Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.500000 - 4.41310i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.199 |
Dual form | 1950.2.y.m.49.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −1.27354 | − | 2.20583i | −0.481351 | − | 0.833725i | 0.518420 | − | 0.855126i | \(-0.326520\pi\) |
−0.999771 | + | 0.0214016i | \(0.993187\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.15713 | − | 0.668069i | −0.348888 | − | 0.201430i | 0.315307 | − | 0.948990i | \(-0.397892\pi\) |
−0.664195 | + | 0.747559i | \(0.731226\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 3.21677 | − | 1.62862i | 0.892171 | − | 0.451698i | ||||
\(14\) | 2.54707 | 0.680733 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.54870 | + | 1.47149i | −0.618150 | + | 0.356889i | −0.776148 | − | 0.630550i | \(-0.782829\pi\) |
0.157998 | + | 0.987439i | \(0.449496\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.05291 | − | 3.49465i | 1.38863 | − | 0.801727i | 0.395471 | − | 0.918479i | \(-0.370581\pi\) |
0.993161 | + | 0.116752i | \(0.0372481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.54707i | 0.555816i | ||||||||
\(22\) | 1.15713 | − | 0.668069i | 0.246701 | − | 0.142433i | ||||
\(23\) | −3.70583 | − | 2.13956i | −0.772719 | − | 0.446129i | 0.0611250 | − | 0.998130i | \(-0.480531\pi\) |
−0.833844 | + | 0.552001i | \(0.813865\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.197956 | + | 3.60011i | −0.0388224 | + | 0.706040i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.27354 | + | 2.20583i | −0.240676 | + | 0.416862i | ||||
\(29\) | 1.07721 | − | 1.86578i | 0.200032 | − | 0.346466i | −0.748506 | − | 0.663128i | \(-0.769229\pi\) |
0.948539 | + | 0.316662i | \(0.102562\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.74779i | 1.57115i | 0.618766 | + | 0.785575i | \(0.287633\pi\) | ||||
−0.618766 | + | 0.785575i | \(0.712367\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.668069 | + | 1.15713i | 0.116296 | + | 0.201430i | ||||
\(34\) | − | 2.94298i | − | 0.504717i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 2.62862 | − | 4.55291i | 0.432143 | − | 0.748493i | −0.564915 | − | 0.825149i | \(-0.691091\pi\) |
0.997058 | + | 0.0766560i | \(0.0244243\pi\) | |||||||
\(38\) | 6.98929i | 1.13381i | ||||||||
\(39\) | −3.60011 | − | 0.197956i | −0.576479 | − | 0.0316983i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.54870 | + | 1.47149i | 0.398040 | + | 0.229808i | 0.685638 | − | 0.727943i | \(-0.259523\pi\) |
−0.287598 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(42\) | −2.20583 | − | 1.27354i | −0.340367 | − | 0.196511i | ||||
\(43\) | −4.70558 | + | 2.71677i | −0.717594 | + | 0.414303i | −0.813867 | − | 0.581052i | \(-0.802641\pi\) |
0.0962724 | + | 0.995355i | \(0.469308\pi\) | |||||||
\(44\) | 1.33614i | 0.201430i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.70583 | − | 2.13956i | 0.546395 | − | 0.315461i | ||||
\(47\) | −11.6908 | −1.70528 | −0.852638 | − | 0.522503i | \(-0.824998\pi\) | ||||
−0.852638 | + | 0.522503i | \(0.824998\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 0.256215 | − | 0.443778i | 0.0366022 | − | 0.0633968i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.94298 | 0.412100 | ||||||||
\(52\) | −3.01881 | − | 1.97149i | −0.418634 | − | 0.273397i | ||||
\(53\) | − | 8.74779i | − | 1.20160i | −0.799399 | − | 0.600801i | \(-0.794848\pi\) | ||
0.799399 | − | 0.600801i | \(-0.205152\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.27354 | − | 2.20583i | −0.170183 | − | 0.294766i | ||||
\(57\) | −6.98929 | −0.925755 | ||||||||
\(58\) | 1.07721 | + | 1.86578i | 0.141444 | + | 0.244988i | ||||
\(59\) | 8.25873 | − | 4.76818i | 1.07520 | − | 0.620764i | 0.145599 | − | 0.989344i | \(-0.453489\pi\) |
0.929596 | + | 0.368579i | \(0.120156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62862 | + | 6.28496i | 0.464597 | + | 0.804706i | 0.999183 | − | 0.0404079i | \(-0.0128657\pi\) |
−0.534586 | + | 0.845114i | \(0.679532\pi\) | |||||||
\(62\) | −7.57581 | − | 4.37390i | −0.962129 | − | 0.555486i | ||||
\(63\) | 1.27354 | − | 2.20583i | 0.160450 | − | 0.277908i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.33614 | −0.164467 | ||||||||
\(67\) | 3.04334 | − | 5.27123i | 0.371804 | − | 0.643983i | −0.618039 | − | 0.786147i | \(-0.712073\pi\) |
0.989843 | + | 0.142164i | \(0.0454061\pi\) | |||||||
\(68\) | 2.54870 | + | 1.47149i | 0.309075 | + | 0.178445i | ||||
\(69\) | 2.13956 | + | 3.70583i | 0.257573 | + | 0.446129i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3470 | + | 6.55122i | −1.34665 | + | 0.777486i | −0.987773 | − | 0.155900i | \(-0.950172\pi\) |
−0.358873 | + | 0.933386i | \(0.616839\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −2.59614 | −0.303855 | −0.151927 | − | 0.988392i | \(-0.548548\pi\) | ||||
−0.151927 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(74\) | 2.62862 | + | 4.55291i | 0.305571 | + | 0.529265i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.05291 | − | 3.49465i | −0.694316 | − | 0.400863i | ||||
\(77\) | 3.40324i | 0.387835i | ||||||||
\(78\) | 1.97149 | − | 3.01881i | 0.223227 | − | 0.341813i | ||||
\(79\) | −13.9773 | −1.57257 | −0.786283 | − | 0.617867i | \(-0.787997\pi\) | ||||
−0.786283 | + | 0.617867i | \(0.787997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.54870 | + | 1.47149i | −0.281457 | + | 0.162499i | ||||
\(83\) | −12.2440 | −1.34395 | −0.671976 | − | 0.740573i | \(-0.734554\pi\) | ||||
−0.671976 | + | 0.740573i | \(0.734554\pi\) | |||||||
\(84\) | 2.20583 | − | 1.27354i | 0.240676 | − | 0.138954i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 5.43353i | − | 0.585913i | ||||||
\(87\) | −1.86578 | + | 1.07721i | −0.200032 | + | 0.115489i | ||||
\(88\) | −1.15713 | − | 0.668069i | −0.123350 | − | 0.0712164i | ||||
\(89\) | −10.0591 | − | 5.80763i | −1.06626 | − | 0.615608i | −0.139105 | − | 0.990278i | \(-0.544423\pi\) |
−0.927158 | + | 0.374670i | \(0.877756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.68913 | − | 5.02153i | −0.806039 | − | 0.526399i | ||||
\(92\) | 4.27912i | 0.446129i | ||||||||
\(93\) | 4.37390 | − | 7.57581i | 0.453552 | − | 0.785575i | ||||
\(94\) | 5.84539 | − | 10.1245i | 0.602906 | − | 1.04426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −0.765663 | − | 1.32617i | −0.0777413 | − | 0.134652i | 0.824534 | − | 0.565813i | \(-0.191437\pi\) |
−0.902275 | + | 0.431161i | \(0.858104\pi\) | |||||||
\(98\) | 0.256215 | + | 0.443778i | 0.0258816 | + | 0.0448283i | ||||
\(99\) | − | 1.33614i | − | 0.134287i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.258932 | − | 0.448484i | 0.0257647 | − | 0.0446258i | −0.852856 | − | 0.522147i | \(-0.825131\pi\) |
0.878620 | + | 0.477521i | \(0.158465\pi\) | |||||||
\(102\) | −1.47149 | + | 2.54870i | −0.145699 | + | 0.252359i | ||||
\(103\) | − | 2.42318i | − | 0.238763i | −0.992848 | − | 0.119382i | \(-0.961909\pi\) | ||
0.992848 | − | 0.119382i | \(-0.0380912\pi\) | |||||||
\(104\) | 3.21677 | − | 1.62862i | 0.315430 | − | 0.159699i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.57581 | + | 4.37390i | 0.735828 | + | 0.424830i | ||||
\(107\) | −5.30455 | − | 3.06258i | −0.512810 | − | 0.296071i | 0.221178 | − | 0.975233i | \(-0.429010\pi\) |
−0.733988 | + | 0.679163i | \(0.762343\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 0.547569i | 0.0524476i | 0.999656 | + | 0.0262238i | \(0.00834825\pi\) | ||||
−0.999656 | + | 0.0262238i | \(0.991652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.55291 | + | 2.62862i | −0.432143 | + | 0.249498i | ||||
\(112\) | 2.54707 | 0.240676 | ||||||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 3.49465 | − | 6.05291i | 0.327304 | − | 0.566907i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.15441 | −0.200032 | ||||||||
\(117\) | 3.01881 | + | 1.97149i | 0.279089 | + | 0.182264i | ||||
\(118\) | 9.53636i | 0.877894i | ||||||||
\(119\) | 6.49171 | + | 3.74799i | 0.595094 | + | 0.343578i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.60737 | − | 7.98019i | −0.418852 | − | 0.725472i | ||||
\(122\) | −7.25724 | −0.657040 | ||||||||
\(123\) | −1.47149 | − | 2.54870i | −0.132680 | − | 0.229808i | ||||
\(124\) | 7.57581 | − | 4.37390i | 0.680328 | − | 0.392788i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.27354 | + | 2.20583i | 0.113456 | + | 0.196511i | ||||
\(127\) | 6.16530 | + | 3.55954i | 0.547082 | + | 0.315858i | 0.747944 | − | 0.663762i | \(-0.231041\pi\) |
−0.200862 | + | 0.979619i | \(0.564374\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.43353 | 0.478396 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.42233 | −0.823233 | −0.411616 | − | 0.911357i | \(-0.635036\pi\) | ||||
−0.411616 | + | 0.911357i | \(0.635036\pi\) | |||||||
\(132\) | 0.668069 | − | 1.15713i | 0.0581480 | − | 0.100715i | ||||
\(133\) | −15.4172 | − | 8.90111i | −1.33684 | − | 0.771824i | ||||
\(134\) | 3.04334 | + | 5.27123i | 0.262905 | + | 0.455365i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.54870 | + | 1.47149i | −0.218549 | + | 0.126179i | ||||
\(137\) | 9.27336 | + | 16.0619i | 0.792277 | + | 1.37226i | 0.924554 | + | 0.381050i | \(0.124438\pi\) |
−0.132278 | + | 0.991213i | \(0.542229\pi\) | |||||||
\(138\) | −4.27912 | −0.364263 | ||||||||
\(139\) | −9.85885 | − | 17.0760i | −0.836216 | − | 1.44837i | −0.893036 | − | 0.449985i | \(-0.851429\pi\) |
0.0568196 | − | 0.998384i | \(-0.481904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1245 | + | 5.84539i | 0.852638 | + | 0.492271i | ||||
\(142\) | − | 13.1024i | − | 1.09953i | ||||||
\(143\) | −4.81025 | − | 0.264497i | −0.402253 | − | 0.0221183i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.29807 | − | 2.24832i | 0.107429 | − | 0.186072i | ||||
\(147\) | −0.443778 | + | 0.256215i | −0.0366022 | + | 0.0211323i | ||||
\(148\) | −5.25724 | −0.432143 | ||||||||
\(149\) | 6.84990 | − | 3.95479i | 0.561165 | − | 0.323989i | −0.192448 | − | 0.981307i | \(-0.561643\pi\) |
0.753613 | + | 0.657318i | \(0.228309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.1864i | − | 1.39861i | −0.714823 | − | 0.699305i | \(-0.753493\pi\) | ||
0.714823 | − | 0.699305i | \(-0.246507\pi\) | |||||||
\(152\) | 6.05291 | − | 3.49465i | 0.490956 | − | 0.283453i | ||||
\(153\) | −2.54870 | − | 1.47149i | −0.206050 | − | 0.118963i | ||||
\(154\) | −2.94729 | − | 1.70162i | −0.237500 | − | 0.137120i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.62862 | + | 3.21677i | 0.130394 | + | 0.257548i | ||||
\(157\) | − | 2.56103i | − | 0.204393i | −0.994764 | − | 0.102196i | \(-0.967413\pi\) | ||
0.994764 | − | 0.102196i | \(-0.0325870\pi\) | |||||||
\(158\) | 6.98864 | − | 12.1047i | 0.555986 | − | 0.962996i | ||||
\(159\) | −4.37390 | + | 7.57581i | −0.346873 | + | 0.600801i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8992i | 0.858979i | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −8.80763 | − | 15.2553i | −0.689867 | − | 1.19488i | −0.971881 | − | 0.235474i | \(-0.924336\pi\) |
0.282014 | − | 0.959410i | \(-0.408998\pi\) | |||||||
\(164\) | − | 2.94298i | − | 0.229808i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.12199 | − | 10.6036i | 0.475159 | − | 0.822999i | ||||
\(167\) | −2.13956 | + | 3.70583i | −0.165564 | + | 0.286766i | −0.936855 | − | 0.349717i | \(-0.886278\pi\) |
0.771291 | + | 0.636482i | \(0.219611\pi\) | |||||||
\(168\) | 2.54707i | 0.196511i | ||||||||
\(169\) | 7.69518 | − | 10.4778i | 0.591937 | − | 0.805984i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.05291 | + | 3.49465i | 0.462877 | + | 0.267242i | ||||
\(172\) | 4.70558 | + | 2.71677i | 0.358797 | + | 0.207152i | ||||
\(173\) | −7.31290 | + | 4.22210i | −0.555989 | + | 0.321001i | −0.751534 | − | 0.659694i | \(-0.770686\pi\) |
0.195545 | + | 0.980695i | \(0.437353\pi\) | |||||||
\(174\) | − | 2.15441i | − | 0.163326i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.15713 | − | 0.668069i | 0.0872220 | − | 0.0503576i | ||||
\(177\) | −9.53636 | −0.716797 | ||||||||
\(178\) | 10.0591 | − | 5.80763i | 0.753962 | − | 0.435300i | ||||
\(179\) | −0.982856 | + | 1.70236i | −0.0734621 | + | 0.127240i | −0.900416 | − | 0.435029i | \(-0.856738\pi\) |
0.826954 | + | 0.562269i | \(0.190071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.61526 | −0.491708 | −0.245854 | − | 0.969307i | \(-0.579068\pi\) | ||||
−0.245854 | + | 0.969307i | \(0.579068\pi\) | |||||||
\(182\) | 8.19333 | − | 4.14821i | 0.607330 | − | 0.307486i | ||||
\(183\) | − | 7.25724i | − | 0.536471i | ||||||
\(184\) | −3.70583 | − | 2.13956i | −0.273197 | − | 0.157731i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.37390 | + | 7.57581i | 0.320710 | + | 0.555486i | ||||
\(187\) | 3.93223 | 0.287553 | ||||||||
\(188\) | 5.84539 | + | 10.1245i | 0.426319 | + | 0.738406i | ||||
\(189\) | −2.20583 | + | 1.27354i | −0.160450 | + | 0.0926361i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.21624 | − | 9.03479i | −0.377434 | − | 0.653735i | 0.613254 | − | 0.789886i | \(-0.289860\pi\) |
−0.990688 | + | 0.136151i | \(0.956527\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −0.407532 | + | 0.705866i | −0.0293348 | + | 0.0508093i | −0.880320 | − | 0.474380i | \(-0.842672\pi\) |
0.850985 | + | 0.525189i | \(0.176006\pi\) | |||||||
\(194\) | 1.53133 | 0.109943 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.512430 | −0.0366022 | ||||||||
\(197\) | −8.41742 | + | 14.5794i | −0.599716 | + | 1.03874i | 0.393146 | + | 0.919476i | \(0.371387\pi\) |
−0.992863 | + | 0.119263i | \(0.961947\pi\) | |||||||
\(198\) | 1.15713 | + | 0.668069i | 0.0822337 | + | 0.0474776i | ||||
\(199\) | −3.36600 | − | 5.83009i | −0.238610 | − | 0.413284i | 0.721706 | − | 0.692200i | \(-0.243358\pi\) |
−0.960316 | + | 0.278916i | \(0.910025\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.27123 | + | 3.04334i | −0.371804 | + | 0.214661i | ||||
\(202\) | 0.258932 | + | 0.448484i | 0.0182184 | + | 0.0315552i | ||||
\(203\) | −5.48744 | −0.385143 | ||||||||
\(204\) | −1.47149 | − | 2.54870i | −0.103025 | − | 0.178445i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.09854 | + | 1.21159i | 0.146212 | + | 0.0844155i | ||||
\(207\) | − | 4.27912i | − | 0.297420i | ||||||
\(208\) | −0.197956 | + | 3.60011i | −0.0137258 | + | 0.249623i | ||||
\(209\) | −9.33867 | −0.645969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00378 | − | 10.3989i | 0.413317 | − | 0.715887i | −0.581933 | − | 0.813237i | \(-0.697703\pi\) |
0.995250 | + | 0.0973501i | \(0.0310367\pi\) | |||||||
\(212\) | −7.57581 | + | 4.37390i | −0.520309 | + | 0.300401i | ||||
\(213\) | 13.1024 | 0.897764 | ||||||||
\(214\) | 5.30455 | − | 3.06258i | 0.362611 | − | 0.209354i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 19.2961 | − | 11.1406i | 1.30991 | − | 0.756275i | ||||
\(218\) | −0.474209 | − | 0.273784i | −0.0321175 | − | 0.0185430i | ||||
\(219\) | 2.24832 | + | 1.29807i | 0.151927 | + | 0.0877154i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.80207 | + | 8.88431i | −0.390289 | + | 0.597623i | ||||
\(222\) | − | 5.25724i | − | 0.352843i | ||||||
\(223\) | 0.253346 | − | 0.438808i | 0.0169653 | − | 0.0293848i | −0.857418 | − | 0.514620i | \(-0.827933\pi\) |
0.874383 | + | 0.485236i | \(0.161266\pi\) | |||||||
\(224\) | −1.27354 | + | 2.20583i | −0.0850917 | + | 0.147383i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.07973 | + | 3.60219i | 0.138036 | + | 0.239086i | 0.926753 | − | 0.375671i | \(-0.122588\pi\) |
−0.788717 | + | 0.614756i | \(0.789254\pi\) | |||||||
\(228\) | 3.49465 | + | 6.05291i | 0.231439 | + | 0.400863i | ||||
\(229\) | 22.3688i | 1.47817i | 0.673611 | + | 0.739086i | \(0.264742\pi\) | ||||
−0.673611 | + | 0.739086i | \(0.735258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.70162 | − | 2.94729i | 0.111958 | − | 0.193918i | ||||
\(232\) | 1.07721 | − | 1.86578i | 0.0707221 | − | 0.122494i | ||||
\(233\) | − | 8.82331i | − | 0.578034i | −0.957324 | − | 0.289017i | \(-0.906672\pi\) | ||
0.957324 | − | 0.289017i | \(-0.0933285\pi\) | |||||||
\(234\) | −3.21677 | + | 1.62862i | −0.210287 | + | 0.106466i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.25873 | − | 4.76818i | −0.537598 | − | 0.310382i | ||||
\(237\) | 12.1047 | + | 6.98864i | 0.786283 | + | 0.453961i | ||||
\(238\) | −6.49171 | + | 3.74799i | −0.420795 | + | 0.242946i | ||||
\(239\) | − | 25.6233i | − | 1.65743i | −0.559669 | − | 0.828716i | \(-0.689072\pi\) | ||
0.559669 | − | 0.828716i | \(-0.310928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9346 | + | 6.89042i | −0.768773 | + | 0.443851i | −0.832437 | − | 0.554120i | \(-0.813055\pi\) |
0.0636639 | + | 0.997971i | \(0.479721\pi\) | |||||||
\(242\) | 9.21473 | 0.592345 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.62862 | − | 6.28496i | 0.232299 | − | 0.402353i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.94298 | 0.187638 | ||||||||
\(247\) | 13.7793 | − | 21.0994i | 0.876758 | − | 1.34252i | ||||
\(248\) | 8.74779i | 0.555486i | ||||||||
\(249\) | 10.6036 | + | 6.12199i | 0.671976 | + | 0.387965i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5296 | + | 18.2378i | 0.664621 | + | 1.15116i | 0.979388 | + | 0.201988i | \(0.0647402\pi\) |
−0.314767 | + | 0.949169i | \(0.601926\pi\) | |||||||
\(252\) | −2.54707 | −0.160450 | ||||||||
\(253\) | 2.85875 | + | 4.95150i | 0.179728 | + | 0.311298i | ||||
\(254\) | −6.16530 | + | 3.55954i | −0.386845 | + | 0.223345i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.3734 | − | 7.14377i | −0.771830 | − | 0.445616i | 0.0616973 | − | 0.998095i | \(-0.480349\pi\) |
−0.833527 | + | 0.552479i | \(0.813682\pi\) | |||||||
\(258\) | −2.71677 | + | 4.70558i | −0.169139 | + | 0.292957i | ||||
\(259\) | −13.3906 | −0.832050 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.15441 | 0.133355 | ||||||||
\(262\) | 4.71117 | − | 8.15998i | 0.291057 | − | 0.504125i | ||||
\(263\) | 22.6272 | + | 13.0638i | 1.39526 | + | 0.805551i | 0.993891 | − | 0.110367i | \(-0.0352027\pi\) |
0.401365 | + | 0.915918i | \(0.368536\pi\) | |||||||
\(264\) | 0.668069 | + | 1.15713i | 0.0411168 | + | 0.0712164i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.4172 | − | 8.90111i | 0.945288 | − | 0.545762i | ||||
\(267\) | 5.80763 | + | 10.0591i | 0.355421 | + | 0.615608i | ||||
\(268\) | −6.08669 | −0.371804 | ||||||||
\(269\) | 7.80743 | + | 13.5229i | 0.476028 | + | 0.824504i | 0.999623 | − | 0.0274633i | \(-0.00874292\pi\) |
−0.523595 | + | 0.851967i | \(0.675410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.6267 | − | 13.0635i | −1.37447 | − | 0.793553i | −0.382987 | − | 0.923754i | \(-0.625105\pi\) |
−0.991488 | + | 0.130201i | \(0.958438\pi\) | |||||||
\(272\) | − | 2.94298i | − | 0.178445i | ||||||
\(273\) | 4.14821 | + | 8.19333i | 0.251061 | + | 0.495883i | ||||
\(274\) | −18.5467 | −1.12045 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.13956 | − | 3.70583i | 0.128786 | − | 0.223065i | ||||
\(277\) | 16.8252 | − | 9.71405i | 1.01093 | − | 0.583661i | 0.0994662 | − | 0.995041i | \(-0.468286\pi\) |
0.911464 | + | 0.411380i | \(0.134953\pi\) | |||||||
\(278\) | 19.7177 | 1.18259 | ||||||||
\(279\) | −7.57581 | + | 4.37390i | −0.453552 | + | 0.261858i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.6630i | − | 0.636102i | −0.948074 | − | 0.318051i | \(-0.896972\pi\) | ||
0.948074 | − | 0.318051i | \(-0.103028\pi\) | |||||||
\(282\) | −10.1245 | + | 5.84539i | −0.602906 | + | 0.348088i | ||||
\(283\) | 1.26513 | + | 0.730424i | 0.0752042 | + | 0.0434192i | 0.537131 | − | 0.843499i | \(-0.319508\pi\) |
−0.461926 | + | 0.886918i | \(0.652842\pi\) | |||||||
\(284\) | 11.3470 | + | 6.55122i | 0.673323 | + | 0.388743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.63419 | − | 4.03355i | 0.155763 | − | 0.238509i | ||||
\(287\) | − | 7.49599i | − | 0.442474i | ||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −4.16943 | + | 7.22166i | −0.245260 | + | 0.424803i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.53133i | 0.0897680i | ||||||||
\(292\) | 1.29807 | + | 2.24832i | 0.0759637 | + | 0.131573i | ||||
\(293\) | −8.86614 | − | 15.3566i | −0.517965 | − | 0.897142i | −0.999782 | − | 0.0208703i | \(-0.993356\pi\) |
0.481817 | − | 0.876272i | \(-0.339977\pi\) | |||||||
\(294\) | − | 0.512430i | − | 0.0298855i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.62862 | − | 4.55291i | 0.152786 | − | 0.264632i | ||||
\(297\) | −0.668069 | + | 1.15713i | −0.0387653 | + | 0.0671435i | ||||
\(298\) | 7.90958i | 0.458190i | ||||||||
\(299\) | −15.4053 | − | 0.847078i | −0.890913 | − | 0.0489878i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9854 | + | 6.91980i | 0.690829 | + | 0.398851i | ||||
\(302\) | 14.8839 | + | 8.59321i | 0.856470 | + | 0.494483i | ||||
\(303\) | −0.448484 | + | 0.258932i | −0.0257647 | + | 0.0148753i | ||||
\(304\) | 6.98929i | 0.400863i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.54870 | − | 1.47149i | 0.145699 | − | 0.0841196i | ||||
\(307\) | 6.66890 | 0.380614 | 0.190307 | − | 0.981725i | \(-0.439052\pi\) | ||||
0.190307 | + | 0.981725i | \(0.439052\pi\) | |||||||
\(308\) | 2.94729 | − | 1.70162i | 0.167938 | − | 0.0969588i | ||||
\(309\) | −1.21159 | + | 2.09854i | −0.0689250 | + | 0.119382i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6233 | 1.11273 | 0.556367 | − | 0.830937i | \(-0.312195\pi\) | ||||
0.556367 | + | 0.830937i | \(0.312195\pi\) | |||||||
\(312\) | −3.60011 | − | 0.197956i | −0.203816 | − | 0.0112071i | ||||
\(313\) | 13.0538i | 0.737846i | 0.929460 | + | 0.368923i | \(0.120273\pi\) | ||||
−0.929460 | + | 0.368923i | \(0.879727\pi\) | |||||||
\(314\) | 2.21792 | + | 1.28052i | 0.125164 | + | 0.0722637i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.98864 | + | 12.1047i | 0.393141 | + | 0.680941i | ||||
\(317\) | −18.7916 | −1.05544 | −0.527719 | − | 0.849419i | \(-0.676953\pi\) | ||||
−0.527719 | + | 0.849419i | \(0.676953\pi\) | |||||||
\(318\) | −4.37390 | − | 7.57581i | −0.245276 | − | 0.424830i | ||||
\(319\) | −2.49294 | + | 1.43930i | −0.139578 | + | 0.0805852i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.06258 | + | 5.30455i | 0.170937 | + | 0.296071i | ||||
\(322\) | −9.43901 | − | 5.44961i | −0.526015 | − | 0.303695i | ||||
\(323\) | −10.2847 | + | 17.8136i | −0.572255 | + | 0.991175i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.6153 | 0.975619 | ||||||||
\(327\) | 0.273784 | − | 0.474209i | 0.0151403 | − | 0.0262238i | ||||
\(328\) | 2.54870 | + | 1.47149i | 0.140728 | + | 0.0812495i | ||||
\(329\) | 14.8886 | + | 25.7878i | 0.820836 | + | 1.42173i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4013 | + | 11.7787i | −1.12136 | + | 0.647417i | −0.941747 | − | 0.336321i | \(-0.890817\pi\) |
−0.179611 | + | 0.983738i | \(0.557484\pi\) | |||||||
\(332\) | 6.12199 | + | 10.6036i | 0.335988 | + | 0.581948i | ||||
\(333\) | 5.25724 | 0.288095 | ||||||||
\(334\) | −2.13956 | − | 3.70583i | −0.117072 | − | 0.202774i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.20583 | − | 1.27354i | −0.120338 | − | 0.0694771i | ||||
\(337\) | 27.2137i | 1.48242i | 0.671271 | + | 0.741212i | \(0.265749\pi\) | ||||
−0.671271 | + | 0.741212i | \(0.734251\pi\) | |||||||
\(338\) | 5.22644 | + | 11.9031i | 0.284281 | + | 0.647444i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.84413 | − | 10.1223i | 0.316478 | − | 0.548155i | ||||
\(342\) | −6.05291 | + | 3.49465i | −0.327304 | + | 0.188969i | ||||
\(343\) | −19.1347 | −1.03318 | ||||||||
\(344\) | −4.70558 | + | 2.71677i | −0.253708 | + | 0.146478i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.44421i | − | 0.453963i | ||||||
\(347\) | 5.52861 | − | 3.19194i | 0.296791 | − | 0.171353i | −0.344209 | − | 0.938893i | \(-0.611853\pi\) |
0.641001 | + | 0.767540i | \(0.278520\pi\) | |||||||
\(348\) | 1.86578 | + | 1.07721i | 0.100016 | + | 0.0577443i | ||||
\(349\) | −7.31585 | − | 4.22381i | −0.391608 | − | 0.226095i | 0.291248 | − | 0.956647i | \(-0.405929\pi\) |
−0.682857 | + | 0.730552i | \(0.739263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.62862 | − | 3.21677i | −0.0869294 | − | 0.171698i | ||||
\(352\) | 1.33614i | 0.0712164i | ||||||||
\(353\) | 7.73075 | − | 13.3901i | 0.411466 | − | 0.712681i | −0.583584 | − | 0.812053i | \(-0.698350\pi\) |
0.995050 | + | 0.0993721i | \(0.0316834\pi\) | |||||||
\(354\) | 4.76818 | − | 8.25873i | 0.253426 | − | 0.438947i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.6153i | 0.615608i | ||||||||
\(357\) | −3.74799 | − | 6.49171i | −0.198365 | − | 0.343578i | ||||
\(358\) | −0.982856 | − | 1.70236i | −0.0519456 | − | 0.0899724i | ||||
\(359\) | 34.4839i | 1.81999i | 0.414617 | + | 0.909996i | \(0.363916\pi\) | ||||
−0.414617 | + | 0.909996i | \(0.636084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9251 | − | 25.8511i | 0.785532 | − | 1.36058i | ||||
\(362\) | 3.30763 | − | 5.72898i | 0.173845 | − | 0.301109i | ||||
\(363\) | 9.21473i | 0.483648i | ||||||||
\(364\) | −0.504208 | + | 9.16974i | −0.0264277 | + | 0.480625i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.28496 | + | 3.62862i | 0.328520 | + | 0.189671i | ||||
\(367\) | 31.9910 | + | 18.4700i | 1.66992 | + | 0.964128i | 0.967678 | + | 0.252188i | \(0.0811501\pi\) |
0.702240 | + | 0.711940i | \(0.252183\pi\) | |||||||
\(368\) | 3.70583 | − | 2.13956i | 0.193180 | − | 0.111532i | ||||
\(369\) | 2.94298i | 0.153206i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.2961 | + | 11.1406i | −1.00181 | + | 0.578393i | ||||
\(372\) | −8.74779 | −0.453552 | ||||||||
\(373\) | 10.5589 | − | 6.09620i | 0.546721 | − | 0.315649i | −0.201078 | − | 0.979575i | \(-0.564444\pi\) |
0.747798 | + | 0.663926i | \(0.231111\pi\) | |||||||
\(374\) | −1.96612 | + | 3.40541i | −0.101665 | + | 0.176090i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.6908 | −0.602906 | ||||||||
\(377\) | 0.426479 | − | 7.75613i | 0.0219648 | − | 0.399461i | ||||
\(378\) | − | 2.54707i | − | 0.131007i | ||||||
\(379\) | 1.24346 | + | 0.717912i | 0.0638723 | + | 0.0368767i | 0.531596 | − | 0.846998i | \(-0.321592\pi\) |
−0.467724 | + | 0.883875i | \(0.654926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.55954 | − | 6.16530i | −0.182361 | − | 0.315858i | ||||
\(382\) | 10.4325 | 0.533772 | ||||||||
\(383\) | 10.1097 | + | 17.5104i | 0.516579 | + | 0.894742i | 0.999815 | + | 0.0192512i | \(0.00612824\pi\) |
−0.483235 | + | 0.875491i | \(0.660538\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.407532 | − | 0.705866i | −0.0207428 | − | 0.0359276i | ||||
\(387\) | −4.70558 | − | 2.71677i | −0.239198 | − | 0.138101i | ||||
\(388\) | −0.765663 | + | 1.32617i | −0.0388707 | + | 0.0673260i | ||||
\(389\) | −2.15441 | −0.109233 | −0.0546165 | − | 0.998507i | \(-0.517394\pi\) | ||||
−0.0546165 | + | 0.998507i | \(0.517394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.5934 | 0.636875 | ||||||||
\(392\) | 0.256215 | − | 0.443778i | 0.0129408 | − | 0.0224142i | ||||
\(393\) | 8.15998 | + | 4.71117i | 0.411616 | + | 0.237647i | ||||
\(394\) | −8.41742 | − | 14.5794i | −0.424063 | − | 0.734499i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.15713 | + | 0.668069i | −0.0581480 | + | 0.0335717i | ||||
\(397\) | 13.4286 | + | 23.2589i | 0.673960 | + | 1.16733i | 0.976772 | + | 0.214282i | \(0.0687412\pi\) |
−0.302812 | + | 0.953050i | \(0.597925\pi\) | |||||||
\(398\) | 6.73201 | 0.337445 | ||||||||
\(399\) | 8.90111 | + | 15.4172i | 0.445613 | + | 0.771824i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8763 | − | 10.3209i | −0.892698 | − | 0.515399i | −0.0178737 | − | 0.999840i | \(-0.505690\pi\) |
−0.874824 | + | 0.484441i | \(0.839023\pi\) | |||||||
\(402\) | − | 6.08669i | − | 0.303576i | ||||||
\(403\) | 14.2468 | + | 28.1396i | 0.709686 | + | 1.40173i | ||||
\(404\) | −0.517864 | −0.0257647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.74372 | − | 4.75226i | 0.136169 | − | 0.235851i | ||||
\(407\) | −6.08331 | + | 3.51220i | −0.301539 | + | 0.174093i | ||||
\(408\) | 2.94298 | 0.145699 | ||||||||
\(409\) | 3.62316 | − | 2.09183i | 0.179154 | − | 0.103434i | −0.407741 | − | 0.913097i | \(-0.633683\pi\) |
0.586895 | + | 0.809663i | \(0.300350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 18.5467i | − | 0.914842i | ||||||
\(412\) | −2.09854 | + | 1.21159i | −0.103387 | + | 0.0596908i | ||||
\(413\) | −21.0356 | − | 12.1449i | −1.03509 | − | 0.597611i | ||||
\(414\) | 3.70583 | + | 2.13956i | 0.182132 | + | 0.105154i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.01881 | − | 1.97149i | −0.148009 | − | 0.0966603i | ||||
\(417\) | 19.7177i | 0.965580i | ||||||||
\(418\) | 4.66933 | − | 8.08752i | 0.228385 | − | 0.395574i | ||||
\(419\) | 14.4210 | − | 24.9779i | 0.704511 | − | 1.22025i | −0.262357 | − | 0.964971i | \(-0.584500\pi\) |
0.966868 | − | 0.255277i | \(-0.0821668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.3986i | − | 0.555532i | −0.960649 | − | 0.277766i | \(-0.910406\pi\) | ||
0.960649 | − | 0.277766i | \(-0.0895939\pi\) | |||||||
\(422\) | 6.00378 | + | 10.3989i | 0.292260 | + | 0.506208i | ||||
\(423\) | −5.84539 | − | 10.1245i | −0.284213 | − | 0.492271i | ||||
\(424\) | − | 8.74779i | − | 0.424830i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.55122 | + | 11.3470i | −0.317407 | + | 0.549766i | ||||
\(427\) | 9.24236 | − | 16.0082i | 0.447269 | − | 0.774693i | ||||
\(428\) | 6.12516i | 0.296071i | ||||||||
\(429\) | 4.03355 | + | 2.63419i | 0.194742 | + | 0.127180i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.5014 | + | 15.3006i | 1.27653 | + | 0.737003i | 0.976208 | − | 0.216836i | \(-0.0695738\pi\) |
0.300318 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 33.0332 | − | 19.0717i | 1.58747 | − | 0.916527i | 0.593750 | − | 0.804649i | \(-0.297647\pi\) |
0.993722 | − | 0.111878i | \(-0.0356866\pi\) | |||||||
\(434\) | 22.2813i | 1.06953i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.474209 | − | 0.273784i | 0.0227105 | − | 0.0131119i | ||||
\(437\) | −29.9080 | −1.43070 | ||||||||
\(438\) | −2.24832 | + | 1.29807i | −0.107429 | + | 0.0620241i | ||||
\(439\) | −7.39969 | + | 12.8166i | −0.353168 | + | 0.611705i | −0.986803 | − | 0.161928i | \(-0.948229\pi\) |
0.633635 | + | 0.773632i | \(0.281562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.512430 | 0.0244014 | ||||||||
\(442\) | −4.79301 | − | 9.46689i | −0.227980 | − | 0.450294i | ||||
\(443\) | 2.07804i | 0.0987309i | 0.998781 | + | 0.0493654i | \(0.0157199\pi\) | ||||
−0.998781 | + | 0.0493654i | \(0.984280\pi\) | |||||||
\(444\) | 4.55291 | + | 2.62862i | 0.216071 | + | 0.124749i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.253346 | + | 0.438808i | 0.0119963 | + | 0.0207782i | ||||
\(447\) | −7.90958 | −0.374110 | ||||||||
\(448\) | −1.27354 | − | 2.20583i | −0.0601689 | − | 0.104216i | ||||
\(449\) | −8.50224 | + | 4.90877i | −0.401246 | + | 0.231659i | −0.687021 | − | 0.726637i | \(-0.741082\pi\) |
0.285776 | + | 0.958297i | \(0.407749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.96612 | − | 3.40541i | −0.0925808 | − | 0.160355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.59321 | + | 14.8839i | −0.403744 | + | 0.699305i | ||||
\(454\) | −4.15945 | −0.195213 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.98929 | −0.327304 | ||||||||
\(457\) | −16.0683 | + | 27.8311i | −0.751642 | + | 1.30188i | 0.195385 | + | 0.980727i | \(0.437404\pi\) |
−0.947027 | + | 0.321155i | \(0.895929\pi\) | |||||||
\(458\) | −19.3719 | − | 11.1844i | −0.905191 | − | 0.522613i | ||||
\(459\) | 1.47149 | + | 2.54870i | 0.0686833 | + | 0.118963i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8943 | − | 10.3313i | 0.833423 | − | 0.481177i | −0.0216003 | − | 0.999767i | \(-0.506876\pi\) |
0.855023 | + | 0.518590i | \(0.173543\pi\) | |||||||
\(462\) | 1.70162 | + | 2.94729i | 0.0791665 | + | 0.137120i | ||||
\(463\) | 18.2175 | 0.846639 | 0.423319 | − | 0.905981i | \(-0.360865\pi\) | ||||
0.423319 | + | 0.905981i | \(0.360865\pi\) | |||||||
\(464\) | 1.07721 | + | 1.86578i | 0.0500081 | + | 0.0866165i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.64121 | + | 4.41166i | 0.353972 | + | 0.204366i | ||||
\(467\) | 5.61909i | 0.260021i | 0.991513 | + | 0.130010i | \(0.0415010\pi\) | ||||
−0.991513 | + | 0.130010i | \(0.958499\pi\) | |||||||
\(468\) | 0.197956 | − | 3.60011i | 0.00915052 | − | 0.166415i | ||||
\(469\) | −15.5032 | −0.715873 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.28052 | + | 2.21792i | −0.0590030 | + | 0.102196i | ||||
\(472\) | 8.25873 | − | 4.76818i | 0.380139 | − | 0.219473i | ||||
\(473\) | 7.25996 | 0.333813 | ||||||||
\(474\) | −12.1047 | + | 6.98864i | −0.555986 | + | 0.320999i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 7.49599i | − | 0.343578i | ||||||
\(477\) | 7.57581 | − | 4.37390i | 0.346873 | − | 0.200267i | ||||
\(478\) | 22.1904 | + | 12.8116i | 1.01497 | + | 0.585991i | ||||
\(479\) | −23.1239 | − | 13.3506i | −1.05656 | − | 0.610003i | −0.132078 | − | 0.991239i | \(-0.542165\pi\) |
−0.924478 | + | 0.381236i | \(0.875498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04070 | − | 18.9267i | 0.0474520 | − | 0.862982i | ||||
\(482\) | − | 13.7808i | − | 0.627700i | ||||||
\(483\) | 5.44961 | − | 9.43901i | 0.247966 | − | 0.429490i | ||||
\(484\) | −4.60737 | + | 7.98019i | −0.209426 | + | 0.362736i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −15.5146 | − | 26.8721i | −0.703035 | − | 1.21769i | −0.967396 | − | 0.253269i | \(-0.918494\pi\) |
0.264361 | − | 0.964424i | \(-0.414839\pi\) | |||||||
\(488\) | 3.62862 | + | 6.28496i | 0.164260 | + | 0.284507i | ||||
\(489\) | 17.6153i | 0.796590i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.27846 | + | 12.6067i | −0.328472 | + | 0.568931i | −0.982209 | − | 0.187791i | \(-0.939867\pi\) |
0.653737 | + | 0.756722i | \(0.273200\pi\) | |||||||
\(492\) | −1.47149 | + | 2.54870i | −0.0663400 | + | 0.114904i | ||||
\(493\) | 6.34040i | 0.285557i | ||||||||
\(494\) | 11.3829 | + | 22.4829i | 0.512142 | + | 1.01155i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.57581 | − | 4.37390i | −0.340164 | − | 0.196394i | ||||
\(497\) | 28.9017 | + | 16.6864i | 1.29642 | + | 0.748488i | ||||
\(498\) | −10.6036 | + | 6.12199i | −0.475159 | + | 0.274333i | ||||
\(499\) | 26.5871i | 1.19020i | 0.803652 | + | 0.595100i | \(0.202888\pi\) | ||||
−0.803652 | + | 0.595100i | \(0.797112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.70583 | − | 2.13956i | 0.165564 | − | 0.0955885i | ||||
\(502\) | −21.0591 | −0.939916 | ||||||||
\(503\) | −11.8562 | + | 6.84516i | −0.528640 | + | 0.305211i | −0.740463 | − | 0.672098i | \(-0.765394\pi\) |
0.211822 | + | 0.977308i | \(0.432060\pi\) | |||||||
\(504\) | 1.27354 | − | 2.20583i | 0.0567278 | − | 0.0982554i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.71750 | −0.254174 | ||||||||
\(507\) | −11.9031 | + | 5.22644i | −0.528636 | + | 0.232114i | ||||
\(508\) | − | 7.11907i | − | 0.315858i | ||||||
\(509\) | −6.53323 | − | 3.77196i | −0.289581 | − | 0.167189i | 0.348172 | − | 0.937431i | \(-0.386802\pi\) |
−0.637753 | + | 0.770241i | \(0.720136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.30627 | + | 5.72663i | 0.146261 | + | 0.253331i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.49465 | − | 6.05291i | −0.154292 | − | 0.267242i | ||||
\(514\) | 12.3734 | − | 7.14377i | 0.545766 | − | 0.315098i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.71677 | − | 4.70558i | −0.119599 | − | 0.207152i | ||||
\(517\) | 13.5278 | + | 7.81025i | 0.594950 | + | 0.343494i | ||||
\(518\) | 6.69529 | − | 11.5966i | 0.294174 | − | 0.509524i | ||||
\(519\) | 8.44421 | 0.370660 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2218 | 0.666881 | 0.333440 | − | 0.942771i | \(-0.391790\pi\) | ||||
0.333440 | + | 0.942771i | \(0.391790\pi\) | |||||||
\(522\) | −1.07721 | + | 1.86578i | −0.0471480 | + | 0.0816628i | ||||
\(523\) | −21.6567 | − | 12.5035i | −0.946980 | − | 0.546739i | −0.0548385 | − | 0.998495i | \(-0.517464\pi\) |
−0.892141 | + | 0.451756i | \(0.850798\pi\) | |||||||
\(524\) | 4.71117 | + | 8.15998i | 0.205808 | + | 0.356470i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.6272 | + | 13.0638i | −0.986595 | + | 0.569611i | ||||
\(527\) | −12.8723 | − | 22.2955i | −0.560726 | − | 0.971207i | ||||
\(528\) | −1.33614 | −0.0581480 | ||||||||
\(529\) | −2.34456 | − | 4.06090i | −0.101937 | − | 0.176561i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.25873 | + | 4.76818i | 0.358399 | + | 0.206921i | ||||
\(532\) | 17.8022i | 0.771824i | ||||||||
\(533\) | 10.5951 | + | 0.582581i | 0.458923 | + | 0.0252344i | ||||
\(534\) | −11.6153 | −0.502641 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.04334 | − | 5.27123i | 0.131452 | − | 0.227682i | ||||
\(537\) | 1.70236 | − | 0.982856i | 0.0734621 | − | 0.0424134i | ||||
\(538\) | −15.6149 | −0.673205 | ||||||||
\(539\) | −0.592949 | + | 0.342339i | −0.0255401 | + | 0.0147456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2610i | 1.38701i | 0.720452 | + | 0.693504i | \(0.243934\pi\) | ||||
−0.720452 | + | 0.693504i | \(0.756066\pi\) | |||||||
\(542\) | 22.6267 | − | 13.0635i | 0.971900 | − | 0.561127i | ||||
\(543\) | 5.72898 | + | 3.30763i | 0.245854 | + | 0.141944i | ||||
\(544\) | 2.54870 | + | 1.47149i | 0.109275 | + | 0.0630897i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.16974 | − | 0.504208i | −0.392429 | − | 0.0215781i | ||||
\(547\) | − | 36.4353i | − | 1.55786i | −0.627110 | − | 0.778931i | \(-0.715762\pi\) | ||
0.627110 | − | 0.778931i | \(-0.284238\pi\) | |||||||
\(548\) | 9.27336 | − | 16.0619i | 0.396138 | − | 0.686132i | ||||
\(549\) | −3.62862 | + | 6.28496i | −0.154866 | + | 0.268235i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.0578i | − | 0.641485i | ||||||
\(552\) | 2.13956 | + | 3.70583i | 0.0910658 | + | 0.157731i | ||||
\(553\) | 17.8005 | + | 30.8315i | 0.756956 | + | 1.31109i | ||||
\(554\) | 19.4281i | 0.825421i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.85885 | + | 17.0760i | −0.418108 | + | 0.724185i | ||||
\(557\) | −18.2648 | + | 31.6356i | −0.773905 | + | 1.34044i | 0.161503 | + | 0.986872i | \(0.448366\pi\) |
−0.935408 | + | 0.353570i | \(0.884968\pi\) | |||||||
\(558\) | − | 8.74779i | − | 0.370324i | ||||||
\(559\) | −10.7122 | + | 16.4028i | −0.453076 | + | 0.693765i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.40541 | − | 1.96612i | −0.143777 | − | 0.0830095i | ||||
\(562\) | 9.23444 | + | 5.33151i | 0.389531 | + | 0.224896i | ||||
\(563\) | 38.9307 | − | 22.4766i | 1.64073 | − | 0.947277i | 0.660158 | − | 0.751127i | \(-0.270489\pi\) |
0.980574 | − | 0.196150i | \(-0.0628441\pi\) | |||||||
\(564\) | − | 11.6908i | − | 0.492271i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.26513 | + | 0.730424i | −0.0531774 | + | 0.0307020i | ||||
\(567\) | 2.54707 | 0.106967 | ||||||||
\(568\) | −11.3470 | + | 6.55122i | −0.476111 | + | 0.274883i | ||||
\(569\) | 4.13745 | − | 7.16627i | 0.173451 | − | 0.300426i | −0.766173 | − | 0.642634i | \(-0.777842\pi\) |
0.939624 | + | 0.342209i | \(0.111175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.2659 | −0.931797 | −0.465899 | − | 0.884838i | \(-0.654269\pi\) | ||||
−0.465899 | + | 0.884838i | \(0.654269\pi\) | |||||||
\(572\) | 2.17606 | + | 4.29805i | 0.0909858 | + | 0.179710i | ||||
\(573\) | 10.4325i | 0.435823i | ||||||||
\(574\) | 6.49171 | + | 3.74799i | 0.270959 | + | 0.156438i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −35.3355 | −1.47104 | −0.735518 | − | 0.677505i | \(-0.763061\pi\) | ||||
−0.735518 | + | 0.677505i | \(0.763061\pi\) | |||||||
\(578\) | −4.16943 | − | 7.22166i | −0.173425 | − | 0.300381i | ||||
\(579\) | 0.705866 | − | 0.407532i | 0.0293348 | − | 0.0169364i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5931 | + | 27.0081i | 0.646913 | + | 1.12049i | ||||
\(582\) | −1.32617 | − | 0.765663i | −0.0549714 | − | 0.0317378i | ||||
\(583\) | −5.84413 | + | 10.1223i | −0.242039 | + | 0.419224i | ||||
\(584\) | −2.59614 | −0.107429 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.7323 | 0.732514 | ||||||||
\(587\) | 2.02271 | − | 3.50343i | 0.0834861 | − | 0.144602i | −0.821259 | − | 0.570556i | \(-0.806728\pi\) |
0.904745 | + | 0.425953i | \(0.140061\pi\) | |||||||
\(588\) | 0.443778 | + | 0.256215i | 0.0183011 | + | 0.0105661i | ||||
\(589\) | 30.5705 | + | 52.9496i | 1.25963 | + | 2.18175i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5794 | − | 8.41742i | 0.599716 | − | 0.346246i | ||||
\(592\) | 2.62862 | + | 4.55291i | 0.108036 | + | 0.187123i | ||||
\(593\) | −7.73381 | −0.317590 | −0.158795 | − | 0.987312i | \(-0.550761\pi\) | ||||
−0.158795 | + | 0.987312i | \(0.550761\pi\) | |||||||
\(594\) | −0.668069 | − | 1.15713i | −0.0274112 | − | 0.0474776i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.84990 | − | 3.95479i | −0.280583 | − | 0.161994i | ||||
\(597\) | 6.73201i | 0.275523i | ||||||||
\(598\) | 8.43625 | − | 12.9179i | 0.344984 | − | 0.528251i | ||||
\(599\) | −23.3807 | −0.955310 | −0.477655 | − | 0.878548i | \(-0.658513\pi\) | ||||
−0.477655 | + | 0.878548i | \(0.658513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.78494 | − | 8.28776i | 0.195182 | − | 0.338065i | −0.751778 | − | 0.659416i | \(-0.770804\pi\) |
0.946960 | + | 0.321351i | \(0.104137\pi\) | |||||||
\(602\) | −11.9854 | + | 6.91980i | −0.488490 | + | 0.282030i | ||||
\(603\) | 6.08669 | 0.247869 | ||||||||
\(604\) | −14.8839 | + | 8.59321i | −0.605616 | + | 0.349653i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 0.517864i | − | 0.0210368i | ||||||
\(607\) | 28.5604 | − | 16.4894i | 1.15923 | − | 0.669283i | 0.208112 | − | 0.978105i | \(-0.433268\pi\) |
0.951120 | + | 0.308822i | \(0.0999347\pi\) | |||||||
\(608\) | −6.05291 | − | 3.49465i | −0.245478 | − | 0.141727i | ||||
\(609\) | 4.75226 | + | 2.74372i | 0.192571 | + | 0.111181i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.6065 | + | 19.0399i | −1.52140 | + | 0.770270i | ||||
\(612\) | 2.94298i | 0.118963i | ||||||||
\(613\) | −3.46687 | + | 6.00479i | −0.140026 | + | 0.242531i | −0.927506 | − | 0.373808i | \(-0.878052\pi\) |
0.787480 | + | 0.616340i | \(0.211385\pi\) | |||||||
\(614\) | −3.33445 | + | 5.77544i | −0.134567 | + | 0.233078i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.40324i | 0.137120i | ||||||||
\(617\) | −17.4915 | − | 30.2962i | −0.704182 | − | 1.21968i | −0.966986 | − | 0.254830i | \(-0.917981\pi\) |
0.262804 | − | 0.964849i | \(-0.415353\pi\) | |||||||
\(618\) | −1.21159 | − | 2.09854i | −0.0487373 | − | 0.0844155i | ||||
\(619\) | − | 31.0002i | − | 1.24600i | −0.782221 | − | 0.623001i | \(-0.785913\pi\) | ||
0.782221 | − | 0.623001i | \(-0.214087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.13956 | + | 3.70583i | −0.0858576 | + | 0.148710i | ||||
\(622\) | −9.81164 | + | 16.9943i | −0.393411 | + | 0.681408i | ||||
\(623\) | 29.5849i | 1.18529i | ||||||||
\(624\) | 1.97149 | − | 3.01881i | 0.0789228 | − | 0.120849i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.3050 | − | 6.52692i | −0.451837 | − | 0.260868i | ||||
\(627\) | 8.08752 | + | 4.66933i | 0.322985 | + | 0.186475i | ||||
\(628\) | −2.21792 | + | 1.28052i | −0.0885046 | + | 0.0510981i | ||||
\(629\) | 15.4720i | 0.616908i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.5912 | − | 7.26955i | 0.501249 | − | 0.289396i | −0.227980 | − | 0.973666i | \(-0.573212\pi\) |
0.729229 | + | 0.684269i | \(0.239879\pi\) | |||||||
\(632\) | −13.9773 | −0.555986 | ||||||||
\(633\) | −10.3989 | + | 6.00378i | −0.413317 | + | 0.238629i | ||||
\(634\) | 9.39578 | − | 16.2740i | 0.373154 | − | 0.646322i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.74779 | 0.346873 | ||||||||
\(637\) | 0.101439 | − | 1.84481i | 0.00401915 | − | 0.0730939i | ||||
\(638\) | − | 2.87859i | − | 0.113965i | ||||||
\(639\) | −11.3470 | − | 6.55122i | −0.448882 | − | 0.259162i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5538 | + | 35.6002i | 0.811825 | + | 1.40612i | 0.911585 | + | 0.411111i | \(0.134859\pi\) |
−0.0997605 | + | 0.995011i | \(0.531808\pi\) | |||||||
\(642\) | −6.12516 | −0.241741 | ||||||||
\(643\) | 12.1347 | + | 21.0180i | 0.478547 | + | 0.828868i | 0.999697 | − | 0.0245971i | \(-0.00783028\pi\) |
−0.521150 | + | 0.853465i | \(0.674497\pi\) | |||||||
\(644\) | 9.43901 | − | 5.44961i | 0.371949 | − | 0.214745i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.2847 | − | 17.8136i | −0.404646 | − | 0.700867i | ||||
\(647\) | 34.9290 | + | 20.1663i | 1.37320 | + | 0.792818i | 0.991330 | − | 0.131397i | \(-0.0419463\pi\) |
0.381872 | + | 0.924215i | \(0.375280\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −12.7419 | −0.500164 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.2813 | −0.873271 | ||||||||
\(652\) | −8.80763 | + | 15.2553i | −0.344933 | + | 0.597442i | ||||
\(653\) | 34.0173 | + | 19.6399i | 1.33120 | + | 0.768568i | 0.985483 | − | 0.169771i | \(-0.0543029\pi\) |
0.345716 | + | 0.938339i | \(0.387636\pi\) | |||||||
\(654\) | 0.273784 | + | 0.474209i | 0.0107058 | + | 0.0185430i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.54870 | + | 1.47149i | −0.0995099 | + | 0.0574521i | ||||
\(657\) | −1.29807 | − | 2.24832i | −0.0506425 | − | 0.0877154i | ||||
\(658\) | −29.7772 | −1.16084 | ||||||||
\(659\) | −10.5336 | − | 18.2448i | −0.410333 | − | 0.710717i | 0.584593 | − | 0.811326i | \(-0.301254\pi\) |
−0.994926 | + | 0.100609i | \(0.967921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.3964 | − | 11.7759i | −0.793330 | − | 0.458029i | 0.0478037 | − | 0.998857i | \(-0.484778\pi\) |
−0.841133 | + | 0.540828i | \(0.818111\pi\) | |||||||
\(662\) | − | 23.5574i | − | 0.915585i | ||||||
\(663\) | 9.46689 | − | 4.79301i | 0.367664 | − | 0.186145i | ||||
\(664\) | −12.2440 | −0.475159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.62862 | + | 4.55291i | −0.101857 | + | 0.176422i | ||||
\(667\) | −7.98388 | + | 4.60950i | −0.309137 | + | 0.178480i | ||||
\(668\) | 4.27912 | 0.165564 | ||||||||
\(669\) | −0.438808 | + | 0.253346i | −0.0169653 | + | 0.00979492i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.69668i | − | 0.374336i | ||||||
\(672\) | 2.20583 | − | 1.27354i | 0.0850917 | − | 0.0491277i | ||||
\(673\) | −11.7603 | − | 6.78980i | −0.453325 | − | 0.261728i | 0.255908 | − | 0.966701i | \(-0.417626\pi\) |
−0.709234 | + | 0.704974i | \(0.750959\pi\) | |||||||
\(674\) | −23.5677 | − | 13.6068i | −0.907795 | − | 0.524116i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9216 | − | 1.42533i | −0.496986 | − | 0.0548203i | ||||
\(677\) | − | 18.1429i | − | 0.697288i | −0.937255 | − | 0.348644i | \(-0.886642\pi\) | ||
0.937255 | − | 0.348644i | \(-0.113358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.95020 | + | 3.37784i | −0.0748418 | + | 0.129630i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.15945i | − | 0.159391i | ||||||
\(682\) | 5.84413 | + | 10.1223i | 0.223783 | + | 0.387604i | ||||
\(683\) | −9.66980 | − | 16.7486i | −0.370005 | − | 0.640867i | 0.619561 | − | 0.784948i | \(-0.287311\pi\) |
−0.989566 | + | 0.144082i | \(0.953977\pi\) | |||||||
\(684\) | − | 6.98929i | − | 0.267242i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.56735 | − | 16.5711i | 0.365283 | − | 0.632689i | ||||
\(687\) | 11.1844 | − | 19.3719i | 0.426711 | − | 0.739086i | ||||
\(688\) | − | 5.43353i | − | 0.207152i | ||||||
\(689\) | −14.2468 | − | 28.1396i | −0.542762 | − | 1.07203i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8778 | + | 9.74437i | 0.642060 | + | 0.370693i | 0.785408 | − | 0.618979i | \(-0.212453\pi\) |
−0.143348 | + | 0.989672i | \(0.545787\pi\) | |||||||
\(692\) | 7.31290 | + | 4.22210i | 0.277995 | + | 0.160500i | ||||
\(693\) | −2.94729 | + | 1.70162i | −0.111958 | + | 0.0646392i | ||||
\(694\) | 6.38389i | 0.242329i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.86578 | + | 1.07721i | −0.0707221 | + | 0.0408314i | ||||
\(697\) | −8.66115 | −0.328064 | ||||||||
\(698\) | 7.31585 | − | 4.22381i | 0.276909 | − | 0.159873i | ||||
\(699\) | −4.41166 | + | 7.64121i | −0.166864 | + | 0.289017i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6682 | 0.402931 | 0.201466 | − | 0.979496i | \(-0.435430\pi\) | ||||
0.201466 | + | 0.979496i | \(0.435430\pi\) | |||||||
\(702\) | 3.60011 | + | 0.197956i | 0.135878 | + | 0.00747137i | ||||
\(703\) | − | 36.7444i | − | 1.38584i | ||||||
\(704\) | −1.15713 | − | 0.668069i | −0.0436110 | − | 0.0251788i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.73075 | + | 13.3901i | 0.290951 | + | 0.503941i | ||||
\(707\) | −1.31904 | −0.0496075 | ||||||||
\(708\) | 4.76818 | + | 8.25873i | 0.179199 | + | 0.310382i | ||||
\(709\) | 35.9403 | − | 20.7502i | 1.34977 | − | 0.779289i | 0.361551 | − | 0.932352i | \(-0.382247\pi\) |
0.988216 | + | 0.153063i | \(0.0489138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.98864 | − | 12.1047i | −0.262094 | − | 0.453961i | ||||
\(712\) | −10.0591 | − | 5.80763i | −0.376981 | − | 0.217650i | ||||
\(713\) | 18.7164 | − | 32.4178i | 0.700936 | − | 1.21406i | ||||
\(714\) | 7.49599 | 0.280530 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.96571 | 0.0734621 | ||||||||
\(717\) | −12.8116 | + | 22.1904i | −0.478459 | + | 0.828716i | ||||
\(718\) | −29.8640 | − | 17.2420i | −1.11451 | − | 0.643464i | ||||
\(719\) | −20.4278 | − | 35.3820i | −0.761828 | − | 1.31953i | −0.941907 | − | 0.335873i | \(-0.890969\pi\) |
0.180079 | − | 0.983652i | \(-0.442365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.34512 | + | 3.08601i | −0.199063 | + | 0.114929i | ||||
\(722\) | 14.9251 | + | 25.8511i | 0.555455 | + | 0.962077i | ||||
\(723\) | 13.7808 | 0.512515 | ||||||||
\(724\) | 3.30763 | + | 5.72898i | 0.122927 | + | 0.212916i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.98019 | − | 4.60737i | −0.296173 | − | 0.170995i | ||||
\(727\) | 6.84248i | 0.253773i | 0.991917 | + | 0.126887i | \(0.0404985\pi\) | ||||
−0.991917 | + | 0.126887i | \(0.959502\pi\) | |||||||
\(728\) | −7.68913 | − | 5.02153i | −0.284978 | − | 0.186110i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.99540 | − | 13.8484i | 0.295721 | − | 0.512203i | ||||
\(732\) | −6.28496 | + | 3.62862i | −0.232299 | + | 0.134118i | ||||
\(733\) | −25.2614 | −0.933051 | −0.466525 | − | 0.884508i | \(-0.654494\pi\) | ||||
−0.466525 | + | 0.884508i | \(0.654494\pi\) | |||||||
\(734\) | −31.9910 | + | 18.4700i | −1.18081 | + | 0.681741i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.27912i | 0.157731i | ||||||||
\(737\) | −7.04309 | + | 4.06633i | −0.259436 | + | 0.149785i | ||||
\(738\) | −2.54870 | − | 1.47149i | −0.0938189 | − | 0.0541663i | ||||
\(739\) | −3.67362 | − | 2.12096i | −0.135136 | − | 0.0780209i | 0.430908 | − | 0.902396i | \(-0.358193\pi\) |
−0.566044 | + | 0.824375i | \(0.691527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.4829 | + | 11.3829i | −0.825931 | + | 0.418162i | ||||
\(742\) | − | 22.2813i | − | 0.817971i | ||||||
\(743\) | −3.04879 | + | 5.28067i | −0.111849 | + | 0.193729i | −0.916516 | − | 0.399998i | \(-0.869011\pi\) |
0.804667 | + | 0.593727i | \(0.202344\pi\) | |||||||
\(744\) | 4.37390 | − | 7.57581i | 0.160355 | − | 0.277743i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.1924i | 0.446395i | ||||||||
\(747\) | −6.12199 | − | 10.6036i | −0.223992 | − | 0.387965i | ||||
\(748\) | −1.96612 | − | 3.40541i | −0.0718883 | − | 0.124514i | ||||
\(749\) | 15.6012i | 0.570056i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3192 | − | 29.9977i | 0.631986 | − | 1.09463i | −0.355160 | − | 0.934806i | \(-0.615574\pi\) |
0.987145 | − | 0.159825i | \(-0.0510931\pi\) | |||||||
\(752\) | 5.84539 | − | 10.1245i | 0.213159 | − | 0.369203i | ||||
\(753\) | − | 21.0591i | − | 0.767438i | ||||||
\(754\) | 6.50377 | + | 4.24741i | 0.236853 | + | 0.154681i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.20583 | + | 1.27354i | 0.0802252 | + | 0.0463180i | ||||
\(757\) | 2.28724 | + | 1.32054i | 0.0831310 | + | 0.0479957i | 0.540989 | − | 0.841029i | \(-0.318050\pi\) |
−0.457858 | + | 0.889025i | \(0.651383\pi\) | |||||||
\(758\) | −1.24346 | + | 0.717912i | −0.0451645 | + | 0.0260757i | ||||
\(759\) | − | 5.71750i | − | 0.207532i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.6508 | − | 27.5112i | 1.72734 | − | 0.997281i | 0.826826 | − | 0.562458i | \(-0.190144\pi\) |
0.900516 | − | 0.434823i | \(-0.143189\pi\) | |||||||
\(762\) | 7.11907 | 0.257897 | ||||||||
\(763\) | 1.20784 | − | 0.697348i | 0.0437268 | − | 0.0252457i | ||||
\(764\) | −5.21624 | + | 9.03479i | −0.188717 | + | 0.326867i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.2193 | −0.730554 | ||||||||
\(767\) | 18.8009 | − | 28.7885i | 0.678860 | − | 1.03949i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 27.7928 | + | 16.0462i | 1.00223 | + | 0.578639i | 0.908908 | − | 0.416997i | \(-0.136917\pi\) |
0.0933243 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.14377 | + | 12.3734i | 0.257277 | + | 0.445616i | ||||
\(772\) | 0.815063 | 0.0293348 | ||||||||
\(773\) | −26.8465 | − | 46.4995i | −0.965601 | − | 1.67247i | −0.707993 | − | 0.706220i | \(-0.750399\pi\) |
−0.257608 | − | 0.966250i | \(-0.582934\pi\) | |||||||
\(774\) | 4.70558 | − | 2.71677i | 0.169139 | − | 0.0976522i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.765663 | − | 1.32617i | −0.0274857 | − | 0.0476067i | ||||
\(777\) | 11.5966 | + | 6.69529i | 0.416025 | + | 0.240192i | ||||
\(778\) | 1.07721 | − | 1.86578i | 0.0386197 | − | 0.0668913i | ||||
\(779\) | 20.5694 | 0.736974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5067 | 0.626438 | ||||||||
\(782\) | −6.29669 | + | 10.9062i | −0.225169 | + | 0.390005i | ||||
\(783\) | −1.86578 | − | 1.07721i | −0.0666774 | − | 0.0384962i | ||||
\(784\) | 0.256215 | + | 0.443778i | 0.00915054 | + | 0.0158492i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.15998 | + | 4.71117i | −0.291057 | + | 0.168042i | ||||
\(787\) | −8.44876 | − | 14.6337i | −0.301166 | − | 0.521635i | 0.675234 | − | 0.737603i | \(-0.264042\pi\) |
−0.976400 | + | 0.215969i | \(0.930709\pi\) | |||||||
\(788\) | 16.8348 | 0.599716 | ||||||||
\(789\) | −13.0638 | − | 22.6272i | −0.465085 | − | 0.805551i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 1.33614i | − | 0.0474776i | ||||||
\(793\) | 21.9082 | + | 14.3076i | 0.777985 | + | 0.508078i | ||||
\(794\) | −26.8571 | −0.953123 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.36600 | + | 5.83009i | −0.119305 | + | 0.206642i | ||||
\(797\) | −13.1928 | + | 7.61687i | −0.467313 | + | 0.269803i | −0.715114 | − | 0.699008i | \(-0.753625\pi\) |
0.247801 | + | 0.968811i | \(0.420292\pi\) | |||||||
\(798\) | −17.8022 | −0.630192 | ||||||||
\(799\) | 29.7963 | − | 17.2029i | 1.05412 | − | 0.608594i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11.6153i | − | 0.410405i | ||||||
\(802\) | 17.8763 | − | 10.3209i | 0.631233 | − | 0.364442i | ||||
\(803\) | 3.00407 | + | 1.73440i | 0.106011 | + | 0.0612057i | ||||
\(804\) | 5.27123 | + | 3.04334i | 0.185902 | + | 0.107330i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31.4930 | − | 1.73168i | −1.10930 | − | 0.0609958i | ||||
\(807\) | − | 15.6149i | − | 0.549669i | ||||||
\(808\) | 0.258932 | − | 0.448484i | 0.00910920 | − | 0.0157776i | ||||
\(809\) | 27.9518 | − | 48.4139i | 0.982733 | − | 1.70214i | 0.331127 | − | 0.943586i | \(-0.392571\pi\) |
0.651606 | − | 0.758557i | \(-0.274095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.263496i | 0.00925261i | 0.999989 | + | 0.00462630i | \(0.00147260\pi\) | ||||
−0.999989 | + | 0.00462630i | \(0.998527\pi\) | |||||||
\(812\) | 2.74372 | + | 4.75226i | 0.0962857 | + | 0.166772i | ||||
\(813\) | 13.0635 | + | 22.6267i | 0.458158 | + | 0.793553i | ||||
\(814\) | − | 7.02441i | − | 0.246205i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.47149 | + | 2.54870i | −0.0515125 | + | 0.0892223i | ||||
\(817\) | −18.9883 | + | 32.8887i | −0.664316 | + | 1.15063i | ||||
\(818\) | 4.18366i | 0.146278i | ||||||||
\(819\) | 0.504208 | − | 9.16974i | 0.0176185 | − | 0.320417i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.0125 | + | 19.6371i | 1.18705 | + | 0.685341i | 0.957634 | − | 0.287989i | \(-0.0929866\pi\) |
0.229411 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(822\) | 16.0619 | + | 9.27336i | 0.560224 | + | 0.323446i | ||||
\(823\) | 19.3855 | − | 11.1922i | 0.675737 | − | 0.390137i | −0.122510 | − | 0.992467i | \(-0.539094\pi\) |
0.798247 | + | 0.602330i | \(0.205761\pi\) | |||||||
\(824\) | − | 2.42318i | − | 0.0844155i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.0356 | − | 12.1449i | 0.731921 | − | 0.422575i | ||||
\(827\) | 10.0484 | 0.349417 | 0.174709 | − | 0.984620i | \(-0.444102\pi\) | ||||
0.174709 | + | 0.984620i | \(0.444102\pi\) | |||||||
\(828\) | −3.70583 | + | 2.13956i | −0.128786 | + | 0.0743549i | ||||
\(829\) | 15.2722 | − | 26.4522i | 0.530425 | − | 0.918723i | −0.468945 | − | 0.883228i | \(-0.655366\pi\) |
0.999370 | − | 0.0354958i | \(-0.0113010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4281 | −0.673953 | ||||||||
\(832\) | 3.21677 | − | 1.62862i | 0.111521 | − | 0.0564623i | ||||
\(833\) | 1.50807i | 0.0522517i | ||||||||
\(834\) | −17.0760 | − | 9.85885i | −0.591294 | − | 0.341384i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.66933 | + | 8.08752i | 0.161492 | + | 0.279713i | ||||
\(837\) | 8.74779 | 0.302368 | ||||||||
\(838\) | 14.4210 | + | 24.9779i | 0.498164 | + | 0.862846i | ||||
\(839\) | 28.8867 | − | 16.6777i | 0.997279 | − | 0.575780i | 0.0898372 | − | 0.995956i | \(-0.471365\pi\) |
0.907442 | + | 0.420177i | \(0.138032\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1793 | + | 21.0951i | 0.419974 | + | 0.727417i | ||||
\(842\) | 9.87144 | + | 5.69928i | 0.340192 | + | 0.196410i | ||||
\(843\) | −5.33151 | + | 9.23444i | −0.183627 | + | 0.318051i | ||||
\(844\) | −12.0076 | −0.413317 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.6908 | 0.401937 | ||||||||
\(847\) | −11.7353 | + | 20.3261i | −0.403229 | + | 0.698414i | ||||
\(848\) | 7.57581 | + | 4.37390i | 0.260154 | + | 0.150200i | ||||
\(849\) | −0.730424 | − | 1.26513i | −0.0250681 | − | 0.0434192i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.4824 | + | 11.2482i | −0.667849 | + | 0.385583i | ||||
\(852\) | −6.55122 | − | 11.3470i | −0.224441 | − | 0.388743i | ||||
\(853\) | 10.4152 | 0.356609 | 0.178305 | − | 0.983975i | \(-0.442939\pi\) | ||||
0.178305 | + | 0.983975i | \(0.442939\pi\) | |||||||
\(854\) | 9.24236 | + | 16.0082i | 0.316267 | + | 0.547790i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.30455 | − | 3.06258i | −0.181306 | − | 0.104677i | ||||
\(857\) | − | 46.7684i | − | 1.59758i | −0.601611 | − | 0.798789i | \(-0.705474\pi\) | ||
0.601611 | − | 0.798789i | \(-0.294526\pi\) | |||||||
\(858\) | −4.29805 | + | 2.17606i | −0.146733 | + | 0.0742896i | ||||
\(859\) | 9.19564 | 0.313751 | 0.156876 | − | 0.987618i | \(-0.449858\pi\) | ||||
0.156876 | + | 0.987618i | \(0.449858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.74799 | + | 6.49171i | −0.127731 | + | 0.221237i | ||||
\(862\) | −26.5014 | + | 15.3006i | −0.902640 | + | 0.521140i | ||||
\(863\) | −25.7961 | −0.878108 | −0.439054 | − | 0.898461i | \(-0.644686\pi\) | ||||
−0.439054 | + | 0.898461i | \(0.644686\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 38.1434i | 1.29617i | ||||||||
\(867\) | 7.22166 | − | 4.16943i | 0.245260 | − | 0.141601i | ||||
\(868\) | −19.2961 | − | 11.1406i | −0.654953 | − | 0.378137i | ||||
\(869\) | 16.1735 | + | 9.33779i | 0.548649 | + | 0.316763i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.20490 | − | 21.9128i | 0.0408264 | − | 0.742486i | ||||
\(872\) | 0.547569i | 0.0185430i | ||||||||
\(873\) | 0.765663 | − | 1.32617i | 0.0259138 | − | 0.0448840i | ||||
\(874\) | 14.9540 | − | 25.9011i | 0.505827 | − | 0.876118i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.59614i | − | 0.0877154i | ||||||
\(877\) | −2.41271 | − | 4.17893i | −0.0814713 | − | 0.141112i | 0.822411 | − | 0.568894i | \(-0.192629\pi\) |
−0.903882 | + | 0.427782i | \(0.859295\pi\) | |||||||
\(878\) | −7.39969 | − | 12.8166i | −0.249727 | − | 0.432541i | ||||
\(879\) | 17.7323i | 0.598095i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.98574 | + | 5.17145i | −0.100592 | + | 0.174231i | −0.911929 | − | 0.410349i | \(-0.865407\pi\) |
0.811337 | + | 0.584579i | \(0.198740\pi\) | |||||||
\(882\) | −0.256215 | + | 0.443778i | −0.00862721 | + | 0.0149428i | ||||
\(883\) | 36.7779i | 1.23767i | 0.785520 | + | 0.618837i | \(0.212396\pi\) | ||||
−0.785520 | + | 0.618837i | \(0.787604\pi\) | |||||||
\(884\) | 10.5951 | + | 0.582581i | 0.356351 | + | 0.0195943i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.79964 | − | 1.03902i | −0.0604601 | − | 0.0349066i | ||||
\(887\) | 42.8974 | + | 24.7668i | 1.44035 | + | 0.831588i | 0.997873 | − | 0.0651906i | \(-0.0207655\pi\) |
0.442480 | + | 0.896779i | \(0.354099\pi\) | |||||||
\(888\) | −4.55291 | + | 2.62862i | −0.152786 | + | 0.0882108i | ||||
\(889\) | − | 18.1328i | − | 0.608154i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.15713 | − | 0.668069i | 0.0387653 | − | 0.0223812i | ||||
\(892\) | −0.506692 | −0.0169653 | ||||||||
\(893\) | −70.7632 | + | 40.8551i | −2.36800 | + | 1.36717i | ||||
\(894\) | 3.95479 | − | 6.84990i | 0.132268 | − | 0.229095i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.54707 | 0.0850917 | ||||||||
\(897\) | 12.9179 | + | 8.43625i | 0.431315 | + | 0.281678i | ||||
\(898\) | − | 9.81754i | − | 0.327616i | ||||||
\(899\) | 16.3214 | + | 9.42318i | 0.544350 | + | 0.314281i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.8723 | + | 22.2955i | 0.428839 | + | 0.742770i | ||||
\(902\) | 3.93223 | 0.130929 | ||||||||
\(903\) | −6.91980 | − | 11.9854i | −0.230276 | − | 0.398851i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.59321 | − | 14.8839i | −0.285490 | − | 0.494483i | ||||
\(907\) | −26.3728 | − | 15.2263i | −0.875694 | − | 0.505582i | −0.00645802 | − | 0.999979i | \(-0.502056\pi\) |
−0.869236 | + | 0.494397i | \(0.835389\pi\) | |||||||
\(908\) | 2.07973 | − | 3.60219i | 0.0690181 | − | 0.119543i | ||||
\(909\) | 0.517864 | 0.0171765 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0258 | 0.464696 | 0.232348 | − | 0.972633i | \(-0.425359\pi\) | ||||
0.232348 | + | 0.972633i | \(0.425359\pi\) | |||||||
\(912\) | 3.49465 | − | 6.05291i | 0.115719 | − | 0.200432i | ||||
\(913\) | 14.1679 | + | 8.17983i | 0.468888 | + | 0.270713i | ||||
\(914\) | −16.0683 | − | 27.8311i | −0.531491 | − | 0.920570i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.3719 | − | 11.1844i | 0.640067 | − | 0.369543i | ||||
\(917\) | 11.9997 | + | 20.7840i | 0.396264 | + | 0.686349i | ||||
\(918\) | −2.94298 | −0.0971329 | ||||||||
\(919\) | −2.17806 | − | 3.77251i | −0.0718476 | − | 0.124444i | 0.827863 | − | 0.560930i | \(-0.189556\pi\) |
−0.899711 | + | 0.436486i | \(0.856223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.77544 | − | 3.33445i | −0.190307 | − | 0.109874i | ||||
\(922\) | 20.6626i | 0.680487i | ||||||||
\(923\) | −25.8313 | + | 39.5538i | −0.850249 | + | 1.30193i | ||||
\(924\) | −3.40324 | −0.111958 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.10874 | + | 15.7768i | −0.299332 | + | 0.518458i | ||||
\(927\) | 2.09854 | − | 1.21159i | 0.0689250 | − | 0.0397939i | ||||
\(928\) | −2.15441 | −0.0707221 | ||||||||
\(929\) | 31.7664 | − | 18.3403i | 1.04222 | − | 0.601727i | 0.121759 | − | 0.992560i | \(-0.461146\pi\) |
0.920462 | + | 0.390833i | \(0.127813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.58153i | − | 0.117380i | ||||||
\(932\) | −7.64121 | + | 4.41166i | −0.250296 | + | 0.144509i | ||||
\(933\) | −16.9943 | − | 9.81164i | −0.556367 | − | 0.321219i | ||||
\(934\) | −4.86628 | − | 2.80955i | −0.159229 | − | 0.0919312i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.01881 | + | 1.97149i | 0.0986729 | + | 0.0644402i | ||||
\(937\) | − | 37.1292i | − | 1.21296i | −0.795100 | − | 0.606478i | \(-0.792582\pi\) | ||
0.795100 | − | 0.606478i | \(-0.207418\pi\) | |||||||
\(938\) | 7.75161 | − | 13.4262i | 0.253099 | − | 0.438381i | ||||
\(939\) | 6.52692 | − | 11.3050i | 0.212998 | − | 0.368923i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.28642i | − | 0.139733i | −0.997556 | − | 0.0698666i | \(-0.977743\pi\) | ||
0.997556 | − | 0.0698666i | \(-0.0222574\pi\) | |||||||
\(942\) | −1.28052 | − | 2.21792i | −0.0417215 | − | 0.0722637i | ||||
\(943\) | −6.29669 | − | 10.9062i | −0.205048 | − | 0.355154i | ||||
\(944\) | 9.53636i | 0.310382i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.62998 | + | 6.28731i | −0.118021 | + | 0.204418i | ||||
\(947\) | 20.6314 | − | 35.7346i | 0.670429 | − | 1.16122i | −0.307353 | − | 0.951596i | \(-0.599443\pi\) |
0.977782 | − | 0.209622i | \(-0.0672234\pi\) | |||||||
\(948\) | − | 13.9773i | − | 0.453961i | ||||||
\(949\) | −8.35117 | + | 4.22813i | −0.271091 | + | 0.137251i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2740 | + | 9.39578i | 0.527719 | + | 0.304679i | ||||
\(952\) | 6.49171 | + | 3.74799i | 0.210398 | + | 0.121473i | ||||
\(953\) | 6.13723 | − | 3.54333i | 0.198804 | − | 0.114780i | −0.397293 | − | 0.917692i | \(-0.630050\pi\) |
0.596098 | + | 0.802912i | \(0.296717\pi\) | |||||||
\(954\) | 8.74779i | 0.283220i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.1904 | + | 12.8116i | −0.717689 | + | 0.414358i | ||||
\(957\) | 2.87859 | 0.0930517 | ||||||||
\(958\) | 23.1239 | − | 13.3506i | 0.747098 | − | 0.431337i | ||||
\(959\) | 23.6199 | − | 40.9109i | 0.762726 | − | 1.32108i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.5239 | −1.46851 | ||||||||
\(962\) | 15.8706 | + | 10.3646i | 0.511689 | + | 0.334168i | ||||
\(963\) | − | 6.12516i | − | 0.197381i | ||||||
\(964\) | 11.9346 | + | 6.89042i | 0.384386 | + | 0.221926i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.44961 | + | 9.43901i | 0.175338 | + | 0.303695i | ||||
\(967\) | −29.4591 | −0.947340 | −0.473670 | − | 0.880702i | \(-0.657071\pi\) | ||||
−0.473670 | + | 0.880702i | \(0.657071\pi\) | |||||||
\(968\) | −4.60737 | − | 7.98019i | −0.148086 | − | 0.256493i | ||||
\(969\) | 17.8136 | − | 10.2847i | 0.572255 | − | 0.330392i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.6123 | − | 44.3618i | −0.821938 | − | 1.42364i | −0.904237 | − | 0.427031i | \(-0.859559\pi\) |
0.0822983 | − | 0.996608i | \(-0.473774\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | −25.1112 | + | 43.4938i | −0.805028 | + | 1.39435i | ||||
\(974\) | 31.0293 | 0.994242 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.25724 | −0.232299 | ||||||||
\(977\) | −1.75058 | + | 3.03210i | −0.0560061 | + | 0.0970054i | −0.892669 | − | 0.450713i | \(-0.851170\pi\) |
0.836663 | + | 0.547718i | \(0.184503\pi\) | |||||||
\(978\) | −15.2553 | − | 8.80763i | −0.487810 | − | 0.281637i | ||||
\(979\) | 7.75980 | + | 13.4404i | 0.248004 | + | 0.429556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.474209 | + | 0.273784i | −0.0151403 | + | 0.00874126i | ||||
\(982\) | −7.27846 | − | 12.6067i | −0.232265 | − | 0.402295i | ||||
\(983\) | −0.473855 | −0.0151136 | −0.00755682 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755682 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(984\) | −1.47149 | − | 2.54870i | −0.0469094 | − | 0.0812495i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.49095 | − | 3.17020i | −0.174867 | − | 0.100960i | ||||
\(987\) | − | 29.7772i | − | 0.947820i | ||||||
\(988\) | −25.1622 | − | 1.38357i | −0.800518 | − | 0.0440173i | ||||
\(989\) | 23.2508 | 0.739331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.50506 | − | 7.80299i | 0.143108 | − | 0.247870i | −0.785558 | − | 0.618789i | \(-0.787624\pi\) |
0.928665 | + | 0.370918i | \(0.120957\pi\) | |||||||
\(992\) | 7.57581 | − | 4.37390i | 0.240532 | − | 0.138871i | ||||
\(993\) | 23.5574 | 0.747572 | ||||||||
\(994\) | −28.9017 | + | 16.6864i | −0.916707 | + | 0.529261i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 12.2440i | − | 0.387965i | ||||||
\(997\) | 27.9096 | − | 16.1136i | 0.883906 | − | 0.510324i | 0.0119620 | − | 0.999928i | \(-0.496192\pi\) |
0.871944 | + | 0.489605i | \(0.162859\pi\) | |||||||
\(998\) | −23.0251 | − | 13.2935i | −0.728846 | − | 0.420799i | ||||
\(999\) | −4.55291 | − | 2.62862i | −0.144048 | − | 0.0831659i |
(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 | 1950.2.y.m.199.1 | 12 | ||
5.2 | odd | 4 | 1950.2.bc.h.901.3 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.bc.k.901.4 | yes | 12 | ||
5.4 | even | 2 | 1950.2.y.n.199.6 | 12 | |||
13.10 | even | 6 | 1950.2.y.n.49.6 | 12 | |||
65.23 | odd | 12 | 1950.2.bc.k.751.4 | yes | 12 | ||
65.49 | even | 6 | inner | 1950.2.y.m.49.1 | 12 | ||
65.62 | odd | 12 | 1950.2.bc.h.751.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.1 | 12 | 65.49 | even | 6 | inner | ||
1950.2.y.m.199.1 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.y.n.49.6 | 12 | 13.10 | even | 6 | |||
1950.2.y.n.199.6 | 12 | 5.4 | even | 2 | |||
1950.2.bc.h.751.3 | ✓ | 12 | 65.62 | odd | 12 | ||
1950.2.bc.h.901.3 | yes | 12 | 5.2 | odd | 4 | ||
1950.2.bc.k.751.4 | yes | 12 | 65.23 | odd | 12 | ||
1950.2.bc.k.901.4 | yes | 12 | 5.3 | odd | 4 |