Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.6 | ||
Root | \(2.69978 - 0.355433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.g.449.6 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 1.62602 | + | 1.62602i | 0.938783 | + | 0.938783i | 0.998231 | − | 0.0594487i | \(-0.0189343\pi\) |
−0.0594487 | + | 0.998231i | \(0.518934\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.16900 | − | 1.16900i | 0.522792 | − | 0.522792i | −0.395621 | − | 0.918414i | \(-0.629471\pi\) |
0.918414 | + | 0.395621i | \(0.129471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.28788i | 0.762626i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39956 | − | 4.39956i | 1.32652 | − | 1.32652i | 0.418130 | − | 0.908387i | \(-0.362686\pi\) |
0.908387 | − | 0.418130i | \(-0.137314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.448377 | − | 0.448377i | −0.124357 | − | 0.124357i | 0.642189 | − | 0.766546i | \(-0.278026\pi\) |
−0.766546 | + | 0.642189i | \(0.778026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.80163 | 0.981576 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.02326 | 1.21832 | 0.609159 | − | 0.793048i | \(-0.291507\pi\) | ||||
0.609159 | + | 0.793048i | \(0.291507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49851 | − | 1.49851i | −0.343782 | − | 0.343782i | 0.514005 | − | 0.857787i | \(-0.328161\pi\) |
−0.857787 | + | 0.514005i | \(0.828161\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.62602 | + | 1.62602i | −0.354826 | + | 0.354826i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.89958i | − | 1.85569i | −0.372965 | − | 0.927845i | \(-0.621659\pi\) | ||
0.372965 | − | 0.927845i | \(-0.378341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.26688i | 0.453377i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.15793 | − | 1.15793i | 0.222843 | − | 0.222843i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.803165 | + | 0.803165i | 0.149144 | + | 0.149144i | 0.777736 | − | 0.628592i | \(-0.216368\pi\) |
−0.628592 | + | 0.777736i | \(0.716368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.27524 | −1.48628 | −0.743139 | − | 0.669137i | \(-0.766664\pi\) | ||||
−0.743139 | + | 0.669137i | \(0.766664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.3075 | 2.49062 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.16900 | + | 1.16900i | 0.197597 | + | 0.197597i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.55173 | + | 1.55173i | −0.255102 | + | 0.255102i | −0.823059 | − | 0.567956i | \(-0.807734\pi\) |
0.567956 | + | 0.823059i | \(0.307734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.45814i | − | 0.233489i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.93020i | − | 0.769968i | −0.922923 | − | 0.384984i | \(-0.874207\pi\) | ||
0.922923 | − | 0.384984i | \(-0.125793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73291 | + | 3.73291i | −0.569263 | + | 0.569263i | −0.931922 | − | 0.362659i | \(-0.881869\pi\) |
0.362659 | + | 0.931922i | \(0.381869\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.67453 | + | 2.67453i | 0.398695 | + | 0.398695i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.68692 | 0.975387 | 0.487693 | − | 0.873015i | \(-0.337838\pi\) | ||||
0.487693 | + | 0.873015i | \(0.337838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.16791 | + | 8.16791i | 1.14374 | + | 1.14374i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.53424 | + | 4.53424i | −0.622826 | + | 0.622826i | −0.946253 | − | 0.323427i | \(-0.895165\pi\) |
0.323427 | + | 0.946253i | \(0.395165\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.2862i | − | 1.38699i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.87321i | − | 0.645473i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.06717 | − | 1.06717i | 0.138934 | − | 0.138934i | −0.634219 | − | 0.773153i | \(-0.718678\pi\) |
0.773153 | + | 0.634219i | \(0.218678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.11346 | + | 5.11346i | 0.654711 | + | 0.654711i | 0.954124 | − | 0.299413i | \(-0.0967907\pi\) |
−0.299413 | + | 0.954124i | \(0.596791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.28788 | −0.288245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.04830 | −0.130026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.47532 | + | 7.47532i | 0.913256 | + | 0.913256i | 0.996527 | − | 0.0832712i | \(-0.0265368\pi\) |
−0.0832712 | + | 0.996527i | \(0.526537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.4709 | − | 14.4709i | 1.74209 | − | 1.74209i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.07354i | − | 0.483440i | −0.970346 | − | 0.241720i | \(-0.922288\pi\) | ||
0.970346 | − | 0.241720i | \(-0.0777116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5063i | 1.58079i | 0.612595 | + | 0.790397i | \(0.290126\pi\) | ||||
−0.612595 | + | 0.790397i | \(0.709874\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.68600 | + | 3.68600i | −0.425622 | + | 0.425622i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.39956 | + | 4.39956i | 0.501376 | + | 0.501376i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.19701 | −1.03474 | −0.517372 | − | 0.855760i | \(-0.673090\pi\) | ||||
−0.517372 | + | 0.855760i | \(0.673090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.6293 | 1.18103 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.62248 | + | 2.62248i | 0.287855 | + | 0.287855i | 0.836231 | − | 0.548377i | \(-0.184754\pi\) |
−0.548377 | + | 0.836231i | \(0.684754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.87218 | − | 5.87218i | 0.636928 | − | 0.636928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.61192i | 0.280028i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.60040i | − | 0.169642i | −0.996396 | − | 0.0848209i | \(-0.972968\pi\) | ||
0.996396 | − | 0.0848209i | \(-0.0270318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.448377 | − | 0.448377i | 0.0470027 | − | 0.0470027i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4557 | − | 13.4557i | −1.39529 | − | 1.39529i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50351 | −0.359453 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0167 | −1.32164 | −0.660822 | − | 0.750543i | \(-0.729792\pi\) | ||||
−0.660822 | + | 0.750543i | \(0.729792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.0657 | + | 10.0657i | 1.01164 | + | 1.01164i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.76253 | − | 3.76253i | 0.374386 | − | 0.374386i | −0.494686 | − | 0.869072i | \(-0.664717\pi\) |
0.869072 | + | 0.494686i | \(0.164717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.91886i | 0.780268i | 0.920758 | + | 0.390134i | \(0.127571\pi\) | ||||
−0.920758 | + | 0.390134i | \(0.872429\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.80163i | 0.371001i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5961 | + | 13.5961i | −1.31438 | + | 1.31438i | −0.396228 | + | 0.918152i | \(0.629681\pi\) |
−0.918152 | + | 0.396228i | \(0.870319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.03367 | + | 7.03367i | 0.673704 | + | 0.673704i | 0.958568 | − | 0.284864i | \(-0.0919485\pi\) |
−0.284864 | + | 0.958568i | \(0.591948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.04627 | −0.478971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.62753 | 0.529394 | 0.264697 | − | 0.964332i | \(-0.414728\pi\) | ||||
0.264697 | + | 0.964332i | \(0.414728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.4036 | − | 10.4036i | −0.970141 | − | 0.970141i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.02583 | − | 1.02583i | 0.0948381 | − | 0.0948381i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.02326i | 0.460481i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 27.7123i | − | 2.51930i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.01660 | − | 8.01660i | 0.722833 | − | 0.722833i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.49498 | + | 8.49498i | 0.759814 | + | 0.759814i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5320 | −1.20077 | −0.600386 | − | 0.799710i | \(-0.704987\pi\) | ||||
−0.600386 | + | 0.799710i | \(0.704987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1396 | −1.06883 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.48631 | − | 1.48631i | −0.129859 | − | 0.129859i | 0.639190 | − | 0.769049i | \(-0.279270\pi\) |
−0.769049 | + | 0.639190i | \(0.779270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.49851 | − | 1.49851i | 0.129937 | − | 0.129937i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.70723i | − | 0.233001i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7463i | 1.00355i | 0.864998 | + | 0.501776i | \(0.167320\pi\) | ||||
−0.864998 | + | 0.501776i | \(0.832680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00812 | + | 8.00812i | −0.679240 | + | 0.679240i | −0.959828 | − | 0.280588i | \(-0.909470\pi\) |
0.280588 | + | 0.959828i | \(0.409470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8731 | + | 10.8731i | 0.915676 | + | 0.915676i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.94532 | −0.329924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.87780 | 0.155943 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.62602 | − | 1.62602i | −0.134112 | − | 0.134112i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.63681 | + | 3.63681i | −0.297939 | + | 0.297939i | −0.840206 | − | 0.542267i | \(-0.817566\pi\) |
0.542267 | + | 0.840206i | \(0.317566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.9697i | − | 1.29959i | −0.760108 | − | 0.649797i | \(-0.774854\pi\) | ||
0.760108 | − | 0.649797i | \(-0.225146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.4926i | 0.929121i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.67375 | + | 9.67375i | −0.777014 | + | 0.777014i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0481 | + | 14.0481i | 1.12116 | + | 1.12116i | 0.991568 | + | 0.129589i | \(0.0413659\pi\) |
0.129589 | + | 0.991568i | \(0.458634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7455 | −1.16940 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.89958 | 0.701385 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2797 | + | 10.2797i | 0.805169 | + | 0.805169i | 0.983898 | − | 0.178729i | \(-0.0571985\pi\) |
−0.178729 | + | 0.983898i | \(0.557199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.7255 | − | 16.7255i | 1.30208 | − | 1.30208i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.4131i | − | 1.50223i | −0.660172 | − | 0.751115i | \(-0.729517\pi\) | ||
0.660172 | − | 0.751115i | \(-0.270483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.5979i | − | 0.969071i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.42841 | − | 3.42841i | 0.262177 | − | 0.262177i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.56281 | + | 4.56281i | 0.346904 | + | 0.346904i | 0.858955 | − | 0.512051i | \(-0.171114\pi\) |
−0.512051 | + | 0.858955i | \(0.671114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.26688 | −0.171360 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.47048 | 0.260857 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.8129 | − | 16.8129i | −1.25665 | − | 1.25665i | −0.952682 | − | 0.303970i | \(-0.901688\pi\) |
−0.303970 | − | 0.952682i | \(-0.598312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.25856 | + | 6.25856i | −0.465195 | + | 0.465195i | −0.900354 | − | 0.435159i | \(-0.856692\pi\) |
0.435159 | + | 0.900354i | \(0.356692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.6292i | 1.22926i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.62793i | 0.266731i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.1001 | − | 22.1001i | 1.61612 | − | 1.61612i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.15793 | + | 1.15793i | 0.0842267 | + | 0.0842267i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8222 | 1.14486 | 0.572428 | − | 0.819955i | \(-0.306001\pi\) | ||||
0.572428 | + | 0.819955i | \(0.306001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.50630 | −0.540315 | −0.270158 | − | 0.962816i | \(-0.587076\pi\) | ||||
−0.270158 | + | 0.962816i | \(0.587076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.70456 | − | 1.70456i | −0.122066 | − | 0.122066i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2320 | + | 17.2320i | −1.22773 | + | 1.22773i | −0.262905 | + | 0.964822i | \(0.584681\pi\) |
−0.964822 | + | 0.262905i | \(0.915319\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.8653i | 1.54999i | 0.631967 | + | 0.774995i | \(0.282248\pi\) | ||||
−0.631967 | + | 0.774995i | \(0.717752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.3100i | 1.71470i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.803165 | + | 0.803165i | −0.0563712 | + | 0.0563712i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.76340 | − | 5.76340i | −0.402533 | − | 0.402533i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.3611 | 1.41520 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.1856 | −0.912065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.78563 | + | 2.78563i | 0.191771 | + | 0.191771i | 0.796461 | − | 0.604690i | \(-0.206703\pi\) |
−0.604690 | + | 0.796461i | \(0.706703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.62366 | − | 6.62366i | 0.453845 | − | 0.453845i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.72753i | 0.595212i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.27524i | − | 0.561760i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.9615 | + | 21.9615i | −1.48402 | + | 1.48402i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.25231 | − | 2.25231i | −0.151507 | − | 0.151507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.64913 | 0.311329 | 0.155665 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155665 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.18635 | −0.345757 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.41312 | − | 4.41312i | −0.292909 | − | 0.292909i | 0.545319 | − | 0.838228i | \(-0.316408\pi\) |
−0.838228 | + | 0.545319i | \(0.816408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4119 | + | 14.4119i | −0.952362 | + | 0.952362i | −0.998916 | − | 0.0465535i | \(-0.985176\pi\) |
0.0465535 | + | 0.998916i | \(0.485176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3075i | 0.941367i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.2765i | − | 0.738746i | −0.929281 | − | 0.369373i | \(-0.879572\pi\) | ||
0.929281 | − | 0.369373i | \(-0.120428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.81700 | − | 7.81700i | 0.509925 | − | 0.509925i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.9545 | − | 14.9545i | −0.971400 | − | 0.971400i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.994605 | −0.0643356 | −0.0321678 | − | 0.999482i | \(-0.510241\pi\) | ||||
−0.0321678 | + | 0.999482i | \(0.510241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1158 | 1.74669 | 0.873343 | − | 0.487107i | \(-0.161948\pi\) | ||||
0.873343 | + | 0.487107i | \(0.161948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8096 | + | 13.8096i | 0.885885 | + | 0.885885i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.16900 | + | 1.16900i | −0.0746846 | + | 0.0746846i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.34379i | 0.0855036i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.52841i | 0.540466i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.47591 | − | 4.47591i | 0.282517 | − | 0.282517i | −0.551595 | − | 0.834112i | \(-0.685981\pi\) |
0.834112 | + | 0.551595i | \(0.185981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.1542 | − | 39.1542i | −2.46161 | − | 2.46161i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.0966 | 1.19587 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.08743 | −0.442102 | −0.221051 | − | 0.975262i | \(-0.570949\pi\) | ||||
−0.221051 | + | 0.975262i | \(0.570949\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.55173 | − | 1.55173i | −0.0964196 | − | 0.0964196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.83754 | + | 1.83754i | −0.113741 | + | 0.113741i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.95421i | 0.428815i | 0.976744 | + | 0.214408i | \(0.0687821\pi\) | ||||
−0.976744 | + | 0.214408i | \(0.931218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6010i | 0.651217i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.60228 | − | 2.60228i | 0.159257 | − | 0.159257i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2606 | + | 13.2606i | 0.808516 | + | 0.808516i | 0.984409 | − | 0.175893i | \(-0.0562814\pi\) |
−0.175893 | + | 0.984409i | \(0.556281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2967 | −0.868463 | −0.434231 | − | 0.900801i | \(-0.642980\pi\) | ||||
−0.434231 | + | 0.900801i | \(0.642980\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.45814 | 0.0882506 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.97329 | + | 9.97329i | 0.601412 | + | 0.601412i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.56248 | + | 1.56248i | −0.0938806 | + | 0.0938806i | −0.752487 | − | 0.658607i | \(-0.771146\pi\) |
0.658607 | + | 0.752487i | \(0.271146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 18.9327i | − | 1.13347i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.06619i | 0.361879i | 0.983494 | + | 0.180939i | \(0.0579138\pi\) | ||||
−0.983494 | + | 0.180939i | \(0.942086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3191 | − | 20.3191i | 1.20785 | − | 1.20785i | 0.236125 | − | 0.971723i | \(-0.424123\pi\) |
0.971723 | − | 0.236125i | \(-0.0758774\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.69678 | − | 5.69678i | −0.337448 | − | 0.337448i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.93020 | 0.291021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.23311 | 0.484301 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.1654 | − | 21.1654i | −1.24074 | − | 1.24074i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.2357 | − | 22.2357i | 1.29903 | − | 1.29903i | 0.369989 | − | 0.929036i | \(-0.379361\pi\) |
0.929036 | − | 0.369989i | \(-0.120639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.49504i | − | 0.145267i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.1887i | − | 0.591210i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.99036 | + | 3.99036i | −0.230769 | + | 0.230769i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.73291 | − | 3.73291i | −0.215161 | − | 0.215161i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.2359 | 0.702934 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.9553 | 0.684556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7656 | − | 17.7656i | −1.01393 | − | 1.01393i | −0.999902 | − | 0.0140326i | \(-0.995533\pi\) |
−0.0140326 | − | 0.999902i | \(-0.504467\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8762 | + | 12.8762i | −0.732502 | + | 0.732502i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.2698i | − | 1.77315i | −0.462588 | − | 0.886574i | \(-0.653079\pi\) | ||
0.462588 | − | 0.886574i | \(-0.346921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.0095i | − | 1.01796i | −0.860778 | − | 0.508980i | \(-0.830023\pi\) | ||
0.860778 | − | 0.508980i | \(-0.169977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.67453 | + | 2.67453i | −0.150692 | + | 0.150692i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2418 | − | 12.2418i | −0.687567 | − | 0.687567i | 0.274127 | − | 0.961694i | \(-0.411611\pi\) |
−0.961694 | + | 0.274127i | \(0.911611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.06715 | 0.395684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −44.2149 | −2.46783 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.52740 | − | 7.52740i | −0.418836 | − | 0.418836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.01642 | − | 1.01642i | 0.0563807 | − | 0.0563807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.8738i | 1.26492i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.68692i | 0.368662i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7456 | − | 11.7456i | 0.645599 | − | 0.645599i | −0.306328 | − | 0.951926i | \(-0.599100\pi\) |
0.951926 | + | 0.306328i | \(0.0991003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.55016 | − | 3.55016i | −0.194548 | − | 0.194548i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.4773 | 0.954886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.23237 | 0.339499 | 0.169750 | − | 0.985487i | \(-0.445704\pi\) | ||||
0.169750 | + | 0.985487i | \(0.445704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.15047 | + | 9.15047i | 0.496986 | + | 0.496986i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.4074 | + | 36.4074i | −1.97157 | + | 1.97157i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 33.8329i | − | 1.82150i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.62041 | + | 6.62041i | −0.355402 | + | 0.355402i | −0.862115 | − | 0.506713i | \(-0.830860\pi\) |
0.506713 | + | 0.862115i | \(0.330860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.7958 | − | 14.7958i | −0.792001 | − | 0.792001i | 0.189819 | − | 0.981819i | \(-0.439210\pi\) |
−0.981819 | + | 0.189819i | \(0.939210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.03837 | −0.0554243 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.7098 | −0.942599 | −0.471300 | − | 0.881973i | \(-0.656215\pi\) | ||||
−0.471300 | + | 0.881973i | \(0.656215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.76196 | − | 4.76196i | −0.252739 | − | 0.252739i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.16791 | + | 8.16791i | −0.432292 | + | 0.432292i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.53643i | − | 0.450535i | −0.974297 | − | 0.225268i | \(-0.927674\pi\) | ||
0.974297 | − | 0.225268i | \(-0.0723257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.5089i | − | 0.763628i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 45.0607 | − | 45.0607i | 2.36507 | − | 2.36507i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7889 | + | 15.7889i | 0.826427 | + | 0.826427i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3226 | 0.591037 | 0.295519 | − | 0.955337i | \(-0.404508\pi\) | ||||
0.295519 | + | 0.955337i | \(0.404508\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.2797 | 0.587198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.53424 | − | 4.53424i | −0.235406 | − | 0.235406i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.88728 | + | 7.88728i | −0.408388 | + | 0.408388i | −0.881176 | − | 0.472788i | \(-0.843248\pi\) |
0.472788 | + | 0.881176i | \(0.343248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.6260i | 1.42660i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.720241i | − | 0.0370943i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.53241 | + | 9.53241i | −0.489647 | + | 0.489647i | −0.908195 | − | 0.418548i | \(-0.862539\pi\) |
0.418548 | + | 0.908195i | \(0.362539\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.0033 | − | 22.0033i | −1.12726 | − | 1.12726i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9261 | 0.967077 | 0.483539 | − | 0.875323i | \(-0.339351\pi\) | ||||
0.483539 | + | 0.875323i | \(0.339351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.2862 | 0.524231 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.54043 | − | 8.54043i | −0.434134 | − | 0.434134i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.78034 | + | 6.78034i | −0.343777 | + | 0.343777i | −0.857785 | − | 0.514008i | \(-0.828160\pi\) |
0.514008 | + | 0.857785i | \(0.328160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 44.7049i | − | 2.26082i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.83352i | − | 0.243819i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7513 | + | 10.7513i | −0.540956 | + | 0.540956i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.93608 | + | 1.93608i | 0.0971692 | + | 0.0971692i | 0.754020 | − | 0.656851i | \(-0.228112\pi\) |
−0.656851 | + | 0.754020i | \(0.728112\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.87321 | 0.243966 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6483 | −0.831378 | −0.415689 | − | 0.909507i | \(-0.636460\pi\) | ||||
−0.415689 | + | 0.909507i | \(0.636460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.71043 | + | 3.71043i | 0.184829 | + | 0.184829i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.4256 | − | 12.4256i | 0.617432 | − | 0.617432i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.6538i | 0.676795i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8706i | 0.834199i | 0.908861 | + | 0.417100i | \(0.136953\pi\) | ||||
−0.908861 | + | 0.417100i | \(0.863047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0997 | + | 19.0997i | −0.942117 | + | 0.942117i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.06717 | + | 1.06717i | 0.0525120 | + | 0.0525120i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.13136 | 0.300976 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.0427 | −1.27532 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.1511 | − | 20.1511i | −0.984444 | − | 0.984444i | 0.0154368 | − | 0.999881i | \(-0.495086\pi\) |
−0.999881 | + | 0.0154368i | \(0.995086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.44015 | + | 6.44015i | −0.313874 | + | 0.313874i | −0.846408 | − | 0.532535i | \(-0.821240\pi\) |
0.532535 | + | 0.846408i | \(0.321240\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.2988i | 0.743855i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.3871i | 0.552357i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.11346 | + | 5.11346i | −0.247458 | + | 0.247458i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.41517 | − | 6.41517i | −0.309727 | − | 0.309727i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6481 | −1.37993 | −0.689965 | − | 0.723843i | \(-0.742374\pi\) | ||||
−0.689965 | + | 0.723843i | \(0.742374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.69574 | −0.225663 | −0.112832 | − | 0.993614i | \(-0.535992\pi\) | ||||
−0.112832 | + | 0.993614i | \(0.535992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.05334 | + | 3.05334i | 0.146396 | + | 0.146396i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.3361 | + | 13.3361i | −0.637953 | + | 0.637953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.6652i | 1.08175i | 0.841103 | + | 0.540874i | \(0.181907\pi\) | ||||
−0.841103 | + | 0.540874i | \(0.818093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.28788i | − | 0.108947i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7935 | + | 17.7935i | −0.845394 | + | 0.845394i | −0.989554 | − | 0.144160i | \(-0.953952\pi\) |
0.144160 | + | 0.989554i | \(0.453952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.87086 | − | 1.87086i | −0.0886875 | − | 0.0886875i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.8270 | −0.559400 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.2262 | −0.529799 | −0.264900 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264900 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.6907 | − | 21.6907i | −1.02138 | − | 1.02138i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.9670 | − | 25.9670i | 1.22004 | − | 1.22004i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.04830i | − | 0.0491452i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8858i | 0.976998i | 0.872564 | + | 0.488499i | \(0.162455\pi\) | ||||
−0.872564 | + | 0.488499i | \(0.837545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.81656 | − | 5.81656i | 0.271494 | − | 0.271494i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.78650 | − | 1.78650i | −0.0832056 | − | 0.0832056i | 0.664279 | − | 0.747485i | \(-0.268739\pi\) |
−0.747485 | + | 0.664279i | \(0.768739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0754 | 0.979457 | 0.489728 | − | 0.871875i | \(-0.337096\pi\) | ||||
0.489728 | + | 0.871875i | \(0.337096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.4594 | −1.45889 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.05590 | − | 8.05590i | −0.372783 | − | 0.372783i | 0.495707 | − | 0.868490i | \(-0.334909\pi\) |
−0.868490 | + | 0.495707i | \(0.834909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.47532 | + | 7.47532i | −0.345178 | + | 0.345178i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45.6848i | 2.10505i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.8463i | 1.51027i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.39695 | − | 3.39695i | 0.155863 | − | 0.155863i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3738 | − | 10.3738i | −0.474983 | − | 0.474983i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.8741 | 0.908070 | 0.454035 | − | 0.890984i | \(-0.349984\pi\) | ||||
0.454035 | + | 0.890984i | \(0.349984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.39152 | 0.0634477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.4709 | + | 14.4709i | 0.658448 | + | 0.658448i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2165 | + | 15.2165i | −0.690945 | + | 0.690945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.2744i | − | 0.873406i | −0.899606 | − | 0.436703i | \(-0.856146\pi\) | ||
0.899606 | − | 0.436703i | \(-0.143854\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.4300i | 1.51176i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.01202 | + | 4.01202i | −0.181060 | + | 0.181060i | −0.791818 | − | 0.610758i | \(-0.790865\pi\) |
0.610758 | + | 0.791818i | \(0.290865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.03451 | + | 4.03451i | 0.181705 | + | 0.181705i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.5335 | 1.05775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.07354 | 0.182723 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10545 | − | 4.10545i | −0.183785 | − | 0.183785i | 0.609218 | − | 0.793003i | \(-0.291484\pi\) |
−0.793003 | + | 0.609218i | \(0.791484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.5660 | − | 31.5660i | 1.41027 | − | 1.41027i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8588i | 0.885460i | 0.896655 | + | 0.442730i | \(0.145990\pi\) | ||||
−0.896655 | + | 0.442730i | \(0.854010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.79680i | − | 0.391452i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.4845 | − | 20.4845i | 0.909747 | − | 0.909747i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.11547 | + | 8.11547i | 0.359712 | + | 0.359712i | 0.863707 | − | 0.503995i | \(-0.168137\pi\) |
−0.503995 | + | 0.863707i | \(0.668137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.5063 | −0.597484 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.47033 | −0.153219 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.25714 | + | 9.25714i | 0.407918 | + | 0.407918i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.4195 | − | 29.4195i | 1.29387 | − | 1.29387i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.8384i | 0.651335i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11.8477i | − | 0.519059i | −0.965735 | − | 0.259530i | \(-0.916432\pi\) | ||
0.965735 | − | 0.259530i | \(-0.0835675\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5435 | + | 19.5435i | −0.854575 | + | 0.854575i | −0.990693 | − | 0.136117i | \(-0.956538\pi\) |
0.136117 | + | 0.990693i | \(0.456538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.68600 | − | 3.68600i | −0.160870 | − | 0.160870i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.5687 | −1.81076 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −56.2025 | −2.44359 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.44155 | + | 2.44155i | 0.105954 | + | 0.105954i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.21059 | + | 2.21059i | −0.0957512 | + | 0.0957512i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.7876i | 1.37430i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 54.6760i | − | 2.35945i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.39956 | + | 4.39956i | −0.189502 | + | 0.189502i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.1223 | + | 29.1223i | 1.25207 | + | 1.25207i | 0.954792 | + | 0.297274i | \(0.0960776\pi\) |
0.297274 | + | 0.954792i | \(0.403922\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.3531 | −0.873434 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.4447 | 0.704414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7023 | + | 12.7023i | 0.543111 | + | 0.543111i | 0.924440 | − | 0.381329i | \(-0.124533\pi\) |
−0.381329 | + | 0.924440i | \(0.624533\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.6990 | + | 11.6990i | −0.499299 | + | 0.499299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.40710i | − | 0.102546i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.19701i | − | 0.391097i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.89909 | + | 5.89909i | −0.250402 | + | 0.250402i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.2855 | + | 18.2855i | 0.774780 | + | 0.774780i | 0.978938 | − | 0.204158i | \(-0.0654456\pi\) |
−0.204158 | + | 0.978938i | \(0.565446\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.34750 | 0.141584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 71.8704 | 3.03437 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.721510 | − | 0.721510i | −0.0304080 | − | 0.0304080i | 0.691739 | − | 0.722147i | \(-0.256845\pi\) |
−0.722147 | + | 0.691739i | \(0.756845\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.57858 | − | 6.57858i | 0.276763 | − | 0.276763i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6293i | 0.446387i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.5555i | 1.40672i | 0.710834 | + | 0.703360i | \(0.248318\pi\) | ||||
−0.710834 | + | 0.703360i | \(0.751682\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.80134 | − | 3.80134i | 0.159081 | − | 0.159081i | −0.623078 | − | 0.782159i | \(-0.714118\pi\) |
0.782159 | + | 0.623078i | \(0.214118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.7273 | + | 25.7273i | 1.07477 | + | 1.07477i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.1743 | 0.841327 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.22515 | −0.0926344 | −0.0463172 | − | 0.998927i | \(-0.514748\pi\) | ||||
−0.0463172 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.2054 | − | 12.2054i | −0.507238 | − | 0.507238i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.62248 | + | 2.62248i | −0.108799 | + | 0.108799i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.8973i | 1.65238i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.39839i | − | 0.0991612i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.33373 | − | 4.33373i | 0.178872 | − | 0.178872i | −0.611992 | − | 0.790864i | \(-0.709631\pi\) |
0.790864 | + | 0.611992i | \(0.209631\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4005 | + | 12.4005i | 0.510955 | + | 0.510955i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −56.0390 | −2.30514 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.8460 | −0.691784 | −0.345892 | − | 0.938274i | \(-0.612424\pi\) | ||||
−0.345892 | + | 0.938274i | \(0.612424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.87218 | + | 5.87218i | 0.240736 | + | 0.240736i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.5534 | + | 35.5534i | −1.45510 | + | 1.45510i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 43.9075i | − | 1.79401i | −0.442018 | − | 0.897006i | \(-0.645737\pi\) | ||
0.442018 | − | 0.897006i | \(-0.354263\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.5257i | − | 1.44912i | −0.689210 | − | 0.724562i | \(-0.742042\pi\) | ||
0.689210 | − | 0.724562i | \(-0.257958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.1026 | + | 17.1026i | −0.696472 | + | 0.696472i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.3956 | − | 32.3956i | −1.31707 | − | 1.31707i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7700 | −0.640084 | −0.320042 | − | 0.947403i | \(-0.603697\pi\) | ||||
−0.320042 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.61192 | −0.105841 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.99826 | − | 2.99826i | −0.121297 | − | 0.121297i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.17171 | − | 8.17171i | 0.330052 | − | 0.330052i | −0.522554 | − | 0.852606i | \(-0.675021\pi\) |
0.852606 | + | 0.522554i | \(0.175021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 18.7428i | − | 0.755783i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23.3938i | − | 0.941800i | −0.882187 | − | 0.470900i | \(-0.843929\pi\) | ||
0.882187 | − | 0.470900i | \(-0.156071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.73711 | + | 2.73711i | −0.110014 | + | 0.110014i | −0.759971 | − | 0.649957i | \(-0.774787\pi\) |
0.649957 | + | 0.759971i | \(0.274787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3051 | − | 10.3051i | −0.413528 | − | 0.413528i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.60040 | 0.0641186 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.52682 | 0.341073 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.4400 | − | 21.4400i | −0.856231 | − | 0.856231i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.79472 | + | 7.79472i | −0.310796 | + | 0.310796i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.9200i | 1.39014i | 0.718941 | + | 0.695071i | \(0.244627\pi\) | ||||
−0.718941 | + | 0.695071i | \(0.755373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.05897i | 0.360062i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.8189 | + | 15.8189i | −0.627755 | + | 0.627755i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.448377 | + | 0.448377i | 0.0177653 | + | 0.0177653i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.31976 | 0.368684 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9662 | −1.69706 | −0.848532 | − | 0.529144i | \(-0.822513\pi\) | ||||
−0.848532 | + | 0.529144i | \(0.822513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5924 | − | 17.5924i | −0.693777 | − | 0.693777i | 0.269284 | − | 0.963061i | \(-0.413213\pi\) |
−0.963061 | + | 0.269284i | \(0.913213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.1911 | + | 14.1911i | −0.558775 | + | 0.558775i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.5883i | − | 1.32049i | −0.751049 | − | 0.660246i | \(-0.770452\pi\) | ||
0.751049 | − | 0.660246i | \(-0.229548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.39016i | − | 0.368596i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4557 | − | 13.4557i | 0.527371 | − | 0.527371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.281193 | + | 0.281193i | 0.0110039 | + | 0.0110039i | 0.712587 | − | 0.701583i | \(-0.247523\pi\) |
−0.701583 | + | 0.712587i | \(0.747523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.47498 | −0.135779 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.9008 | −1.20555 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.25405 | + | 1.25405i | 0.0488508 | + | 0.0488508i | 0.731110 | − | 0.682259i | \(-0.239003\pi\) |
−0.682259 | + | 0.731110i | \(0.739003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7505 | − | 30.7505i | 1.19605 | − | 1.19605i | 0.220717 | − | 0.975338i | \(-0.429160\pi\) |
0.975338 | − | 0.220717i | \(-0.0708396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.32460i | − | 0.284464i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.50351i | − | 0.135860i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.14783 | − | 7.14783i | 0.276765 | − | 0.276765i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.55958 | + | 7.55958i | 0.292270 | + | 0.292270i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.9939 | 1.73697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.2711 | −0.858486 | −0.429243 | − | 0.903189i | \(-0.641220\pi\) | ||||
−0.429243 | + | 0.903189i | \(0.641220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.62488 | + | 2.62488i | 0.101032 | + | 0.101032i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3508 | − | 29.3508i | 1.12804 | − | 1.12804i | 0.137547 | − | 0.990495i | \(-0.456078\pi\) |
0.990495 | − | 0.137547i | \(-0.0439218\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.0167i | − | 0.499535i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 14.3516i | − | 0.549956i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.79560 | − | 1.79560i | 0.0687066 | − | 0.0687066i | −0.671918 | − | 0.740625i | \(-0.734529\pi\) |
0.740625 | + | 0.671918i | \(0.234529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.7314 | + | 13.7314i | 0.524649 | + | 0.524649i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.8679 | −1.78812 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.06610 | 0.154906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7289 | − | 11.7289i | −0.446188 | − | 0.446188i | 0.447897 | − | 0.894085i | \(-0.352173\pi\) |
−0.894085 | + | 0.447897i | \(0.852173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.0657 | + | 10.0657i | −0.382363 | + | 0.382363i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.7230i | 0.710202i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 24.7657i | − | 0.938067i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.3358 | − | 18.3358i | 0.693522 | − | 0.693522i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.5050 | + | 23.5050i | 0.887772 | + | 0.887772i | 0.994309 | − | 0.106536i | \(-0.0339761\pi\) |
−0.106536 | + | 0.994309i | \(0.533976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.65056 | 0.175399 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.4212 | 0.957417 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.76253 | + | 3.76253i | 0.141505 | + | 0.141505i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.55617 | + | 1.55617i | −0.0584430 | + | 0.0584430i | −0.735724 | − | 0.677281i | \(-0.763158\pi\) |
0.677281 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 21.0416i | − | 0.789123i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 73.6462i | 2.75807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.61208 | + | 4.61208i | −0.172482 | + | 0.172482i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.61725 | − | 1.61725i | −0.0603972 | − | 0.0603972i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.97452 | 0.260106 | 0.130053 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130053 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.91886 | −0.294914 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.0909 | + | 44.0909i | 1.63976 | + | 1.63976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.82068 | + | 1.82068i | −0.0676184 | + | 0.0676184i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.7285i | − | 0.472073i | −0.971744 | − | 0.236037i | \(-0.924151\pi\) | ||
0.971744 | − | 0.236037i | \(-0.0758485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0216i | 0.482280i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.7513 | + | 18.7513i | −0.693544 | + | 0.693544i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0786 | − | 14.0786i | −0.520006 | − | 0.520006i | 0.397567 | − | 0.917573i | \(-0.369855\pi\) |
−0.917573 | + | 0.397567i | \(0.869855\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.80163 | −0.140225 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 65.7762 | 2.42290 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.9779 | + | 36.9779i | 1.36026 | + | 1.36026i | 0.873587 | + | 0.486669i | \(0.161788\pi\) |
0.486669 | + | 0.873587i | \(0.338212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.18504 | + | 2.18504i | −0.0802693 | + | 0.0802693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.0453i | 0.368527i | 0.982877 | + | 0.184263i | \(0.0589900\pi\) | ||||
−0.982877 | + | 0.184263i | \(0.941010\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.50285i | 0.311520i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.99992 | + | 5.99992i | −0.219525 | + | 0.219525i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.5961 | − | 13.5961i | −0.496789 | − | 0.496789i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.4776 | −1.55003 | −0.775014 | − | 0.631944i | \(-0.782257\pi\) | ||||
−0.775014 | + | 0.631944i | \(0.782257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.5558 | 0.530443 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.6685 | − | 18.6685i | −0.679417 | − | 0.679417i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7792 | − | 29.7792i | 1.08234 | − | 1.08234i | 0.0860518 | − | 0.996291i | \(-0.472575\pi\) |
0.996291 | − | 0.0860518i | \(-0.0274251\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 127.331i | − | 4.62183i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.54784i | 0.237359i | 0.992933 | + | 0.118679i | \(0.0378661\pi\) | ||||
−0.992933 | + | 0.118679i | \(0.962134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.03367 | + | 7.03367i | −0.254636 | + | 0.254636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.4348 | + | 13.4348i | 0.485737 | + | 0.485737i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.956988 | −0.0345549 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6203 | 1.14026 | 0.570129 | − | 0.821555i | \(-0.306893\pi\) | ||||
0.570129 | + | 0.821555i | \(0.306893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5243 | − | 11.5243i | −0.415037 | − | 0.415037i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6240 | − | 10.6240i | 0.382118 | − | 0.382118i | −0.489747 | − | 0.871865i | \(-0.662911\pi\) |
0.871865 | + | 0.489747i | \(0.162911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 18.7590i | − | 0.673843i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.04627i | − | 0.181034i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.38796 | + | 7.38796i | −0.264701 | + | 0.264701i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.9218 | − | 17.9218i | −0.641292 | − | 0.641292i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.86001 | 0.0664714 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.8443 | 1.17226 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2598 | + | 34.2598i | 1.22123 | + | 1.22123i | 0.967195 | + | 0.254035i | \(0.0817580\pi\) |
0.254035 | + | 0.967195i | \(0.418242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.3077 | + | 11.3077i | −0.402564 | + | 0.402564i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.62753i | 0.200092i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.58551i | − | 0.162836i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.2375 | + | 17.2375i | −0.611351 | + | 0.611351i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.55176 | + | 8.55176i | 0.302919 | + | 0.302919i | 0.842155 | − | 0.539236i | \(-0.181287\pi\) |
−0.539236 | + | 0.842155i | \(0.681287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.5901 | 1.18833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.66151 | 0.129373 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.4218 | + | 59.4218i | 2.09695 | + | 2.09695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.4036 | − | 10.4036i | 0.366679 | − | 0.366679i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.1241i | 1.51804i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.6145i | 1.28730i | 0.765321 | + | 0.643649i | \(0.222580\pi\) | ||||
−0.765321 | + | 0.643649i | \(0.777420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6562 | − | 25.6562i | 0.900911 | − | 0.900911i | −0.0946041 | − | 0.995515i | \(-0.530159\pi\) |
0.995515 | + | 0.0946041i | \(0.0301585\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.2467 | − | 23.2467i | −0.815298 | − | 0.815298i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0340 | 0.841873 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1876 | 0.391405 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.02583 | + | 1.02583i | 0.0358454 | + | 0.0358454i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.7635 | + | 12.7635i | −0.445450 | + | 0.445450i | −0.893839 | − | 0.448389i | \(-0.851998\pi\) |
0.448389 | + | 0.893839i | \(0.351998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.1501i | 1.26011i | 0.776549 | + | 0.630057i | \(0.216968\pi\) | ||||
−0.776549 | + | 0.630057i | \(0.783032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.4335i | 1.12919i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2708 | − | 27.2708i | 0.948297 | − | 0.948297i | −0.0504301 | − | 0.998728i | \(-0.516059\pi\) |
0.998728 | + | 0.0504301i | \(0.0160592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.10352 | + | 5.10352i | 0.177253 | + | 0.177253i | 0.790157 | − | 0.612904i | \(-0.209999\pi\) |
−0.612904 | + | 0.790157i | \(0.709999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.08126 | −0.176267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.02326 | −0.174046 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6939 | − | 22.6939i | −0.785354 | − | 0.785354i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.58212 | + | 9.58212i | −0.331206 | + | 0.331206i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 34.6198i | − | 1.19521i | −0.801791 | − | 0.597604i | \(-0.796120\pi\) | ||
0.801791 | − | 0.597604i | \(-0.203880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 27.7099i | − | 0.955512i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.86374 | + | 9.86374i | −0.339725 | + | 0.339725i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.7270 | − | 14.7270i | −0.506623 | − | 0.506623i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7123 | 0.952205 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 66.0786 | 2.26781 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8097 | + | 13.8097i | 0.473391 | + | 0.473391i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.0575 | − | 37.0575i | 1.26882 | − | 1.26882i | 0.322128 | − | 0.946696i | \(-0.395602\pi\) |
0.946696 | − | 0.322128i | \(-0.104398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.01561i | − | 0.274128i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.9647i | 0.647823i | 0.946087 | + | 0.323912i | \(0.104998\pi\) | ||||
−0.946087 | + | 0.323912i | \(0.895002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9539 | + | 17.9539i | −0.612577 | + | 0.612577i | −0.943617 | − | 0.331039i | \(-0.892601\pi\) |
0.331039 | + | 0.943617i | \(0.392601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.01660 | + | 8.01660i | 0.273205 | + | 0.273205i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.5403 | −0.392837 | −0.196418 | − | 0.980520i | \(-0.562931\pi\) | ||||
−0.196418 | + | 0.980520i | \(0.562931\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.6678 | 0.362717 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.3872 | + | 13.3872i | 0.454653 | + | 0.454653i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.4628 | + | 40.4628i | −1.37261 | + | 1.37261i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.70352i | − | 0.227140i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 29.7806i | − | 1.00792i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.49498 | + | 8.49498i | −0.287183 | + | 0.287183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0524 | + | 14.0524i | 0.474516 | + | 0.474516i | 0.903373 | − | 0.428857i | \(-0.141083\pi\) |
−0.428857 | + | 0.903373i | \(0.641083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 72.3114 | 2.43900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.1071 | −1.58708 | −0.793539 | − | 0.608519i | \(-0.791764\pi\) | ||||
−0.793539 | + | 0.608519i | \(0.791764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9886 | + | 16.9886i | 0.571711 | + | 0.571711i | 0.932606 | − | 0.360896i | \(-0.117529\pi\) |
−0.360896 | + | 0.932606i | \(0.617529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.05698 | − | 4.05698i | 0.136374 | − | 0.136374i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 33.3126i | − | 1.11853i | −0.828990 | − | 0.559263i | \(-0.811084\pi\) | ||
0.828990 | − | 0.559263i | \(-0.188916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.5320i | − | 0.453850i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.7640 | − | 46.7640i | 1.56665 | − | 1.56665i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0204 | − | 10.0204i | −0.335320 | − | 0.335320i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.3084 | −1.31394 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.9768 | −0.433283 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.64639 | − | 6.64639i | −0.221669 | − | 0.221669i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7767 | + | 22.7767i | −0.758801 | + | 0.758801i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 12.1396i | − | 0.403979i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.6325i | 0.486401i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.65953 | − | 5.65953i | 0.187922 | − | 0.187922i | −0.606875 | − | 0.794797i | \(-0.707577\pi\) |
0.794797 | + | 0.606875i | \(0.207577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.60821 | + | 8.60821i | 0.285516 | + | 0.285516i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.8870 | 1.38778 | 0.693889 | − | 0.720082i | \(-0.255896\pi\) | ||||
0.693889 | + | 0.720082i | \(0.255896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.0755 | 0.763689 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.4395 | + | 19.4395i | 0.642649 | + | 0.642649i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.48631 | − | 1.48631i | 0.0490821 | − | 0.0490821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4978i | 0.478237i | 0.970990 | + | 0.239119i | \(0.0768585\pi\) | ||||
−0.970990 | + | 0.239119i | \(0.923142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 57.7743i | − | 1.90373i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.82648 | + | 1.82648i | −0.0601193 | + | 0.0601193i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.51758 | − | 3.51758i | −0.115657 | − | 0.115657i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.1174 | −0.595053 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.5646 | 0.707513 | 0.353756 | − | 0.935338i | \(-0.384904\pi\) | ||||
0.353756 | + | 0.935338i | \(0.384904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49851 | + | 1.49851i | 0.0491117 | + | 0.0491117i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.8453 | − | 50.8453i | 1.66460 | − | 1.66460i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 51.6700i | − | 1.68979i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.51782i | − | 0.114922i | −0.998348 | − | 0.0574611i | \(-0.981699\pi\) | ||
0.998348 | − | 0.0574611i | \(-0.0183005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.2839 | − | 29.2839i | 0.955643 | − | 0.955643i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.768500 | − | 0.768500i | −0.0250524 | − | 0.0250524i | 0.694470 | − | 0.719522i | \(-0.255639\pi\) |
−0.719522 | + | 0.694470i | \(0.755639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.8767 | −1.42882 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.70723 | 0.0880661 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3253 | − | 11.3253i | −0.368022 | − | 0.368022i | 0.498733 | − | 0.866755i | \(-0.333799\pi\) |
−0.866755 | + | 0.498733i | \(0.833799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.05592 | − | 6.05592i | 0.196583 | − | 0.196583i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 39.8107i | − | 1.29095i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.82914i | 0.318397i | 0.987247 | + | 0.159199i | \(0.0508910\pi\) | ||||
−0.987247 | + | 0.159199i | \(0.949109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.4962 | − | 18.4962i | 0.598522 | − | 0.598522i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.4913 | + | 11.4913i | 0.371462 | + | 0.371462i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.7463 | −0.379307 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.4796 | 1.20902 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.1061 | − | 31.1061i | −1.00238 | − | 1.00238i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.77485 | + | 8.77485i | −0.282472 | + | 0.282472i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.71372i | − | 0.183741i | −0.995771 | − | 0.0918705i | \(-0.970715\pi\) | ||
0.995771 | − | 0.0918705i | \(-0.0292846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 24.4794i | − | 0.786392i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3515 | − | 13.3515i | 0.428469 | − | 0.428469i | −0.459638 | − | 0.888106i | \(-0.652021\pi\) |
0.888106 | + | 0.459638i | \(0.152021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00812 | − | 8.00812i | −0.256728 | − | 0.256728i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.30543 | 0.105858 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.3043 | 0.809556 | 0.404778 | − | 0.914415i | \(-0.367349\pi\) | ||||
0.404778 | + | 0.914415i | \(0.367349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.04105 | − | 7.04105i | −0.225033 | − | 0.225033i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0922 | + | 16.0922i | −0.513784 | + | 0.513784i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.4206i | 0.396157i | 0.980186 | + | 0.198078i | \(0.0634701\pi\) | ||||
−0.980186 | + | 0.198078i | \(0.936530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.2883i | 1.28369i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.8731 | + | 10.8731i | −0.346093 | + | 0.346093i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.2213 | + | 33.2213i | 1.05638 | + | 1.05638i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.4013 | −0.965729 | −0.482865 | − | 0.875695i | \(-0.660404\pi\) | ||||
−0.482865 | + | 0.875695i | \(0.660404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.1973 | 1.21215 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.5605 | + | 25.5605i | 0.810323 | + | 0.810323i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48812 | − | 8.48812i | 0.268821 | − | 0.268821i | −0.559804 | − | 0.828625i | \(-0.689123\pi\) |
0.828625 | + | 0.559804i | \(0.189123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.59357i | 0.113695i |
(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 | 1792.2.m.g.1345.6 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.e.1345.3 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.h.1345.6 | yes | 16 | ||
8.5 | even | 2 | 1792.2.m.f.1345.3 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.h.449.6 | yes | 16 | ||
16.5 | even | 4 | inner | 1792.2.m.g.449.6 | yes | 16 | |
16.11 | odd | 4 | 1792.2.m.e.449.3 | ✓ | 16 | ||
16.13 | even | 4 | 1792.2.m.f.449.3 | yes | 16 | ||
32.5 | even | 8 | 7168.2.a.be.1.2 | 8 | |||
32.11 | odd | 8 | 7168.2.a.bb.1.2 | 8 | |||
32.21 | even | 8 | 7168.2.a.ba.1.7 | 8 | |||
32.27 | odd | 8 | 7168.2.a.bf.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.3 | ✓ | 16 | 16.11 | odd | 4 | ||
1792.2.m.e.1345.3 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.f.449.3 | yes | 16 | 16.13 | even | 4 | ||
1792.2.m.f.1345.3 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.g.449.6 | yes | 16 | 16.5 | even | 4 | inner | |
1792.2.m.g.1345.6 | yes | 16 | 1.1 | even | 1 | trivial | |
1792.2.m.h.449.6 | yes | 16 | 16.3 | odd | 4 | ||
1792.2.m.h.1345.6 | yes | 16 | 8.3 | odd | 2 | ||
7168.2.a.ba.1.7 | 8 | 32.21 | even | 8 | |||
7168.2.a.bb.1.2 | 8 | 32.11 | odd | 8 | |||
7168.2.a.be.1.2 | 8 | 32.5 | even | 8 | |||
7168.2.a.bf.1.7 | 8 | 32.27 | odd | 8 |