Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(737,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.s (of order \(4\), 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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.8 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.a.2393.8 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.13155 | + | 1.92862i | −0.506046 | + | 0.862507i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43117 | + | 2.43117i | 0.918894 | + | 0.918894i | 0.996949 | − | 0.0780549i | \(-0.0248709\pi\) |
−0.0780549 | + | 0.996949i | \(0.524871\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.50191i | − | 1.65889i | −0.558589 | − | 0.829444i | \(-0.688657\pi\) | ||
0.558589 | − | 0.829444i | \(-0.311343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.03447 | − | 1.03447i | 0.286910 | − | 0.286910i | −0.548947 | − | 0.835857i | \(-0.684971\pi\) |
0.835857 | + | 0.548947i | \(0.184971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.543774 | − | 0.543774i | 0.131885 | − | 0.131885i | −0.638083 | − | 0.769968i | \(-0.720272\pi\) |
0.769968 | + | 0.638083i | \(0.220272\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.88294i | − | 1.34964i | −0.737983 | − | 0.674819i | \(-0.764222\pi\) | ||
0.737983 | − | 0.674819i | \(-0.235778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.43918 | − | 4.36468i | −0.487836 | − | 0.872936i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.99217 | −1.48411 | −0.742054 | − | 0.670340i | \(-0.766148\pi\) | ||||
−0.742054 | + | 0.670340i | \(0.766148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.34888 | 0.601476 | 0.300738 | − | 0.953707i | \(-0.402767\pi\) | ||||
0.300738 | + | 0.953707i | \(0.402767\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.43979 | + | 1.93781i | −1.25755 | + | 0.327550i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.41524 | − | 3.41524i | −0.561462 | − | 0.561462i | 0.368260 | − | 0.929723i | \(-0.379954\pi\) |
−0.929723 | + | 0.368260i | \(0.879954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.57386i | − | 0.714316i | −0.934044 | − | 0.357158i | \(-0.883746\pi\) | ||
0.934044 | − | 0.357158i | \(-0.116254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70225 | + | 1.70225i | −0.259591 | + | 0.259591i | −0.824888 | − | 0.565297i | \(-0.808762\pi\) |
0.565297 | + | 0.824888i | \(0.308762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.40852 | + | 7.40852i | −1.08064 | + | 1.08064i | −0.0841949 | + | 0.996449i | \(0.526832\pi\) |
−0.996449 | + | 0.0841949i | \(0.973168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.82113i | 0.688733i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73776 | − | 4.73776i | −0.650782 | − | 0.650782i | 0.302400 | − | 0.953181i | \(-0.402212\pi\) |
−0.953181 | + | 0.302400i | \(0.902212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.6111 | + | 6.22570i | 1.43080 | + | 0.839473i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.2790 | −1.46840 | −0.734200 | − | 0.678934i | \(-0.762442\pi\) | ||||
−0.734200 | + | 0.678934i | \(0.762442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2845 | −1.57288 | −0.786438 | − | 0.617670i | \(-0.788077\pi\) | ||||
−0.786438 | + | 0.617670i | \(0.788077\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.824546 | + | 3.16566i | 0.102272 | + | 0.392652i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.06469 | + | 3.06469i | 0.374412 | + | 0.374412i | 0.869081 | − | 0.494669i | \(-0.164711\pi\) |
−0.494669 | + | 0.869081i | \(0.664711\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1224i | − | 1.20130i | −0.799510 | − | 0.600652i | \(-0.794908\pi\) | ||
0.799510 | − | 0.600652i | \(-0.205092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.22335 | + | 2.22335i | −0.260223 | + | 0.260223i | −0.825145 | − | 0.564922i | \(-0.808906\pi\) |
0.564922 | + | 0.825145i | \(0.308906\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.3761 | − | 13.3761i | 1.52434 | − | 1.52434i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.61129i | − | 0.743828i | −0.928267 | − | 0.371914i | \(-0.878702\pi\) | ||
0.928267 | − | 0.371914i | \(-0.121298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00107 | − | 3.00107i | −0.329410 | − | 0.329410i | 0.522952 | − | 0.852362i | \(-0.324831\pi\) |
−0.852362 | + | 0.522952i | \(0.824831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.433427 | + | 1.66404i | 0.0470117 | + | 0.180491i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.16535 | −0.229527 | −0.114763 | − | 0.993393i | \(-0.536611\pi\) | ||||
−0.114763 | + | 0.993393i | \(0.536611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.02993 | 0.527280 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3460 | + | 6.65685i | 1.16407 | + | 0.682979i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3198 | + | 11.3198i | 1.14936 | + | 1.14936i | 0.986680 | + | 0.162676i | \(0.0520126\pi\) |
0.162676 | + | 0.986680i | \(0.447987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.0590i | − | 1.29942i | −0.760182 | − | 0.649710i | \(-0.774890\pi\) | ||
0.760182 | − | 0.649710i | \(-0.225110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.36524 | + | 5.36524i | −0.528653 | + | 0.528653i | −0.920171 | − | 0.391518i | \(-0.871950\pi\) |
0.391518 | + | 0.920171i | \(0.371950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.53778 | + | 7.53778i | −0.728704 | + | 0.728704i | −0.970362 | − | 0.241657i | \(-0.922309\pi\) |
0.241657 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.6981i | − | 1.21625i | −0.793840 | − | 0.608127i | \(-0.791921\pi\) | ||
0.793840 | − | 0.608127i | \(-0.208079\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.86315 | − | 7.86315i | −0.739703 | − | 0.739703i | 0.232818 | − | 0.972520i | \(-0.425206\pi\) |
−0.972520 | + | 0.232818i | \(0.925206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.16387 | + | 0.563614i | −0.201782 | + | 0.0525573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.64401 | 0.242376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.2710 | −1.75191 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1779 | + | 0.234605i | 0.999780 | + | 0.0209837i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.27967 | + | 9.27967i | 0.823437 | + | 0.823437i | 0.986599 | − | 0.163162i | \(-0.0521694\pi\) |
−0.163162 | + | 0.986599i | \(0.552169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.1597i | − | 1.67399i | −0.547213 | − | 0.836993i | \(-0.684311\pi\) | ||
0.547213 | − | 0.836993i | \(-0.315689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.3024 | − | 14.3024i | 1.24017 | − | 1.24017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.44031 | + | 2.44031i | −0.208490 | + | 0.208490i | −0.803625 | − | 0.595136i | \(-0.797098\pi\) |
0.595136 | + | 0.803625i | \(0.297098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.32867i | − | 0.621610i | −0.950474 | − | 0.310805i | \(-0.899401\pi\) | ||
0.950474 | − | 0.310805i | \(-0.100599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.69156 | − | 5.69156i | −0.475952 | − | 0.475952i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.04356 | − | 15.4139i | 0.751027 | − | 1.28005i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.9993 | 1.31071 | 0.655355 | − | 0.755321i | \(-0.272519\pi\) | ||||
0.655355 | + | 0.755321i | \(0.272519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8746 | 1.61737 | 0.808686 | − | 0.588241i | \(-0.200179\pi\) | ||||
0.808686 | + | 0.588241i | \(0.200179\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.78943 | + | 6.45872i | −0.304374 | + | 0.518777i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1539 | − | 13.1539i | −1.04980 | − | 1.04980i | −0.998693 | − | 0.0511019i | \(-0.983727\pi\) |
−0.0511019 | − | 0.998693i | \(-0.516273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.43819i | 0.270967i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13445 | − | 1.13445i | 0.0888571 | − | 0.0888571i | −0.661281 | − | 0.750138i | \(-0.729987\pi\) |
0.750138 | + | 0.661281i | \(0.229987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1205 | − | 15.1205i | 1.17006 | − | 1.17006i | 0.187864 | − | 0.982195i | \(-0.439844\pi\) |
0.982195 | − | 0.187864i | \(-0.0601563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8597i | 0.835365i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.8189 | + | 13.8189i | 1.05063 | + | 1.05063i | 0.998648 | + | 0.0519851i | \(0.0165548\pi\) |
0.0519851 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68121 | − | 16.5413i | 0.353866 | − | 1.25040i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0507 | −0.900715 | −0.450358 | − | 0.892848i | \(-0.648704\pi\) | ||||
−0.450358 | + | 0.892848i | \(0.648704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3662 | 1.21649 | 0.608247 | − | 0.793748i | \(-0.291873\pi\) | ||||
0.608247 | + | 0.793748i | \(0.291873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.4512 | − | 2.72219i | 0.768391 | − | 0.200140i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.99180 | − | 2.99180i | −0.218782 | − | 0.218782i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6033i | 1.56316i | 0.623806 | + | 0.781579i | \(0.285585\pi\) | ||||
−0.623806 | + | 0.781579i | \(0.714415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.48521 | − | 3.48521i | 0.250871 | − | 0.250871i | −0.570457 | − | 0.821328i | \(-0.693234\pi\) |
0.821328 | + | 0.570457i | \(0.193234\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.46794 | + | 8.46794i | −0.603315 | + | 0.603315i | −0.941191 | − | 0.337875i | \(-0.890292\pi\) |
0.337875 | + | 0.941191i | \(0.390292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.8671i | − | 0.983012i | −0.870874 | − | 0.491506i | \(-0.836447\pi\) | ||
0.870874 | − | 0.491506i | \(-0.163553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.4303 | − | 19.4303i | −1.36374 | − | 1.36374i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.82124 | + | 5.17556i | 0.616102 | + | 0.361477i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.3674 | −2.23890 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4602 | 0.857796 | 0.428898 | − | 0.903353i | \(-0.358902\pi\) | ||||
0.428898 | + | 0.903353i | \(0.358902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.35682 | − | 5.20919i | −0.0925341 | − | 0.355264i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.14167 | + | 8.14167i | 0.552693 | + | 0.552693i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.12504i | − | 0.0756781i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8400 | − | 12.8400i | 0.859832 | − | 0.859832i | −0.131486 | − | 0.991318i | \(-0.541975\pi\) |
0.991318 | + | 0.131486i | \(0.0419748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.525112 | + | 0.525112i | −0.0348529 | + | 0.0348529i | −0.724318 | − | 0.689466i | \(-0.757845\pi\) |
0.689466 | + | 0.724318i | \(0.257845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.40850i | 0.159158i | 0.996829 | + | 0.0795791i | \(0.0253576\pi\) | ||||
−0.996829 | + | 0.0795791i | \(0.974642\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.22336 | − | 6.22336i | −0.407706 | − | 0.407706i | 0.473232 | − | 0.880938i | \(-0.343087\pi\) |
−0.880938 | + | 0.473232i | \(0.843087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.90512 | − | 22.6714i | −0.385208 | − | 1.47892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.02140 | 0.0660692 | 0.0330346 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330346 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.6183 | −0.812815 | −0.406407 | − | 0.913692i | \(-0.633219\pi\) | ||||
−0.406407 | + | 0.913692i | \(0.633219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.29815 | − | 5.45536i | −0.594037 | − | 0.348530i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.08572 | − | 6.08572i | −0.387225 | − | 0.387225i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.2549i | 0.710404i | 0.934790 | + | 0.355202i | \(0.115588\pi\) | ||||
−0.934790 | + | 0.355202i | \(0.884412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.89044 | − | 3.89044i | 0.244590 | − | 0.244590i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1697 | − | 17.1697i | 1.07102 | − | 1.07102i | 0.0737395 | − | 0.997278i | \(-0.476507\pi\) |
0.997278 | − | 0.0737395i | \(-0.0234933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.6060i | − | 1.03185i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.45359 | + | 7.45359i | 0.459608 | + | 0.459608i | 0.898527 | − | 0.438919i | \(-0.144638\pi\) |
−0.438919 | + | 0.898527i | \(0.644638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.4984 | − | 3.77633i | 0.890629 | − | 0.231978i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.25579 | −0.0765668 | −0.0382834 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382834 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6861 | −1.01361 | −0.506803 | − | 0.862062i | \(-0.669173\pi\) | ||||
−0.506803 | + | 0.862062i | \(0.669173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.0141 | + | 13.4201i | −1.44810 | + | 0.809265i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.10754 | + | 9.10754i | 0.547219 | + | 0.547219i | 0.925635 | − | 0.378416i | \(-0.123531\pi\) |
−0.378416 | + | 0.925635i | \(0.623531\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.72230i | − | 0.401019i | −0.979692 | − | 0.200509i | \(-0.935740\pi\) | ||
0.979692 | − | 0.200509i | \(-0.0642597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.1094 | + | 17.1094i | −1.01705 | + | 1.01705i | −0.0171964 | + | 0.999852i | \(0.505474\pi\) |
−0.999852 | + | 0.0171964i | \(0.994526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1198 | − | 11.1198i | 0.656381 | − | 0.656381i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4086i | 0.965213i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.20891 | − | 5.20891i | −0.304308 | − | 0.304308i | 0.538389 | − | 0.842697i | \(-0.319033\pi\) |
−0.842697 | + | 0.538389i | \(0.819033\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7628 | − | 21.7529i | 0.743077 | − | 1.26650i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.46296 | 0.0846052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.27692 | −0.477074 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9006 | − | 23.6923i | 0.795947 | − | 1.35662i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2971 | − | 20.2971i | −1.15842 | − | 1.15842i | −0.984816 | − | 0.173601i | \(-0.944460\pi\) |
−0.173601 | − | 0.984816i | \(-0.555540\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.1661i | − | 0.859990i | −0.902831 | − | 0.429995i | \(-0.858515\pi\) | ||
0.902831 | − | 0.429995i | \(-0.141485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6121 | − | 12.6121i | 0.712879 | − | 0.712879i | −0.254258 | − | 0.967137i | \(-0.581831\pi\) |
0.967137 | + | 0.254258i | \(0.0818311\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.87599 | + | 7.87599i | −0.442360 | + | 0.442360i | −0.892804 | − | 0.450445i | \(-0.851265\pi\) |
0.450445 | + | 0.892804i | \(0.351265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.9722i | 2.46197i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.19899 | − | 3.19899i | −0.177997 | − | 0.177997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.03838 | − | 1.99187i | −0.390419 | − | 0.110489i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −36.0227 | −1.98600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.60135 | −0.252913 | −0.126457 | − | 0.991972i | \(-0.540360\pi\) | ||||
−0.126457 | + | 0.991972i | \(0.540360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.37850 | + | 2.44278i | −0.512402 | + | 0.133463i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8178 | − | 21.8178i | −1.18849 | − | 1.18849i | −0.977484 | − | 0.211009i | \(-0.932325\pi\) |
−0.211009 | − | 0.977484i | \(-0.567675\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 18.4252i | − | 0.997782i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.29719 | − | 5.29719i | 0.286021 | − | 0.286021i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.9533 | + | 18.9533i | −1.01747 | + | 1.01747i | −0.0176207 | + | 0.999845i | \(0.505609\pi\) |
−0.999845 | + | 0.0176207i | \(0.994391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.3433i | 1.83836i | 0.393842 | + | 0.919178i | \(0.371146\pi\) | ||||
−0.393842 | + | 0.919178i | \(0.628854\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.97379 | + | 8.97379i | 0.477626 | + | 0.477626i | 0.904372 | − | 0.426745i | \(-0.140340\pi\) |
−0.426745 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.5222 | + | 11.4540i | 1.03613 | + | 0.607915i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.12425 | −0.428782 | −0.214391 | − | 0.976748i | \(-0.568777\pi\) | ||||
−0.214391 | + | 0.976748i | \(0.568777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6089 | −0.821524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.77217 | − | 6.80383i | −0.0927594 | − | 0.356129i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.56152 | − | 4.56152i | −0.238109 | − | 0.238109i | 0.577958 | − | 0.816067i | \(-0.303850\pi\) |
−0.816067 | + | 0.577958i | \(0.803850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 23.0366i | − | 1.19600i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7177 | − | 19.7177i | 1.02095 | − | 1.02095i | 0.0211700 | − | 0.999776i | \(-0.493261\pi\) |
0.999776 | − | 0.0211700i | \(-0.00673911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.26765 | + | 8.26765i | −0.425806 | + | 0.425806i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.9209i | 1.63967i | 0.572603 | + | 0.819833i | \(0.305934\pi\) | ||||
−0.572603 | + | 0.819833i | \(0.694066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.56531 | − | 9.56531i | −0.488765 | − | 0.488765i | 0.419152 | − | 0.907916i | \(-0.362328\pi\) |
−0.907916 | + | 0.419152i | \(0.862328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.6617 | + | 40.9331i | 0.543369 | + | 2.08614i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.48156 | −0.176522 | −0.0882610 | − | 0.996097i | \(-0.528131\pi\) | ||||
−0.0882610 | + | 0.996097i | \(0.528131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.769013 | 0.0388906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7507 | + | 7.48102i | 0.641557 | + | 0.376411i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2108 | − | 11.2108i | −0.562652 | − | 0.562652i | 0.367408 | − | 0.930060i | \(-0.380245\pi\) |
−0.930060 | + | 0.367408i | \(0.880245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.63851i | − | 0.281574i | −0.990040 | − | 0.140787i | \(-0.955037\pi\) | ||
0.990040 | − | 0.140787i | \(-0.0449632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.46431 | − | 3.46431i | 0.172570 | − | 0.172570i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.7904 | + | 18.7904i | −0.931404 | + | 0.931404i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.91715i | 0.292584i | 0.989241 | + | 0.146292i | \(0.0467340\pi\) | ||||
−0.989241 | + | 0.146292i | \(0.953266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.4211 | − | 27.4211i | −1.34930 | − | 1.34930i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.18381 | − | 2.39207i | 0.450815 | − | 0.117422i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.6493 | −0.715667 | −0.357833 | − | 0.933785i | \(-0.616484\pi\) | ||||
−0.357833 | + | 0.933785i | \(0.616484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3727 | 1.18785 | 0.593927 | − | 0.804519i | \(-0.297577\pi\) | ||||
0.593927 | + | 0.804519i | \(0.297577\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.69976 | − | 1.04704i | −0.179465 | − | 0.0507887i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.8658 | − | 29.8658i | −1.44531 | − | 1.44531i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.77024i | 0.0852693i | 0.999091 | + | 0.0426346i | \(0.0135751\pi\) | ||||
−0.999091 | + | 0.0426346i | \(0.986425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.671303 | + | 0.671303i | −0.0322608 | + | 0.0322608i | −0.723053 | − | 0.690792i | \(-0.757262\pi\) |
0.690792 | + | 0.723053i | \(0.257262\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.15986 | − | 4.15986i | 0.198993 | − | 0.198993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17.2380i | − | 0.822723i | −0.911472 | − | 0.411361i | \(-0.865053\pi\) | ||
0.911472 | − | 0.411361i | \(-0.134947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.6013 | + | 12.6013i | 0.598704 | + | 0.598704i | 0.939968 | − | 0.341264i | \(-0.110855\pi\) |
−0.341264 | + | 0.939968i | \(0.610855\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.45021 | − | 4.17615i | 0.116151 | − | 0.197968i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9451 | 0.894075 | 0.447038 | − | 0.894515i | \(-0.352479\pi\) | ||||
0.447038 | + | 0.894515i | \(0.352479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.1649 | −1.18497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.69163 | + | 9.70085i | −0.266828 | + | 0.454783i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.6660 | + | 21.6660i | 1.01349 | + | 1.01349i | 0.999908 | + | 0.0135859i | \(0.00432466\pi\) |
0.0135859 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.90901i | 0.414934i | 0.978242 | + | 0.207467i | \(0.0665220\pi\) | ||||
−0.978242 | + | 0.207467i | \(0.933478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.0201 | + | 25.0201i | −1.16278 | + | 1.16278i | −0.178918 | + | 0.983864i | \(0.557260\pi\) |
−0.983864 | + | 0.178918i | \(0.942740\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.09287 | + | 6.09287i | −0.281944 | + | 0.281944i | −0.833884 | − | 0.551940i | \(-0.813888\pi\) |
0.551940 | + | 0.833884i | \(0.313888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.9016i | 0.688090i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.36564 | + | 9.36564i | 0.430633 | + | 0.430633i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.6771 | + | 14.3495i | −1.17815 | + | 0.658402i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.1992 | 1.19707 | 0.598537 | − | 0.801095i | \(-0.295749\pi\) | ||||
0.598537 | + | 0.801095i | \(0.295749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.06593 | −0.322179 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.6407 | + | 9.02272i | −1.57295 | + | 0.409701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.2014 | − | 20.2014i | −0.915414 | − | 0.915414i | 0.0812776 | − | 0.996692i | \(-0.474100\pi\) |
−0.996692 | + | 0.0812776i | \(0.974100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0638160i | 0.00287998i | 0.999999 | + | 0.00143999i | \(0.000458363\pi\) | ||||
−0.999999 | + | 0.00143999i | \(0.999542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.34594 | + | 4.34594i | −0.195731 | + | 0.195731i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.6092 | − | 24.6092i | 1.10387 | − | 1.10387i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.0911i | 1.34706i | 0.739160 | + | 0.673530i | \(0.235223\pi\) | ||||
−0.739160 | + | 0.673530i | \(0.764777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.7215 | + | 29.7215i | 1.32522 | + | 1.32522i | 0.909489 | + | 0.415729i | \(0.136474\pi\) |
0.415729 | + | 0.909489i | \(0.363526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1859 | + | 14.7769i | 1.12076 | + | 0.657565i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.3528 | 1.92158 | 0.960790 | − | 0.277277i | \(-0.0894320\pi\) | ||||
0.960790 | + | 0.277277i | \(0.0894320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8106 | −0.478235 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.27648 | − | 16.4186i | −0.188444 | − | 0.723489i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.7610 | + | 40.7610i | 1.79267 | + | 1.79267i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.24151i | − | 0.142013i | −0.997476 | − | 0.0710067i | \(-0.977379\pi\) | ||
0.997476 | − | 0.0710067i | \(-0.0226212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3439 | − | 24.3439i | 1.06448 | − | 1.06448i | 0.0667125 | − | 0.997772i | \(-0.478749\pi\) |
0.997772 | − | 0.0667125i | \(-0.0212510\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.82103 | − | 1.82103i | 0.0793254 | − | 0.0793254i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.73151 | − | 4.73151i | −0.204945 | − | 0.204945i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00814 | − | 23.0669i | −0.259755 | − | 0.997270i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.5254 | 1.14253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.11905 | −0.0911050 | −0.0455525 | − | 0.998962i | \(-0.514505\pi\) | ||||
−0.0455525 | + | 0.998962i | \(0.514505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.4898 | + | 14.3685i | 1.04903 | + | 0.615480i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.30193 | − | 3.30193i | −0.141180 | − | 0.141180i | 0.632984 | − | 0.774165i | \(-0.281830\pi\) |
−0.774165 | + | 0.632984i | \(0.781830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.0174i | 2.00301i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0731 | − | 16.0731i | 0.683499 | − | 0.683499i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.5875 | − | 10.5875i | 0.448605 | − | 0.448605i | −0.446285 | − | 0.894891i | \(-0.647253\pi\) |
0.894891 | + | 0.446285i | \(0.147253\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.52186i | 0.148959i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.5540 | + | 22.5540i | 0.950536 | + | 0.950536i | 0.998833 | − | 0.0482965i | \(-0.0153793\pi\) |
−0.0482965 | + | 0.998833i | \(0.515379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.0626 | − | 6.26749i | 1.01232 | − | 0.263675i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.18571 | 0.343163 | 0.171581 | − | 0.985170i | \(-0.445112\pi\) | ||||
0.171581 | + | 0.985170i | \(0.445112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.32436 | 0.0972716 | 0.0486358 | − | 0.998817i | \(-0.484513\pi\) | ||||
0.0486358 | + | 0.998817i | \(0.484513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.36153 | − | 4.81105i | 0.0567799 | − | 0.200635i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.19241 | − | 8.19241i | −0.341054 | − | 0.341054i | 0.515709 | − | 0.856764i | \(-0.327528\pi\) |
−0.856764 | + | 0.515709i | \(0.827528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 14.5922i | − | 0.605387i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.0667 | + | 26.0667i | −1.07957 | + | 1.07957i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2250 | + | 10.2250i | −0.422029 | + | 0.422029i | −0.885902 | − | 0.463873i | \(-0.846459\pi\) |
0.463873 | + | 0.885902i | \(0.346459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 19.7012i | − | 0.811775i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5865 | + | 23.5865i | 0.968583 | + | 0.968583i | 0.999521 | − | 0.0309386i | \(-0.00984962\pi\) |
−0.0309386 | + | 0.999521i | \(0.509850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.99184 | + | 5.09930i | −0.122653 | + | 0.209051i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.5916 | −1.41337 | −0.706687 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706687 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.38323 | −0.341959 | −0.170980 | − | 0.985275i | \(-0.554693\pi\) | ||||
−0.170980 | + | 0.985275i | \(0.554693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.8062 | − | 37.1666i | 0.886547 | − | 1.51104i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.5852 | − | 26.5852i | −1.07906 | − | 1.07906i | −0.996594 | − | 0.0824646i | \(-0.973721\pi\) |
−0.0824646 | − | 0.996594i | \(-0.526279\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.3278i | 0.620096i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.8848 | − | 32.8848i | 1.32820 | − | 1.32820i | 0.421265 | − | 0.906938i | \(-0.361586\pi\) |
0.906938 | − | 0.421265i | \(-0.138414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8211 | − | 17.8211i | 0.717449 | − | 0.717449i | −0.250633 | − | 0.968082i | \(-0.580639\pi\) |
0.968082 | + | 0.250633i | \(0.0806387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.590511i | 0.0237346i | 0.999930 | + | 0.0118673i | \(0.00377757\pi\) | ||||
−0.999930 | + | 0.0118673i | \(0.996222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.26433 | − | 5.26433i | −0.210911 | − | 0.210911i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.1008 | + | 21.2925i | −0.524033 | + | 0.851698i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.71424 | −0.148097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.3481 | −1.12852 | −0.564260 | − | 0.825597i | \(-0.690838\pi\) | ||||
−0.564260 | + | 0.825597i | \(0.690838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.3974 | + | 7.39655i | −1.12692 | + | 0.293523i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.98731 | + | 4.98731i | 0.197604 | + | 0.197604i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.2235i | − | 0.482798i | −0.970426 | − | 0.241399i | \(-0.922394\pi\) | ||
0.970426 | − | 0.241399i | \(-0.0776062\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.523304 | − | 0.523304i | 0.0206371 | − | 0.0206371i | −0.696713 | − | 0.717350i | \(-0.745355\pi\) |
0.717350 | + | 0.696713i | \(0.245355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6991 | − | 24.6991i | 0.971023 | − | 0.971023i | −0.0285693 | − | 0.999592i | \(-0.509095\pi\) |
0.999592 | + | 0.0285693i | \(0.00909513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 62.0560i | 2.43591i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.4307 | + | 34.4307i | 1.34738 | + | 1.34738i | 0.888498 | + | 0.458881i | \(0.151749\pi\) |
0.458881 | + | 0.888498i | \(0.348251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.9518 | + | 21.6802i | 1.44382 | + | 0.847114i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.4303 | −1.61390 | −0.806948 | − | 0.590623i | \(-0.798882\pi\) | ||||
−0.806948 | + | 0.590623i | \(0.798882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9008 | 0.618470 | 0.309235 | − | 0.950986i | \(-0.399927\pi\) | ||||
0.309235 | + | 0.950986i | \(0.399927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.4000 | + | 43.7678i | 0.442074 | + | 1.69724i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.65132 | − | 5.65132i | −0.218820 | − | 0.218820i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.5885i | 2.60922i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1513 | − | 11.1513i | 0.429851 | − | 0.429851i | −0.458726 | − | 0.888578i | \(-0.651694\pi\) |
0.888578 | + | 0.458726i | \(0.151694\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.0871 | − | 17.0871i | 0.656710 | − | 0.656710i | −0.297890 | − | 0.954600i | \(-0.596283\pi\) |
0.954600 | + | 0.297890i | \(0.0962829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.0408i | 2.11227i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3471 | − | 15.3471i | −0.587240 | − | 0.587240i | 0.349643 | − | 0.936883i | \(-0.386303\pi\) |
−0.936883 | + | 0.349643i | \(0.886303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.94510 | − | 7.46777i | −0.0743184 | − | 0.285329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.80214 | −0.373432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.9705 | −0.873838 | −0.436919 | − | 0.899501i | \(-0.643930\pi\) | ||||
−0.436919 | + | 0.899501i | \(0.643930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1342 | + | 8.29278i | 0.536143 | + | 0.314563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.48714 | − | 2.48714i | −0.0942073 | − | 0.0942073i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.15435i | − | 0.345755i | −0.984943 | − | 0.172877i | \(-0.944694\pi\) | ||
0.984943 | − | 0.172877i | \(-0.0553065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0917 | + | 20.0917i | −0.757771 | + | 0.757771i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.7486 | − | 31.7486i | 1.19403 | − | 1.19403i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 20.5975i | − | 0.773556i | −0.922173 | − | 0.386778i | \(-0.873588\pi\) | ||
0.922173 | − | 0.386778i | \(-0.126412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.36801 | + | 2.36801i | 0.0886828 | + | 0.0886828i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.4172 | − | 4.53658i | 0.651365 | − | 0.169658i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.5055 | 1.32413 | 0.662065 | − | 0.749446i | \(-0.269680\pi\) | ||||
0.662065 | + | 0.749446i | \(0.269680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.0876 | −0.971552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.4943 | + | 34.8832i | 0.724001 | + | 1.29553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9915 | − | 23.9915i | −0.889796 | − | 0.889796i | 0.104707 | − | 0.994503i | \(-0.466610\pi\) |
−0.994503 | + | 0.104707i | \(0.966610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.85128i | 0.0684722i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5305 | − | 11.5305i | 0.425890 | − | 0.425890i | −0.461336 | − | 0.887226i | \(-0.652630\pi\) |
0.887226 | + | 0.461336i | \(0.152630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.8617 | − | 16.8617i | 0.621108 | − | 0.621108i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 29.7815i | − | 1.09553i | −0.836633 | − | 0.547764i | \(-0.815479\pi\) | ||
0.836633 | − | 0.547764i | \(-0.184521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.19752 | + | 4.19752i | 0.153992 | + | 0.153992i | 0.779898 | − | 0.625906i | \(-0.215271\pi\) |
−0.625906 | + | 0.779898i | \(0.715271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.1040 | + | 30.8565i | −0.663279 | + | 1.13050i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.6512 | −1.33920 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.6039 | 1.15324 | 0.576621 | − | 0.817012i | \(-0.304371\pi\) | ||||
0.576621 | + | 0.817012i | \(0.304371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.4891 | + | 38.3306i | −0.818464 | + | 1.39499i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9099 | − | 25.9099i | −0.941712 | − | 0.941712i | 0.0566800 | − | 0.998392i | \(-0.481949\pi\) |
−0.998392 | + | 0.0566800i | \(0.981949\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5166i | 0.489977i | 0.969526 | + | 0.244989i | \(0.0787842\pi\) | ||||
−0.969526 | + | 0.244989i | \(0.921216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.8711 | − | 30.8711i | 1.11761 | − | 1.11761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.6678 | + | 11.6678i | −0.421299 | + | 0.421299i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.5764i | − | 0.597760i | −0.954291 | − | 0.298880i | \(-0.903387\pi\) | ||
0.954291 | − | 0.298880i | \(-0.0966130\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.2301 | + | 22.2301i | 0.799562 | + | 0.799562i | 0.983026 | − | 0.183464i | \(-0.0587311\pi\) |
−0.183464 | + | 0.983026i | \(0.558731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.16851 | − | 14.6168i | −0.293421 | − | 0.525050i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.9077 | −0.964068 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.6924 | −1.99283 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.2532 | − | 10.4846i | 1.43670 | − | 0.374211i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.85030 | + | 5.85030i | 0.208541 | + | 0.208541i | 0.803647 | − | 0.595106i | \(-0.202890\pi\) |
−0.595106 | + | 0.803647i | \(0.702890\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 38.2332i | − | 1.35942i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7080 | + | 12.7080i | −0.451274 | + | 0.451274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.35974 | − | 2.35974i | 0.0835861 | − | 0.0835861i | −0.664078 | − | 0.747664i | \(-0.731176\pi\) |
0.747664 | + | 0.664078i | \(0.231176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.05713i | 0.285041i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2327 | + | 12.2327i | 0.431681 | + | 0.431681i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.63097 | − | 3.89049i | −0.233711 | − | 0.137122i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.25285 | 0.184680 | 0.0923402 | − | 0.995728i | \(-0.470565\pi\) | ||||
0.0923402 | + | 0.995728i | \(0.470565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.60570 | −0.0563836 | −0.0281918 | − | 0.999603i | \(-0.508975\pi\) | ||||
−0.0281918 | + | 0.999603i | \(0.508975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.904238 | + | 3.47162i | 0.0316741 | + | 0.121606i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0142 | + | 10.0142i | 0.350354 | + | 0.350354i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.95002i | 0.312358i | 0.987729 | + | 0.156179i | \(0.0499176\pi\) | ||||
−0.987729 | + | 0.156179i | \(0.950082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.39852 | − | 1.39852i | 0.0487494 | − | 0.0487494i | −0.682312 | − | 0.731061i | \(-0.739025\pi\) |
0.731061 | + | 0.682312i | \(0.239025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.842785 | + | 0.842785i | −0.0293065 | + | 0.0293065i | −0.721608 | − | 0.692302i | \(-0.756597\pi\) |
0.692302 | + | 0.721608i | \(0.256597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.1812i | − | 0.353607i | −0.984246 | − | 0.176804i | \(-0.943424\pi\) | ||
0.984246 | − | 0.176804i | \(-0.0565757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.62161 | + | 2.62161i | 0.0908333 | + | 0.0908333i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0521 | + | 46.2714i | 0.417080 | + | 1.60129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.69579 | 0.300212 | 0.150106 | − | 0.988670i | \(-0.452039\pi\) | ||||
0.150106 | + | 0.988670i | \(0.452039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.8748 | 1.20258 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.9444 | − | 12.2884i | −0.720508 | − | 0.422733i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.8510 | − | 46.8510i | −1.60982 | − | 1.60982i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.82988i | − | 0.165566i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.3988 | + | 18.3988i | −0.629962 | + | 0.629962i | −0.948058 | − | 0.318096i | \(-0.896957\pi\) |
0.318096 | + | 0.948058i | \(0.396957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.82302 | + | 8.82302i | −0.301388 | + | 0.301388i | −0.841557 | − | 0.540168i | \(-0.818361\pi\) |
0.540168 | + | 0.841557i | \(0.318361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.70365i | 0.194606i | 0.995255 | + | 0.0973031i | \(0.0310216\pi\) | ||||
−0.995255 | + | 0.0973031i | \(0.968978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.8104 | − | 29.8104i | −1.01476 | − | 1.01476i | −0.999889 | − | 0.0148680i | \(-0.995267\pi\) |
−0.0148680 | − | 0.999889i | \(-0.504733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.2883 | + | 11.0147i | −1.43785 | + | 0.374510i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.3747 | −1.23393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.34066 | 0.214845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.6049 | + | 27.7456i | 0.899410 | + | 0.937974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.684837 | − | 0.684837i | −0.0231253 | − | 0.0231253i | 0.695450 | − | 0.718575i | \(-0.255205\pi\) |
−0.718575 | + | 0.695450i | \(0.755205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 28.4255i | − | 0.957680i | −0.877902 | − | 0.478840i | \(-0.841057\pi\) | ||
0.877902 | − | 0.478840i | \(-0.158943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1329 | + | 24.1329i | −0.812136 | + | 0.812136i | −0.984954 | − | 0.172818i | \(-0.944713\pi\) |
0.172818 | + | 0.984954i | \(0.444713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.1374 | + | 32.1374i | −1.07907 | + | 1.07907i | −0.0824752 | + | 0.996593i | \(0.526283\pi\) |
−0.996593 | + | 0.0824752i | \(0.973717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.1208i | 1.51330i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.5839 | + | 43.5839i | 1.45848 | + | 1.45848i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6361 | − | 23.2414i | 0.455803 | − | 0.776873i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.7648 | −0.892656 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.15255 | −0.171656 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.5193 | + | 31.5643i | −0.615601 | + | 1.04923i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4365 | − | 25.4365i | −0.844604 | − | 0.844604i | 0.144850 | − | 0.989454i | \(-0.453730\pi\) |
−0.989454 | + | 0.144850i | \(0.953730\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4306i | 0.478108i | 0.971006 | + | 0.239054i | \(0.0768373\pi\) | ||||
−0.971006 | + | 0.239054i | \(0.923163\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.5116 | + | 16.5116i | −0.546455 | + | 0.546455i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.5803 | − | 46.5803i | 1.53822 | − | 1.53822i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.67732i | − | 0.0553298i | −0.999617 | − | 0.0276649i | \(-0.991193\pi\) | ||
0.999617 | − | 0.0276649i | \(-0.00880713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4713 | − | 10.4713i | −0.344667 | − | 0.344667i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.57605 | + | 23.2368i | −0.216219 | + | 0.764022i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.4353 | −0.506417 | −0.253209 | − | 0.967412i | \(-0.581486\pi\) | ||||
−0.253209 | + | 0.967412i | \(0.581486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.3624 | 0.929540 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.15543 | − | 2.38468i | 0.299414 | − | 0.0779872i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.7315 | − | 27.7315i | −0.905950 | − | 0.905950i | 0.0899926 | − | 0.995942i | \(-0.471316\pi\) |
−0.995942 | + | 0.0899926i | \(0.971316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.0993439i | 0.00323852i | 0.999999 | + | 0.00161926i | \(0.000515427\pi\) | ||||
−0.999999 | + | 0.00161926i | \(0.999485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.23420 | − | 3.23420i | 0.105320 | − | 0.105320i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.6359 | − | 23.6359i | 0.768062 | − | 0.768062i | −0.209703 | − | 0.977765i | \(-0.567250\pi\) |
0.977765 | + | 0.209703i | \(0.0672496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.59997i | 0.149321i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.5781 | + | 18.5781i | 0.601803 | + | 0.601803i | 0.940791 | − | 0.338988i | \(-0.110085\pi\) |
−0.338988 | + | 0.940791i | \(0.610085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.6646 | − | 24.4452i | −1.34823 | − | 0.791029i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.8656 | −0.383160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7850 | −0.638227 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.77796 | + | 10.6654i | 0.0894257 | + | 0.343330i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.6457 | + | 31.6457i | 1.01766 | + | 1.01766i | 0.999841 | + | 0.0178154i | \(0.00567113\pi\) |
0.0178154 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.33918i | 0.235526i | 0.993042 | + | 0.117763i | \(0.0375722\pi\) | ||||
−0.993042 | + | 0.117763i | \(0.962428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.8172 | − | 17.8172i | 0.571194 | − | 0.571194i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0849 | + | 11.0849i | −0.354637 | + | 0.354637i | −0.861831 | − | 0.507195i | \(-0.830682\pi\) |
0.507195 | + | 0.861831i | \(0.330682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9136i | 0.380759i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4968 | + | 19.4968i | 0.621852 | + | 0.621852i | 0.946005 | − | 0.324153i | \(-0.105079\pi\) |
−0.324153 | + | 0.946005i | \(0.605079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.74955 | − | 25.9134i | −0.215058 | − | 0.825669i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.40735 | −0.0765493 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7812 | −0.755435 | −0.377717 | − | 0.925921i | \(-0.623291\pi\) | ||||
−0.377717 | + | 0.925921i | \(0.623291\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.7444 | + | 15.6913i | 0.847854 | + | 0.497449i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.63985 | + | 6.63985i | 0.210286 | + | 0.210286i | 0.804389 | − | 0.594103i | \(-0.202493\pi\) |
−0.594103 | + | 0.804389i | \(0.702493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4140.2.s.a.737.8 | ✓ | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.a.737.15 | yes | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.a.2393.15 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.a.2393.8 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.a.737.8 | ✓ | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.a.737.15 | yes | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.a.2393.8 | yes | 44 | 15.8 | even | 4 | inner | |
4140.2.s.a.2393.15 | yes | 44 | 5.3 | odd | 4 | inner |