Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,5,Mod(19,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.d (of order \(6\), 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: | \(5.06512819111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 8 x^{15} - 140 x^{14} + 1120 x^{13} + 8358 x^{12} - 65072 x^{11} - 277636 x^{10} + \cdots + 4890937156 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.7 | ||
Root | \(5.32803 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.19 |
Dual form | 49.5.d.c.31.7 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.49543 | − | 6.05426i | 0.873857 | − | 1.51356i | 0.0158815 | − | 0.999874i | \(-0.494945\pi\) |
0.857975 | − | 0.513691i | \(-0.171722\pi\) | |||||||
\(3\) | −6.83370 | + | 3.94544i | −0.759299 | + | 0.438382i | −0.829044 | − | 0.559183i | \(-0.811115\pi\) |
0.0697447 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(4\) | −16.4360 | − | 28.4680i | −1.02725 | − | 1.77925i | ||||
\(5\) | −19.0608 | − | 11.0048i | −0.762433 | − | 0.440191i | 0.0677359 | − | 0.997703i | \(-0.478422\pi\) |
−0.830168 | + | 0.557513i | \(0.811756\pi\) | |||||||
\(6\) | 55.1639i | 1.53233i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −117.950 | −1.84297 | ||||||||
\(9\) | −9.36707 | + | 16.2242i | −0.115643 | + | 0.200299i | ||||
\(10\) | −133.251 | + | 76.9327i | −1.33251 | + | 0.769327i | ||||
\(11\) | −22.3838 | − | 38.7698i | −0.184990 | − | 0.320412i | 0.758583 | − | 0.651576i | \(-0.225892\pi\) |
−0.943573 | + | 0.331164i | \(0.892559\pi\) | |||||||
\(12\) | 224.638 | + | 129.695i | 1.55998 | + | 0.900657i | ||||
\(13\) | − | 311.907i | − | 1.84560i | −0.385274 | − | 0.922802i | \(-0.625893\pi\) | ||
0.385274 | − | 0.922802i | \(-0.374107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 173.674 | 0.771886 | ||||||||
\(16\) | −149.310 | + | 258.612i | −0.583241 | + | 1.01020i | ||||
\(17\) | −61.9673 | + | 35.7768i | −0.214420 | + | 0.123795i | −0.603364 | − | 0.797466i | \(-0.706173\pi\) |
0.388944 | + | 0.921261i | \(0.372840\pi\) | |||||||
\(18\) | 65.4838 | + | 113.421i | 0.202111 | + | 0.350066i | ||||
\(19\) | 241.552 | + | 139.460i | 0.669119 | + | 0.386316i | 0.795743 | − | 0.605635i | \(-0.207081\pi\) |
−0.126624 | + | 0.991951i | \(0.540414\pi\) | |||||||
\(20\) | 723.499i | 1.80875i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −312.963 | −0.646618 | ||||||||
\(23\) | 257.422 | − | 445.867i | 0.486619 | − | 0.842849i | −0.513262 | − | 0.858232i | \(-0.671563\pi\) |
0.999882 | + | 0.0153823i | \(0.00489653\pi\) | |||||||
\(24\) | 806.035 | − | 465.365i | 1.39937 | − | 0.807925i | ||||
\(25\) | −70.2902 | − | 121.746i | −0.112464 | − | 0.194794i | ||||
\(26\) | −1888.37 | − | 1090.25i | −2.79344 | − | 1.61279i | ||||
\(27\) | − | 786.989i | − | 1.07955i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 866.138 | 1.02989 | 0.514945 | − | 0.857223i | \(-0.327812\pi\) | ||||
0.514945 | + | 0.857223i | \(0.327812\pi\) | |||||||
\(30\) | 607.066 | − | 1051.47i | 0.674518 | − | 1.16830i | ||||
\(31\) | −591.823 | + | 341.689i | −0.615841 | + | 0.355556i | −0.775248 | − | 0.631657i | \(-0.782375\pi\) |
0.159407 | + | 0.987213i | \(0.449042\pi\) | |||||||
\(32\) | 100.202 | + | 173.554i | 0.0978531 | + | 0.169487i | ||||
\(33\) | 305.928 | + | 176.627i | 0.280925 | + | 0.162192i | ||||
\(34\) | 500.221i | 0.432717i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 615.830 | 0.475177 | ||||||||
\(37\) | −972.097 | + | 1683.72i | −0.710078 | + | 1.22989i | 0.254749 | + | 0.967007i | \(0.418007\pi\) |
−0.964827 | + | 0.262884i | \(0.915326\pi\) | |||||||
\(38\) | 1688.65 | − | 974.945i | 1.16943 | − | 0.675169i | ||||
\(39\) | 1230.61 | + | 2131.48i | 0.809079 | + | 1.40137i | ||||
\(40\) | 2248.23 | + | 1298.01i | 1.40514 | + | 0.811259i | ||||
\(41\) | 102.538i | 0.0609983i | 0.999535 | + | 0.0304991i | \(0.00970969\pi\) | ||||
−0.999535 | + | 0.0304991i | \(0.990290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −885.919 | −0.479134 | −0.239567 | − | 0.970880i | \(-0.577006\pi\) | ||||
−0.239567 | + | 0.970880i | \(0.577006\pi\) | |||||||
\(44\) | −735.800 | + | 1274.44i | −0.380062 | + | 0.658287i | ||||
\(45\) | 357.088 | − | 206.165i | 0.176340 | − | 0.101810i | ||||
\(46\) | −1799.60 | − | 3116.99i | −0.850471 | − | 1.47306i | ||||
\(47\) | 2447.98 | + | 1413.34i | 1.10819 | + | 0.639812i | 0.938359 | − | 0.345662i | \(-0.112346\pi\) |
0.169827 | + | 0.985474i | \(0.445679\pi\) | |||||||
\(48\) | − | 2356.37i | − | 1.02273i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −982.778 | −0.393111 | ||||||||
\(51\) | 282.310 | − | 488.976i | 0.108539 | − | 0.187995i | ||||
\(52\) | −8879.38 | + | 5126.52i | −3.28380 | + | 1.89590i | ||||
\(53\) | 664.901 | + | 1151.64i | 0.236704 | + | 0.409983i | 0.959766 | − | 0.280799i | \(-0.0905996\pi\) |
−0.723063 | + | 0.690782i | \(0.757266\pi\) | |||||||
\(54\) | −4764.64 | − | 2750.86i | −1.63396 | − | 0.943369i | ||||
\(55\) | 985.312i | 0.325723i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2200.92 | −0.677415 | ||||||||
\(58\) | 3027.52 | − | 5243.82i | 0.899977 | − | 1.55881i | ||||
\(59\) | 4193.07 | − | 2420.87i | 1.20456 | − | 0.695452i | 0.242993 | − | 0.970028i | \(-0.421871\pi\) |
0.961565 | + | 0.274576i | \(0.0885374\pi\) | |||||||
\(60\) | −2854.52 | − | 4944.17i | −0.792922 | − | 1.37338i | ||||
\(61\) | −340.317 | − | 196.482i | −0.0914585 | − | 0.0528036i | 0.453573 | − | 0.891219i | \(-0.350149\pi\) |
−0.545032 | + | 0.838415i | \(0.683482\pi\) | |||||||
\(62\) | 4777.40i | 1.24282i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3376.92 | −0.824444 | ||||||||
\(65\) | −3432.47 | + | 5945.20i | −0.812418 | + | 1.40715i | ||||
\(66\) | 2138.70 | − | 1234.78i | 0.490977 | − | 0.283466i | ||||
\(67\) | −2123.27 | − | 3677.61i | −0.472994 | − | 0.819249i | 0.526529 | − | 0.850157i | \(-0.323493\pi\) |
−0.999522 | + | 0.0309083i | \(0.990160\pi\) | |||||||
\(68\) | 2036.99 | + | 1176.06i | 0.440526 | + | 0.254338i | ||||
\(69\) | 4062.56i | 0.853300i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1188.97 | 0.235860 | 0.117930 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117930 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(72\) | 1104.85 | − | 1913.65i | 0.213126 | − | 0.369146i | ||||
\(73\) | −0.185820 | + | 0.107283i | −3.48695e−5 | + | 2.01319e-5i | −0.500017 | − | 0.866015i | \(-0.666673\pi\) |
0.499983 | + | 0.866035i | \(0.333340\pi\) | |||||||
\(74\) | 6795.79 | + | 11770.7i | 1.24101 | + | 2.14950i | ||||
\(75\) | 960.684 | + | 554.651i | 0.170788 | + | 0.0986047i | ||||
\(76\) | − | 9168.67i | − | 1.58737i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17206.0 | 2.82808 | ||||||||
\(79\) | 789.481 | − | 1367.42i | 0.126499 | − | 0.219103i | −0.795819 | − | 0.605535i | \(-0.792959\pi\) |
0.922318 | + | 0.386432i | \(0.126293\pi\) | |||||||
\(80\) | 5691.93 | − | 3286.24i | 0.889364 | − | 0.513475i | ||||
\(81\) | 2346.28 | + | 4063.88i | 0.357611 | + | 0.619400i | ||||
\(82\) | 620.792 | + | 358.415i | 0.0923249 | + | 0.0533038i | ||||
\(83\) | − | 9056.29i | − | 1.31460i | −0.753628 | − | 0.657301i | \(-0.771698\pi\) | ||
0.753628 | − | 0.657301i | \(-0.228302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1574.86 | 0.217974 | ||||||||
\(86\) | −3096.67 | + | 5363.59i | −0.418695 | + | 0.725201i | ||||
\(87\) | −5918.92 | + | 3417.29i | −0.781995 | + | 0.451485i | ||||
\(88\) | 2640.17 | + | 4572.90i | 0.340931 | + | 0.590509i | ||||
\(89\) | −3018.67 | − | 1742.83i | −0.381097 | − | 0.220026i | 0.297198 | − | 0.954816i | \(-0.403948\pi\) |
−0.678295 | + | 0.734789i | \(0.737281\pi\) | |||||||
\(90\) | − | 2882.54i | − | 0.355869i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16924.0 | −1.99952 | ||||||||
\(93\) | 2696.23 | − | 4670.00i | 0.311738 | − | 0.539947i | ||||
\(94\) | 17113.5 | − | 9880.48i | 1.93679 | − | 1.11821i | ||||
\(95\) | −3069.45 | − | 5316.44i | −0.340105 | − | 0.589079i | ||||
\(96\) | −1369.49 | − | 790.678i | −0.148600 | − | 0.0857940i | ||||
\(97\) | 7941.40i | 0.844022i | 0.906591 | + | 0.422011i | \(0.138676\pi\) | ||||
−0.906591 | + | 0.422011i | \(0.861324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 838.681 | 0.0855710 | ||||||||
\(100\) | −2310.58 | + | 4002.05i | −0.231058 | + | 0.400205i | ||||
\(101\) | −499.644 | + | 288.470i | −0.0489799 | + | 0.0282786i | −0.524290 | − | 0.851540i | \(-0.675669\pi\) |
0.475310 | + | 0.879818i | \(0.342336\pi\) | |||||||
\(102\) | −1973.59 | − | 3418.36i | −0.189695 | − | 0.328562i | ||||
\(103\) | −12415.6 | − | 7168.17i | −1.17029 | − | 0.675669i | −0.216543 | − | 0.976273i | \(-0.569478\pi\) |
−0.953749 | + | 0.300604i | \(0.902812\pi\) | |||||||
\(104\) | 36789.5i | 3.40140i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9296.45 | 0.827381 | ||||||||
\(107\) | 10610.1 | − | 18377.3i | 0.926730 | − | 1.60514i | 0.137976 | − | 0.990436i | \(-0.455940\pi\) |
0.788755 | − | 0.614708i | \(-0.210726\pi\) | |||||||
\(108\) | −22404.0 | + | 12935.0i | −1.92079 | + | 1.10897i | ||||
\(109\) | −4030.73 | − | 6981.42i | −0.339258 | − | 0.587612i | 0.645035 | − | 0.764153i | \(-0.276843\pi\) |
−0.984293 | + | 0.176541i | \(0.943509\pi\) | |||||||
\(110\) | 5965.33 | + | 3444.09i | 0.493003 | + | 0.284635i | ||||
\(111\) | − | 15341.4i | − | 1.24514i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4563.77 | −0.357410 | −0.178705 | − | 0.983903i | \(-0.557191\pi\) | ||||
−0.178705 | + | 0.983903i | \(0.557191\pi\) | |||||||
\(114\) | −7693.16 | + | 13324.9i | −0.591964 | + | 1.02531i | ||||
\(115\) | −9813.33 | + | 5665.73i | −0.742029 | + | 0.428411i | ||||
\(116\) | −14235.9 | − | 24657.2i | −1.05796 | − | 1.83243i | ||||
\(117\) | 5060.46 | + | 2921.66i | 0.369673 | + | 0.213431i | ||||
\(118\) | − | 33847.9i | − | 2.43090i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −20484.9 | −1.42256 | ||||||||
\(121\) | 6318.44 | − | 10943.9i | 0.431558 | − | 0.747480i | ||||
\(122\) | −2379.11 | + | 1373.58i | −0.159843 | + | 0.0922855i | ||||
\(123\) | −404.558 | − | 700.714i | −0.0267405 | − | 0.0463160i | ||||
\(124\) | 19454.4 | + | 11232.0i | 1.26525 | + | 0.730491i | ||||
\(125\) | 16850.1i | 1.07840i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21712.4 | 1.34617 | 0.673085 | − | 0.739565i | \(-0.264969\pi\) | ||||
0.673085 | + | 0.739565i | \(0.264969\pi\) | |||||||
\(128\) | −13407.0 | + | 23221.6i | −0.818299 | + | 1.41734i | ||||
\(129\) | 6054.10 | − | 3495.34i | 0.363806 | − | 0.210044i | ||||
\(130\) | 23995.9 | + | 41562.1i | 1.41987 | + | 2.45929i | ||||
\(131\) | 234.269 | + | 135.255i | 0.0136512 | + | 0.00788154i | 0.506810 | − | 0.862058i | \(-0.330825\pi\) |
−0.493159 | + | 0.869939i | \(0.664158\pi\) | |||||||
\(132\) | − | 11612.2i | − | 0.666449i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −29686.9 | −1.65332 | ||||||||
\(135\) | −8660.63 | + | 15000.7i | −0.475206 | + | 0.823081i | ||||
\(136\) | 7309.05 | − | 4219.88i | 0.395169 | − | 0.228151i | ||||
\(137\) | 4107.78 | + | 7114.89i | 0.218860 | + | 0.379076i | 0.954460 | − | 0.298340i | \(-0.0964329\pi\) |
−0.735600 | + | 0.677416i | \(0.763100\pi\) | |||||||
\(138\) | 24595.8 | + | 14200.4i | 1.29153 | + | 0.745662i | ||||
\(139\) | 11669.2i | 0.603962i | 0.953314 | + | 0.301981i | \(0.0976480\pi\) | ||||
−0.953314 | + | 0.301981i | \(0.902352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22305.0 | −1.12193 | ||||||||
\(142\) | 4155.95 | − | 7198.32i | 0.206108 | − | 0.356989i | ||||
\(143\) | −12092.6 | + | 6981.65i | −0.591353 | + | 0.341418i | ||||
\(144\) | −2797.19 | − | 4844.87i | −0.134895 | − | 0.233646i | ||||
\(145\) | −16509.3 | − | 9531.64i | −0.785222 | − | 0.453348i | ||||
\(146\) | 1.50000i | 7.03698e-5i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 63909.7 | 2.91772 | ||||||||
\(149\) | −14153.8 | + | 24515.2i | −0.637531 | + | 1.10424i | 0.348442 | + | 0.937331i | \(0.386711\pi\) |
−0.985973 | + | 0.166906i | \(0.946622\pi\) | |||||||
\(150\) | 6716.00 | − | 3877.49i | 0.298489 | − | 0.172333i | ||||
\(151\) | −11067.6 | − | 19169.7i | −0.485401 | − | 0.840739i | 0.514458 | − | 0.857515i | \(-0.327993\pi\) |
−0.999859 | + | 0.0167763i | \(0.994660\pi\) | |||||||
\(152\) | −28491.1 | − | 16449.3i | −1.23317 | − | 0.711969i | ||||
\(153\) | − | 1340.50i | − | 0.0572641i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15040.8 | 0.626049 | ||||||||
\(156\) | 40452.7 | − | 70066.1i | 1.66226 | − | 2.87911i | ||||
\(157\) | 38375.0 | − | 22155.8i | 1.55686 | − | 0.898852i | 0.559303 | − | 0.828964i | \(-0.311069\pi\) |
0.997555 | − | 0.0698885i | \(-0.0222644\pi\) | |||||||
\(158\) | −5519.15 | − | 9559.45i | −0.221084 | − | 0.382929i | ||||
\(159\) | −9087.46 | − | 5246.65i | −0.359458 | − | 0.207533i | ||||
\(160\) | − | 4410.78i | − | 0.172296i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 32805.1 | 1.25000 | ||||||||
\(163\) | 12810.8 | − | 22189.0i | 0.482173 | − | 0.835148i | −0.517618 | − | 0.855612i | \(-0.673181\pi\) |
0.999791 | + | 0.0204642i | \(0.00651440\pi\) | |||||||
\(164\) | 2919.06 | − | 1685.32i | 0.108531 | − | 0.0626606i | ||||
\(165\) | −3887.49 | − | 6733.32i | −0.142791 | − | 0.247321i | ||||
\(166\) | −54829.1 | − | 31655.6i | −1.98973 | − | 1.14877i | ||||
\(167\) | − | 5822.23i | − | 0.208764i | −0.994537 | − | 0.104382i | \(-0.966713\pi\) | ||
0.994537 | − | 0.104382i | \(-0.0332865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −68725.1 | −2.40626 | ||||||||
\(170\) | 5504.82 | − | 9534.62i | 0.190478 | − | 0.329918i | ||||
\(171\) | −4525.27 | + | 2612.66i | −0.154758 | + | 0.0893493i | ||||
\(172\) | 14561.0 | + | 25220.4i | 0.492192 | + | 0.852501i | ||||
\(173\) | 34244.4 | + | 19771.0i | 1.14419 | + | 0.660596i | 0.947464 | − | 0.319863i | \(-0.103637\pi\) |
0.196723 | + | 0.980459i | \(0.436970\pi\) | |||||||
\(174\) | 47779.6i | 1.57813i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13368.4 | 0.431574 | ||||||||
\(177\) | −19102.8 | + | 33087.0i | −0.609747 | + | 1.05611i | ||||
\(178\) | −21103.1 | + | 12183.9i | −0.666049 | + | 0.384543i | ||||
\(179\) | 24041.6 | + | 41641.2i | 0.750338 | + | 1.29962i | 0.947659 | + | 0.319285i | \(0.103443\pi\) |
−0.197321 | + | 0.980339i | \(0.563224\pi\) | |||||||
\(180\) | −11738.2 | − | 6777.06i | −0.362291 | − | 0.209169i | ||||
\(181\) | 47562.9i | 1.45181i | 0.687793 | + | 0.725907i | \(0.258580\pi\) | ||||
−0.687793 | + | 0.725907i | \(0.741420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3100.83 | 0.0925925 | ||||||||
\(184\) | −30362.9 | + | 52590.1i | −0.896825 | + | 1.55335i | ||||
\(185\) | 37057.9 | − | 21395.4i | 1.08277 | − | 0.625139i | ||||
\(186\) | −18848.9 | − | 32647.3i | −0.544829 | − | 0.943672i | ||||
\(187\) | 2774.12 | + | 1601.64i | 0.0793309 | + | 0.0458017i | ||||
\(188\) | − | 92919.0i | − | 2.62899i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −42916.2 | −1.18881 | ||||||||
\(191\) | −4912.84 | + | 8509.29i | −0.134668 | + | 0.233253i | −0.925471 | − | 0.378819i | \(-0.876330\pi\) |
0.790802 | + | 0.612072i | \(0.209664\pi\) | |||||||
\(192\) | 23076.9 | − | 13323.4i | 0.626000 | − | 0.361421i | ||||
\(193\) | 4867.31 | + | 8430.43i | 0.130670 | + | 0.226326i | 0.923935 | − | 0.382550i | \(-0.124954\pi\) |
−0.793265 | + | 0.608876i | \(0.791621\pi\) | |||||||
\(194\) | 48079.3 | + | 27758.6i | 1.27748 | + | 0.737555i | ||||
\(195\) | − | 54170.3i | − | 1.42460i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 58038.9 | 1.49550 | 0.747750 | − | 0.663981i | \(-0.231134\pi\) | ||||
0.747750 | + | 0.663981i | \(0.231134\pi\) | |||||||
\(198\) | 2931.55 | − | 5077.59i | 0.0747768 | − | 0.129517i | ||||
\(199\) | −54183.8 | + | 31283.0i | −1.36824 | + | 0.789955i | −0.990704 | − | 0.136039i | \(-0.956563\pi\) |
−0.377539 | + | 0.925994i | \(0.623230\pi\) | |||||||
\(200\) | 8290.74 | + | 14360.0i | 0.207269 | + | 0.359000i | ||||
\(201\) | 29019.5 | + | 16754.4i | 0.718288 | + | 0.414704i | ||||
\(202\) | 4033.30i | 0.0988458i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −18560.2 | −0.445988 | ||||||||
\(205\) | 1128.41 | − | 1954.46i | 0.0268509 | − | 0.0465071i | ||||
\(206\) | −86795.9 | + | 50111.6i | −2.04534 | + | 1.18088i | ||||
\(207\) | 4822.57 | + | 8352.94i | 0.112548 | + | 0.194939i | ||||
\(208\) | 80662.9 | + | 46570.8i | 1.86444 | + | 1.07643i | ||||
\(209\) | − | 12486.6i | − | 0.285858i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26674.3 | 0.599140 | 0.299570 | − | 0.954074i | \(-0.403157\pi\) | ||||
0.299570 | + | 0.954074i | \(0.403157\pi\) | |||||||
\(212\) | 21856.7 | − | 37856.9i | 0.486309 | − | 0.842312i | ||||
\(213\) | −8125.05 | + | 4691.00i | −0.179088 | + | 0.103397i | ||||
\(214\) | −74173.9 | − | 128473.i | −1.61966 | − | 2.80533i | ||||
\(215\) | 16886.3 | + | 9749.34i | 0.365308 | + | 0.210910i | ||||
\(216\) | 92825.5i | 1.98957i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −56356.4 | −1.18585 | ||||||||
\(219\) | 0.846557 | − | 1.46628i | 1.76510e−5 | − | 3.05723e-5i | ||||
\(220\) | 28049.9 | − | 16194.6i | 0.579543 | − | 0.334600i | ||||
\(221\) | 11159.0 | + | 19328.0i | 0.228477 | + | 0.395734i | ||||
\(222\) | −92880.7 | − | 53624.7i | −1.88460 | − | 1.08808i | ||||
\(223\) | − | 21285.7i | − | 0.428035i | −0.976830 | − | 0.214017i | \(-0.931345\pi\) | ||
0.976830 | − | 0.214017i | \(-0.0686549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2633.65 | 0.0520228 | ||||||||
\(226\) | −15952.3 | + | 27630.3i | −0.312326 | + | 0.540964i | ||||
\(227\) | 18678.4 | − | 10784.0i | 0.362483 | − | 0.209280i | −0.307686 | − | 0.951488i | \(-0.599555\pi\) |
0.670169 | + | 0.742208i | \(0.266221\pi\) | |||||||
\(228\) | 36174.4 | + | 62655.9i | 0.695876 | + | 1.20529i | ||||
\(229\) | −17253.3 | − | 9961.17i | −0.329003 | − | 0.189950i | 0.326395 | − | 0.945233i | \(-0.394166\pi\) |
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(230\) | 79216.6i | 1.49748i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −102161. | −1.89806 | ||||||||
\(233\) | −2013.92 | + | 3488.22i | −0.0370964 | + | 0.0642528i | −0.883977 | − | 0.467529i | \(-0.845144\pi\) |
0.846881 | + | 0.531782i | \(0.178478\pi\) | |||||||
\(234\) | 35376.9 | − | 20424.9i | 0.646083 | − | 0.373016i | ||||
\(235\) | −31107.0 | − | 53879.0i | −0.563278 | − | 0.975626i | ||||
\(236\) | −137835. | − | 79579.0i | −2.47477 | − | 1.42881i | ||||
\(237\) | 12459.4i | 0.221820i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 35321.2 | 0.618358 | 0.309179 | − | 0.951004i | \(-0.399946\pi\) | ||||
0.309179 | + | 0.951004i | \(0.399946\pi\) | |||||||
\(240\) | −25931.3 | + | 44914.3i | −0.450196 | + | 0.779762i | ||||
\(241\) | −68620.0 | + | 39617.7i | −1.18145 | + | 0.682112i | −0.956350 | − | 0.292223i | \(-0.905605\pi\) |
−0.225102 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(242\) | −44171.3 | − | 76506.9i | −0.754239 | − | 1.30638i | ||||
\(243\) | 23138.2 | + | 13358.8i | 0.391848 | + | 0.226233i | ||||
\(244\) | 12917.5i | 0.216970i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5656.41 | −0.0934696 | ||||||||
\(247\) | 43498.6 | − | 75341.7i | 0.712986 | − | 1.23493i | ||||
\(248\) | 69805.6 | − | 40302.3i | 1.13498 | − | 0.655279i | ||||
\(249\) | 35731.0 | + | 61887.9i | 0.576297 | + | 0.998176i | ||||
\(250\) | 102015. | + | 58898.2i | 1.63223 | + | 0.942371i | ||||
\(251\) | − | 100747.i | − | 1.59914i | −0.600575 | − | 0.799569i | \(-0.705061\pi\) | ||
0.600575 | − | 0.799569i | \(-0.294939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23048.3 | −0.360078 | ||||||||
\(254\) | 75894.0 | − | 131452.i | 1.17636 | − | 2.03751i | ||||
\(255\) | −10762.1 | + | 6213.52i | −0.165508 | + | 0.0955558i | ||||
\(256\) | 66711.1 | + | 115547.i | 1.01793 | + | 1.76311i | ||||
\(257\) | −42453.8 | − | 24510.7i | −0.642763 | − | 0.371099i | 0.142915 | − | 0.989735i | \(-0.454352\pi\) |
−0.785678 | + | 0.618636i | \(0.787686\pi\) | |||||||
\(258\) | − | 48870.8i | − | 0.734193i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 225664. | 3.33823 | ||||||||
\(261\) | −8113.17 | + | 14052.4i | −0.119099 | + | 0.206286i | ||||
\(262\) | 1637.74 | − | 945.549i | 0.0238585 | − | 0.0137747i | ||||
\(263\) | 1435.46 | + | 2486.30i | 0.0207530 | + | 0.0359453i | 0.876215 | − | 0.481920i | \(-0.160060\pi\) |
−0.855462 | + | 0.517865i | \(0.826727\pi\) | |||||||
\(264\) | −36084.2 | − | 20833.2i | −0.517737 | − | 0.298916i | ||||
\(265\) | − | 29268.3i | − | 0.416779i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27504.9 | 0.385822 | ||||||||
\(268\) | −69796.2 | + | 120891.i | −0.971767 | + | 1.68315i | ||||
\(269\) | 40644.7 | − | 23466.2i | 0.561693 | − | 0.324294i | −0.192132 | − | 0.981369i | \(-0.561540\pi\) |
0.753825 | + | 0.657076i | \(0.228207\pi\) | |||||||
\(270\) | 60545.2 | + | 104867.i | 0.830525 | + | 1.43851i | ||||
\(271\) | 50712.6 | + | 29278.9i | 0.690521 | + | 0.398673i | 0.803807 | − | 0.594890i | \(-0.202804\pi\) |
−0.113286 | + | 0.993562i | \(0.536138\pi\) | |||||||
\(272\) | − | 21367.3i | − | 0.288810i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 57433.8 | 0.765009 | ||||||||
\(275\) | −3146.72 | + | 5450.28i | −0.0416095 | + | 0.0720698i | ||||
\(276\) | 115653. | − | 66772.4i | 1.51824 | − | 0.876554i | ||||
\(277\) | −29810.0 | − | 51632.4i | −0.388510 | − | 0.672919i | 0.603739 | − | 0.797182i | \(-0.293677\pi\) |
−0.992249 | + | 0.124263i | \(0.960343\pi\) | |||||||
\(278\) | 70648.1 | + | 40788.7i | 0.914136 | + | 0.527777i | ||||
\(279\) | − | 12802.5i | − | 0.164470i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −47369.7 | −0.599912 | −0.299956 | − | 0.953953i | \(-0.596972\pi\) | ||||
−0.299956 | + | 0.953953i | \(0.596972\pi\) | |||||||
\(282\) | −77965.6 | + | 135040.i | −0.980404 | + | 1.69811i | ||||
\(283\) | 81975.3 | − | 47328.5i | 1.02355 | − | 0.590949i | 0.108422 | − | 0.994105i | \(-0.465420\pi\) |
0.915131 | + | 0.403156i | \(0.132087\pi\) | |||||||
\(284\) | −19541.9 | − | 33847.6i | −0.242287 | − | 0.419654i | ||||
\(285\) | 41951.4 | + | 24220.6i | 0.516483 | + | 0.298192i | ||||
\(286\) | 97615.4i | 1.19340i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3754.38 | −0.0452640 | ||||||||
\(289\) | −39200.5 | + | 67897.3i | −0.469349 | + | 0.812937i | ||||
\(290\) | −115414. | + | 66634.3i | −1.37234 | + | 0.792323i | ||||
\(291\) | −31332.3 | − | 54269.1i | −0.370004 | − | 0.640866i | ||||
\(292\) | 6.10828 | + | 3.52662i | 7.16396e−5 | + | 4.13612e-5i | ||||
\(293\) | 73528.8i | 0.856490i | 0.903663 | + | 0.428245i | \(0.140868\pi\) | ||||
−0.903663 | + | 0.428245i | \(0.859132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −106564. | −1.22453 | ||||||||
\(296\) | 114659. | − | 198595.i | 1.30865 | − | 2.26665i | ||||
\(297\) | −30511.4 | + | 17615.8i | −0.345899 | + | 0.199705i | ||||
\(298\) | 98947.4 | + | 171382.i | 1.11422 | + | 1.92989i | ||||
\(299\) | −139069. | − | 80291.6i | −1.55557 | − | 0.898107i | ||||
\(300\) | − | 36465.1i | − | 0.405167i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −154744. | −1.69668 | ||||||||
\(303\) | 2276.28 | − | 3942.63i | 0.0247936 | − | 0.0429438i | ||||
\(304\) | −72132.1 | + | 41645.5i | −0.780515 | + | 0.450630i | ||||
\(305\) | 4324.48 | + | 7490.22i | 0.0464873 | + | 0.0805183i | ||||
\(306\) | −8115.71 | − | 4685.61i | −0.0866730 | − | 0.0500407i | ||||
\(307\) | 117853.i | 1.25045i | 0.780445 | + | 0.625224i | \(0.214992\pi\) | ||||
−0.780445 | + | 0.625224i | \(0.785008\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 113126. | 1.18480 | ||||||||
\(310\) | 52574.2 | − | 91061.1i | 0.547078 | − | 0.947566i | ||||
\(311\) | 3740.82 | − | 2159.77i | 0.0386764 | − | 0.0223298i | −0.480537 | − | 0.876974i | \(-0.659558\pi\) |
0.519214 | + | 0.854645i | \(0.326225\pi\) | |||||||
\(312\) | −145151. | − | 251408.i | −1.49111 | − | 2.58268i | ||||
\(313\) | −103292. | − | 59635.5i | −1.05433 | − | 0.608718i | −0.130472 | − | 0.991452i | \(-0.541649\pi\) |
−0.923859 | + | 0.382734i | \(0.874983\pi\) | |||||||
\(314\) | − | 309776.i | − | 3.14187i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −51903.8 | −0.519786 | ||||||||
\(317\) | 6999.30 | − | 12123.1i | 0.0696524 | − | 0.120641i | −0.829096 | − | 0.559106i | \(-0.811144\pi\) |
0.898748 | + | 0.438465i | \(0.144478\pi\) | |||||||
\(318\) | −63529.1 | + | 36678.6i | −0.628230 | + | 0.362709i | ||||
\(319\) | −19387.4 | − | 33580.0i | −0.190519 | − | 0.329989i | ||||
\(320\) | 64366.9 | + | 37162.2i | 0.628583 | + | 0.362912i | ||||
\(321\) | 167446.i | 1.62505i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19957.7 | −0.191296 | ||||||||
\(324\) | 77127.2 | − | 133588.i | 0.734712 | − | 1.27256i | ||||
\(325\) | −37973.5 | + | 21924.0i | −0.359513 | + | 0.207565i | ||||
\(326\) | −89558.8 | − | 155120.i | −0.842700 | − | 1.45960i | ||||
\(327\) | 55089.5 | + | 31805.9i | 0.515197 | + | 0.297449i | ||||
\(328\) | − | 12094.4i | − | 0.112418i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −54353.7 | −0.499116 | ||||||||
\(331\) | −15376.5 | + | 26632.8i | −0.140346 | + | 0.243087i | −0.927627 | − | 0.373508i | \(-0.878155\pi\) |
0.787281 | + | 0.616595i | \(0.211488\pi\) | |||||||
\(332\) | −257815. | + | 148849.i | −2.33901 | + | 1.35043i | ||||
\(333\) | −18211.4 | − | 31543.1i | −0.164231 | − | 0.284456i | ||||
\(334\) | −35249.3 | − | 20351.2i | −0.315978 | − | 0.182430i | ||||
\(335\) | 93464.3i | 0.832830i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22396.7 | −0.197208 | −0.0986040 | − | 0.995127i | \(-0.531438\pi\) | ||||
−0.0986040 | + | 0.995127i | \(0.531438\pi\) | |||||||
\(338\) | −240223. | + | 416079.i | −2.10272 | + | 3.64202i | ||||
\(339\) | 31187.4 | − | 18006.1i | 0.271382 | − | 0.156682i | ||||
\(340\) | −25884.5 | − | 44833.2i | −0.223914 | − | 0.387831i | ||||
\(341\) | 26494.4 | + | 15296.6i | 0.227848 | + | 0.131548i | ||||
\(342\) | 36529.5i | 0.312314i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 104494. | 0.883031 | ||||||||
\(345\) | 44707.6 | − | 77435.8i | 0.375615 | − | 0.650584i | ||||
\(346\) | 239397. | − | 138216.i | 1.99971 | − | 1.15453i | ||||
\(347\) | 106902. | + | 185159.i | 0.887820 | + | 1.53775i | 0.842447 | + | 0.538780i | \(0.181115\pi\) |
0.0453739 | + | 0.998970i | \(0.485552\pi\) | |||||||
\(348\) | 194567. | + | 112333.i | 1.60661 | + | 0.927578i | ||||
\(349\) | − | 63672.4i | − | 0.522758i | −0.965236 | − | 0.261379i | \(-0.915823\pi\) | ||
0.965236 | − | 0.261379i | \(-0.0841772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −245468. | −1.99242 | ||||||||
\(352\) | 4485.77 | − | 7769.59i | 0.0362036 | − | 0.0627065i | ||||
\(353\) | 121927. | − | 70394.8i | 0.978480 | − | 0.564926i | 0.0766693 | − | 0.997057i | \(-0.475571\pi\) |
0.901811 | + | 0.432131i | \(0.142238\pi\) | |||||||
\(354\) | 133545. | + | 231306.i | 1.06566 | + | 1.84578i | ||||
\(355\) | −22662.7 | − | 13084.3i | −0.179827 | − | 0.103823i | ||||
\(356\) | 114581.i | 0.904090i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 336142. | 2.62275 | ||||||||
\(359\) | 18382.6 | − | 31839.5i | 0.142632 | − | 0.247046i | −0.785855 | − | 0.618411i | \(-0.787777\pi\) |
0.928487 | + | 0.371365i | \(0.121110\pi\) | |||||||
\(360\) | −42118.6 | + | 24317.2i | −0.324989 | + | 0.187633i | ||||
\(361\) | −26262.3 | − | 45487.7i | −0.201520 | − | 0.349043i | ||||
\(362\) | 287958. | + | 166253.i | 2.19741 | + | 1.26868i | ||||
\(363\) | 99715.9i | 0.756748i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.72250 | 3.54476e−5 | ||||||||
\(366\) | 10838.7 | − | 18773.2i | 0.0809126 | − | 0.140145i | ||||
\(367\) | −21449.9 | + | 12384.1i | −0.159255 | + | 0.0919459i | −0.577509 | − | 0.816384i | \(-0.695975\pi\) |
0.418255 | + | 0.908330i | \(0.362642\pi\) | |||||||
\(368\) | 76871.1 | + | 133145.i | 0.567633 | + | 0.983169i | ||||
\(369\) | −1663.60 | − | 960.482i | −0.0122179 | − | 0.00705402i | ||||
\(370\) | − | 299144.i | − | 2.18513i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −177261. | −1.28094 | ||||||||
\(373\) | 16096.3 | − | 27879.6i | 0.115693 | − | 0.200387i | −0.802363 | − | 0.596836i | \(-0.796424\pi\) |
0.918057 | + | 0.396449i | \(0.129758\pi\) | |||||||
\(374\) | 19393.5 | − | 11196.8i | 0.138648 | − | 0.0800482i | ||||
\(375\) | −66480.9 | − | 115148.i | −0.472753 | − | 0.818832i | ||||
\(376\) | −288740. | − | 166704.i | −2.04236 | − | 1.17915i | ||||
\(377\) | − | 270154.i | − | 1.90077i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 187516. | 1.30545 | 0.652726 | − | 0.757594i | \(-0.273625\pi\) | ||||
0.652726 | + | 0.757594i | \(0.273625\pi\) | |||||||
\(380\) | −100899. | + | 174762.i | −0.698747 | + | 1.21027i | ||||
\(381\) | −148376. | + | 85664.8i | −1.02215 | + | 0.590136i | ||||
\(382\) | 34345.0 | + | 59487.2i | 0.235362 | + | 0.407659i | ||||
\(383\) | 22205.2 | + | 12820.2i | 0.151376 | + | 0.0873972i | 0.573775 | − | 0.819013i | \(-0.305478\pi\) |
−0.422399 | + | 0.906410i | \(0.638812\pi\) | |||||||
\(384\) | − | 211586.i | − | 1.43491i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 68053.4 | 0.456746 | ||||||||
\(387\) | 8298.47 | − | 14373.4i | 0.0554085 | − | 0.0959703i | ||||
\(388\) | 226076. | − | 130525.i | 1.50173 | − | 0.867023i | ||||
\(389\) | −36228.0 | − | 62748.7i | −0.239412 | − | 0.414673i | 0.721134 | − | 0.692796i | \(-0.243621\pi\) |
−0.960546 | + | 0.278123i | \(0.910288\pi\) | |||||||
\(390\) | −327961. | − | 189348.i | −2.15622 | − | 1.24489i | ||||
\(391\) | 36838.9i | 0.240965i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2134.56 | −0.0138205 | ||||||||
\(394\) | 202871. | − | 351382.i | 1.30685 | − | 2.26354i | ||||
\(395\) | −30096.3 | + | 17376.1i | −0.192894 | + | 0.111368i | ||||
\(396\) | −13784.6 | − | 23875.6i | −0.0879029 | − | 0.152252i | ||||
\(397\) | −110506. | − | 63800.7i | −0.701140 | − | 0.404803i | 0.106632 | − | 0.994299i | \(-0.465993\pi\) |
−0.807772 | + | 0.589495i | \(0.799327\pi\) | |||||||
\(398\) | 437390.i | 2.76123i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 41980.1 | 0.262375 | ||||||||
\(401\) | 69224.8 | − | 119901.i | 0.430500 | − | 0.745648i | −0.566416 | − | 0.824119i | \(-0.691671\pi\) |
0.996916 | + | 0.0784714i | \(0.0250039\pi\) | |||||||
\(402\) | 202871. | − | 117128.i | 1.25536 | − | 0.724783i | ||||
\(403\) | 106575. | + | 184594.i | 0.656215 | + | 1.13660i | ||||
\(404\) | 16424.3 | + | 9482.60i | 0.100629 | + | 0.0580985i | ||||
\(405\) | − | 103281.i | − | 0.629667i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 87036.7 | 0.525428 | ||||||||
\(408\) | −33298.5 | + | 57674.8i | −0.200035 | + | 0.346470i | ||||
\(409\) | −66455.9 | + | 38368.3i | −0.397271 | + | 0.229365i | −0.685306 | − | 0.728255i | \(-0.740331\pi\) |
0.288035 | + | 0.957620i | \(0.406998\pi\) | |||||||
\(410\) | −7888.54 | − | 13663.4i | −0.0469277 | − | 0.0812811i | ||||
\(411\) | −56142.7 | − | 32414.0i | −0.332360 | − | 0.191888i | ||||
\(412\) | 471265.i | 2.77633i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 67427.8 | 0.393404 | ||||||||
\(415\) | −99662.3 | + | 172620.i | −0.578675 | + | 1.00229i | ||||
\(416\) | 54132.8 | − | 31253.6i | 0.312805 | − | 0.180598i | ||||
\(417\) | −46039.9 | − | 79743.5i | −0.264766 | − | 0.458588i | ||||
\(418\) | −75596.8 | − | 43645.8i | −0.432664 | − | 0.249799i | ||||
\(419\) | 179909.i | 1.02476i | 0.858757 | + | 0.512382i | \(0.171237\pi\) | ||||
−0.858757 | + | 0.512382i | \(0.828763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6114.46 | −0.0344980 | −0.0172490 | − | 0.999851i | \(-0.505491\pi\) | ||||
−0.0172490 | + | 0.999851i | \(0.505491\pi\) | |||||||
\(422\) | 93238.1 | − | 161493.i | 0.523563 | − | 0.906837i | ||||
\(423\) | −45860.9 | + | 26477.8i | −0.256308 | + | 0.147979i | ||||
\(424\) | −78425.2 | − | 135836.i | −0.436238 | − | 0.755587i | ||||
\(425\) | 8711.39 | + | 5029.52i | 0.0482291 | + | 0.0278451i | ||||
\(426\) | 65588.2i | 0.361415i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −697554. | −3.80794 | ||||||||
\(429\) | 55091.3 | − | 95421.0i | 0.299343 | − | 0.518477i | ||||
\(430\) | 118050. | − | 68156.2i | 0.638453 | − | 0.368611i | ||||
\(431\) | −112648. | − | 195112.i | −0.606412 | − | 1.05034i | −0.991827 | − | 0.127593i | \(-0.959275\pi\) |
0.385414 | − | 0.922744i | \(-0.374058\pi\) | |||||||
\(432\) | 203525. | + | 117505.i | 1.09056 | + | 0.629636i | ||||
\(433\) | − | 291349.i | − | 1.55395i | −0.629531 | − | 0.776976i | \(-0.716753\pi\) | ||
0.629531 | − | 0.776976i | \(-0.283247\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 150426. | 0.794958 | ||||||||
\(436\) | −132498. | + | 229494.i | −0.697007 | + | 1.20725i | ||||
\(437\) | 124361. | − | 71800.0i | 0.651212 | − | 0.375977i | ||||
\(438\) | −5.91816 | − | 10.2506i | −3.08488e−5 | − | 5.34317e-5i | ||||
\(439\) | 234560. | + | 135424.i | 1.21710 | + | 0.702692i | 0.964296 | − | 0.264826i | \(-0.0853144\pi\) |
0.252802 | + | 0.967518i | \(0.418648\pi\) | |||||||
\(440\) | − | 116218.i | − | 0.600298i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 156023. | 0.798625 | ||||||||
\(443\) | −31592.2 | + | 54719.2i | −0.160980 | + | 0.278825i | −0.935220 | − | 0.354066i | \(-0.884799\pi\) |
0.774240 | + | 0.632892i | \(0.218132\pi\) | |||||||
\(444\) | −436739. | + | 252151.i | −2.21542 | + | 1.27907i | ||||
\(445\) | 38358.9 | + | 66439.5i | 0.193707 | + | 0.335511i | ||||
\(446\) | −128869. | − | 74402.8i | −0.647858 | − | 0.374041i | ||||
\(447\) | − | 223372.i | − | 1.11793i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 328951. | 1.63169 | 0.815846 | − | 0.578269i | \(-0.196272\pi\) | ||||
0.815846 | + | 0.578269i | \(0.196272\pi\) | |||||||
\(450\) | 9205.75 | − | 15944.8i | 0.0454605 | − | 0.0787399i | ||||
\(451\) | 3975.38 | − | 2295.19i | 0.0195446 | − | 0.0112841i | ||||
\(452\) | 75010.3 | + | 129922.i | 0.367151 | + | 0.635923i | ||||
\(453\) | 151266. | + | 87333.2i | 0.737129 | + | 0.425582i | ||||
\(454\) | − | 150778.i | − | 0.731522i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 259599. | 1.24846 | ||||||||
\(457\) | 15613.7 | − | 27043.7i | 0.0747607 | − | 0.129489i | −0.826222 | − | 0.563345i | \(-0.809514\pi\) |
0.900982 | + | 0.433856i | \(0.142847\pi\) | |||||||
\(458\) | −120615. | + | 69637.1i | −0.575003 | + | 0.331978i | ||||
\(459\) | 28156.0 | + | 48767.6i | 0.133643 | + | 0.231476i | ||||
\(460\) | 322584. | + | 186244.i | 1.52450 | + | 0.880171i | ||||
\(461\) | − | 193095.i | − | 0.908591i | −0.890851 | − | 0.454296i | \(-0.849891\pi\) | ||
0.890851 | − | 0.454296i | \(-0.150109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −246667. | −1.15067 | −0.575333 | − | 0.817919i | \(-0.695127\pi\) | ||||
−0.575333 | + | 0.817919i | \(0.695127\pi\) | |||||||
\(464\) | −129323. | + | 223994.i | −0.600674 | + | 1.04040i | ||||
\(465\) | −102784. | + | 59342.7i | −0.475359 | + | 0.274449i | ||||
\(466\) | 14079.1 | + | 24385.6i | 0.0648338 | + | 0.112295i | ||||
\(467\) | −289328. | − | 167043.i | −1.32665 | − | 0.765942i | −0.341870 | − | 0.939747i | \(-0.611060\pi\) |
−0.984780 | + | 0.173806i | \(0.944394\pi\) | |||||||
\(468\) | − | 192082.i | − | 0.876989i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −434930. | −1.96890 | ||||||||
\(471\) | −174829. | + | 302812.i | −0.788081 | + | 1.36500i | ||||
\(472\) | −494573. | + | 285542.i | −2.21997 | + | 1.28170i | ||||
\(473\) | 19830.2 | + | 34346.9i | 0.0886349 | + | 0.153520i | ||||
\(474\) | 75432.4 | + | 43550.9i | 0.335739 | + | 0.193839i | ||||
\(475\) | − | 39210.7i | − | 0.173787i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24912.7 | −0.109492 | ||||||||
\(478\) | 123463. | − | 213844.i | 0.540356 | − | 0.935924i | ||||
\(479\) | 130274. | − | 75214.0i | 0.567790 | − | 0.327814i | −0.188476 | − | 0.982078i | \(-0.560355\pi\) |
0.756266 | + | 0.654264i | \(0.227021\pi\) | |||||||
\(480\) | 17402.4 | + | 30141.9i | 0.0755314 | + | 0.130824i | ||||
\(481\) | 525165. | + | 303204.i | 2.26989 | + | 1.31052i | ||||
\(482\) | 553924.i | 2.38427i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −415400. | −1.77327 | ||||||||
\(485\) | 87393.3 | − | 151370.i | 0.371531 | − | 0.643510i | ||||
\(486\) | 161756. | − | 93389.8i | 0.684837 | − | 0.395391i | ||||
\(487\) | 140032. | + | 242542.i | 0.590429 | + | 1.02265i | 0.994175 | + | 0.107782i | \(0.0343750\pi\) |
−0.403745 | + | 0.914872i | \(0.632292\pi\) | |||||||
\(488\) | 40140.4 | + | 23175.1i | 0.168555 | + | 0.0973154i | ||||
\(489\) | 202178.i | 0.845503i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −227539. | −0.943829 | −0.471914 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471914 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(492\) | −13298.6 | + | 23033.9i | −0.0549385 | + | 0.0951564i | ||||
\(493\) | −53672.2 | + | 30987.7i | −0.220829 | + | 0.127495i | ||||
\(494\) | −304092. | − | 526703.i | −1.24610 | − | 2.15830i | ||||
\(495\) | −15985.9 | − | 9229.49i | −0.0652421 | − | 0.0376675i | ||||
\(496\) | − | 204070.i | − | 0.829499i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 499581. | 2.01441 | ||||||||
\(499\) | −115300. | + | 199705.i | −0.463049 | + | 0.802025i | −0.999111 | − | 0.0421540i | \(-0.986578\pi\) |
0.536062 | + | 0.844179i | \(0.319911\pi\) | |||||||
\(500\) | 479688. | − | 276948.i | 1.91875 | − | 1.10779i | ||||
\(501\) | 22971.2 | + | 39787.3i | 0.0915185 | + | 0.158515i | ||||
\(502\) | −609950. | − | 352155.i | −2.42040 | − | 1.39742i | ||||
\(503\) | 434537.i | 1.71748i | 0.512415 | + | 0.858738i | \(0.328751\pi\) | ||||
−0.512415 | + | 0.858738i | \(0.671249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12698.2 | 0.0497919 | ||||||||
\(506\) | −80563.5 | + | 139540.i | −0.314657 | + | 0.545002i | ||||
\(507\) | 469646. | − | 271150.i | 1.82707 | − | 1.05486i | ||||
\(508\) | −356865. | − | 618109.i | −1.38286 | − | 2.39518i | ||||
\(509\) | −196800. | − | 113622.i | −0.759606 | − | 0.438559i | 0.0695482 | − | 0.997579i | \(-0.477844\pi\) |
−0.829154 | + | 0.559020i | \(0.811178\pi\) | |||||||
\(510\) | 86875.6i | 0.334009i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 503711. | 1.92151 | ||||||||
\(513\) | 109754. | − | 190099.i | 0.417046 | − | 0.722344i | ||||
\(514\) | −296789. | + | 171351.i | −1.12337 | + | 0.648575i | ||||
\(515\) | 157768. | + | 273262.i | 0.594846 | + | 1.03030i | ||||
\(516\) | −199011. | − | 114899.i | −0.747442 | − | 0.431536i | ||||
\(517\) | − | 126544.i | − | 0.473434i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −312021. | −1.15837 | ||||||||
\(520\) | 404860. | − | 701238.i | 1.49726 | − | 2.59333i | ||||
\(521\) | −206209. | + | 119055.i | −0.759683 | + | 0.438603i | −0.829182 | − | 0.558979i | \(-0.811193\pi\) |
0.0694987 | + | 0.997582i | \(0.477860\pi\) | |||||||
\(522\) | 56718.0 | + | 98238.5i | 0.208152 | + | 0.360529i | ||||
\(523\) | 172592. | + | 99646.0i | 0.630982 | + | 0.364298i | 0.781132 | − | 0.624366i | \(-0.214642\pi\) |
−0.150150 | + | 0.988663i | \(0.547976\pi\) | |||||||
\(524\) | − | 8892.23i | − | 0.0323853i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20070.3 | 0.0725406 | ||||||||
\(527\) | 24449.1 | − | 42347.1i | 0.0880322 | − | 0.152476i | ||||
\(528\) | −91355.9 | + | 52744.4i | −0.327694 | + | 0.189194i | ||||
\(529\) | 7388.68 | + | 12797.6i | 0.0264032 | + | 0.0457316i | ||||
\(530\) | −177198. | − | 102305.i | −0.630822 | − | 0.364205i | ||||
\(531\) | 90705.8i | 0.321696i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31982.4 | 0.112579 | ||||||||
\(534\) | 96141.4 | − | 166522.i | 0.337154 | − | 0.583967i | ||||
\(535\) | −404476. | + | 233524.i | −1.41314 | + | 0.815876i | ||||
\(536\) | 250440. | + | 433775.i | 0.871714 | + | 1.50985i | ||||
\(537\) | −328586. | − | 189709.i | −1.13946 | − | 0.657869i | ||||
\(538\) | − | 328098.i | − | 1.13354i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 569386. | 1.95263 | ||||||||
\(541\) | −139832. | + | 242195.i | −0.477761 | + | 0.827506i | −0.999675 | − | 0.0254918i | \(-0.991885\pi\) |
0.521914 | + | 0.852998i | \(0.325218\pi\) | |||||||
\(542\) | 354524. | − | 204685.i | 1.20683 | − | 0.696766i | ||||
\(543\) | −187656. | − | 325030.i | −0.636448 | − | 1.10236i | ||||
\(544\) | −12418.4 | − | 7169.79i | −0.0419632 | − | 0.0242275i | ||||
\(545\) | 177429.i | 0.597353i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 322945. | 1.07933 | 0.539664 | − | 0.841881i | \(-0.318551\pi\) | ||||
0.539664 | + | 0.841881i | \(0.318551\pi\) | |||||||
\(548\) | 135031. | − | 233881.i | 0.449649 | − | 0.778814i | ||||
\(549\) | 6375.55 | − | 3680.92i | 0.0211530 | − | 0.0122127i | ||||
\(550\) | 21998.3 | + | 38102.1i | 0.0727215 | + | 0.125957i | ||||
\(551\) | 209217. | + | 120792.i | 0.689119 | + | 0.397863i | ||||
\(552\) | − | 479180.i | − | 1.57261i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −416795. | −1.35801 | ||||||||
\(555\) | −168828. | + | 292419.i | −0.548099 | + | 0.949336i | ||||
\(556\) | 332198. | − | 191795.i | 1.07460 | − | 0.620422i | ||||
\(557\) | 204004. | + | 353346.i | 0.657551 | + | 1.13891i | 0.981248 | + | 0.192751i | \(0.0617408\pi\) |
−0.323697 | + | 0.946161i | \(0.604926\pi\) | |||||||
\(558\) | −77509.7 | − | 44750.2i | −0.248936 | − | 0.143723i | ||||
\(559\) | 276325.i | 0.884292i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25276.7 | −0.0803145 | ||||||||
\(562\) | −165577. | + | 286788.i | −0.524237 | + | 0.908006i | ||||
\(563\) | 502811. | − | 290298.i | 1.58631 | − | 0.915856i | 0.592401 | − | 0.805643i | \(-0.298180\pi\) |
0.993908 | − | 0.110213i | \(-0.0351533\pi\) | |||||||
\(564\) | 366606. | + | 634980.i | 1.15250 | + | 1.99619i | ||||
\(565\) | 86989.2 | + | 50223.3i | 0.272501 | + | 0.157329i | ||||
\(566\) | − | 661733.i | − | 2.06562i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −140239. | −0.434682 | ||||||||
\(569\) | −168768. | + | 292314.i | −0.521273 | + | 0.902870i | 0.478421 | + | 0.878130i | \(0.341209\pi\) |
−0.999694 | + | 0.0247401i | \(0.992124\pi\) | |||||||
\(570\) | 293276. | − | 169323.i | 0.902665 | − | 0.521154i | ||||
\(571\) | −109154. | − | 189060.i | −0.334786 | − | 0.579866i | 0.648658 | − | 0.761080i | \(-0.275331\pi\) |
−0.983444 | + | 0.181214i | \(0.941997\pi\) | |||||||
\(572\) | 397508. | + | 229501.i | 1.21494 | + | 0.701444i | ||||
\(573\) | − | 77533.2i | − | 0.236145i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −72376.9 | −0.218909 | ||||||||
\(576\) | 31631.9 | − | 54788.0i | 0.0953410 | − | 0.165136i | ||||
\(577\) | 197760. | − | 114177.i | 0.594001 | − | 0.342947i | −0.172677 | − | 0.984978i | \(-0.555242\pi\) |
0.766678 | + | 0.642032i | \(0.221908\pi\) | |||||||
\(578\) | 274045. | + | 474660.i | 0.820289 | + | 1.42078i | ||||
\(579\) | −66523.5 | − | 38407.3i | −0.198435 | − | 0.114566i | ||||
\(580\) | 626649.i | 1.86281i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −438079. | −1.29332 | ||||||||
\(583\) | 29766.0 | − | 51556.2i | 0.0875755 | − | 0.151685i | ||||
\(584\) | 21.9175 | − | 12.6541i | 6.42636e−5 | − | 3.71026e-5i | ||||
\(585\) | −64304.3 | − | 111378.i | −0.187901 | − | 0.325453i | ||||
\(586\) | 445162. | + | 257015.i | 1.29635 | + | 0.748450i | ||||
\(587\) | − | 235281.i | − | 0.682827i | −0.939913 | − | 0.341413i | \(-0.889094\pi\) | ||
0.939913 | − | 0.341413i | \(-0.110906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −190608. | −0.549427 | ||||||||
\(590\) | −372488. | + | 645168.i | −1.07006 | + | 1.85340i | ||||
\(591\) | −396620. | + | 228989.i | −1.13553 | + | 0.655600i | ||||
\(592\) | −290287. | − | 502792.i | −0.828293 | − | 1.43465i | ||||
\(593\) | −48847.7 | − | 28202.2i | −0.138910 | − | 0.0802000i | 0.428934 | − | 0.903336i | \(-0.358889\pi\) |
−0.567845 | + | 0.823136i | \(0.692223\pi\) | |||||||
\(594\) | 246299.i | 0.698054i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 930531. | 2.61962 | ||||||||
\(597\) | 246850. | − | 427557.i | 0.692604 | − | 1.19962i | ||||
\(598\) | −972213. | + | 561307.i | −2.71869 | + | 1.56963i | ||||
\(599\) | −54321.5 | − | 94087.6i | −0.151397 | − | 0.262228i | 0.780344 | − | 0.625350i | \(-0.215044\pi\) |
−0.931741 | + | 0.363123i | \(0.881711\pi\) | |||||||
\(600\) | −113313. | − | 65421.2i | −0.314758 | − | 0.181726i | ||||
\(601\) | − | 11012.9i | − | 0.0304897i | −0.999884 | − | 0.0152448i | \(-0.995147\pi\) | ||
0.999884 | − | 0.0152448i | \(-0.00485277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 79555.2 | 0.218793 | ||||||||
\(604\) | −363816. | + | 630147.i | −0.997258 | + | 1.72730i | ||||
\(605\) | −240869. | + | 139066.i | −0.658067 | + | 0.379935i | ||||
\(606\) | −15913.1 | − | 27562.4i | −0.0433322 | − | 0.0750535i | ||||
\(607\) | 165640. | + | 95632.6i | 0.449561 | + | 0.259554i | 0.707645 | − | 0.706568i | \(-0.249758\pi\) |
−0.258084 | + | 0.966123i | \(0.583091\pi\) | |||||||
\(608\) | 55896.4i | 0.151209i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 60463.6 | 0.162493 | ||||||||
\(611\) | 440832. | − | 763543.i | 1.18084 | − | 2.04527i | ||||
\(612\) | −38161.3 | + | 22032.4i | −0.101887 | + | 0.0588247i | ||||
\(613\) | −155499. | − | 269332.i | −0.413816 | − | 0.716749i | 0.581488 | − | 0.813555i | \(-0.302471\pi\) |
−0.995303 | + | 0.0968056i | \(0.969137\pi\) | |||||||
\(614\) | 713515. | + | 411948.i | 1.89263 | + | 1.09271i | ||||
\(615\) | 17808.2i | 0.0470837i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 452960. | 1.18984 | 0.594922 | − | 0.803784i | \(-0.297183\pi\) | ||||
0.594922 | + | 0.803784i | \(0.297183\pi\) | |||||||
\(618\) | 395424. | − | 684895.i | 1.03535 | − | 1.79328i | ||||
\(619\) | 605159. | − | 349389.i | 1.57939 | − | 0.911859i | 0.584441 | − | 0.811436i | \(-0.301314\pi\) |
0.994945 | − | 0.100423i | \(-0.0320195\pi\) | |||||||
\(620\) | −247212. | − | 428183.i | −0.643110 | − | 1.11390i | ||||
\(621\) | −350893. | − | 202588.i | −0.909895 | − | 0.525328i | ||||
\(622\) | − | 30197.2i | − | 0.0780524i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −734968. | −1.88755 | ||||||||
\(625\) | 141500. | − | 245085.i | 0.362239 | − | 0.627417i | ||||
\(626\) | −722098. | + | 416903.i | −1.84267 | + | 1.06387i | ||||
\(627\) | 49264.9 | + | 85329.3i | 0.125315 | + | 0.217052i | ||||
\(628\) | −1.26146e6 | − | 728307.i | −3.19857 | − | 1.84670i | ||||
\(629\) | − | 139114.i | − | 0.351617i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −401495. | −1.00837 | −0.504187 | − | 0.863595i | \(-0.668208\pi\) | ||||
−0.504187 | + | 0.863595i | \(0.668208\pi\) | |||||||
\(632\) | −93119.5 | + | 161288.i | −0.233134 | + | 0.403801i | ||||
\(633\) | −182284. | + | 105242.i | −0.454927 | + | 0.262652i | ||||
\(634\) | −48931.1 | − | 84751.1i | −0.121732 | − | 0.210847i | ||||
\(635\) | −413855. | − | 238940.i | −1.02636 | − | 0.592571i | ||||
\(636\) | 344936.i | 0.852756i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −271069. | −0.665946 | ||||||||
\(639\) | −11137.2 | + | 19290.1i | −0.0272755 | + | 0.0472425i | ||||
\(640\) | 511097. | − | 295082.i | 1.24780 | − | 0.720415i | ||||
\(641\) | −368465. | − | 638201.i | −0.896769 | − | 1.55325i | −0.831599 | − | 0.555376i | \(-0.812574\pi\) |
−0.0651699 | − | 0.997874i | \(-0.520759\pi\) | |||||||
\(642\) | 1.01376e6 | + | 585297.i | 2.45961 | + | 1.42006i | ||||
\(643\) | − | 328825.i | − | 0.795323i | −0.917532 | − | 0.397661i | \(-0.869822\pi\) | ||
0.917532 | − | 0.397661i | \(-0.130178\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −153862. | −0.369837 | ||||||||
\(646\) | −69760.8 | + | 120829.i | −0.167166 | + | 0.289539i | ||||
\(647\) | −503584. | + | 290745.i | −1.20299 | + | 0.694549i | −0.961220 | − | 0.275783i | \(-0.911063\pi\) |
−0.241775 | + | 0.970332i | \(0.577729\pi\) | |||||||
\(648\) | −276744. | − | 479335.i | −0.659066 | − | 1.14154i | ||||
\(649\) | −187713. | − | 108376.i | −0.445662 | − | 0.257303i | ||||
\(650\) | 306535.i | 0.725527i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −842238. | −1.98125 | ||||||||
\(653\) | −298234. | + | 516556.i | −0.699407 | + | 1.21141i | 0.269265 | + | 0.963066i | \(0.413219\pi\) |
−0.968672 | + | 0.248343i | \(0.920114\pi\) | |||||||
\(654\) | 385123. | − | 222351.i | 0.900417 | − | 0.519856i | ||||
\(655\) | −2976.90 | − | 5156.15i | −0.00693876 | − | 0.0120183i | ||||
\(656\) | −26517.6 | − | 15309.9i | −0.0616207 | − | 0.0355767i | ||||
\(657\) | − | 4.01971i | − | 9.31246e-6i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −82075.1 | −0.188991 | −0.0944954 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944954 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(660\) | −127790. | + | 221338.i | −0.293365 | + | 0.508123i | ||||
\(661\) | −133678. | + | 77179.0i | −0.305955 | + | 0.176643i | −0.645115 | − | 0.764086i | \(-0.723190\pi\) |
0.339160 | + | 0.940729i | \(0.389857\pi\) | |||||||
\(662\) | 107495. | + | 186186.i | 0.245285 | + | 0.424846i | ||||
\(663\) | −152515. | − | 88054.6i | −0.346965 | − | 0.200320i | ||||
\(664\) | 1.06819e6i | 2.42277i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −254627. | −0.574057 | ||||||||
\(667\) | 222963. | − | 386182.i | 0.501164 | − | 0.868042i | ||||
\(668\) | −165747. | + | 95694.3i | −0.371444 | + | 0.214454i | ||||
\(669\) | 83981.5 | + | 145460.i | 0.187643 | + | 0.325007i | ||||
\(670\) | 565857. | + | 326698.i | 1.26054 | + | 0.727774i | ||||
\(671\) | 17592.0i | 0.0390725i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 675260. | 1.49087 | 0.745437 | − | 0.666576i | \(-0.232241\pi\) | ||||
0.745437 | + | 0.666576i | \(0.232241\pi\) | |||||||
\(674\) | −78286.1 | + | 135595.i | −0.172332 | + | 0.298487i | ||||
\(675\) | −95813.0 | + | 55317.7i | −0.210289 | + | 0.121411i | ||||
\(676\) | 1.12957e6 | + | 1.95647e6i | 2.47183 | + | 4.28134i | ||||
\(677\) | −180907. | − | 104447.i | −0.394710 | − | 0.227886i | 0.289489 | − | 0.957181i | \(-0.406515\pi\) |
−0.684199 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(678\) | − | 251756.i | − | 0.547671i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −185755. | −0.401720 | ||||||||
\(681\) | −85094.9 | + | 147389.i | −0.183489 | + | 0.317812i | ||||
\(682\) | 185219. | − | 106936.i | 0.398214 | − | 0.229909i | ||||
\(683\) | 21159.8 | + | 36649.9i | 0.0453598 | + | 0.0785655i | 0.887814 | − | 0.460203i | \(-0.152223\pi\) |
−0.842454 | + | 0.538768i | \(0.818890\pi\) | |||||||
\(684\) | 148755. | + | 85883.6i | 0.317950 | + | 0.183569i | ||||
\(685\) | − | 180821.i | − | 0.385360i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 157205. | 0.333083 | ||||||||
\(688\) | 132276. | − | 229109.i | 0.279451 | − | 0.484023i | ||||
\(689\) | 359205. | − | 207387.i | 0.756666 | − | 0.436862i | ||||
\(690\) | −312544. | − | 541342.i | −0.656467 | − | 1.13703i | ||||
\(691\) | −20361.7 | − | 11755.8i | −0.0426439 | − | 0.0246205i | 0.478526 | − | 0.878073i | \(-0.341171\pi\) |
−0.521170 | + | 0.853453i | \(0.674504\pi\) | |||||||
\(692\) | − | 1.29983e6i | − | 2.71440i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.49467e6 | 3.10331 | ||||||||
\(695\) | 128416. | − | 222424.i | 0.265859 | − | 0.460481i | ||||
\(696\) | 698137. | − | 403070.i | 1.44119 | − | 0.832074i | ||||
\(697\) | −3668.49 | − | 6354.01i | −0.00755130 | − | 0.0130792i | ||||
\(698\) | −385489. | − | 222562.i | −0.791227 | − | 0.456815i | ||||
\(699\) | − | 31783.2i | − | 0.0650495i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −161942. | −0.329552 | −0.164776 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164776 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(702\) | −858014. | + | 1.48612e6i | −1.74109 | + | 3.01565i | ||||
\(703\) | −469623. | + | 271137.i | −0.950253 | + | 0.548629i | ||||
\(704\) | 75588.2 | + | 130923.i | 0.152514 | + | 0.264161i | ||||
\(705\) | 425152. | + | 245462.i | 0.855394 | + | 0.493862i | ||||
\(706\) | − | 984240.i | − | 1.97466i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.25589e6 | 2.50546 | ||||||||
\(709\) | −30803.0 | + | 53352.3i | −0.0612774 | + | 0.106136i | −0.895037 | − | 0.445993i | \(-0.852851\pi\) |
0.833759 | + | 0.552128i | \(0.186184\pi\) | |||||||
\(710\) | −158432. | + | 91470.6i | −0.314286 | + | 0.181453i | ||||
\(711\) | 14790.3 | + | 25617.5i | 0.0292575 | + | 0.0506754i | ||||
\(712\) | 356053. | + | 205567.i | 0.702351 | + | 0.405502i | ||||
\(713\) | 351833.i | 0.692081i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 307326. | 0.601156 | ||||||||
\(716\) | 790296. | − | 1.36883e6i | 1.54157 | − | 2.67008i | ||||
\(717\) | −241374. | + | 139358.i | −0.469519 | + | 0.271077i | ||||
\(718\) | −128510. | − | 222586.i | −0.249280 | − | 0.431766i | ||||
\(719\) | 209510. | + | 120961.i | 0.405272 | + | 0.233984i | 0.688756 | − | 0.724993i | \(-0.258157\pi\) |
−0.283484 | + | 0.958977i | \(0.591490\pi\) | |||||||
\(720\) | 123130.i | 0.237519i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −367192. | −0.704400 | ||||||||
\(723\) | 312619. | − | 541471.i | 0.598051 | − | 1.03585i | ||||
\(724\) | 1.35402e6 | − | 781744.i | 2.58314 | − | 1.49138i | ||||
\(725\) | −60881.0 | − | 105449.i | −0.115826 | − | 0.200616i | ||||
\(726\) | 603706. | + | 348550.i | 1.14539 | + | 0.661289i | ||||
\(727\) | − | 75734.6i | − | 0.143293i | −0.997430 | − | 0.0716466i | \(-0.977175\pi\) | ||
0.997430 | − | 0.0716466i | \(-0.0228254\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −590924. | −1.11193 | ||||||||
\(730\) | 16.5072 | − | 28.5913i | 3.09761e−5 | − | 5.36522e-5i | ||||
\(731\) | 54898.0 | − | 31695.4i | 0.102736 | − | 0.0593146i | ||||
\(732\) | −50965.3 | − | 88274.5i | −0.0951158 | − | 0.164745i | ||||
\(733\) | −302681. | − | 174753.i | −0.563349 | − | 0.325250i | 0.191140 | − | 0.981563i | \(-0.438782\pi\) |
−0.754489 | + | 0.656313i | \(0.772115\pi\) | |||||||
\(734\) | 173151.i | 0.321390i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 103176. | 0.190469 | ||||||||
\(737\) | −95053.5 | + | 164637.i | −0.174998 | + | 0.303105i | ||||
\(738\) | −11630.0 | + | 6714.59i | −0.0213534 | + | 0.0123284i | ||||
\(739\) | 434781. | + | 753064.i | 0.796127 | + | 1.37893i | 0.922121 | + | 0.386901i | \(0.126454\pi\) |
−0.125995 | + | 0.992031i | \(0.540212\pi\) | |||||||
\(740\) | −1.21817e6 | − | 703311.i | −2.22456 | − | 1.28435i | ||||
\(741\) | 686483.i | 1.25024i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 95108.3 | 0.172282 | 0.0861412 | − | 0.996283i | \(-0.472546\pi\) | ||||
0.0861412 | + | 0.996283i | \(0.472546\pi\) | |||||||
\(744\) | −318020. | + | 550827.i | −0.574525 | + | 0.995106i | ||||
\(745\) | 539567. | − | 311519.i | 0.972149 | − | 0.561271i | ||||
\(746\) | −112527. | − | 194902.i | −0.202199 | − | 0.350219i | ||||
\(747\) | 146931. | + | 84830.9i | 0.263314 | + | 0.152024i | ||||
\(748\) | − | 105298.i | − | 0.188199i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −929516. | −1.65247 | ||||||||
\(751\) | −376603. | + | 652296.i | −0.667735 | + | 1.15655i | 0.310801 | + | 0.950475i | \(0.399403\pi\) |
−0.978536 | + | 0.206076i | \(0.933931\pi\) | |||||||
\(752\) | −731015. | + | 422052.i | −1.29268 | + | 0.746329i | ||||
\(753\) | 397492. | + | 688476.i | 0.701033 | + | 1.21422i | ||||
\(754\) | −1.63558e6 | − | 944305.i | −2.87694 | − | 1.66100i | ||||
\(755\) | 487187.i | 0.854676i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −293022. | −0.511338 | −0.255669 | − | 0.966764i | \(-0.582296\pi\) | ||||
−0.255669 | + | 0.966764i | \(0.582296\pi\) | |||||||
\(758\) | 655450. | − | 1.13527e6i | 1.14078 | − | 1.97589i | ||||
\(759\) | 157505. | − | 90935.4i | 0.273407 | − | 0.157852i | ||||
\(760\) | 362042. | + | 627075.i | 0.626804 | + | 1.08566i | ||||
\(761\) | 451698. | + | 260788.i | 0.779972 | + | 0.450317i | 0.836420 | − | 0.548088i | \(-0.184644\pi\) |
−0.0564483 | + | 0.998406i | \(0.517978\pi\) | |||||||
\(762\) | 1.19774e6i | 2.06278i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 322990. | 0.553354 | ||||||||
\(765\) | −14751.8 | + | 25551.0i | −0.0252071 | + | 0.0436600i | ||||
\(766\) | 155234. | − | 89624.2i | 0.264562 | − | 0.152745i | ||||
\(767\) | −755086. | − | 1.30785e6i | −1.28353 | − | 2.22314i | ||||
\(768\) | −911767. | − | 526409.i | −1.54583 | − | 0.892485i | ||||
\(769\) | 920553.i | 1.55667i | 0.627850 | + | 0.778334i | \(0.283935\pi\) | ||||
−0.627850 | + | 0.778334i | \(0.716065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 386822. | 0.650732 | ||||||||
\(772\) | 159999. | − | 277126.i | 0.268461 | − | 0.464988i | ||||
\(773\) | 395771. | − | 228498.i | 0.662346 | − | 0.382406i | −0.130824 | − | 0.991406i | \(-0.541762\pi\) |
0.793170 | + | 0.609000i | \(0.208429\pi\) | |||||||
\(774\) | −58013.4 | − | 100482.i | −0.0968381 | − | 0.167729i | ||||
\(775\) | 83198.7 | + | 48034.8i | 0.138520 | + | 0.0799747i | ||||
\(776\) | − | 936690.i | − | 1.55551i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −506530. | −0.836846 | ||||||||
\(779\) | −14300.0 | + | 24768.3i | −0.0235646 | + | 0.0408151i | ||||
\(780\) | −1.54212e6 | + | 890344.i | −2.53472 | + | 1.46342i | ||||
\(781\) | −26613.6 | − | 46096.1i | −0.0436316 | − | 0.0755721i | ||||
\(782\) | 223032. | + | 128768.i | 0.364716 | + | 0.210569i | ||||
\(783\) | − | 681641.i | − | 1.11181i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −975278. | −1.58267 | ||||||||
\(786\) | −7461.21 | + | 12923.2i | −0.0120771 | + | 0.0209182i | ||||
\(787\) | 282970. | − | 163373.i | 0.456868 | − | 0.263773i | −0.253859 | − | 0.967241i | \(-0.581700\pi\) |
0.710726 | + | 0.703469i | \(0.248366\pi\) | |||||||
\(788\) | −953928. | − | 1.65225e6i | −1.53626 | − | 2.66087i | ||||
\(789\) | −19619.1 | − | 11327.1i | −0.0315155 | − | 0.0181955i | ||||
\(790\) | 242948.i | 0.389277i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −98922.5 | −0.157705 | ||||||||
\(793\) | −61284.2 | + | 106147.i | −0.0974545 | + | 0.168796i | ||||
\(794\) | −772531. | + | 446021.i | −1.22539 | + | 0.707481i | ||||
\(795\) | 115476. | + | 200011.i | 0.182708 | + | 0.316460i | ||||
\(796\) | 1.78113e6 | + | 1.02834e6i | 2.81106 | + | 1.62297i | ||||
\(797\) | − | 580079.i | − | 0.913210i | −0.889669 | − | 0.456605i | \(-0.849065\pi\) | ||
0.889669 | − | 0.456605i | \(-0.150935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −202260. | −0.316823 | ||||||||
\(800\) | 14086.4 | − | 24398.3i | 0.0220100 | − | 0.0381224i | ||||
\(801\) | 56552.2 | − | 32650.4i | 0.0881423 | − | 0.0508890i | ||||
\(802\) | −483941. | − | 838210.i | −0.752391 | − | 1.30318i | ||||
\(803\) | 8.31869 | + | 4.80280i | 1.29010e−5 | + | 7.44840e-6i | ||||
\(804\) | − | 1.10151e6i | − | 1.70402i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.49010e6 | 2.29375 | ||||||||
\(807\) | −185169. | + | 320722.i | −0.284329 | + | 0.492472i | ||||
\(808\) | 58933.1 | − | 34025.1i | 0.0902686 | − | 0.0521166i | ||||
\(809\) | 402559. | + | 697253.i | 0.615081 | + | 1.06535i | 0.990370 | + | 0.138444i | \(0.0442101\pi\) |
−0.375289 | + | 0.926908i | \(0.622457\pi\) | |||||||
\(810\) | −625291. | − | 361012.i | −0.953042 | − | 0.550239i | ||||
\(811\) | − | 633160.i | − | 0.962657i | −0.876540 | − | 0.481328i | \(-0.840154\pi\) | ||
0.876540 | − | 0.481328i | \(-0.159846\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −462072. | −0.699083 | ||||||||
\(814\) | 304231. | − | 526943.i | 0.459149 | − | 0.795270i | ||||
\(815\) | −488370. | + | 281961.i | −0.735249 | + | 0.424496i | ||||
\(816\) | 84303.4 | + | 146018.i | 0.126609 | + | 0.219293i | ||||
\(817\) | −213995. | − | 123550.i | −0.320598 | − | 0.185097i | ||||
\(818\) | 536455.i | 0.801728i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −74186.2 | −0.110330 | ||||||||
\(821\) | −307818. | + | 533156.i | −0.456675 | + | 0.790984i | −0.998783 | − | 0.0493246i | \(-0.984293\pi\) |
0.542108 | + | 0.840309i | \(0.317626\pi\) | |||||||
\(822\) | −392485. | + | 226601.i | −0.580871 | + | 0.335366i | ||||
\(823\) | −64378.0 | − | 111506.i | −0.0950469 | − | 0.164626i | 0.814581 | − | 0.580049i | \(-0.196967\pi\) |
−0.909628 | + | 0.415423i | \(0.863633\pi\) | |||||||
\(824\) | 1.46443e6 | + | 845487.i | 2.15682 | + | 1.24524i | ||||
\(825\) | − | 49660.7i | − | 0.0729634i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.05631e6 | 1.54447 | 0.772235 | − | 0.635337i | \(-0.219139\pi\) | ||||
0.772235 | + | 0.635337i | \(0.219139\pi\) | |||||||
\(828\) | 158528. | − | 274578.i | 0.231231 | − | 0.400503i | ||||
\(829\) | 547883. | − | 316320.i | 0.797221 | − | 0.460276i | −0.0452777 | − | 0.998974i | \(-0.514417\pi\) |
0.842498 | + | 0.538699i | \(0.181084\pi\) | |||||||
\(830\) | 696725. | + | 1.20676e6i | 1.01136 | + | 1.75172i | ||||
\(831\) | 407425. | + | 235227.i | 0.589991 | + | 0.340631i | ||||
\(832\) | 1.05329e6i | 1.52160i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −643717. | −0.925471 | ||||||||
\(835\) | −64072.3 | + | 110976.i | −0.0918961 | + | 0.159169i | ||||
\(836\) | −355468. | + | 205229.i | −0.508613 | + | 0.293648i | ||||
\(837\) | 268906. | + | 465758.i | 0.383839 | + | 0.664829i | ||||
\(838\) | 1.08921e6 | + | 628858.i | 1.55105 | + | 0.895498i | ||||
\(839\) | − | 249268.i | − | 0.354114i | −0.984201 | − | 0.177057i | \(-0.943342\pi\) | ||
0.984201 | − | 0.177057i | \(-0.0566577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42913.2 | 0.0606735 | ||||||||
\(842\) | −21372.6 | + | 37018.5i | −0.0301463 | + | 0.0522149i | ||||
\(843\) | 323710. | − | 186894.i | 0.455513 | − | 0.262991i | ||||
\(844\) | −438420. | − | 759365.i | −0.615468 | − | 1.06602i | ||||
\(845\) | 1.30996e6 | + | 756303.i | 1.83461 | + | 1.05921i | ||||
\(846\) | 370205.i | 0.517251i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −397105. | −0.552222 | ||||||||
\(849\) | −373463. | + | 646857.i | −0.518122 | + | 0.897414i | ||||
\(850\) | 60900.1 | − | 35160.7i | 0.0842907 | − | 0.0486653i | ||||
\(851\) | 500478. | + | 866852.i | 0.691075 | + | 1.19698i | ||||
\(852\) | 267087. | + | 154203.i | 0.367937 | + | 0.212429i | ||||
\(853\) | 1.16100e6i | 1.59564i | 0.602898 | + | 0.797818i | \(0.294012\pi\) | ||||
−0.602898 | + | 0.797818i | \(0.705988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 115007. | 0.157323 | ||||||||
\(856\) | −1.25147e6 | + | 2.16760e6i | −1.70794 | + | 2.95823i | ||||
\(857\) | −191594. | + | 110617.i | −0.260867 | + | 0.150612i | −0.624730 | − | 0.780841i | \(-0.714791\pi\) |
0.363863 | + | 0.931453i | \(0.381458\pi\) | |||||||
\(858\) | −385135. | − | 667074.i | −0.523165 | − | 0.906149i | ||||
\(859\) | −989322. | − | 571185.i | −1.34076 | − | 0.774089i | −0.353842 | − | 0.935305i | \(-0.615125\pi\) |
−0.986919 | + | 0.161217i | \(0.948458\pi\) | |||||||
\(860\) | − | 640962.i | − | 0.866633i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.57501e6 | −2.11967 | ||||||||
\(863\) | −560434. | + | 970701.i | −0.752494 | + | 1.30336i | 0.194117 | + | 0.980978i | \(0.437816\pi\) |
−0.946611 | + | 0.322379i | \(0.895517\pi\) | |||||||
\(864\) | 136585. | − | 78857.6i | 0.182969 | − | 0.105637i | ||||
\(865\) | −435150. | − | 753702.i | −0.581577 | − | 1.00732i | ||||
\(866\) | −1.76390e6 | − | 1.01839e6i | −2.35201 | − | 1.35793i | ||||
\(867\) | − | 618653.i | − | 0.823017i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −70686.2 | −0.0936042 | ||||||||
\(870\) | 525803. | − | 910717.i | 0.694680 | − | 1.20322i | ||||
\(871\) | −1.14707e6 | + | 662263.i | −1.51201 | + | 0.872959i | ||||
\(872\) | 475425. | + | 823460.i | 0.625243 | + | 1.08295i | ||||
\(873\) | −128843. | − | 74387.7i | −0.169057 | − | 0.0976051i | ||||
\(874\) | − | 1.00389e6i | − | 1.31420i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −55.6562 | −7.25279e−5 | ||||||||
\(877\) | 367056. | − | 635760.i | 0.477236 | − | 0.826598i | −0.522423 | − | 0.852686i | \(-0.674972\pi\) |
0.999660 | + | 0.0260885i | \(0.00830518\pi\) | |||||||
\(878\) | 1.63978e6 | − | 946727.i | 2.12714 | − | 1.22811i | ||||
\(879\) | −290103. | − | 502473.i | −0.375470 | − | 0.650332i | ||||
\(880\) | −254814. | − | 147117.i | −0.329046 | − | 0.189975i | ||||
\(881\) | − | 567852.i | − | 0.731616i | −0.930690 | − | 0.365808i | \(-0.880793\pi\) | ||
0.930690 | − | 0.365808i | \(-0.119207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40795.8 | 0.0523232 | 0.0261616 | − | 0.999658i | \(-0.491672\pi\) | ||||
0.0261616 | + | 0.999658i | \(0.491672\pi\) | |||||||
\(884\) | 366821. | − | 635352.i | 0.469407 | − | 0.813037i | ||||
\(885\) | 728229. | − | 420443.i | 0.929782 | − | 0.536810i | ||||
\(886\) | 220856. | + | 382534.i | 0.281347 | + | 0.487307i | ||||
\(887\) | 120455. | + | 69544.4i | 0.153100 | + | 0.0883925i | 0.574593 | − | 0.818439i | \(-0.305160\pi\) |
−0.421493 | + | 0.906832i | \(0.638494\pi\) | |||||||
\(888\) | 1.80952e6i | 2.29476i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 536323. | 0.677090 | ||||||||
\(891\) | 105037. | − | 181930.i | 0.132309 | − | 0.229165i | ||||
\(892\) | −605963. | + | 349853.i | −0.761582 | + | 0.439700i | ||||
\(893\) | 394210. | + | 682791.i | 0.494339 | + | 0.856220i | ||||
\(894\) | −1.35235e6 | − | 780781.i | −1.69206 | − | 0.976909i | ||||
\(895\) | − | 1.05829e6i | − | 1.32117i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.26714e6 | 1.57485 | ||||||||
\(898\) | 1.14982e6 | − | 1.99155e6i | 1.42587 | − | 2.46967i | ||||
\(899\) | −512600. | + | 295950.i | −0.634248 | + | 0.366183i | ||||
\(900\) | −43286.8 | − | 74975.0i | −0.0534405 | − | 0.0925617i | ||||
\(901\) | −82404.2 | − | 47576.1i | −0.101508 | − | 0.0586056i | ||||
\(902\) | − | 32090.7i | − | 0.0394426i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 538298. | 0.658697 | ||||||||
\(905\) | 523418. | − | 906587.i | 0.639075 | − | 1.10691i | ||||
\(906\) | 1.05748e6 | − | 610534.i | 1.28829 | − | 0.743795i | ||||
\(907\) | −371706. | − | 643813.i | −0.451840 | − | 0.782610i | 0.546661 | − | 0.837354i | \(-0.315899\pi\) |
−0.998500 | + | 0.0547448i | \(0.982565\pi\) | |||||||
\(908\) | −613997. | − | 354491.i | −0.744723 | − | 0.429966i | ||||
\(909\) | − | 10808.5i | − | 0.0130809i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −549043. | −0.661560 | −0.330780 | − | 0.943708i | \(-0.607312\pi\) | ||||
−0.330780 | + | 0.943708i | \(0.607312\pi\) | |||||||
\(912\) | 328619. | − | 569185.i | 0.395096 | − | 0.684327i | ||||
\(913\) | −351110. | + | 202714.i | −0.421213 | + | 0.243188i | ||||
\(914\) | −109153. | − | 189059.i | −0.130660 | − | 0.226310i | ||||
\(915\) | −59104.3 | − | 34123.9i | −0.0705955 | − | 0.0407583i | ||||
\(916\) | 654888.i | 0.780506i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 393669. | 0.467138 | ||||||||
\(919\) | 820048. | − | 1.42037e6i | 0.970976 | − | 1.68178i | 0.278354 | − | 0.960479i | \(-0.410211\pi\) |
0.692622 | − | 0.721301i | \(-0.256455\pi\) | |||||||
\(920\) | 1.15748e6 | − | 668274.i | 1.36754 | − | 0.789548i | ||||
\(921\) | −464983. | − | 805375.i | −0.548174 | − | 0.949464i | ||||
\(922\) | −1.16905e6 | − | 674949.i | −1.37521 | − | 0.793979i | ||||
\(923\) | − | 370848.i | − | 0.435303i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 273316. | 0.319434 | ||||||||
\(926\) | −862207. | + | 1.49339e6i | −1.00552 | + | 1.74161i | ||||
\(927\) | 232596. | − | 134290.i | 0.270672 | − | 0.156273i | ||||
\(928\) | 86788.3 | + | 150322.i | 0.100778 | + | 0.174552i | ||||
\(929\) | 942167. | + | 543960.i | 1.09168 | + | 0.630283i | 0.934024 | − | 0.357210i | \(-0.116272\pi\) |
0.157659 | + | 0.987494i | \(0.449605\pi\) | |||||||
\(930\) | 829712.i | 0.959315i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 132404. | 0.152429 | ||||||||
\(933\) | −17042.4 | + | 29518.4i | −0.0195780 | + | 0.0339101i | ||||
\(934\) | −2.02265e6 | + | 1.16778e6i | −2.31860 | + | 1.33865i | ||||
\(935\) | −35251.3 | − | 61057.1i | −0.0403230 | − | 0.0698414i | ||||
\(936\) | −596882. | − | 344610.i | −0.681297 | − | 0.393347i | ||||
\(937\) | 347157.i | 0.395409i | 0.980262 | + | 0.197704i | \(0.0633486\pi\) | ||||
−0.980262 | + | 0.197704i | \(0.936651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 941152. | 1.06740 | ||||||||
\(940\) | −1.02255e6 | + | 1.77111e6i | −1.15726 | + | 2.00443i | ||||
\(941\) | 144915. | − | 83666.7i | 0.163657 | − | 0.0944873i | −0.415935 | − | 0.909395i | \(-0.636545\pi\) |
0.579591 | + | 0.814907i | \(0.303212\pi\) | |||||||
\(942\) | 1.22220e6 | + | 2.11692e6i | 1.37734 | + | 2.38562i | ||||
\(943\) | 45718.4 | + | 26395.5i | 0.0514124 | + | 0.0296830i | ||||
\(944\) | 1.44584e6i | 1.62247i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 277260. | 0.309817 | ||||||||
\(947\) | 263561. | − | 456501.i | 0.293887 | − | 0.509028i | −0.680838 | − | 0.732434i | \(-0.738384\pi\) |
0.974725 | + | 0.223406i | \(0.0717176\pi\) | |||||||
\(948\) | 354695. | − | 204783.i | 0.394673 | − | 0.227865i | ||||
\(949\) | 33.4624 | + | 57.9585i | 3.71556e−5 | + | 6.43554e-5i | ||||
\(950\) | −237392. | − | 137058.i | −0.263038 | − | 0.151865i | ||||
\(951\) | 110461.i | 0.122137i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.67904e6 | −1.84873 | −0.924366 | − | 0.381506i | \(-0.875406\pi\) | ||||
−0.924366 | + | 0.381506i | \(0.875406\pi\) | |||||||
\(954\) | −87080.5 | + | 150828.i | −0.0956807 | + | 0.165724i | ||||
\(955\) | 187285. | − | 108129.i | 0.205351 | − | 0.118560i | ||||
\(956\) | −580540. | − | 1.00553e6i | −0.635209 | − | 1.10021i | ||||
\(957\) | 264975. | + | 152984.i | 0.289322 | + | 0.167040i | ||||
\(958\) | − | 1.05162e6i | − | 1.14585i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −586485. | −0.636377 | ||||||||
\(961\) | −228258. | + | 395354.i | −0.247160 | + | 0.428094i | ||||
\(962\) | 3.67135e6 | − | 2.11965e6i | 3.96712 | − | 2.29042i | ||||
\(963\) | 198772. | + | 344283.i | 0.214339 | + | 0.371247i | ||||
\(964\) | 2.25568e6 | + | 1.30232e6i | 2.42730 | + | 1.40140i | ||||
\(965\) | − | 214255.i | − | 0.230078i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 797832. | 0.853215 | 0.426608 | − | 0.904437i | \(-0.359709\pi\) | ||||
0.426608 | + | 0.904437i | \(0.359709\pi\) | |||||||
\(968\) | −745260. | + | 1.29083e6i | −0.795348 | + | 1.37758i | ||||
\(969\) | 136385. | − | 78742.0i | 0.145251 | − | 0.0838608i | ||||
\(970\) | −610954. | − | 1.05820e6i | −0.649329 | − | 1.12467i | ||||
\(971\) | −808590. | − | 466839.i | −0.857610 | − | 0.495141i | 0.00560133 | − | 0.999984i | \(-0.498217\pi\) |
−0.863211 | + | 0.504843i | \(0.831550\pi\) | |||||||
\(972\) | − | 878266.i | − | 0.929594i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.95788e6 | 2.06380 | ||||||||
\(975\) | 173000. | − | 299644.i | 0.181985 | − | 0.315208i | ||||
\(976\) | 101625. | − | 58673.4i | 0.106685 | − | 0.0615944i | ||||
\(977\) | 719883. | + | 1.24687e6i | 0.754176 | + | 1.30627i | 0.945783 | + | 0.324799i | \(0.105297\pi\) |
−0.191607 | + | 0.981472i | \(0.561370\pi\) | |||||||
\(978\) | 1.22404e6 | + | 706697.i | 1.27972 | + | 0.738849i | ||||
\(979\) | 156044.i | 0.162811i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 151024. | 0.156931 | ||||||||
\(982\) | −795347. | + | 1.37758e6i | −0.824772 | + | 1.42855i | ||||
\(983\) | −1.29753e6 | + | 749128.i | −1.34279 | + | 0.775263i | −0.987217 | − | 0.159384i | \(-0.949049\pi\) |
−0.355578 | + | 0.934647i | \(0.615716\pi\) | |||||||
\(984\) | 47717.6 | + | 82649.4i | 0.0492820 | + | 0.0853590i | ||||
\(985\) | −1.10627e6 | − | 638704.i | −1.14022 | − | 0.658305i | ||||
\(986\) | 433260.i | 0.445651i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.85977e6 | −2.92966 | ||||||||
\(989\) | −228055. | + | 395003.i | −0.233156 | + | 0.403838i | ||||
\(990\) | −111755. | + | 64522.0i | −0.114024 | + | 0.0658321i | ||||
\(991\) | 494541. | + | 856570.i | 0.503564 | + | 0.872199i | 0.999992 | + | 0.00412045i | \(0.00131158\pi\) |
−0.496427 | + | 0.868078i | \(0.665355\pi\) | |||||||
\(992\) | −118603. | − | 68475.6i | −0.120524 | − | 0.0695845i | ||||
\(993\) | − | 242668.i | − | 0.246101i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.37705e6 | 1.39092 | ||||||||
\(996\) | 1.17455e6 | − | 2.03438e6i | 1.18400 | − | 2.05076i | ||||
\(997\) | −1.07127e6 | + | 618500.i | −1.07773 | + | 0.622228i | −0.930283 | − | 0.366842i | \(-0.880439\pi\) |
−0.147447 | + | 0.989070i | \(0.547106\pi\) | |||||||
\(998\) | 806044. | + | 1.39611e6i | 0.809277 | + | 1.40171i | ||||
\(999\) | 1.32507e6 | + | 765030.i | 1.32772 | + | 0.766562i |
(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 | 49.5.d.c.19.7 | 16 | ||
7.2 | even | 3 | 49.5.b.b.48.1 | ✓ | 8 | ||
7.3 | odd | 6 | inner | 49.5.d.c.31.7 | 16 | ||
7.4 | even | 3 | inner | 49.5.d.c.31.8 | 16 | ||
7.5 | odd | 6 | 49.5.b.b.48.2 | yes | 8 | ||
7.6 | odd | 2 | inner | 49.5.d.c.19.8 | 16 | ||
21.2 | odd | 6 | 441.5.d.g.244.7 | 8 | |||
21.5 | even | 6 | 441.5.d.g.244.8 | 8 | |||
28.19 | even | 6 | 784.5.c.g.97.3 | 8 | |||
28.23 | odd | 6 | 784.5.c.g.97.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.5.b.b.48.1 | ✓ | 8 | 7.2 | even | 3 | ||
49.5.b.b.48.2 | yes | 8 | 7.5 | odd | 6 | ||
49.5.d.c.19.7 | 16 | 1.1 | even | 1 | trivial | ||
49.5.d.c.19.8 | 16 | 7.6 | odd | 2 | inner | ||
49.5.d.c.31.7 | 16 | 7.3 | odd | 6 | inner | ||
49.5.d.c.31.8 | 16 | 7.4 | even | 3 | inner | ||
441.5.d.g.244.7 | 8 | 21.2 | odd | 6 | |||
441.5.d.g.244.8 | 8 | 21.5 | even | 6 | |||
784.5.c.g.97.3 | 8 | 28.19 | even | 6 | |||
784.5.c.g.97.6 | 8 | 28.23 | odd | 6 |