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 | 737.15 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.a.2393.15 |
$q$-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 | \(0.311343\pi\) | ||||
−0.558589 | + | 0.829444i | \(0.688657\pi\) | |||||||
\(12\) | 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 | −0.769968 | − | 0.638083i | \(-0.779728\pi\) |
0.638083 | + | 0.769968i | \(0.279728\pi\) | |||||||
\(18\) | 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 | \(-0.233852\pi\) | ||||
0.742054 | + | 0.670340i | \(0.233852\pi\) | |||||||
\(30\) | 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 | \(0.116254\pi\) | ||||
−0.934044 | + | 0.357158i | \(0.883746\pi\) | |||||||
\(42\) | 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 | \(-0.473168\pi\) |
0.996449 | − | 0.0841949i | \(-0.0268318\pi\) | |||||||
\(48\) | 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 | 0.953181 | − | 0.302400i | \(-0.0977877\pi\) |
−0.302400 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(54\) | 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 | \(-0.237558\pi\) | ||||
0.734200 | + | 0.678934i | \(0.237558\pi\) | |||||||
\(60\) | 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 | \(0.205092\pi\) | ||||
−0.799510 | + | 0.600652i | \(0.794908\pi\) | |||||||
\(72\) | 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 | 0.852362 | − | 0.522952i | \(-0.175169\pi\) |
−0.522952 | + | 0.852362i | \(0.675169\pi\) | |||||||
\(84\) | 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 | \(-0.463389\pi\) | ||||
0.114763 | + | 0.993393i | \(0.463389\pi\) | |||||||
\(90\) | 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 | \(0.225110\pi\) | ||||
−0.760182 | + | 0.649710i | \(0.774890\pi\) | |||||||
\(102\) | 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 | −0.241657 | − | 0.970362i | \(-0.577691\pi\) |
0.970362 | + | 0.241657i | \(0.0776910\pi\) | |||||||
\(108\) | 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 | 0.972520 | − | 0.232818i | \(-0.0747945\pi\) |
−0.232818 | + | 0.972520i | \(0.574794\pi\) | |||||||
\(114\) | 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 | \(0.315689\pi\) | ||||
−0.547213 | + | 0.836993i | \(0.684311\pi\) | |||||||
\(132\) | 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 | −0.595136 | − | 0.803625i | \(-0.702902\pi\) |
0.803625 | + | 0.595136i | \(0.202902\pi\) | |||||||
\(138\) | 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 | \(-0.727481\pi\) | ||||
−0.655355 | + | 0.755321i | \(0.727481\pi\) | |||||||
\(150\) | 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 | \(0.560156\pi\) |
−0.982195 | + | 0.187864i | \(0.939844\pi\) | |||||||
\(168\) | 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 | \(-0.983445\pi\) |
−0.0519851 | − | 0.998648i | \(-0.516555\pi\) | |||||||
\(174\) | 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 | \(-0.351296\pi\) | ||||
0.450358 | + | 0.892848i | \(0.351296\pi\) | |||||||
\(180\) | 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 | \(-0.714415\pi\) | ||
0.623806 | − | 0.781579i | \(-0.285585\pi\) | |||||||
\(192\) | 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 | −0.337875 | − | 0.941191i | \(-0.609708\pi\) |
0.941191 | + | 0.337875i | \(0.109708\pi\) | |||||||
\(198\) | 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 | −0.689466 | − | 0.724318i | \(-0.742155\pi\) |
0.724318 | + | 0.689466i | \(0.242155\pi\) | |||||||
\(228\) | 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 | 0.880938 | − | 0.473232i | \(-0.156913\pi\) |
−0.473232 | + | 0.880938i | \(0.656913\pi\) | |||||||
\(234\) | 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 | \(-0.510517\pi\) | ||||
−0.0330346 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(240\) | 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 | \(-0.884412\pi\) | ||
0.934790 | − | 0.355202i | \(-0.115588\pi\) | |||||||
\(252\) | 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 | \(0.523493\pi\) |
−0.997278 | + | 0.0737395i | \(0.976507\pi\) | |||||||
\(258\) | 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 | 0.438919 | − | 0.898527i | \(-0.355362\pi\) |
−0.898527 | + | 0.438919i | \(0.855362\pi\) | |||||||
\(264\) | 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 | \(-0.487811\pi\) | ||||
0.0382834 | + | 0.999267i | \(0.487811\pi\) | |||||||
\(270\) | 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 | \(0.0642597\pi\) | ||||
−0.979692 | + | 0.200509i | \(0.935740\pi\) | |||||||
\(282\) | 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 | 0.842697 | − | 0.538389i | \(-0.180967\pi\) |
−0.538389 | + | 0.842697i | \(0.680967\pi\) | |||||||
\(294\) | 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 | \(0.141485\pi\) | ||||
−0.902831 | + | 0.429995i | \(0.858515\pi\) | |||||||
\(312\) | 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 | −0.450445 | − | 0.892804i | \(-0.648735\pi\) |
0.892804 | + | 0.450445i | \(0.148735\pi\) | |||||||
\(318\) | 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 | \(-0.494391\pi\) |
0.999845 | − | 0.0176207i | \(-0.00560914\pi\) | |||||||
\(348\) | 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 | 0.426745 | − | 0.904372i | \(-0.359660\pi\) |
−0.904372 | + | 0.426745i | \(0.859660\pi\) | |||||||
\(354\) | 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 | \(-0.431223\pi\) | ||||
0.214391 | + | 0.976748i | \(0.431223\pi\) | |||||||
\(360\) | 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 | 0.907916 | − | 0.419152i | \(-0.137672\pi\) |
−0.419152 | + | 0.907916i | \(0.637672\pi\) | |||||||
\(384\) | 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 | \(-0.471869\pi\) | ||||
0.0882610 | + | 0.996097i | \(0.471869\pi\) | |||||||
\(390\) | 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 | \(0.0449632\pi\) | ||||
−0.990040 | + | 0.140787i | \(0.955037\pi\) | |||||||
\(402\) | 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 | \(-0.383516\pi\) | ||||
0.357833 | + | 0.933785i | \(0.383516\pi\) | |||||||
\(420\) | 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 | \(-0.986425\pi\) | ||
0.999091 | − | 0.0426346i | \(-0.0135751\pi\) | |||||||
\(432\) | 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 | 0.341264 | − | 0.939968i | \(-0.389145\pi\) |
−0.939968 | + | 0.341264i | \(0.889145\pi\) | |||||||
\(444\) | 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 | \(-0.647521\pi\) | ||||
−0.447038 | + | 0.894515i | \(0.647521\pi\) | |||||||
\(450\) | 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 | \(-0.933478\pi\) | ||
0.978242 | − | 0.207467i | \(-0.0665220\pi\) | |||||||
\(462\) | 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 | −0.551940 | − | 0.833884i | \(-0.686112\pi\) |
0.833884 | + | 0.551940i | \(0.186112\pi\) | |||||||
\(468\) | 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 | \(-0.704251\pi\) | ||||
−0.598537 | + | 0.801095i | \(0.704251\pi\) | |||||||
\(480\) | 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 | \(-0.999542\pi\) | ||
0.999999 | − | 0.00143999i | \(-0.000458363\pi\) | |||||||
\(492\) | 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 | \(-0.863526\pi\) |
−0.415729 | − | 0.909489i | \(-0.636474\pi\) | |||||||
\(504\) | 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 | \(-0.910568\pi\) | ||||
−0.960790 | + | 0.277277i | \(0.910568\pi\) | |||||||
\(510\) | 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 | \(0.0226212\pi\) | ||||
−0.997476 | + | 0.0710067i | \(0.977379\pi\) | |||||||
\(522\) | 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 | −0.894891 | − | 0.446285i | \(-0.852747\pi\) |
0.446285 | + | 0.894891i | \(0.352747\pi\) | |||||||
\(558\) | 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 | 0.0482965 | − | 0.998833i | \(-0.484621\pi\) |
−0.998833 | + | 0.0482965i | \(0.984621\pi\) | |||||||
\(564\) | 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 | \(-0.554888\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554888\pi\) | |||||||
\(570\) | 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 | −0.463873 | − | 0.885902i | \(-0.653541\pi\) |
0.885902 | + | 0.463873i | \(0.153541\pi\) | |||||||
\(588\) | 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 | 0.0309386 | − | 0.999521i | \(-0.490150\pi\) |
−0.999521 | + | 0.0309386i | \(0.990150\pi\) | |||||||
\(594\) | 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 | \(-0.250189\pi\) | ||||
0.706687 | + | 0.707527i | \(0.250189\pi\) | |||||||
\(600\) | 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 | −0.968082 | − | 0.250633i | \(-0.919361\pi\) |
0.250633 | + | 0.968082i | \(0.419361\pi\) | |||||||
\(618\) | 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 | \(0.0776062\pi\) | ||||
−0.970426 | + | 0.241399i | \(0.922394\pi\) | |||||||
\(642\) | 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 | −0.999592 | − | 0.0285693i | \(-0.990905\pi\) |
0.0285693 | + | 0.999592i | \(0.490905\pi\) | |||||||
\(648\) | 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 | \(-0.848251\pi\) |
−0.458881 | − | 0.888498i | \(-0.651749\pi\) | |||||||
\(654\) | 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 | \(-0.201118\pi\) | ||||
0.806948 | + | 0.590623i | \(0.201118\pi\) | |||||||
\(660\) | 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 | −0.954600 | − | 0.297890i | \(-0.903717\pi\) |
0.297890 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(678\) | 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 | 0.936883 | − | 0.349643i | \(-0.113697\pi\) |
−0.349643 | + | 0.936883i | \(0.613697\pi\) | |||||||
\(684\) | 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 | \(0.0553065\pi\) | ||||
−0.984943 | + | 0.172877i | \(0.944694\pi\) | |||||||
\(702\) | 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 | \(-0.730320\pi\) | ||||
−0.662065 | + | 0.749446i | \(0.730320\pi\) | |||||||
\(720\) | 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 | 0.625906 | − | 0.779898i | \(-0.284729\pi\) |
−0.779898 | + | 0.625906i | \(0.784729\pi\) | |||||||
\(744\) | 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 | \(-0.921216\pi\) | ||
0.969526 | − | 0.244989i | \(-0.0787842\pi\) | |||||||
\(762\) | 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 | 0.183464 | − | 0.983026i | \(-0.441269\pi\) |
−0.983026 | + | 0.183464i | \(0.941269\pi\) | |||||||
\(774\) | 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 | −0.747664 | − | 0.664078i | \(-0.768824\pi\) |
0.664078 | + | 0.747664i | \(0.268824\pi\) | |||||||
\(798\) | 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 | \(-0.529435\pi\) | ||||
−0.0923402 | + | 0.995728i | \(0.529435\pi\) | |||||||
\(810\) | 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 | \(-0.950082\pi\) | ||
0.987729 | − | 0.156179i | \(-0.0499176\pi\) | |||||||
\(822\) | 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 | −0.692302 | − | 0.721608i | \(-0.743403\pi\) |
0.721608 | + | 0.692302i | \(0.243403\pi\) | |||||||
\(828\) | 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 | \(-0.547961\pi\) | ||||
−0.150106 | + | 0.988670i | \(0.547961\pi\) | |||||||
\(840\) | 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 | −0.540168 | − | 0.841557i | \(-0.681639\pi\) |
0.841557 | + | 0.540168i | \(0.181639\pi\) | |||||||
\(858\) | 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 | \(0.00473279\pi\) |
0.0148680 | + | 0.999889i | \(0.495267\pi\) | |||||||
\(864\) | 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 | \(0.158943\pi\) | ||||
−0.877902 | + | 0.478840i | \(0.841057\pi\) | |||||||
\(882\) | 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 | \(-0.473717\pi\) |
0.996593 | − | 0.0824752i | \(-0.0262825\pi\) | |||||||
\(888\) | 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 | \(-0.923163\pi\) | ||
0.971006 | − | 0.239054i | \(-0.0768373\pi\) | |||||||
\(912\) | 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 | \(-0.418514\pi\) | ||||
0.253209 | + | 0.967412i | \(0.418514\pi\) | |||||||
\(930\) | 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 | \(-0.999485\pi\) | ||
0.999999 | − | 0.00161926i | \(-0.000515427\pi\) | |||||||
\(942\) | 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 | −0.977765 | − | 0.209703i | \(-0.932750\pi\) |
0.209703 | + | 0.977765i | \(0.432750\pi\) | |||||||
\(948\) | 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 | 0.338988 | − | 0.940791i | \(-0.389915\pi\) |
−0.940791 | + | 0.338988i | \(0.889915\pi\) | |||||||
\(954\) | 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 | \(-0.962428\pi\) | ||
0.993042 | − | 0.117763i | \(-0.0375722\pi\) | |||||||
\(972\) | 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 | −0.507195 | − | 0.861831i | \(-0.669318\pi\) |
0.861831 | + | 0.507195i | \(0.169318\pi\) | |||||||
\(978\) | 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 | 0.324153 | − | 0.946005i | \(-0.394921\pi\) |
−0.946005 | + | 0.324153i | \(0.894921\pi\) | |||||||
\(984\) | 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.737.15 | yes | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.a.737.8 | ✓ | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.a.2393.8 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.a.2393.15 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.a.737.8 | ✓ | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.a.737.15 | yes | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.a.2393.8 | yes | 44 | 5.3 | odd | 4 | inner | |
4140.2.s.a.2393.15 | yes | 44 | 15.8 | even | 4 | inner |