Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,3,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.64580135835\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.9 | ||
Root | \(0.969662 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.3.d.a.235.19 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0.969662 | 0.193932 | 0.0969662 | − | 0.995288i | \(-0.469086\pi\) | ||||
0.0969662 | + | 0.995288i | \(0.469086\pi\) | |||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 3.05407 | 0.436296 | 0.218148 | − | 0.975916i | \(-0.429998\pi\) | ||||
0.218148 | + | 0.975916i | \(0.429998\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 1.37131i | − | 0.137131i | ||||||
\(11\) | − | 3.80377i | − | 0.345797i | −0.984940 | − | 0.172899i | \(-0.944687\pi\) | ||
0.984940 | − | 0.172899i | \(-0.0553133\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | − | 11.7231i | − | 0.901777i | −0.892580 | − | 0.450889i | \(-0.851107\pi\) | ||
0.892580 | − | 0.450889i | \(-0.148893\pi\) | |||||||
\(14\) | − | 4.31911i | − | 0.308508i | ||||||
\(15\) | 1.67950 | 0.111967 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 18.5750 | 1.09265 | 0.546323 | − | 0.837574i | \(-0.316027\pi\) | ||||
0.546323 | + | 0.837574i | \(0.316027\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 19.0796 | 1.00419 | 0.502095 | − | 0.864813i | \(-0.332563\pi\) | ||||
0.502095 | + | 0.864813i | \(0.332563\pi\) | |||||||
\(20\) | −1.93932 | −0.0969662 | ||||||||
\(21\) | 5.28981 | 0.251895 | ||||||||
\(22\) | −5.37934 | −0.244516 | ||||||||
\(23\) | − | 12.7703i | − | 0.555230i | −0.960692 | − | 0.277615i | \(-0.910456\pi\) | ||
0.960692 | − | 0.277615i | \(-0.0895439\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −24.0598 | −0.962390 | ||||||||
\(26\) | −16.5790 | −0.637653 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −6.10814 | −0.218148 | ||||||||
\(29\) | 33.5722 | 1.15766 | 0.578832 | − | 0.815447i | \(-0.303509\pi\) | ||||
0.578832 | + | 0.815447i | \(0.303509\pi\) | |||||||
\(30\) | − | 2.37518i | − | 0.0791726i | ||||||
\(31\) | − | 34.8029i | − | 1.12267i | −0.827587 | − | 0.561337i | \(-0.810287\pi\) | ||
0.827587 | − | 0.561337i | \(-0.189713\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | − | 6.58832i | − | 0.199646i | ||||||
\(34\) | − | 26.2690i | − | 0.772618i | ||||||
\(35\) | 2.96142 | 0.0846119 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 5.62133i | − | 0.151928i | −0.997111 | − | 0.0759639i | \(-0.975797\pi\) | ||
0.997111 | − | 0.0759639i | \(-0.0242034\pi\) | |||||||
\(38\) | − | 26.9826i | − | 0.710069i | ||||||
\(39\) | − | 20.3050i | − | 0.520641i | ||||||
\(40\) | 2.74262i | 0.0685655i | ||||||||
\(41\) | 2.32258 | 0.0566483 | 0.0283242 | − | 0.999599i | \(-0.490983\pi\) | ||||
0.0283242 | + | 0.999599i | \(0.490983\pi\) | |||||||
\(42\) | − | 7.48091i | − | 0.178117i | ||||||
\(43\) | 3.84313i | 0.0893750i | 0.999001 | + | 0.0446875i | \(0.0142292\pi\) | ||||
−0.999001 | + | 0.0446875i | \(0.985771\pi\) | |||||||
\(44\) | 7.60754i | 0.172899i | ||||||||
\(45\) | 2.90899 | 0.0646441 | ||||||||
\(46\) | −18.0599 | −0.392607 | ||||||||
\(47\) | 53.4193i | 1.13658i | 0.822828 | + | 0.568291i | \(0.192395\pi\) | ||||
−0.822828 | + | 0.568291i | \(0.807605\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −39.6727 | −0.809646 | ||||||||
\(50\) | 34.0256i | 0.680513i | ||||||||
\(51\) | 32.1728 | 0.630840 | ||||||||
\(52\) | 23.4462i | 0.450889i | ||||||||
\(53\) | 9.70038 | 0.183026 | 0.0915130 | − | 0.995804i | \(-0.470830\pi\) | ||||
0.0915130 | + | 0.995804i | \(0.470830\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | − | 3.68837i | − | 0.0670613i | ||||||
\(56\) | 8.63822i | 0.154254i | ||||||||
\(57\) | 33.0468 | 0.579769 | ||||||||
\(58\) | − | 47.4783i | − | 0.818592i | ||||||
\(59\) | −57.6355 | + | 12.6155i | −0.976873 | + | 0.213822i | ||||
\(60\) | −3.35901 | −0.0559835 | ||||||||
\(61\) | − | 6.26746i | − | 0.102745i | −0.998680 | − | 0.0513727i | \(-0.983640\pi\) | ||
0.998680 | − | 0.0513727i | \(-0.0163596\pi\) | |||||||
\(62\) | −49.2188 | −0.793851 | ||||||||
\(63\) | 9.16221 | 0.145432 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 11.3674i | − | 0.174884i | ||||||
\(66\) | −9.31729 | −0.141171 | ||||||||
\(67\) | − | 46.7320i | − | 0.697493i | −0.937217 | − | 0.348747i | \(-0.886607\pi\) | ||
0.937217 | − | 0.348747i | \(-0.113393\pi\) | |||||||
\(68\) | −37.1500 | −0.546323 | ||||||||
\(69\) | − | 22.1188i | − | 0.320562i | ||||||
\(70\) | − | 4.18807i | − | 0.0598296i | ||||||
\(71\) | 58.6411 | 0.825931 | 0.412966 | − | 0.910747i | \(-0.364493\pi\) | ||||
0.412966 | + | 0.910747i | \(0.364493\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | − | 3.41033i | − | 0.0467168i | −0.999727 | − | 0.0233584i | \(-0.992564\pi\) | ||
0.999727 | − | 0.0233584i | \(-0.00743589\pi\) | |||||||
\(74\) | −7.94975 | −0.107429 | ||||||||
\(75\) | −41.6727 | −0.555636 | ||||||||
\(76\) | −38.1592 | −0.502095 | ||||||||
\(77\) | − | 11.6170i | − | 0.150870i | ||||||
\(78\) | −28.7156 | −0.368149 | ||||||||
\(79\) | −44.9144 | −0.568537 | −0.284269 | − | 0.958745i | \(-0.591751\pi\) | ||||
−0.284269 | + | 0.958745i | \(0.591751\pi\) | |||||||
\(80\) | 3.87865 | 0.0484831 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 3.28463i | − | 0.0400564i | ||||||
\(83\) | 147.198i | 1.77346i | 0.462283 | + | 0.886732i | \(0.347030\pi\) | ||||
−0.462283 | + | 0.886732i | \(0.652970\pi\) | |||||||
\(84\) | −10.5796 | −0.125948 | ||||||||
\(85\) | 18.0115 | 0.211900 | ||||||||
\(86\) | 5.43500 | 0.0631977 | ||||||||
\(87\) | 58.1488 | 0.668377 | ||||||||
\(88\) | 10.7587 | 0.122258 | ||||||||
\(89\) | 92.3380i | 1.03751i | 0.854924 | + | 0.518753i | \(0.173603\pi\) | ||||
−0.854924 | + | 0.518753i | \(0.826397\pi\) | |||||||
\(90\) | − | 4.11393i | − | 0.0457103i | ||||||
\(91\) | − | 35.8032i | − | 0.393442i | ||||||
\(92\) | 25.5406i | 0.277615i | ||||||||
\(93\) | − | 60.2804i | − | 0.648177i | ||||||
\(94\) | 75.5463 | 0.803684 | ||||||||
\(95\) | 18.5008 | 0.194745 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | − | 123.134i | − | 1.26942i | −0.772749 | − | 0.634712i | \(-0.781119\pi\) | ||
0.772749 | − | 0.634712i | \(-0.218881\pi\) | |||||||
\(98\) | 56.1056i | 0.572506i | ||||||||
\(99\) | − | 11.4113i | − | 0.115266i | ||||||
\(100\) | 48.1195 | 0.481195 | ||||||||
\(101\) | 126.506i | 1.25254i | 0.779607 | + | 0.626269i | \(0.215419\pi\) | ||||
−0.779607 | + | 0.626269i | \(0.784581\pi\) | |||||||
\(102\) | − | 45.4993i | − | 0.446071i | ||||||
\(103\) | 11.2967i | 0.109677i | 0.998495 | + | 0.0548386i | \(0.0174644\pi\) | ||||
−0.998495 | + | 0.0548386i | \(0.982536\pi\) | |||||||
\(104\) | 33.1579 | 0.318826 | ||||||||
\(105\) | 5.12932 | 0.0488507 | ||||||||
\(106\) | − | 13.7184i | − | 0.129419i | ||||||
\(107\) | −40.1705 | −0.375425 | −0.187713 | − | 0.982224i | \(-0.560107\pi\) | ||||
−0.187713 | + | 0.982224i | \(0.560107\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | 199.994i | 1.83481i | 0.397958 | + | 0.917404i | \(0.369719\pi\) | ||||
−0.397958 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(110\) | −5.21614 | −0.0474195 | ||||||||
\(111\) | − | 9.73642i | − | 0.0877155i | ||||||
\(112\) | 12.2163 | 0.109074 | ||||||||
\(113\) | 100.676i | 0.890935i | 0.895298 | + | 0.445467i | \(0.146962\pi\) | ||||
−0.895298 | + | 0.445467i | \(0.853038\pi\) | |||||||
\(114\) | − | 46.7353i | − | 0.409959i | ||||||
\(115\) | − | 12.3829i | − | 0.107677i | ||||||
\(116\) | −67.1445 | −0.578832 | ||||||||
\(117\) | − | 35.1693i | − | 0.300592i | ||||||
\(118\) | 17.8410 | + | 81.5089i | 0.151195 | + | 0.690753i | ||||
\(119\) | 56.7293 | 0.476717 | ||||||||
\(120\) | 4.75035i | 0.0395863i | ||||||||
\(121\) | 106.531 | 0.880424 | ||||||||
\(122\) | −8.86353 | −0.0726519 | ||||||||
\(123\) | 4.02283 | 0.0327059 | ||||||||
\(124\) | 69.6058i | 0.561337i | ||||||||
\(125\) | −47.5714 | −0.380571 | ||||||||
\(126\) | − | 12.9573i | − | 0.102836i | ||||||
\(127\) | 50.1279 | 0.394708 | 0.197354 | − | 0.980332i | \(-0.436765\pi\) | ||||
0.197354 | + | 0.980332i | \(0.436765\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 6.65649i | 0.0516007i | ||||||||
\(130\) | −16.0760 | −0.123662 | ||||||||
\(131\) | 121.775i | 0.929582i | 0.885421 | + | 0.464791i | \(0.153870\pi\) | ||||
−0.885421 | + | 0.464791i | \(0.846130\pi\) | |||||||
\(132\) | 13.1766i | 0.0998230i | ||||||||
\(133\) | 58.2704 | 0.438124 | ||||||||
\(134\) | −66.0891 | −0.493202 | ||||||||
\(135\) | 5.03851 | 0.0373223 | ||||||||
\(136\) | 52.5380i | 0.386309i | ||||||||
\(137\) | 105.904 | 0.773023 | 0.386511 | − | 0.922285i | \(-0.373680\pi\) | ||||
0.386511 | + | 0.922285i | \(0.373680\pi\) | |||||||
\(138\) | −31.2807 | −0.226672 | ||||||||
\(139\) | −156.327 | −1.12466 | −0.562328 | − | 0.826914i | \(-0.690094\pi\) | ||||
−0.562328 | + | 0.826914i | \(0.690094\pi\) | |||||||
\(140\) | −5.92283 | −0.0423059 | ||||||||
\(141\) | 92.5250i | 0.656206i | ||||||||
\(142\) | − | 82.9311i | − | 0.584022i | ||||||
\(143\) | −44.5920 | −0.311832 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 32.5537 | 0.224508 | ||||||||
\(146\) | −4.82293 | −0.0330338 | ||||||||
\(147\) | −68.7151 | −0.467449 | ||||||||
\(148\) | 11.2427i | 0.0759639i | ||||||||
\(149\) | 34.6796i | 0.232749i | 0.993205 | + | 0.116374i | \(0.0371273\pi\) | ||||
−0.993205 | + | 0.116374i | \(0.962873\pi\) | |||||||
\(150\) | 58.9341i | 0.392894i | ||||||||
\(151\) | 86.9280i | 0.575682i | 0.957678 | + | 0.287841i | \(0.0929375\pi\) | ||||
−0.957678 | + | 0.287841i | \(0.907062\pi\) | |||||||
\(152\) | 53.9653i | 0.355035i | ||||||||
\(153\) | 55.7250 | 0.364216 | ||||||||
\(154\) | −16.4289 | −0.106681 | ||||||||
\(155\) | − | 33.7471i | − | 0.217723i | ||||||
\(156\) | 40.6100i | 0.260321i | ||||||||
\(157\) | 17.2533i | 0.109894i | 0.998489 | + | 0.0549468i | \(0.0174989\pi\) | ||||
−0.998489 | + | 0.0549468i | \(0.982501\pi\) | |||||||
\(158\) | 63.5186i | 0.402017i | ||||||||
\(159\) | 16.8015 | 0.105670 | ||||||||
\(160\) | − | 5.48524i | − | 0.0342827i | ||||||
\(161\) | − | 39.0013i | − | 0.242244i | ||||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | −226.562 | −1.38995 | −0.694977 | − | 0.719032i | \(-0.744585\pi\) | ||||
−0.694977 | + | 0.719032i | \(0.744585\pi\) | |||||||
\(164\) | −4.64516 | −0.0283242 | ||||||||
\(165\) | − | 6.38844i | − | 0.0387178i | ||||||
\(166\) | 208.169 | 1.25403 | ||||||||
\(167\) | −101.977 | −0.610642 | −0.305321 | − | 0.952249i | \(-0.598764\pi\) | ||||
−0.305321 | + | 0.952249i | \(0.598764\pi\) | |||||||
\(168\) | 14.9618i | 0.0890585i | ||||||||
\(169\) | 31.5688 | 0.186798 | ||||||||
\(170\) | − | 25.4721i | − | 0.149836i | ||||||
\(171\) | 57.2388 | 0.334730 | ||||||||
\(172\) | − | 7.68625i | − | 0.0446875i | ||||||
\(173\) | 11.9091i | 0.0688388i | 0.999407 | + | 0.0344194i | \(0.0109582\pi\) | ||||
−0.999407 | + | 0.0344194i | \(0.989042\pi\) | |||||||
\(174\) | − | 82.2349i | − | 0.472614i | ||||||
\(175\) | −73.4802 | −0.419887 | ||||||||
\(176\) | − | 15.2151i | − | 0.0864493i | ||||||
\(177\) | −99.8276 | + | 21.8507i | −0.563998 | + | 0.123450i | ||||
\(178\) | 130.586 | 0.733627 | ||||||||
\(179\) | − | 139.070i | − | 0.776929i | −0.921464 | − | 0.388465i | \(-0.873006\pi\) | ||
0.921464 | − | 0.388465i | \(-0.126994\pi\) | |||||||
\(180\) | −5.81797 | −0.0323221 | ||||||||
\(181\) | 64.1460 | 0.354398 | 0.177199 | − | 0.984175i | \(-0.443296\pi\) | ||||
0.177199 | + | 0.984175i | \(0.443296\pi\) | |||||||
\(182\) | −50.6334 | −0.278205 | ||||||||
\(183\) | − | 10.8556i | − | 0.0593200i | ||||||
\(184\) | 36.1198 | 0.196303 | ||||||||
\(185\) | − | 5.45079i | − | 0.0294637i | ||||||
\(186\) | −85.2494 | −0.458330 | ||||||||
\(187\) | − | 70.6550i | − | 0.377834i | ||||||
\(188\) | − | 106.839i | − | 0.568291i | ||||||
\(189\) | 15.8694 | 0.0839652 | ||||||||
\(190\) | − | 26.1640i | − | 0.137705i | ||||||
\(191\) | − | 54.5048i | − | 0.285365i | −0.989768 | − | 0.142683i | \(-0.954427\pi\) | ||
0.989768 | − | 0.142683i | \(-0.0455728\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | −60.7454 | −0.314743 | −0.157371 | − | 0.987539i | \(-0.550302\pi\) | ||||
−0.157371 | + | 0.987539i | \(0.550302\pi\) | |||||||
\(194\) | −174.138 | −0.897618 | ||||||||
\(195\) | − | 19.6890i | − | 0.100969i | ||||||
\(196\) | 79.3453 | 0.404823 | ||||||||
\(197\) | 28.7769 | 0.146076 | 0.0730378 | − | 0.997329i | \(-0.476731\pi\) | ||||
0.0730378 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(198\) | −16.1380 | −0.0815052 | ||||||||
\(199\) | −135.026 | −0.678521 | −0.339260 | − | 0.940692i | \(-0.610177\pi\) | ||||
−0.339260 | + | 0.940692i | \(0.610177\pi\) | |||||||
\(200\) | − | 68.0513i | − | 0.340256i | ||||||
\(201\) | − | 80.9423i | − | 0.402698i | ||||||
\(202\) | 178.907 | 0.885679 | ||||||||
\(203\) | 102.532 | 0.505084 | ||||||||
\(204\) | −64.3457 | −0.315420 | ||||||||
\(205\) | 2.25212 | 0.0109859 | ||||||||
\(206\) | 15.9760 | 0.0775534 | ||||||||
\(207\) | − | 38.3108i | − | 0.185077i | ||||||
\(208\) | − | 46.8924i | − | 0.225444i | ||||||
\(209\) | − | 72.5744i | − | 0.347246i | ||||||
\(210\) | − | 7.25396i | − | 0.0345427i | ||||||
\(211\) | 35.8765i | 0.170031i | 0.996380 | + | 0.0850153i | \(0.0270939\pi\) | ||||
−0.996380 | + | 0.0850153i | \(0.972906\pi\) | |||||||
\(212\) | −19.4008 | −0.0915130 | ||||||||
\(213\) | 101.569 | 0.476852 | ||||||||
\(214\) | 56.8097i | 0.265466i | ||||||||
\(215\) | 3.72653i | 0.0173327i | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | − | 106.291i | − | 0.489818i | ||||||
\(218\) | 282.834 | 1.29740 | ||||||||
\(219\) | − | 5.90686i | − | 0.0269720i | ||||||
\(220\) | 7.37674i | 0.0335306i | ||||||||
\(221\) | − | 217.757i | − | 0.985324i | ||||||
\(222\) | −13.7694 | −0.0620242 | ||||||||
\(223\) | −237.561 | −1.06530 | −0.532648 | − | 0.846337i | \(-0.678803\pi\) | ||||
−0.532648 | + | 0.846337i | \(0.678803\pi\) | |||||||
\(224\) | − | 17.2764i | − | 0.0771269i | ||||||
\(225\) | −72.1793 | −0.320797 | ||||||||
\(226\) | 142.377 | 0.629986 | ||||||||
\(227\) | − | 413.471i | − | 1.82146i | −0.413007 | − | 0.910728i | \(-0.635521\pi\) | ||
0.413007 | − | 0.910728i | \(-0.364479\pi\) | |||||||
\(228\) | −66.0937 | −0.289885 | ||||||||
\(229\) | − | 390.250i | − | 1.70415i | −0.523422 | − | 0.852074i | \(-0.675345\pi\) | ||
0.523422 | − | 0.852074i | \(-0.324655\pi\) | |||||||
\(230\) | −17.5120 | −0.0761392 | ||||||||
\(231\) | − | 20.1212i | − | 0.0871047i | ||||||
\(232\) | 94.9566i | 0.409296i | ||||||||
\(233\) | − | 16.5386i | − | 0.0709810i | −0.999370 | − | 0.0354905i | \(-0.988701\pi\) | ||
0.999370 | − | 0.0354905i | \(-0.0112993\pi\) | |||||||
\(234\) | −49.7369 | −0.212551 | ||||||||
\(235\) | 51.7987i | 0.220420i | ||||||||
\(236\) | 115.271 | − | 25.2311i | 0.488436 | − | 0.106911i | ||||
\(237\) | −77.7941 | −0.328245 | ||||||||
\(238\) | − | 80.2274i | − | 0.337090i | ||||||
\(239\) | −133.927 | −0.560366 | −0.280183 | − | 0.959947i | \(-0.590395\pi\) | ||||
−0.280183 | + | 0.959947i | \(0.590395\pi\) | |||||||
\(240\) | 6.71802 | 0.0279917 | ||||||||
\(241\) | 21.5710 | 0.0895064 | 0.0447532 | − | 0.998998i | \(-0.485750\pi\) | ||||
0.0447532 | + | 0.998998i | \(0.485750\pi\) | |||||||
\(242\) | − | 150.658i | − | 0.622554i | ||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 12.5349i | 0.0513727i | ||||||||
\(245\) | −38.4691 | −0.157017 | ||||||||
\(246\) | − | 5.68914i | − | 0.0231266i | ||||||
\(247\) | − | 223.672i | − | 0.905555i | ||||||
\(248\) | 98.4375 | 0.396925 | ||||||||
\(249\) | 254.954i | 1.02391i | ||||||||
\(250\) | 67.2761i | 0.269104i | ||||||||
\(251\) | −372.149 | −1.48266 | −0.741332 | − | 0.671138i | \(-0.765806\pi\) | ||||
−0.741332 | + | 0.671138i | \(0.765806\pi\) | |||||||
\(252\) | −18.3244 | −0.0727160 | ||||||||
\(253\) | −48.5752 | −0.191997 | ||||||||
\(254\) | − | 70.8915i | − | 0.279100i | ||||||
\(255\) | 31.1968 | 0.122340 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 16.5399 | 0.0643577 | 0.0321789 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321789 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(258\) | 9.41370 | 0.0364872 | ||||||||
\(259\) | − | 17.1679i | − | 0.0662854i | ||||||
\(260\) | 22.7349i | 0.0874419i | ||||||||
\(261\) | 100.717 | 0.385888 | ||||||||
\(262\) | 172.216 | 0.657314 | ||||||||
\(263\) | −115.110 | −0.437679 | −0.218839 | − | 0.975761i | \(-0.570227\pi\) | ||||
−0.218839 | + | 0.975761i | \(0.570227\pi\) | |||||||
\(264\) | 18.6346 | 0.0705856 | ||||||||
\(265\) | 9.40609 | 0.0354947 | ||||||||
\(266\) | − | 82.4068i | − | 0.309800i | ||||||
\(267\) | 159.934i | 0.599004i | ||||||||
\(268\) | 93.4641i | 0.348747i | ||||||||
\(269\) | − | 144.984i | − | 0.538975i | −0.963004 | − | 0.269488i | \(-0.913146\pi\) | ||
0.963004 | − | 0.269488i | \(-0.0868543\pi\) | |||||||
\(270\) | − | 7.12553i | − | 0.0263909i | ||||||
\(271\) | −189.948 | −0.700914 | −0.350457 | − | 0.936579i | \(-0.613974\pi\) | ||||
−0.350457 | + | 0.936579i | \(0.613974\pi\) | |||||||
\(272\) | 74.3000 | 0.273162 | ||||||||
\(273\) | − | 62.0129i | − | 0.227154i | ||||||
\(274\) | − | 149.771i | − | 0.546610i | ||||||
\(275\) | 91.5177i | 0.332792i | ||||||||
\(276\) | 44.2376i | 0.160281i | ||||||||
\(277\) | 136.541 | 0.492928 | 0.246464 | − | 0.969152i | \(-0.420731\pi\) | ||||
0.246464 | + | 0.969152i | \(0.420731\pi\) | |||||||
\(278\) | 221.080i | 0.795252i | ||||||||
\(279\) | − | 104.409i | − | 0.374225i | ||||||
\(280\) | 8.37615i | 0.0299148i | ||||||||
\(281\) | 200.718 | 0.714300 | 0.357150 | − | 0.934047i | \(-0.383748\pi\) | ||||
0.357150 | + | 0.934047i | \(0.383748\pi\) | |||||||
\(282\) | 130.850 | 0.464007 | ||||||||
\(283\) | − | 13.9031i | − | 0.0491276i | −0.999698 | − | 0.0245638i | \(-0.992180\pi\) | ||
0.999698 | − | 0.0245638i | \(-0.00781969\pi\) | |||||||
\(284\) | −117.282 | −0.412966 | ||||||||
\(285\) | 32.0443 | 0.112436 | ||||||||
\(286\) | 63.0626i | 0.220499i | ||||||||
\(287\) | 7.09333 | 0.0247154 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 56.0303 | 0.193877 | ||||||||
\(290\) | − | 46.0379i | − | 0.158751i | ||||||
\(291\) | − | 213.274i | − | 0.732902i | ||||||
\(292\) | 6.82065i | 0.0233584i | ||||||||
\(293\) | 403.295 | 1.37644 | 0.688218 | − | 0.725504i | \(-0.258393\pi\) | ||||
0.688218 | + | 0.725504i | \(0.258393\pi\) | |||||||
\(294\) | 97.1778i | 0.330537i | ||||||||
\(295\) | −55.8869 | + | 12.2328i | −0.189447 | + | 0.0414671i | ||||
\(296\) | 15.8995 | 0.0537146 | ||||||||
\(297\) | − | 19.7650i | − | 0.0665487i | ||||||
\(298\) | 49.0444 | 0.164578 | ||||||||
\(299\) | −149.707 | −0.500693 | ||||||||
\(300\) | 83.3454 | 0.277818 | ||||||||
\(301\) | 11.7372i | 0.0389939i | ||||||||
\(302\) | 122.935 | 0.407069 | ||||||||
\(303\) | 219.116i | 0.723153i | ||||||||
\(304\) | 76.3184 | 0.251047 | ||||||||
\(305\) | − | 6.07732i | − | 0.0199256i | ||||||
\(306\) | − | 78.8070i | − | 0.257539i | ||||||
\(307\) | −111.858 | −0.364359 | −0.182180 | − | 0.983265i | \(-0.558315\pi\) | ||||
−0.182180 | + | 0.983265i | \(0.558315\pi\) | |||||||
\(308\) | 23.2340i | 0.0754349i | ||||||||
\(309\) | 19.5665i | 0.0633221i | ||||||||
\(310\) | −47.7256 | −0.153953 | ||||||||
\(311\) | −5.80597 | −0.0186687 | −0.00933435 | − | 0.999956i | \(-0.502971\pi\) | ||||
−0.00933435 | + | 0.999956i | \(0.502971\pi\) | |||||||
\(312\) | 57.4312 | 0.184075 | ||||||||
\(313\) | 500.889i | 1.60029i | 0.599810 | + | 0.800143i | \(0.295243\pi\) | ||||
−0.599810 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(314\) | 24.3998 | 0.0777065 | ||||||||
\(315\) | 8.88425 | 0.0282040 | ||||||||
\(316\) | 89.8289 | 0.284269 | ||||||||
\(317\) | 184.778 | 0.582895 | 0.291448 | − | 0.956587i | \(-0.405863\pi\) | ||||
0.291448 | + | 0.956587i | \(0.405863\pi\) | |||||||
\(318\) | − | 23.7610i | − | 0.0747200i | ||||||
\(319\) | − | 127.701i | − | 0.400317i | ||||||
\(320\) | −7.75730 | −0.0242416 | ||||||||
\(321\) | −69.5774 | −0.216752 | ||||||||
\(322\) | −55.1562 | −0.171293 | ||||||||
\(323\) | 354.403 | 1.09722 | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 282.055i | 0.867862i | ||||||||
\(326\) | 320.408i | 0.982846i | ||||||||
\(327\) | 346.400i | 1.05933i | ||||||||
\(328\) | 6.56925i | 0.0200282i | ||||||||
\(329\) | 163.146i | 0.495886i | ||||||||
\(330\) | −9.03462 | −0.0273777 | ||||||||
\(331\) | −249.926 | −0.755063 | −0.377531 | − | 0.925997i | \(-0.623227\pi\) | ||||
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(332\) | − | 294.395i | − | 0.886732i | ||||||
\(333\) | − | 16.8640i | − | 0.0506426i | ||||||
\(334\) | 144.218i | 0.431789i | ||||||||
\(335\) | − | 45.3143i | − | 0.135267i | ||||||
\(336\) | 21.1592 | 0.0629739 | ||||||||
\(337\) | − | 296.758i | − | 0.880588i | −0.897854 | − | 0.440294i | \(-0.854874\pi\) | ||
0.897854 | − | 0.440294i | \(-0.145126\pi\) | |||||||
\(338\) | − | 44.6451i | − | 0.132086i | ||||||
\(339\) | 174.375i | 0.514381i | ||||||||
\(340\) | −36.0229 | −0.105950 | ||||||||
\(341\) | −132.382 | −0.388218 | ||||||||
\(342\) | − | 80.9479i | − | 0.236690i | ||||||
\(343\) | −270.813 | −0.789541 | ||||||||
\(344\) | −10.8700 | −0.0315988 | ||||||||
\(345\) | − | 21.4477i | − | 0.0621674i | ||||||
\(346\) | 16.8420 | 0.0486764 | ||||||||
\(347\) | − | 441.458i | − | 1.27221i | −0.771601 | − | 0.636106i | \(-0.780544\pi\) | ||
0.771601 | − | 0.636106i | \(-0.219456\pi\) | |||||||
\(348\) | −116.298 | −0.334189 | ||||||||
\(349\) | 325.743i | 0.933362i | 0.884426 | + | 0.466681i | \(0.154550\pi\) | ||||
−0.884426 | + | 0.466681i | \(0.845450\pi\) | |||||||
\(350\) | 103.917i | 0.296905i | ||||||||
\(351\) | − | 60.9150i | − | 0.173547i | ||||||
\(352\) | −21.5174 | −0.0611289 | ||||||||
\(353\) | 183.504i | 0.519843i | 0.965630 | + | 0.259921i | \(0.0836967\pi\) | ||||
−0.965630 | + | 0.259921i | \(0.916303\pi\) | |||||||
\(354\) | 30.9016 | + | 141.178i | 0.0872927 | + | 0.398807i | ||||
\(355\) | 56.8621 | 0.160175 | ||||||||
\(356\) | − | 184.676i | − | 0.518753i | ||||||
\(357\) | 98.2581 | 0.275233 | ||||||||
\(358\) | −196.675 | −0.549372 | ||||||||
\(359\) | 223.722 | 0.623181 | 0.311591 | − | 0.950216i | \(-0.399138\pi\) | ||||
0.311591 | + | 0.950216i | \(0.399138\pi\) | |||||||
\(360\) | 8.22786i | 0.0228552i | ||||||||
\(361\) | 3.03112 | 0.00839645 | ||||||||
\(362\) | − | 90.7162i | − | 0.250597i | ||||||
\(363\) | 184.518 | 0.508313 | ||||||||
\(364\) | 71.6064i | 0.196721i | ||||||||
\(365\) | − | 3.30686i | − | 0.00905990i | ||||||
\(366\) | −15.3521 | −0.0419456 | ||||||||
\(367\) | 300.765i | 0.819524i | 0.912192 | + | 0.409762i | \(0.134388\pi\) | ||||
−0.912192 | + | 0.409762i | \(0.865612\pi\) | |||||||
\(368\) | − | 51.0811i | − | 0.138807i | ||||||
\(369\) | 6.96775 | 0.0188828 | ||||||||
\(370\) | −7.70858 | −0.0208340 | ||||||||
\(371\) | 29.6256 | 0.0798535 | ||||||||
\(372\) | 120.561i | 0.324088i | ||||||||
\(373\) | 521.430 | 1.39793 | 0.698967 | − | 0.715153i | \(-0.253643\pi\) | ||||
0.698967 | + | 0.715153i | \(0.253643\pi\) | |||||||
\(374\) | −99.9212 | −0.267169 | ||||||||
\(375\) | −82.3961 | −0.219723 | ||||||||
\(376\) | −151.093 | −0.401842 | ||||||||
\(377\) | − | 393.571i | − | 1.04395i | ||||||
\(378\) | − | 22.4427i | − | 0.0593723i | ||||||
\(379\) | −671.504 | −1.77178 | −0.885889 | − | 0.463897i | \(-0.846451\pi\) | ||||
−0.885889 | + | 0.463897i | \(0.846451\pi\) | |||||||
\(380\) | −37.0015 | −0.0973724 | ||||||||
\(381\) | 86.8240 | 0.227885 | ||||||||
\(382\) | −77.0814 | −0.201784 | ||||||||
\(383\) | 216.586 | 0.565498 | 0.282749 | − | 0.959194i | \(-0.408754\pi\) | ||||
0.282749 | + | 0.959194i | \(0.408754\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | − | 11.2645i | − | 0.0292586i | ||||||
\(386\) | 85.9070i | 0.222557i | ||||||||
\(387\) | 11.5294i | 0.0297917i | ||||||||
\(388\) | 246.268i | 0.634712i | ||||||||
\(389\) | 376.763 | 0.968542 | 0.484271 | − | 0.874918i | \(-0.339085\pi\) | ||||
0.484271 | + | 0.874918i | \(0.339085\pi\) | |||||||
\(390\) | −27.8445 | −0.0713960 | ||||||||
\(391\) | − | 237.208i | − | 0.606670i | ||||||
\(392\) | − | 112.211i | − | 0.286253i | ||||||
\(393\) | 210.921i | 0.536694i | ||||||||
\(394\) | − | 40.6967i | − | 0.103291i | ||||||
\(395\) | −43.5518 | −0.110258 | ||||||||
\(396\) | 22.8226i | 0.0576329i | ||||||||
\(397\) | 353.417i | 0.890219i | 0.895476 | + | 0.445109i | \(0.146835\pi\) | ||||
−0.895476 | + | 0.445109i | \(0.853165\pi\) | |||||||
\(398\) | 190.955i | 0.479787i | ||||||||
\(399\) | 100.927 | 0.252951 | ||||||||
\(400\) | −96.2390 | −0.240598 | ||||||||
\(401\) | − | 89.4353i | − | 0.223031i | −0.993763 | − | 0.111515i | \(-0.964430\pi\) | ||
0.993763 | − | 0.111515i | \(-0.0355704\pi\) | |||||||
\(402\) | −114.470 | −0.284750 | ||||||||
\(403\) | −407.998 | −1.01240 | ||||||||
\(404\) | − | 253.013i | − | 0.626269i | ||||||
\(405\) | 8.72696 | 0.0215480 | ||||||||
\(406\) | − | 145.002i | − | 0.357148i | ||||||
\(407\) | −21.3822 | −0.0525362 | ||||||||
\(408\) | 90.9985i | 0.223036i | ||||||||
\(409\) | − | 178.484i | − | 0.436392i | −0.975905 | − | 0.218196i | \(-0.929983\pi\) | ||
0.975905 | − | 0.218196i | \(-0.0700173\pi\) | |||||||
\(410\) | − | 3.18498i | − | 0.00776824i | ||||||
\(411\) | 183.431 | 0.446305 | ||||||||
\(412\) | − | 22.5935i | − | 0.0548386i | ||||||
\(413\) | −176.023 | + | 38.5287i | −0.426205 | + | 0.0932899i | ||||
\(414\) | −54.1797 | −0.130869 | ||||||||
\(415\) | 142.732i | 0.343932i | ||||||||
\(416\) | −66.3159 | −0.159413 | ||||||||
\(417\) | −270.767 | −0.649321 | ||||||||
\(418\) | −102.636 | −0.245540 | ||||||||
\(419\) | − | 380.870i | − | 0.908997i | −0.890748 | − | 0.454498i | \(-0.849819\pi\) | ||
0.890748 | − | 0.454498i | \(-0.150181\pi\) | |||||||
\(420\) | −10.2586 | −0.0244253 | ||||||||
\(421\) | 327.539i | 0.778002i | 0.921237 | + | 0.389001i | \(0.127180\pi\) | ||||
−0.921237 | + | 0.389001i | \(0.872820\pi\) | |||||||
\(422\) | 50.7370 | 0.120230 | ||||||||
\(423\) | 160.258i | 0.378860i | ||||||||
\(424\) | 27.4368i | 0.0647094i | ||||||||
\(425\) | −446.910 | −1.05155 | ||||||||
\(426\) | − | 143.641i | − | 0.337185i | ||||||
\(427\) | − | 19.1413i | − | 0.0448274i | ||||||
\(428\) | 80.3410 | 0.187713 | ||||||||
\(429\) | −77.2356 | −0.180036 | ||||||||
\(430\) | 5.27011 | 0.0122561 | ||||||||
\(431\) | − | 108.076i | − | 0.250757i | −0.992109 | − | 0.125378i | \(-0.959985\pi\) | ||
0.992109 | − | 0.125378i | \(-0.0400145\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 684.264 | 1.58029 | 0.790143 | − | 0.612923i | \(-0.210006\pi\) | ||||
0.790143 | + | 0.612923i | \(0.210006\pi\) | |||||||
\(434\) | −150.318 | −0.346354 | ||||||||
\(435\) | 56.3847 | 0.129620 | ||||||||
\(436\) | − | 399.988i | − | 0.917404i | ||||||
\(437\) | − | 243.652i | − | 0.557556i | ||||||
\(438\) | −8.35356 | −0.0190721 | ||||||||
\(439\) | 473.516 | 1.07862 | 0.539312 | − | 0.842106i | \(-0.318684\pi\) | ||||
0.539312 | + | 0.842106i | \(0.318684\pi\) | |||||||
\(440\) | 10.4323 | 0.0237097 | ||||||||
\(441\) | −119.018 | −0.269882 | ||||||||
\(442\) | −307.954 | −0.696729 | ||||||||
\(443\) | 741.937i | 1.67480i | 0.546590 | + | 0.837400i | \(0.315926\pi\) | ||||
−0.546590 | + | 0.837400i | \(0.684074\pi\) | |||||||
\(444\) | 19.4728i | 0.0438578i | ||||||||
\(445\) | 89.5366i | 0.201206i | ||||||||
\(446\) | 335.962i | 0.753278i | ||||||||
\(447\) | 60.0668i | 0.134378i | ||||||||
\(448\) | −24.4326 | −0.0545370 | ||||||||
\(449\) | −504.574 | −1.12377 | −0.561887 | − | 0.827214i | \(-0.689924\pi\) | ||||
−0.561887 | + | 0.827214i | \(0.689924\pi\) | |||||||
\(450\) | 102.077i | 0.226838i | ||||||||
\(451\) | − | 8.83457i | − | 0.0195888i | ||||||
\(452\) | − | 201.351i | − | 0.445467i | ||||||
\(453\) | 150.564i | 0.332370i | ||||||||
\(454\) | −584.736 | −1.28796 | ||||||||
\(455\) | − | 34.7170i | − | 0.0763011i | ||||||
\(456\) | 93.4706i | 0.204979i | ||||||||
\(457\) | 578.102i | 1.26499i | 0.774563 | + | 0.632497i | \(0.217970\pi\) | ||||
−0.774563 | + | 0.632497i | \(0.782030\pi\) | |||||||
\(458\) | −551.897 | −1.20501 | ||||||||
\(459\) | 96.5185 | 0.210280 | ||||||||
\(460\) | 24.7657i | 0.0538385i | ||||||||
\(461\) | 375.853 | 0.815299 | 0.407649 | − | 0.913139i | \(-0.366349\pi\) | ||||
0.407649 | + | 0.913139i | \(0.366349\pi\) | |||||||
\(462\) | −28.4557 | −0.0615924 | ||||||||
\(463\) | 415.083i | 0.896507i | 0.893906 | + | 0.448254i | \(0.147954\pi\) | ||||
−0.893906 | + | 0.448254i | \(0.852046\pi\) | |||||||
\(464\) | 134.289 | 0.289416 | ||||||||
\(465\) | − | 58.4516i | − | 0.125702i | ||||||
\(466\) | −23.3891 | −0.0501911 | ||||||||
\(467\) | 522.188i | 1.11818i | 0.829108 | + | 0.559088i | \(0.188849\pi\) | ||||
−0.829108 | + | 0.559088i | \(0.811151\pi\) | |||||||
\(468\) | 70.3386i | 0.150296i | ||||||||
\(469\) | − | 142.723i | − | 0.304313i | ||||||
\(470\) | 73.2544 | 0.155860 | ||||||||
\(471\) | 29.8836i | 0.0634471i | ||||||||
\(472\) | −35.6821 | − | 163.018i | −0.0755977 | − | 0.345377i | ||||
\(473\) | 14.6184 | 0.0309056 | ||||||||
\(474\) | 110.017i | 0.232104i | ||||||||
\(475\) | −459.051 | −0.966422 | ||||||||
\(476\) | −113.459 | −0.238359 | ||||||||
\(477\) | 29.1011 | 0.0610087 | ||||||||
\(478\) | 189.402i | 0.396239i | ||||||||
\(479\) | 663.872 | 1.38595 | 0.692977 | − | 0.720960i | \(-0.256299\pi\) | ||||
0.692977 | + | 0.720960i | \(0.256299\pi\) | |||||||
\(480\) | − | 9.50071i | − | 0.0197931i | ||||||
\(481\) | −65.8994 | −0.137005 | ||||||||
\(482\) | − | 30.5060i | − | 0.0632906i | ||||||
\(483\) | − | 67.5523i | − | 0.139860i | ||||||
\(484\) | −213.063 | −0.440212 | ||||||||
\(485\) | − | 119.398i | − | 0.246182i | ||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | 505.567 | 1.03813 | 0.519063 | − | 0.854736i | \(-0.326281\pi\) | ||||
0.519063 | + | 0.854736i | \(0.326281\pi\) | |||||||
\(488\) | 17.7271 | 0.0363260 | ||||||||
\(489\) | −392.418 | −0.802490 | ||||||||
\(490\) | 54.4035i | 0.111027i | ||||||||
\(491\) | −758.053 | −1.54390 | −0.771948 | − | 0.635686i | \(-0.780717\pi\) | ||||
−0.771948 | + | 0.635686i | \(0.780717\pi\) | |||||||
\(492\) | −8.04566 | −0.0163530 | ||||||||
\(493\) | 623.604 | 1.26492 | ||||||||
\(494\) | −316.320 | −0.640324 | ||||||||
\(495\) | − | 11.0651i | − | 0.0223538i | ||||||
\(496\) | − | 139.212i | − | 0.280669i | ||||||
\(497\) | 179.094 | 0.360350 | ||||||||
\(498\) | 360.559 | 0.724014 | ||||||||
\(499\) | −217.463 | −0.435797 | −0.217898 | − | 0.975971i | \(-0.569920\pi\) | ||||
−0.217898 | + | 0.975971i | \(0.569920\pi\) | |||||||
\(500\) | 95.1428 | 0.190286 | ||||||||
\(501\) | −176.630 | −0.352554 | ||||||||
\(502\) | 526.298i | 1.04840i | ||||||||
\(503\) | 100.548i | 0.199896i | 0.994993 | + | 0.0999481i | \(0.0318677\pi\) | ||||
−0.994993 | + | 0.0999481i | \(0.968132\pi\) | |||||||
\(504\) | 25.9146i | 0.0514180i | ||||||||
\(505\) | 122.668i | 0.242908i | ||||||||
\(506\) | 68.6957i | 0.135762i | ||||||||
\(507\) | 54.6788 | 0.107848 | ||||||||
\(508\) | −100.256 | −0.197354 | ||||||||
\(509\) | 379.333i | 0.745251i | 0.927982 | + | 0.372626i | \(0.121542\pi\) | ||||
−0.927982 | + | 0.372626i | \(0.878458\pi\) | |||||||
\(510\) | − | 44.1189i | − | 0.0865076i | ||||||
\(511\) | − | 10.4154i | − | 0.0203823i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 99.1405 | 0.193256 | ||||||||
\(514\) | − | 23.3910i | − | 0.0455078i | ||||||
\(515\) | 10.9540i | 0.0212700i | ||||||||
\(516\) | − | 13.3130i | − | 0.0258003i | ||||||
\(517\) | 203.195 | 0.393027 | ||||||||
\(518\) | −24.2791 | −0.0468709 | ||||||||
\(519\) | 20.6272i | 0.0397441i | ||||||||
\(520\) | 32.1520 | 0.0618308 | ||||||||
\(521\) | 275.414 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(522\) | − | 142.435i | − | 0.272864i | ||||||
\(523\) | −184.170 | −0.352141 | −0.176071 | − | 0.984378i | \(-0.556339\pi\) | ||||
−0.176071 | + | 0.984378i | \(0.556339\pi\) | |||||||
\(524\) | − | 243.550i | − | 0.464791i | ||||||
\(525\) | −127.271 | −0.242422 | ||||||||
\(526\) | 162.789i | 0.309486i | ||||||||
\(527\) | − | 646.464i | − | 1.22669i | ||||||
\(528\) | − | 26.3533i | − | 0.0499115i | ||||||
\(529\) | 365.920 | 0.691720 | ||||||||
\(530\) | − | 13.3022i | − | 0.0250985i | ||||||
\(531\) | −172.906 | + | 37.8466i | −0.325624 | + | 0.0712742i | ||||
\(532\) | −116.541 | −0.219062 | ||||||||
\(533\) | − | 27.2279i | − | 0.0510842i | ||||||
\(534\) | 226.181 | 0.423560 | ||||||||
\(535\) | −38.9518 | −0.0728071 | ||||||||
\(536\) | 132.178 | 0.246601 | ||||||||
\(537\) | − | 240.877i | − | 0.448560i | ||||||
\(538\) | −205.039 | −0.381113 | ||||||||
\(539\) | 150.906i | 0.279973i | ||||||||
\(540\) | −10.0770 | −0.0186612 | ||||||||
\(541\) | − | 93.8888i | − | 0.173547i | −0.996228 | − | 0.0867734i | \(-0.972344\pi\) | ||
0.996228 | − | 0.0867734i | \(-0.0276556\pi\) | |||||||
\(542\) | 268.626i | 0.495621i | ||||||||
\(543\) | 111.104 | 0.204612 | ||||||||
\(544\) | − | 105.076i | − | 0.193154i | ||||||
\(545\) | 193.927i | 0.355829i | ||||||||
\(546\) | −87.6995 | −0.160622 | ||||||||
\(547\) | −391.002 | −0.714811 | −0.357405 | − | 0.933949i | \(-0.616339\pi\) | ||||
−0.357405 | + | 0.933949i | \(0.616339\pi\) | |||||||
\(548\) | −211.808 | −0.386511 | ||||||||
\(549\) | − | 18.8024i | − | 0.0342484i | ||||||
\(550\) | 129.426 | 0.235319 | ||||||||
\(551\) | 640.545 | 1.16251 | ||||||||
\(552\) | 62.5614 | 0.113336 | ||||||||
\(553\) | −137.172 | −0.248050 | ||||||||
\(554\) | − | 193.098i | − | 0.348552i | ||||||
\(555\) | − | 9.44104i | − | 0.0170109i | ||||||
\(556\) | 312.655 | 0.562328 | ||||||||
\(557\) | −27.5357 | −0.0494357 | −0.0247178 | − | 0.999694i | \(-0.507869\pi\) | ||||
−0.0247178 | + | 0.999694i | \(0.507869\pi\) | |||||||
\(558\) | −147.656 | −0.264617 | ||||||||
\(559\) | 45.0534 | 0.0805963 | ||||||||
\(560\) | 11.8457 | 0.0211530 | ||||||||
\(561\) | − | 122.378i | − | 0.218143i | ||||||
\(562\) | − | 283.859i | − | 0.505086i | ||||||
\(563\) | 607.725i | 1.07944i | 0.841845 | + | 0.539720i | \(0.181470\pi\) | ||||
−0.841845 | + | 0.539720i | \(0.818530\pi\) | |||||||
\(564\) | − | 185.050i | − | 0.328103i | ||||||
\(565\) | 97.6213i | 0.172781i | ||||||||
\(566\) | −19.6620 | −0.0347385 | ||||||||
\(567\) | 27.4866 | 0.0484773 | ||||||||
\(568\) | 165.862i | 0.292011i | ||||||||
\(569\) | − | 774.788i | − | 1.36167i | −0.732439 | − | 0.680833i | \(-0.761618\pi\) | ||
0.732439 | − | 0.680833i | \(-0.238382\pi\) | |||||||
\(570\) | − | 45.3174i | − | 0.0795043i | ||||||
\(571\) | − | 997.703i | − | 1.74729i | −0.486563 | − | 0.873646i | \(-0.661750\pi\) | ||
0.486563 | − | 0.873646i | \(-0.338250\pi\) | |||||||
\(572\) | 89.1840 | 0.155916 | ||||||||
\(573\) | − | 94.4051i | − | 0.164756i | ||||||
\(574\) | − | 10.0315i | − | 0.0174765i | ||||||
\(575\) | 307.250i | 0.534348i | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 979.641 | 1.69782 | 0.848909 | − | 0.528539i | \(-0.177260\pi\) | ||||
0.848909 | + | 0.528539i | \(0.177260\pi\) | |||||||
\(578\) | − | 79.2389i | − | 0.137091i | ||||||
\(579\) | −105.214 | −0.181717 | ||||||||
\(580\) | −65.1075 | −0.112254 | ||||||||
\(581\) | 449.552i | 0.773755i | ||||||||
\(582\) | −301.616 | −0.518240 | ||||||||
\(583\) | − | 36.8980i | − | 0.0632899i | ||||||
\(584\) | 9.64586 | 0.0165169 | ||||||||
\(585\) | − | 34.1023i | − | 0.0582946i | ||||||
\(586\) | − | 570.346i | − | 0.973287i | ||||||
\(587\) | − | 564.199i | − | 0.961156i | −0.876952 | − | 0.480578i | \(-0.840427\pi\) | ||
0.876952 | − | 0.480578i | \(-0.159573\pi\) | |||||||
\(588\) | 137.430 | 0.233725 | ||||||||
\(589\) | − | 664.026i | − | 1.12738i | ||||||
\(590\) | 17.2998 | + | 79.0361i | 0.0293217 | + | 0.133959i | ||||
\(591\) | 49.8431 | 0.0843368 | ||||||||
\(592\) | − | 22.4853i | − | 0.0379819i | ||||||
\(593\) | −474.066 | −0.799437 | −0.399718 | − | 0.916638i | \(-0.630892\pi\) | ||||
−0.399718 | + | 0.916638i | \(0.630892\pi\) | |||||||
\(594\) | −27.9519 | −0.0470570 | ||||||||
\(595\) | 55.0083 | 0.0924509 | ||||||||
\(596\) | − | 69.3592i | − | 0.116374i | ||||||
\(597\) | −233.871 | −0.391744 | ||||||||
\(598\) | 211.718i | 0.354044i | ||||||||
\(599\) | 327.543 | 0.546816 | 0.273408 | − | 0.961898i | \(-0.411849\pi\) | ||||
0.273408 | + | 0.961898i | \(0.411849\pi\) | |||||||
\(600\) | − | 117.868i | − | 0.196447i | ||||||
\(601\) | − | 672.230i | − | 1.11852i | −0.828992 | − | 0.559260i | \(-0.811085\pi\) | ||
0.828992 | − | 0.559260i | \(-0.188915\pi\) | |||||||
\(602\) | 16.5989 | 0.0275729 | ||||||||
\(603\) | − | 140.196i | − | 0.232498i | ||||||
\(604\) | − | 173.856i | − | 0.287841i | ||||||
\(605\) | 103.299 | 0.170743 | ||||||||
\(606\) | 309.876 | 0.511347 | ||||||||
\(607\) | 787.877 | 1.29799 | 0.648993 | − | 0.760794i | \(-0.275190\pi\) | ||||
0.648993 | + | 0.760794i | \(0.275190\pi\) | |||||||
\(608\) | − | 107.931i | − | 0.177517i | ||||||
\(609\) | 177.591 | 0.291610 | ||||||||
\(610\) | −8.59463 | −0.0140896 | ||||||||
\(611\) | 626.240 | 1.02494 | ||||||||
\(612\) | −111.450 | −0.182108 | ||||||||
\(613\) | − | 1092.68i | − | 1.78251i | −0.453506 | − | 0.891253i | \(-0.649827\pi\) | ||
0.453506 | − | 0.891253i | \(-0.350173\pi\) | |||||||
\(614\) | 158.192i | 0.257641i | ||||||||
\(615\) | 3.90079 | 0.00634274 | ||||||||
\(616\) | 32.8578 | 0.0533405 | ||||||||
\(617\) | −1049.24 | −1.70056 | −0.850278 | − | 0.526333i | \(-0.823566\pi\) | ||||
−0.850278 | + | 0.526333i | \(0.823566\pi\) | |||||||
\(618\) | 27.6713 | 0.0447755 | ||||||||
\(619\) | 1.94598 | 0.00314376 | 0.00157188 | − | 0.999999i | \(-0.499500\pi\) | ||||
0.00157188 | + | 0.999999i | \(0.499500\pi\) | |||||||
\(620\) | 67.4941i | 0.108861i | ||||||||
\(621\) | − | 66.3563i | − | 0.106854i | ||||||
\(622\) | 8.21088i | 0.0132008i | ||||||||
\(623\) | 282.007i | 0.452659i | ||||||||
\(624\) | − | 81.2201i | − | 0.130160i | ||||||
\(625\) | 555.366 | 0.888585 | ||||||||
\(626\) | 708.364 | 1.13157 | ||||||||
\(627\) | − | 125.703i | − | 0.200482i | ||||||
\(628\) | − | 34.5066i | − | 0.0549468i | ||||||
\(629\) | − | 104.416i | − | 0.166003i | ||||||
\(630\) | − | 12.5642i | − | 0.0199432i | ||||||
\(631\) | 989.890 | 1.56876 | 0.784382 | − | 0.620278i | \(-0.212980\pi\) | ||||
0.784382 | + | 0.620278i | \(0.212980\pi\) | |||||||
\(632\) | − | 127.037i | − | 0.201008i | ||||||
\(633\) | 62.1398i | 0.0981672i | ||||||||
\(634\) | − | 261.315i | − | 0.412169i | ||||||
\(635\) | 48.6071 | 0.0765466 | ||||||||
\(636\) | −33.6031 | −0.0528350 | ||||||||
\(637\) | 465.087i | 0.730120i | ||||||||
\(638\) | −180.597 | −0.283067 | ||||||||
\(639\) | 175.923 | 0.275310 | ||||||||
\(640\) | 10.9705i | 0.0171414i | ||||||||
\(641\) | −740.216 | −1.15478 | −0.577391 | − | 0.816468i | \(-0.695929\pi\) | ||||
−0.577391 | + | 0.816468i | \(0.695929\pi\) | |||||||
\(642\) | 98.3972i | 0.153267i | ||||||||
\(643\) | 318.669 | 0.495598 | 0.247799 | − | 0.968812i | \(-0.420293\pi\) | ||||
0.247799 | + | 0.968812i | \(0.420293\pi\) | |||||||
\(644\) | 78.0027i | 0.121122i | ||||||||
\(645\) | 6.45454i | 0.0100070i | ||||||||
\(646\) | − | 501.202i | − | 0.775855i | ||||||
\(647\) | 15.5155 | 0.0239807 | 0.0119903 | − | 0.999928i | \(-0.496183\pi\) | ||||
0.0119903 | + | 0.999928i | \(0.496183\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | 47.9865 | + | 219.232i | 0.0739392 | + | 0.337800i | ||||
\(650\) | 398.886 | 0.613671 | ||||||||
\(651\) | − | 184.101i | − | 0.282797i | ||||||
\(652\) | 453.125 | 0.694977 | ||||||||
\(653\) | −692.123 | −1.05991 | −0.529956 | − | 0.848025i | \(-0.677792\pi\) | ||||
−0.529956 | + | 0.848025i | \(0.677792\pi\) | |||||||
\(654\) | 489.883 | 0.749057 | ||||||||
\(655\) | 118.081i | 0.180276i | ||||||||
\(656\) | 9.29033 | 0.0141621 | ||||||||
\(657\) | − | 10.2310i | − | 0.0155723i | ||||||
\(658\) | 230.724 | 0.350644 | ||||||||
\(659\) | − | 665.193i | − | 1.00940i | −0.863296 | − | 0.504699i | \(-0.831604\pi\) | ||
0.863296 | − | 0.504699i | \(-0.168396\pi\) | |||||||
\(660\) | 12.7769i | 0.0193589i | ||||||||
\(661\) | −818.559 | −1.23836 | −0.619182 | − | 0.785248i | \(-0.712536\pi\) | ||||
−0.619182 | + | 0.785248i | \(0.712536\pi\) | |||||||
\(662\) | 353.448i | 0.533910i | ||||||||
\(663\) | − | 377.165i | − | 0.568877i | ||||||
\(664\) | −416.338 | −0.627014 | ||||||||
\(665\) | 56.5026 | 0.0849664 | ||||||||
\(666\) | −23.8493 | −0.0358097 | ||||||||
\(667\) | − | 428.727i | − | 0.642769i | ||||||
\(668\) | 203.954 | 0.305321 | ||||||||
\(669\) | −411.468 | −0.615049 | ||||||||
\(670\) | −64.0841 | −0.0956479 | ||||||||
\(671\) | −23.8400 | −0.0355290 | ||||||||
\(672\) | − | 29.9237i | − | 0.0445293i | ||||||
\(673\) | 1061.63i | 1.57746i | 0.614739 | + | 0.788731i | \(0.289261\pi\) | ||||
−0.614739 | + | 0.788731i | \(0.710739\pi\) | |||||||
\(674\) | −419.679 | −0.622670 | ||||||||
\(675\) | −125.018 | −0.185212 | ||||||||
\(676\) | −63.1376 | −0.0933989 | ||||||||
\(677\) | 66.2865 | 0.0979121 | 0.0489561 | − | 0.998801i | \(-0.484411\pi\) | ||||
0.0489561 | + | 0.998801i | \(0.484411\pi\) | |||||||
\(678\) | 246.604 | 0.363723 | ||||||||
\(679\) | − | 376.060i | − | 0.553844i | ||||||
\(680\) | 50.9441i | 0.0749178i | ||||||||
\(681\) | − | 716.152i | − | 1.05162i | ||||||
\(682\) | 187.217i | 0.274511i | ||||||||
\(683\) | 767.960i | 1.12439i | 0.827004 | + | 0.562196i | \(0.190043\pi\) | ||||
−0.827004 | + | 0.562196i | \(0.809957\pi\) | |||||||
\(684\) | −114.478 | −0.167365 | ||||||||
\(685\) | 102.691 | 0.149914 | ||||||||
\(686\) | 382.987i | 0.558290i | ||||||||
\(687\) | − | 675.933i | − | 0.983890i | ||||||
\(688\) | 15.3725i | 0.0223438i | ||||||||
\(689\) | − | 113.719i | − | 0.165049i | ||||||
\(690\) | −30.3317 | −0.0439590 | ||||||||
\(691\) | 333.252i | 0.482275i | 0.970491 | + | 0.241137i | \(0.0775204\pi\) | ||||
−0.970491 | + | 0.241137i | \(0.922480\pi\) | |||||||
\(692\) | − | 23.8182i | − | 0.0344194i | ||||||
\(693\) | − | 34.8509i | − | 0.0502899i | ||||||
\(694\) | −624.316 | −0.899590 | ||||||||
\(695\) | −151.585 | −0.218107 | ||||||||
\(696\) | 164.470i | 0.236307i | ||||||||
\(697\) | 43.1419 | 0.0618966 | ||||||||
\(698\) | 460.671 | 0.659987 | ||||||||
\(699\) | − | 28.6456i | − | 0.0409809i | ||||||
\(700\) | 146.960 | 0.209943 | ||||||||
\(701\) | − | 510.070i | − | 0.727632i | −0.931471 | − | 0.363816i | \(-0.881474\pi\) | ||
0.931471 | − | 0.363816i | \(-0.118526\pi\) | |||||||
\(702\) | −86.1469 | −0.122716 | ||||||||
\(703\) | − | 107.253i | − | 0.152564i | ||||||
\(704\) | 30.4302i | 0.0432246i | ||||||||
\(705\) | 89.7180i | 0.127260i | ||||||||
\(706\) | 259.515 | 0.367584 | ||||||||
\(707\) | 386.359i | 0.546477i | ||||||||
\(708\) | 199.655 | − | 43.7015i | 0.281999 | − | 0.0617252i | ||||
\(709\) | 176.053 | 0.248312 | 0.124156 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124156 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(710\) | − | 80.4151i | − | 0.113261i | ||||||
\(711\) | −134.743 | −0.189512 | ||||||||
\(712\) | −261.171 | −0.366813 | ||||||||
\(713\) | −444.443 | −0.623342 | ||||||||
\(714\) | − | 138.958i | − | 0.194619i | ||||||
\(715\) | −43.2391 | −0.0604743 | ||||||||
\(716\) | 278.141i | 0.388465i | ||||||||
\(717\) | −231.969 | −0.323527 | ||||||||
\(718\) | − | 316.391i | − | 0.440656i | ||||||
\(719\) | − | 170.417i | − | 0.237019i | −0.992953 | − | 0.118510i | \(-0.962188\pi\) | ||
0.992953 | − | 0.118510i | \(-0.0378116\pi\) | |||||||
\(720\) | 11.6359 | 0.0161610 | ||||||||
\(721\) | 34.5011i | 0.0478517i | ||||||||
\(722\) | − | 4.28665i | − | 0.00593719i | ||||||
\(723\) | 37.3621 | 0.0516765 | ||||||||
\(724\) | −128.292 | −0.177199 | ||||||||
\(725\) | −807.740 | −1.11412 | ||||||||
\(726\) | − | 260.947i | − | 0.359432i | ||||||
\(727\) | 440.331 | 0.605683 | 0.302841 | − | 0.953041i | \(-0.402065\pi\) | ||||
0.302841 | + | 0.953041i | \(0.402065\pi\) | |||||||
\(728\) | 101.267 | 0.139103 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −4.67661 | −0.00640632 | ||||||||
\(731\) | 71.3860i | 0.0976553i | ||||||||
\(732\) | 21.7111i | 0.0296600i | ||||||||
\(733\) | 1011.75 | 1.38029 | 0.690144 | − | 0.723672i | \(-0.257547\pi\) | ||||
0.690144 | + | 0.723672i | \(0.257547\pi\) | |||||||
\(734\) | 425.347 | 0.579491 | ||||||||
\(735\) | −66.6304 | −0.0906536 | ||||||||
\(736\) | −72.2396 | −0.0981517 | ||||||||
\(737\) | −177.758 | −0.241191 | ||||||||
\(738\) | − | 9.85388i | − | 0.0133521i | ||||||
\(739\) | 37.6364i | 0.0509288i | 0.999676 | + | 0.0254644i | \(0.00810644\pi\) | ||||
−0.999676 | + | 0.0254644i | \(0.991894\pi\) | |||||||
\(740\) | 10.9016i | 0.0147319i | ||||||||
\(741\) | − | 387.412i | − | 0.522823i | ||||||
\(742\) | − | 41.8970i | − | 0.0564649i | ||||||
\(743\) | 136.717 | 0.184007 | 0.0920034 | − | 0.995759i | \(-0.470673\pi\) | ||||
0.0920034 | + | 0.995759i | \(0.470673\pi\) | |||||||
\(744\) | 170.499 | 0.229165 | ||||||||
\(745\) | 33.6275i | 0.0451376i | ||||||||
\(746\) | − | 737.413i | − | 0.988489i | ||||||
\(747\) | 441.593i | 0.591155i | ||||||||
\(748\) | 141.310i | 0.188917i | ||||||||
\(749\) | −122.684 | −0.163796 | ||||||||
\(750\) | 116.526i | 0.155367i | ||||||||
\(751\) | − | 1034.25i | − | 1.37716i | −0.725160 | − | 0.688581i | \(-0.758234\pi\) | ||
0.725160 | − | 0.688581i | \(-0.241766\pi\) | |||||||
\(752\) | 213.677i | 0.284145i | ||||||||
\(753\) | −644.581 | −0.856017 | ||||||||
\(754\) | −556.593 | −0.738187 | ||||||||
\(755\) | 84.2908i | 0.111643i | ||||||||
\(756\) | −31.7388 | −0.0419826 | ||||||||
\(757\) | −901.318 | −1.19064 | −0.595322 | − | 0.803487i | \(-0.702976\pi\) | ||||
−0.595322 | + | 0.803487i | \(0.702976\pi\) | |||||||
\(758\) | 949.650i | 1.25284i | ||||||||
\(759\) | −84.1347 | −0.110849 | ||||||||
\(760\) | 52.3281i | 0.0688527i | ||||||||
\(761\) | −884.001 | −1.16163 | −0.580815 | − | 0.814035i | \(-0.697266\pi\) | ||||
−0.580815 | + | 0.814035i | \(0.697266\pi\) | |||||||
\(762\) | − | 122.788i | − | 0.161139i | ||||||
\(763\) | 610.796i | 0.800519i | ||||||||
\(764\) | 109.010i | 0.142683i | ||||||||
\(765\) | 54.0344 | 0.0706332 | ||||||||
\(766\) | − | 306.298i | − | 0.399867i | ||||||
\(767\) | 147.893 | + | 675.667i | 0.192820 | + | 0.880921i | ||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | − | 982.068i | − | 1.27707i | −0.769592 | − | 0.638536i | \(-0.779540\pi\) | ||
0.769592 | − | 0.638536i | \(-0.220460\pi\) | |||||||
\(770\) | −15.9305 | −0.0206889 | ||||||||
\(771\) | 28.6480 | 0.0371569 | ||||||||
\(772\) | 121.491 | 0.157371 | ||||||||
\(773\) | 882.142i | 1.14119i | 0.821230 | + | 0.570597i | \(0.193288\pi\) | ||||
−0.821230 | + | 0.570597i | \(0.806712\pi\) | |||||||
\(774\) | 16.3050 | 0.0210659 | ||||||||
\(775\) | 837.350i | 1.08045i | ||||||||
\(776\) | 348.276 | 0.448809 | ||||||||
\(777\) | − | 29.7357i | − | 0.0382699i | ||||||
\(778\) | − | 532.823i | − | 0.684862i | ||||||
\(779\) | 44.3139 | 0.0568857 | ||||||||
\(780\) | 39.3780i | 0.0504846i | ||||||||
\(781\) | − | 223.057i | − | 0.285605i | ||||||
\(782\) | −335.463 | −0.428980 | ||||||||
\(783\) | 174.446 | 0.222792 | ||||||||
\(784\) | −158.691 | −0.202411 | ||||||||
\(785\) | 16.7299i | 0.0213119i | ||||||||
\(786\) | 298.287 | 0.379500 | ||||||||
\(787\) | −261.379 | −0.332121 | −0.166060 | − | 0.986116i | \(-0.553105\pi\) | ||||
−0.166060 | + | 0.986116i | \(0.553105\pi\) | |||||||
\(788\) | −57.5538 | −0.0730378 | ||||||||
\(789\) | −199.376 | −0.252694 | ||||||||
\(790\) | 61.5916i | 0.0779640i | ||||||||
\(791\) | 307.470i | 0.388711i | ||||||||
\(792\) | 32.2760 | 0.0407526 | ||||||||
\(793\) | −73.4741 | −0.0926534 | ||||||||
\(794\) | 499.807 | 0.629480 | ||||||||
\(795\) | 16.2918 | 0.0204929 | ||||||||
\(796\) | 270.051 | 0.339260 | ||||||||
\(797\) | 79.4352i | 0.0996677i | 0.998758 | + | 0.0498339i | \(0.0158692\pi\) | ||||
−0.998758 | + | 0.0498339i | \(0.984131\pi\) | |||||||
\(798\) | − | 142.733i | − | 0.178863i | ||||||
\(799\) | 992.264i | 1.24188i | ||||||||
\(800\) | 136.103i | 0.170128i | ||||||||
\(801\) | 277.014i | 0.345835i | ||||||||
\(802\) | −126.481 | −0.157706 | ||||||||
\(803\) | −12.9721 | −0.0161545 | ||||||||
\(804\) | 161.885i | 0.201349i | ||||||||
\(805\) | − | 37.8181i | − | 0.0469790i | ||||||
\(806\) | 576.997i | 0.715877i | ||||||||
\(807\) | − | 251.120i | − | 0.311177i | ||||||
\(808\) | −357.814 | −0.442839 | ||||||||
\(809\) | 547.235i | 0.676434i | 0.941068 | + | 0.338217i | \(0.109824\pi\) | ||||
−0.941068 | + | 0.338217i | \(0.890176\pi\) | |||||||
\(810\) | − | 12.3418i | − | 0.0152368i | ||||||
\(811\) | − | 964.881i | − | 1.18974i | −0.803821 | − | 0.594871i | \(-0.797203\pi\) | ||
0.803821 | − | 0.594871i | \(-0.202797\pi\) | |||||||
\(812\) | −205.064 | −0.252542 | ||||||||
\(813\) | −328.999 | −0.404673 | ||||||||
\(814\) | 30.2390i | 0.0371487i | ||||||||
\(815\) | −219.689 | −0.269557 | ||||||||
\(816\) | 128.691 | 0.157710 | ||||||||
\(817\) | 73.3253i | 0.0897494i | ||||||||
\(818\) | −252.415 | −0.308576 | ||||||||
\(819\) | − | 107.410i | − | 0.131147i | ||||||
\(820\) | −4.50424 | −0.00549297 | ||||||||
\(821\) | 528.438i | 0.643652i | 0.946799 | + | 0.321826i | \(0.104297\pi\) | ||||
−0.946799 | + | 0.321826i | \(0.895703\pi\) | |||||||
\(822\) | − | 259.411i | − | 0.315585i | ||||||
\(823\) | − | 540.168i | − | 0.656341i | −0.944619 | − | 0.328170i | \(-0.893568\pi\) | ||
0.944619 | − | 0.328170i | \(-0.106432\pi\) | |||||||
\(824\) | −31.9520 | −0.0387767 | ||||||||
\(825\) | 158.513i | 0.192137i | ||||||||
\(826\) | 54.4878 | + | 248.934i | 0.0659659 | + | 0.301373i | ||||
\(827\) | 326.126 | 0.394349 | 0.197174 | − | 0.980368i | \(-0.436823\pi\) | ||||
0.197174 | + | 0.980368i | \(0.436823\pi\) | |||||||
\(828\) | 76.6217i | 0.0925383i | ||||||||
\(829\) | −1184.50 | −1.42883 | −0.714414 | − | 0.699723i | \(-0.753307\pi\) | ||||
−0.714414 | + | 0.699723i | \(0.753307\pi\) | |||||||
\(830\) | 201.853 | 0.243197 | ||||||||
\(831\) | 236.496 | 0.284592 | ||||||||
\(832\) | 93.7848i | 0.112722i | ||||||||
\(833\) | −736.919 | −0.884657 | ||||||||
\(834\) | 382.922i | 0.459139i | ||||||||
\(835\) | −98.8834 | −0.118423 | ||||||||
\(836\) | 145.149i | 0.173623i | ||||||||
\(837\) | − | 180.841i | − | 0.216059i | ||||||
\(838\) | −538.631 | −0.642758 | ||||||||
\(839\) | 70.1546i | 0.0836169i | 0.999126 | + | 0.0418085i | \(0.0133119\pi\) | ||||
−0.999126 | + | 0.0418085i | \(0.986688\pi\) | |||||||
\(840\) | 14.5079i | 0.0172713i | ||||||||
\(841\) | 286.096 | 0.340185 | ||||||||
\(842\) | 463.210 | 0.550130 | ||||||||
\(843\) | 347.654 | 0.412401 | ||||||||
\(844\) | − | 71.7529i | − | 0.0850153i | ||||||
\(845\) | 30.6111 | 0.0362261 | ||||||||
\(846\) | 226.639 | 0.267895 | ||||||||
\(847\) | 325.354 | 0.384125 | ||||||||
\(848\) | 38.8015 | 0.0457565 | ||||||||
\(849\) | − | 24.0809i | − | 0.0283638i | ||||||
\(850\) | 632.026i | 0.743560i | ||||||||
\(851\) | −71.7859 | −0.0843548 | ||||||||
\(852\) | −203.139 | −0.238426 | ||||||||
\(853\) | −456.456 | −0.535118 | −0.267559 | − | 0.963541i | \(-0.586217\pi\) | ||||
−0.267559 | + | 0.963541i | \(0.586217\pi\) | |||||||
\(854\) | −27.0699 | −0.0316977 | ||||||||
\(855\) | 55.5023 | 0.0649150 | ||||||||
\(856\) | − | 113.619i | − | 0.132733i | ||||||
\(857\) | 1020.65i | 1.19096i | 0.803371 | + | 0.595479i | \(0.203038\pi\) | ||||
−0.803371 | + | 0.595479i | \(0.796962\pi\) | |||||||
\(858\) | 109.228i | 0.127305i | ||||||||
\(859\) | 896.658i | 1.04384i | 0.852995 | + | 0.521919i | \(0.174784\pi\) | ||||
−0.852995 | + | 0.521919i | \(0.825216\pi\) | |||||||
\(860\) | − | 7.45307i | − | 0.00866635i | ||||||
\(861\) | 12.2860 | 0.0142695 | ||||||||
\(862\) | −152.843 | −0.177312 | ||||||||
\(863\) | 1118.41i | 1.29596i | 0.761659 | + | 0.647978i | \(0.224385\pi\) | ||||
−0.761659 | + | 0.647978i | \(0.775615\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 11.5478i | 0.0133501i | ||||||||
\(866\) | − | 967.695i | − | 1.11743i | ||||||
\(867\) | 97.0474 | 0.111935 | ||||||||
\(868\) | 212.581i | 0.244909i | ||||||||
\(869\) | 170.844i | 0.196599i | ||||||||
\(870\) | − | 79.7400i | − | 0.0916552i | ||||||
\(871\) | −547.845 | −0.628984 | ||||||||
\(872\) | −565.669 | −0.648702 | ||||||||
\(873\) | − | 369.402i | − | 0.423141i | ||||||
\(874\) | −344.576 | −0.394251 | ||||||||
\(875\) | −145.286 | −0.166042 | ||||||||
\(876\) | 11.8137i | 0.0134860i | ||||||||
\(877\) | −501.541 | −0.571882 | −0.285941 | − | 0.958247i | \(-0.592306\pi\) | ||||
−0.285941 | + | 0.958247i | \(0.592306\pi\) | |||||||
\(878\) | − | 669.653i | − | 0.762703i | ||||||
\(879\) | 698.528 | 0.794685 | ||||||||
\(880\) | − | 14.7535i | − | 0.0167653i | ||||||
\(881\) | − | 1329.21i | − | 1.50875i | −0.656444 | − | 0.754375i | \(-0.727940\pi\) | ||
0.656444 | − | 0.754375i | \(-0.272060\pi\) | |||||||
\(882\) | 168.317i | 0.190835i | ||||||||
\(883\) | 57.4848 | 0.0651017 | 0.0325509 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325509 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(884\) | 435.513i | 0.492662i | ||||||||
\(885\) | −96.7990 | + | 21.1878i | −0.109377 | + | 0.0239410i | ||||
\(886\) | 1049.26 | 1.18426 | ||||||||
\(887\) | 361.486i | 0.407538i | 0.979019 | + | 0.203769i | \(0.0653192\pi\) | ||||
−0.979019 | + | 0.203769i | \(0.934681\pi\) | |||||||
\(888\) | 27.5388 | 0.0310121 | ||||||||
\(889\) | 153.094 | 0.172209 | ||||||||
\(890\) | 126.624 | 0.142274 | ||||||||
\(891\) | − | 34.2339i | − | 0.0384219i | ||||||
\(892\) | 475.122 | 0.532648 | ||||||||
\(893\) | 1019.22i | 1.14134i | ||||||||
\(894\) | 84.9473 | 0.0950194 | ||||||||
\(895\) | − | 134.851i | − | 0.150672i | ||||||
\(896\) | 34.5529i | 0.0385635i | ||||||||
\(897\) | −259.301 | −0.289076 | ||||||||
\(898\) | 713.576i | 0.794628i | ||||||||
\(899\) | − | 1168.41i | − | 1.29968i | ||||||
\(900\) | 144.359 | 0.160398 | ||||||||
\(901\) | 180.184 | 0.199983 | ||||||||
\(902\) | −12.4940 | −0.0138514 | ||||||||
\(903\) | 20.3294i | 0.0225132i | ||||||||
\(904\) | −284.754 | −0.314993 | ||||||||
\(905\) | 62.2000 | 0.0687292 | ||||||||
\(906\) | 212.929 | 0.235021 | ||||||||
\(907\) | −121.679 | −0.134156 | −0.0670780 | − | 0.997748i | \(-0.521368\pi\) | ||||
−0.0670780 | + | 0.997748i | \(0.521368\pi\) | |||||||
\(908\) | 826.941i | 0.910728i | ||||||||
\(909\) | 379.519i | 0.417513i | ||||||||
\(910\) | −49.0972 | −0.0539530 | ||||||||
\(911\) | 1116.36 | 1.22543 | 0.612713 | − | 0.790306i | \(-0.290078\pi\) | ||||
0.612713 | + | 0.790306i | \(0.290078\pi\) | |||||||
\(912\) | 132.187 | 0.144942 | ||||||||
\(913\) | 559.906 | 0.613259 | ||||||||
\(914\) | 817.560 | 0.894485 | ||||||||
\(915\) | − | 10.5262i | − | 0.0115041i | ||||||
\(916\) | 780.500i | 0.852074i | ||||||||
\(917\) | 371.910i | 0.405573i | ||||||||
\(918\) | − | 136.498i | − | 0.148690i | ||||||
\(919\) | 1734.76i | 1.88766i | 0.330431 | + | 0.943830i | \(0.392806\pi\) | ||||
−0.330431 | + | 0.943830i | \(0.607194\pi\) | |||||||
\(920\) | 35.0240 | 0.0380696 | ||||||||
\(921\) | −193.744 | −0.210363 | ||||||||
\(922\) | − | 531.536i | − | 0.576503i | ||||||
\(923\) | − | 687.456i | − | 0.744806i | ||||||
\(924\) | 40.2424i | 0.0435524i | ||||||||
\(925\) | 135.248i | 0.146214i | ||||||||
\(926\) | 587.016 | 0.633926 | ||||||||
\(927\) | 33.8902i | 0.0365590i | ||||||||
\(928\) | − | 189.913i | − | 0.204648i | ||||||
\(929\) | 81.3239i | 0.0875392i | 0.999042 | + | 0.0437696i | \(0.0139367\pi\) | ||||
−0.999042 | + | 0.0437696i | \(0.986063\pi\) | |||||||
\(930\) | −82.6631 | −0.0888850 | ||||||||
\(931\) | −756.938 | −0.813038 | ||||||||
\(932\) | 33.0771i | 0.0354905i | ||||||||
\(933\) | −10.0562 | −0.0107784 | ||||||||
\(934\) | 738.485 | 0.790670 | ||||||||
\(935\) | − | 68.5114i | − | 0.0732743i | ||||||
\(936\) | 99.4738 | 0.106275 | ||||||||
\(937\) | − | 639.885i | − | 0.682908i | −0.939898 | − | 0.341454i | \(-0.889081\pi\) | ||
0.939898 | − | 0.341454i | \(-0.110919\pi\) | |||||||
\(938\) | −201.841 | −0.215182 | ||||||||
\(939\) | 867.566i | 0.923925i | ||||||||
\(940\) | − | 103.597i | − | 0.110210i | ||||||
\(941\) | − | 873.925i | − | 0.928719i | −0.885647 | − | 0.464360i | \(-0.846285\pi\) | ||
0.885647 | − | 0.464360i | \(-0.153715\pi\) | |||||||
\(942\) | 42.2617 | 0.0448638 | ||||||||
\(943\) | − | 29.6600i | − | 0.0314528i | ||||||
\(944\) | −230.542 | + | 50.4621i | −0.244218 | + | 0.0534556i | ||||
\(945\) | 15.3880 | 0.0162836 | ||||||||
\(946\) | − | 20.6735i | − | 0.0218536i | ||||||
\(947\) | −962.998 | −1.01689 | −0.508447 | − | 0.861093i | \(-0.669780\pi\) | ||||
−0.508447 | + | 0.861093i | \(0.669780\pi\) | |||||||
\(948\) | 155.588 | 0.164123 | ||||||||
\(949\) | −39.9796 | −0.0421282 | ||||||||
\(950\) | 649.195i | 0.683364i | ||||||||
\(951\) | 320.044 | 0.336535 | ||||||||
\(952\) | 160.455i | 0.168545i | ||||||||
\(953\) | 665.805 | 0.698641 | 0.349321 | − | 0.937003i | \(-0.386412\pi\) | ||||
0.349321 | + | 0.937003i | \(0.386412\pi\) | |||||||
\(954\) | − | 41.1552i | − | 0.0431396i | ||||||
\(955\) | − | 52.8512i | − | 0.0553416i | ||||||
\(956\) | 267.855 | 0.280183 | ||||||||
\(957\) | − | 221.185i | − | 0.231123i | ||||||
\(958\) | − | 938.856i | − | 0.980017i | ||||||
\(959\) | 323.439 | 0.337267 | ||||||||
\(960\) | −13.4360 | −0.0139959 | ||||||||
\(961\) | −250.243 | −0.260398 | ||||||||
\(962\) | 93.1958i | 0.0968771i | ||||||||
\(963\) | −120.512 | −0.125142 | ||||||||
\(964\) | −43.1421 | −0.0447532 | ||||||||
\(965\) | −58.9025 | −0.0610389 | ||||||||
\(966\) | −95.5334 | −0.0988958 | ||||||||
\(967\) | − | 1070.88i | − | 1.10742i | −0.832708 | − | 0.553712i | \(-0.813211\pi\) | ||
0.832708 | − | 0.553712i | \(-0.186789\pi\) | |||||||
\(968\) | 301.316i | 0.311277i | ||||||||
\(969\) | 613.845 | 0.633483 | ||||||||
\(970\) | −168.855 | −0.174077 | ||||||||
\(971\) | −229.115 | −0.235958 | −0.117979 | − | 0.993016i | \(-0.537642\pi\) | ||||
−0.117979 | + | 0.993016i | \(0.537642\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −477.434 | −0.490683 | ||||||||
\(974\) | − | 714.980i | − | 0.734066i | ||||||
\(975\) | 488.534i | 0.501060i | ||||||||
\(976\) | − | 25.0699i | − | 0.0256863i | ||||||
\(977\) | 133.975i | 0.137129i | 0.997647 | + | 0.0685643i | \(0.0218418\pi\) | ||||
−0.997647 | + | 0.0685643i | \(0.978158\pi\) | |||||||
\(978\) | 554.963i | 0.567446i | ||||||||
\(979\) | 351.232 | 0.358766 | ||||||||
\(980\) | 76.9381 | 0.0785083 | ||||||||
\(981\) | 599.982i | 0.611603i | ||||||||
\(982\) | 1072.05i | 1.09170i | ||||||||
\(983\) | 337.982i | 0.343827i | 0.985112 | + | 0.171914i | \(0.0549950\pi\) | ||||
−0.985112 | + | 0.171914i | \(0.945005\pi\) | |||||||
\(984\) | 11.3783i | 0.0115633i | ||||||||
\(985\) | 27.9039 | 0.0283288 | ||||||||
\(986\) | − | 881.909i | − | 0.894432i | ||||||
\(987\) | 282.578i | 0.286300i | ||||||||
\(988\) | 447.344i | 0.452778i | ||||||||
\(989\) | 49.0778 | 0.0496237 | ||||||||
\(990\) | −15.6484 | −0.0158065 | ||||||||
\(991\) | 314.003i | 0.316855i | 0.987371 | + | 0.158427i | \(0.0506424\pi\) | ||||
−0.987371 | + | 0.158427i | \(0.949358\pi\) | |||||||
\(992\) | −196.875 | −0.198463 | ||||||||
\(993\) | −432.884 | −0.435936 | ||||||||
\(994\) | − | 253.277i | − | 0.254806i | ||||||
\(995\) | −130.929 | −0.131587 | ||||||||
\(996\) | − | 509.907i | − | 0.511955i | ||||||
\(997\) | 650.977 | 0.652936 | 0.326468 | − | 0.945208i | \(-0.394141\pi\) | ||||
0.326468 | + | 0.945208i | \(0.394141\pi\) | |||||||
\(998\) | 307.539i | 0.308155i | ||||||||
\(999\) | − | 29.2093i | − | 0.0292385i |
(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 | 354.3.d.a.235.9 | ✓ | 20 | |
3.2 | odd | 2 | 1062.3.d.f.235.14 | 20 | |||
59.58 | odd | 2 | inner | 354.3.d.a.235.19 | yes | 20 | |
177.176 | even | 2 | 1062.3.d.f.235.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.3.d.a.235.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
354.3.d.a.235.19 | yes | 20 | 59.58 | odd | 2 | inner | |
1062.3.d.f.235.4 | 20 | 177.176 | even | 2 | |||
1062.3.d.f.235.14 | 20 | 3.2 | odd | 2 |