Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(47,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.l (of order \(6\), degree \(2\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.5 | ||
Character | \(\chi\) | \(=\) | 966.47 |
Dual form | 966.2.l.c.185.5 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −1.13768 | − | 1.30602i | −0.656837 | − | 0.754032i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.890465 | − | 1.54233i | 0.398228 | − | 0.689751i | −0.595279 | − | 0.803519i | \(-0.702959\pi\) |
0.993507 | + | 0.113768i | \(0.0362919\pi\) | |||||||
\(6\) | 0.332245 | + | 1.69989i | 0.135638 | + | 0.693976i | ||||
\(7\) | −2.00001 | − | 1.73204i | −0.755933 | − | 0.654649i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.411389 | + | 2.97166i | −0.137130 | + | 0.990553i | ||||
\(10\) | −1.54233 | + | 0.890465i | −0.487728 | + | 0.281590i | ||||
\(11\) | −0.864424 | + | 0.499076i | −0.260634 | + | 0.150477i | −0.624624 | − | 0.780926i | \(-0.714748\pi\) |
0.363990 | + | 0.931403i | \(0.381414\pi\) | |||||||
\(12\) | 0.562211 | − | 1.63827i | 0.162296 | − | 0.472927i | ||||
\(13\) | 6.26372i | 1.73724i | 0.495476 | + | 0.868622i | \(0.334994\pi\) | ||||
−0.495476 | + | 0.868622i | \(0.665006\pi\) | |||||||
\(14\) | 0.866040 | + | 2.50000i | 0.231459 | + | 0.668152i | ||||
\(15\) | −3.02738 | + | 0.591704i | −0.781666 | + | 0.152777i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.67970 | + | 2.90933i | 0.407388 | + | 0.705617i | 0.994596 | − | 0.103819i | \(-0.0331063\pi\) |
−0.587208 | + | 0.809436i | \(0.699773\pi\) | |||||||
\(18\) | 1.84210 | − | 2.36784i | 0.434188 | − | 0.558105i | ||||
\(19\) | −1.42779 | − | 0.824336i | −0.327558 | − | 0.189116i | 0.327198 | − | 0.944956i | \(-0.393895\pi\) |
−0.654756 | + | 0.755840i | \(0.727229\pi\) | |||||||
\(20\) | 1.78093 | 0.398228 | ||||||||
\(21\) | 0.0132797 | + | 4.58256i | 0.00289787 | + | 0.999996i | ||||
\(22\) | 0.998151 | 0.212807 | ||||||||
\(23\) | 0.866025 | + | 0.500000i | 0.180579 | + | 0.104257i | ||||
\(24\) | −1.30602 | + | 1.13768i | −0.266591 | + | 0.232227i | ||||
\(25\) | 0.914144 | + | 1.58334i | 0.182829 | + | 0.316669i | ||||
\(26\) | 3.13186 | − | 5.42454i | 0.614208 | − | 1.06384i | ||||
\(27\) | 4.34908 | − | 2.84350i | 0.836981 | − | 0.547232i | ||||
\(28\) | 0.499985 | − | 2.59808i | 0.0944883 | − | 0.490991i | ||||
\(29\) | 1.24938i | 0.232004i | 0.993249 | + | 0.116002i | \(0.0370080\pi\) | ||||
−0.993249 | + | 0.116002i | \(0.962992\pi\) | |||||||
\(30\) | 2.91764 | + | 1.00126i | 0.532686 | + | 0.182804i | ||||
\(31\) | −6.98992 | + | 4.03563i | −1.25543 | + | 0.724821i | −0.972182 | − | 0.234227i | \(-0.924744\pi\) |
−0.283245 | + | 0.959048i | \(0.591411\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 1.63524 | + | 0.561171i | 0.284658 | + | 0.0976874i | ||||
\(34\) | − | 3.35941i | − | 0.576134i | ||||||
\(35\) | −4.45232 | + | 1.54236i | −0.752579 | + | 0.260706i | ||||
\(36\) | −2.77923 | + | 1.12956i | −0.463204 | + | 0.188259i | ||||
\(37\) | 0.235496 | − | 0.407891i | 0.0387153 | − | 0.0670569i | −0.846018 | − | 0.533154i | \(-0.821007\pi\) |
0.884734 | + | 0.466097i | \(0.154340\pi\) | |||||||
\(38\) | 0.824336 | + | 1.42779i | 0.133725 | + | 0.231618i | ||||
\(39\) | 8.18056 | − | 7.12608i | 1.30994 | − | 1.14109i | ||||
\(40\) | −1.54233 | − | 0.890465i | −0.243864 | − | 0.140795i | ||||
\(41\) | −4.34340 | −0.678325 | −0.339162 | − | 0.940728i | \(-0.610144\pi\) | ||||
−0.339162 | + | 0.940728i | \(0.610144\pi\) | |||||||
\(42\) | 2.27978 | − | 3.97525i | 0.351777 | − | 0.613394i | ||||
\(43\) | 4.79063 | 0.730565 | 0.365282 | − | 0.930897i | \(-0.380972\pi\) | ||||
0.365282 | + | 0.930897i | \(0.380972\pi\) | |||||||
\(44\) | −0.864424 | − | 0.499076i | −0.130317 | − | 0.0752385i | ||||
\(45\) | 4.21695 | + | 3.28066i | 0.628626 | + | 0.489051i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 4.22866 | − | 7.32426i | 0.616814 | − | 1.06835i | −0.373250 | − | 0.927731i | \(-0.621757\pi\) |
0.990063 | − | 0.140622i | \(-0.0449101\pi\) | |||||||
\(48\) | 1.69989 | − | 0.332245i | 0.245357 | − | 0.0479554i | ||||
\(49\) | 1.00008 | + | 6.92819i | 0.142868 | + | 0.989742i | ||||
\(50\) | − | 1.82829i | − | 0.258559i | ||||||
\(51\) | 1.88870 | − | 5.50361i | 0.264470 | − | 0.770659i | ||||
\(52\) | −5.42454 | + | 3.13186i | −0.752248 | + | 0.434311i | ||||
\(53\) | −5.24099 | + | 3.02589i | −0.719906 | + | 0.415638i | −0.814718 | − | 0.579857i | \(-0.803108\pi\) |
0.0948123 | + | 0.995495i | \(0.469775\pi\) | |||||||
\(54\) | −5.18816 | + | 0.288003i | −0.706020 | + | 0.0391923i | ||||
\(55\) | 1.77764i | 0.239697i | ||||||||
\(56\) | −1.73204 | + | 2.00001i | −0.231454 | + | 0.267263i | ||||
\(57\) | 0.547762 | + | 2.80256i | 0.0725529 | + | 0.371207i | ||||
\(58\) | 0.624691 | − | 1.08200i | 0.0820260 | − | 0.142073i | ||||
\(59\) | 0.600268 | + | 1.03970i | 0.0781483 | + | 0.135357i | 0.902451 | − | 0.430792i | \(-0.141766\pi\) |
−0.824303 | + | 0.566149i | \(0.808433\pi\) | |||||||
\(60\) | −2.02612 | − | 2.32593i | −0.261571 | − | 0.300277i | ||||
\(61\) | 1.01927 | + | 0.588474i | 0.130504 | + | 0.0753464i | 0.563831 | − | 0.825890i | \(-0.309327\pi\) |
−0.433327 | + | 0.901237i | \(0.642660\pi\) | |||||||
\(62\) | 8.07127 | 1.02505 | ||||||||
\(63\) | 5.96981 | − | 5.23081i | 0.752126 | − | 0.659020i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 9.66073 | + | 5.57762i | 1.19827 | + | 0.691819i | ||||
\(66\) | −1.13557 | − | 1.30361i | −0.139779 | − | 0.160463i | ||||
\(67\) | 4.81654 | + | 8.34250i | 0.588435 | + | 1.01920i | 0.994438 | + | 0.105327i | \(0.0335889\pi\) |
−0.406003 | + | 0.913872i | \(0.633078\pi\) | |||||||
\(68\) | −1.67970 | + | 2.90933i | −0.203694 | + | 0.352809i | ||||
\(69\) | −0.332245 | − | 1.69989i | −0.0399976 | − | 0.204642i | ||||
\(70\) | 4.62700 | + | 0.890439i | 0.553032 | + | 0.106428i | ||||
\(71\) | 9.62306i | 1.14205i | 0.820934 | + | 0.571023i | \(0.193453\pi\) | ||||
−0.820934 | + | 0.571023i | \(0.806547\pi\) | |||||||
\(72\) | 2.97166 | + | 0.411389i | 0.350213 | + | 0.0484827i | ||||
\(73\) | 9.57661 | − | 5.52906i | 1.12086 | − | 0.647128i | 0.179238 | − | 0.983806i | \(-0.442637\pi\) |
0.941620 | + | 0.336678i | \(0.109303\pi\) | |||||||
\(74\) | −0.407891 | + | 0.235496i | −0.0474164 | + | 0.0273759i | ||||
\(75\) | 1.02788 | − | 2.99523i | 0.118690 | − | 0.345859i | ||||
\(76\) | − | 1.64867i | − | 0.189116i | ||||||
\(77\) | 2.59328 | + | 0.499061i | 0.295531 | + | 0.0568733i | ||||
\(78\) | −10.6476 | + | 2.08109i | −1.20560 | + | 0.235637i | ||||
\(79\) | 0.576636 | − | 0.998763i | 0.0648766 | − | 0.112370i | −0.831763 | − | 0.555131i | \(-0.812668\pi\) |
0.896639 | + | 0.442762i | \(0.146001\pi\) | |||||||
\(80\) | 0.890465 | + | 1.54233i | 0.0995570 | + | 0.172438i | ||||
\(81\) | −8.66152 | − | 2.44502i | −0.962391 | − | 0.271668i | ||||
\(82\) | 3.76149 | + | 2.17170i | 0.415387 | + | 0.239824i | ||||
\(83\) | −7.53838 | −0.827445 | −0.413722 | − | 0.910403i | \(-0.635772\pi\) | ||||
−0.413722 | + | 0.910403i | \(0.635772\pi\) | |||||||
\(84\) | −3.96197 | + | 2.30278i | −0.432286 | + | 0.251254i | ||||
\(85\) | 5.98287 | 0.648934 | ||||||||
\(86\) | −4.14881 | − | 2.39532i | −0.447378 | − | 0.258294i | ||||
\(87\) | 1.63172 | − | 1.42139i | 0.174939 | − | 0.152389i | ||||
\(88\) | 0.499076 | + | 0.864424i | 0.0532016 | + | 0.0921480i | ||||
\(89\) | 4.81612 | − | 8.34177i | 0.510508 | − | 0.884225i | −0.489418 | − | 0.872049i | \(-0.662791\pi\) |
0.999926 | − | 0.0121761i | \(-0.00387588\pi\) | |||||||
\(90\) | −2.01166 | − | 4.94961i | −0.212048 | − | 0.521735i | ||||
\(91\) | 10.8490 | − | 12.5275i | 1.13729 | − | 1.31324i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 13.2229 | + | 4.53775i | 1.37115 | + | 0.470543i | ||||
\(94\) | −7.32426 | + | 4.22866i | −0.755439 | + | 0.436153i | ||||
\(95\) | −2.54280 | + | 1.46808i | −0.260885 | + | 0.150622i | ||||
\(96\) | −1.63827 | − | 0.562211i | −0.167205 | − | 0.0573804i | ||||
\(97\) | 11.6654i | 1.18444i | 0.805776 | + | 0.592220i | \(0.201748\pi\) | ||||
−0.805776 | + | 0.592220i | \(0.798252\pi\) | |||||||
\(98\) | 2.59800 | − | 6.50003i | 0.262438 | − | 0.656602i | ||||
\(99\) | −1.12747 | − | 2.77409i | −0.113315 | − | 0.278806i | ||||
\(100\) | −0.914144 | + | 1.58334i | −0.0914144 | + | 0.158334i | ||||
\(101\) | −8.67140 | − | 15.0193i | −0.862836 | − | 1.49448i | −0.869180 | − | 0.494496i | \(-0.835353\pi\) |
0.00634380 | − | 0.999980i | \(-0.497981\pi\) | |||||||
\(102\) | −4.38746 | + | 3.82192i | −0.434424 | + | 0.378426i | ||||
\(103\) | 7.08086 | + | 4.08814i | 0.697698 | + | 0.402816i | 0.806490 | − | 0.591248i | \(-0.201365\pi\) |
−0.108791 | + | 0.994065i | \(0.534698\pi\) | |||||||
\(104\) | 6.26372 | 0.614208 | ||||||||
\(105\) | 7.07964 | + | 4.06012i | 0.690902 | + | 0.396228i | ||||
\(106\) | 6.05178 | 0.587800 | ||||||||
\(107\) | 17.0877 | + | 9.86556i | 1.65193 | + | 0.953740i | 0.976279 | + | 0.216514i | \(0.0694688\pi\) |
0.675647 | + | 0.737226i | \(0.263865\pi\) | |||||||
\(108\) | 4.63708 | + | 2.34466i | 0.446204 | + | 0.225615i | ||||
\(109\) | 7.96954 | + | 13.8036i | 0.763343 | + | 1.32215i | 0.941118 | + | 0.338078i | \(0.109777\pi\) |
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(110\) | 0.888819 | − | 1.53948i | 0.0847455 | − | 0.146784i | ||||
\(111\) | −0.800633 | + | 0.156485i | −0.0759927 | + | 0.0148529i | ||||
\(112\) | 2.50000 | − | 0.866040i | 0.236227 | − | 0.0818330i | ||||
\(113\) | − | 6.36516i | − | 0.598784i | −0.954130 | − | 0.299392i | \(-0.903216\pi\) | ||
0.954130 | − | 0.299392i | \(-0.0967839\pi\) | |||||||
\(114\) | 0.926901 | − | 2.70097i | 0.0868123 | − | 0.252969i | ||||
\(115\) | 1.54233 | − | 0.890465i | 0.143823 | − | 0.0830363i | ||||
\(116\) | −1.08200 | + | 0.624691i | −0.100461 | + | 0.0580011i | ||||
\(117\) | −18.6136 | − | 2.57683i | −1.72083 | − | 0.238228i | ||||
\(118\) | − | 1.20054i | − | 0.110518i | ||||||
\(119\) | 1.67966 | − | 8.72801i | 0.153974 | − | 0.800095i | ||||
\(120\) | 0.591704 | + | 3.02738i | 0.0540150 | + | 0.276361i | ||||
\(121\) | −5.00185 | + | 8.66345i | −0.454713 | + | 0.787587i | ||||
\(122\) | −0.588474 | − | 1.01927i | −0.0532780 | − | 0.0922802i | ||||
\(123\) | 4.94138 | + | 5.67257i | 0.445549 | + | 0.511479i | ||||
\(124\) | −6.98992 | − | 4.03563i | −0.627713 | − | 0.362411i | ||||
\(125\) | 12.1607 | 1.08769 | ||||||||
\(126\) | −7.78541 | + | 1.54510i | −0.693580 | + | 0.137649i | ||||
\(127\) | −1.66680 | −0.147904 | −0.0739522 | − | 0.997262i | \(-0.523561\pi\) | ||||
−0.0739522 | + | 0.997262i | \(0.523561\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −5.45019 | − | 6.25668i | −0.479862 | − | 0.550870i | ||||
\(130\) | −5.57762 | − | 9.66073i | −0.489190 | − | 0.847302i | ||||
\(131\) | 0.963948 | − | 1.66961i | 0.0842205 | − | 0.145874i | −0.820838 | − | 0.571161i | \(-0.806493\pi\) |
0.905059 | + | 0.425286i | \(0.139827\pi\) | |||||||
\(132\) | 0.331630 | + | 1.69674i | 0.0288647 | + | 0.147683i | ||||
\(133\) | 1.42782 | + | 4.12167i | 0.123807 | + | 0.357394i | ||||
\(134\) | − | 9.63309i | − | 0.832172i | ||||||
\(135\) | −0.512914 | − | 9.23976i | −0.0441446 | − | 0.795232i | ||||
\(136\) | 2.90933 | − | 1.67970i | 0.249473 | − | 0.144033i | ||||
\(137\) | −7.54322 | + | 4.35508i | −0.644461 | + | 0.372080i | −0.786331 | − | 0.617806i | \(-0.788022\pi\) |
0.141870 | + | 0.989885i | \(0.454688\pi\) | |||||||
\(138\) | −0.562211 | + | 1.63827i | −0.0478586 | + | 0.139459i | ||||
\(139\) | 0.941550i | 0.0798613i | 0.999202 | + | 0.0399306i | \(0.0127137\pi\) | ||||
−0.999202 | + | 0.0399306i | \(0.987286\pi\) | |||||||
\(140\) | −3.56188 | − | 3.08464i | −0.301034 | − | 0.260700i | ||||
\(141\) | −14.3765 | + | 2.80990i | −1.21072 | + | 0.236636i | ||||
\(142\) | 4.81153 | − | 8.33381i | 0.403774 | − | 0.699358i | ||||
\(143\) | −3.12607 | − | 5.41451i | −0.261415 | − | 0.452784i | ||||
\(144\) | −2.36784 | − | 1.84210i | −0.197320 | − | 0.153509i | ||||
\(145\) | 1.92696 | + | 1.11253i | 0.160025 | + | 0.0923907i | ||||
\(146\) | −11.0581 | −0.915177 | ||||||||
\(147\) | 7.91061 | − | 9.18816i | 0.652456 | − | 0.757827i | ||||
\(148\) | 0.470992 | 0.0387153 | ||||||||
\(149\) | 0.753321 | + | 0.434930i | 0.0617144 | + | 0.0356309i | 0.530540 | − | 0.847660i | \(-0.321989\pi\) |
−0.468825 | + | 0.883291i | \(0.655323\pi\) | |||||||
\(150\) | −2.38779 | + | 2.08000i | −0.194962 | + | 0.169831i | ||||
\(151\) | 3.57086 | + | 6.18491i | 0.290593 | + | 0.503321i | 0.973950 | − | 0.226763i | \(-0.0728142\pi\) |
−0.683357 | + | 0.730084i | \(0.739481\pi\) | |||||||
\(152\) | −0.824336 | + | 1.42779i | −0.0668625 | + | 0.115809i | ||||
\(153\) | −9.33656 | + | 3.79464i | −0.754816 | + | 0.306779i | ||||
\(154\) | −1.99631 | − | 1.72884i | −0.160867 | − | 0.139314i | ||||
\(155\) | 14.3744i | 1.15458i | ||||||||
\(156\) | 10.2616 | + | 3.52153i | 0.821589 | + | 0.281948i | ||||
\(157\) | −11.8872 | + | 6.86308i | −0.948702 | + | 0.547733i | −0.892677 | − | 0.450696i | \(-0.851176\pi\) |
−0.0560243 | + | 0.998429i | \(0.517842\pi\) | |||||||
\(158\) | −0.998763 | + | 0.576636i | −0.0794573 | + | 0.0458747i | ||||
\(159\) | 9.91443 | + | 3.40237i | 0.786265 | + | 0.269826i | ||||
\(160\) | − | 1.78093i | − | 0.140795i | ||||||
\(161\) | −0.866040 | − | 2.50000i | −0.0682535 | − | 0.197027i | ||||
\(162\) | 6.27859 | + | 6.44821i | 0.493292 | + | 0.506619i | ||||
\(163\) | 4.67610 | − | 8.09924i | 0.366260 | − | 0.634381i | −0.622717 | − | 0.782447i | \(-0.713971\pi\) |
0.988978 | + | 0.148066i | \(0.0473047\pi\) | |||||||
\(164\) | −2.17170 | − | 3.76149i | −0.169581 | − | 0.293723i | ||||
\(165\) | 2.32163 | − | 2.02237i | 0.180739 | − | 0.157442i | ||||
\(166\) | 6.52843 | + | 3.76919i | 0.506704 | + | 0.292546i | ||||
\(167\) | −24.8198 | −1.92061 | −0.960307 | − | 0.278945i | \(-0.910015\pi\) | ||||
−0.960307 | + | 0.278945i | \(0.910015\pi\) | |||||||
\(168\) | 4.58256 | − | 0.0132797i | 0.353552 | − | 0.00102455i | ||||
\(169\) | −26.2342 | −2.01801 | ||||||||
\(170\) | −5.18132 | − | 2.99144i | −0.397389 | − | 0.229433i | ||||
\(171\) | 3.03702 | − | 3.90379i | 0.232247 | − | 0.298530i | ||||
\(172\) | 2.39532 | + | 4.14881i | 0.182641 | + | 0.316344i | ||||
\(173\) | −1.64788 | + | 2.85421i | −0.125286 | + | 0.217002i | −0.921845 | − | 0.387560i | \(-0.873318\pi\) |
0.796559 | + | 0.604561i | \(0.206651\pi\) | |||||||
\(174\) | −2.12381 | + | 0.415101i | −0.161005 | + | 0.0314687i | ||||
\(175\) | 0.914118 | − | 4.75004i | 0.0691008 | − | 0.359069i | ||||
\(176\) | − | 0.998151i | − | 0.0752385i | ||||||
\(177\) | 0.674955 | − | 1.96680i | 0.0507327 | − | 0.147834i | ||||
\(178\) | −8.34177 | + | 4.81612i | −0.625242 | + | 0.360984i | ||||
\(179\) | −19.3860 | + | 11.1925i | −1.44897 | + | 0.836566i | −0.998420 | − | 0.0561832i | \(-0.982107\pi\) |
−0.450554 | + | 0.892749i | \(0.648774\pi\) | |||||||
\(180\) | −0.732655 | + | 5.29232i | −0.0546089 | + | 0.394466i | ||||
\(181\) | 2.62713i | 0.195273i | 0.995222 | + | 0.0976366i | \(0.0311283\pi\) | ||||
−0.995222 | + | 0.0976366i | \(0.968872\pi\) | |||||||
\(182\) | −15.6593 | + | 5.42463i | −1.16074 | + | 0.402100i | ||||
\(183\) | −0.391035 | − | 2.00068i | −0.0289061 | − | 0.147894i | ||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −0.419402 | − | 0.726425i | −0.0308350 | − | 0.0534079i | ||||
\(186\) | −9.18248 | − | 10.5413i | −0.673292 | − | 0.772922i | ||||
\(187\) | −2.90396 | − | 1.67660i | −0.212358 | − | 0.122605i | ||||
\(188\) | 8.45732 | 0.616814 | ||||||||
\(189\) | −13.6233 | − | 1.84575i | −0.990946 | − | 0.134259i | ||||
\(190\) | 2.93617 | 0.213012 | ||||||||
\(191\) | −4.07616 | − | 2.35337i | −0.294941 | − | 0.170284i | 0.345227 | − | 0.938519i | \(-0.387802\pi\) |
−0.640168 | + | 0.768235i | \(0.721135\pi\) | |||||||
\(192\) | 1.13768 | + | 1.30602i | 0.0821047 | + | 0.0942540i | ||||
\(193\) | 0.532666 | + | 0.922605i | 0.0383422 | + | 0.0664106i | 0.884560 | − | 0.466427i | \(-0.154459\pi\) |
−0.846218 | + | 0.532838i | \(0.821126\pi\) | |||||||
\(194\) | 5.83269 | − | 10.1025i | 0.418763 | − | 0.725318i | ||||
\(195\) | −3.70627 | − | 18.9626i | −0.265412 | − | 1.35794i | ||||
\(196\) | −5.49995 | + | 4.33019i | −0.392854 | + | 0.309299i | ||||
\(197\) | 16.9781i | 1.20964i | 0.796362 | + | 0.604820i | \(0.206755\pi\) | ||||
−0.796362 | + | 0.604820i | \(0.793245\pi\) | |||||||
\(198\) | −0.410628 | + | 2.96617i | −0.0291821 | + | 0.210796i | ||||
\(199\) | 1.85652 | − | 1.07186i | 0.131605 | − | 0.0759823i | −0.432752 | − | 0.901513i | \(-0.642457\pi\) |
0.564357 | + | 0.825531i | \(0.309124\pi\) | |||||||
\(200\) | 1.58334 | − | 0.914144i | 0.111959 | − | 0.0646398i | ||||
\(201\) | 5.41583 | − | 15.7816i | 0.382003 | − | 1.11315i | ||||
\(202\) | 17.3428i | 1.22023i | ||||||||
\(203\) | 2.16398 | − | 2.49878i | 0.151882 | − | 0.175380i | ||||
\(204\) | 5.71061 | − | 1.11615i | 0.399823 | − | 0.0781458i | ||||
\(205\) | −3.86764 | + | 6.69895i | −0.270128 | + | 0.467875i | ||||
\(206\) | −4.08814 | − | 7.08086i | −0.284834 | − | 0.493347i | ||||
\(207\) | −1.84210 | + | 2.36784i | −0.128035 | + | 0.164576i | ||||
\(208\) | −5.42454 | − | 3.13186i | −0.376124 | − | 0.217155i | ||||
\(209\) | 1.64562 | 0.113830 | ||||||||
\(210\) | −4.10109 | − | 7.05599i | −0.283002 | − | 0.486910i | ||||
\(211\) | −25.7800 | −1.77477 | −0.887385 | − | 0.461029i | \(-0.847480\pi\) | ||||
−0.887385 | + | 0.461029i | \(0.847480\pi\) | |||||||
\(212\) | −5.24099 | − | 3.02589i | −0.359953 | − | 0.207819i | ||||
\(213\) | 12.5679 | − | 10.9479i | 0.861140 | − | 0.750139i | ||||
\(214\) | −9.86556 | − | 17.0877i | −0.674396 | − | 1.16809i | ||||
\(215\) | 4.26589 | − | 7.38874i | 0.290931 | − | 0.503908i | ||||
\(216\) | −2.84350 | − | 4.34908i | −0.193476 | − | 0.295917i | ||||
\(217\) | 20.9698 | + | 4.03551i | 1.42352 | + | 0.273949i | ||||
\(218\) | − | 15.9391i | − | 1.07953i | ||||||
\(219\) | −18.1162 | − | 6.21700i | −1.22418 | − | 0.420106i | ||||
\(220\) | −1.53948 | + | 0.888819i | −0.103792 | + | 0.0599241i | ||||
\(221\) | −18.2233 | + | 10.5212i | −1.22583 | + | 0.707732i | ||||
\(222\) | 0.771611 | + | 0.264797i | 0.0517871 | + | 0.0177720i | ||||
\(223\) | 10.0664i | 0.674094i | 0.941488 | + | 0.337047i | \(0.109428\pi\) | ||||
−0.941488 | + | 0.337047i | \(0.890572\pi\) | |||||||
\(224\) | −2.59808 | − | 0.499985i | −0.173591 | − | 0.0334067i | ||||
\(225\) | −5.08123 | + | 2.06516i | −0.338749 | + | 0.137677i | ||||
\(226\) | −3.18258 | + | 5.51239i | −0.211702 | + | 0.366679i | ||||
\(227\) | 13.1471 | + | 22.7715i | 0.872604 | + | 1.51140i | 0.859293 | + | 0.511484i | \(0.170904\pi\) |
0.0133113 | + | 0.999911i | \(0.495763\pi\) | |||||||
\(228\) | −2.15320 | + | 1.87565i | −0.142599 | + | 0.124218i | ||||
\(229\) | −17.0205 | − | 9.82677i | −1.12474 | − | 0.649371i | −0.182136 | − | 0.983273i | \(-0.558301\pi\) |
−0.942608 | + | 0.333902i | \(0.891635\pi\) | |||||||
\(230\) | −1.78093 | −0.117431 | ||||||||
\(231\) | −2.29852 | − | 3.95465i | −0.151232 | − | 0.260197i | ||||
\(232\) | 1.24938 | 0.0820260 | ||||||||
\(233\) | 2.78352 | + | 1.60706i | 0.182354 | + | 0.105282i | 0.588398 | − | 0.808571i | \(-0.299759\pi\) |
−0.406044 | + | 0.913853i | \(0.633092\pi\) | |||||||
\(234\) | 14.8315 | + | 11.5384i | 0.969564 | + | 0.754290i | ||||
\(235\) | −7.53095 | − | 13.0440i | −0.491265 | − | 0.850896i | ||||
\(236\) | −0.600268 | + | 1.03970i | −0.0390741 | + | 0.0676784i | ||||
\(237\) | −1.96043 | + | 0.383168i | −0.127344 | + | 0.0248895i | ||||
\(238\) | −5.81863 | + | 6.71885i | −0.377166 | + | 0.435518i | ||||
\(239\) | − | 8.42177i | − | 0.544759i | −0.962190 | − | 0.272380i | \(-0.912189\pi\) | ||
0.962190 | − | 0.272380i | \(-0.0878106\pi\) | |||||||
\(240\) | 1.00126 | − | 2.91764i | 0.0646309 | − | 0.188333i | ||||
\(241\) | 7.66278 | − | 4.42411i | 0.493603 | − | 0.284982i | −0.232465 | − | 0.972605i | \(-0.574679\pi\) |
0.726068 | + | 0.687623i | \(0.241346\pi\) | |||||||
\(242\) | 8.66345 | − | 5.00185i | 0.556908 | − | 0.321531i | ||||
\(243\) | 6.66075 | + | 14.0938i | 0.427287 | + | 0.904116i | ||||
\(244\) | 1.17695i | 0.0753464i | ||||||||
\(245\) | 11.5761 | + | 4.62686i | 0.739570 | + | 0.295599i | ||||
\(246\) | −1.44307 | − | 7.38328i | −0.0920068 | − | 0.470741i | ||||
\(247\) | 5.16341 | − | 8.94329i | 0.328540 | − | 0.569048i | ||||
\(248\) | 4.03563 | + | 6.98992i | 0.256263 | + | 0.443860i | ||||
\(249\) | 8.57623 | + | 9.84529i | 0.543497 | + | 0.623920i | ||||
\(250\) | −10.5315 | − | 6.08035i | −0.666069 | − | 0.384555i | ||||
\(251\) | −28.0228 | −1.76879 | −0.884393 | − | 0.466743i | \(-0.845427\pi\) | ||||
−0.884393 | + | 0.466743i | \(0.845427\pi\) | |||||||
\(252\) | 7.51492 | + | 2.55461i | 0.473395 | + | 0.160925i | ||||
\(253\) | −0.998151 | −0.0627532 | ||||||||
\(254\) | 1.44349 | + | 0.833399i | 0.0905726 | + | 0.0522921i | ||||
\(255\) | −6.80657 | − | 7.81376i | −0.426244 | − | 0.489317i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.26044 | − | 10.8434i | 0.390516 | − | 0.676393i | −0.602002 | − | 0.798495i | \(-0.705630\pi\) |
0.992518 | + | 0.122102i | \(0.0389634\pi\) | |||||||
\(258\) | 1.59166 | + | 8.14353i | 0.0990926 | + | 0.506994i | ||||
\(259\) | −1.17748 | + | 0.407898i | −0.0731649 | + | 0.0253455i | ||||
\(260\) | 11.1552i | 0.691819i | ||||||||
\(261\) | −3.71274 | − | 0.513982i | −0.229813 | − | 0.0318147i | ||||
\(262\) | −1.66961 | + | 0.963948i | −0.103149 | + | 0.0595529i | ||||
\(263\) | −7.36275 | + | 4.25089i | −0.454007 | + | 0.262121i | −0.709521 | − | 0.704684i | \(-0.751089\pi\) |
0.255514 | + | 0.966805i | \(0.417755\pi\) | |||||||
\(264\) | 0.561171 | − | 1.63524i | 0.0345377 | − | 0.100642i | ||||
\(265\) | 10.7778i | 0.662074i | ||||||||
\(266\) | 0.824312 | − | 4.28338i | 0.0505418 | − | 0.262631i | ||||
\(267\) | −16.3737 | + | 3.20026i | −1.00206 | + | 0.195853i | ||||
\(268\) | −4.81654 | + | 8.34250i | −0.294217 | + | 0.509599i | ||||
\(269\) | 5.33348 | + | 9.23785i | 0.325188 | + | 0.563242i | 0.981550 | − | 0.191204i | \(-0.0612391\pi\) |
−0.656363 | + | 0.754446i | \(0.727906\pi\) | |||||||
\(270\) | −4.17568 | + | 8.25832i | −0.254124 | + | 0.502585i | ||||
\(271\) | 10.1811 | + | 5.87807i | 0.618459 | + | 0.357067i | 0.776269 | − | 0.630402i | \(-0.217110\pi\) |
−0.157810 | + | 0.987469i | \(0.550443\pi\) | |||||||
\(272\) | −3.35941 | −0.203694 | ||||||||
\(273\) | −28.7038 | + | 0.0831803i | −1.73724 | + | 0.00503430i | ||||
\(274\) | 8.71016 | 0.526200 | ||||||||
\(275\) | −1.58042 | − | 0.912454i | −0.0953028 | − | 0.0550231i | ||||
\(276\) | 1.30602 | − | 1.13768i | 0.0786133 | − | 0.0684800i | ||||
\(277\) | 8.89694 | + | 15.4099i | 0.534565 | + | 0.925894i | 0.999184 | + | 0.0403832i | \(0.0128579\pi\) |
−0.464619 | + | 0.885511i | \(0.653809\pi\) | |||||||
\(278\) | 0.470775 | − | 0.815407i | 0.0282352 | − | 0.0489048i | ||||
\(279\) | −9.11695 | − | 22.4319i | −0.545817 | − | 1.34296i | ||||
\(280\) | 1.54236 | + | 4.45232i | 0.0921734 | + | 0.266077i | ||||
\(281\) | − | 1.55697i | − | 0.0928810i | −0.998921 | − | 0.0464405i | \(-0.985212\pi\) | ||
0.998921 | − | 0.0464405i | \(-0.0147878\pi\) | |||||||
\(282\) | 13.8554 | + | 4.75480i | 0.825074 | + | 0.283144i | ||||
\(283\) | 24.6744 | − | 14.2458i | 1.46674 | − | 0.846822i | 0.467432 | − | 0.884029i | \(-0.345179\pi\) |
0.999308 | + | 0.0372070i | \(0.0118461\pi\) | |||||||
\(284\) | −8.33381 | + | 4.81153i | −0.494521 | + | 0.285512i | ||||
\(285\) | 4.81023 | + | 1.65075i | 0.284933 | + | 0.0977818i | ||||
\(286\) | 6.25214i | 0.369697i | ||||||||
\(287\) | 8.68684 | + | 7.52294i | 0.512768 | + | 0.444065i | ||||
\(288\) | 1.12956 | + | 2.77923i | 0.0665597 | + | 0.163768i | ||||
\(289\) | 2.85719 | − | 4.94879i | 0.168070 | − | 0.291105i | ||||
\(290\) | −1.11253 | − | 1.92696i | −0.0653301 | − | 0.113155i | ||||
\(291\) | 15.2352 | − | 13.2714i | 0.893106 | − | 0.777984i | ||||
\(292\) | 9.57661 | + | 5.52906i | 0.560429 | + | 0.323564i | ||||
\(293\) | 13.8727 | 0.810454 | 0.405227 | − | 0.914216i | \(-0.367193\pi\) | ||||
0.405227 | + | 0.914216i | \(0.367193\pi\) | |||||||
\(294\) | −11.4449 | + | 4.00187i | −0.667478 | + | 0.233394i | ||||
\(295\) | 2.13807 | 0.124483 | ||||||||
\(296\) | −0.407891 | − | 0.235496i | −0.0237082 | − | 0.0136879i | ||||
\(297\) | −2.34033 | + | 4.62851i | −0.135800 | + | 0.268573i | ||||
\(298\) | −0.434930 | − | 0.753321i | −0.0251948 | − | 0.0436387i | ||||
\(299\) | −3.13186 | + | 5.42454i | −0.181120 | + | 0.313709i | ||||
\(300\) | 3.10788 | − | 0.607439i | 0.179434 | − | 0.0350705i | ||||
\(301\) | −9.58132 | − | 8.29757i | −0.552258 | − | 0.478264i | ||||
\(302\) | − | 7.14172i | − | 0.410960i | ||||||
\(303\) | −9.75030 | + | 28.4121i | −0.560140 | + | 1.63223i | ||||
\(304\) | 1.42779 | − | 0.824336i | 0.0818895 | − | 0.0472789i | ||||
\(305\) | 1.81524 | − | 1.04803i | 0.103941 | − | 0.0600101i | ||||
\(306\) | 9.98302 | + | 1.38202i | 0.570691 | + | 0.0790051i | ||||
\(307\) | − | 26.0728i | − | 1.48805i | −0.668151 | − | 0.744025i | \(-0.732914\pi\) | ||
0.668151 | − | 0.744025i | \(-0.267086\pi\) | |||||||
\(308\) | 0.864439 | + | 2.49537i | 0.0492560 | + | 0.142187i | ||||
\(309\) | −2.71652 | − | 13.8987i | −0.154538 | − | 0.790672i | ||||
\(310\) | 7.18718 | − | 12.4486i | 0.408204 | − | 0.707031i | ||||
\(311\) | −4.89012 | − | 8.46993i | −0.277293 | − | 0.480286i | 0.693418 | − | 0.720536i | \(-0.256104\pi\) |
−0.970711 | + | 0.240250i | \(0.922771\pi\) | |||||||
\(312\) | −7.12608 | − | 8.18056i | −0.403435 | − | 0.463133i | ||||
\(313\) | −14.9080 | − | 8.60715i | −0.842651 | − | 0.486505i | 0.0155136 | − | 0.999880i | \(-0.495062\pi\) |
−0.858164 | + | 0.513375i | \(0.828395\pi\) | |||||||
\(314\) | 13.7262 | 0.774612 | ||||||||
\(315\) | −2.75172 | − | 13.8653i | −0.155042 | − | 0.781220i | ||||
\(316\) | 1.15327 | 0.0648766 | ||||||||
\(317\) | 7.16590 | + | 4.13723i | 0.402477 | + | 0.232370i | 0.687552 | − | 0.726135i | \(-0.258685\pi\) |
−0.285075 | + | 0.958505i | \(0.592019\pi\) | |||||||
\(318\) | −6.88496 | − | 7.90376i | −0.386089 | − | 0.443221i | ||||
\(319\) | −0.623536 | − | 1.08000i | −0.0349113 | − | 0.0604682i | ||||
\(320\) | −0.890465 | + | 1.54233i | −0.0497785 | + | 0.0862189i | ||||
\(321\) | −6.55556 | − | 33.5407i | −0.365896 | − | 1.87206i | ||||
\(322\) | −0.499985 | + | 2.59808i | −0.0278631 | + | 0.144785i | ||||
\(323\) | − | 5.53856i | − | 0.308174i | ||||||
\(324\) | −2.21331 | − | 8.72360i | −0.122962 | − | 0.484645i | ||||
\(325\) | −9.91763 | + | 5.72594i | −0.550131 | + | 0.317618i | ||||
\(326\) | −8.09924 | + | 4.67610i | −0.448575 | + | 0.258985i | ||||
\(327\) | 8.96112 | − | 26.1125i | 0.495551 | − | 1.44402i | ||||
\(328\) | 4.34340i | 0.239824i | ||||||||
\(329\) | −21.1433 | + | 7.32438i | −1.16567 | + | 0.403806i | ||||
\(330\) | −3.02178 | + | 0.590611i | −0.166344 | + | 0.0325120i | ||||
\(331\) | 8.69571 | − | 15.0614i | 0.477959 | − | 0.827850i | −0.521721 | − | 0.853116i | \(-0.674710\pi\) |
0.999681 | + | 0.0252659i | \(0.00804325\pi\) | |||||||
\(332\) | −3.76919 | − | 6.52843i | −0.206861 | − | 0.358294i | ||||
\(333\) | 1.11523 | + | 0.867616i | 0.0611144 | + | 0.0475451i | ||||
\(334\) | 21.4946 | + | 12.4099i | 1.17613 | + | 0.679040i | ||||
\(335\) | 17.1559 | 0.937325 | ||||||||
\(336\) | −3.97525 | − | 2.27978i | −0.216868 | − | 0.124372i | ||||
\(337\) | 24.0061 | 1.30770 | 0.653848 | − | 0.756626i | \(-0.273153\pi\) | ||||
0.653848 | + | 0.756626i | \(0.273153\pi\) | |||||||
\(338\) | 22.7195 | + | 13.1171i | 1.23578 | + | 0.713476i | ||||
\(339\) | −8.31305 | + | 7.24149i | −0.451503 | + | 0.393304i | ||||
\(340\) | 2.99144 | + | 5.18132i | 0.162233 | + | 0.280996i | ||||
\(341\) | 4.02817 | − | 6.97700i | 0.218138 | − | 0.377826i | ||||
\(342\) | −4.58203 | + | 1.86227i | −0.247768 | + | 0.100700i | ||||
\(343\) | 9.99974 | − | 15.5886i | 0.539935 | − | 0.841707i | ||||
\(344\) | − | 4.79063i | − | 0.258294i | ||||||
\(345\) | −2.91764 | − | 1.00126i | −0.157080 | − | 0.0539059i | ||||
\(346\) | 2.85421 | − | 1.64788i | 0.153443 | − | 0.0885905i | ||||
\(347\) | −20.7550 | + | 11.9829i | −1.11419 | + | 0.643276i | −0.939911 | − | 0.341420i | \(-0.889092\pi\) |
−0.174277 | + | 0.984697i | \(0.555759\pi\) | |||||||
\(348\) | 2.04682 | + | 0.702416i | 0.109721 | + | 0.0376535i | ||||
\(349\) | 25.6100i | 1.37087i | 0.728132 | + | 0.685437i | \(0.240389\pi\) | ||||
−0.728132 | + | 0.685437i | \(0.759611\pi\) | |||||||
\(350\) | −3.16667 | + | 3.65660i | −0.169266 | + | 0.195453i | ||||
\(351\) | 17.8109 | + | 27.2414i | 0.950675 | + | 1.45404i | ||||
\(352\) | −0.499076 | + | 0.864424i | −0.0266008 | + | 0.0460740i | ||||
\(353\) | 3.17800 | + | 5.50445i | 0.169148 | + | 0.292972i | 0.938120 | − | 0.346309i | \(-0.112565\pi\) |
−0.768973 | + | 0.639281i | \(0.779232\pi\) | |||||||
\(354\) | −1.56793 | + | 1.36582i | −0.0833344 | + | 0.0725926i | ||||
\(355\) | 14.8419 | + | 8.56899i | 0.787728 | + | 0.454795i | ||||
\(356\) | 9.63224 | 0.510508 | ||||||||
\(357\) | −13.3099 | + | 7.73598i | −0.704434 | + | 0.409431i | ||||
\(358\) | 22.3850 | 1.18308 | ||||||||
\(359\) | 21.2047 | + | 12.2425i | 1.11914 | + | 0.646136i | 0.941181 | − | 0.337902i | \(-0.109717\pi\) |
0.177959 | + | 0.984038i | \(0.443051\pi\) | |||||||
\(360\) | 3.28066 | − | 4.21695i | 0.172906 | − | 0.222253i | ||||
\(361\) | −8.14094 | − | 14.1005i | −0.428471 | − | 0.742133i | ||||
\(362\) | 1.31357 | − | 2.27516i | 0.0690395 | − | 0.119580i | ||||
\(363\) | 17.0051 | − | 3.32367i | 0.892539 | − | 0.174448i | ||||
\(364\) | 16.2736 | + | 3.13177i | 0.852970 | + | 0.164149i | ||||
\(365\) | − | 19.6937i | − | 1.03082i | ||||||
\(366\) | −0.661693 | + | 1.92816i | −0.0345873 | + | 0.100786i | ||||
\(367\) | −25.7670 | + | 14.8766i | −1.34503 | + | 0.776552i | −0.987540 | − | 0.157365i | \(-0.949700\pi\) |
−0.357488 | + | 0.933918i | \(0.616367\pi\) | |||||||
\(368\) | −0.866025 | + | 0.500000i | −0.0451447 | + | 0.0260643i | ||||
\(369\) | 1.78683 | − | 12.9071i | 0.0930184 | − | 0.671917i | ||||
\(370\) | 0.838804i | 0.0436073i | ||||||||
\(371\) | 15.7230 | + | 3.02580i | 0.816297 | + | 0.157092i | ||||
\(372\) | 2.68163 | + | 13.7202i | 0.139036 | + | 0.711361i | ||||
\(373\) | −4.84352 | + | 8.38922i | −0.250788 | + | 0.434377i | −0.963743 | − | 0.266832i | \(-0.914023\pi\) |
0.712955 | + | 0.701210i | \(0.247356\pi\) | |||||||
\(374\) | 1.67660 | + | 2.90396i | 0.0866949 | + | 0.150160i | ||||
\(375\) | −13.8349 | − | 15.8822i | −0.714433 | − | 0.820151i | ||||
\(376\) | −7.32426 | − | 4.22866i | −0.377720 | − | 0.218077i | ||||
\(377\) | −7.82578 | −0.403048 | ||||||||
\(378\) | 10.8752 | + | 8.41010i | 0.559361 | + | 0.432569i | ||||
\(379\) | −20.7752 | −1.06715 | −0.533576 | − | 0.845752i | \(-0.679152\pi\) | ||||
−0.533576 | + | 0.845752i | \(0.679152\pi\) | |||||||
\(380\) | −2.54280 | − | 1.46808i | −0.130443 | − | 0.0753112i | ||||
\(381\) | 1.89628 | + | 2.17688i | 0.0971491 | + | 0.111525i | ||||
\(382\) | 2.35337 | + | 4.07616i | 0.120409 | + | 0.208555i | ||||
\(383\) | 4.36899 | − | 7.56732i | 0.223245 | − | 0.386672i | −0.732546 | − | 0.680717i | \(-0.761668\pi\) |
0.955791 | + | 0.294045i | \(0.0950016\pi\) | |||||||
\(384\) | −0.332245 | − | 1.69989i | −0.0169548 | − | 0.0867470i | ||||
\(385\) | 3.07894 | − | 3.55529i | 0.156917 | − | 0.181194i | ||||
\(386\) | − | 1.06533i | − | 0.0542240i | ||||||
\(387\) | −1.97081 | + | 14.2361i | −0.100182 | + | 0.723663i | ||||
\(388\) | −10.1025 | + | 5.83269i | −0.512878 | + | 0.296110i | ||||
\(389\) | −20.6982 | + | 11.9501i | −1.04944 | + | 0.605895i | −0.922493 | − | 0.386015i | \(-0.873851\pi\) |
−0.126948 | + | 0.991909i | \(0.540518\pi\) | |||||||
\(390\) | −6.27160 | + | 18.2753i | −0.317575 | + | 0.925404i | ||||
\(391\) | 3.35941i | 0.169893i | ||||||||
\(392\) | 6.92819 | − | 1.00008i | 0.349927 | − | 0.0505116i | ||||
\(393\) | −3.27720 | + | 0.640533i | −0.165313 | + | 0.0323106i | ||||
\(394\) | 8.48905 | − | 14.7035i | 0.427672 | − | 0.740750i | ||||
\(395\) | −1.02695 | − | 1.77873i | −0.0516714 | − | 0.0894974i | ||||
\(396\) | 1.83870 | − | 2.36346i | 0.0923980 | − | 0.118768i | ||||
\(397\) | 26.7399 | + | 15.4383i | 1.34204 | + | 0.774825i | 0.987106 | − | 0.160067i | \(-0.0511711\pi\) |
0.354931 | + | 0.934893i | \(0.384504\pi\) | |||||||
\(398\) | −2.14372 | −0.107455 | ||||||||
\(399\) | 3.75861 | − | 6.55388i | 0.188166 | − | 0.328105i | ||||
\(400\) | −1.82829 | −0.0914144 | ||||||||
\(401\) | 28.6452 | + | 16.5383i | 1.43047 | + | 0.825883i | 0.997156 | − | 0.0753598i | \(-0.0240105\pi\) |
0.433315 | + | 0.901243i | \(0.357344\pi\) | |||||||
\(402\) | −12.5810 | + | 10.9593i | −0.627485 | + | 0.546602i | ||||
\(403\) | −25.2781 | − | 43.7829i | −1.25919 | − | 2.18098i | ||||
\(404\) | 8.67140 | − | 15.0193i | 0.431418 | − | 0.747238i | ||||
\(405\) | −11.4838 | + | 11.1817i | −0.570635 | + | 0.555624i | ||||
\(406\) | −3.12345 | + | 1.08201i | −0.155014 | + | 0.0536995i | ||||
\(407\) | 0.470121i | 0.0233031i | ||||||||
\(408\) | −5.50361 | − | 1.88870i | −0.272469 | − | 0.0935044i | ||||
\(409\) | 30.8832 | − | 17.8304i | 1.52707 | − | 0.881657i | 0.527591 | − | 0.849498i | \(-0.323095\pi\) |
0.999483 | − | 0.0321581i | \(-0.0102380\pi\) | |||||||
\(410\) | 6.69895 | − | 3.86764i | 0.330838 | − | 0.191009i | ||||
\(411\) | 14.2696 | + | 4.89695i | 0.703866 | + | 0.241549i | ||||
\(412\) | 8.17628i | 0.402816i | ||||||||
\(413\) | 0.600251 | − | 3.11909i | 0.0295364 | − | 0.153480i | ||||
\(414\) | 2.77923 | − | 1.12956i | 0.136592 | − | 0.0555147i | ||||
\(415\) | −6.71266 | + | 11.6267i | −0.329512 | + | 0.570731i | ||||
\(416\) | 3.13186 | + | 5.42454i | 0.153552 | + | 0.265960i | ||||
\(417\) | 1.22969 | − | 1.07118i | 0.0602180 | − | 0.0524559i | ||||
\(418\) | −1.42515 | − | 0.822812i | −0.0697065 | − | 0.0402451i | ||||
\(419\) | −22.3712 | −1.09291 | −0.546454 | − | 0.837489i | \(-0.684022\pi\) | ||||
−0.546454 | + | 0.837489i | \(0.684022\pi\) | |||||||
\(420\) | 0.0236502 | + | 8.16121i | 0.00115401 | + | 0.398226i | ||||
\(421\) | −7.17807 | −0.349838 | −0.174919 | − | 0.984583i | \(-0.555966\pi\) | ||||
−0.174919 | + | 0.984583i | \(0.555966\pi\) | |||||||
\(422\) | 22.3262 | + | 12.8900i | 1.08682 | + | 0.627476i | ||||
\(423\) | 20.0256 | + | 15.5793i | 0.973677 | + | 0.757490i | ||||
\(424\) | 3.02589 | + | 5.24099i | 0.146950 | + | 0.254525i | ||||
\(425\) | −3.07099 | + | 5.31910i | −0.148965 | + | 0.258014i | ||||
\(426\) | −16.3581 | + | 3.19721i | −0.792553 | + | 0.154905i | ||||
\(427\) | −1.01928 | − | 2.94237i | −0.0493266 | − | 0.142391i | ||||
\(428\) | 19.7311i | 0.953740i | ||||||||
\(429\) | −3.51502 | + | 10.2427i | −0.169707 | + | 0.494521i | ||||
\(430\) | −7.38874 | + | 4.26589i | −0.356317 | + | 0.205720i | ||||
\(431\) | 12.9486 | − | 7.47587i | 0.623712 | − | 0.360100i | −0.154601 | − | 0.987977i | \(-0.549409\pi\) |
0.778313 | + | 0.627877i | \(0.216076\pi\) | |||||||
\(432\) | 0.288003 | + | 5.18816i | 0.0138566 | + | 0.249616i | ||||
\(433\) | 15.7882i | 0.758735i | 0.925246 | + | 0.379367i | \(0.123858\pi\) | ||||
−0.925246 | + | 0.379367i | \(0.876142\pi\) | |||||||
\(434\) | −16.1426 | − | 13.9798i | −0.774870 | − | 0.671050i | ||||
\(435\) | −0.739265 | − | 3.78235i | −0.0354450 | − | 0.181350i | ||||
\(436\) | −7.96954 | + | 13.8036i | −0.381672 | + | 0.661075i | ||||
\(437\) | −0.824336 | − | 1.42779i | −0.0394333 | − | 0.0683005i | ||||
\(438\) | 12.5806 | + | 14.4422i | 0.601122 | + | 0.690073i | ||||
\(439\) | −35.6172 | − | 20.5636i | −1.69992 | − | 0.981448i | −0.945824 | − | 0.324681i | \(-0.894743\pi\) |
−0.754094 | − | 0.656767i | \(-0.771924\pi\) | |||||||
\(440\) | 1.77764 | 0.0847455 | ||||||||
\(441\) | −20.9996 | + | 0.121710i | −0.999983 | + | 0.00579571i | ||||
\(442\) | 21.0424 | 1.00088 | ||||||||
\(443\) | −12.6002 | − | 7.27471i | −0.598652 | − | 0.345632i | 0.169859 | − | 0.985468i | \(-0.445669\pi\) |
−0.768511 | + | 0.639837i | \(0.779002\pi\) | |||||||
\(444\) | −0.535836 | − | 0.615126i | −0.0254297 | − | 0.0291926i | ||||
\(445\) | −8.57717 | − | 14.8561i | −0.406597 | − | 0.704247i | ||||
\(446\) | 5.03319 | − | 8.71774i | 0.238328 | − | 0.412797i | ||||
\(447\) | −0.289006 | − | 1.47866i | −0.0136695 | − | 0.0699384i | ||||
\(448\) | 2.00001 | + | 1.73204i | 0.0944916 | + | 0.0818312i | ||||
\(449\) | 5.90954i | 0.278889i | 0.990230 | + | 0.139444i | \(0.0445316\pi\) | ||||
−0.990230 | + | 0.139444i | \(0.955468\pi\) | |||||||
\(450\) | 5.43305 | + | 0.752138i | 0.256117 | + | 0.0354561i | ||||
\(451\) | 3.75454 | − | 2.16768i | 0.176794 | − | 0.102072i | ||||
\(452\) | 5.51239 | − | 3.18258i | 0.259281 | − | 0.149696i | ||||
\(453\) | 4.01515 | − | 11.7001i | 0.188648 | − | 0.549716i | ||||
\(454\) | − | 26.2942i | − | 1.23405i | ||||||
\(455\) | −9.66088 | − | 27.8881i | −0.452909 | − | 1.30741i | ||||
\(456\) | 2.80256 | − | 0.547762i | 0.131242 | − | 0.0256513i | ||||
\(457\) | 3.47842 | − | 6.02479i | 0.162713 | − | 0.281828i | −0.773127 | − | 0.634251i | \(-0.781309\pi\) |
0.935841 | + | 0.352423i | \(0.114642\pi\) | |||||||
\(458\) | 9.82677 | + | 17.0205i | 0.459175 | + | 0.795314i | ||||
\(459\) | 15.5779 | + | 7.87669i | 0.727112 | + | 0.367652i | ||||
\(460\) | 1.54233 | + | 0.890465i | 0.0719115 | + | 0.0415181i | ||||
\(461\) | 18.8889 | 0.879742 | 0.439871 | − | 0.898061i | \(-0.355024\pi\) | ||||
0.439871 | + | 0.898061i | \(0.355024\pi\) | |||||||
\(462\) | 0.0132551 | + | 4.57408i | 0.000616685 | + | 0.212806i | ||||
\(463\) | 17.2700 | 0.802607 | 0.401304 | − | 0.915945i | \(-0.368557\pi\) | ||||
0.401304 | + | 0.915945i | \(0.368557\pi\) | |||||||
\(464\) | −1.08200 | − | 0.624691i | −0.0502304 | − | 0.0290006i | ||||
\(465\) | 18.7732 | − | 16.3534i | 0.870588 | − | 0.758369i | ||||
\(466\) | −1.60706 | − | 2.78352i | −0.0744458 | − | 0.128944i | ||||
\(467\) | −9.47185 | + | 16.4057i | −0.438305 | + | 0.759166i | −0.997559 | − | 0.0698300i | \(-0.977754\pi\) |
0.559254 | + | 0.828996i | \(0.311088\pi\) | |||||||
\(468\) | −7.07522 | − | 17.4083i | −0.327052 | − | 0.804699i | ||||
\(469\) | 4.81640 | − | 25.0275i | 0.222401 | − | 1.15566i | ||||
\(470\) | 15.0619i | 0.694754i | ||||||||
\(471\) | 22.4871 | + | 7.71699i | 1.03615 | + | 0.355580i | ||||
\(472\) | 1.03970 | − | 0.600268i | 0.0478558 | − | 0.0276296i | ||||
\(473\) | −4.14114 | + | 2.39089i | −0.190410 | + | 0.109933i | ||||
\(474\) | 1.88937 | + | 0.648382i | 0.0867815 | + | 0.0297812i | ||||
\(475\) | − | 3.01425i | − | 0.138303i | ||||||
\(476\) | 8.39851 | − | 2.90938i | 0.384945 | − | 0.133351i | ||||
\(477\) | −6.83582 | − | 16.8193i | −0.312991 | − | 0.770101i | ||||
\(478\) | −4.21089 | + | 7.29347i | −0.192601 | + | 0.333595i | ||||
\(479\) | −0.290036 | − | 0.502357i | −0.0132521 | − | 0.0229533i | 0.859323 | − | 0.511433i | \(-0.170885\pi\) |
−0.872575 | + | 0.488479i | \(0.837552\pi\) | |||||||
\(480\) | −2.32593 | + | 2.02612i | −0.106164 | + | 0.0924793i | ||||
\(481\) | 2.55492 | + | 1.47508i | 0.116494 | + | 0.0672579i | ||||
\(482\) | −8.84821 | −0.403025 | ||||||||
\(483\) | −2.27978 | + | 3.97525i | −0.103733 | + | 0.180880i | ||||
\(484\) | −10.0037 | −0.454713 | ||||||||
\(485\) | 17.9919 | + | 10.3876i | 0.816969 | + | 0.471677i | ||||
\(486\) | 1.27851 | − | 15.5359i | 0.0579942 | − | 0.704725i | ||||
\(487\) | −7.33055 | − | 12.6969i | −0.332179 | − | 0.575351i | 0.650760 | − | 0.759284i | \(-0.274450\pi\) |
−0.982939 | + | 0.183933i | \(0.941117\pi\) | |||||||
\(488\) | 0.588474 | − | 1.01927i | 0.0266390 | − | 0.0461401i | ||||
\(489\) | −15.8977 | + | 3.10722i | −0.718917 | + | 0.140513i | ||||
\(490\) | −7.71176 | − | 9.79503i | −0.348382 | − | 0.442494i | ||||
\(491\) | 21.9498i | 0.990579i | 0.868728 | + | 0.495290i | \(0.164938\pi\) | ||||
−0.868728 | + | 0.495290i | \(0.835062\pi\) | |||||||
\(492\) | −2.44191 | + | 7.11564i | −0.110090 | + | 0.320798i | ||||
\(493\) | −3.63487 | + | 2.09859i | −0.163706 | + | 0.0945159i | ||||
\(494\) | −8.94329 | + | 5.16341i | −0.402378 | + | 0.232313i | ||||
\(495\) | −5.28253 | − | 0.731301i | −0.237432 | − | 0.0328695i | ||||
\(496\) | − | 8.07127i | − | 0.362411i | ||||||
\(497\) | 16.6675 | − | 19.2462i | 0.747640 | − | 0.863310i | ||||
\(498\) | −2.50459 | − | 12.8144i | −0.112233 | − | 0.574227i | ||||
\(499\) | −16.6874 | + | 28.9034i | −0.747029 | + | 1.29389i | 0.202212 | + | 0.979342i | \(0.435187\pi\) |
−0.949241 | + | 0.314550i | \(0.898146\pi\) | |||||||
\(500\) | 6.08035 | + | 10.5315i | 0.271922 | + | 0.470982i | ||||
\(501\) | 28.2369 | + | 32.4152i | 1.26153 | + | 1.44821i | ||||
\(502\) | 24.2685 | + | 14.0114i | 1.08316 | + | 0.625360i | ||||
\(503\) | 13.0707 | 0.582793 | 0.291396 | − | 0.956602i | \(-0.405880\pi\) | ||||
0.291396 | + | 0.956602i | \(0.405880\pi\) | |||||||
\(504\) | −5.23081 | − | 5.96981i | −0.232999 | − | 0.265917i | ||||
\(505\) | −30.8863 | −1.37442 | ||||||||
\(506\) | 0.864424 | + | 0.499076i | 0.0384284 | + | 0.0221866i | ||||
\(507\) | 29.8460 | + | 34.2624i | 1.32551 | + | 1.52165i | ||||
\(508\) | −0.833399 | − | 1.44349i | −0.0369761 | − | 0.0640445i | ||||
\(509\) | 7.51025 | − | 13.0081i | 0.332886 | − | 0.576575i | −0.650190 | − | 0.759771i | \(-0.725311\pi\) |
0.983076 | + | 0.183196i | \(0.0586442\pi\) | |||||||
\(510\) | 1.98778 | + | 10.1702i | 0.0880203 | + | 0.450344i | ||||
\(511\) | −28.7299 | − | 5.52890i | −1.27093 | − | 0.244584i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −8.55358 | + | 0.474823i | −0.377650 | + | 0.0209640i | ||||
\(514\) | −10.8434 | + | 6.26044i | −0.478282 | + | 0.276136i | ||||
\(515\) | 12.6105 | − | 7.28069i | 0.555686 | − | 0.320825i | ||||
\(516\) | 2.69335 | − | 7.84834i | 0.118568 | − | 0.345504i | ||||
\(517\) | 8.44169i | 0.371265i | ||||||||
\(518\) | 1.22367 | + | 0.235489i | 0.0537652 | + | 0.0103468i | ||||
\(519\) | 5.60241 | − | 1.09500i | 0.245919 | − | 0.0480651i | ||||
\(520\) | 5.57762 | − | 9.66073i | 0.244595 | − | 0.423651i | ||||
\(521\) | −1.62224 | − | 2.80981i | −0.0710718 | − | 0.123100i | 0.828300 | − | 0.560286i | \(-0.189309\pi\) |
−0.899371 | + | 0.437186i | \(0.855975\pi\) | |||||||
\(522\) | 2.95833 | + | 2.30149i | 0.129483 | + | 0.100734i | ||||
\(523\) | 15.4763 | + | 8.93522i | 0.676730 | + | 0.390710i | 0.798622 | − | 0.601833i | \(-0.205563\pi\) |
−0.121892 | + | 0.992543i | \(0.538896\pi\) | |||||||
\(524\) | 1.92790 | 0.0842205 | ||||||||
\(525\) | −7.24363 | + | 4.21014i | −0.316138 | + | 0.183746i | ||||
\(526\) | 8.50177 | 0.370695 | ||||||||
\(527\) | −23.4820 | − | 13.5573i | −1.02289 | − | 0.590567i | ||||
\(528\) | −1.30361 | + | 1.13557i | −0.0567323 | + | 0.0494194i | ||||
\(529\) | 0.500000 | + | 0.866025i | 0.0217391 | + | 0.0376533i | ||||
\(530\) | 5.38889 | − | 9.33384i | 0.234079 | − | 0.405436i | ||||
\(531\) | −3.33656 | + | 1.35607i | −0.144795 | + | 0.0588486i | ||||
\(532\) | −2.85557 | + | 3.29736i | −0.123804 | + | 0.142959i | ||||
\(533\) | − | 27.2058i | − | 1.17841i | ||||||
\(534\) | 15.7802 | + | 5.41535i | 0.682875 | + | 0.234345i | ||||
\(535\) | 30.4319 | − | 17.5699i | 1.31569 | − | 0.759612i | ||||
\(536\) | 8.34250 | − | 4.81654i | 0.360341 | − | 0.208043i | ||||
\(537\) | 36.6726 | + | 12.5851i | 1.58254 | + | 0.543086i | ||||
\(538\) | − | 10.6670i | − | 0.459885i | ||||||
\(539\) | −4.32218 | − | 5.48978i | −0.186170 | − | 0.236462i | ||||
\(540\) | 7.74541 | − | 5.06408i | 0.333309 | − | 0.217923i | ||||
\(541\) | −14.0263 | + | 24.2942i | −0.603037 | + | 1.04449i | 0.389321 | + | 0.921102i | \(0.372710\pi\) |
−0.992358 | + | 0.123389i | \(0.960624\pi\) | |||||||
\(542\) | −5.87807 | − | 10.1811i | −0.252485 | − | 0.437316i | ||||
\(543\) | 3.43109 | − | 2.98882i | 0.147242 | − | 0.128263i | ||||
\(544\) | 2.90933 | + | 1.67970i | 0.124737 | + | 0.0720167i | ||||
\(545\) | 28.3864 | 1.21594 | ||||||||
\(546\) | 24.8999 | + | 14.2799i | 1.06562 | + | 0.611123i | ||||
\(547\) | 1.55799 | 0.0666150 | 0.0333075 | − | 0.999445i | \(-0.489396\pi\) | ||||
0.0333075 | + | 0.999445i | \(0.489396\pi\) | |||||||
\(548\) | −7.54322 | − | 4.35508i | −0.322230 | − | 0.186040i | ||||
\(549\) | −2.16806 | + | 2.78682i | −0.0925306 | + | 0.118939i | ||||
\(550\) | 0.912454 | + | 1.58042i | 0.0389072 | + | 0.0673892i | ||||
\(551\) | 1.02991 | − | 1.78386i | 0.0438757 | − | 0.0759949i | ||||
\(552\) | −1.69989 | + | 0.332245i | −0.0723520 | + | 0.0141413i | ||||
\(553\) | −2.88317 | + | 0.998779i | −0.122605 | + | 0.0424724i | ||||
\(554\) | − | 17.7939i | − | 0.755989i | ||||||
\(555\) | −0.471585 | + | 1.37418i | −0.0200177 | + | 0.0583309i | ||||
\(556\) | −0.815407 | + | 0.470775i | −0.0345809 | + | 0.0199653i | ||||
\(557\) | 2.17616 | − | 1.25641i | 0.0922068 | − | 0.0532356i | −0.453188 | − | 0.891415i | \(-0.649713\pi\) |
0.545394 | + | 0.838180i | \(0.316380\pi\) | |||||||
\(558\) | −3.32043 | + | 23.9851i | −0.140565 | + | 1.01537i | ||||
\(559\) | 30.0072i | 1.26917i | ||||||||
\(560\) | 0.890439 | − | 4.62700i | 0.0376279 | − | 0.195526i | ||||
\(561\) | 1.11408 | + | 5.70006i | 0.0470366 | + | 0.240657i | ||||
\(562\) | −0.778484 | + | 1.34837i | −0.0328384 | + | 0.0568778i | ||||
\(563\) | 8.48717 | + | 14.7002i | 0.357691 | + | 0.619540i | 0.987575 | − | 0.157150i | \(-0.0502306\pi\) |
−0.629883 | + | 0.776690i | \(0.716897\pi\) | |||||||
\(564\) | −9.62169 | − | 11.0455i | −0.405146 | − | 0.465098i | ||||
\(565\) | −9.81719 | − | 5.66795i | −0.413012 | − | 0.238453i | ||||
\(566\) | −28.4915 | −1.19759 | ||||||||
\(567\) | 13.0883 | + | 19.8921i | 0.549655 | + | 0.835392i | ||||
\(568\) | 9.62306 | 0.403774 | ||||||||
\(569\) | −11.0775 | − | 6.39562i | −0.464395 | − | 0.268118i | 0.249496 | − | 0.968376i | \(-0.419735\pi\) |
−0.713890 | + | 0.700258i | \(0.753068\pi\) | |||||||
\(570\) | −3.34041 | − | 3.83470i | −0.139914 | − | 0.160618i | ||||
\(571\) | 18.6681 | + | 32.3341i | 0.781236 | + | 1.35314i | 0.931222 | + | 0.364452i | \(0.118744\pi\) |
−0.149986 | + | 0.988688i | \(0.547923\pi\) | |||||||
\(572\) | 3.12607 | − | 5.41451i | 0.130708 | − | 0.226392i | ||||
\(573\) | 1.56379 | + | 8.00093i | 0.0653283 | + | 0.334244i | ||||
\(574\) | −3.76155 | − | 10.8585i | −0.157004 | − | 0.453224i | ||||
\(575\) | 1.82829i | 0.0762449i | ||||||||
\(576\) | 0.411389 | − | 2.97166i | 0.0171412 | − | 0.123819i | ||||
\(577\) | 1.30824 | − | 0.755315i | 0.0544629 | − | 0.0314442i | −0.472521 | − | 0.881319i | \(-0.656656\pi\) |
0.526984 | + | 0.849875i | \(0.323323\pi\) | |||||||
\(578\) | −4.94879 | + | 2.85719i | −0.205843 | + | 0.118843i | ||||
\(579\) | 0.598941 | − | 1.74530i | 0.0248912 | − | 0.0725322i | ||||
\(580\) | 2.22506i | 0.0923907i | ||||||||
\(581\) | 15.0768 | + | 13.0568i | 0.625493 | + | 0.541686i | ||||
\(582\) | −19.8298 | + | 3.87576i | −0.821973 | + | 0.160655i | ||||
\(583\) | 3.02029 | − | 5.23130i | 0.125088 | − | 0.216658i | ||||
\(584\) | −5.52906 | − | 9.57661i | −0.228794 | − | 0.396283i | ||||
\(585\) | −20.5491 | + | 26.4138i | −0.849601 | + | 1.09208i | ||||
\(586\) | −12.0141 | − | 6.93637i | −0.496299 | − | 0.286539i | ||||
\(587\) | 19.3744 | 0.799666 | 0.399833 | − | 0.916588i | \(-0.369068\pi\) | ||||
0.399833 | + | 0.916588i | \(0.369068\pi\) | |||||||
\(588\) | 11.9125 | + | 2.25671i | 0.491263 | + | 0.0930651i | ||||
\(589\) | 13.3069 | 0.548300 | ||||||||
\(590\) | −1.85162 | − | 1.06904i | −0.0762302 | − | 0.0440115i | ||||
\(591\) | 22.1738 | − | 19.3156i | 0.912108 | − | 0.794537i | ||||
\(592\) | 0.235496 | + | 0.407891i | 0.00967883 | + | 0.0167642i | ||||
\(593\) | 13.3874 | − | 23.1877i | 0.549756 | − | 0.952204i | −0.448535 | − | 0.893765i | \(-0.648054\pi\) |
0.998291 | − | 0.0584394i | \(-0.0186125\pi\) | |||||||
\(594\) | 4.34104 | − | 2.83824i | 0.178115 | − | 0.116455i | ||||
\(595\) | −11.9658 | − | 10.3626i | −0.490550 | − | 0.424824i | ||||
\(596\) | 0.869860i | 0.0356309i | ||||||||
\(597\) | −3.51199 | − | 1.20523i | −0.143736 | − | 0.0493266i | ||||
\(598\) | 5.42454 | − | 3.13186i | 0.221826 | − | 0.128071i | ||||
\(599\) | 17.3871 | − | 10.0384i | 0.710417 | − | 0.410159i | −0.100799 | − | 0.994907i | \(-0.532140\pi\) |
0.811215 | + | 0.584748i | \(0.198806\pi\) | |||||||
\(600\) | −2.99523 | − | 1.02788i | −0.122280 | − | 0.0419632i | ||||
\(601\) | 1.39900i | 0.0570663i | 0.999593 | + | 0.0285331i | \(0.00908361\pi\) | ||||
−0.999593 | + | 0.0285331i | \(0.990916\pi\) | |||||||
\(602\) | 4.14888 | + | 11.9766i | 0.169096 | + | 0.488128i | ||||
\(603\) | −26.7725 | + | 10.8811i | −1.09026 | + | 0.443113i | ||||
\(604\) | −3.57086 | + | 6.18491i | −0.145296 | + | 0.251661i | ||||
\(605\) | 8.90794 | + | 15.4290i | 0.362159 | + | 0.627278i | ||||
\(606\) | 22.6501 | − | 19.7305i | 0.920096 | − | 0.801495i | ||||
\(607\) | −21.5959 | − | 12.4684i | −0.876553 | − | 0.506078i | −0.00703239 | − | 0.999975i | \(-0.502238\pi\) |
−0.869520 | + | 0.493897i | \(0.835572\pi\) | |||||||
\(608\) | −1.64867 | −0.0668625 | ||||||||
\(609\) | −5.72537 | + | 0.0165914i | −0.232004 | + | 0.000672318i | ||||
\(610\) | −2.09606 | −0.0848671 | ||||||||
\(611\) | 45.8771 | + | 26.4872i | 1.85599 | + | 1.07156i | ||||
\(612\) | −7.95454 | − | 6.18838i | −0.321543 | − | 0.250150i | ||||
\(613\) | −21.9558 | − | 38.0285i | −0.886785 | − | 1.53596i | −0.843654 | − | 0.536887i | \(-0.819600\pi\) |
−0.0431305 | − | 0.999069i | \(-0.513733\pi\) | |||||||
\(614\) | −13.0364 | + | 22.5797i | −0.526105 | + | 0.911241i | ||||
\(615\) | 13.1491 | − | 2.57001i | 0.530223 | − | 0.103633i | ||||
\(616\) | 0.499061 | − | 2.59328i | 0.0201077 | − | 0.104486i | ||||
\(617\) | 39.3657i | 1.58480i | 0.609999 | + | 0.792402i | \(0.291170\pi\) | ||||
−0.609999 | + | 0.792402i | \(0.708830\pi\) | |||||||
\(618\) | −4.59679 | + | 13.3949i | −0.184910 | + | 0.538823i | ||||
\(619\) | −3.83941 | + | 2.21668i | −0.154319 | + | 0.0890960i | −0.575171 | − | 0.818033i | \(-0.695064\pi\) |
0.420852 | + | 0.907129i | \(0.361731\pi\) | |||||||
\(620\) | −12.4486 | + | 7.18718i | −0.499946 | + | 0.288644i | ||||
\(621\) | 5.18816 | − | 0.288003i | 0.208194 | − | 0.0115572i | ||||
\(622\) | 9.78023i | 0.392152i | ||||||||
\(623\) | −24.0806 | + | 8.34190i | −0.964767 | + | 0.334211i | ||||
\(624\) | 2.08109 | + | 10.6476i | 0.0833102 | + | 0.426246i | ||||
\(625\) | 6.25796 | − | 10.8391i | 0.250318 | − | 0.433564i | ||||
\(626\) | 8.60715 | + | 14.9080i | 0.344011 | + | 0.595844i | ||||
\(627\) | −1.87219 | − | 2.14922i | −0.0747679 | − | 0.0858317i | ||||
\(628\) | −11.8872 | − | 6.86308i | −0.474351 | − | 0.273867i | ||||
\(629\) | 1.58226 | 0.0630886 | ||||||||
\(630\) | −4.54958 | + | 13.3835i | −0.181259 | + | 0.533213i | ||||
\(631\) | 26.8091 | 1.06725 | 0.533626 | − | 0.845721i | \(-0.320829\pi\) | ||||
0.533626 | + | 0.845721i | \(0.320829\pi\) | |||||||
\(632\) | −0.998763 | − | 0.576636i | −0.0397286 | − | 0.0229373i | ||||
\(633\) | 29.3293 | + | 33.6693i | 1.16573 | + | 1.33823i | ||||
\(634\) | −4.13723 | − | 7.16590i | −0.164310 | − | 0.284594i | ||||
\(635\) | −1.48423 | + | 2.57075i | −0.0588997 | + | 0.102017i | ||||
\(636\) | 2.01067 | + | 10.2873i | 0.0797283 | + | 0.407919i | ||||
\(637\) | −43.3963 | + | 6.26421i | −1.71942 | + | 0.248197i | ||||
\(638\) | 1.24707i | 0.0493721i | ||||||||
\(639\) | −28.5964 | − | 3.95882i | −1.13126 | − | 0.156608i | ||||
\(640\) | 1.54233 | − | 0.890465i | 0.0609660 | − | 0.0351987i | ||||
\(641\) | −13.7645 | + | 7.94693i | −0.543664 | + | 0.313885i | −0.746563 | − | 0.665315i | \(-0.768297\pi\) |
0.202898 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(642\) | −11.0931 | + | 32.3249i | −0.437808 | + | 1.27576i | ||||
\(643\) | − | 35.5512i | − | 1.40200i | −0.713161 | − | 0.701001i | \(-0.752737\pi\) | ||
0.713161 | − | 0.701001i | \(-0.247263\pi\) | |||||||
\(644\) | 1.73204 | − | 2.00001i | 0.0682519 | − | 0.0788114i | ||||
\(645\) | −14.5031 | + | 2.83464i | −0.571058 | + | 0.111614i | ||||
\(646\) | −2.76928 | + | 4.79654i | −0.108956 | + | 0.188717i | ||||
\(647\) | −0.832081 | − | 1.44121i | −0.0327125 | − | 0.0566596i | 0.849206 | − | 0.528062i | \(-0.177081\pi\) |
−0.881918 | + | 0.471403i | \(0.843748\pi\) | |||||||
\(648\) | −2.44502 | + | 8.66152i | −0.0960493 | + | 0.340257i | ||||
\(649\) | −1.03777 | − | 0.599159i | −0.0407362 | − | 0.0235190i | ||||
\(650\) | 11.4519 | 0.449180 | ||||||||
\(651\) | −18.5863 | − | 31.9781i | −0.728456 | − | 1.25332i | ||||
\(652\) | 9.35219 | 0.366260 | ||||||||
\(653\) | −29.9085 | − | 17.2677i | −1.17041 | − | 0.675737i | −0.216634 | − | 0.976253i | \(-0.569508\pi\) |
−0.953777 | + | 0.300516i | \(0.902841\pi\) | |||||||
\(654\) | −20.8168 | + | 18.1335i | −0.814001 | + | 0.709076i | ||||
\(655\) | −1.71672 | − | 2.97345i | −0.0670780 | − | 0.116182i | ||||
\(656\) | 2.17170 | − | 3.76149i | 0.0847906 | − | 0.146862i | ||||
\(657\) | 12.4908 | + | 30.7330i | 0.487311 | + | 1.19901i | ||||
\(658\) | 21.9728 | + | 4.22854i | 0.856589 | + | 0.164846i | ||||
\(659\) | 9.87817i | 0.384799i | 0.981317 | + | 0.192399i | \(0.0616269\pi\) | ||||
−0.981317 | + | 0.192399i | \(0.938373\pi\) | |||||||
\(660\) | 2.91224 | + | 0.999407i | 0.113359 | + | 0.0389019i | ||||
\(661\) | −33.4283 | + | 19.2999i | −1.30021 | + | 0.750678i | −0.980440 | − | 0.196817i | \(-0.936940\pi\) |
−0.319772 | + | 0.947495i | \(0.603606\pi\) | |||||||
\(662\) | −15.0614 | + | 8.69571i | −0.585378 | + | 0.337968i | ||||
\(663\) | 34.4731 | + | 11.8303i | 1.33882 | + | 0.459449i | ||||
\(664\) | 7.53838i | 0.292546i | ||||||||
\(665\) | 7.62840 | + | 1.46804i | 0.295817 | + | 0.0569282i | ||||
\(666\) | −0.532012 | − | 1.30899i | −0.0206150 | − | 0.0507225i | ||||
\(667\) | −0.624691 | + | 1.08200i | −0.0241881 | + | 0.0418951i | ||||
\(668\) | −12.4099 | − | 21.4946i | −0.480154 | − | 0.831650i | ||||
\(669\) | 13.1469 | − | 11.4523i | 0.508289 | − | 0.442770i | ||||
\(670\) | −14.8574 | − | 8.57793i | −0.573992 | − | 0.331394i | ||||
\(671\) | −1.17477 | −0.0453516 | ||||||||
\(672\) | 2.30278 | + | 3.96197i | 0.0888316 | + | 0.152836i | ||||
\(673\) | 31.5214 | 1.21506 | 0.607531 | − | 0.794296i | \(-0.292160\pi\) | ||||
0.607531 | + | 0.794296i | \(0.292160\pi\) | |||||||
\(674\) | −20.7899 | − | 12.0031i | −0.800797 | − | 0.462341i | ||||
\(675\) | 8.47793 | + | 4.28672i | 0.326316 | + | 0.164996i | ||||
\(676\) | −13.1171 | − | 22.7195i | −0.504504 | − | 0.873826i | ||||
\(677\) | −25.3117 | + | 43.8411i | −0.972807 | + | 1.68495i | −0.285817 | + | 0.958284i | \(0.592265\pi\) |
−0.686990 | + | 0.726667i | \(0.741068\pi\) | |||||||
\(678\) | 10.8201 | − | 2.11479i | 0.415542 | − | 0.0812181i | ||||
\(679\) | 20.2049 | − | 23.3309i | 0.775393 | − | 0.895357i | ||||
\(680\) | − | 5.98287i | − | 0.229433i | ||||||
\(681\) | 14.7829 | − | 43.0770i | 0.566482 | − | 1.65071i | ||||
\(682\) | −6.97700 | + | 4.02817i | −0.267163 | + | 0.154247i | ||||
\(683\) | 31.2495 | − | 18.0419i | 1.19573 | − | 0.690355i | 0.236130 | − | 0.971722i | \(-0.424121\pi\) |
0.959600 | + | 0.281367i | \(0.0907877\pi\) | |||||||
\(684\) | 4.89929 | + | 0.678246i | 0.187329 | + | 0.0259334i | ||||
\(685\) | 15.5122i | 0.592690i | ||||||||
\(686\) | −16.4543 | + | 8.50028i | −0.628230 | + | 0.324542i | ||||
\(687\) | 6.52978 | + | 33.4088i | 0.249127 | + | 1.27462i | ||||
\(688\) | −2.39532 | + | 4.14881i | −0.0913206 | + | 0.158172i | ||||
\(689\) | −18.9533 | − | 32.8281i | −0.722064 | − | 1.25065i | ||||
\(690\) | 2.02612 | + | 2.32593i | 0.0771331 | + | 0.0885468i | ||||
\(691\) | −19.7530 | − | 11.4044i | −0.751441 | − | 0.433845i | 0.0747732 | − | 0.997201i | \(-0.476177\pi\) |
−0.826214 | + | 0.563356i | \(0.809510\pi\) | |||||||
\(692\) | −3.29576 | −0.125286 | ||||||||
\(693\) | −2.54988 | + | 7.50102i | −0.0968621 | + | 0.284940i | ||||
\(694\) | 23.9658 | 0.909730 | ||||||||
\(695\) | 1.45218 | + | 0.838418i | 0.0550844 | + | 0.0318030i | ||||
\(696\) | −1.42139 | − | 1.63172i | −0.0538777 | − | 0.0618502i | ||||
\(697\) | −7.29562 | − | 12.6364i | −0.276341 | − | 0.478637i | ||||
\(698\) | 12.8050 | − | 22.1789i | 0.484677 | − | 0.839485i | ||||
\(699\) | −1.06788 | − | 5.46365i | −0.0403908 | − | 0.206654i | ||||
\(700\) | 4.57071 | − | 1.58337i | 0.172757 | − | 0.0598458i | ||||
\(701\) | − | 9.21264i | − | 0.347956i | −0.984749 | − | 0.173978i | \(-0.944338\pi\) | ||
0.984749 | − | 0.173978i | \(-0.0556622\pi\) | |||||||
\(702\) | −1.80397 | − | 32.4972i | −0.0680866 | − | 1.22653i | ||||
\(703\) | −0.672479 | + | 0.388256i | −0.0253630 | + | 0.0146433i | ||||
\(704\) | 0.864424 | − | 0.499076i | 0.0325792 | − | 0.0188096i | ||||
\(705\) | −8.46796 | + | 24.6754i | −0.318922 | + | 0.929330i | ||||
\(706\) | − | 6.35599i | − | 0.239211i | ||||||
\(707\) | −8.67114 | + | 45.0579i | −0.326112 | + | 1.69458i | ||||
\(708\) | 2.04078 | − | 0.398872i | 0.0766970 | − | 0.0149905i | ||||
\(709\) | 4.44249 | − | 7.69463i | 0.166841 | − | 0.288978i | −0.770466 | − | 0.637481i | \(-0.779977\pi\) |
0.937308 | + | 0.348503i | \(0.113310\pi\) | |||||||
\(710\) | −8.56899 | − | 14.8419i | −0.321589 | − | 0.557008i | ||||
\(711\) | 2.73076 | + | 2.12445i | 0.102412 | + | 0.0796729i | ||||
\(712\) | −8.34177 | − | 4.81612i | −0.312621 | − | 0.180492i | ||||
\(713\) | −8.07127 | −0.302271 | ||||||||
\(714\) | 15.3947 | − | 0.0446119i | 0.576131 | − | 0.00166956i | ||||
\(715\) | −11.1346 | −0.416411 | ||||||||
\(716\) | −19.3860 | − | 11.1925i | −0.724487 | − | 0.418283i | ||||
\(717\) | −10.9990 | + | 9.58124i | −0.410766 | + | 0.357818i | ||||
\(718\) | −12.2425 | − | 21.2047i | −0.456887 | − | 0.791352i | ||||
\(719\) | 16.2393 | − | 28.1273i | 0.605624 | − | 1.04897i | −0.386329 | − | 0.922361i | \(-0.626257\pi\) |
0.991953 | − | 0.126610i | \(-0.0404096\pi\) | |||||||
\(720\) | −4.94961 | + | 2.01166i | −0.184461 | + | 0.0749702i | ||||
\(721\) | −7.08098 | − | 20.4406i | −0.263709 | − | 0.761250i | ||||
\(722\) | 16.2819i | 0.605949i | ||||||||
\(723\) | −14.4957 | − | 4.97456i | −0.539102 | − | 0.185006i | ||||
\(724\) | −2.27516 | + | 1.31357i | −0.0845558 | + | 0.0488183i | ||||
\(725\) | −1.97820 | + | 1.14212i | −0.0734686 | + | 0.0424171i | ||||
\(726\) | −16.3887 | − | 5.62419i | −0.608243 | − | 0.208733i | ||||
\(727\) | − | 45.2760i | − | 1.67919i | −0.543210 | − | 0.839597i | \(-0.682791\pi\) | ||
0.543210 | − | 0.839597i | \(-0.317209\pi\) | |||||||
\(728\) | −12.5275 | − | 10.8490i | −0.464300 | − | 0.402091i | ||||
\(729\) | 10.8290 | − | 24.7332i | 0.401074 | − | 0.916045i | ||||
\(730\) | −9.84687 | + | 17.0553i | −0.364449 | + | 0.631244i | ||||
\(731\) | 8.04685 | + | 13.9376i | 0.297624 | + | 0.515499i | ||||
\(732\) | 1.53712 | − | 1.33899i | 0.0568136 | − | 0.0494903i | ||||
\(733\) | −36.8605 | − | 21.2814i | −1.36147 | − | 0.786048i | −0.371654 | − | 0.928371i | \(-0.621209\pi\) |
−0.989820 | + | 0.142324i | \(0.954543\pi\) | |||||||
\(734\) | 29.7532 | 1.09821 | ||||||||
\(735\) | −7.12706 | − | 20.3825i | −0.262885 | − | 0.751820i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −8.32708 | − | 4.80764i | −0.306732 | − | 0.177092i | ||||
\(738\) | −8.00099 | + | 10.2845i | −0.294520 | + | 0.378576i | ||||
\(739\) | 15.0275 | + | 26.0284i | 0.552795 | + | 0.957469i | 0.998071 | + | 0.0620755i | \(0.0197720\pi\) |
−0.445277 | + | 0.895393i | \(0.646895\pi\) | |||||||
\(740\) | 0.419402 | − | 0.726425i | 0.0154175 | − | 0.0267039i | ||||
\(741\) | −17.5544 | + | 3.43103i | −0.644878 | + | 0.126042i | ||||
\(742\) | −12.1036 | − | 10.4819i | −0.444338 | − | 0.384803i | ||||
\(743\) | − | 21.1026i | − | 0.774179i | −0.922042 | − | 0.387090i | \(-0.873480\pi\) | ||
0.922042 | − | 0.387090i | \(-0.126520\pi\) | |||||||
\(744\) | 4.53775 | − | 13.2229i | 0.166362 | − | 0.484775i | ||||
\(745\) | 1.34161 | − | 0.774580i | 0.0491528 | − | 0.0283784i | ||||
\(746\) | 8.38922 | − | 4.84352i | 0.307151 | − | 0.177334i | ||||
\(747\) | 3.10121 | − | 22.4015i | 0.113467 | − | 0.819628i | ||||
\(748\) | − | 3.35320i | − | 0.122605i | ||||||
\(749\) | −17.0879 | − | 49.3277i | −0.624380 | − | 1.80240i | ||||
\(750\) | 4.04033 | + | 20.6718i | 0.147532 | + | 0.754828i | ||||
\(751\) | 3.69047 | − | 6.39208i | 0.134667 | − | 0.233250i | −0.790803 | − | 0.612071i | \(-0.790337\pi\) |
0.925470 | + | 0.378820i | \(0.123670\pi\) | |||||||
\(752\) | 4.22866 | + | 7.32426i | 0.154203 | + | 0.267088i | ||||
\(753\) | 31.8809 | + | 36.5984i | 1.16180 | + | 1.33372i | ||||
\(754\) | 6.77732 | + | 3.91289i | 0.246816 | + | 0.142499i | ||||
\(755\) | 12.7189 | 0.462889 | ||||||||
\(756\) | −5.21316 | − | 12.7210i | −0.189601 | − | 0.462657i | ||||
\(757\) | 39.1757 | 1.42386 | 0.711932 | − | 0.702248i | \(-0.247820\pi\) | ||||
0.711932 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(758\) | 17.9919 | + | 10.3876i | 0.653494 | + | 0.377295i | ||||
\(759\) | 1.13557 | + | 1.30361i | 0.0412187 | + | 0.0473180i | ||||
\(760\) | 1.46808 | + | 2.54280i | 0.0532530 | + | 0.0922369i | ||||
\(761\) | 24.8222 | − | 42.9934i | 0.899805 | − | 1.55851i | 0.0720632 | − | 0.997400i | \(-0.477042\pi\) |
0.827742 | − | 0.561109i | \(-0.189625\pi\) | |||||||
\(762\) | −0.553785 | − | 2.83337i | −0.0200615 | − | 0.102642i | ||||
\(763\) | 7.96930 | − | 41.4110i | 0.288508 | − | 1.49918i | ||||
\(764\) | − | 4.70674i | − | 0.170284i | ||||||
\(765\) | −2.46129 | + | 17.7791i | −0.0889880 | + | 0.642803i | ||||
\(766\) | −7.56732 | + | 4.36899i | −0.273418 | + | 0.157858i | ||||
\(767\) | −6.51236 | + | 3.75991i | −0.235148 | + | 0.135763i | ||||
\(768\) | −0.562211 | + | 1.63827i | −0.0202870 | + | 0.0591159i | ||||
\(769\) | 26.5055i | 0.955814i | 0.878411 | + | 0.477907i | \(0.158604\pi\) | ||||
−0.878411 | + | 0.477907i | \(0.841396\pi\) | |||||||
\(770\) | −4.44408 | + | 1.53950i | −0.160154 | + | 0.0554799i | ||||
\(771\) | −21.2841 | + | 4.16000i | −0.766528 | + | 0.149819i | ||||
\(772\) | −0.532666 | + | 0.922605i | −0.0191711 | + | 0.0332053i | ||||
\(773\) | −20.2511 | − | 35.0760i | −0.728382 | − | 1.26160i | −0.957567 | − | 0.288212i | \(-0.906939\pi\) |
0.229184 | − | 0.973383i | \(-0.426394\pi\) | |||||||
\(774\) | 8.82484 | − | 11.3434i | 0.317202 | − | 0.407732i | ||||
\(775\) | −12.7796 | − | 7.37830i | −0.459057 | − | 0.265036i | ||||
\(776\) | 11.6654 | 0.418763 | ||||||||
\(777\) | 1.87231 | + | 1.07376i | 0.0671688 | + | 0.0385208i | ||||
\(778\) | 23.9002 | 0.856864 | ||||||||
\(779\) | 6.20147 | + | 3.58042i | 0.222191 | + | 0.128282i | ||||
\(780\) | 14.5690 | − | 12.6910i | 0.521654 | − | 0.454412i | ||||
\(781\) | −4.80263 | − | 8.31840i | −0.171852 | − | 0.297656i | ||||
\(782\) | 1.67970 | − | 2.90933i | 0.0600661 | − | 0.104038i | ||||
\(783\) | 3.55262 | + | 5.43366i | 0.126960 | + | 0.194183i | ||||
\(784\) | −6.50003 | − | 2.59800i | −0.232144 | − | 0.0927858i | ||||
\(785\) | 24.4453i | 0.872491i | ||||||||
\(786\) | 3.15841 | + | 1.08388i | 0.112657 | + | 0.0386609i | ||||
\(787\) | 23.1463 | − | 13.3636i | 0.825078 | − | 0.476359i | −0.0270863 | − | 0.999633i | \(-0.508623\pi\) |
0.852165 | + | 0.523274i | \(0.175290\pi\) | |||||||
\(788\) | −14.7035 | + | 8.48905i | −0.523790 | + | 0.302410i | ||||
\(789\) | 13.9282 | + | 4.77979i | 0.495856 | + | 0.170165i | ||||
\(790\) | 2.05390i | 0.0730743i | ||||||||
\(791\) | −11.0247 | + | 12.7304i | −0.391994 | + | 0.452641i | ||||
\(792\) | −2.77409 | + | 1.12747i | −0.0985730 | + | 0.0400628i | ||||
\(793\) | −3.68604 | + | 6.38441i | −0.130895 | + | 0.226717i | ||||
\(794\) | −15.4383 | − | 26.7399i | −0.547884 | − | 0.948963i | ||||
\(795\) | 14.0760 | − | 12.2616i | 0.499225 | − | 0.434875i | ||||
\(796\) | 1.85652 | + | 1.07186i | 0.0658026 | + | 0.0379912i | ||||
\(797\) | −30.0145 | −1.06317 | −0.531584 | − | 0.847006i | \(-0.678403\pi\) | ||||
−0.531584 | + | 0.847006i | \(0.678403\pi\) | |||||||
\(798\) | −6.53199 | + | 3.79653i | −0.231230 | + | 0.134396i | ||||
\(799\) | 28.4116 | 1.00513 | ||||||||
\(800\) | 1.58334 | + | 0.914144i | 0.0559797 | + | 0.0323199i | ||||
\(801\) | 22.8076 | + | 17.7436i | 0.805866 | + | 0.626939i | ||||
\(802\) | −16.5383 | − | 28.6452i | −0.583987 | − | 1.01150i | ||||
\(803\) | −5.51884 | + | 9.55891i | −0.194756 | + | 0.337327i | ||||
\(804\) | 16.3752 | − | 3.20054i | 0.577507 | − | 0.112874i | ||||
\(805\) | −4.62700 | − | 0.890439i | −0.163080 | − | 0.0313838i | ||||
\(806\) | 50.5561i | 1.78076i | ||||||||
\(807\) | 5.99708 | − | 17.4753i | 0.211107 | − | 0.615160i | ||||
\(808\) | −15.0193 | + | 8.67140i | −0.528377 | + | 0.305059i | ||||
\(809\) | 24.3548 | − | 14.0613i | 0.856271 | − | 0.494368i | −0.00649108 | − | 0.999979i | \(-0.502066\pi\) |
0.862762 | + | 0.505611i | \(0.168733\pi\) | |||||||
\(810\) | 15.5361 | − | 3.94176i | 0.545884 | − | 0.138499i | ||||
\(811\) | 32.9090i | 1.15559i | 0.816182 | + | 0.577795i | \(0.196087\pi\) | ||||
−0.816182 | + | 0.577795i | \(0.803913\pi\) | |||||||
\(812\) | 3.24599 | + | 0.624673i | 0.113912 | + | 0.0219217i | ||||
\(813\) | −3.90591 | − | 19.9841i | −0.136986 | − | 0.700873i | ||||
\(814\) | 0.235061 | − | 0.407137i | 0.00823887 | − | 0.0142701i | ||||
\(815\) | −8.32780 | − | 14.4242i | −0.291710 | − | 0.505257i | ||||
\(816\) | 3.82192 | + | 4.38746i | 0.133794 | + | 0.153592i | ||||
\(817\) | −6.84003 | − | 3.94909i | −0.239302 | − | 0.138161i | ||||
\(818\) | −35.6608 | −1.24685 | ||||||||
\(819\) | 32.7643 | + | 37.3932i | 1.14488 | + | 1.30663i | ||||
\(820\) | −7.73529 | −0.270128 | ||||||||
\(821\) | −13.1079 | − | 7.56785i | −0.457469 | − | 0.264120i | 0.253510 | − | 0.967333i | \(-0.418415\pi\) |
−0.710979 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(822\) | −9.90934 | − | 11.3757i | −0.345628 | − | 0.396772i | ||||
\(823\) | 15.9647 | + | 27.6517i | 0.556494 | + | 0.963876i | 0.997786 | + | 0.0665125i | \(0.0211872\pi\) |
−0.441291 | + | 0.897364i | \(0.645479\pi\) | |||||||
\(824\) | 4.08814 | − | 7.08086i | 0.142417 | − | 0.246674i | ||||
\(825\) | 0.606316 | + | 3.10214i | 0.0211092 | + | 0.108003i | ||||
\(826\) | −2.07938 | + | 2.40108i | −0.0723508 | + | 0.0835444i | ||||
\(827\) | − | 47.2478i | − | 1.64297i | −0.570233 | − | 0.821483i | \(-0.693147\pi\) | ||
0.570233 | − | 0.821483i | \(-0.306853\pi\) | |||||||
\(828\) | −2.97166 | − | 0.411389i | −0.103272 | − | 0.0142968i | ||||
\(829\) | −8.53322 | + | 4.92666i | −0.296371 | + | 0.171110i | −0.640811 | − | 0.767698i | \(-0.721402\pi\) |
0.344440 | + | 0.938808i | \(0.388069\pi\) | |||||||
\(830\) | 11.6267 | − | 6.71266i | 0.403568 | − | 0.233000i | ||||
\(831\) | 10.0039 | − | 29.1511i | 0.347032 | − | 1.01124i | ||||
\(832\) | − | 6.26372i | − | 0.217155i | ||||||
\(833\) | −18.4766 | + | 14.5469i | −0.640176 | + | 0.504019i | ||||
\(834\) | −1.60053 | + | 0.312825i | −0.0554218 | + | 0.0108322i | ||||
\(835\) | −22.1012 | + | 38.2803i | −0.764842 | + | 1.32475i | ||||
\(836\) | 0.822812 | + | 1.42515i | 0.0284576 | + | 0.0492899i | ||||
\(837\) | −18.9244 | + | 37.4271i | −0.654123 | + | 1.29367i | ||||
\(838\) | 19.3741 | + | 11.1856i | 0.669266 | + | 0.386401i | ||||
\(839\) | −8.06261 | −0.278352 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(840\) | 4.06012 | − | 7.07964i | 0.140088 | − | 0.244271i | ||||
\(841\) | 27.4390 | 0.946174 | ||||||||
\(842\) | 6.21639 | + | 3.58904i | 0.214231 | + | 0.123686i | ||||
\(843\) | −2.03344 | + | 1.77133i | −0.0700353 | + | 0.0610077i | ||||
\(844\) | −12.8900 | − | 22.3262i | −0.443692 | − | 0.768498i | ||||
\(845\) | −23.3606 | + | 40.4618i | −0.803630 | + | 1.39193i | ||||
\(846\) | −9.55302 | − | 23.5048i | −0.328440 | − | 0.808112i | ||||
\(847\) | 25.0092 | − | 8.66359i | 0.859326 | − | 0.297685i | ||||
\(848\) | − | 6.05178i | − | 0.207819i | ||||||
\(849\) | −46.6767 | − | 16.0182i | −1.60194 | − | 0.549744i | ||||
\(850\) | 5.31910 | − | 3.07099i | 0.182444 | − | 0.105334i | ||||
\(851\) | 0.407891 | − | 0.235496i | 0.0139823 | − | 0.00807270i | ||||
\(852\) | 15.7651 | + | 5.41019i | 0.540105 | + | 0.185350i | ||||
\(853\) | − | 28.1001i | − | 0.962128i | −0.876686 | − | 0.481064i | \(-0.840251\pi\) | ||
0.876686 | − | 0.481064i | \(-0.159749\pi\) | |||||||
\(854\) | −0.588457 | + | 3.05781i | −0.0201366 | + | 0.104636i | ||||
\(855\) | −3.31657 | − | 8.16028i | −0.113424 | − | 0.279076i | ||||
\(856\) | 9.86556 | − | 17.0877i | 0.337198 | − | 0.584044i | ||||
\(857\) | −8.71262 | − | 15.0907i | −0.297618 | − | 0.515489i | 0.677973 | − | 0.735087i | \(-0.262859\pi\) |
−0.975590 | + | 0.219598i | \(0.929525\pi\) | |||||||
\(858\) | 8.16543 | − | 7.11291i | 0.278763 | − | 0.242831i | ||||
\(859\) | −15.1009 | − | 8.71853i | −0.515237 | − | 0.297472i | 0.219747 | − | 0.975557i | \(-0.429477\pi\) |
−0.734984 | + | 0.678085i | \(0.762810\pi\) | |||||||
\(860\) | 8.53178 | 0.290931 | ||||||||
\(861\) | −0.0576790 | − | 19.9039i | −0.00196570 | − | 0.678322i | ||||
\(862\) | −14.9517 | −0.509258 | ||||||||
\(863\) | −33.8050 | − | 19.5173i | −1.15074 | − | 0.664378i | −0.201669 | − | 0.979454i | \(-0.564637\pi\) |
−0.949066 | + | 0.315076i | \(0.897970\pi\) | |||||||
\(864\) | 2.34466 | − | 4.63708i | 0.0797671 | − | 0.157757i | ||||
\(865\) | 2.93476 | + | 5.08315i | 0.0997847 | + | 0.172832i | ||||
\(866\) | 7.89412 | − | 13.6730i | 0.268253 | − | 0.464628i | ||||
\(867\) | −9.71378 | + | 1.89857i | −0.329897 | + | 0.0644788i | ||||
\(868\) | 6.99004 | + | 20.1781i | 0.237257 | + | 0.684890i | ||||
\(869\) | 1.15114i | 0.0390497i | ||||||||
\(870\) | −1.25095 | + | 3.64525i | −0.0424113 | + | 0.123585i | ||||
\(871\) | −52.2551 | + | 30.1695i | −1.77060 | + | 1.02225i | ||||
\(872\) | 13.8036 | − | 7.96954i | 0.467450 | − | 0.269883i | ||||
\(873\) | −34.6655 | − | 4.79901i | −1.17325 | − | 0.162422i | ||||
\(874\) | 1.64867i | 0.0557672i | ||||||||
\(875\) | −24.3215 | − | 21.0628i | −0.822218 | − | 0.712053i | ||||
\(876\) | −3.67400 | − | 18.7975i | −0.124133 | − | 0.635110i | ||||
\(877\) | 0.839003 | − | 1.45320i | 0.0283311 | − | 0.0490710i | −0.851512 | − | 0.524335i | \(-0.824314\pi\) |
0.879843 | + | 0.475264i | \(0.157647\pi\) | |||||||
\(878\) | 20.5636 | + | 35.6172i | 0.693988 | + | 1.20202i | ||||
\(879\) | −15.7827 | − | 18.1181i | −0.532336 | − | 0.611108i | ||||
\(880\) | −1.53948 | − | 0.888819i | −0.0518958 | − | 0.0299621i | ||||
\(881\) | 41.0614 | 1.38339 | 0.691696 | − | 0.722189i | \(-0.256864\pi\) | ||||
0.691696 | + | 0.722189i | \(0.256864\pi\) | |||||||
\(882\) | 18.2471 | + | 10.3944i | 0.614411 | + | 0.349998i | ||||
\(883\) | −51.3510 | −1.72810 | −0.864049 | − | 0.503408i | \(-0.832079\pi\) | ||||
−0.864049 | + | 0.503408i | \(0.832079\pi\) | |||||||
\(884\) | −18.2233 | − | 10.5212i | −0.612914 | − | 0.353866i | ||||
\(885\) | −2.43243 | − | 2.79237i | −0.0817653 | − | 0.0938645i | ||||
\(886\) | 7.27471 | + | 12.6002i | 0.244399 | + | 0.423311i | ||||
\(887\) | −21.8703 | + | 37.8805i | −0.734334 | + | 1.27190i | 0.220681 | + | 0.975346i | \(0.429172\pi\) |
−0.955015 | + | 0.296558i | \(0.904161\pi\) | |||||||
\(888\) | 0.156485 | + | 0.800633i | 0.00525128 | + | 0.0268675i | ||||
\(889\) | 3.33361 | + | 2.88696i | 0.111806 | + | 0.0968256i | ||||
\(890\) | 17.1543i | 0.575015i | ||||||||
\(891\) | 8.70748 | − | 2.20922i | 0.291711 | − | 0.0740117i | ||||
\(892\) | −8.71774 | + | 5.03319i | −0.291891 | + | 0.168524i | ||||
\(893\) | −12.0753 | + | 6.97168i | −0.404084 | + | 0.233298i | ||||
\(894\) | −0.489045 | + | 1.42506i | −0.0163561 | + | 0.0476612i | ||||
\(895\) | 39.8661i | 1.33258i | ||||||||
\(896\) | −0.866040 | − | 2.50000i | −0.0289324 | − | 0.0835190i | ||||
\(897\) | 10.6476 | − | 2.08109i | 0.355513 | − | 0.0694855i | ||||
\(898\) | 2.95477 | − | 5.11782i | 0.0986020 | − | 0.170784i | ||||
\(899\) | −5.04205 | − | 8.73308i | −0.168162 | − | 0.291265i | ||||
\(900\) | −4.32909 | − | 3.36790i | −0.144303 | − | 0.112263i | ||||
\(901\) | −17.6066 | − | 10.1652i | −0.586562 | − | 0.338652i | ||||
\(902\) | −4.33537 | −0.144352 | ||||||||
\(903\) | 0.0636182 | + | 21.9534i | 0.00211708 | + | 0.730562i | ||||
\(904\) | −6.36516 | −0.211702 | ||||||||
\(905\) | 4.05191 | + | 2.33937i | 0.134690 | + | 0.0777633i | ||||
\(906\) | −9.32725 | + | 8.12496i | −0.309877 | + | 0.269934i | ||||
\(907\) | 24.9311 | + | 43.1819i | 0.827824 | + | 1.43383i | 0.899742 | + | 0.436422i | \(0.143755\pi\) |
−0.0719181 | + | 0.997411i | \(0.522912\pi\) | |||||||
\(908\) | −13.1471 | + | 22.7715i | −0.436302 | + | 0.755698i | ||||
\(909\) | 48.1996 | − | 19.5897i | 1.59868 | − | 0.649748i | ||||
\(910\) | −5.57746 | + | 28.9822i | −0.184891 | + | 0.960751i | ||||
\(911\) | 35.8440i | 1.18757i | 0.804625 | + | 0.593783i | \(0.202366\pi\) | ||||
−0.804625 | + | 0.593783i | \(0.797634\pi\) | |||||||
\(912\) | −2.70097 | − | 0.926901i | −0.0894379 | − | 0.0306928i | ||||
\(913\) | 6.51636 | − | 3.76222i | 0.215660 | − | 0.124511i | ||||
\(914\) | −6.02479 | + | 3.47842i | −0.199282 | + | 0.115056i | ||||
\(915\) | −3.43391 | − | 1.17843i | −0.113522 | − | 0.0389577i | ||||
\(916\) | − | 19.6535i | − | 0.649371i | ||||||
\(917\) | −4.81973 | + | 1.66963i | −0.159162 | + | 0.0551362i | ||||
\(918\) | −9.55248 | − | 14.6103i | −0.315279 | − | 0.482213i | ||||
\(919\) | −13.3474 | + | 23.1183i | −0.440289 | + | 0.762603i | −0.997711 | − | 0.0676268i | \(-0.978457\pi\) |
0.557422 | + | 0.830229i | \(0.311791\pi\) | |||||||
\(920\) | −0.890465 | − | 1.54233i | −0.0293578 | − | 0.0508491i | ||||
\(921\) | −34.0516 | + | 29.6623i | −1.12204 | + | 0.977407i | ||||
\(922\) | −16.3582 | − | 9.44443i | −0.538729 | − | 0.311036i | ||||
\(923\) | −60.2761 | −1.98401 | ||||||||
\(924\) | 2.27556 | − | 3.96790i | 0.0748605 | − | 0.130534i | ||||
\(925\) | 0.861110 | 0.0283131 | ||||||||
\(926\) | −14.9563 | − | 8.63502i | −0.491495 | − | 0.283764i | ||||
\(927\) | −15.0615 | + | 19.3601i | −0.494686 | + | 0.635869i | ||||
\(928\) | 0.624691 | + | 1.08200i | 0.0205065 | + | 0.0355183i | ||||
\(929\) | −11.2304 | + | 19.4516i | −0.368457 | + | 0.638186i | −0.989325 | − | 0.145729i | \(-0.953447\pi\) |
0.620867 | + | 0.783916i | \(0.286781\pi\) | |||||||
\(930\) | −24.4348 | + | 4.77580i | −0.801248 | + | 0.156605i | ||||
\(931\) | 4.28325 | − | 10.7164i | 0.140378 | − | 0.351216i | ||||
\(932\) | 3.21413i | 0.105282i | ||||||||
\(933\) | −5.49855 | + | 16.0226i | −0.180015 | + | 0.524558i | ||||
\(934\) | 16.4057 | − | 9.47185i | 0.536812 | − | 0.309928i | ||||
\(935\) | −5.17174 | + | 2.98591i | −0.169134 | + | 0.0976496i | ||||
\(936\) | −2.57683 | + | 18.6136i | −0.0842262 | + | 0.608406i | ||||
\(937\) | − | 36.9477i | − | 1.20703i | −0.797353 | − | 0.603514i | \(-0.793767\pi\) | ||
0.797353 | − | 0.603514i | \(-0.206233\pi\) | |||||||
\(938\) | −16.6849 | + | 19.2663i | −0.544781 | + | 0.629066i | ||||
\(939\) | 5.71936 | + | 29.2623i | 0.186644 | + | 0.954940i | ||||
\(940\) | 7.53095 | − | 13.0440i | 0.245633 | − | 0.425448i | ||||
\(941\) | −25.9527 | − | 44.9514i | −0.846034 | − | 1.46537i | −0.884720 | − | 0.466122i | \(-0.845651\pi\) |
0.0386864 | − | 0.999251i | \(-0.487683\pi\) | |||||||
\(942\) | −15.6159 | − | 17.9267i | −0.508794 | − | 0.584082i | ||||
\(943\) | −3.76149 | − | 2.17170i | −0.122491 | − | 0.0707202i | ||||
\(944\) | −1.20054 | −0.0390741 | ||||||||
\(945\) | −14.9778 | + | 19.3680i | −0.487228 | + | 0.630041i | ||||
\(946\) | 4.78178 | 0.155469 | ||||||||
\(947\) | −3.70407 | − | 2.13855i | −0.120366 | − | 0.0694934i | 0.438608 | − | 0.898678i | \(-0.355472\pi\) |
−0.558974 | + | 0.829185i | \(0.688805\pi\) | |||||||
\(948\) | −1.31205 | − | 1.50620i | −0.0426134 | − | 0.0489191i | ||||
\(949\) | 34.6325 | + | 59.9852i | 1.12422 | + | 1.94720i | ||||
\(950\) | −1.50712 | + | 2.61042i | −0.0488976 | + | 0.0846931i | ||||
\(951\) | −2.74915 | − | 14.0656i | −0.0891472 | − | 0.456110i | ||||
\(952\) | −8.72801 | − | 1.67966i | −0.282876 | − | 0.0544379i | ||||
\(953\) | − | 28.0861i | − | 0.909798i | −0.890543 | − | 0.454899i | \(-0.849675\pi\) | ||
0.890543 | − | 0.454899i | \(-0.150325\pi\) | |||||||
\(954\) | −2.48963 | + | 17.9838i | −0.0806049 | + | 0.582248i | ||||
\(955\) | −7.25936 | + | 4.19119i | −0.234907 | + | 0.135624i | ||||
\(956\) | 7.29347 | − | 4.21089i | 0.235888 | − | 0.136190i | ||||
\(957\) | −0.701118 | + | 2.04304i | −0.0226639 | + | 0.0660420i | ||||
\(958\) | 0.580072i | 0.0187413i | ||||||||
\(959\) | 22.6297 | + | 4.35495i | 0.730751 | + | 0.140629i | ||||
\(960\) | 3.02738 | − | 0.591704i | 0.0977082 | − | 0.0190972i | ||||
\(961\) | 17.0727 | − | 29.5707i | 0.550731 | − | 0.953894i | ||||
\(962\) | −1.47508 | − | 2.55492i | −0.0475585 | − | 0.0823738i | ||||
\(963\) | −36.3468 | + | 46.7201i | −1.17126 | + | 1.50553i | ||||
\(964\) | 7.66278 | + | 4.42411i | 0.246801 | + | 0.142491i | ||||
\(965\) | 1.89728 | 0.0610757 | ||||||||
\(966\) | 3.96197 | − | 2.30278i | 0.127474 | − | 0.0740907i | ||||
\(967\) | 41.1377 | 1.32290 | 0.661450 | − | 0.749989i | \(-0.269941\pi\) | ||||
0.661450 | + | 0.749989i | \(0.269941\pi\) | |||||||
\(968\) | 8.66345 | + | 5.00185i | 0.278454 | + | 0.160765i | ||||
\(969\) | −7.23349 | + | 6.30109i | −0.232373 | + | 0.202420i | ||||
\(970\) | −10.3876 | − | 17.9919i | −0.333526 | − | 0.577684i | ||||
\(971\) | −10.4551 | + | 18.1087i | −0.335519 | + | 0.581135i | −0.983584 | − | 0.180449i | \(-0.942245\pi\) |
0.648066 | + | 0.761584i | \(0.275578\pi\) | |||||||
\(972\) | −8.87519 | + | 12.8153i | −0.284672 | + | 0.411050i | ||||
\(973\) | 1.63080 | − | 1.88311i | 0.0522811 | − | 0.0603697i | ||||
\(974\) | 14.6611i | 0.469772i | ||||||||
\(975\) | 18.7613 | + | 6.43838i | 0.600841 | + | 0.206193i | ||||
\(976\) | −1.01927 | + | 0.588474i | −0.0326260 | + | 0.0188366i | ||||
\(977\) | −24.0409 | + | 13.8800i | −0.769137 | + | 0.444062i | −0.832567 | − | 0.553925i | \(-0.813130\pi\) |
0.0634294 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(978\) | 15.3214 | + | 5.25791i | 0.489924 | + | 0.168129i | ||||
\(979\) | 9.61443i | 0.307279i | ||||||||
\(980\) | 1.78107 | + | 12.3386i | 0.0568942 | + | 0.394143i | ||||
\(981\) | −44.2983 | + | 18.0041i | −1.41434 | + | 0.574826i | ||||
\(982\) | 10.9749 | − | 19.0091i | 0.350223 | − | 0.606604i | ||||
\(983\) | −9.28941 | − | 16.0897i | −0.296286 | − | 0.513183i | 0.678997 | − | 0.734141i | \(-0.262415\pi\) |
−0.975283 | + | 0.220958i | \(0.929082\pi\) | |||||||
\(984\) | 5.67257 | − | 4.94138i | 0.180835 | − | 0.157525i | ||||
\(985\) | 26.1859 | + | 15.1184i | 0.834351 | + | 0.481713i | ||||
\(986\) | 4.19719 | 0.133666 | ||||||||
\(987\) | 33.6200 | + | 19.2808i | 1.07014 | + | 0.613715i | ||||
\(988\) | 10.3268 | 0.328540 | ||||||||
\(989\) | 4.14881 | + | 2.39532i | 0.131925 | + | 0.0761667i | ||||
\(990\) | 4.20916 | + | 3.27459i | 0.133776 | + | 0.104073i | ||||
\(991\) | 4.39574 | + | 7.61365i | 0.139635 | + | 0.241856i | 0.927359 | − | 0.374174i | \(-0.122074\pi\) |
−0.787723 | + | 0.616029i | \(0.788740\pi\) | |||||||
\(992\) | −4.03563 | + | 6.98992i | −0.128131 | + | 0.221930i | ||||
\(993\) | −29.5634 | + | 5.77821i | −0.938167 | + | 0.183366i | ||||
\(994\) | −24.0576 | + | 8.33395i | −0.763061 | + | 0.264337i | ||||
\(995\) | − | 3.81782i | − | 0.121033i | ||||||
\(996\) | −4.23816 | + | 12.3499i | −0.134291 | + | 0.391321i | ||||
\(997\) | 3.42951 | − | 1.98003i | 0.108614 | − | 0.0627081i | −0.444709 | − | 0.895675i | \(-0.646693\pi\) |
0.553323 | + | 0.832967i | \(0.313360\pi\) | |||||||
\(998\) | 28.9034 | − | 16.6874i | 0.914920 | − | 0.528229i | ||||
\(999\) | −0.135647 | − | 2.44358i | −0.00429169 | − | 0.0773116i |
(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 | 966.2.l.c.47.5 | ✓ | 56 | |
3.2 | odd | 2 | inner | 966.2.l.c.47.24 | yes | 56 | |
7.3 | odd | 6 | inner | 966.2.l.c.185.24 | yes | 56 | |
21.17 | even | 6 | inner | 966.2.l.c.185.5 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.l.c.47.5 | ✓ | 56 | 1.1 | even | 1 | trivial | |
966.2.l.c.47.24 | yes | 56 | 3.2 | odd | 2 | inner | |
966.2.l.c.185.5 | yes | 56 | 21.17 | even | 6 | inner | |
966.2.l.c.185.24 | yes | 56 | 7.3 | odd | 6 | inner |