Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), 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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.6.e.i.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | + | 5.19615i | 0.530330 | + | 0.918559i | 0.999374 | + | 0.0353837i | \(0.0112653\pi\) |
−0.469044 | + | 0.883175i | \(0.655401\pi\) | |||||||
\(3\) | −4.50000 | + | 7.79423i | −0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.0625000 | + | 0.108253i | ||||
\(5\) | 39.0000 | + | 67.5500i | 0.697653 | + | 1.20837i | 0.969278 | + | 0.245968i | \(0.0791057\pi\) |
−0.271625 | + | 0.962403i | \(0.587561\pi\) | |||||||
\(6\) | −54.0000 | −0.612372 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 168.000 | 0.928078 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | −234.000 | + | 405.300i | −0.739973 | + | 1.28167i | ||||
\(11\) | −222.000 | + | 384.515i | −0.553186 | + | 0.958146i | 0.444856 | + | 0.895602i | \(0.353255\pi\) |
−0.998042 | + | 0.0625444i | \(0.980079\pi\) | |||||||
\(12\) | −18.0000 | − | 31.1769i | −0.0360844 | − | 0.0625000i | ||||
\(13\) | 442.000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −702.000 | −0.805581 | ||||||||
\(16\) | 568.000 | + | 983.805i | 0.554688 | + | 0.960747i | ||||
\(17\) | −63.0000 | + | 109.119i | −0.0528711 | + | 0.0915754i | −0.891250 | − | 0.453513i | \(-0.850171\pi\) |
0.838379 | + | 0.545088i | \(0.183504\pi\) | |||||||
\(18\) | 243.000 | − | 420.888i | 0.176777 | − | 0.306186i | ||||
\(19\) | 1342.00 | + | 2324.41i | 0.852842 | + | 1.47717i | 0.878633 | + | 0.477498i | \(0.158456\pi\) |
−0.0257909 | + | 0.999667i | \(0.508210\pi\) | |||||||
\(20\) | −312.000 | −0.174413 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2664.00 | −1.17348 | ||||||||
\(23\) | −2100.00 | − | 3637.31i | −0.827751 | − | 1.43371i | −0.899799 | − | 0.436306i | \(-0.856287\pi\) |
0.0720476 | − | 0.997401i | \(-0.477047\pi\) | |||||||
\(24\) | −756.000 | + | 1309.43i | −0.267913 | + | 0.464039i | ||||
\(25\) | −1479.50 | + | 2562.57i | −0.473440 | + | 0.820022i | ||||
\(26\) | 1326.00 | + | 2296.70i | 0.384689 | + | 0.666301i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5442.00 | −1.20161 | −0.600805 | − | 0.799396i | \(-0.705153\pi\) | ||||
−0.600805 | + | 0.799396i | \(0.705153\pi\) | |||||||
\(30\) | −2106.00 | − | 3647.70i | −0.427224 | − | 0.739973i | ||||
\(31\) | 40.0000 | − | 69.2820i | 0.00747577 | − | 0.0129484i | −0.862263 | − | 0.506460i | \(-0.830954\pi\) |
0.869739 | + | 0.493512i | \(0.164287\pi\) | |||||||
\(32\) | −720.000 | + | 1247.08i | −0.124296 | + | 0.215287i | ||||
\(33\) | −1998.00 | − | 3460.64i | −0.319382 | − | 0.553186i | ||||
\(34\) | −756.000 | −0.112157 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 324.000 | 0.0416667 | ||||||||
\(37\) | 2717.00 | + | 4705.98i | 0.326276 | + | 0.565127i | 0.981770 | − | 0.190074i | \(-0.0608727\pi\) |
−0.655494 | + | 0.755201i | \(0.727539\pi\) | |||||||
\(38\) | −8052.00 | + | 13946.5i | −0.904575 | + | 1.56677i | ||||
\(39\) | −1989.00 | + | 3445.05i | −0.209398 | + | 0.362689i | ||||
\(40\) | 6552.00 | + | 11348.4i | 0.647476 | + | 1.12146i | ||||
\(41\) | −7962.00 | −0.739712 | −0.369856 | − | 0.929089i | \(-0.620593\pi\) | ||||
−0.369856 | + | 0.929089i | \(0.620593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11524.0 | −0.950456 | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475228 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(44\) | −888.000 | − | 1538.06i | −0.0691483 | − | 0.119768i | ||||
\(45\) | 3159.00 | − | 5471.55i | 0.232551 | − | 0.402790i | ||||
\(46\) | 12600.0 | − | 21823.8i | 0.877962 | − | 1.52068i | ||||
\(47\) | −6960.00 | − | 12055.1i | −0.459584 | − | 0.796022i | 0.539355 | − | 0.842078i | \(-0.318668\pi\) |
−0.998939 | + | 0.0460561i | \(0.985335\pi\) | |||||||
\(48\) | −10224.0 | −0.640498 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17754.0 | −1.00432 | ||||||||
\(51\) | −567.000 | − | 982.073i | −0.0305251 | − | 0.0528711i | ||||
\(52\) | −884.000 | + | 1531.13i | −0.0453361 | + | 0.0785244i | ||||
\(53\) | 4797.00 | − | 8308.65i | 0.234574 | − | 0.406294i | −0.724575 | − | 0.689196i | \(-0.757964\pi\) |
0.959149 | + | 0.282902i | \(0.0912971\pi\) | |||||||
\(54\) | 2187.00 | + | 3788.00i | 0.102062 | + | 0.176777i | ||||
\(55\) | −34632.0 | −1.54373 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24156.0 | −0.984777 | ||||||||
\(58\) | −16326.0 | − | 28277.5i | −0.637250 | − | 1.10375i | ||||
\(59\) | 13746.0 | − | 23808.8i | 0.514098 | − | 0.890445i | −0.485768 | − | 0.874088i | \(-0.661460\pi\) |
0.999866 | − | 0.0163567i | \(-0.00520675\pi\) | |||||||
\(60\) | 1404.00 | − | 2431.80i | 0.0503488 | − | 0.0872067i | ||||
\(61\) | 24739.0 | + | 42849.2i | 0.851251 | + | 1.47441i | 0.880080 | + | 0.474825i | \(0.157489\pi\) |
−0.0288292 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(62\) | 480.000 | 0.0158585 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 27712.0 | 0.845703 | ||||||||
\(65\) | 17238.0 | + | 29857.1i | 0.506062 | + | 0.876525i | ||||
\(66\) | 11988.0 | − | 20763.8i | 0.338756 | − | 0.586742i | ||||
\(67\) | 29678.0 | − | 51403.8i | 0.807695 | − | 1.39897i | −0.106761 | − | 0.994285i | \(-0.534048\pi\) |
0.914456 | − | 0.404685i | \(-0.132619\pi\) | |||||||
\(68\) | −252.000 | − | 436.477i | −0.00660889 | − | 0.0114469i | ||||
\(69\) | 37800.0 | 0.955805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32040.0 | 0.754304 | 0.377152 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377152 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(72\) | −6804.00 | − | 11784.9i | −0.154680 | − | 0.267913i | ||||
\(73\) | −30923.0 | + | 53560.2i | −0.679164 | + | 1.17635i | 0.296069 | + | 0.955166i | \(0.404324\pi\) |
−0.975233 | + | 0.221180i | \(0.929009\pi\) | |||||||
\(74\) | −16302.0 | + | 28235.9i | −0.346068 | + | 0.599408i | ||||
\(75\) | −13315.5 | − | 23063.1i | −0.273341 | − | 0.473440i | ||||
\(76\) | −10736.0 | −0.213210 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −23868.0 | −0.444201 | ||||||||
\(79\) | 32888.0 | + | 56963.7i | 0.592884 | + | 1.02691i | 0.993842 | + | 0.110809i | \(0.0353441\pi\) |
−0.400958 | + | 0.916097i | \(0.631323\pi\) | |||||||
\(80\) | −44304.0 | + | 76736.8i | −0.773959 | + | 1.34054i | ||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −23886.0 | − | 41371.8i | −0.392291 | − | 0.679469i | ||||
\(83\) | −40188.0 | −0.640326 | −0.320163 | − | 0.947362i | \(-0.603738\pi\) | ||||
−0.320163 | + | 0.947362i | \(0.603738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9828.00 | −0.147543 | ||||||||
\(86\) | −34572.0 | − | 59880.5i | −0.504056 | − | 0.873050i | ||||
\(87\) | 24489.0 | − | 42416.2i | 0.346875 | − | 0.600805i | ||||
\(88\) | −37296.0 | + | 64598.6i | −0.513400 | + | 0.889234i | ||||
\(89\) | −3987.00 | − | 6905.69i | −0.0533545 | − | 0.0924127i | 0.838115 | − | 0.545494i | \(-0.183658\pi\) |
−0.891469 | + | 0.453081i | \(0.850325\pi\) | |||||||
\(90\) | 37908.0 | 0.493315 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16800.0 | 0.206938 | ||||||||
\(93\) | 360.000 | + | 623.538i | 0.00431614 | + | 0.00747577i | ||||
\(94\) | 41760.0 | − | 72330.4i | 0.487462 | − | 0.844309i | ||||
\(95\) | −104676. | + | 181304.i | −1.18998 | + | 2.06110i | ||||
\(96\) | −6480.00 | − | 11223.7i | −0.0717624 | − | 0.124296i | ||||
\(97\) | 143662. | 1.55029 | 0.775144 | − | 0.631784i | \(-0.217677\pi\) | ||||
0.775144 | + | 0.631784i | \(0.217677\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 35964.0 | 0.368791 | ||||||||
\(100\) | −5918.00 | − | 10250.3i | −0.0591800 | − | 0.102503i | ||||
\(101\) | −1353.00 | + | 2343.46i | −0.0131976 | + | 0.0228589i | −0.872549 | − | 0.488527i | \(-0.837534\pi\) |
0.859351 | + | 0.511386i | \(0.170868\pi\) | |||||||
\(102\) | 3402.00 | − | 5892.44i | 0.0323768 | − | 0.0560783i | ||||
\(103\) | 65884.0 | + | 114114.i | 0.611909 | + | 1.05986i | 0.990918 | + | 0.134465i | \(0.0429315\pi\) |
−0.379009 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(104\) | 74256.0 | 0.673206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 57564.0 | 0.497607 | ||||||||
\(107\) | 64458.0 | + | 111645.i | 0.544274 | + | 0.942710i | 0.998652 | + | 0.0519010i | \(0.0165280\pi\) |
−0.454378 | + | 0.890809i | \(0.650139\pi\) | |||||||
\(108\) | −1458.00 | + | 2525.33i | −0.0120281 | + | 0.0208333i | ||||
\(109\) | 50489.0 | − | 87449.5i | 0.407034 | − | 0.705003i | −0.587522 | − | 0.809208i | \(-0.699896\pi\) |
0.994556 | + | 0.104205i | \(0.0332298\pi\) | |||||||
\(110\) | −103896. | − | 179953.i | −0.818686 | − | 1.41800i | ||||
\(111\) | −48906.0 | −0.376751 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 220146. | 1.62186 | 0.810932 | − | 0.585140i | \(-0.198960\pi\) | ||||
0.810932 | + | 0.585140i | \(0.198960\pi\) | |||||||
\(114\) | −72468.0 | − | 125518.i | −0.522257 | − | 0.904575i | ||||
\(115\) | 163800. | − | 283710.i | 1.15497 | − | 2.00046i | ||||
\(116\) | 10884.0 | − | 18851.6i | 0.0751006 | − | 0.130078i | ||||
\(117\) | −17901.0 | − | 31005.4i | −0.120896 | − | 0.209398i | ||||
\(118\) | 164952. | 1.09057 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −117936. | −0.747641 | ||||||||
\(121\) | −18042.5 | − | 31250.5i | −0.112030 | − | 0.194041i | ||||
\(122\) | −148434. | + | 257095.i | −0.902888 | + | 1.56385i | ||||
\(123\) | 35829.0 | − | 62057.6i | 0.213536 | − | 0.369856i | ||||
\(124\) | 160.000 | + | 277.128i | 0.000934471 | + | 0.00161855i | ||||
\(125\) | 12948.0 | 0.0741187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −74320.0 | −0.408880 | −0.204440 | − | 0.978879i | \(-0.565537\pi\) | ||||
−0.204440 | + | 0.978879i | \(0.565537\pi\) | |||||||
\(128\) | 106176. | + | 183902.i | 0.572798 | + | 0.992115i | ||||
\(129\) | 51858.0 | − | 89820.7i | 0.274373 | − | 0.475228i | ||||
\(130\) | −103428. | + | 179143.i | −0.536760 | + | 0.929695i | ||||
\(131\) | −77658.0 | − | 134508.i | −0.395374 | − | 0.684808i | 0.597775 | − | 0.801664i | \(-0.296052\pi\) |
−0.993149 | + | 0.116856i | \(0.962718\pi\) | |||||||
\(132\) | 15984.0 | 0.0798455 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 356136. | 1.71338 | ||||||||
\(135\) | 28431.0 | + | 49243.9i | 0.134263 | + | 0.232551i | ||||
\(136\) | −10584.0 | + | 18332.0i | −0.0490685 | + | 0.0849891i | ||||
\(137\) | 132123. | − | 228844.i | 0.601419 | − | 1.04169i | −0.391188 | − | 0.920311i | \(-0.627936\pi\) |
0.992606 | − | 0.121377i | \(-0.0387310\pi\) | |||||||
\(138\) | 113400. | + | 196415.i | 0.506892 | + | 0.877962i | ||||
\(139\) | −224612. | −0.986043 | −0.493022 | − | 0.870017i | \(-0.664108\pi\) | ||||
−0.493022 | + | 0.870017i | \(0.664108\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125280. | 0.530682 | ||||||||
\(142\) | 96120.0 | + | 166485.i | 0.400030 | + | 0.692873i | ||||
\(143\) | −98124.0 | + | 169956.i | −0.401269 | + | 0.695018i | ||||
\(144\) | 46008.0 | − | 79688.2i | 0.184896 | − | 0.320249i | ||||
\(145\) | −212238. | − | 367607.i | −0.838307 | − | 1.45199i | ||||
\(146\) | −371076. | −1.44072 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21736.0 | −0.0815690 | ||||||||
\(149\) | 41037.0 | + | 71078.2i | 0.151429 | + | 0.262283i | 0.931753 | − | 0.363092i | \(-0.118279\pi\) |
−0.780324 | + | 0.625376i | \(0.784946\pi\) | |||||||
\(150\) | 79893.0 | − | 138379.i | 0.289922 | − | 0.502159i | ||||
\(151\) | 143516. | − | 248577.i | 0.512222 | − | 0.887194i | −0.487678 | − | 0.873024i | \(-0.662156\pi\) |
0.999900 | − | 0.0141703i | \(-0.00451071\pi\) | |||||||
\(152\) | 225456. | + | 390501.i | 0.791503 | + | 1.37092i | ||||
\(153\) | 10206.0 | 0.0352474 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6240.00 | 0.0208620 | ||||||||
\(156\) | −7956.00 | − | 13780.2i | −0.0261748 | − | 0.0453361i | ||||
\(157\) | 64939.0 | − | 112478.i | 0.210260 | − | 0.364181i | −0.741536 | − | 0.670913i | \(-0.765902\pi\) |
0.951796 | + | 0.306732i | \(0.0992356\pi\) | |||||||
\(158\) | −197328. | + | 341782.i | −0.628848 | + | 1.08920i | ||||
\(159\) | 43173.0 | + | 74777.8i | 0.135431 | + | 0.234574i | ||||
\(160\) | −112320. | −0.346862 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −39366.0 | −0.117851 | ||||||||
\(163\) | −277642. | − | 480890.i | −0.818495 | − | 1.41768i | −0.906791 | − | 0.421581i | \(-0.861475\pi\) |
0.0882955 | − | 0.996094i | \(-0.471858\pi\) | |||||||
\(164\) | 15924.0 | − | 27581.2i | 0.0462320 | − | 0.0800761i | ||||
\(165\) | 155844. | − | 269930.i | 0.445636 | − | 0.771864i | ||||
\(166\) | −120564. | − | 208823.i | −0.339584 | − | 0.588177i | ||||
\(167\) | −43512.0 | −0.120731 | −0.0603654 | − | 0.998176i | \(-0.519227\pi\) | ||||
−0.0603654 | + | 0.998176i | \(0.519227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −175929. | −0.473828 | ||||||||
\(170\) | −29484.0 | − | 51067.8i | −0.0782464 | − | 0.135527i | ||||
\(171\) | 108702. | − | 188277.i | 0.284281 | − | 0.492388i | ||||
\(172\) | 23048.0 | − | 39920.3i | 0.0594035 | − | 0.102890i | ||||
\(173\) | −9165.00 | − | 15874.2i | −0.0232818 | − | 0.0403253i | 0.854150 | − | 0.520027i | \(-0.174078\pi\) |
−0.877432 | + | 0.479702i | \(0.840745\pi\) | |||||||
\(174\) | 293868. | 0.735833 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −504384. | −1.22738 | ||||||||
\(177\) | 123714. | + | 214279.i | 0.296815 | + | 0.514098i | ||||
\(178\) | 23922.0 | − | 41434.1i | 0.0565910 | − | 0.0980185i | ||||
\(179\) | 76662.0 | − | 132782.i | 0.178833 | − | 0.309748i | −0.762648 | − | 0.646814i | \(-0.776101\pi\) |
0.941481 | + | 0.337066i | \(0.109434\pi\) | |||||||
\(180\) | 12636.0 | + | 21886.2i | 0.0290689 | + | 0.0503488i | ||||
\(181\) | 382066. | 0.866846 | 0.433423 | − | 0.901191i | \(-0.357306\pi\) | ||||
0.433423 | + | 0.901191i | \(0.357306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −445302. | −0.982940 | ||||||||
\(184\) | −352800. | − | 611068.i | −0.768217 | − | 1.33059i | ||||
\(185\) | −211926. | + | 367067.i | −0.455255 | + | 0.788525i | ||||
\(186\) | −2160.00 | + | 3741.23i | −0.00457795 | + | 0.00792925i | ||||
\(187\) | −27972.0 | − | 48448.9i | −0.0584951 | − | 0.101316i | ||||
\(188\) | 55680.0 | 0.114896 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.25611e6 | −2.52432 | ||||||||
\(191\) | 136704. | + | 236778.i | 0.271143 | + | 0.469633i | 0.969155 | − | 0.246453i | \(-0.0792652\pi\) |
−0.698012 | + | 0.716086i | \(0.745932\pi\) | |||||||
\(192\) | −124704. | + | 215994.i | −0.244133 | + | 0.422852i | ||||
\(193\) | −76801.0 | + | 133023.i | −0.148414 | + | 0.257060i | −0.930641 | − | 0.365933i | \(-0.880750\pi\) |
0.782228 | + | 0.622993i | \(0.214083\pi\) | |||||||
\(194\) | 430986. | + | 746490.i | 0.822165 | + | 1.42403i | ||||
\(195\) | −310284. | −0.584350 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 154422. | 0.283494 | 0.141747 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141747 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(198\) | 107892. | + | 186874.i | 0.195581 | + | 0.338756i | ||||
\(199\) | −183428. | + | 317707.i | −0.328347 | + | 0.568714i | −0.982184 | − | 0.187922i | \(-0.939825\pi\) |
0.653837 | + | 0.756635i | \(0.273158\pi\) | |||||||
\(200\) | −248556. | + | 430512.i | −0.439389 | + | 0.761044i | ||||
\(201\) | 267102. | + | 462634.i | 0.466323 | + | 0.807695i | ||||
\(202\) | −16236.0 | −0.0279963 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4536.00 | 0.00763128 | ||||||||
\(205\) | −310518. | − | 537833.i | −0.516062 | − | 0.893846i | ||||
\(206\) | −395304. | + | 684687.i | −0.649028 | + | 1.12415i | ||||
\(207\) | −170100. | + | 294622.i | −0.275917 | + | 0.477902i | ||||
\(208\) | 251056. | + | 434842.i | 0.402358 | + | 0.696904i | ||||
\(209\) | −1.19170e6 | −1.88712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 520244. | 0.804453 | 0.402227 | − | 0.915540i | \(-0.368236\pi\) | ||||
0.402227 | + | 0.915540i | \(0.368236\pi\) | |||||||
\(212\) | 19188.0 | + | 33234.6i | 0.0293218 | + | 0.0507868i | ||||
\(213\) | −144180. | + | 249727.i | −0.217749 | + | 0.377152i | ||||
\(214\) | −386748. | + | 669867.i | −0.577289 | + | 0.999895i | ||||
\(215\) | −449436. | − | 778446.i | −0.663089 | − | 1.14850i | ||||
\(216\) | 122472. | 0.178609 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 605868. | 0.863449 | ||||||||
\(219\) | −278307. | − | 482042.i | −0.392115 | − | 0.679164i | ||||
\(220\) | 69264.0 | − | 119969.i | 0.0964830 | − | 0.167113i | ||||
\(221\) | −27846.0 | + | 48230.7i | −0.0383515 | + | 0.0664267i | ||||
\(222\) | −146718. | − | 254123.i | −0.199803 | − | 0.346068i | ||||
\(223\) | −304736. | −0.410357 | −0.205178 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205178 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 239679. | 0.315627 | ||||||||
\(226\) | 660438. | + | 1.14391e6i | 0.860124 | + | 1.48978i | ||||
\(227\) | 144294. | − | 249925.i | 0.185859 | − | 0.321917i | −0.758007 | − | 0.652247i | \(-0.773827\pi\) |
0.943866 | + | 0.330330i | \(0.107160\pi\) | |||||||
\(228\) | 48312.0 | − | 83678.8i | 0.0615486 | − | 0.106605i | ||||
\(229\) | 386095. | + | 668736.i | 0.486525 | + | 0.842687i | 0.999880 | − | 0.0154899i | \(-0.00493079\pi\) |
−0.513355 | + | 0.858177i | \(0.671597\pi\) | |||||||
\(230\) | 1.96560e6 | 2.45005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −914256. | −1.11519 | ||||||||
\(233\) | −126117. | − | 218441.i | −0.152189 | − | 0.263599i | 0.779843 | − | 0.625975i | \(-0.215299\pi\) |
−0.932032 | + | 0.362376i | \(0.881966\pi\) | |||||||
\(234\) | 107406. | − | 186033.i | 0.128230 | − | 0.222100i | ||||
\(235\) | 542880. | − | 940296.i | 0.641260 | − | 1.11069i | ||||
\(236\) | 54984.0 | + | 95235.1i | 0.0642623 | + | 0.111306i | ||||
\(237\) | −591984. | −0.684603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.45114e6 | −1.64329 | −0.821643 | − | 0.570002i | \(-0.806942\pi\) | ||||
−0.821643 | + | 0.570002i | \(0.806942\pi\) | |||||||
\(240\) | −398736. | − | 690631.i | −0.446845 | − | 0.773959i | ||||
\(241\) | −73199.0 | + | 126784.i | −0.0811825 | + | 0.140612i | −0.903758 | − | 0.428043i | \(-0.859203\pi\) |
0.822576 | + | 0.568656i | \(0.192536\pi\) | |||||||
\(242\) | 108255. | − | 187503.i | 0.118825 | − | 0.205812i | ||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −197912. | −0.212813 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 429948. | 0.452979 | ||||||||
\(247\) | 593164. | + | 1.02739e6i | 0.618632 | + | 1.07150i | ||||
\(248\) | 6720.00 | − | 11639.4i | 0.00693809 | − | 0.0120171i | ||||
\(249\) | 180846. | − | 313234.i | 0.184846 | − | 0.320163i | ||||
\(250\) | 38844.0 | + | 67279.8i | 0.0393074 | + | 0.0680824i | ||||
\(251\) | −607860. | −0.609003 | −0.304501 | − | 0.952512i | \(-0.598490\pi\) | ||||
−0.304501 | + | 0.952512i | \(0.598490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.86480e6 | 1.83160 | ||||||||
\(254\) | −222960. | − | 386178.i | −0.216842 | − | 0.375581i | ||||
\(255\) | 44226.0 | − | 76601.7i | 0.0425919 | − | 0.0737714i | ||||
\(256\) | −193664. | + | 335436.i | −0.184692 | + | 0.319897i | ||||
\(257\) | 47793.0 | + | 82779.9i | 0.0451369 | + | 0.0781794i | 0.887711 | − | 0.460401i | \(-0.152294\pi\) |
−0.842574 | + | 0.538580i | \(0.818961\pi\) | |||||||
\(258\) | 622296. | 0.582033 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −137904. | −0.126515 | ||||||||
\(261\) | 220401. | + | 381746.i | 0.200268 | + | 0.346875i | ||||
\(262\) | 465948. | − | 807046.i | 0.419357 | − | 0.726348i | ||||
\(263\) | 1.10017e6 | − | 1.90555e6i | 0.980779 | − | 1.69876i | 0.321410 | − | 0.946940i | \(-0.395843\pi\) |
0.659370 | − | 0.751819i | \(-0.270823\pi\) | |||||||
\(264\) | −335664. | − | 581387.i | −0.296411 | − | 0.513400i | ||||
\(265\) | 748332. | 0.654605 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 71766.0 | 0.0616085 | ||||||||
\(268\) | 118712. | + | 205615.i | 0.100962 | + | 0.174871i | ||||
\(269\) | 885123. | − | 1.53308e6i | 0.745801 | − | 1.29177i | −0.204019 | − | 0.978967i | \(-0.565400\pi\) |
0.949820 | − | 0.312798i | \(-0.101266\pi\) | |||||||
\(270\) | −170586. | + | 295464.i | −0.142408 | + | 0.246658i | ||||
\(271\) | −111752. | − | 193560.i | −0.0924341 | − | 0.160101i | 0.816101 | − | 0.577910i | \(-0.196131\pi\) |
−0.908535 | + | 0.417809i | \(0.862798\pi\) | |||||||
\(272\) | −143136. | −0.117308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.58548e6 | 1.27580 | ||||||||
\(275\) | −656898. | − | 1.13778e6i | −0.523801 | − | 0.907250i | ||||
\(276\) | −75600.0 | + | 130943.i | −0.0597378 | + | 0.103469i | ||||
\(277\) | 171389. | − | 296854.i | 0.134210 | − | 0.232458i | −0.791086 | − | 0.611705i | \(-0.790484\pi\) |
0.925295 | + | 0.379248i | \(0.123817\pi\) | |||||||
\(278\) | −673836. | − | 1.16712e6i | −0.522928 | − | 0.905739i | ||||
\(279\) | −6480.00 | −0.00498384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 480378. | 0.362925 | 0.181463 | − | 0.983398i | \(-0.441917\pi\) | ||||
0.181463 | + | 0.983398i | \(0.441917\pi\) | |||||||
\(282\) | 375840. | + | 650974.i | 0.281436 | + | 0.487462i | ||||
\(283\) | −14990.0 | + | 25963.4i | −0.0111259 | + | 0.0192706i | −0.871535 | − | 0.490334i | \(-0.836875\pi\) |
0.860409 | + | 0.509604i | \(0.170208\pi\) | |||||||
\(284\) | −64080.0 | + | 110990.i | −0.0471440 | + | 0.0816558i | ||||
\(285\) | −942084. | − | 1.63174e6i | −0.687033 | − | 1.18998i | ||||
\(286\) | −1.17749e6 | −0.851219 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 116640. | 0.0828641 | ||||||||
\(289\) | 701990. | + | 1.21588e6i | 0.494409 | + | 0.856342i | ||||
\(290\) | 1.27343e6 | − | 2.20564e6i | 0.889159 | − | 1.54007i | ||||
\(291\) | −646479. | + | 1.11973e6i | −0.447530 | + | 0.775144i | ||||
\(292\) | −123692. | − | 214241.i | −0.0848955 | − | 0.147043i | ||||
\(293\) | 198066. | 0.134785 | 0.0673924 | − | 0.997727i | \(-0.478532\pi\) | ||||
0.0673924 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.14438e6 | 1.43465 | ||||||||
\(296\) | 456456. | + | 790605.i | 0.302810 | + | 0.524482i | ||||
\(297\) | −161838. | + | 280312.i | −0.106461 | + | 0.184395i | ||||
\(298\) | −246222. | + | 426469.i | −0.160615 | + | 0.278193i | ||||
\(299\) | −928200. | − | 1.60769e6i | −0.600432 | − | 1.03998i | ||||
\(300\) | 106524. | 0.0683352 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.72219e6 | 1.08659 | ||||||||
\(303\) | −12177.0 | − | 21091.2i | −0.00761963 | − | 0.0131976i | ||||
\(304\) | −1.52451e6 | + | 2.64053e6i | −0.946121 | + | 1.63873i | ||||
\(305\) | −1.92964e6 | + | 3.34224e6i | −1.18776 | + | 2.05725i | ||||
\(306\) | 30618.0 | + | 53031.9i | 0.0186928 | + | 0.0323768i | ||||
\(307\) | 1.04564e6 | 0.633191 | 0.316595 | − | 0.948561i | \(-0.397460\pi\) | ||||
0.316595 | + | 0.948561i | \(0.397460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.18591e6 | −0.706572 | ||||||||
\(310\) | 18720.0 | + | 32424.0i | 0.0110637 | + | 0.0191629i | ||||
\(311\) | 918588. | − | 1.59104e6i | 0.538542 | − | 0.932783i | −0.460441 | − | 0.887691i | \(-0.652309\pi\) |
0.998983 | − | 0.0450920i | \(-0.0143581\pi\) | |||||||
\(312\) | −334152. | + | 578768.i | −0.194338 | + | 0.336603i | ||||
\(313\) | −182747. | − | 316527.i | −0.105436 | − | 0.182621i | 0.808480 | − | 0.588523i | \(-0.200291\pi\) |
−0.913916 | + | 0.405903i | \(0.866957\pi\) | |||||||
\(314\) | 779268. | 0.446029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −263104. | −0.148221 | ||||||||
\(317\) | 14169.0 | + | 24541.4i | 0.00791938 | + | 0.0137168i | 0.869958 | − | 0.493126i | \(-0.164146\pi\) |
−0.862039 | + | 0.506843i | \(0.830812\pi\) | |||||||
\(318\) | −259038. | + | 448667.i | −0.143647 | + | 0.248803i | ||||
\(319\) | 1.20812e6 | − | 2.09253e6i | 0.664714 | − | 1.15132i | ||||
\(320\) | 1.08077e6 | + | 1.87195e6i | 0.590007 | + | 1.02192i | ||||
\(321\) | −1.16024e6 | −0.628473 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −338184. | −0.180363 | ||||||||
\(324\) | −13122.0 | − | 22728.0i | −0.00694444 | − | 0.0120281i | ||||
\(325\) | −653939. | + | 1.13266e6i | −0.343423 | + | 0.594825i | ||||
\(326\) | 1.66585e6 | − | 2.88534e6i | 0.868145 | − | 1.50367i | ||||
\(327\) | 454401. | + | 787046.i | 0.235001 | + | 0.407034i | ||||
\(328\) | −1.33762e6 | −0.686510 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.87013e6 | 0.945337 | ||||||||
\(331\) | −966958. | − | 1.67482e6i | −0.485107 | − | 0.840230i | 0.514746 | − | 0.857342i | \(-0.327886\pi\) |
−0.999854 | + | 0.0171123i | \(0.994553\pi\) | |||||||
\(332\) | 80376.0 | − | 139215.i | 0.0400204 | − | 0.0693173i | ||||
\(333\) | 220077. | − | 381185.i | 0.108759 | − | 0.188376i | ||||
\(334\) | −130536. | − | 226095.i | −0.0640271 | − | 0.110898i | ||||
\(335\) | 4.62977e6 | 2.25397 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.88817e6 | −0.905664 | −0.452832 | − | 0.891596i | \(-0.649586\pi\) | ||||
−0.452832 | + | 0.891596i | \(0.649586\pi\) | |||||||
\(338\) | −527787. | − | 914154.i | −0.251285 | − | 0.435239i | ||||
\(339\) | −990657. | + | 1.71587e6i | −0.468192 | + | 0.810932i | ||||
\(340\) | 19656.0 | − | 34045.2i | 0.00922142 | − | 0.0159720i | ||||
\(341\) | 17760.0 | + | 30761.2i | 0.00827098 | + | 0.0143258i | ||||
\(342\) | 1.30442e6 | 0.603050 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.93603e6 | −0.882097 | ||||||||
\(345\) | 1.47420e6 | + | 2.55339e6i | 0.666820 | + | 1.15497i | ||||
\(346\) | 54990.0 | − | 95245.5i | 0.0246941 | − | 0.0427715i | ||||
\(347\) | −1.45969e6 | + | 2.52825e6i | −0.650782 | + | 1.12719i | 0.332151 | + | 0.943226i | \(0.392226\pi\) |
−0.982933 | + | 0.183962i | \(0.941108\pi\) | |||||||
\(348\) | 97956.0 | + | 169665.i | 0.0433594 | + | 0.0751006i | ||||
\(349\) | 780682. | 0.343092 | 0.171546 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171546 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 322218. | 0.139599 | ||||||||
\(352\) | −319680. | − | 553702.i | −0.137518 | − | 0.238188i | ||||
\(353\) | 667185. | − | 1.15560e6i | 0.284977 | − | 0.493594i | −0.687627 | − | 0.726064i | \(-0.741347\pi\) |
0.972604 | + | 0.232470i | \(0.0746808\pi\) | |||||||
\(354\) | −742284. | + | 1.28567e6i | −0.314820 | + | 0.545284i | ||||
\(355\) | 1.24956e6 | + | 2.16430e6i | 0.526243 | + | 0.911479i | ||||
\(356\) | 31896.0 | 0.0133386 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 919944. | 0.379362 | ||||||||
\(359\) | −508716. | − | 881122.i | −0.208324 | − | 0.360828i | 0.742863 | − | 0.669444i | \(-0.233468\pi\) |
−0.951187 | + | 0.308616i | \(0.900134\pi\) | |||||||
\(360\) | 530712. | − | 919220.i | 0.215825 | − | 0.373821i | ||||
\(361\) | −2.36388e6 | + | 4.09436e6i | −0.954679 | + | 1.65355i | ||||
\(362\) | 1.14620e6 | + | 1.98527e6i | 0.459715 | + | 0.796249i | ||||
\(363\) | 324765. | 0.129361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.82399e6 | −1.89528 | ||||||||
\(366\) | −1.33591e6 | − | 2.31386e6i | −0.521283 | − | 0.902888i | ||||
\(367\) | 418840. | − | 725452.i | 0.162324 | − | 0.281154i | −0.773378 | − | 0.633946i | \(-0.781434\pi\) |
0.935702 | + | 0.352792i | \(0.114768\pi\) | |||||||
\(368\) | 2.38560e6 | − | 4.13198e6i | 0.918286 | − | 1.59052i | ||||
\(369\) | 322461. | + | 558519.i | 0.123285 | + | 0.213536i | ||||
\(370\) | −2.54311e6 | −0.965742 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2880.00 | −0.00107903 | ||||||||
\(373\) | 759965. | + | 1.31630e6i | 0.282827 | + | 0.489871i | 0.972080 | − | 0.234650i | \(-0.0753943\pi\) |
−0.689253 | + | 0.724521i | \(0.742061\pi\) | |||||||
\(374\) | 167832. | − | 290694.i | 0.0620434 | − | 0.107462i | ||||
\(375\) | −58266.0 | + | 100920.i | −0.0213962 | + | 0.0370593i | ||||
\(376\) | −1.16928e6 | − | 2.02525e6i | −0.426529 | − | 0.738770i | ||||
\(377\) | −2.40536e6 | −0.871620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.64465e6 | 0.945737 | 0.472869 | − | 0.881133i | \(-0.343219\pi\) | ||||
0.472869 | + | 0.881133i | \(0.343219\pi\) | |||||||
\(380\) | −418704. | − | 725217.i | −0.148747 | − | 0.257637i | ||||
\(381\) | 334440. | − | 579267.i | 0.118034 | − | 0.204440i | ||||
\(382\) | −820224. | + | 1.42067e6i | −0.287590 | + | 0.498121i | ||||
\(383\) | 1.00668e6 | + | 1.74362e6i | 0.350667 | + | 0.607373i | 0.986366 | − | 0.164564i | \(-0.0526217\pi\) |
−0.635700 | + | 0.771936i | \(0.719288\pi\) | |||||||
\(384\) | −1.91117e6 | −0.661410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −921612. | −0.314833 | ||||||||
\(387\) | 466722. | + | 808386.i | 0.158409 | + | 0.274373i | ||||
\(388\) | −287324. | + | 497660.i | −0.0968930 | + | 0.167824i | ||||
\(389\) | 363117. | − | 628937.i | 0.121667 | − | 0.210733i | −0.798758 | − | 0.601652i | \(-0.794509\pi\) |
0.920425 | + | 0.390919i | \(0.127843\pi\) | |||||||
\(390\) | −930852. | − | 1.61228e6i | −0.309898 | − | 0.536760i | ||||
\(391\) | 529200. | 0.175056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.39784e6 | 0.456538 | ||||||||
\(394\) | 463266. | + | 802400.i | 0.150345 | + | 0.260406i | ||||
\(395\) | −2.56526e6 | + | 4.44317e6i | −0.827255 | + | 1.43285i | ||||
\(396\) | −71928.0 | + | 124583.i | −0.0230494 | + | 0.0399228i | ||||
\(397\) | 2.28789e6 | + | 3.96274e6i | 0.728549 | + | 1.26188i | 0.957496 | + | 0.288446i | \(0.0931385\pi\) |
−0.228947 | + | 0.973439i | \(0.573528\pi\) | |||||||
\(398\) | −2.20114e6 | −0.696529 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.36142e6 | −1.05045 | ||||||||
\(401\) | 16935.0 | + | 29332.3i | 0.00525926 | + | 0.00910930i | 0.868643 | − | 0.495438i | \(-0.164993\pi\) |
−0.863384 | + | 0.504548i | \(0.831659\pi\) | |||||||
\(402\) | −1.60261e6 | + | 2.77581e6i | −0.494610 | + | 0.856690i | ||||
\(403\) | 17680.0 | − | 30622.7i | 0.00542275 | − | 0.00939248i | ||||
\(404\) | −5412.00 | − | 9373.86i | −0.00164970 | − | 0.00285736i | ||||
\(405\) | −511758. | −0.155034 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.41270e6 | −0.721966 | ||||||||
\(408\) | −95256.0 | − | 164988.i | −0.0283297 | − | 0.0490685i | ||||
\(409\) | −2.93089e6 | + | 5.07645e6i | −0.866346 | + | 1.50056i | −0.000641640 | 1.00000i | \(0.500204\pi\) | |
−0.865704 | + | 0.500556i | \(0.833129\pi\) | |||||||
\(410\) | 1.86311e6 | − | 3.22700e6i | 0.547367 | − | 0.948067i | ||||
\(411\) | 1.18911e6 | + | 2.05959e6i | 0.347229 | + | 0.601419i | ||||
\(412\) | −527072. | −0.152977 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.04120e6 | −0.585308 | ||||||||
\(415\) | −1.56733e6 | − | 2.71470e6i | −0.446726 | − | 0.773751i | ||||
\(416\) | −318240. | + | 551208.i | −0.0901616 | + | 0.156164i | ||||
\(417\) | 1.01075e6 | − | 1.75068e6i | 0.284646 | − | 0.493022i | ||||
\(418\) | −3.57509e6 | − | 6.19223e6i | −1.00080 | − | 1.73343i | ||||
\(419\) | −302748. | −0.0842454 | −0.0421227 | − | 0.999112i | \(-0.513412\pi\) | ||||
−0.0421227 | + | 0.999112i | \(0.513412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.36708e6 | −1.47582 | −0.737909 | − | 0.674900i | \(-0.764187\pi\) | ||||
−0.737909 | + | 0.674900i | \(0.764187\pi\) | |||||||
\(422\) | 1.56073e6 | + | 2.70327e6i | 0.426626 | + | 0.738938i | ||||
\(423\) | −563760. | + | 976461.i | −0.153195 | + | 0.265341i | ||||
\(424\) | 805896. | − | 1.39585e6i | 0.217703 | − | 0.377073i | ||||
\(425\) | −186417. | − | 322884.i | −0.0500626 | − | 0.0867109i | ||||
\(426\) | −1.73016e6 | −0.461915 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −515664. | −0.136068 | ||||||||
\(429\) | −883116. | − | 1.52960e6i | −0.231673 | − | 0.401269i | ||||
\(430\) | 2.69662e6 | − | 4.67068e6i | 0.703312 | − | 1.21817i | ||||
\(431\) | −588528. | + | 1.01936e6i | −0.152607 | + | 0.264323i | −0.932185 | − | 0.361982i | \(-0.882100\pi\) |
0.779578 | + | 0.626305i | \(0.215433\pi\) | |||||||
\(432\) | 414072. | + | 717194.i | 0.106750 | + | 0.184896i | ||||
\(433\) | 3.66249e6 | 0.938766 | 0.469383 | − | 0.882995i | \(-0.344476\pi\) | ||||
0.469383 | + | 0.882995i | \(0.344476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.82028e6 | 0.967994 | ||||||||
\(436\) | 201956. | + | 349798.i | 0.0508792 | + | 0.0881254i | ||||
\(437\) | 5.63640e6 | − | 9.76253e6i | 1.41188 | − | 2.44545i | ||||
\(438\) | 1.66984e6 | − | 2.89225e6i | 0.415901 | − | 0.720362i | ||||
\(439\) | −1.26837e6 | − | 2.19688e6i | −0.314113 | − | 0.544059i | 0.665136 | − | 0.746722i | \(-0.268374\pi\) |
−0.979248 | + | 0.202663i | \(0.935040\pi\) | |||||||
\(440\) | −5.81818e6 | −1.43270 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −334152. | −0.0813558 | ||||||||
\(443\) | −3.00752e6 | − | 5.20917e6i | −0.728113 | − | 1.26113i | −0.957680 | − | 0.287836i | \(-0.907064\pi\) |
0.229566 | − | 0.973293i | \(-0.426269\pi\) | |||||||
\(444\) | 97812.0 | − | 169415.i | 0.0235470 | − | 0.0407845i | ||||
\(445\) | 310986. | − | 538644.i | 0.0744459 | − | 0.128944i | ||||
\(446\) | −914208. | − | 1.58345e6i | −0.217625 | − | 0.376937i | ||||
\(447\) | −738666. | −0.174856 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65965e6 | 1.32487 | 0.662436 | − | 0.749119i | \(-0.269523\pi\) | ||||
0.662436 | + | 0.749119i | \(0.269523\pi\) | |||||||
\(450\) | 719037. | + | 1.24541e6i | 0.167386 | + | 0.289922i | ||||
\(451\) | 1.76756e6 | − | 3.06151e6i | 0.409198 | − | 0.708752i | ||||
\(452\) | −440292. | + | 762608.i | −0.101367 | + | 0.175572i | ||||
\(453\) | 1.29164e6 | + | 2.23719e6i | 0.295731 | + | 0.512222i | ||||
\(454\) | 1.73153e6 | 0.394267 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.05821e6 | −0.913949 | ||||||||
\(457\) | 3.23080e6 | + | 5.59590e6i | 0.723634 | + | 1.25337i | 0.959534 | + | 0.281593i | \(0.0908629\pi\) |
−0.235900 | + | 0.971777i | \(0.575804\pi\) | |||||||
\(458\) | −2.31657e6 | + | 4.01242e6i | −0.516038 | + | 0.893804i | ||||
\(459\) | −45927.0 | + | 79547.9i | −0.0101750 | + | 0.0176237i | ||||
\(460\) | 655200. | + | 1.13484e6i | 0.144371 | + | 0.250058i | ||||
\(461\) | 3.37353e6 | 0.739320 | 0.369660 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369660 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.54974e6 | −0.986358 | −0.493179 | − | 0.869928i | \(-0.664165\pi\) | ||||
−0.493179 | + | 0.869928i | \(0.664165\pi\) | |||||||
\(464\) | −3.09106e6 | − | 5.35387e6i | −0.666518 | − | 1.15444i | ||||
\(465\) | −28080.0 | + | 48636.0i | −0.00602233 | + | 0.0104310i | ||||
\(466\) | 756702. | − | 1.31065e6i | 0.161421 | − | 0.279589i | ||||
\(467\) | 1.00568e6 | + | 1.74189e6i | 0.213386 | + | 0.369596i | 0.952772 | − | 0.303686i | \(-0.0982173\pi\) |
−0.739386 | + | 0.673282i | \(0.764884\pi\) | |||||||
\(468\) | 143208. | 0.0302240 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.51456e6 | 1.36032 | ||||||||
\(471\) | 584451. | + | 1.01230e6i | 0.121394 | + | 0.210260i | ||||
\(472\) | 2.30933e6 | − | 3.99987e6i | 0.477123 | − | 0.826402i | ||||
\(473\) | 2.55833e6 | − | 4.43115e6i | 0.525779 | − | 0.910676i | ||||
\(474\) | −1.77595e6 | − | 3.07604e6i | −0.363066 | − | 0.628848i | ||||
\(475\) | −7.94196e6 | −1.61508 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −777114. | −0.156383 | ||||||||
\(478\) | −4.35341e6 | − | 7.54032e6i | −0.871484 | − | 1.50946i | ||||
\(479\) | −3.80201e6 | + | 6.58527e6i | −0.757137 | + | 1.31140i | 0.187168 | + | 0.982328i | \(0.440069\pi\) |
−0.944305 | + | 0.329071i | \(0.893264\pi\) | |||||||
\(480\) | 505440. | − | 875448.i | 0.100131 | − | 0.173431i | ||||
\(481\) | 1.20091e6 | + | 2.08004e6i | 0.236673 | + | 0.409930i | ||||
\(482\) | −878388. | −0.172214 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 144340. | 0.0280074 | ||||||||
\(485\) | 5.60282e6 | + | 9.70437e6i | 1.08156 | + | 1.87332i | ||||
\(486\) | 177147. | − | 306828.i | 0.0340207 | − | 0.0589256i | ||||
\(487\) | −336556. | + | 582932.i | −0.0643035 | + | 0.111377i | −0.896385 | − | 0.443277i | \(-0.853816\pi\) |
0.832081 | + | 0.554654i | \(0.187149\pi\) | |||||||
\(488\) | 4.15615e6 | + | 7.19867e6i | 0.790027 | + | 1.36837i | ||||
\(489\) | 4.99756e6 | 0.945117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.47170e6 | −0.462692 | −0.231346 | − | 0.972872i | \(-0.574313\pi\) | ||||
−0.231346 | + | 0.972872i | \(0.574313\pi\) | |||||||
\(492\) | 143316. | + | 248231.i | 0.0266920 | + | 0.0462320i | ||||
\(493\) | 342846. | − | 593827.i | 0.0635304 | − | 0.110038i | ||||
\(494\) | −3.55898e6 | + | 6.16434e6i | −0.656158 | + | 1.13650i | ||||
\(495\) | 1.40260e6 | + | 2.42937e6i | 0.257288 | + | 0.445636i | ||||
\(496\) | 90880.0 | 0.0165869 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.17015e6 | 0.392118 | ||||||||
\(499\) | −3.04076e6 | − | 5.26675e6i | −0.546677 | − | 0.946873i | −0.998499 | − | 0.0547648i | \(-0.982559\pi\) |
0.451822 | − | 0.892108i | \(-0.350774\pi\) | |||||||
\(500\) | −25896.0 | + | 44853.2i | −0.00463242 | + | 0.00802358i | ||||
\(501\) | 195804. | − | 339142.i | 0.0348520 | − | 0.0603654i | ||||
\(502\) | −1.82358e6 | − | 3.15853e6i | −0.322972 | − | 0.559405i | ||||
\(503\) | 846216. | 0.149129 | 0.0745644 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745644 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −211068. | −0.0368293 | ||||||||
\(506\) | 5.59440e6 | + | 9.68979e6i | 0.971353 | + | 1.68243i | ||||
\(507\) | 791680. | − | 1.37123e6i | 0.136782 | − | 0.236914i | ||||
\(508\) | 148640. | − | 257452.i | 0.0255550 | − | 0.0442626i | ||||
\(509\) | −3.83392e6 | − | 6.64055e6i | −0.655917 | − | 1.13608i | −0.981663 | − | 0.190625i | \(-0.938949\pi\) |
0.325746 | − | 0.945457i | \(-0.394385\pi\) | |||||||
\(510\) | 530712. | 0.0903511 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.47130e6 | 0.753804 | ||||||||
\(513\) | 978318. | + | 1.69450e6i | 0.164129 | + | 0.284281i | ||||
\(514\) | −286758. | + | 496679.i | −0.0478749 | + | 0.0829217i | ||||
\(515\) | −5.13895e6 | + | 8.90093e6i | −0.853801 | + | 1.47883i | ||||
\(516\) | 207432. | + | 359283.i | 0.0342966 | + | 0.0594035i | ||||
\(517\) | 6.18048e6 | 1.01694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 164970. | 0.0268835 | ||||||||
\(520\) | 2.89598e6 | + | 5.01599e6i | 0.469665 | + | 0.813483i | ||||
\(521\) | −4.84469e6 | + | 8.39125e6i | −0.781937 | + | 1.35435i | 0.148875 | + | 0.988856i | \(0.452435\pi\) |
−0.930812 | + | 0.365499i | \(0.880898\pi\) | |||||||
\(522\) | −1.32241e6 | + | 2.29047e6i | −0.212417 | + | 0.367916i | ||||
\(523\) | −3.75839e6 | − | 6.50972e6i | −0.600824 | − | 1.04066i | −0.992696 | − | 0.120639i | \(-0.961506\pi\) |
0.391872 | − | 0.920020i | \(-0.371828\pi\) | |||||||
\(524\) | 621264. | 0.0988435 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.32021e7 | 2.08055 | ||||||||
\(527\) | 5040.00 | + | 8729.54i | 0.000790504 | + | 0.00136919i | ||||
\(528\) | 2.26973e6 | − | 3.93128e6i | 0.354315 | − | 0.613691i | ||||
\(529\) | −5.60183e6 | + | 9.70265e6i | −0.870343 | + | 1.50748i | ||||
\(530\) | 2.24500e6 | + | 3.88845e6i | 0.347157 | + | 0.601294i | ||||
\(531\) | −2.22685e6 | −0.342732 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.51920e6 | −0.536570 | ||||||||
\(534\) | 215298. | + | 372907.i | 0.0326728 | + | 0.0565910i | ||||
\(535\) | −5.02772e6 | + | 8.70827e6i | −0.759429 | + | 1.31537i | ||||
\(536\) | 4.98590e6 | − | 8.63584e6i | 0.749604 | − | 1.29835i | ||||
\(537\) | 689958. | + | 1.19504e6i | 0.103249 | + | 0.178833i | ||||
\(538\) | 1.06215e7 | 1.58208 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −227448. | −0.0335659 | ||||||||
\(541\) | −3.67162e6 | − | 6.35944e6i | −0.539343 | − | 0.934169i | −0.998940 | − | 0.0460415i | \(-0.985339\pi\) |
0.459597 | − | 0.888128i | \(-0.347994\pi\) | |||||||
\(542\) | 670512. | − | 1.16136e6i | 0.0980411 | − | 0.169812i | ||||
\(543\) | −1.71930e6 | + | 2.97791e6i | −0.250237 | + | 0.433423i | ||||
\(544\) | −90720.0 | − | 157132.i | −0.0131433 | − | 0.0227649i | ||||
\(545\) | 7.87628e6 | 1.13587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.18296e6 | 0.311945 | 0.155973 | − | 0.987761i | \(-0.450149\pi\) | ||||
0.155973 | + | 0.987761i | \(0.450149\pi\) | |||||||
\(548\) | 528492. | + | 915375.i | 0.0751774 | + | 0.130211i | ||||
\(549\) | 2.00386e6 | − | 3.47079e6i | 0.283750 | − | 0.491470i | ||||
\(550\) | 3.94139e6 | − | 6.82668e6i | 0.555575 | − | 0.962284i | ||||
\(551\) | −7.30316e6 | − | 1.26495e7i | −1.02478 | − | 1.77498i | ||||
\(552\) | 6.35040e6 | 0.887061 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.05667e6 | 0.284702 | ||||||||
\(555\) | −1.90733e6 | − | 3.30360e6i | −0.262842 | − | 0.455255i | ||||
\(556\) | 449224. | − | 778079.i | 0.0616277 | − | 0.106742i | ||||
\(557\) | −6.27328e6 | + | 1.08656e7i | −0.856755 | + | 1.48394i | 0.0182524 | + | 0.999833i | \(0.494190\pi\) |
−0.875007 | + | 0.484110i | \(0.839144\pi\) | |||||||
\(558\) | −19440.0 | − | 33671.1i | −0.00264308 | − | 0.00457795i | ||||
\(559\) | −5.09361e6 | −0.689439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 503496. | 0.0675443 | ||||||||
\(562\) | 1.44113e6 | + | 2.49612e6i | 0.192470 | + | 0.333368i | ||||
\(563\) | 2.57986e6 | − | 4.46845e6i | 0.343025 | − | 0.594136i | −0.641968 | − | 0.766731i | \(-0.721882\pi\) |
0.984993 | + | 0.172595i | \(0.0552152\pi\) | |||||||
\(564\) | −250560. | + | 433983.i | −0.0331676 | + | 0.0574480i | ||||
\(565\) | 8.58569e6 | + | 1.48709e7i | 1.13150 | + | 1.95981i | ||||
\(566\) | −179880. | −0.0236016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.38272e6 | 0.700053 | ||||||||
\(569\) | −5.87260e6 | − | 1.01717e7i | −0.760414 | − | 1.31708i | −0.942637 | − | 0.333819i | \(-0.891663\pi\) |
0.182223 | − | 0.983257i | \(-0.441671\pi\) | |||||||
\(570\) | 5.65250e6 | − | 9.79042e6i | 0.728708 | − | 1.26216i | ||||
\(571\) | 3.77364e6 | − | 6.53614e6i | 0.484362 | − | 0.838940i | −0.515476 | − | 0.856904i | \(-0.672385\pi\) |
0.999839 | + | 0.0179636i | \(0.00571829\pi\) | |||||||
\(572\) | −392496. | − | 679823.i | −0.0501586 | − | 0.0868772i | ||||
\(573\) | −2.46067e6 | −0.313089 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.24278e7 | 1.56756 | ||||||||
\(576\) | −1.12234e6 | − | 1.94394e6i | −0.140951 | − | 0.244133i | ||||
\(577\) | 4.64242e6 | − | 8.04090e6i | 0.580503 | − | 1.00546i | −0.414916 | − | 0.909859i | \(-0.636189\pi\) |
0.995420 | − | 0.0956015i | \(-0.0304775\pi\) | |||||||
\(578\) | −4.21194e6 | + | 7.29530e6i | −0.524400 | + | 0.908288i | ||||
\(579\) | −691209. | − | 1.19721e6i | −0.0856866 | − | 0.148414i | ||||
\(580\) | 1.69790e6 | 0.209577 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.75775e6 | −0.949354 | ||||||||
\(583\) | 2.12987e6 | + | 3.68904e6i | 0.259526 | + | 0.449513i | ||||
\(584\) | −5.19506e6 | + | 8.99811e6i | −0.630317 | + | 1.09174i | ||||
\(585\) | 1.39628e6 | − | 2.41842e6i | 0.168687 | − | 0.292175i | ||||
\(586\) | 594198. | + | 1.02918e6i | 0.0714804 | + | 0.123808i | ||||
\(587\) | −1.47623e6 | −0.176831 | −0.0884155 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884155 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 214720. | 0.0255026 | ||||||||
\(590\) | 6.43313e6 | + | 1.11425e7i | 0.760838 | + | 1.31781i | ||||
\(591\) | −694899. | + | 1.20360e6i | −0.0818376 | + | 0.141747i | ||||
\(592\) | −3.08651e6 | + | 5.34600e6i | −0.361963 | + | 0.626938i | ||||
\(593\) | −6.20034e6 | − | 1.07393e7i | −0.724067 | − | 1.25412i | −0.959357 | − | 0.282196i | \(-0.908937\pi\) |
0.235289 | − | 0.971925i | \(-0.424396\pi\) | |||||||
\(594\) | −1.94206e6 | −0.225837 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −328296. | −0.0378573 | ||||||||
\(597\) | −1.65085e6 | − | 2.85936e6i | −0.189571 | − | 0.328347i | ||||
\(598\) | 5.56920e6 | − | 9.64614e6i | 0.636854 | − | 1.10306i | ||||
\(599\) | 1.84564e6 | − | 3.19674e6i | 0.210174 | − | 0.364032i | −0.741595 | − | 0.670848i | \(-0.765930\pi\) |
0.951769 | + | 0.306816i | \(0.0992636\pi\) | |||||||
\(600\) | −2.23700e6 | − | 3.87460e6i | −0.253681 | − | 0.439389i | ||||
\(601\) | −9.12223e6 | −1.03018 | −0.515092 | − | 0.857135i | \(-0.672242\pi\) | ||||
−0.515092 | + | 0.857135i | \(0.672242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.80784e6 | −0.538464 | ||||||||
\(604\) | 574064. | + | 994308.i | 0.0640277 | + | 0.110899i | ||||
\(605\) | 1.40732e6 | − | 2.43754e6i | 0.156316 | − | 0.270747i | ||||
\(606\) | 73062.0 | − | 126547.i | 0.00808184 | − | 0.0139981i | ||||
\(607\) | −2.83957e6 | − | 4.91828e6i | −0.312810 | − | 0.541803i | 0.666160 | − | 0.745809i | \(-0.267937\pi\) |
−0.978970 | + | 0.204007i | \(0.934604\pi\) | |||||||
\(608\) | −3.86496e6 | −0.424020 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.31557e7 | −2.51961 | ||||||||
\(611\) | −3.07632e6 | − | 5.32834e6i | −0.333372 | − | 0.577416i | ||||
\(612\) | −20412.0 | + | 35354.6i | −0.00220296 | + | 0.00381564i | ||||
\(613\) | 7.00529e6 | − | 1.21335e7i | 0.752966 | − | 1.30417i | −0.193414 | − | 0.981117i | \(-0.561956\pi\) |
0.946379 | − | 0.323057i | \(-0.104711\pi\) | |||||||
\(614\) | 3.13691e6 | + | 5.43328e6i | 0.335800 | + | 0.581623i | ||||
\(615\) | 5.58932e6 | 0.595897 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −253686. | −0.0268277 | −0.0134139 | − | 0.999910i | \(-0.504270\pi\) | ||||
−0.0134139 | + | 0.999910i | \(0.504270\pi\) | |||||||
\(618\) | −3.55774e6 | − | 6.16218e6i | −0.374716 | − | 0.649028i | ||||
\(619\) | 2.15017e6 | − | 3.72420e6i | 0.225552 | − | 0.390667i | −0.730933 | − | 0.682449i | \(-0.760915\pi\) |
0.956485 | + | 0.291782i | \(0.0942482\pi\) | |||||||
\(620\) | −12480.0 | + | 21616.0i | −0.00130387 | + | 0.00225837i | ||||
\(621\) | −1.53090e6 | − | 2.65160e6i | −0.159301 | − | 0.275917i | ||||
\(622\) | 1.10231e7 | 1.14242 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.51901e6 | −0.464603 | ||||||||
\(625\) | 5.12841e6 | + | 8.88267e6i | 0.525149 | + | 0.909585i | ||||
\(626\) | 1.09648e6 | − | 1.89916e6i | 0.111832 | − | 0.193699i | ||||
\(627\) | 5.36263e6 | − | 9.28835e6i | 0.544765 | − | 0.943561i | ||||
\(628\) | 259756. | + | 449911.i | 0.0262825 | + | 0.0455226i | ||||
\(629\) | −684684. | −0.0690023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.04150e7 | 1.04132 | 0.520662 | − | 0.853763i | \(-0.325685\pi\) | ||||
0.520662 | + | 0.853763i | \(0.325685\pi\) | |||||||
\(632\) | 5.52518e6 | + | 9.56990e6i | 0.550242 | + | 0.953048i | ||||
\(633\) | −2.34110e6 | + | 4.05490e6i | −0.232226 | + | 0.402227i | ||||
\(634\) | −85014.0 | + | 147249.i | −0.00839977 | + | 0.0145488i | ||||
\(635\) | −2.89848e6 | − | 5.02031e6i | −0.285257 | − | 0.494079i | ||||
\(636\) | −345384. | −0.0338579 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.44975e7 | 1.41007 | ||||||||
\(639\) | −1.29762e6 | − | 2.24754e6i | −0.125717 | − | 0.217749i | ||||
\(640\) | −8.28173e6 | + | 1.43444e7i | −0.799229 | + | 1.38430i | ||||
\(641\) | −2.26357e6 | + | 3.92062e6i | −0.217595 | + | 0.376885i | −0.954072 | − | 0.299577i | \(-0.903154\pi\) |
0.736477 | + | 0.676462i | \(0.236488\pi\) | |||||||
\(642\) | −3.48073e6 | − | 6.02880e6i | −0.333298 | − | 0.577289i | ||||
\(643\) | −1.49687e7 | −1.42776 | −0.713882 | − | 0.700266i | \(-0.753065\pi\) | ||||
−0.713882 | + | 0.700266i | \(0.753065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.08985e6 | 0.765669 | ||||||||
\(646\) | −1.01455e6 | − | 1.75726e6i | −0.0956518 | − | 0.165674i | ||||
\(647\) | −8.65098e6 | + | 1.49839e7i | −0.812465 | + | 1.40723i | 0.0986691 | + | 0.995120i | \(0.468541\pi\) |
−0.911134 | + | 0.412110i | \(0.864792\pi\) | |||||||
\(648\) | −551124. | + | 954575.i | −0.0515599 | + | 0.0893043i | ||||
\(649\) | 6.10322e6 | + | 1.05711e7i | 0.568784 | + | 0.985163i | ||||
\(650\) | −7.84727e6 | −0.728509 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.22114e6 | 0.204624 | ||||||||
\(653\) | −2.03735e6 | − | 3.52880e6i | −0.186975 | − | 0.323850i | 0.757265 | − | 0.653107i | \(-0.226535\pi\) |
−0.944240 | + | 0.329258i | \(0.893202\pi\) | |||||||
\(654\) | −2.72641e6 | + | 4.72227e6i | −0.249256 | + | 0.431725i | ||||
\(655\) | 6.05732e6 | − | 1.04916e7i | 0.551668 | − | 0.955516i | ||||
\(656\) | −4.52242e6 | − | 7.83305e6i | −0.410309 | − | 0.710676i | ||||
\(657\) | 5.00953e6 | 0.452776 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.79475e6 | −0.340384 | −0.170192 | − | 0.985411i | \(-0.554439\pi\) | ||||
−0.170192 | + | 0.985411i | \(0.554439\pi\) | |||||||
\(660\) | 623376. | + | 1.07972e6i | 0.0557045 | + | 0.0964830i | ||||
\(661\) | 8.21307e6 | − | 1.42255e7i | 0.731142 | − | 1.26638i | −0.225253 | − | 0.974300i | \(-0.572321\pi\) |
0.956395 | − | 0.292075i | \(-0.0943458\pi\) | |||||||
\(662\) | 5.80175e6 | − | 1.00489e7i | 0.514534 | − | 0.891199i | ||||
\(663\) | −250614. | − | 434076.i | −0.0221422 | − | 0.0383515i | ||||
\(664\) | −6.75158e6 | −0.594272 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.64092e6 | 0.230712 | ||||||||
\(667\) | 1.14282e7 | + | 1.97942e7i | 0.994634 | + | 1.72276i | ||||
\(668\) | 87024.0 | − | 150730.i | 0.00754567 | − | 0.0130695i | ||||
\(669\) | 1.37131e6 | − | 2.37518e6i | 0.118460 | − | 0.205178i | ||||
\(670\) | 1.38893e7 | + | 2.40570e7i | 1.19535 | + | 2.07040i | ||||
\(671\) | −2.19682e7 | −1.88360 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.50675e6 | 0.468660 | 0.234330 | − | 0.972157i | \(-0.424710\pi\) | ||||
0.234330 | + | 0.972157i | \(0.424710\pi\) | |||||||
\(674\) | −5.66452e6 | − | 9.81124e6i | −0.480301 | − | 0.831906i | ||||
\(675\) | −1.07856e6 | + | 1.86811e6i | −0.0911136 | + | 0.157813i | ||||
\(676\) | 351858. | − | 609436.i | 0.0296142 | − | 0.0512934i | ||||
\(677\) | 9.19787e6 | + | 1.59312e7i | 0.771286 | + | 1.33591i | 0.936858 | + | 0.349709i | \(0.113720\pi\) |
−0.165572 | + | 0.986198i | \(0.552947\pi\) | |||||||
\(678\) | −1.18879e7 | −0.993185 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.65110e6 | −0.136931 | ||||||||
\(681\) | 1.29865e6 | + | 2.24932e6i | 0.107306 | + | 0.185859i | ||||
\(682\) | −106560. | + | 184567.i | −0.00877270 | + | 0.0151948i | ||||
\(683\) | −879174. | + | 1.52277e6i | −0.0721146 | + | 0.124906i | −0.899828 | − | 0.436245i | \(-0.856308\pi\) |
0.827713 | + | 0.561151i | \(0.189641\pi\) | |||||||
\(684\) | 434808. | + | 753110.i | 0.0355351 | + | 0.0615486i | ||||
\(685\) | 2.06112e7 | 1.67833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.94971e6 | −0.561791 | ||||||||
\(688\) | −6.54563e6 | − | 1.13374e7i | −0.527206 | − | 0.913148i | ||||
\(689\) | 2.12027e6 | − | 3.67242e6i | 0.170155 | − | 0.294717i | ||||
\(690\) | −8.84520e6 | + | 1.53203e7i | −0.707270 | + | 1.22503i | ||||
\(691\) | −2.68157e6 | − | 4.64462e6i | −0.213646 | − | 0.370045i | 0.739207 | − | 0.673478i | \(-0.235200\pi\) |
−0.952853 | + | 0.303433i | \(0.901867\pi\) | |||||||
\(692\) | 73320.0 | 0.00582046 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.75162e7 | −1.38052 | ||||||||
\(695\) | −8.75987e6 | − | 1.51725e7i | −0.687916 | − | 1.19151i | ||||
\(696\) | 4.11415e6 | − | 7.12592e6i | 0.321927 | − | 0.557594i | ||||
\(697\) | 501606. | − | 868807.i | 0.0391094 | − | 0.0677394i | ||||
\(698\) | 2.34205e6 | + | 4.05654e6i | 0.181952 | + | 0.315150i | ||||
\(699\) | 2.27011e6 | 0.175733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.12606e7 | −1.63411 | −0.817054 | − | 0.576561i | \(-0.804394\pi\) | ||||
−0.817054 | + | 0.576561i | \(0.804394\pi\) | |||||||
\(702\) | 966654. | + | 1.67429e6i | 0.0740335 | + | 0.128230i | ||||
\(703\) | −7.29243e6 | + | 1.26309e7i | −0.556524 | + | 0.963928i | ||||
\(704\) | −6.15206e6 | + | 1.06557e7i | −0.467831 | + | 0.810307i | ||||
\(705\) | 4.88592e6 | + | 8.46266e6i | 0.370232 | + | 0.641260i | ||||
\(706\) | 8.00622e6 | 0.604527 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −989712. | −0.0742037 | ||||||||
\(709\) | −1.03864e6 | − | 1.79898e6i | −0.0775980 | − | 0.134404i | 0.824615 | − | 0.565694i | \(-0.191392\pi\) |
−0.902213 | + | 0.431290i | \(0.858058\pi\) | |||||||
\(710\) | −7.49736e6 | + | 1.29858e7i | −0.558165 | + | 0.966770i | ||||
\(711\) | 2.66393e6 | − | 4.61406e6i | 0.197628 | − | 0.342302i | ||||
\(712\) | −669816. | − | 1.16016e6i | −0.0495171 | − | 0.0857662i | ||||
\(713\) | −336000. | −0.0247523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.53073e7 | −1.11979 | ||||||||
\(716\) | 306648. | + | 531130.i | 0.0223541 | + | 0.0387185i | ||||
\(717\) | 6.53011e6 | − | 1.13105e7i | 0.474376 | − | 0.821643i | ||||
\(718\) | 3.05230e6 | − | 5.28673e6i | 0.220961 | − | 0.382716i | ||||
\(719\) | 2.11810e6 | + | 3.66865e6i | 0.152800 | + | 0.264657i | 0.932256 | − | 0.361800i | \(-0.117838\pi\) |
−0.779456 | + | 0.626457i | \(0.784504\pi\) | |||||||
\(720\) | 7.17725e6 | 0.515973 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.83665e7 | −2.02518 | ||||||||
\(723\) | −658791. | − | 1.14106e6i | −0.0468708 | − | 0.0811825i | ||||
\(724\) | −764132. | + | 1.32352e6i | −0.0541779 | + | 0.0938388i | ||||
\(725\) | 8.05144e6 | − | 1.39455e7i | 0.568890 | − | 0.985347i | ||||
\(726\) | 974295. | + | 1.68753e6i | 0.0686039 | + | 0.118825i | ||||
\(727\) | −2.14524e7 | −1.50536 | −0.752678 | − | 0.658389i | \(-0.771238\pi\) | ||||
−0.752678 | + | 0.658389i | \(0.771238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.44720e7 | − | 2.50662e7i | −1.00513 | − | 1.74093i | ||||
\(731\) | 726012. | − | 1.25749e6i | 0.0502517 | − | 0.0870384i | ||||
\(732\) | 890604. | − | 1.54257e6i | 0.0614337 | − | 0.106406i | ||||
\(733\) | −7.44459e6 | − | 1.28944e7i | −0.511777 | − | 0.886424i | −0.999907 | − | 0.0136528i | \(-0.995654\pi\) |
0.488130 | − | 0.872771i | \(-0.337679\pi\) | |||||||
\(734\) | 5.02608e6 | 0.344341 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.04800e6 | 0.411545 | ||||||||
\(737\) | 1.31770e7 | + | 2.28233e7i | 0.893612 | + | 1.54778i | ||||
\(738\) | −1.93477e6 | + | 3.35111e6i | −0.130764 | + | 0.226490i | ||||
\(739\) | −3.49662e6 | + | 6.05632e6i | −0.235525 | + | 0.407941i | −0.959425 | − | 0.281963i | \(-0.909014\pi\) |
0.723900 | + | 0.689905i | \(0.242348\pi\) | |||||||
\(740\) | −847704. | − | 1.46827e6i | −0.0569069 | − | 0.0985656i | ||||
\(741\) | −1.06770e7 | −0.714335 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.90428e6 | 0.126549 | 0.0632745 | − | 0.997996i | \(-0.479846\pi\) | ||||
0.0632745 | + | 0.997996i | \(0.479846\pi\) | |||||||
\(744\) | 60480.0 | + | 104754.i | 0.00400571 | + | 0.00693809i | ||||
\(745\) | −3.20089e6 | + | 5.54410e6i | −0.211290 | + | 0.365966i | ||||
\(746\) | −4.55979e6 | + | 7.89779e6i | −0.299984 | + | 0.519587i | ||||
\(747\) | 1.62761e6 | + | 2.81911e6i | 0.106721 | + | 0.184846i | ||||
\(748\) | 223776. | 0.0146238 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −699192. | −0.0453882 | ||||||||
\(751\) | −9.76806e6 | − | 1.69188e7i | −0.631988 | − | 1.09463i | −0.987145 | − | 0.159828i | \(-0.948906\pi\) |
0.355157 | − | 0.934807i | \(-0.384427\pi\) | |||||||
\(752\) | 7.90656e6 | − | 1.36946e7i | 0.509851 | − | 0.883087i | ||||
\(753\) | 2.73537e6 | − | 4.73780e6i | 0.175804 | − | 0.304501i | ||||
\(754\) | −7.21609e6 | − | 1.24986e7i | −0.462247 | − | 0.800635i | ||||
\(755\) | 2.23885e7 | 1.42941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.25183e6 | 0.0793973 | 0.0396986 | − | 0.999212i | \(-0.487360\pi\) | ||||
0.0396986 | + | 0.999212i | \(0.487360\pi\) | |||||||
\(758\) | 7.93396e6 | + | 1.37420e7i | 0.501553 | + | 0.868715i | ||||
\(759\) | −8.39160e6 | + | 1.45347e7i | −0.528738 | + | 0.915801i | ||||
\(760\) | −1.75856e7 | + | 3.04591e7i | −1.10439 | + | 1.91286i | ||||
\(761\) | 1.02236e7 | + | 1.77078e7i | 0.639944 | + | 1.10841i | 0.985445 | + | 0.169997i | \(0.0543757\pi\) |
−0.345501 | + | 0.938418i | \(0.612291\pi\) | |||||||
\(762\) | 4.01328e6 | 0.250387 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.09363e6 | −0.0677857 | ||||||||
\(765\) | 398034. | + | 689415.i | 0.0245905 | + | 0.0425919i | ||||
\(766\) | −6.04008e6 | + | 1.04617e7i | −0.371938 | + | 0.644216i | ||||
\(767\) | 6.07573e6 | − | 1.05235e7i | 0.372915 | − | 0.645908i | ||||
\(768\) | −1.74298e6 | − | 3.01892e6i | −0.106632 | − | 0.184692i | ||||
\(769\) | −2.21064e6 | −0.134804 | −0.0674020 | − | 0.997726i | \(-0.521471\pi\) | ||||
−0.0674020 | + | 0.997726i | \(0.521471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −860274. | −0.0521196 | ||||||||
\(772\) | −307204. | − | 532093.i | −0.0185517 | − | 0.0321325i | ||||
\(773\) | 6.45753e6 | − | 1.11848e7i | 0.388703 | − | 0.673253i | −0.603573 | − | 0.797308i | \(-0.706257\pi\) |
0.992275 | + | 0.124055i | \(0.0395900\pi\) | |||||||
\(774\) | −2.80033e6 | + | 4.85032e6i | −0.168019 | + | 0.291017i | ||||
\(775\) | 118360. | + | 205006.i | 0.00707865 | + | 0.0122606i | ||||
\(776\) | 2.41352e7 | 1.43879 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.35740e6 | 0.258095 | ||||||||
\(779\) | −1.06850e7 | − | 1.85070e7i | −0.630857 | − | 1.09268i | ||||
\(780\) | 620568. | − | 1.07486e6i | 0.0365219 | − | 0.0632577i | ||||
\(781\) | −7.11288e6 | + | 1.23199e7i | −0.417271 | + | 0.722734i | ||||
\(782\) | 1.58760e6 | + | 2.74980e6i | 0.0928377 | + | 0.160800i | ||||
\(783\) | −3.96722e6 | −0.231250 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.01305e7 | 0.586754 | ||||||||
\(786\) | 4.19353e6 | + | 7.26341e6i | 0.242116 | + | 0.419357i | ||||
\(787\) | −6.77496e6 | + | 1.17346e7i | −0.389915 | + | 0.675353i | −0.992438 | − | 0.122749i | \(-0.960829\pi\) |
0.602523 | + | 0.798102i | \(0.294162\pi\) | |||||||
\(788\) | −308844. | + | 534933.i | −0.0177184 | + | 0.0306891i | ||||
\(789\) | 9.90155e6 | + | 1.71500e7i | 0.566253 | + | 0.980779i | ||||
\(790\) | −3.07832e7 | −1.75487 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.04195e6 | 0.342266 | ||||||||
\(793\) | 1.09346e7 | + | 1.89393e7i | 0.617478 | + | 1.06950i | ||||
\(794\) | −1.37273e7 | + | 2.37765e7i | −0.772743 | + | 1.33843i | ||||
\(795\) | −3.36749e6 | + | 5.83267e6i | −0.188968 | + | 0.327303i | ||||
\(796\) | −733712. | − | 1.27083e6i | −0.0410434 | − | 0.0710892i | ||||
\(797\) | 2.45956e7 | 1.37155 | 0.685776 | − | 0.727813i | \(-0.259463\pi\) | ||||
0.685776 | + | 0.727813i | \(0.259463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.75392e6 | 0.0971948 | ||||||||
\(800\) | −2.13048e6 | − | 3.69010e6i | −0.117694 | − | 0.203851i | ||||
\(801\) | −322947. | + | 559361.i | −0.0177848 | + | 0.0308042i | ||||
\(802\) | −101610. | + | 175994.i | −0.00557828 | + | 0.00966187i | ||||
\(803\) | −1.37298e7 | − | 2.37807e7i | −0.751408 | − | 1.30148i | ||||
\(804\) | −2.13682e6 | −0.116581 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 212160. | 0.0115034 | ||||||||
\(807\) | 7.96611e6 | + | 1.37977e7i | 0.430588 | + | 0.745801i | ||||
\(808\) | −227304. | + | 393702.i | −0.0122484 | + | 0.0212148i | ||||
\(809\) | −7.76186e6 | + | 1.34439e7i | −0.416960 | + | 0.722196i | −0.995632 | − | 0.0933643i | \(-0.970238\pi\) |
0.578672 | + | 0.815560i | \(0.303571\pi\) | |||||||
\(810\) | −1.53527e6 | − | 2.65917e6i | −0.0822192 | − | 0.142408i | ||||
\(811\) | 2.66262e7 | 1.42153 | 0.710766 | − | 0.703429i | \(-0.248349\pi\) | ||||
0.710766 | + | 0.703429i | \(0.248349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.01154e6 | 0.106734 | ||||||||
\(814\) | −7.23809e6 | − | 1.25367e7i | −0.382880 | − | 0.663168i | ||||
\(815\) | 2.16561e7 | − | 3.75094e7i | 1.14205 | − | 1.97809i | ||||
\(816\) | 644112. | − | 1.11563e6i | 0.0338638 | − | 0.0586539i | ||||
\(817\) | −1.54652e7 | − | 2.67865e7i | −0.810589 | − | 1.40398i | ||||
\(818\) | −3.51707e7 | −1.83780 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.48414e6 | 0.129016 | ||||||||
\(821\) | 6.19454e6 | + | 1.07293e7i | 0.320739 | + | 0.555536i | 0.980641 | − | 0.195816i | \(-0.0627356\pi\) |
−0.659902 | + | 0.751352i | \(0.729402\pi\) | |||||||
\(822\) | −7.13464e6 | + | 1.23576e7i | −0.368292 | + | 0.637901i | ||||
\(823\) | 1.82815e6 | − | 3.16645e6i | 0.0940831 | − | 0.162957i | −0.815142 | − | 0.579261i | \(-0.803341\pi\) |
0.909226 | + | 0.416304i | \(0.136675\pi\) | |||||||
\(824\) | 1.10685e7 | + | 1.91712e7i | 0.567899 | + | 0.983630i | ||||
\(825\) | 1.18242e7 | 0.604833 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.80463e7 | 1.42597 | 0.712987 | − | 0.701178i | \(-0.247342\pi\) | ||||
0.712987 | + | 0.701178i | \(0.247342\pi\) | |||||||
\(828\) | −680400. | − | 1.17849e6i | −0.0344896 | − | 0.0597378i | ||||
\(829\) | 1.05577e7 | − | 1.82864e7i | 0.533558 | − | 0.924150i | −0.465674 | − | 0.884957i | \(-0.654188\pi\) |
0.999232 | − | 0.0391930i | \(-0.0124787\pi\) | |||||||
\(830\) | 9.40399e6 | − | 1.62882e7i | 0.473824 | − | 0.820687i | ||||
\(831\) | 1.54250e6 | + | 2.67169e6i | 0.0774859 | + | 0.134210i | ||||
\(832\) | 1.22487e7 | 0.613454 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.21290e7 | 0.603826 | ||||||||
\(835\) | −1.69697e6 | − | 2.93923e6i | −0.0842282 | − | 0.145888i | ||||
\(836\) | 2.38339e6 | − | 4.12816e6i | 0.117945 | − | 0.204287i | ||||
\(837\) | 29160.0 | − | 50506.6i | 0.00143871 | − | 0.00249192i | ||||
\(838\) | −908244. | − | 1.57312e6i | −0.0446779 | − | 0.0773843i | ||||
\(839\) | −1.33947e7 | −0.656944 | −0.328472 | − | 0.944514i | \(-0.606534\pi\) | ||||
−0.328472 | + | 0.944514i | \(0.606534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.10422e6 | 0.443867 | ||||||||
\(842\) | −1.61012e7 | − | 2.78882e7i | −0.782671 | − | 1.35563i | ||||
\(843\) | −2.16170e6 | + | 3.74418e6i | −0.104768 | + | 0.181463i | ||||
\(844\) | −1.04049e6 | + | 1.80218e6i | −0.0502783 | + | 0.0870846i | ||||
\(845\) | −6.86123e6 | − | 1.18840e7i | −0.330568 | − | 0.572560i | ||||
\(846\) | −6.76512e6 | −0.324975 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.08988e7 | 0.520461 | ||||||||
\(849\) | −134910. | − | 233671.i | −0.00642355 | − | 0.0111259i | ||||
\(850\) | 1.11850e6 | − | 1.93730e6i | 0.0530994 | − | 0.0919708i | ||||
\(851\) | 1.14114e7 | − | 1.97651e7i | 0.540151 | − | 0.935569i | ||||
\(852\) | −576720. | − | 998908.i | −0.0272186 | − | 0.0471440i | ||||
\(853\) | −3.01513e7 | −1.41884 | −0.709420 | − | 0.704786i | \(-0.751043\pi\) | ||||
−0.709420 | + | 0.704786i | \(0.751043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.69575e7 | 0.793317 | ||||||||
\(856\) | 1.08289e7 | + | 1.87563e7i | 0.505128 | + | 0.874908i | ||||
\(857\) | 1.19947e7 | − | 2.07754e7i | 0.557875 | − | 0.966268i | −0.439798 | − | 0.898097i | \(-0.644950\pi\) |
0.997674 | − | 0.0681717i | \(-0.0217166\pi\) | |||||||
\(858\) | 5.29870e6 | − | 9.17761e6i | 0.245726 | − | 0.425610i | ||||
\(859\) | −4.43788e6 | − | 7.68663e6i | −0.205207 | − | 0.355429i | 0.744992 | − | 0.667074i | \(-0.232453\pi\) |
−0.950199 | + | 0.311645i | \(0.899120\pi\) | |||||||
\(860\) | 3.59549e6 | 0.165772 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.06234e6 | −0.323728 | ||||||||
\(863\) | 4.35643e6 | + | 7.54556e6i | 0.199115 | + | 0.344877i | 0.948242 | − | 0.317549i | \(-0.102860\pi\) |
−0.749127 | + | 0.662427i | \(0.769527\pi\) | |||||||
\(864\) | −524880. | + | 909119.i | −0.0239208 | + | 0.0414320i | ||||
\(865\) | 714870. | − | 1.23819e6i | 0.0324853 | − | 0.0562662i | ||||
\(866\) | 1.09875e7 | + | 1.90309e7i | 0.497856 | + | 0.862311i | ||||
\(867\) | −1.26358e7 | −0.570895 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.92045e7 | −1.31190 | ||||||||
\(870\) | 1.14609e7 | + | 1.98508e7i | 0.513356 | + | 0.889159i | ||||
\(871\) | 1.31177e7 | − | 2.27205e7i | 0.585884 | − | 1.01478i | ||||
\(872\) | 8.48215e6 | − | 1.46915e7i | 0.377759 | − | 0.654298i | ||||
\(873\) | −5.81831e6 | − | 1.00776e7i | −0.258381 | − | 0.447530i | ||||
\(874\) | 6.76368e7 | 2.99505 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.22646e6 | 0.0980288 | ||||||||
\(877\) | 1.47894e7 | + | 2.56160e7i | 0.649310 | + | 1.12464i | 0.983288 | + | 0.182057i | \(0.0582755\pi\) |
−0.333978 | + | 0.942581i | \(0.608391\pi\) | |||||||
\(878\) | 7.61023e6 | − | 1.31813e7i | 0.333167 | − | 0.577062i | ||||
\(879\) | −891297. | + | 1.54377e6i | −0.0389090 | + | 0.0673924i | ||||
\(880\) | −1.96710e7 | − | 3.40711e7i | −0.856287 | − | 1.48313i | ||||
\(881\) | −2.45670e7 | −1.06638 | −0.533190 | − | 0.845995i | \(-0.679007\pi\) | ||||
−0.533190 | + | 0.845995i | \(0.679007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.45682e7 | 0.628788 | 0.314394 | − | 0.949293i | \(-0.398199\pi\) | ||||
0.314394 | + | 0.949293i | \(0.398199\pi\) | |||||||
\(884\) | −111384. | − | 192923.i | −0.00479394 | − | 0.00830334i | ||||
\(885\) | −9.64969e6 | + | 1.67138e7i | −0.414148 | + | 0.717325i | ||||
\(886\) | 1.80451e7 | − | 3.12550e7i | 0.772281 | − | 1.33763i | ||||
\(887\) | 8.08568e6 | + | 1.40048e7i | 0.345070 | + | 0.597679i | 0.985367 | − | 0.170449i | \(-0.0545217\pi\) |
−0.640296 | + | 0.768128i | \(0.721188\pi\) | |||||||
\(888\) | −8.21621e6 | −0.349654 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.73183e6 | 0.157924 | ||||||||
\(891\) | −1.45654e6 | − | 2.52280e6i | −0.0614651 | − | 0.106461i | ||||
\(892\) | 609472. | − | 1.05564e6i | 0.0256473 | − | 0.0444224i | ||||
\(893\) | 1.86806e7 | − | 3.23558e7i | 0.783904 | − | 1.35776i | ||||
\(894\) | −2.21600e6 | − | 3.83822e6i | −0.0927311 | − | 0.160615i | ||||
\(895\) | 1.19593e7 | 0.499054 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.67076e7 | 0.693319 | ||||||||
\(898\) | 1.69790e7 | + | 2.94084e7i | 0.702619 | + | 1.21697i | ||||
\(899\) | −217680. | + | 377033.i | −0.00898296 | + | 0.0155589i | ||||
\(900\) | −479358. | + | 830272.i | −0.0197267 | + | 0.0341676i | ||||
\(901\) | 604422. | + | 1.04689e6i | 0.0248044 | + | 0.0429624i | ||||
\(902\) | 2.12108e7 | 0.868041 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.69845e7 | 1.50522 | ||||||||
\(905\) | 1.49006e7 | + | 2.58086e7i | 0.604758 | + | 1.04747i | ||||
\(906\) | −7.74986e6 | + | 1.34232e7i | −0.313670 | + | 0.543293i | ||||
\(907\) | −1.57223e7 | + | 2.72318e7i | −0.634596 | + | 1.09915i | 0.352005 | + | 0.935998i | \(0.385500\pi\) |
−0.986601 | + | 0.163154i | \(0.947833\pi\) | |||||||
\(908\) | 577176. | + | 999698.i | 0.0232324 | + | 0.0402397i | ||||
\(909\) | 219186. | 0.00879839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.51427e7 | 0.604514 | 0.302257 | − | 0.953227i | \(-0.402260\pi\) | ||||
0.302257 | + | 0.953227i | \(0.402260\pi\) | |||||||
\(912\) | −1.37206e7 | − | 2.37648e7i | −0.546243 | − | 0.946121i | ||||
\(913\) | 8.92174e6 | − | 1.54529e7i | 0.354219 | − | 0.613526i | ||||
\(914\) | −1.93848e7 | + | 3.35754e7i | −0.767530 | + | 1.32940i | ||||
\(915\) | −1.73668e7 | − | 3.00801e7i | −0.685751 | − | 1.18776i | ||||
\(916\) | −3.08876e6 | −0.121631 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −551124. | −0.0215845 | ||||||||
\(919\) | −2.07438e7 | − | 3.59293e7i | −0.810214 | − | 1.40333i | −0.912714 | − | 0.408598i | \(-0.866018\pi\) |
0.102500 | − | 0.994733i | \(-0.467316\pi\) | |||||||
\(920\) | 2.75184e7 | − | 4.76633e7i | 1.07190 | − | 1.85658i | ||||
\(921\) | −4.70536e6 | + | 8.14993e6i | −0.182786 | + | 0.316595i | ||||
\(922\) | 1.01206e7 | + | 1.75294e7i | 0.392083 | + | 0.679108i | ||||
\(923\) | 1.41617e7 | 0.547155 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.60792e7 | −0.617889 | ||||||||
\(926\) | −1.36492e7 | − | 2.36412e7i | −0.523095 | − | 0.906027i | ||||
\(927\) | 5.33660e6 | − | 9.24327e6i | 0.203970 | − | 0.353286i | ||||
\(928\) | 3.91824e6 | − | 6.78659e6i | 0.149355 | − | 0.258691i | ||||
\(929\) | −8.92473e6 | − | 1.54581e7i | −0.339278 | − | 0.587647i | 0.645019 | − | 0.764166i | \(-0.276849\pi\) |
−0.984297 | + | 0.176520i | \(0.943516\pi\) | |||||||
\(930\) | −336960. | −0.0127753 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.00894e6 | 0.0380473 | ||||||||
\(933\) | 8.26729e6 | + | 1.43194e7i | 0.310928 | + | 0.538542i | ||||
\(934\) | −6.03407e6 | + | 1.04513e7i | −0.226330 | + | 0.392016i | ||||
\(935\) | 2.18182e6 | − | 3.77902e6i | 0.0816186 | − | 0.141368i | ||||
\(936\) | −3.00737e6 | − | 5.20891e6i | −0.112201 | − | 0.194338i | ||||
\(937\) | −2.96399e7 | −1.10288 | −0.551439 | − | 0.834215i | \(-0.685921\pi\) | ||||
−0.551439 | + | 0.834215i | \(0.685921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.28945e6 | 0.121747 | ||||||||
\(940\) | 2.17152e6 | + | 3.76118e6i | 0.0801575 | + | 0.138837i | ||||
\(941\) | −1.61141e7 | + | 2.79104e7i | −0.593242 | + | 1.02753i | 0.400550 | + | 0.916275i | \(0.368819\pi\) |
−0.993792 | + | 0.111251i | \(0.964514\pi\) | |||||||
\(942\) | −3.50671e6 | + | 6.07379e6i | −0.128757 | + | 0.223014i | ||||
\(943\) | 1.67202e7 | + | 2.89602e7i | 0.612297 | + | 1.06053i | ||||
\(944\) | 3.12309e7 | 1.14066 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.06999e7 | 1.11535 | ||||||||
\(947\) | −2.42442e7 | − | 4.19923e7i | −0.878484 | − | 1.52158i | −0.853005 | − | 0.521903i | \(-0.825222\pi\) |
−0.0254787 | − | 0.999675i | \(-0.508111\pi\) | |||||||
\(948\) | 1.18397e6 | − | 2.05069e6i | 0.0427877 | − | 0.0741105i | ||||
\(949\) | −1.36680e7 | + | 2.36736e7i | −0.492650 | + | 0.853295i | ||||
\(950\) | −2.38259e7 | − | 4.12676e7i | −0.856524 | − | 1.48354i | ||||
\(951\) | −255042. | −0.00914451 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.03264e7 | −0.724983 | −0.362491 | − | 0.931987i | \(-0.618074\pi\) | ||||
−0.362491 | + | 0.931987i | \(0.618074\pi\) | |||||||
\(954\) | −2.33134e6 | − | 4.03800e6i | −0.0829345 | − | 0.143647i | ||||
\(955\) | −1.06629e7 | + | 1.84687e7i | −0.378327 | + | 0.655282i | ||||
\(956\) | 2.90227e6 | − | 5.02688e6i | 0.102705 | − | 0.177891i | ||||
\(957\) | 1.08731e7 | + | 1.88328e7i | 0.383773 | + | 0.664714i | ||||
\(958\) | −4.56241e7 | −1.60613 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.94538e7 | −0.681282 | ||||||||
\(961\) | 1.43114e7 | + | 2.47880e7i | 0.499888 | + | 0.865832i | ||||
\(962\) | −7.20548e6 | + | 1.24803e7i | −0.251030 | + | 0.434797i | ||||
\(963\) | 5.22110e6 | − | 9.04321e6i | 0.181425 | − | 0.314237i | ||||
\(964\) | −292796. | − | 507138.i | −0.0101478 | − | 0.0175765i | ||||
\(965\) | −1.19810e7 | −0.414165 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.66292e6 | −0.125968 | −0.0629841 | − | 0.998015i | \(-0.520062\pi\) | ||||
−0.0629841 | + | 0.998015i | \(0.520062\pi\) | |||||||
\(968\) | −3.03114e6 | − | 5.25009e6i | −0.103972 | − | 0.180085i | ||||
\(969\) | 1.52183e6 | − | 2.63588e6i | 0.0520662 | − | 0.0901814i | ||||
\(970\) | −3.36169e7 | + | 5.82262e7i | −1.14717 | + | 1.98696i | ||||
\(971\) | 743706. | + | 1.28814e6i | 0.0253136 | + | 0.0438444i | 0.878405 | − | 0.477918i | \(-0.158608\pi\) |
−0.853091 | + | 0.521762i | \(0.825275\pi\) | |||||||
\(972\) | 236196. | 0.00801875 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.03867e6 | −0.136408 | ||||||||
\(975\) | −5.88545e6 | − | 1.01939e7i | −0.198275 | − | 0.343423i | ||||
\(976\) | −2.81035e7 | + | 4.86767e7i | −0.944356 | + | 1.63567i | ||||
\(977\) | −2.03965e7 | + | 3.53278e7i | −0.683627 | + | 1.18408i | 0.290239 | + | 0.956954i | \(0.406265\pi\) |
−0.973866 | + | 0.227123i | \(0.927068\pi\) | |||||||
\(978\) | 1.49927e7 | + | 2.59681e7i | 0.501224 | + | 0.868145i | ||||
\(979\) | 3.54046e6 | 0.118060 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.17922e6 | −0.271356 | ||||||||
\(982\) | −7.41510e6 | − | 1.28433e7i | −0.245380 | − | 0.425010i | ||||
\(983\) | −4.63163e6 | + | 8.02222e6i | −0.152880 | + | 0.264795i | −0.932285 | − | 0.361725i | \(-0.882188\pi\) |
0.779405 | + | 0.626520i | \(0.215521\pi\) | |||||||
\(984\) | 6.01927e6 | − | 1.04257e7i | 0.198178 | − | 0.343255i | ||||
\(985\) | 6.02246e6 | + | 1.04312e7i | 0.197780 | + | 0.342566i | ||||
\(986\) | 4.11415e6 | 0.134768 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.74531e6 | −0.154658 | ||||||||
\(989\) | 2.42004e7 | + | 4.19163e7i | 0.786741 | + | 1.36268i | ||||
\(990\) | −8.41558e6 | + | 1.45762e7i | −0.272895 | + | 0.472668i | ||||
\(991\) | 2.61025e7 | − | 4.52109e7i | 0.844303 | − | 1.46238i | −0.0419218 | − | 0.999121i | \(-0.513348\pi\) |
0.886225 | − | 0.463255i | \(-0.153319\pi\) | |||||||
\(992\) | 57600.0 | + | 99766.1i | 0.00185842 | + | 0.00321887i | ||||
\(993\) | 1.74052e7 | 0.560153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.86148e7 | −0.916289 | ||||||||
\(996\) | 723384. | + | 1.25294e6i | 0.0231058 | + | 0.0400204i | ||||
\(997\) | −9.33047e6 | + | 1.61609e7i | −0.297280 | + | 0.514904i | −0.975513 | − | 0.219943i | \(-0.929413\pi\) |
0.678233 | + | 0.734847i | \(0.262746\pi\) | |||||||
\(998\) | 1.82446e7 | − | 3.16005e7i | 0.579839 | − | 1.00431i | ||||
\(999\) | 1.98069e6 | + | 3.43066e6i | 0.0627919 | + | 0.108759i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 147.6.e.i.67.1 | 2 | ||
7.2 | even | 3 | inner | 147.6.e.i.79.1 | 2 | ||
7.3 | odd | 6 | 21.6.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 147.6.a.b.1.1 | 1 | |||
7.5 | odd | 6 | 147.6.e.j.79.1 | 2 | |||
7.6 | odd | 2 | 147.6.e.j.67.1 | 2 | |||
21.11 | odd | 6 | 441.6.a.j.1.1 | 1 | |||
21.17 | even | 6 | 63.6.a.d.1.1 | 1 | |||
28.3 | even | 6 | 336.6.a.r.1.1 | 1 | |||
35.3 | even | 12 | 525.6.d.b.274.2 | 2 | |||
35.17 | even | 12 | 525.6.d.b.274.1 | 2 | |||
35.24 | odd | 6 | 525.6.a.d.1.1 | 1 | |||
84.59 | odd | 6 | 1008.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
63.6.a.d.1.1 | 1 | 21.17 | even | 6 | |||
147.6.a.b.1.1 | 1 | 7.4 | even | 3 | |||
147.6.e.i.67.1 | 2 | 1.1 | even | 1 | trivial | ||
147.6.e.i.79.1 | 2 | 7.2 | even | 3 | inner | ||
147.6.e.j.67.1 | 2 | 7.6 | odd | 2 | |||
147.6.e.j.79.1 | 2 | 7.5 | odd | 6 | |||
336.6.a.r.1.1 | 1 | 28.3 | even | 6 | |||
441.6.a.j.1.1 | 1 | 21.11 | odd | 6 | |||
525.6.a.d.1.1 | 1 | 35.24 | odd | 6 | |||
525.6.d.b.274.1 | 2 | 35.17 | even | 12 | |||
525.6.d.b.274.2 | 2 | 35.3 | even | 12 | |||
1008.6.a.c.1.1 | 1 | 84.59 | odd | 6 |