Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(289,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.bl (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.11 | ||
Character | \(\chi\) | \(=\) | 1920.289 |
Dual form | 1920.2.bl.b.1249.11 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23019 | + | 0.162008i | 0.997372 | + | 0.0724524i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93661 | 1.10994 | 0.554968 | − | 0.831872i | \(-0.312731\pi\) | ||||
0.554968 | + | 0.831872i | \(0.312731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.663996 | + | 0.663996i | −0.200202 | + | 0.200202i | −0.800087 | − | 0.599884i | \(-0.795213\pi\) |
0.599884 | + | 0.800087i | \(0.295213\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.12767 | − | 1.12767i | 0.312758 | − | 0.312758i | −0.533219 | − | 0.845977i | \(-0.679018\pi\) |
0.845977 | + | 0.533219i | \(0.179018\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.69154 | + | 1.46243i | −0.436754 | + | 0.377597i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.47528i | − | 1.81302i | −0.422182 | − | 0.906511i | \(-0.638736\pi\) | ||
0.422182 | − | 0.906511i | \(-0.361264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.423555 | + | 0.423555i | 0.0971702 | + | 0.0971702i | 0.754021 | − | 0.656851i | \(-0.228112\pi\) |
−0.656851 | + | 0.754021i | \(0.728112\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.07650 | + | 2.07650i | −0.453129 | + | 0.453129i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.17642 | 1.28787 | 0.643936 | − | 0.765079i | \(-0.277300\pi\) | ||||
0.643936 | + | 0.765079i | \(0.277300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.94751 | + | 0.722620i | 0.989501 | + | 0.144524i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.95128 | + | 2.95128i | 0.548038 | + | 0.548038i | 0.925873 | − | 0.377835i | \(-0.123331\pi\) |
−0.377835 | + | 0.925873i | \(0.623331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82581 | −0.327924 | −0.163962 | − | 0.986467i | \(-0.552428\pi\) | ||||
−0.163962 | + | 0.986467i | \(0.552428\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.939032i | − | 0.163465i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.54921 | + | 0.475756i | 1.10702 | + | 0.0804175i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.53509 | − | 5.53509i | −0.909963 | − | 0.909963i | 0.0863055 | − | 0.996269i | \(-0.472494\pi\) |
−0.996269 | + | 0.0863055i | \(0.972494\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.59476i | 0.255366i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12.3694i | − | 1.93178i | −0.258959 | − | 0.965888i | \(-0.583380\pi\) | ||
0.258959 | − | 0.965888i | \(-0.416620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.897614 | − | 0.897614i | −0.136885 | − | 0.136885i | 0.635344 | − | 0.772229i | \(-0.280858\pi\) |
−0.772229 | + | 0.635344i | \(0.780858\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.162008 | − | 2.23019i | 0.0241508 | − | 0.332457i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.12733i | − | 0.602033i | −0.953619 | − | 0.301017i | \(-0.902674\pi\) | ||
0.953619 | − | 0.301017i | \(-0.0973260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.62370 | 0.231956 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.28582 | + | 5.28582i | 0.740163 | + | 0.740163i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.146479 | + | 0.146479i | 0.0201204 | + | 0.0201204i | 0.717095 | − | 0.696975i | \(-0.245471\pi\) |
−0.696975 | + | 0.717095i | \(0.745471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58841 | + | 1.37327i | −0.214181 | + | 0.185171i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.598997 | −0.0793391 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.72645 | + | 7.72645i | −1.00590 | + | 1.00590i | −0.00591515 | + | 0.999983i | \(0.501883\pi\) |
−0.999983 | + | 0.00591515i | \(0.998117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.37519 | + | 7.37519i | 0.944297 | + | 0.944297i | 0.998528 | − | 0.0542318i | \(-0.0172710\pi\) |
−0.0542318 | + | 0.998528i | \(0.517271\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.93661i | − | 0.369978i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.69760 | − | 2.33222i | 0.334597 | − | 0.289276i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.68265 | + | 8.68265i | −1.06075 | + | 1.06075i | −0.0627239 | + | 0.998031i | \(0.519979\pi\) |
−0.998031 | + | 0.0627239i | \(0.980021\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.36739 | + | 4.36739i | −0.525772 | + | 0.525772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.95735i | 1.06304i | 0.847045 | + | 0.531521i | \(0.178379\pi\) | ||||
−0.847045 | + | 0.531521i | \(0.821621\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.174246 | −0.0203940 | −0.0101970 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101970 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.00938 | + | 2.98745i | −0.462964 | + | 0.344961i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.94990 | + | 1.94990i | −0.222212 | + | 0.222212i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.06488 | −0.344826 | −0.172413 | − | 0.985025i | \(-0.555156\pi\) | ||||
−0.172413 | + | 0.985025i | \(0.555156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.18751 | − | 9.18751i | 1.00846 | − | 1.00846i | 0.00849620 | − | 0.999964i | \(-0.497296\pi\) |
0.999964 | − | 0.00849620i | \(-0.00270446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21106 | − | 16.6713i | 0.131358 | − | 1.80826i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.17374 | −0.447471 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.71473i | 0.923760i | 0.886942 | + | 0.461880i | \(0.152825\pi\) | ||||
−0.886942 | + | 0.461880i | \(0.847175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.31152 | − | 3.31152i | 0.347142 | − | 0.347142i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.29104 | − | 1.29104i | 0.133875 | − | 0.133875i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.875989 | + | 1.01323i | 0.0898746 | + | 0.103955i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.5481i | − | 1.07100i | −0.844535 | − | 0.535500i | \(-0.820123\pi\) | ||
0.844535 | − | 0.535500i | \(-0.179877\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.663996 | + | 0.663996i | 0.0667341 | + | 0.0667341i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.65550 | − | 9.65550i | 0.960758 | − | 0.960758i | −0.0385005 | − | 0.999259i | \(-0.512258\pi\) |
0.999259 | + | 0.0385005i | \(0.0122581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5564 | 1.43428 | 0.717141 | − | 0.696928i | \(-0.245450\pi\) | ||||
0.717141 | + | 0.696928i | \(0.245450\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.96740 | + | 4.29458i | −0.484769 | + | 0.419108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.86260 | + | 5.86260i | 0.566759 | + | 0.566759i | 0.931219 | − | 0.364460i | \(-0.118747\pi\) |
−0.364460 | + | 0.931219i | \(0.618747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.91625 | − | 4.91625i | −0.470891 | − | 0.470891i | 0.431312 | − | 0.902203i | \(-0.358051\pi\) |
−0.902203 | + | 0.431312i | \(0.858051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.82780 | 0.742982 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.8334i | 1.20726i | 0.797263 | + | 0.603632i | \(0.206280\pi\) | ||||
−0.797263 | + | 0.603632i | \(0.793720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.7746 | + | 1.00063i | 1.28449 | + | 0.0933094i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12767 | − | 1.12767i | −0.104253 | − | 0.104253i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 21.9520i | − | 2.01234i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1182i | 0.919838i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.74649 | + | 8.74649i | 0.788644 | + | 0.788644i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9168 | + | 2.41312i | 0.976430 | + | 0.215836i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.07042i | 0.0949847i | 0.998872 | + | 0.0474924i | \(0.0151230\pi\) | ||||
−0.998872 | + | 0.0474924i | \(0.984877\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.26942 | 0.111766 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9024 | − | 10.9024i | −0.952545 | − | 0.952545i | 0.0463789 | − | 0.998924i | \(-0.485232\pi\) |
−0.998924 | + | 0.0463789i | \(0.985232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.24382 | + | 1.24382i | 0.107853 | + | 0.107853i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.46243 | + | 1.69154i | 0.125866 | + | 0.145585i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0549 | 0.859046 | 0.429523 | − | 0.903056i | \(-0.358682\pi\) | ||||
0.429523 | + | 0.903056i | \(0.358682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.90773 | − | 2.90773i | 0.246630 | − | 0.246630i | −0.572956 | − | 0.819586i | \(-0.694203\pi\) |
0.819586 | + | 0.572956i | \(0.194203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.91847 | + | 2.91847i | 0.245779 | + | 0.245779i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.49753i | 0.125230i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.10378 | + | 7.06004i | 0.506891 | + | 0.586305i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.14813 | + | 1.14813i | −0.0946958 | + | 0.0946958i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.26131 | − | 1.26131i | 0.103331 | − | 0.103331i | −0.653551 | − | 0.756882i | \(-0.726722\pi\) |
0.756882 | + | 0.653551i | \(0.226722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4739i | 1.66614i | 0.553169 | + | 0.833069i | \(0.313418\pi\) | ||||
−0.553169 | + | 0.833069i | \(0.686582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.47528 | −0.604341 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.07190 | − | 0.295796i | −0.327063 | − | 0.0237589i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.13344 | + | 8.13344i | −0.649119 | + | 0.649119i | −0.952780 | − | 0.303661i | \(-0.901791\pi\) |
0.303661 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.207152 | −0.0164282 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.1377 | 1.42945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.08947 | − | 4.08947i | 0.320312 | − | 0.320312i | −0.528575 | − | 0.848887i | \(-0.677273\pi\) |
0.848887 | + | 0.528575i | \(0.177273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.152131 | − | 2.09422i | 0.0118434 | − | 0.163035i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.52867 | 0.737350 | 0.368675 | − | 0.929558i | \(-0.379811\pi\) | ||||
0.368675 | + | 0.929558i | \(0.379811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4567i | 0.804364i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.423555 | − | 0.423555i | 0.0323901 | − | 0.0323901i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.18234 | − | 6.18234i | 0.470035 | − | 0.470035i | −0.431891 | − | 0.901926i | \(-0.642153\pi\) |
0.901926 | + | 0.431891i | \(0.142153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.5289 | + | 2.12205i | 1.09828 | + | 0.160412i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.9268i | − | 0.821312i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3548 | − | 10.3548i | −0.773954 | − | 0.773954i | 0.204841 | − | 0.978795i | \(-0.434332\pi\) |
−0.978795 | + | 0.204841i | \(0.934332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.98013 | + | 5.98013i | −0.444500 | + | 0.444500i | −0.893521 | − | 0.449021i | \(-0.851773\pi\) |
0.449021 | + | 0.893521i | \(0.351773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4301 | −0.771015 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.4476 | − | 13.2410i | −0.841643 | − | 0.973501i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.96356 | + | 4.96356i | 0.362971 | + | 0.362971i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.07650 | + | 2.07650i | 0.151043 | + | 0.151043i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.404932 | 0.0292998 | 0.0146499 | − | 0.999893i | \(-0.495337\pi\) | ||||
0.0146499 | + | 0.999893i | \(0.495337\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.48969i | − | 0.467138i | −0.972340 | − | 0.233569i | \(-0.924959\pi\) | ||
0.972340 | − | 0.233569i | \(-0.0750405\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.258365 | + | 3.55662i | −0.0185019 | + | 0.254695i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.4425 | + | 18.4425i | 1.31397 | + | 1.31397i | 0.918460 | + | 0.395514i | \(0.129434\pi\) |
0.395514 | + | 0.918460i | \(0.370566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4696i | 0.954833i | 0.878677 | + | 0.477417i | \(0.158427\pi\) | ||||
−0.878677 | + | 0.477417i | \(0.841573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 12.2791i | − | 0.866103i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.66676 | + | 8.66676i | 0.608287 | + | 0.608287i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00395 | − | 27.5861i | 0.139962 | − | 1.92670i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.17642i | − | 0.429291i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.562478 | −0.0389074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.07749 | + | 6.07749i | 0.418392 | + | 0.418392i | 0.884649 | − | 0.466257i | \(-0.154398\pi\) |
−0.466257 | + | 0.884649i | \(0.654398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.33380 | − | 6.33380i | −0.433985 | − | 0.433985i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.85643 | − | 2.14727i | −0.126607 | − | 0.146443i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.36168 | −0.363975 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.123211 | − | 0.123211i | 0.00832581 | − | 0.00832581i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.42963 | − | 8.42963i | −0.567038 | − | 0.567038i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0794i | 1.47855i | 0.673405 | + | 0.739273i | \(0.264831\pi\) | ||||
−0.673405 | + | 0.739273i | \(0.735169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.722620 | − | 4.94751i | 0.0481746 | − | 0.329834i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.55919 | − | 5.55919i | 0.368977 | − | 0.368977i | −0.498127 | − | 0.867104i | \(-0.665979\pi\) |
0.867104 | + | 0.498127i | \(0.165979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8223 | + | 11.8223i | −0.781242 | + | 0.781242i | −0.980040 | − | 0.198798i | \(-0.936296\pi\) |
0.198798 | + | 0.980040i | \(0.436296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.75757i | − | 0.181435i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.92024 | 0.584385 | 0.292192 | − | 0.956360i | \(-0.405615\pi\) | ||||
0.292192 | + | 0.956360i | \(0.405615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.668663 | − | 9.20474i | 0.0436188 | − | 0.600451i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.16720 | − | 2.16720i | 0.140775 | − | 0.140775i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9320 | −1.48335 | −0.741673 | − | 0.670762i | \(-0.765967\pi\) | ||||
−0.741673 | + | 0.670762i | \(0.765967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.48232 | −0.417563 | −0.208781 | − | 0.977962i | \(-0.566950\pi\) | ||||
−0.208781 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.62115 | + | 0.263052i | 0.231347 | + | 0.0168058i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.955258 | 0.0607816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9931i | 0.823404i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.4218 | − | 14.4218i | 0.910293 | − | 0.910293i | −0.0860018 | − | 0.996295i | \(-0.527409\pi\) |
0.996295 | + | 0.0860018i | \(0.0274091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.10112 | + | 4.10112i | −0.257835 | + | 0.257835i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.9320 | + | 12.6447i | 0.684591 | + | 0.791844i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.193739i | 0.0120851i | 0.999982 | + | 0.00604256i | \(0.00192342\pi\) | ||||
−0.999982 | + | 0.00604256i | \(0.998077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.2544 | − | 16.2544i | −1.01000 | − | 1.01000i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.95128 | − | 2.95128i | 0.182679 | − | 0.182679i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.5708 | −1.02180 | −0.510900 | − | 0.859640i | \(-0.670688\pi\) | ||||
−0.510900 | + | 0.859640i | \(0.670688\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.302944 | + | 0.350406i | 0.0186097 | + | 0.0215253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.16225 | − | 6.16225i | −0.377123 | − | 0.377123i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.09381 | − | 7.09381i | −0.432517 | − | 0.432517i | 0.456967 | − | 0.889484i | \(-0.348936\pi\) |
−0.889484 | + | 0.456967i | \(0.848936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.62278 | −0.159323 | −0.0796613 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796613 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.68320i | 0.283440i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.76494 | + | 2.80531i | −0.227035 | + | 0.169166i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.97533 | − | 7.97533i | −0.479191 | − | 0.479191i | 0.425682 | − | 0.904873i | \(-0.360034\pi\) |
−0.904873 | + | 0.425682i | \(0.860034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.82581i | 0.109308i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.97850i | 0.595267i | 0.954680 | + | 0.297634i | \(0.0961974\pi\) | ||||
−0.954680 | + | 0.297634i | \(0.903803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4056 | − | 20.4056i | −1.21299 | − | 1.21299i | −0.970040 | − | 0.242946i | \(-0.921886\pi\) |
−0.242946 | − | 0.970040i | \(-0.578114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.33588 | − | 0.0970426i | −0.0791306 | − | 0.00574831i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 36.3242i | − | 2.14415i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.8798 | −2.28705 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.45865 | + | 7.45865i | 0.437234 | + | 0.437234i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.65889 | + | 4.65889i | 0.272175 | + | 0.272175i | 0.829975 | − | 0.557800i | \(-0.188354\pi\) |
−0.557800 | + | 0.829975i | \(0.688354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.4832 | + | 15.9797i | −1.07613 | + | 0.930374i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.939032 | −0.0544882 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.96494 | − | 6.96494i | 0.402793 | − | 0.402793i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.63594 | − | 2.63594i | −0.151933 | − | 0.151933i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.6549i | 0.784456i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.2532 | + | 17.6429i | 0.873398 | + | 1.01023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.05487 | + | 9.05487i | −0.516789 | + | 0.516789i | −0.916598 | − | 0.399810i | \(-0.869076\pi\) |
0.399810 | + | 0.916598i | \(0.369076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.2929 | + | 10.2929i | −0.585543 | + | 0.585543i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.39349i | 0.192427i | 0.995361 | + | 0.0962137i | \(0.0306732\pi\) | ||||
−0.995361 | + | 0.0962137i | \(0.969327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8943 | −0.615784 | −0.307892 | − | 0.951421i | \(-0.599624\pi\) | ||||
−0.307892 | + | 0.951421i | \(0.599624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.475756 | − | 6.54921i | 0.0268058 | − | 0.369006i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.45776 | − | 3.45776i | 0.194207 | − | 0.194207i | −0.603304 | − | 0.797511i | \(-0.706149\pi\) |
0.797511 | + | 0.603304i | \(0.206149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.91927 | −0.219437 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.29096 | −0.462756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.16619 | − | 3.16619i | 0.176172 | − | 0.176172i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.39401 | − | 4.76426i | 0.354676 | − | 0.264274i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.95263 | 0.384481 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.1204i | − | 0.668218i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.9246 | + | 24.9246i | −1.36998 | + | 1.36998i | −0.509526 | + | 0.860455i | \(0.670179\pi\) |
−0.860455 | + | 0.509526i | \(0.829821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.53509 | + | 5.53509i | −0.303321 | + | 0.303321i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.7706 | + | 17.9573i | −1.13482 | + | 0.981113i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.62502i | 0.524308i | 0.965026 | + | 0.262154i | \(0.0844329\pi\) | ||||
−0.965026 | + | 0.262154i | \(0.915567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.07458 | − | 9.07458i | −0.492863 | − | 0.492863i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.21233 | − | 1.21233i | 0.0656512 | − | 0.0656512i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7881 | −0.852479 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.4477 | + | 9.03256i | −0.562483 | + | 0.486296i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.9302 | − | 15.9302i | −0.855178 | − | 0.855178i | 0.135588 | − | 0.990765i | \(-0.456708\pi\) |
−0.990765 | + | 0.135588i | \(0.956708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.56134 | + | 4.56134i | 0.244163 | + | 0.244163i | 0.818570 | − | 0.574407i | \(-0.194767\pi\) |
−0.574407 | + | 0.818570i | \(0.694767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.59476 | 0.0851221 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1314i | 0.752141i | 0.926591 | + | 0.376070i | \(0.122725\pi\) | ||||
−0.926591 | + | 0.376070i | \(0.877275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.45117 | + | 19.9766i | −0.0770199 | + | 1.06025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.5224 | + | 15.5224i | 0.821533 | + | 0.821533i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.2588i | − | 1.33311i | −0.745456 | − | 0.666555i | \(-0.767768\pi\) | ||
0.745456 | − | 0.666555i | \(-0.232232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.6412i | − | 0.981116i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.15466 | − | 7.15466i | −0.375522 | − | 0.375522i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.388602 | − | 0.0282294i | −0.0203404 | − | 0.00147759i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.01381i | − | 0.157320i | −0.996902 | − | 0.0786598i | \(-0.974936\pi\) | ||
0.996902 | − | 0.0786598i | \(-0.0250641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3694 | −0.643925 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.430151 | + | 0.430151i | 0.0223323 | + | 0.0223323i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1060 | + | 13.1060i | 0.678604 | + | 0.678604i | 0.959684 | − | 0.281080i | \(-0.0906927\pi\) |
−0.281080 | + | 0.959684i | \(0.590693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.42569 | + | 6.01302i | −0.486740 | + | 0.310511i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.65611 | 0.342807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.34584 | − | 8.34584i | 0.428697 | − | 0.428697i | −0.459487 | − | 0.888184i | \(-0.651967\pi\) |
0.888184 | + | 0.459487i | \(0.151967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.756904 | − | 0.756904i | −0.0387774 | − | 0.0387774i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 25.5695i | − | 1.30654i | −0.757124 | − | 0.653271i | \(-0.773396\pi\) | ||
0.757124 | − | 0.653271i | \(-0.226604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.66455 | + | 4.03275i | −0.237727 | + | 0.205528i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.897614 | + | 0.897614i | −0.0456283 | + | 0.0456283i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.31954 | + | 4.31954i | −0.219009 | + | 0.219009i | −0.808081 | − | 0.589072i | \(-0.799494\pi\) |
0.589072 | + | 0.808081i | \(0.299494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 46.1705i | − | 2.33494i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.4183 | 0.777750 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.83528 | − | 0.496537i | −0.343920 | − | 0.0249835i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.5750 | + | 23.5750i | −1.18319 | + | 1.18319i | −0.204281 | + | 0.978912i | \(0.565485\pi\) |
−0.978912 | + | 0.204281i | \(0.934515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.75902 | −0.0880613 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1100 | 0.854430 | 0.427215 | − | 0.904150i | \(-0.359495\pi\) | ||||
0.427215 | + | 0.904150i | \(0.359495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.05890 | + | 2.05890i | −0.102561 | + | 0.102561i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.23019 | − | 0.162008i | −0.110819 | − | 0.00805026i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.35056 | 0.364354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2659i | 1.24932i | 0.780897 | + | 0.624659i | \(0.214762\pi\) | ||||
−0.780897 | + | 0.624659i | \(0.785238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.10987 | + | 7.10987i | −0.350704 | + | 0.350704i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.6896 | + | 22.6896i | −1.11648 | + | 1.11648i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.9784 | − | 19.0014i | 1.07888 | − | 0.932744i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.11215i | 0.201373i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.7885 | − | 15.7885i | −0.771317 | − | 0.771317i | 0.207020 | − | 0.978337i | \(-0.433624\pi\) |
−0.978337 | + | 0.207020i | \(0.933624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.64861 | − | 4.64861i | 0.226559 | − | 0.226559i | −0.584694 | − | 0.811254i | \(-0.698786\pi\) |
0.811254 | + | 0.584694i | \(0.198786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.12733 | −0.200678 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.40179 | − | 36.9840i | 0.262025 | − | 1.79399i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.6581 | + | 21.6581i | 1.04811 | + | 1.04811i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.05892 | − | 1.05892i | −0.0511249 | − | 0.0511249i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6320 | 1.37915 | 0.689577 | − | 0.724213i | \(-0.257797\pi\) | ||||
0.689577 | + | 0.724213i | \(0.257797\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.14954i | 0.295528i | 0.989023 | + | 0.147764i | \(0.0472076\pi\) | ||||
−0.989023 | + | 0.147764i | \(0.952792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.30823 | − | 0.676180i | −0.446295 | − | 0.0324204i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.61605 | + | 2.61605i | 0.125143 | + | 0.125143i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 37.8541i | − | 1.80668i | −0.428926 | − | 0.903340i | \(-0.641108\pi\) | ||
0.428926 | − | 0.903340i | \(-0.358892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.62370i | − | 0.0773188i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.41746 | + | 3.41746i | 0.162368 | + | 0.162368i | 0.783615 | − | 0.621247i | \(-0.213373\pi\) |
−0.621247 | + | 0.783615i | \(0.713373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.41186 | + | 19.4355i | −0.0669286 | + | 0.921332i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.78376i | 0.0843691i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.6935 | −1.49571 | −0.747855 | − | 0.663862i | \(-0.768916\pi\) | ||||
−0.747855 | + | 0.663862i | \(0.768916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.21324 | + | 8.21324i | 0.386746 | + | 0.386746i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4772 | − | 14.4772i | −0.680198 | − | 0.680198i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.92182 | − | 6.84883i | 0.371381 | − | 0.321078i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.26208 | 0.339706 | 0.169853 | − | 0.985469i | \(-0.445671\pi\) | ||||
0.169853 | + | 0.985469i | \(0.445671\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.28582 | − | 5.28582i | 0.246721 | − | 0.246721i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.1568 | − | 16.1568i | −0.752499 | − | 0.752499i | 0.222446 | − | 0.974945i | \(-0.428596\pi\) |
−0.974945 | + | 0.222446i | \(0.928596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.4637i | − | 0.625710i | −0.949801 | − | 0.312855i | \(-0.898715\pi\) | ||
0.949801 | − | 0.312855i | \(-0.101285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.08842 | − | 2.67011i | 0.143222 | − | 0.123823i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.5630 | + | 10.5630i | −0.488795 | + | 0.488795i | −0.907926 | − | 0.419131i | \(-0.862335\pi\) |
0.419131 | + | 0.907926i | \(0.362335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.4976 | + | 25.4976i | −1.17737 | + | 1.17737i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.5024i | − | 0.530003i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.19202 | 0.0548093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.78947 | + | 2.40161i | 0.0821066 | + | 0.110193i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.146479 | − | 0.146479i | 0.00670679 | − | 0.00670679i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.2747 | −1.56605 | −0.783026 | − | 0.621989i | \(-0.786325\pi\) | ||||
−0.783026 | + | 0.621989i | \(0.786325\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.4835 | −0.569197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.8253 | + | 12.8253i | −0.583573 | + | 0.583573i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.70888 | − | 23.5243i | 0.0775964 | − | 1.06818i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.4994 | −1.51800 | −0.759002 | − | 0.651088i | \(-0.774313\pi\) | ||||
−0.759002 | + | 0.651088i | \(0.774313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.78338i | 0.261533i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.491541 | − | 0.491541i | 0.0221829 | − | 0.0221829i | −0.695928 | − | 0.718111i | \(-0.745007\pi\) |
0.718111 | + | 0.695928i | \(0.245007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0616 | − | 22.0616i | 0.993606 | − | 0.993606i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.37327 | + | 1.58841i | 0.0617237 | + | 0.0713938i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.3043i | 1.17991i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.863504 | − | 0.863504i | −0.0386557 | − | 0.0386557i | 0.687515 | − | 0.726170i | \(-0.258702\pi\) |
−0.726170 | + | 0.687515i | \(0.758702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.73779 | + | 6.73779i | −0.301022 | + | 0.301022i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.8335 | 0.572218 | 0.286109 | − | 0.958197i | \(-0.407638\pi\) | ||||
0.286109 | + | 0.958197i | \(0.407638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.0979 | − | 19.9693i | 1.02784 | − | 0.888624i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.39403 | − | 7.39403i | −0.328380 | − | 0.328380i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6692 | + | 12.6692i | 0.561554 | + | 0.561554i | 0.929749 | − | 0.368194i | \(-0.120024\pi\) |
−0.368194 | + | 0.929749i | \(0.620024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.511694 | −0.0226360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.598997i | 0.0264464i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.4635 | + | 2.35825i | 1.43051 | + | 0.103917i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.74053 | + | 2.74053i | 0.120529 | + | 0.120529i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.74315i | 0.383782i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.2561i | 1.32554i | 0.748821 | + | 0.662772i | \(0.230620\pi\) | ||||
−0.748821 | + | 0.662772i | \(0.769380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.01063 | − | 4.01063i | −0.175373 | − | 0.175373i | 0.613962 | − | 0.789335i | \(-0.289575\pi\) |
−0.789335 | + | 0.613962i | \(0.789575\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.7740 | + | 8.77297i | −0.513860 | + | 0.382884i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.6484i | 0.594534i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1481 | 0.658615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.72645 | + | 7.72645i | 0.335299 | + | 0.335299i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.9486 | − | 13.9486i | −0.604179 | − | 0.604179i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1249 | + | 14.0245i | 0.524206 | + | 0.606332i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.6439 | 0.631931 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.07813 | + | 1.07813i | −0.0464382 | + | 0.0464382i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.53130 | + | 5.53130i | 0.237809 | + | 0.237809i | 0.815942 | − | 0.578133i | \(-0.196219\pi\) |
−0.578133 | + | 0.815942i | \(0.696219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.45718i | − | 0.362932i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.1677 | − | 11.7607i | −0.435537 | − | 0.503771i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6141 | + | 22.6141i | −0.966908 | + | 0.966908i | −0.999470 | − | 0.0325622i | \(-0.989633\pi\) |
0.0325622 | + | 0.999470i | \(0.489633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.37519 | − | 7.37519i | 0.314766 | − | 0.314766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.50006i | 0.106506i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.00038 | −0.382735 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.4575 | + | 1.26817i | 0.741029 | + | 0.0538308i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.08239 | + | 6.08239i | −0.257719 | + | 0.257719i | −0.824126 | − | 0.566407i | \(-0.808333\pi\) |
0.566407 | + | 0.824126i | \(0.308333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.02442 | −0.0856238 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.01953 | −0.296365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.1946 | + | 23.1946i | −0.977536 | + | 0.977536i | −0.999753 | − | 0.0222176i | \(-0.992927\pi\) |
0.0222176 | + | 0.999753i | \(0.492927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.07912 | + | 28.6209i | −0.0874692 | + | 1.20409i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.93661 | −0.123326 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.31584i | 0.0551629i | 0.999620 | + | 0.0275815i | \(0.00878056\pi\) | ||||
−0.999620 | + | 0.0275815i | \(0.991219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2083 | − | 18.2083i | 0.761993 | − | 0.761993i | −0.214690 | − | 0.976682i | \(-0.568874\pi\) |
0.976682 | + | 0.214690i | \(0.0688740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.286330 | + | 0.286330i | −0.0119616 | + | 0.0119616i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.5579 | + | 4.46320i | 1.27435 | + | 0.186128i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 8.13617i | − | 0.338713i | −0.985555 | − | 0.169357i | \(-0.945831\pi\) | ||
0.985555 | − | 0.169357i | \(-0.0541689\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.58891 | + | 4.58891i | 0.190708 | + | 0.190708i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.9802 | − | 26.9802i | 1.11933 | − | 1.11933i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.194522 | −0.00805629 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.33222 | − | 2.69760i | −0.0964255 | − | 0.111532i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.4231 | − | 13.4231i | −0.554030 | − | 0.554030i | 0.373572 | − | 0.927601i | \(-0.378133\pi\) |
−0.927601 | + | 0.373572i | \(0.878133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.773329 | − | 0.773329i | −0.0318645 | − | 0.0318645i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.0816 | −1.07286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.9386i | − | 0.736649i | −0.929697 | − | 0.368324i | \(-0.879932\pi\) | ||
0.929697 | − | 0.368324i | \(-0.120068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.55641 | − | 48.9572i | 0.145799 | − | 2.00705i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.52443 | − | 9.52443i | −0.389809 | − | 0.389809i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.98863i | 0.162971i | 0.996675 | + | 0.0814855i | \(0.0259664\pi\) | ||||
−0.996675 | + | 0.0814855i | \(0.974034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.7775i | − | 0.847532i | −0.905772 | − | 0.423766i | \(-0.860708\pi\) | ||
0.905772 | − | 0.423766i | \(-0.139292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.68265 | + | 8.68265i | 0.353585 | + | 0.353585i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63924 | + | 22.5656i | −0.0666445 | + | 0.917421i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.0393i | 1.86868i | 0.356384 | + | 0.934340i | \(0.384010\pi\) | ||||
−0.356384 | + | 0.934340i | \(0.615990\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.2566 | −0.496664 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.65426 | − | 4.65426i | −0.188291 | − | 0.188291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9783 | + | 13.9783i | 0.564580 | + | 0.564580i | 0.930605 | − | 0.366025i | \(-0.119282\pi\) |
−0.366025 | + | 0.930605i | \(0.619282\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.0893 | + | 20.9234i | 0.729433 | + | 0.843711i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.5135 | 1.34920 | 0.674601 | − | 0.738182i | \(-0.264316\pi\) | ||||
0.674601 | + | 0.738182i | \(0.264316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.64277 | + | 4.64277i | −0.186609 | + | 0.186609i | −0.794228 | − | 0.607620i | \(-0.792125\pi\) |
0.607620 | + | 0.794228i | \(0.292125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.36739 | + | 4.36739i | 0.175257 | + | 0.175257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.5918i | 1.02531i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9556 | + | 7.15033i | 0.958226 | + | 0.286013i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.397732 | − | 0.397732i | 0.0158839 | − | 0.0158839i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.3764 | + | 41.3764i | −1.64978 | + | 1.64978i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.43412i | − | 0.176519i | −0.996097 | − | 0.0882597i | \(-0.971869\pi\) | ||
0.996097 | − | 0.0882597i | \(-0.0281305\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.59487 | −0.341615 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.173418 | + | 2.38725i | −0.00688187 | + | 0.0947351i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.83099 | − | 1.83099i | 0.0725464 | − | 0.0725464i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.95735 | 0.354347 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.2735 | −1.15623 | −0.578116 | − | 0.815954i | \(-0.696212\pi\) | ||||
−0.578116 | + | 0.815954i | \(0.696212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.69367 | + | 5.69367i | −0.224536 | + | 0.224536i | −0.810406 | − | 0.585869i | \(-0.800753\pi\) |
0.585869 | + | 0.810406i | \(0.300753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.83104 | + | 0.205656i | 0.111472 | + | 0.00809771i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.78788 | 0.109603 | 0.0548015 | − | 0.998497i | \(-0.482547\pi\) | ||||
0.0548015 | + | 0.998497i | \(0.482547\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.2607i | − | 0.402766i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.79128 | − | 3.79128i | 0.148592 | − | 0.148592i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9931 | − | 19.9931i | 0.782389 | − | 0.782389i | −0.197844 | − | 0.980233i | \(-0.563394\pi\) |
0.980233 | + | 0.197844i | \(0.0633940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.5481 | − | 26.0807i | −0.881027 | − | 1.01906i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.174246i | 0.00679799i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.26656 | − | 6.26656i | −0.244110 | − | 0.244110i | 0.574438 | − | 0.818548i | \(-0.305221\pi\) |
−0.818548 | + | 0.574438i | \(0.805221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.89073 | − | 2.89073i | 0.112436 | − | 0.112436i | −0.648650 | − | 0.761087i | \(-0.724666\pi\) |
0.761087 | + | 0.648650i | \(0.224666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.9213 | 0.462985 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.57244 | + | 2.97546i | 0.0997550 | + | 0.115383i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2283 | + | 18.2283i | 0.705803 | + | 0.705803i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.6125 | − | 15.6125i | −0.603614 | − | 0.603614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.79420 | −0.378101 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.9133i | − | 1.19162i | −0.803125 | − | 0.595810i | \(-0.796831\pi\) | ||
0.803125 | − | 0.595810i | \(-0.203169\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.98745 | + | 4.00938i | 0.114987 | + | 0.154321i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.28850 | + | 5.28850i | 0.203253 | + | 0.203253i | 0.801392 | − | 0.598139i | \(-0.204093\pi\) |
−0.598139 | + | 0.801392i | \(0.704093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 30.9757i | − | 1.18874i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.86189i | 0.301268i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.6055 | − | 10.6055i | −0.405809 | − | 0.405809i | 0.474465 | − | 0.880274i | \(-0.342641\pi\) |
−0.880274 | + | 0.474465i | \(0.842641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.4243 | + | 1.62897i | 0.856788 | + | 0.0622399i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16.7193i | − | 0.637882i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.330358 | 0.0125856 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.1363 | + | 32.1363i | 1.22252 | + | 1.22252i | 0.966732 | + | 0.255790i | \(0.0823357\pi\) |
0.255790 | + | 0.966732i | \(0.417664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.94990 | + | 1.94990i | 0.0740706 | + | 0.0740706i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.95587 | − | 6.01372i | 0.263851 | − | 0.228113i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −92.4648 | −3.50235 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.30756 | + | 6.30756i | −0.238574 | + | 0.238574i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0526 | − | 13.0526i | −0.492989 | − | 0.492989i | 0.416258 | − | 0.909247i | \(-0.363341\pi\) |
−0.909247 | + | 0.416258i | \(0.863341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.68883i | − | 0.176843i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.03592 | + | 6.98155i | 0.227326 | + | 0.262940i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.3545 | − | 28.3545i | 1.06638 | − | 1.06638i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.03016 | − | 7.03016i | 0.264023 | − | 0.264023i | −0.562663 | − | 0.826686i | \(-0.690223\pi\) |
0.826686 | + | 0.562663i | \(0.190223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.06488i | 0.114942i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2769 | −0.422325 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.242613 | + | 3.33978i | −0.00907321 | + | 0.124901i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.2153 | − | 16.2153i | 0.605573 | − | 0.605573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.9753 | 0.595778 | 0.297889 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297889 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.7464 | 1.59196 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.58369 | − | 4.58369i | 0.170469 | − | 0.170469i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4688 | + | 16.7341i | 0.463080 | + | 0.621489i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.60073 | 0.356071 | 0.178036 | − | 0.984024i | \(-0.443026\pi\) | ||||
0.178036 | + | 0.984024i | \(0.443026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.70992 | + | 6.70992i | −0.248175 | + | 0.248175i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.23740 | + | 5.23740i | −0.193448 | + | 0.193448i | −0.797184 | − | 0.603736i | \(-0.793678\pi\) |
0.603736 | + | 0.797184i | \(0.293678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.74655 | + | 2.37453i | −0.101308 | + | 0.0875860i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.5305i | − | 0.424731i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0809 | − | 18.0809i | −0.665118 | − | 0.665118i | 0.291464 | − | 0.956582i | \(-0.405858\pi\) |
−0.956582 | + | 0.291464i | \(0.905858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.675469 | + | 0.675469i | −0.0248140 | + | 0.0248140i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.96005 | −0.218653 | −0.109326 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109326 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.01731 | − | 2.60862i | 0.110546 | − | 0.0955725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.18751 | − | 9.18751i | −0.336153 | − | 0.336153i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.2162 | + | 17.2162i | 0.629065 | + | 0.629065i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.6552 | 1.19160 | 0.595802 | − | 0.803131i | \(-0.296834\pi\) | ||||
0.595802 | + | 0.803131i | \(0.296834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.3954i | 0.743251i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.31694 | + | 45.6606i | −0.120716 | + | 1.66176i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0760 | − | 34.0760i | −1.23851 | − | 1.23851i | −0.960609 | − | 0.277903i | \(-0.910361\pi\) |
−0.277903 | − | 0.960609i | \(-0.589639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.79986i | − | 0.210521i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.5888i | 1.07259i | 0.844030 | + | 0.536296i | \(0.180177\pi\) | ||||
−0.844030 | + | 0.536296i | \(0.819823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4371 | − | 14.4371i | −0.522659 | − | 0.522659i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.6713 | − | 1.21106i | −0.602752 | − | 0.0437859i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.4257i | 0.629206i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.1544 | 1.05133 | 0.525667 | − | 0.850690i | \(-0.323816\pi\) | ||||
0.525667 | + | 0.850690i | \(0.323816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.136994 | − | 0.136994i | −0.00493373 | − | 0.00493373i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.3728 | + | 16.3728i | 0.588889 | + | 0.588889i | 0.937331 | − | 0.348441i | \(-0.113289\pi\) |
−0.348441 | + | 0.937331i | \(0.613289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.03318 | − | 1.31936i | −0.324482 | − | 0.0473929i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.9872 | 0.824662 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.23912 | − | 5.23912i | 0.187711 | − | 0.187711i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.94764 | − | 5.94764i | −0.212823 | − | 0.212823i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.17374i | 0.149157i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4568 | + | 16.8214i | −0.694443 | + | 0.600383i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.4334 | − | 27.4334i | 0.977894 | − | 0.977894i | −0.0218667 | − | 0.999761i | \(-0.506961\pi\) |
0.999761 | + | 0.0218667i | \(0.00696095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.7173 | − | 11.7173i | 0.417148 | − | 0.417148i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.6867i | 1.33999i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.6335 | 0.590673 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.461989 | − | 0.0335604i | −0.0163850 | − | 0.00119026i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.30833 | − | 1.30833i | 0.0463434 | − | 0.0463434i | −0.683555 | − | 0.729899i | \(-0.739567\pi\) |
0.729899 | + | 0.683555i | \(0.239567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8530 | −1.09150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.71473 | 0.307920 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.115699 | − | 0.115699i | 0.00408292 | − | 0.00408292i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.4507 | + | 2.93847i | 1.42570 | + | 0.103567i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0322 | 0.353149 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.40398i | 0.189994i | 0.995478 | + | 0.0949970i | \(0.0302841\pi\) | ||||
−0.995478 | + | 0.0949970i | \(0.969716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.63507 | − | 5.63507i | 0.197874 | − | 0.197874i | −0.601214 | − | 0.799088i | \(-0.705316\pi\) |
0.799088 | + | 0.601214i | \(0.205316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.85459 | − | 1.85459i | 0.0650432 | − | 0.0650432i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.78282 | − | 8.45776i | 0.342677 | − | 0.296262i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.760378i | − | 0.0266023i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.31152 | − | 3.31152i | −0.115714 | − | 0.115714i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.6911 | − | 11.6911i | 0.408022 | − | 0.408022i | −0.473027 | − | 0.881048i | \(-0.656839\pi\) |
0.881048 | + | 0.473027i | \(0.156839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7721 | 0.445207 | 0.222604 | − | 0.974909i | \(-0.428544\pi\) | ||||
0.222604 | + | 0.974909i | \(0.428544\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.678563 | − | 4.64587i | 0.0236245 | − | 0.161748i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.00790410 | + | 0.00790410i | 0.000274852 | + | 0.000274852i | 0.707244 | − | 0.706969i | \(-0.249938\pi\) |
−0.706969 | + | 0.707244i | \(0.749938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.93843 | + | 2.93843i | 0.102056 | + | 0.102056i | 0.756291 | − | 0.654235i | \(-0.227009\pi\) |
−0.654235 | + | 0.756291i | \(0.727009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2788 | 0.391258 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 12.1376i | − | 0.420542i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.2508 | + | 1.54372i | 0.735413 | + | 0.0534228i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.29104 | − | 1.29104i | −0.0446249 | − | 0.0446249i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.0990i | 1.34985i | 0.737888 | + | 0.674923i | \(0.235823\pi\) | ||||
−0.737888 | + | 0.674923i | \(0.764177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.5799i | − | 0.399308i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.05586 | − | 7.05586i | −0.243017 | − | 0.243017i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.69408 | + | 23.3205i | −0.0582781 | + | 0.802250i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.7133i | 1.02096i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.8579 | 0.990399 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.1870 | − | 34.1870i | −1.17192 | − | 1.17192i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.788780 | + | 0.788780i | 0.0270073 | + | 0.0270073i | 0.720481 | − | 0.693474i | \(-0.243921\pi\) |
−0.693474 | + | 0.720481i | \(0.743921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.01323 | − | 0.875989i | 0.0346517 | − | 0.0299582i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.0264 | −1.53807 | −0.769036 | − | 0.639206i | \(-0.779263\pi\) | ||||
−0.769036 | + | 0.639206i | \(0.779263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.5188 | + | 21.5188i | −0.734212 | + | 0.734212i | −0.971451 | − | 0.237239i | \(-0.923757\pi\) |
0.237239 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.6851 | + | 25.6851i | 0.875344 | + | 0.875344i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.30436i | 0.282684i | 0.989961 | + | 0.141342i | \(0.0451417\pi\) | ||||
−0.989961 | + | 0.141342i | \(0.954858\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7894 | − | 12.7862i | 0.502855 | − | 0.434744i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.4922 | − | 27.4922i | 0.933684 | − | 0.933684i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.03507 | − | 2.03507i | 0.0690351 | − | 0.0690351i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5823i | 0.663520i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.5481 | −0.357000 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.0585 | + | 7.08639i | 1.08377 | + | 0.239564i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6134 | − | 17.6134i | 0.594764 | − | 0.594764i | −0.344151 | − | 0.938914i | \(-0.611833\pi\) |
0.938914 | + | 0.344151i | \(0.111833\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.58866 | −0.222230 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.5717 | 1.09737 | 0.548684 | − | 0.836030i | \(-0.315129\pi\) | ||||
0.548684 | + | 0.836030i | \(0.315129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6327 | − | 11.6327i | 0.391472 | − | 0.391472i | −0.483740 | − | 0.875212i | \(-0.660722\pi\) |
0.875212 | + | 0.483740i | \(0.160722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77024 | − | 24.3690i | 0.0595060 | − | 0.819153i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.0203 | −1.34375 | −0.671875 | − | 0.740665i | \(-0.734511\pi\) | ||||
−0.671875 | + | 0.740665i | \(0.734511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.14342i | 0.105427i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.663996 | − | 0.663996i | 0.0222447 | − | 0.0222447i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.74815 | − | 1.74815i | 0.0584997 | − | 0.0584997i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.4156 | − | 24.7708i | −0.715845 | − | 0.827995i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.84991i | 0.328879i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.38846 | − | 5.38846i | −0.179715 | − | 0.179715i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09497 | − | 1.09497i | 0.0364787 | − | 0.0364787i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.72779 | 0.124053 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.3057 | + | 12.3680i | −0.475536 | + | 0.411126i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.81050 | − | 5.81050i | −0.192934 | − | 0.192934i | 0.604028 | − | 0.796963i | \(-0.293561\pi\) |
−0.796963 | + | 0.604028i | \(0.793561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.65550 | − | 9.65550i | −0.320253 | − | 0.320253i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4809 | −0.347248 | −0.173624 | − | 0.984812i | \(-0.555548\pi\) | ||||
−0.173624 | + | 0.984812i | \(0.555548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2009i | 0.403792i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.2611 | − | 1.68976i | −0.768989 | − | 0.0558619i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.0161 | − | 32.0161i | −1.05726 | − | 1.05726i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.8755i | 1.71121i | 0.517626 | + | 0.855607i | \(0.326816\pi\) | ||||
−0.517626 | + | 0.855607i | \(0.673184\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 12.8055i | − | 0.421956i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1009 | + | 10.1009i | 0.332475 | + | 0.332475i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.3851 | − | 31.3847i | −0.768898 | − | 1.03192i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 14.5564i | − | 0.478094i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.54673 | −0.181982 | −0.0909912 | − | 0.995852i | \(-0.529004\pi\) | ||||
−0.0909912 | + | 0.995852i | \(0.529004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.687724 | + | 0.687724i | 0.0225393 | + | 0.0225393i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.39956 | − | 2.39956i | −0.0785581 | − | 0.0785581i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.2655 | + | 11.8738i | 0.335719 | + | 0.388315i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.31790 | −0.304402 | −0.152201 | − | 0.988350i | \(-0.548636\pi\) | ||||
−0.152201 | + | 0.988350i | \(0.548636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.70346 | − | 7.70346i | 0.251393 | − | 0.251393i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.9832 | − | 21.9832i | −0.716630 | − | 0.716630i | 0.251283 | − | 0.967914i | \(-0.419147\pi\) |
−0.967914 | + | 0.251283i | \(0.919147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 76.3986i | − | 2.48788i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.29458 | + | 4.96740i | 0.139703 | + | 0.161590i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.4966 | − | 15.4966i | 0.503572 | − | 0.503572i | −0.408974 | − | 0.912546i | \(-0.634113\pi\) |
0.912546 | + | 0.408974i | \(0.134113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.196492 | + | 0.196492i | −0.00637839 | + | 0.00637839i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.89001i | 0.158569i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.72390 | 0.185415 | 0.0927076 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927076 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.903075 | + | 0.0656024i | 0.0292228 | + | 0.00212284i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.77134 | − | 2.77134i | 0.0895848 | − | 0.0895848i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.5273 | 0.953485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6664 | −0.892466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.86260 | − | 5.86260i | 0.188920 | − | 0.188920i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05139 | − | 14.4733i | 0.0338453 | − | 0.465911i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.80514 | 0.283154 | 0.141577 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141577 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.47767i | 0.143844i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8032 | + | 26.8032i | −0.860157 | + | 0.860157i | −0.991356 | − | 0.131199i | \(-0.958117\pi\) |
0.131199 | + | 0.991356i | \(0.458117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.53888 | − | 8.53888i | 0.273744 | − | 0.273744i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.15241 | + | 7.89009i | −0.0369065 | + | 0.252685i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 36.2126i | − | 1.15854i | −0.815134 | − | 0.579272i | \(-0.803337\pi\) | ||
0.815134 | − | 0.579272i | \(-0.196663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.78655 | − | 5.78655i | −0.184939 | − | 0.184939i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.91625 | + | 4.91625i | −0.156964 | + | 0.156964i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.7547 | −0.502496 | −0.251248 | − | 0.967923i | \(-0.580841\pi\) | ||||
−0.251248 | + | 0.967923i | \(0.580841\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.1425 | + | 44.1182i | 1.21532 | + | 1.40572i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.57040 | + | 8.57040i | 0.272799 | + | 0.272799i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.54404 | − | 5.54404i | −0.176290 | − | 0.176290i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5049 | −0.397230 | −0.198615 | − | 0.980078i | \(-0.563644\pi\) | ||||
−0.198615 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 35.2487i | − | 1.11859i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.18219 | + | 30.0397i | −0.0691799 | + | 0.952324i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.59749 | + | 4.59749i | 0.145604 | + | 0.145604i | 0.776151 | − | 0.630547i | \(-0.217169\pi\) |
−0.630547 | + | 0.776151i | \(0.717169\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.82780i | − | 0.247661i |
(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 | 1920.2.bl.b.289.11 | 48 | ||
4.3 | odd | 2 | 1920.2.bl.a.289.14 | 48 | |||
5.4 | even | 2 | inner | 1920.2.bl.b.289.14 | 48 | ||
8.3 | odd | 2 | 240.2.bl.a.109.16 | yes | 48 | ||
8.5 | even | 2 | 960.2.bl.a.529.13 | 48 | |||
16.3 | odd | 4 | 240.2.bl.a.229.9 | yes | 48 | ||
16.5 | even | 4 | inner | 1920.2.bl.b.1249.14 | 48 | ||
16.11 | odd | 4 | 1920.2.bl.a.1249.11 | 48 | |||
16.13 | even | 4 | 960.2.bl.a.49.6 | 48 | |||
20.19 | odd | 2 | 1920.2.bl.a.289.11 | 48 | |||
24.11 | even | 2 | 720.2.bm.h.109.9 | 48 | |||
40.19 | odd | 2 | 240.2.bl.a.109.9 | ✓ | 48 | ||
40.29 | even | 2 | 960.2.bl.a.529.6 | 48 | |||
48.35 | even | 4 | 720.2.bm.h.469.16 | 48 | |||
80.19 | odd | 4 | 240.2.bl.a.229.16 | yes | 48 | ||
80.29 | even | 4 | 960.2.bl.a.49.13 | 48 | |||
80.59 | odd | 4 | 1920.2.bl.a.1249.14 | 48 | |||
80.69 | even | 4 | inner | 1920.2.bl.b.1249.11 | 48 | ||
120.59 | even | 2 | 720.2.bm.h.109.16 | 48 | |||
240.179 | even | 4 | 720.2.bm.h.469.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.9 | ✓ | 48 | 40.19 | odd | 2 | ||
240.2.bl.a.109.16 | yes | 48 | 8.3 | odd | 2 | ||
240.2.bl.a.229.9 | yes | 48 | 16.3 | odd | 4 | ||
240.2.bl.a.229.16 | yes | 48 | 80.19 | odd | 4 | ||
720.2.bm.h.109.9 | 48 | 24.11 | even | 2 | |||
720.2.bm.h.109.16 | 48 | 120.59 | even | 2 | |||
720.2.bm.h.469.9 | 48 | 240.179 | even | 4 | |||
720.2.bm.h.469.16 | 48 | 48.35 | even | 4 | |||
960.2.bl.a.49.6 | 48 | 16.13 | even | 4 | |||
960.2.bl.a.49.13 | 48 | 80.29 | even | 4 | |||
960.2.bl.a.529.6 | 48 | 40.29 | even | 2 | |||
960.2.bl.a.529.13 | 48 | 8.5 | even | 2 | |||
1920.2.bl.a.289.11 | 48 | 20.19 | odd | 2 | |||
1920.2.bl.a.289.14 | 48 | 4.3 | odd | 2 | |||
1920.2.bl.a.1249.11 | 48 | 16.11 | odd | 4 | |||
1920.2.bl.a.1249.14 | 48 | 80.59 | odd | 4 | |||
1920.2.bl.b.289.11 | 48 | 1.1 | even | 1 | trivial | ||
1920.2.bl.b.289.14 | 48 | 5.4 | even | 2 | inner | ||
1920.2.bl.b.1249.11 | 48 | 80.69 | even | 4 | inner | ||
1920.2.bl.b.1249.14 | 48 | 16.5 | even | 4 | inner |