − | 0.338817i | \(-0.889973\pi\) | ||
0.940852 | − | 0.338817i | \(-0.110027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.15464e7 | −1.81573 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.72494e6 | − | 3.54938e6i | −0.265751 | − | 0.199632i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.74829e6i | − | 0.480901i | −0.970661 | − | 0.240451i | \(-0.922705\pi\) | ||
0.970661 | − | 0.240451i | \(-0.0772953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.69366e6 | 0.520895 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.34542e7 | + | 2.69342e7i | 0.706843 | + | 1.41504i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.28060e7i | − | 1.17163i | −0.810444 | − | 0.585816i | \(-0.800774\pi\) | ||
0.810444 | − | 0.585816i | \(-0.199226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.15949e7 | 0.582584 | 0.291292 | − | 0.956634i | \(-0.405915\pi\) | ||||
0.291292 | + | 0.956634i | \(0.405915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.58110e6 | − | 4.78596e6i | 0.470899 | − | 0.235224i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.43770e6i | − | 0.165299i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44035e7 | 0.677688 | 0.338844 | − | 0.940843i | \(-0.389964\pi\) | ||||
0.338844 | + | 0.940843i | \(0.389964\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −336588. | + | 448067.i | −0.0154984 | + | 0.0206315i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.74318e7i | 1.68703i | 0.537108 | + | 0.843514i | \(0.319517\pi\) | ||||
−0.537108 | + | 0.843514i | \(0.680483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.16540e7 | −0.955384 | −0.477692 | − | 0.878527i | \(-0.658527\pi\) | ||||
−0.477692 | + | 0.878527i | \(0.658527\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.19671e6 | − | 1.04034e7i | −0.224489 | − | 0.449408i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.13346e6i | − | 0.259454i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.08827e7 | −2.93661 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.40602e6 | + | 3.69946e6i | −0.300543 | + | 0.150127i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.13642e6i | − | 0.0451790i | −0.999745 | − | 0.0225895i | \(-0.992809\pi\) | ||
0.999745 | − | 0.0225895i | \(-0.00719107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.73320e6 | −0.301227 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.12988e7 | − | 3.89785e6i | −0.812992 | − | 0.148784i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.75442e7i | − | 0.656325i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.30042e7 | 1.94362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.73259e7 | + | 3.46852e7i | 0.622829 | + | 1.24685i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.55781e7i | − | 0.549054i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.32583e7 | 1.84065 | 0.920326 | − | 0.391151i | \(-0.127923\pi\) | ||||
0.920326 | + | 0.391151i | \(0.127923\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.74551e7 | − | 1.87096e7i | 1.26951 | − | 0.634145i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.42770e7i | − | 1.80441i | −0.431309 | − | 0.902204i | \(-0.641948\pi\) | ||
0.431309 | − | 0.902204i | \(-0.358052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.24188e6 | 0.170944 | 0.0854721 | − | 0.996341i | \(-0.472760\pi\) | ||||
0.0854721 | + | 0.996341i | \(0.472760\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.42328e7 | − | 1.06917e7i | −0.455364 | − | 0.342069i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.90245e6i | − | 0.0911143i | −0.998962 | − | 0.0455572i | \(-0.985494\pi\) | ||
0.998962 | − | 0.0455572i | \(-0.0145063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.91758e6 | 0.274710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.24270e7 | + | 2.48779e7i | 0.375709 | + | 0.752140i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.51046e7i | − | 2.22874i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.83776e6 | −0.0826658 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.18983e7 | + | 1.09386e7i | −0.626277 | + | 0.312838i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.61910e7i | − | 0.454659i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.14619e6 | −0.141906 | −0.0709532 | − | 0.997480i | \(-0.522604\pi\) | ||||
−0.0709532 | + | 0.997480i | \(0.522604\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.16210e7 | − | 4.20939e7i | 0.856333 | − | 1.13995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.37854e6i | − | 0.143064i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.69798e7 | −0.443652 | −0.221826 | − | 0.975086i | \(-0.571202\pi\) | ||||
−0.221826 | + | 0.975086i | \(0.571202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.07308e7 | + | 2.14822e7i | 0.275443 | + | 0.551416i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 845655.i | − | 0.0213270i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.94341e7 | 0.481596 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.60870e7 | + | 1.30310e7i | −0.635282 | + | 0.317336i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.99529e7i | 0.956225i | 0.878299 | + | 0.478112i | \(0.158679\pi\) | ||||
−0.878299 | + | 0.478112i | \(0.841321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.61186e6 | −0.132017 | −0.0660086 | − | 0.997819i | \(-0.521026\pi\) | ||||
−0.0660086 | + | 0.997819i | \(0.521026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.21761e6 | + | 1.75818e7i | −0.0744068 | + | 0.406576i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.35649e7i | 1.44508i | 0.691327 | + | 0.722542i | \(0.257027\pi\) | ||||
−0.691327 | + | 0.722542i | \(0.742973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.89134e7 | 0.422752 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.13749e7 | − | 1.02849e8i | −1.12914 | − | 2.26044i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.08068e7i | 0.449699i | 0.974393 | + | 0.224850i | \(0.0721891\pi\) | ||||
−0.974393 | + | 0.224850i | \(0.927811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23173e7 | 0.261814 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.35607e7 | + | 6.77383e6i | −0.283505 | + | 0.141617i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.09658e6i | 0.0431155i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.33583e7 | 1.28176 | 0.640878 | − | 0.767642i | \(-0.278570\pi\) | ||||
0.640878 | + | 0.767642i | \(0.278570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.18418e6 | + | 6.14796e6i | 0.162891 | + | 0.122363i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.57462e7i | 1.48333i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.53615e7 | −1.45219 | −0.726094 | − | 0.687595i | \(-0.758666\pi\) | ||||
−0.726094 | + | 0.687595i | \(0.758666\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.10776e6 | + | 4.21956e6i | 0.0399693 | + | 0.0800153i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.36131e6i | − | 0.137382i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.07995e8 | −1.98375 | −0.991877 | − | 0.127204i | \(-0.959400\pi\) | ||||
−0.991877 | + | 0.127204i | \(0.959400\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.96026e7 | − | 3.47679e7i | 1.25849 | − | 0.628642i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.99874e7i | 1.60171i | 0.598855 | + | 0.800857i | \(0.295622\pi\) | ||||
−0.598855 | + | 0.800857i | \(0.704378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.68621e7 | 0.470715 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.31295e7 | + | 7.07261e7i | −0.916648 | + | 1.22024i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.17288e7i | 0.878788i | 0.898295 | + | 0.439394i | \(0.144807\pi\) | ||||
−0.898295 | + | 0.439394i | \(0.855193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.88328e8 | −3.15054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.57615e6 | − | 1.51669e7i | −0.124816 | − | 0.249872i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.03481e7i | 0.654683i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.90854e7 | 0.944297 | 0.472149 | − | 0.881519i | \(-0.343479\pi\) | ||||
0.472149 | + | 0.881519i | \(0.343479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.12921e7 | − | 4.06071e7i | 1.27976 | − | 0.639268i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.40805e7i | 0.218366i | 0.994022 | + | 0.109183i | \(0.0348235\pi\) | ||||
−0.994022 | + | 0.109183i | \(0.965177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −698073. | −0.0106656 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.85329e7 | − | 8.27457e6i | 0.429517 | − | 0.124560i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.94456e7i | 1.17838i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.05471e8 | 1.54157 | 0.770783 | − | 0.637097i | \(-0.219865\pi\) | ||||
0.770783 | + | 0.637097i | \(0.219865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.82668e7 | − | 9.66263e7i | −0.695221 | − | 1.39178i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.04272e7i | − | 0.857792i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.73838e7 | 0.243221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.79934e7 | + | 4.89497e7i | −1.35141 | + | 0.675059i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.26383e7i | 0.171809i | 0.996303 | + | 0.0859046i | \(0.0273780\pi\) | ||||
−0.996303 | + | 0.0859046i | \(0.972622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64436e6 | 0.102446 | 0.0512230 | − | 0.998687i | \(-0.483688\pi\) | ||||
0.0512230 | + | 0.998687i | \(0.483688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.16044e7 | + | 1.62293e7i | 0.285444 | + | 0.214426i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.04620e7i | 0.396818i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.21727e8 | 1.56352 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.20528e7 | − | 2.41288e7i | −0.152657 | − | 0.305607i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.11755e8i | − | 1.39583i | −0.716179 | − | 0.697917i | \(-0.754111\pi\) | ||
0.716179 | − | 0.697917i | \(-0.245889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.93268e7 | −0.730781 | −0.365390 | − | 0.930854i | \(-0.619065\pi\) | ||||
−0.365390 | + | 0.930854i | \(0.619065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.09458e7 | + | 5.46763e6i | −0.132978 | + | 0.0664250i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.48856e8i | − | 1.78370i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.07400e6 | −0.0363338 | −0.0181669 | − | 0.999835i | \(-0.505783\pi\) | ||||
−0.0181669 | + | 0.999835i | \(0.505783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.20323e7 | − | 4.26415e7i | 0.373484 | − | 0.497183i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.68560e7i | 0.884029i | 0.897008 | + | 0.442014i | \(0.145736\pi\) | ||||
−0.897008 | + | 0.442014i | \(0.854264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.23357e7 | 0.707386 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.85195e7 | − | 7.71130e7i | −0.431279 | − | 0.863386i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.60168e8i | 1.76945i | 0.466117 | + | 0.884723i | \(0.345653\pi\) | ||||
−0.466117 | + | 0.884723i | \(0.654347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54463e7 | −0.168382 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.71202e7 | − | 2.35375e7i | 0.506889 | − | 0.253201i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.21742e7i | − | 0.235404i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.10136e7 | −0.953581 | −0.476790 | − | 0.879017i | \(-0.658200\pi\) | ||||
−0.476790 | + | 0.879017i | \(0.658200\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.88732e8 | + | 3.45395e7i | 1.95168 | + | 0.357173i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.62811e7i | 0.574460i | 0.957862 | + | 0.287230i | \(0.0927344\pi\) | ||||
−0.957862 | + | 0.287230i | \(0.907266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.87451e7 | −0.793378 | −0.396689 | − | 0.917953i | \(-0.629841\pi\) | ||||
−0.396689 | + | 0.917953i | \(0.629841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 518496. | + | 1.03799e6i | 0.00515688 | + | 0.0103237i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3.51383e7i | − | 0.345009i | −0.985009 | − | 0.172504i | \(-0.944814\pi\) | ||
0.985009 | − | 0.172504i | \(-0.0551859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.20279e7 | 0.407398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.45963e7 | + | 4.72528e7i | −0.905340 | + | 0.452236i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.33484e8i | − | 1.26138i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.40773e7 | −0.224661 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.01072e8 | − | 7.59252e7i | −0.931269 | − | 0.699569i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.04950e7i | − | 0.0954942i | −0.998859 | − | 0.0477471i | \(-0.984796\pi\) | ||
0.998859 | − | 0.0477471i | \(-0.0152042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.55810e7 | 0.589309 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.01824e8 | − | 2.03843e8i | −0.903667 | − | 1.80907i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.71403e7i | 0.150242i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.61647e7 | 0.746007 | 0.373003 | − | 0.927830i | \(-0.378328\pi\) | ||||
0.373003 | + | 0.927830i | \(0.378328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.86420e7 | − | 4.42785e7i | 0.758076 | − | 0.378674i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.04932e7i | − | 0.680009i | −0.940424 | − | 0.340005i | \(-0.889571\pi\) | ||
0.940424 | − | 0.340005i | \(-0.110429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.90201e7 | −0.659472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.69256e7 | + | 3.58435e7i | −0.221999 | + | 0.295525i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.47789e8i | 1.20386i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.12437e8 | 1.70974 | 0.854869 | − | 0.518845i | \(-0.173638\pi\) | ||||
0.854869 | + | 0.518845i | \(0.173638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.82039e7 | + | 7.64813e7i | 0.303805 | + | 0.608194i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.26961e8i | − | 0.997625i | −0.866710 | − | 0.498812i | \(-0.833770\pi\) | ||
0.866710 | − | 0.498812i | \(-0.166230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.02743e7 | 0.623308 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.66696e7 | − | 4.82884e7i | 0.741765 | − | 0.370527i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.99418e8i | − | 1.51221i | −0.654452 | − | 0.756104i | \(-0.727101\pi\) | ||
0.654452 | − | 0.756104i | \(-0.272899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.63827e7 | −0.122779 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.73002e7 | + | 1.49175e8i | −0.202216 | + | 1.10495i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.66849e7i | − | 0.634632i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.07749e7 | −0.295068 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.00807e7 | + | 1.40296e8i | 0.501298 | + | 1.00356i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.85935e7i | 0.343609i | 0.985131 | + | 0.171805i | \(0.0549598\pi\) | ||||
−0.985131 | + | 0.171805i | \(0.945040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.79820e7 | −0.405311 | −0.202655 | − | 0.979250i | \(-0.564957\pi\) | ||||
−0.202655 | + | 0.979250i | \(0.564957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.29716e7 | + | 1.64700e7i | −0.227857 | + | 0.113819i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.49348e6i | 0.0511979i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.25226e8 | −1.52143 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.06309e7 | + | 6.05700e7i | 0.538540 | + | 0.404552i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.27507e7i | 0.0842077i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.75767e7 | 0.375998 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.57404e7 | + | 1.51626e8i | 0.489108 | + | 0.979155i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.04790e7i | 0.513944i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.20855e7 | 0.265791 | 0.132896 | − | 0.991130i | \(-0.457572\pi\) | ||||
0.132896 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.01611e7 | + | 1.50661e7i | −0.188386 | + | 0.0941024i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.06807e7i | 0.313078i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51378e7 | 0.459088 | 0.229544 | − | 0.973298i | \(-0.426276\pi\) | ||||
0.229544 | + | 0.973298i | \(0.426276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.22015e8 | + | 1.62426e8i | −0.737387 | + | 0.981611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.24580e7i | − | 0.373364i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.15279e8 | −1.86432 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.87105e7 | − | 9.75145e7i | −0.284933 | − | 0.570414i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.38895e7i | 0.0803750i | 0.999192 | + | 0.0401875i | \(0.0127955\pi\) | ||||
−0.999192 | + | 0.0401875i | \(0.987204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.10189e8 | −0.630816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.59011e8 | + | 1.29381e8i | −1.46700 | + | 0.732795i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.69248e8i | − | 1.50878i | −0.656424 | − | 0.754392i | \(-0.727932\pi\) | ||
0.656424 | − | 0.754392i | \(-0.272068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.97177e7 | 0.275655 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.46574e7 | + | 2.22955e8i | 0.354706 | + | 1.22312i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.49380e8i | 0.810878i | 0.914122 | + | 0.405439i | \(0.132881\pi\) | ||||
−0.914122 | + | 0.405439i | \(0.867119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.01093e7 | −0.0543015 | −0.0271507 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271507 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.91458e7 | + | 1.78463e8i | 0.473846 | + | 0.948602i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.03750e7i | 0.317580i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.19578e8 | −0.622477 | −0.311238 | − | 0.950332i | \(-0.600744\pi\) | ||||
−0.311238 | + | 0.950332i | \(0.600744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.17708e7 | − | 1.08750e7i | 0.112160 | − | 0.0560263i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.35837e8i | 0.692610i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.90757e8 | 0.962664 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.95882e7 | + | 2.22266e7i | 0.147792 | + | 0.111021i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.77627e7i | 0.137261i | 0.997642 | + | 0.0686305i | \(0.0218630\pi\) | ||||
−0.997642 | + | 0.0686305i | \(0.978137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.92289e6 | −0.0289860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.44051e7 | − | 1.88992e8i | −0.457334 | − | 0.915546i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.85398e7i | 0.472550i | 0.971686 | + | 0.236275i | \(0.0759266\pi\) | ||||
−0.971686 | + | 0.236275i | \(0.924073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.38030e8 | −1.13000 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.18324e8 | + | 5.91052e7i | −0.556096 | + | 0.277781i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.51155e7i | − | 0.302973i | −0.988459 | − | 0.151486i | \(-0.951594\pi\) | ||
0.988459 | − | 0.151486i | \(-0.0484060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.53264e8 | 1.16668 | 0.583339 | − | 0.812229i | \(-0.301746\pi\) | ||||
0.583339 | + | 0.812229i | \(0.301746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.21272e7 | + | 5.60799e7i | −0.192137 | + | 0.255773i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.13844e7i | 0.141726i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.70547e7 | −0.255109 | −0.127554 | − | 0.991832i | \(-0.540713\pi\) | ||||
−0.127554 | + | 0.991832i | \(0.540713\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.27240e7 | − | 8.55301e7i | −0.189156 | − | 0.378675i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.36590e7i | 0.147563i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.26889e8 | 1.41912 | 0.709560 | − | 0.704645i | \(-0.248894\pi\) | ||||
0.709560 | + | 0.704645i | \(0.248894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.89594e7 | − | 9.47061e6i | 0.0815079 | − | 0.0407148i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.01353e8i | − | 1.70872i | −0.519680 | − | 0.854361i | \(-0.673949\pi\) | ||
0.519680 | − | 0.854361i | \(-0.326051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.37298e8 | 0.578884 | 0.289442 | − | 0.957195i | \(-0.406530\pi\) | ||||
0.289442 | + | 0.957195i | \(0.406530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.74063e8 | + | 6.84566e7i | 1.56196 | + | 0.285851i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.87090e8i | 2.01440i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.02264e8 | − | 2.04724e8i | −0.414876 | − | 0.830550i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.03980e8i | − | 2.82884i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.95608e8 | −0.778572 | −0.389286 | − | 0.921117i | \(-0.627278\pi\) | ||||
−0.389286 | + | 0.921117i | \(0.627278\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.55463e8 | − | 1.27609e8i | 1.00720 | − | 0.503118i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.61086e8i | − | 0.629125i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.64340e7 | 0.257023 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.97203e8 | − | 1.48139e8i | −0.755806 | − | 0.567762i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.86584e8i | − | 0.708437i | −0.935163 | − | 0.354219i | \(-0.884747\pi\) | ||
0.935163 | − | 0.354219i | \(-0.115253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.74191e8 | 1.40754 | 0.703770 | − | 0.710427i | \(-0.251498\pi\) | ||||
0.703770 | + | 0.710427i | \(0.251498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.18432e7 | + | 1.63844e8i | 0.305003 | + | 0.610591i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.66258e8i | − | 1.35230i | −0.736762 | − | 0.676152i | \(-0.763646\pi\) | ||
0.736762 | − | 0.676152i | \(-0.236354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.52178e8 | −0.556696 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.11083e6 | + | 4.05152e6i | −0.0293983 | + | 0.0146850i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.50492e8i | − | 0.540472i | −0.962794 | − | 0.270236i | \(-0.912898\pi\) | ||
0.962794 | − | 0.270236i | \(-0.0871017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.51017e7 | −0.124912 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.64214e7 | − | 2.18602e7i | 0.0579048 | − | 0.0770830i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.31848e8i | 1.50895i | 0.656329 | + | 0.754475i | \(0.272109\pi\) | ||||
−0.656329 | + | 0.754475i | \(0.727891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.04838e8 | −0.363007 | −0.181504 | − | 0.983390i | \(-0.558096\pi\) | ||||
−0.181504 | + | 0.983390i | \(0.558096\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.06802e8 | + | 2.13809e8i | 0.366470 | + | 0.733644i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.88140e8i | − | 0.639759i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.56616e8 | −0.527787 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.35084e8 | + | 1.17429e8i | −0.785135 | + | 0.392191i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.06554e8i | − | 1.01470i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.07160e8 | 0.679611 | 0.339805 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339805 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.10728e7 | − | 6.05045e7i | 0.0360037 | − | 0.196733i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.59856e8i | 1.48203i | 0.671491 | + | 0.741013i | \(0.265654\pi\) | ||||
−0.671491 | + | 0.741013i | \(0.734346\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.33934e8 | −0.427840 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.35361e7 | + | 1.27194e8i | 0.201177 | + | 0.402741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.04044e8i | 1.26814i | 0.773277 | + | 0.634069i | \(0.218616\pi\) | ||||
−0.773277 | + | 0.634069i | \(0.781384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.23629e8 | −0.695755 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.79919e8 | − | 2.39729e8i | 1.48012 | − | 0.739351i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.57467e8i | − | 0.481428i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.98324e8 | −0.904179 | −0.452090 | − | 0.891973i | \(-0.649321\pi\) | ||||
−0.452090 | + | 0.891973i | \(0.649321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.80080e8 | − | 2.10396e8i | −0.841556 | − | 0.632177i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.26793e8i | 0.675578i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.36872e8 | 0.404220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.92602e8 | − | 5.85767e8i | −0.856735 | − | 1.71512i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.10378e8i | − | 1.19132i | −0.803235 | − | 0.595662i | \(-0.796890\pi\) | ||
0.803235 | − | 0.595662i | \(-0.203110\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.56430e8 | 1.60157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.00487e7 | − | 2.50003e7i | 0.142832 | − | 0.0713474i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.27262e8i | 1.77497i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.38412e8 | −1.23011 | −0.615054 | − | 0.788485i | \(-0.710866\pi\) | ||||
−0.615054 | + | 0.788485i | \(0.710866\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.16024e8 | − | 4.20693e8i | 0.879249 | − | 1.17046i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.48519e7i | 0.0409745i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.58430e7 | −0.152774 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.13222e8 | + | 2.26661e8i | 0.307166 | + | 0.614921i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.35325e8i | − | 0.364076i | −0.983291 | − | 0.182038i | \(-0.941731\pi\) | ||
0.983291 | − | 0.182038i | \(-0.0582694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.77355e8 | 1.80722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.78657e6 | + | 2.89051e6i | −0.0153111 | + | 0.00764821i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.53326e7i | 0.0664761i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.04885e7 | 0.0272966 | 0.0136483 | − | 0.999907i | \(-0.495655\pi\) | ||||
0.0136483 | + | 0.999907i | \(0.495655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.62311e8 | − | 1.37207e8i | −0.935187 | − | 0.354155i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.18283e9i | 3.02809i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.59655e7 | −0.0659303 | −0.0329652 | − | 0.999457i | \(-0.510495\pi\) | ||||
−0.0329652 | + | 0.999457i | \(0.510495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.93441e7 | − | 9.87829e7i | −0.124272 | − | 0.248783i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.05842e8i | − | 0.264396i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.95717e8 | 0.484948 | 0.242474 | − | 0.970158i | \(-0.422041\pi\) | ||||
0.242474 | + | 0.970158i | \(0.422041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.68996e8 | + | 8.44169e7i | −0.415357 | + | 0.207479i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.21923e8i | − | 0.297247i | −0.988894 | − | 0.148624i | \(-0.952516\pi\) | ||
0.988894 | − | 0.148624i | \(-0.0474843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.78468e8 | −0.431610 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.81254e8 | − | 1.36158e8i | −0.434835 | − | 0.326648i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.49903e8i | 1.07071i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.28855e8 | −0.776399 | −0.388199 | − | 0.921575i | \(-0.626903\pi\) | ||||
−0.388199 | + | 0.921575i | \(0.626903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.02949e7 | − | 6.06480e7i | −0.0709553 | − | 0.142047i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.09054e8i | − | 0.253396i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.45441e8 | −0.565797 | −0.282898 | − | 0.959150i | \(-0.591296\pi\) | ||||
−0.282898 | + | 0.959150i | \(0.591296\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.13354e8 | + | 2.56431e8i | −1.17406 | + | 0.586468i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.19490e8i | 1.17875i | 0.807858 | + | 0.589377i | \(0.200627\pi\) | ||||
−0.807858 | + | 0.589377i | \(0.799373\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.96018e8 | −0.891541 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.38592e8 | − | 3.17615e8i | 0.532932 | − | 0.709441i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.25620e8i | 0.278403i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.01913e8 | 0.883797 | 0.441899 | − | 0.897065i | \(-0.354305\pi\) | ||||
0.441899 | + | 0.897065i | \(0.354305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.38784e8 | + | 2.77835e8i | 0.302814 | + | 0.606211i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.45715e8i | 0.748478i | 0.927332 | + | 0.374239i | \(0.122096\pi\) | ||||
−0.927332 | + | 0.374239i | \(0.877904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.40229e6 | 0.00516084 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.61977e8 | − | 3.80623e8i | 1.62435 | − | 0.811394i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08185e8i | 0.228852i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.72189e8 | 0.781286 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.56952e8 | + | 2.87235e7i | 0.326950 | + | 0.0598345i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.18931e8i | 0.452583i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.70491e8 | −1.58068 | −0.790339 | − | 0.612670i | \(-0.790095\pi\) | ||||
−0.790339 | + | 0.612670i | \(0.790095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.05553e8 | + | 2.11308e8i | 0.214901 | + | 0.430214i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.88494e8i | 0.784973i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.53055e8 | −0.507453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.34142e8 | + | 1.16959e8i | −0.465992 | + | 0.232772i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.84076e8i | − | 0.561125i | −0.959836 | − | 0.280563i | \(-0.909479\pi\) | ||
0.959836 | − | 0.280563i | \(-0.0905210\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.61313e8 | 0.708343 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.49948e8 | − | 4.88241e8i | −1.26468 | − | 0.950029i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.12577e7i | 0.0796817i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.71769e8 | −0.904362 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.75165e8 | + | 5.50859e8i | 0.523568 | + | 1.04814i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.17256e8i | − | 1.16579i | −0.812548 | − | 0.582894i | \(-0.801920\pi\) | ||
0.812548 | − | 0.582894i | \(-0.198080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.32210e8 | 0.997748 | 0.498874 | − | 0.866675i | \(-0.333747\pi\) | ||||
0.498874 | + | 0.866675i | \(0.333747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.80065e8 | + | 1.39898e8i | −0.521179 | + | 0.260339i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.05150e8i | − | 0.378965i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.34913e8 | −1.71437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.73679e8 | + | 2.31202e8i | −0.316151 | + | 0.420861i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.60333e8i | 0.651140i | 0.945518 | + | 0.325570i | \(0.105556\pi\) | ||||
−0.945518 | + | 0.325570i | \(0.894444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.46142e7 | 0.169729 | 0.0848646 | − | 0.996392i | \(-0.472954\pi\) | ||||
0.0848646 | + | 0.996392i | \(0.472954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.14775e7 | + | 8.30347e7i | 0.0738671 | + | 0.147876i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.55768e8i | 1.33620i | 0.744070 | + | 0.668101i | \(0.232893\pi\) | ||||
−0.744070 | + | 0.668101i | \(0.767107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.78503e8 | 0.839887 | 0.419944 | − | 0.907550i | \(-0.362050\pi\) | ||||
0.419944 | + | 0.907550i | \(0.362050\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.47906e8 | + | 1.73786e8i | −0.606259 | + | 0.302839i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 7.13137e8i | − | 1.23378i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.77006e8 | 0.304039 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.72385e6 | − | 1.48838e7i | 0.00464523 | − | 0.0253826i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.45796e8i | 0.246866i | 0.992353 | + | 0.123433i | \(0.0393903\pi\) | ||||
−0.992353 | + | 0.123433i | \(0.960610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.29109e8 | 0.889523 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.51634e8 | − | 9.04135e8i | −0.753882 | − | 1.50921i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 2.23729e8i | − | 0.370811i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.45238e8 | −0.403587 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.23033e8 | − | 2.61266e8i | 0.854685 | − | 0.426933i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.39527e9i | − | 2.26397i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.64922e8 | 1.23245 | 0.616226 | − | 0.787569i | \(-0.288661\pi\) | ||||
0.616226 | + | 0.787569i | \(0.288661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.51045e8 | + | 1.88585e8i | 0.401654 | + | 0.301723i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4.79513e8i | − | 0.761830i | −0.924610 | − | 0.380915i | \(-0.875609\pi\) | ||
0.924610 | − | 0.380915i | \(-0.124391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.90859e8 | −0.458884 | −0.229442 | − | 0.973322i | \(-0.573690\pi\) | ||||
−0.229442 | + | 0.973322i | \(0.573690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.40032e7 | + | 1.48149e8i | 0.115942 | + | 0.232107i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.78195e8i | − | 0.588415i | −0.955742 | − | 0.294207i | \(-0.904944\pi\) | ||
0.955742 | − | 0.294207i | \(-0.0950556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.24697e8 | 0.501683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.71211e9 | − | 8.55235e8i | 2.62709 | − | 1.31229i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.93990e8i | 1.20992i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.73706e7 | −0.132224 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.34250e8 | − | 1.78715e8i | 0.201778 | − | 0.268607i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.63085e7i | 0.113907i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.32209e8 | 0.492508 | 0.246254 | − | 0.969205i | \(-0.420800\pi\) | ||||
0.246254 | + | 0.969205i | \(0.420800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.37115e7 | + | 2.74493e7i | 0.0201891 | + | 0.0404171i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.22274e9i | − | 1.78815i | −0.447914 | − | 0.894077i | \(-0.647833\pi\) | ||
0.447914 | − | 0.894077i | \(-0.352167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.56383e8 | −1.24390 | −0.621951 | − | 0.783056i | \(-0.713660\pi\) | ||||
−0.621951 | + | 0.783056i | \(0.713660\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.86789e8 | − | 9.33049e7i | 0.269477 | − | 0.134609i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 5.70473e8i | − | 0.817456i | −0.912656 | − | 0.408728i | \(-0.865973\pi\) | ||
0.912656 | − | 0.408728i | \(-0.134027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.25873e9 | 1.79154 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.61485e8 | − | 1.62831e8i | 0.793788 | − | 0.230200i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.85584e8i | 0.401033i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.50919e8 | 0.489484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.11679e8 | + | 4.23765e8i | 0.293292 | + | 0.587148i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.23167e6i | 0.00857680i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.69033e9 | −2.31098 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.28027e9 | + | 6.39522e8i | −1.73876 | + | 0.868545i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.98040e7i | 0.0941747i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.31544e8 | −0.310321 | −0.155160 | − | 0.987889i | \(-0.549589\pi\) | ||||
−0.155160 | + | 0.987889i | \(0.549589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.36987e8 | − | 6.28745e8i | −1.11436 | − | 0.837111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.23991e8i | − | 0.560792i | −0.959884 | − | 0.280396i | \(-0.909534\pi\) | ||
0.959884 | − | 0.280396i | \(-0.0904658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.42087e8 | 0.449495 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.87957e8 | + | 3.76276e8i | 0.245356 | + | 0.491183i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.74285e8i | − | 0.355708i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08546e9 | 1.39852 | 0.699259 | − | 0.714869i | \(-0.253514\pi\) | ||||
0.699259 | + | 0.714869i | \(0.253514\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.28641e9 | + | 6.42587e8i | −1.64665 | + | 0.822533i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.07236e8i | − | 0.390721i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.25685e8 | −0.285152 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.78956e8 | + | 9.03828e8i | −0.852319 | + | 1.13461i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.68457e7i | 0.108318i | 0.998532 | + | 0.0541591i | \(0.0172478\pi\) | ||||
−0.998532 | + | 0.0541591i | \(0.982752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.63668e8 | 0.698513 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.54879e8 | + | 1.31102e9i | 0.806336 | + | 1.61422i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99447e8i | 0.733358i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.79010e8 | −0.460715 | −0.230358 | − | 0.973106i | \(-0.573990\pi\) | ||||
−0.230358 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.26613e8 | + | 6.32459e7i | −0.152926 | + | 0.0763898i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.55151e6i | 0.00666258i | 0.999994 | + | 0.00333129i | \(0.00106038\pi\) | ||||
−0.999994 | + | 0.00333129i | \(0.998940\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.71278e8 | 0.323504 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.72782e8 | + | 8.65228e7i | 0.560228 | + | 0.102526i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 5.18303e8i | − | 0.610286i | −0.952306 | − | 0.305143i | \(-0.901296\pi\) | ||
0.952306 | − | 0.305143i | \(-0.0987043\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.40575e7 | 0.0398487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.50195e7 | + | 7.01062e7i | 0.0407163 | + | 0.0815108i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.23349e8i | − | 0.373588i | −0.982399 | − | 0.186794i | \(-0.940190\pi\) | ||
0.982399 | − | 0.186794i | \(-0.0598097\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.13029e8 | 0.474210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.15397e8 | + | 1.07595e8i | −0.245755 | + | 0.122760i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.74743e9i | − | 1.98128i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.86913e8 | −0.999334 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00328e8 | − | 4.50967e8i | −0.672218 | − | 0.504970i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.03857e7i | − | 0.0560694i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.56777e9 | −1.73381 | −0.866907 | − | 0.498470i | \(-0.833895\pi\) | ||||
−0.866907 | + | 0.498470i | \(0.833895\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.06175e8 | + | 1.81409e9i | 0.995957 | + | 1.99383i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.19138e9i | 1.30135i | 0.759358 | + | 0.650673i | \(0.225513\pi\) | ||||
−0.759358 | + | 0.650673i | \(0.774487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.77216e9 | −1.92382 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.85437e7 | − | 3.42390e7i | 0.0739527 | − | 0.0369409i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.83913e8i | − | 0.304440i | −0.988347 | − | 0.152220i | \(-0.951358\pi\) | ||
0.988347 | − | 0.152220i | \(-0.0486422\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.22667e9 | 1.30732 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.96954e8 | − | 5.28427e8i | 0.420468 | − | 0.559729i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.30425e8i | − | 0.242587i | −0.992617 | − | 0.121294i | \(-0.961296\pi\) | ||
0.992617 | − | 0.121294i | \(-0.0387043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.37397e8 | −0.457685 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.95352e8 | + | 3.91080e8i | 0.203173 | + | 0.406737i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.34433e9i | 2.42343i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.46001e8 | −0.150015 | −0.0750076 | − | 0.997183i | \(-0.523898\pi\) | ||||
−0.0750076 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.24302e8 | − | 6.20914e7i | 0.126949 | − | 0.0634138i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.73846e8i | 0.277995i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.78931e8 | 0.180551 | 0.0902756 | − | 0.995917i | \(-0.471225\pi\) | ||||
0.0902756 | + | 0.995917i | \(0.471225\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.55894e8 | + | 1.39827e9i | −0.256663 | + | 1.40247i |
(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 | 60.7.g.a.41.2 | yes | 8 | |
3.2 | odd | 2 | inner | 60.7.g.a.41.1 | ✓ | 8 | |
4.3 | odd | 2 | 240.7.l.c.161.7 | 8 | |||
5.2 | odd | 4 | 300.7.b.e.149.12 | 16 | |||
5.3 | odd | 4 | 300.7.b.e.149.5 | 16 | |||
5.4 | even | 2 | 300.7.g.h.101.7 | 8 | |||
12.11 | even | 2 | 240.7.l.c.161.8 | 8 | |||
15.2 | even | 4 | 300.7.b.e.149.6 | 16 | |||
15.8 | even | 4 | 300.7.b.e.149.11 | 16 | |||
15.14 | odd | 2 | 300.7.g.h.101.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.g.a.41.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
60.7.g.a.41.2 | yes | 8 | 1.1 | even | 1 | trivial | |
240.7.l.c.161.7 | 8 | 4.3 | odd | 2 | |||
240.7.l.c.161.8 | 8 | 12.11 | even | 2 | |||
300.7.b.e.149.5 | 16 | 5.3 | odd | 4 | |||
300.7.b.e.149.6 | 16 | 15.2 | even | 4 | |||
300.7.b.e.149.11 | 16 | 15.8 | even | 4 | |||
300.7.b.e.149.12 | 16 | 5.2 | odd | 4 | |||
300.7.g.h.101.7 | 8 | 5.4 | even | 2 | |||
300.7.g.h.101.8 | 8 | 15.14 | odd | 2 |