Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), 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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.12 | ||
Root | \(1.24938i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.j.1084.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24938i | 0.883447i | 0.897151 | + | 0.441724i | \(0.145633\pi\) | ||||
−0.897151 | + | 0.441724i | \(0.854367\pi\) | |||||||
\(3\) | 1.51315i | 0.873616i | 0.899555 | + | 0.436808i | \(0.143891\pi\) | ||||
−0.899555 | + | 0.436808i | \(0.856109\pi\) | |||||||
\(4\) | 0.439042 | 0.219521 | ||||||||
\(5\) | −1.95031 | + | 1.09375i | −0.872206 | + | 0.489138i | ||||
\(6\) | −1.89050 | −0.771793 | ||||||||
\(7\) | 0.568589i | 0.214907i | 0.994210 | + | 0.107453i | \(0.0342696\pi\) | ||||
−0.994210 | + | 0.107453i | \(0.965730\pi\) | |||||||
\(8\) | 3.04730i | 1.07738i | ||||||||
\(9\) | 0.710386 | 0.236795 | ||||||||
\(10\) | −1.36651 | − | 2.43669i | −0.432128 | − | 0.770548i | ||||
\(11\) | 3.18990 | 0.961792 | 0.480896 | − | 0.876778i | \(-0.340312\pi\) | ||||
0.480896 | + | 0.876778i | \(0.340312\pi\) | |||||||
\(12\) | 0.664336i | 0.191777i | ||||||||
\(13\) | 2.28031i | 0.632443i | 0.948685 | + | 0.316222i | \(0.102414\pi\) | ||||
−0.948685 | + | 0.316222i | \(0.897586\pi\) | |||||||
\(14\) | −0.710386 | −0.189859 | ||||||||
\(15\) | −1.65500 | − | 2.95111i | −0.427319 | − | 0.761973i | ||||
\(16\) | −2.92916 | −0.732289 | ||||||||
\(17\) | 2.21494i | 0.537203i | 0.963251 | + | 0.268601i | \(0.0865615\pi\) | ||||
−0.963251 | + | 0.268601i | \(0.913439\pi\) | |||||||
\(18\) | 0.887544i | 0.209196i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.856270 | + | 0.480201i | −0.191468 | + | 0.107376i | ||||
\(21\) | −0.860359 | −0.187746 | ||||||||
\(22\) | 3.98541i | 0.849692i | ||||||||
\(23\) | − | 0.0101715i | − | 0.00212090i | −0.999999 | − | 0.00106045i | \(-0.999662\pi\) | ||
0.999999 | − | 0.00106045i | \(-0.000337552\pi\) | |||||||
\(24\) | −4.61101 | −0.941219 | ||||||||
\(25\) | 2.60744 | − | 4.26630i | 0.521487 | − | 0.853259i | ||||
\(26\) | −2.84898 | −0.558730 | ||||||||
\(27\) | 5.61436i | 1.08048i | ||||||||
\(28\) | 0.249635i | 0.0471765i | ||||||||
\(29\) | −1.14455 | −0.212537 | −0.106268 | − | 0.994337i | \(-0.533890\pi\) | ||||
−0.106268 | + | 0.994337i | \(0.533890\pi\) | |||||||
\(30\) | 3.68707 | − | 2.06773i | 0.673163 | − | 0.377514i | ||||
\(31\) | −9.12067 | −1.63812 | −0.819060 | − | 0.573708i | \(-0.805505\pi\) | ||||
−0.819060 | + | 0.573708i | \(0.805505\pi\) | |||||||
\(32\) | 2.43496i | 0.430444i | ||||||||
\(33\) | 4.82679i | 0.840236i | ||||||||
\(34\) | −2.76731 | −0.474590 | ||||||||
\(35\) | −0.621893 | − | 1.10893i | −0.105119 | − | 0.187443i | ||||
\(36\) | 0.311889 | 0.0519816 | ||||||||
\(37\) | 8.97487i | 1.47546i | 0.675096 | + | 0.737730i | \(0.264102\pi\) | ||||
−0.675096 | + | 0.737730i | \(0.735898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.45044 | −0.552512 | ||||||||
\(40\) | −3.33297 | − | 5.94318i | −0.526989 | − | 0.939700i | ||||
\(41\) | 10.5778 | 1.65197 | 0.825985 | − | 0.563692i | \(-0.190619\pi\) | ||||
0.825985 | + | 0.563692i | \(0.190619\pi\) | |||||||
\(42\) | − | 1.07492i | − | 0.165863i | ||||||
\(43\) | 7.91273i | 1.20668i | 0.797484 | + | 0.603340i | \(0.206164\pi\) | ||||
−0.797484 | + | 0.603340i | \(0.793836\pi\) | |||||||
\(44\) | 1.40050 | 0.211134 | ||||||||
\(45\) | −1.38547 | + | 0.776982i | −0.206534 | + | 0.115826i | ||||
\(46\) | 0.0127081 | 0.00187370 | ||||||||
\(47\) | − | 12.5442i | − | 1.82976i | −0.403731 | − | 0.914878i | \(-0.632287\pi\) | ||
0.403731 | − | 0.914878i | \(-0.367713\pi\) | |||||||
\(48\) | − | 4.43225i | − | 0.639740i | ||||||
\(49\) | 6.67671 | 0.953815 | ||||||||
\(50\) | 5.33024 | + | 3.25769i | 0.753809 | + | 0.460706i | ||||
\(51\) | −3.35154 | −0.469309 | ||||||||
\(52\) | 1.00115i | 0.138835i | ||||||||
\(53\) | − | 7.43944i | − | 1.02189i | −0.859615 | − | 0.510943i | \(-0.829296\pi\) | ||
0.859615 | − | 0.510943i | \(-0.170704\pi\) | |||||||
\(54\) | −7.01448 | −0.954550 | ||||||||
\(55\) | −6.22130 | + | 3.48894i | −0.838881 | + | 0.470449i | ||||
\(56\) | −1.73266 | −0.231537 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.42998i | − | 0.187765i | ||||||
\(59\) | −8.46844 | −1.10250 | −0.551249 | − | 0.834341i | \(-0.685848\pi\) | ||||
−0.551249 | + | 0.834341i | \(0.685848\pi\) | |||||||
\(60\) | −0.726615 | − | 1.29566i | −0.0938056 | − | 0.167269i | ||||
\(61\) | −7.36372 | −0.942828 | −0.471414 | − | 0.881912i | \(-0.656256\pi\) | ||||
−0.471414 | + | 0.881912i | \(0.656256\pi\) | |||||||
\(62\) | − | 11.3952i | − | 1.44719i | ||||||
\(63\) | 0.403918i | 0.0508888i | ||||||||
\(64\) | −8.90051 | −1.11256 | ||||||||
\(65\) | −2.49408 | − | 4.44731i | −0.309352 | − | 0.551621i | ||||
\(66\) | −6.03051 | −0.742304 | ||||||||
\(67\) | 3.51270i | 0.429144i | 0.976708 | + | 0.214572i | \(0.0688357\pi\) | ||||
−0.976708 | + | 0.214572i | \(0.931164\pi\) | |||||||
\(68\) | 0.972455i | 0.117927i | ||||||||
\(69\) | 0.0153909 | 0.00185285 | ||||||||
\(70\) | 1.38547 | − | 0.776982i | 0.165596 | − | 0.0928671i | ||||
\(71\) | 4.56784 | 0.542103 | 0.271052 | − | 0.962565i | \(-0.412629\pi\) | ||||
0.271052 | + | 0.962565i | \(0.412629\pi\) | |||||||
\(72\) | 2.16476i | 0.255119i | ||||||||
\(73\) | − | 9.66012i | − | 1.13063i | −0.824875 | − | 0.565316i | \(-0.808754\pi\) | ||
0.824875 | − | 0.565316i | \(-0.191246\pi\) | |||||||
\(74\) | −11.2130 | −1.30349 | ||||||||
\(75\) | 6.45553 | + | 3.94543i | 0.745421 | + | 0.455579i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.81374i | 0.206695i | ||||||||
\(78\) | − | 4.31092i | − | 0.488115i | ||||||
\(79\) | 7.97511 | 0.897270 | 0.448635 | − | 0.893715i | \(-0.351910\pi\) | ||||
0.448635 | + | 0.893715i | \(0.351910\pi\) | |||||||
\(80\) | 5.71277 | − | 3.20376i | 0.638707 | − | 0.358191i | ||||
\(81\) | −6.36420 | −0.707133 | ||||||||
\(82\) | 13.2157i | 1.45943i | ||||||||
\(83\) | − | 13.7395i | − | 1.50811i | −0.656810 | − | 0.754056i | \(-0.728095\pi\) | ||
0.656810 | − | 0.754056i | \(-0.271905\pi\) | |||||||
\(84\) | −0.377734 | −0.0412142 | ||||||||
\(85\) | −2.42259 | − | 4.31983i | −0.262767 | − | 0.468552i | ||||
\(86\) | −9.88603 | −1.06604 | ||||||||
\(87\) | − | 1.73187i | − | 0.185676i | ||||||
\(88\) | 9.72058i | 1.03622i | ||||||||
\(89\) | 3.41038 | 0.361500 | 0.180750 | − | 0.983529i | \(-0.442148\pi\) | ||||
0.180750 | + | 0.983529i | \(0.442148\pi\) | |||||||
\(90\) | −0.970748 | − | 1.73099i | −0.102326 | − | 0.182462i | ||||
\(91\) | −1.29656 | −0.135916 | ||||||||
\(92\) | − | 0.00446571i | − | 0.000465582i | ||||||
\(93\) | − | 13.8009i | − | 1.43109i | ||||||
\(94\) | 15.6725 | 1.61649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.68445 | −0.376042 | ||||||||
\(97\) | 3.01777i | 0.306408i | 0.988195 | + | 0.153204i | \(0.0489592\pi\) | ||||
−0.988195 | + | 0.153204i | \(0.951041\pi\) | |||||||
\(98\) | 8.34176i | 0.842645i | ||||||||
\(99\) | 2.26606 | 0.227748 | ||||||||
\(100\) | 1.14478 | − | 1.87308i | 0.114478 | − | 0.187308i | ||||
\(101\) | −14.4164 | −1.43449 | −0.717243 | − | 0.696823i | \(-0.754596\pi\) | ||||
−0.717243 | + | 0.696823i | \(0.754596\pi\) | |||||||
\(102\) | − | 4.18735i | − | 0.414610i | ||||||
\(103\) | 4.41406i | 0.434931i | 0.976068 | + | 0.217465i | \(0.0697789\pi\) | ||||
−0.976068 | + | 0.217465i | \(0.930221\pi\) | |||||||
\(104\) | −6.94877 | −0.681383 | ||||||||
\(105\) | 1.67797 | − | 0.941015i | 0.163753 | − | 0.0918337i | ||||
\(106\) | 9.29471 | 0.902782 | ||||||||
\(107\) | − | 13.8931i | − | 1.34309i | −0.740962 | − | 0.671547i | \(-0.765630\pi\) | ||
0.740962 | − | 0.671547i | \(-0.234370\pi\) | |||||||
\(108\) | 2.46494i | 0.237189i | ||||||||
\(109\) | −3.59943 | −0.344762 | −0.172381 | − | 0.985030i | \(-0.555146\pi\) | ||||
−0.172381 | + | 0.985030i | \(0.555146\pi\) | |||||||
\(110\) | −4.35903 | − | 7.77279i | −0.415617 | − | 0.741107i | ||||
\(111\) | −13.5803 | −1.28898 | ||||||||
\(112\) | − | 1.66549i | − | 0.157374i | ||||||
\(113\) | − | 15.7601i | − | 1.48258i | −0.671183 | − | 0.741291i | \(-0.734214\pi\) | ||
0.671183 | − | 0.741291i | \(-0.265786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0111250 | + | 0.0198375i | 0.00103741 | + | 0.00184986i | ||||
\(116\) | −0.502505 | −0.0466564 | ||||||||
\(117\) | 1.61990i | 0.149759i | ||||||||
\(118\) | − | 10.5803i | − | 0.973998i | ||||||
\(119\) | −1.25939 | −0.115448 | ||||||||
\(120\) | 8.99291 | − | 5.04328i | 0.820937 | − | 0.460386i | ||||
\(121\) | −0.824527 | −0.0749570 | ||||||||
\(122\) | − | 9.20011i | − | 0.832939i | ||||||
\(123\) | 16.0057i | 1.44319i | ||||||||
\(124\) | −4.00436 | −0.359602 | ||||||||
\(125\) | −0.419067 | + | 11.1725i | −0.0374825 | + | 0.999297i | ||||
\(126\) | −0.504648 | −0.0449576 | ||||||||
\(127\) | 1.35801i | 0.120504i | 0.998183 | + | 0.0602518i | \(0.0191904\pi\) | ||||
−0.998183 | + | 0.0602518i | \(0.980810\pi\) | |||||||
\(128\) | − | 6.25023i | − | 0.552447i | ||||||
\(129\) | −11.9731 | −1.05417 | ||||||||
\(130\) | 5.55639 | − | 3.11606i | 0.487328 | − | 0.273296i | ||||
\(131\) | 13.9257 | 1.21669 | 0.608346 | − | 0.793672i | \(-0.291833\pi\) | ||||
0.608346 | + | 0.793672i | \(0.291833\pi\) | |||||||
\(132\) | 2.11917i | 0.184450i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.38870 | −0.379126 | ||||||||
\(135\) | −6.14069 | − | 10.9498i | −0.528506 | − | 0.942405i | ||||
\(136\) | −6.74960 | −0.578773 | ||||||||
\(137\) | 16.6294i | 1.42074i | 0.703826 | + | 0.710372i | \(0.251473\pi\) | ||||
−0.703826 | + | 0.710372i | \(0.748527\pi\) | |||||||
\(138\) | 0.0192292i | 0.00163690i | ||||||||
\(139\) | 4.26670 | 0.361897 | 0.180948 | − | 0.983493i | \(-0.442083\pi\) | ||||
0.180948 | + | 0.983493i | \(0.442083\pi\) | |||||||
\(140\) | −0.273037 | − | 0.486866i | −0.0230759 | − | 0.0411477i | ||||
\(141\) | 18.9812 | 1.59850 | ||||||||
\(142\) | 5.70698i | 0.478919i | ||||||||
\(143\) | 7.27395i | 0.608278i | ||||||||
\(144\) | −2.08083 | −0.173403 | ||||||||
\(145\) | 2.23222 | − | 1.25184i | 0.185376 | − | 0.103960i | ||||
\(146\) | 12.0692 | 0.998853 | ||||||||
\(147\) | 10.1028i | 0.833268i | ||||||||
\(148\) | 3.94035i | 0.323895i | ||||||||
\(149\) | 9.16824 | 0.751092 | 0.375546 | − | 0.926804i | \(-0.377455\pi\) | ||||
0.375546 | + | 0.926804i | \(0.377455\pi\) | |||||||
\(150\) | −4.92936 | + | 8.06543i | −0.402480 | + | 0.658540i | ||||
\(151\) | −5.58655 | −0.454627 | −0.227314 | − | 0.973822i | \(-0.572994\pi\) | ||||
−0.227314 | + | 0.973822i | \(0.572994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.57346i | 0.127207i | ||||||||
\(154\) | −2.26606 | −0.182604 | ||||||||
\(155\) | 17.7881 | − | 9.97570i | 1.42878 | − | 0.801268i | ||||
\(156\) | −1.51489 | −0.121288 | ||||||||
\(157\) | − | 16.7284i | − | 1.33507i | −0.744578 | − | 0.667535i | \(-0.767349\pi\) | ||
0.744578 | − | 0.667535i | \(-0.232651\pi\) | |||||||
\(158\) | 9.96397i | 0.792691i | ||||||||
\(159\) | 11.2570 | 0.892736 | ||||||||
\(160\) | −2.66323 | − | 4.74893i | −0.210547 | − | 0.375436i | ||||
\(161\) | 0.00578339 | 0.000455795 | ||||||||
\(162\) | − | 7.95132i | − | 0.624714i | ||||||
\(163\) | 24.3332i | 1.90592i | 0.303090 | + | 0.952962i | \(0.401982\pi\) | ||||
−0.303090 | + | 0.952962i | \(0.598018\pi\) | |||||||
\(164\) | 4.64409 | 0.362643 | ||||||||
\(165\) | −5.27929 | − | 9.41375i | −0.410992 | − | 0.732859i | ||||
\(166\) | 17.1660 | 1.33234 | ||||||||
\(167\) | − | 3.96229i | − | 0.306611i | −0.988179 | − | 0.153305i | \(-0.951008\pi\) | ||
0.988179 | − | 0.153305i | \(-0.0489918\pi\) | |||||||
\(168\) | − | 2.62177i | − | 0.202274i | ||||||
\(169\) | 7.80021 | 0.600016 | ||||||||
\(170\) | 5.39713 | − | 3.02674i | 0.413941 | − | 0.232140i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.47402i | 0.264892i | ||||||||
\(173\) | 22.4611i | 1.70769i | 0.520528 | + | 0.853844i | \(0.325735\pi\) | ||||
−0.520528 | + | 0.853844i | \(0.674265\pi\) | |||||||
\(174\) | 2.16377 | 0.164035 | ||||||||
\(175\) | 2.42577 | + | 1.48256i | 0.183371 | + | 0.112071i | ||||
\(176\) | −9.34372 | −0.704310 | ||||||||
\(177\) | − | 12.8140i | − | 0.963159i | ||||||
\(178\) | 4.26087i | 0.319366i | ||||||||
\(179\) | 8.56842 | 0.640434 | 0.320217 | − | 0.947344i | \(-0.396244\pi\) | ||||
0.320217 | + | 0.947344i | \(0.396244\pi\) | |||||||
\(180\) | −0.608282 | + | 0.341128i | −0.0453387 | + | 0.0254262i | ||||
\(181\) | −21.5945 | −1.60511 | −0.802554 | − | 0.596580i | \(-0.796526\pi\) | ||||
−0.802554 | + | 0.596580i | \(0.796526\pi\) | |||||||
\(182\) | − | 1.61990i | − | 0.120075i | ||||||
\(183\) | − | 11.1424i | − | 0.823670i | ||||||
\(184\) | 0.0309955 | 0.00228502 | ||||||||
\(185\) | −9.81623 | − | 17.5038i | −0.721704 | − | 1.28690i | ||||
\(186\) | 17.2426 | 1.26429 | ||||||||
\(187\) | 7.06545i | 0.516677i | ||||||||
\(188\) | − | 5.50742i | − | 0.401670i | ||||||
\(189\) | −3.19226 | −0.232203 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.25980 | 0.380586 | 0.190293 | − | 0.981727i | \(-0.439056\pi\) | ||||
0.190293 | + | 0.981727i | \(0.439056\pi\) | |||||||
\(192\) | − | 13.4678i | − | 0.971953i | ||||||
\(193\) | 6.86172i | 0.493918i | 0.969026 | + | 0.246959i | \(0.0794312\pi\) | ||||
−0.969026 | + | 0.246959i | \(0.920569\pi\) | |||||||
\(194\) | −3.77035 | −0.270696 | ||||||||
\(195\) | 6.72943 | − | 3.77391i | 0.481905 | − | 0.270255i | ||||
\(196\) | 2.93136 | 0.209383 | ||||||||
\(197\) | 3.97259i | 0.283035i | 0.989936 | + | 0.141518i | \(0.0451982\pi\) | ||||
−0.989936 | + | 0.141518i | \(0.954802\pi\) | |||||||
\(198\) | 2.83118i | 0.201203i | ||||||||
\(199\) | 13.8356 | 0.980780 | 0.490390 | − | 0.871503i | \(-0.336854\pi\) | ||||
0.490390 | + | 0.871503i | \(0.336854\pi\) | |||||||
\(200\) | 13.0007 | + | 7.94563i | 0.919286 | + | 0.561841i | ||||
\(201\) | −5.31523 | −0.374907 | ||||||||
\(202\) | − | 18.0116i | − | 1.26729i | ||||||
\(203\) | − | 0.650777i | − | 0.0456756i | ||||||
\(204\) | −1.47147 | −0.103023 | ||||||||
\(205\) | −20.6300 | + | 11.5694i | −1.44086 | + | 0.808042i | ||||
\(206\) | −5.51486 | −0.384238 | ||||||||
\(207\) | − | 0.00722567i | − | 0.000502219i | ||||||
\(208\) | − | 6.67937i | − | 0.463131i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.17569 | + | 2.09643i | 0.0811302 | + | 0.144667i | ||||
\(211\) | 11.5957 | 0.798282 | 0.399141 | − | 0.916890i | \(-0.369308\pi\) | ||||
0.399141 | + | 0.916890i | \(0.369308\pi\) | |||||||
\(212\) | − | 3.26623i | − | 0.224326i | ||||||
\(213\) | 6.91182i | 0.473590i | ||||||||
\(214\) | 17.3578 | 1.18655 | ||||||||
\(215\) | −8.65452 | − | 15.4323i | −0.590233 | − | 1.05247i | ||||
\(216\) | −17.1086 | −1.16409 | ||||||||
\(217\) | − | 5.18591i | − | 0.352043i | ||||||
\(218\) | − | 4.49706i | − | 0.304579i | ||||||
\(219\) | 14.6172 | 0.987737 | ||||||||
\(220\) | −2.73142 | + | 1.53179i | −0.184152 | + | 0.103274i | ||||
\(221\) | −5.05075 | −0.339750 | ||||||||
\(222\) | − | 16.9670i | − | 1.13875i | ||||||
\(223\) | − | 1.95798i | − | 0.131116i | −0.997849 | − | 0.0655580i | \(-0.979117\pi\) | ||
0.997849 | − | 0.0655580i | \(-0.0208827\pi\) | |||||||
\(224\) | −1.38449 | −0.0925052 | ||||||||
\(225\) | 1.85228 | − | 3.03072i | 0.123486 | − | 0.202048i | ||||
\(226\) | 19.6904 | 1.30978 | ||||||||
\(227\) | 7.20506i | 0.478217i | 0.970993 | + | 0.239108i | \(0.0768551\pi\) | ||||
−0.970993 | + | 0.239108i | \(0.923145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4984 | 1.15632 | 0.578162 | − | 0.815922i | \(-0.303770\pi\) | ||||
0.578162 | + | 0.815922i | \(0.303770\pi\) | |||||||
\(230\) | −0.0247847 | + | 0.0138994i | −0.00163425 | + | 0.000916499i | ||||
\(231\) | −2.74446 | −0.180572 | ||||||||
\(232\) | − | 3.48777i | − | 0.228984i | ||||||
\(233\) | 3.79613i | 0.248693i | 0.992239 | + | 0.124346i | \(0.0396834\pi\) | ||||
−0.992239 | + | 0.124346i | \(0.960317\pi\) | |||||||
\(234\) | −2.02387 | −0.132305 | ||||||||
\(235\) | 13.7201 | + | 24.4651i | 0.895004 | + | 1.59592i | ||||
\(236\) | −3.71801 | −0.242022 | ||||||||
\(237\) | 12.0675i | 0.783870i | ||||||||
\(238\) | − | 1.57346i | − | 0.101993i | ||||||
\(239\) | −10.4757 | −0.677614 | −0.338807 | − | 0.940856i | \(-0.610023\pi\) | ||||
−0.338807 | + | 0.940856i | \(0.610023\pi\) | |||||||
\(240\) | 4.84775 | + | 8.64426i | 0.312921 | + | 0.557985i | ||||
\(241\) | 2.86967 | 0.184851 | 0.0924257 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924257 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(242\) | − | 1.03015i | − | 0.0662205i | ||||||
\(243\) | 7.21311i | 0.462721i | ||||||||
\(244\) | −3.23299 | −0.206971 | ||||||||
\(245\) | −13.0217 | + | 7.30263i | −0.831923 | + | 0.466548i | ||||
\(246\) | −19.9973 | −1.27498 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 27.7934i | − | 1.76488i | ||||||
\(249\) | 20.7900 | 1.31751 | ||||||||
\(250\) | −13.9587 | − | 0.523575i | −0.882826 | − | 0.0331138i | ||||
\(251\) | −19.1428 | −1.20828 | −0.604141 | − | 0.796877i | \(-0.706484\pi\) | ||||
−0.604141 | + | 0.796877i | \(0.706484\pi\) | |||||||
\(252\) | 0.177337i | 0.0111712i | ||||||||
\(253\) | − | 0.0324460i | − | 0.00203986i | ||||||
\(254\) | −1.69667 | −0.106459 | ||||||||
\(255\) | 6.53654 | − | 3.66573i | 0.409334 | − | 0.229557i | ||||
\(256\) | −9.99209 | −0.624506 | ||||||||
\(257\) | − | 10.2306i | − | 0.638169i | −0.947726 | − | 0.319085i | \(-0.896625\pi\) | ||
0.947726 | − | 0.319085i | \(-0.103375\pi\) | |||||||
\(258\) | − | 14.9590i | − | 0.931308i | ||||||
\(259\) | −5.10301 | −0.317086 | ||||||||
\(260\) | −1.09501 | − | 1.95256i | −0.0679094 | − | 0.121092i | ||||
\(261\) | −0.813069 | −0.0503277 | ||||||||
\(262\) | 17.3985i | 1.07488i | ||||||||
\(263\) | 6.62838i | 0.408723i | 0.978895 | + | 0.204362i | \(0.0655119\pi\) | ||||
−0.978895 | + | 0.204362i | \(0.934488\pi\) | |||||||
\(264\) | −14.7087 | −0.905256 | ||||||||
\(265\) | 8.13686 | + | 14.5092i | 0.499844 | + | 0.891295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.16041i | 0.315812i | ||||||||
\(268\) | 1.54222i | 0.0942062i | ||||||||
\(269\) | −12.8640 | −0.784333 | −0.392167 | − | 0.919894i | \(-0.628274\pi\) | ||||
−0.392167 | + | 0.919894i | \(0.628274\pi\) | |||||||
\(270\) | 13.6804 | − | 7.67207i | 0.832565 | − | 0.466907i | ||||
\(271\) | 9.26123 | 0.562579 | 0.281290 | − | 0.959623i | \(-0.409238\pi\) | ||||
0.281290 | + | 0.959623i | \(0.409238\pi\) | |||||||
\(272\) | − | 6.48792i | − | 0.393388i | ||||||
\(273\) | − | 1.96188i | − | 0.118739i | ||||||
\(274\) | −20.7765 | −1.25515 | ||||||||
\(275\) | 8.31746 | − | 13.6091i | 0.501562 | − | 0.820657i | ||||
\(276\) | 0.00675727 | 0.000406740 | ||||||||
\(277\) | − | 12.6774i | − | 0.761712i | −0.924634 | − | 0.380856i | \(-0.875629\pi\) | ||
0.924634 | − | 0.380856i | \(-0.124371\pi\) | |||||||
\(278\) | 5.33074i | 0.319717i | ||||||||
\(279\) | −6.47919 | −0.387899 | ||||||||
\(280\) | 3.37923 | − | 1.89509i | 0.201948 | − | 0.113253i | ||||
\(281\) | 28.6975 | 1.71195 | 0.855976 | − | 0.517016i | \(-0.172957\pi\) | ||||
0.855976 | + | 0.517016i | \(0.172957\pi\) | |||||||
\(282\) | 23.7148i | 1.41219i | ||||||||
\(283\) | − | 13.9723i | − | 0.830565i | −0.909692 | − | 0.415283i | \(-0.863683\pi\) | ||
0.909692 | − | 0.415283i | \(-0.136317\pi\) | |||||||
\(284\) | 2.00548 | 0.119003 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.08795 | −0.537382 | ||||||||
\(287\) | 6.01441i | 0.355019i | ||||||||
\(288\) | 1.72976i | 0.101927i | ||||||||
\(289\) | 12.0940 | 0.711413 | ||||||||
\(290\) | 1.56403 | + | 2.78890i | 0.0918432 | + | 0.163770i | ||||
\(291\) | −4.56634 | −0.267683 | ||||||||
\(292\) | − | 4.24120i | − | 0.248198i | ||||||
\(293\) | 5.77232i | 0.337223i | 0.985683 | + | 0.168611i | \(0.0539283\pi\) | ||||
−0.985683 | + | 0.168611i | \(0.946072\pi\) | |||||||
\(294\) | −12.6223 | −0.736148 | ||||||||
\(295\) | 16.5161 | − | 9.26233i | 0.961605 | − | 0.539274i | ||||
\(296\) | −27.3491 | −1.58963 | ||||||||
\(297\) | 17.9093i | 1.03920i | ||||||||
\(298\) | 11.4546i | 0.663550i | ||||||||
\(299\) | 0.0231941 | 0.00134135 | ||||||||
\(300\) | 2.83425 | + | 1.73221i | 0.163636 | + | 0.100009i | ||||
\(301\) | −4.49909 | −0.259323 | ||||||||
\(302\) | − | 6.97975i | − | 0.401639i | ||||||
\(303\) | − | 21.8141i | − | 1.25319i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3616 | − | 8.05405i | 0.822340 | − | 0.461173i | ||||
\(306\) | −1.96586 | −0.112381 | ||||||||
\(307\) | − | 10.3450i | − | 0.590419i | −0.955433 | − | 0.295209i | \(-0.904611\pi\) | ||
0.955433 | − | 0.295209i | \(-0.0953894\pi\) | |||||||
\(308\) | 0.796311i | 0.0453740i | ||||||||
\(309\) | −6.67913 | −0.379962 | ||||||||
\(310\) | 12.4635 | + | 22.2242i | 0.707878 | + | 1.26225i | ||||
\(311\) | −14.8195 | −0.840339 | −0.420169 | − | 0.907446i | \(-0.638029\pi\) | ||||
−0.420169 | + | 0.907446i | \(0.638029\pi\) | |||||||
\(312\) | − | 10.5145i | − | 0.595267i | ||||||
\(313\) | 18.3966i | 1.03984i | 0.854216 | + | 0.519919i | \(0.174038\pi\) | ||||
−0.854216 | + | 0.519919i | \(0.825962\pi\) | |||||||
\(314\) | 20.9002 | 1.17946 | ||||||||
\(315\) | −0.441784 | − | 0.787765i | −0.0248917 | − | 0.0443856i | ||||
\(316\) | 3.50141 | 0.196970 | ||||||||
\(317\) | 0.484179i | 0.0271942i | 0.999908 | + | 0.0135971i | \(0.00432823\pi\) | ||||
−0.999908 | + | 0.0135971i | \(0.995672\pi\) | |||||||
\(318\) | 14.0643i | 0.788685i | ||||||||
\(319\) | −3.65099 | −0.204416 | ||||||||
\(320\) | 17.3588 | − | 9.73490i | 0.970385 | − | 0.544198i | ||||
\(321\) | 21.0223 | 1.17335 | ||||||||
\(322\) | 0.00722567i | 0.000402671i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.79415 | −0.155231 | ||||||||
\(325\) | 9.72846 | + | 5.94575i | 0.539638 | + | 0.329811i | ||||
\(326\) | −30.4015 | −1.68378 | ||||||||
\(327\) | − | 5.44646i | − | 0.301190i | ||||||
\(328\) | 32.2336i | 1.77980i | ||||||||
\(329\) | 7.13248 | 0.393226 | ||||||||
\(330\) | 11.7614 | − | 6.59585i | 0.647443 | − | 0.363090i | ||||
\(331\) | −27.6808 | −1.52147 | −0.760737 | − | 0.649060i | \(-0.775162\pi\) | ||||
−0.760737 | + | 0.649060i | \(0.775162\pi\) | |||||||
\(332\) | − | 6.03225i | − | 0.331062i | ||||||
\(333\) | 6.37562i | 0.349382i | ||||||||
\(334\) | 4.95041 | 0.270875 | ||||||||
\(335\) | −3.84200 | − | 6.85085i | −0.209911 | − | 0.374302i | ||||
\(336\) | 2.52013 | 0.137484 | ||||||||
\(337\) | 9.97412i | 0.543325i | 0.962393 | + | 0.271663i | \(0.0875734\pi\) | ||||
−0.962393 | + | 0.271663i | \(0.912427\pi\) | |||||||
\(338\) | 9.74544i | 0.530082i | ||||||||
\(339\) | 23.8473 | 1.29521 | ||||||||
\(340\) | −1.06362 | − | 1.89659i | −0.0576828 | − | 0.102857i | ||||
\(341\) | −29.0940 | −1.57553 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.77643i | 0.419888i | ||||||||
\(344\) | −24.1124 | −1.30006 | ||||||||
\(345\) | −0.0300171 | + | 0.0168338i | −0.00161607 | + | 0.000906300i | ||||
\(346\) | −28.0626 | −1.50865 | ||||||||
\(347\) | 29.0836i | 1.56129i | 0.624975 | + | 0.780645i | \(0.285109\pi\) | ||||
−0.624975 | + | 0.780645i | \(0.714891\pi\) | |||||||
\(348\) | − | 0.760363i | − | 0.0407598i | ||||||
\(349\) | 28.5033 | 1.52575 | 0.762874 | − | 0.646547i | \(-0.223788\pi\) | ||||
0.762874 | + | 0.646547i | \(0.223788\pi\) | |||||||
\(350\) | −1.85228 | + | 3.03072i | −0.0990088 | + | 0.161999i | ||||
\(351\) | −12.8025 | −0.683345 | ||||||||
\(352\) | 7.76727i | 0.413997i | ||||||||
\(353\) | − | 6.01136i | − | 0.319952i | −0.987121 | − | 0.159976i | \(-0.948858\pi\) | ||
0.987121 | − | 0.159976i | \(-0.0511417\pi\) | |||||||
\(354\) | 16.0096 | 0.850900 | ||||||||
\(355\) | −8.90872 | + | 4.99606i | −0.472826 | + | 0.265163i | ||||
\(356\) | 1.49730 | 0.0793569 | ||||||||
\(357\) | − | 1.90565i | − | 0.100858i | ||||||
\(358\) | 10.7052i | 0.565789i | ||||||||
\(359\) | 10.5528 | 0.556953 | 0.278477 | − | 0.960443i | \(-0.410170\pi\) | ||||
0.278477 | + | 0.960443i | \(0.410170\pi\) | |||||||
\(360\) | −2.36770 | − | 4.22195i | −0.124789 | − | 0.222516i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 26.9798i | − | 1.41803i | ||||||
\(363\) | − | 1.24763i | − | 0.0654836i | ||||||
\(364\) | −0.569244 | −0.0298365 | ||||||||
\(365\) | 10.5657 | + | 18.8402i | 0.553035 | + | 0.986144i | ||||
\(366\) | 13.9211 | 0.727668 | ||||||||
\(367\) | 4.20063i | 0.219271i | 0.993972 | + | 0.109636i | \(0.0349684\pi\) | ||||
−0.993972 | + | 0.109636i | \(0.965032\pi\) | |||||||
\(368\) | 0.0297938i | 0.00155311i | ||||||||
\(369\) | 7.51430 | 0.391179 | ||||||||
\(370\) | 21.8689 | − | 12.2642i | 1.13691 | − | 0.637587i | ||||
\(371\) | 4.22998 | 0.219610 | ||||||||
\(372\) | − | 6.05919i | − | 0.314154i | ||||||
\(373\) | 20.6921i | 1.07140i | 0.844410 | + | 0.535698i | \(0.179951\pi\) | ||||
−0.844410 | + | 0.535698i | \(0.820049\pi\) | |||||||
\(374\) | −8.82746 | −0.456457 | ||||||||
\(375\) | −16.9056 | − | 0.634110i | −0.873002 | − | 0.0327453i | ||||
\(376\) | 38.2258 | 1.97135 | ||||||||
\(377\) | − | 2.60992i | − | 0.134418i | ||||||
\(378\) | − | 3.98836i | − | 0.205139i | ||||||
\(379\) | −4.75485 | −0.244240 | −0.122120 | − | 0.992515i | \(-0.538969\pi\) | ||||
−0.122120 | + | 0.992515i | \(0.538969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.05487 | −0.105274 | ||||||||
\(382\) | 6.57150i | 0.336227i | ||||||||
\(383\) | − | 8.35408i | − | 0.426874i | −0.976957 | − | 0.213437i | \(-0.931534\pi\) | ||
0.976957 | − | 0.213437i | \(-0.0684658\pi\) | |||||||
\(384\) | 9.45751 | 0.482627 | ||||||||
\(385\) | −1.98378 | − | 3.53737i | −0.101103 | − | 0.180281i | ||||
\(386\) | −8.57292 | −0.436350 | ||||||||
\(387\) | 5.62109i | 0.285736i | ||||||||
\(388\) | 1.32493i | 0.0672632i | ||||||||
\(389\) | 38.3140 | 1.94260 | 0.971298 | − | 0.237867i | \(-0.0764483\pi\) | ||||
0.971298 | + | 0.237867i | \(0.0764483\pi\) | |||||||
\(390\) | 4.71505 | + | 8.40764i | 0.238756 | + | 0.425737i | ||||
\(391\) | 0.0225292 | 0.00113935 | ||||||||
\(392\) | 20.3459i | 1.02762i | ||||||||
\(393\) | 21.0716i | 1.06292i | ||||||||
\(394\) | −4.96328 | −0.250047 | ||||||||
\(395\) | −15.5540 | + | 8.72276i | −0.782605 | + | 0.438889i | ||||
\(396\) | 0.994897 | 0.0499954 | ||||||||
\(397\) | 30.6407i | 1.53781i | 0.639362 | + | 0.768906i | \(0.279198\pi\) | ||||
−0.639362 | + | 0.768906i | \(0.720802\pi\) | |||||||
\(398\) | 17.2860i | 0.866467i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.63759 | + | 12.4966i | −0.381879 | + | 0.624832i | ||||
\(401\) | 9.79094 | 0.488936 | 0.244468 | − | 0.969657i | \(-0.421387\pi\) | ||||
0.244468 | + | 0.969657i | \(0.421387\pi\) | |||||||
\(402\) | − | 6.64075i | − | 0.331211i | ||||||
\(403\) | − | 20.7979i | − | 1.03602i | ||||||
\(404\) | −6.32941 | −0.314900 | ||||||||
\(405\) | 12.4122 | − | 6.96082i | 0.616766 | − | 0.345886i | ||||
\(406\) | 0.813069 | 0.0403520 | ||||||||
\(407\) | 28.6289i | 1.41908i | ||||||||
\(408\) | − | 10.2131i | − | 0.505625i | ||||||
\(409\) | −11.1987 | −0.553742 | −0.276871 | − | 0.960907i | \(-0.589297\pi\) | ||||
−0.276871 | + | 0.960907i | \(0.589297\pi\) | |||||||
\(410\) | −14.4546 | − | 25.7747i | −0.713863 | − | 1.27292i | ||||
\(411\) | −25.1627 | −1.24119 | ||||||||
\(412\) | 1.93796i | 0.0954765i | ||||||||
\(413\) | − | 4.81507i | − | 0.236934i | ||||||
\(414\) | 0.00902762 | 0.000443684 | ||||||||
\(415\) | 15.0276 | + | 26.7964i | 0.737675 | + | 1.31538i | ||||
\(416\) | −5.55245 | −0.272231 | ||||||||
\(417\) | 6.45615i | 0.316159i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.38783 | −0.214359 | −0.107180 | − | 0.994240i | \(-0.534182\pi\) | ||||
−0.107180 | + | 0.994240i | \(0.534182\pi\) | |||||||
\(420\) | 0.736700 | − | 0.413146i | 0.0359473 | − | 0.0201594i | ||||
\(421\) | −18.3686 | −0.895231 | −0.447615 | − | 0.894226i | \(-0.647727\pi\) | ||||
−0.447615 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(422\) | 14.4875i | 0.705240i | ||||||||
\(423\) | − | 8.91120i | − | 0.433277i | ||||||
\(424\) | 22.6702 | 1.10096 | ||||||||
\(425\) | 9.44961 | + | 5.77533i | 0.458373 | + | 0.280144i | ||||
\(426\) | −8.63551 | −0.418392 | ||||||||
\(427\) | − | 4.18693i | − | 0.202620i | ||||||
\(428\) | − | 6.09965i | − | 0.294838i | ||||||
\(429\) | −11.0066 | −0.531402 | ||||||||
\(430\) | 19.2808 | − | 10.8128i | 0.929805 | − | 0.521440i | ||||
\(431\) | −6.90083 | −0.332401 | −0.166201 | − | 0.986092i | \(-0.553150\pi\) | ||||
−0.166201 | + | 0.986092i | \(0.553150\pi\) | |||||||
\(432\) | − | 16.4453i | − | 0.791227i | ||||||
\(433\) | − | 7.72000i | − | 0.371000i | −0.982644 | − | 0.185500i | \(-0.940610\pi\) | ||
0.982644 | − | 0.185500i | \(-0.0593904\pi\) | |||||||
\(434\) | 6.47919 | 0.311011 | ||||||||
\(435\) | 1.89422 | + | 3.37768i | 0.0908211 | + | 0.161947i | ||||
\(436\) | −1.58030 | −0.0756827 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 18.2625i | 0.872614i | ||||||||
\(439\) | 34.7457 | 1.65832 | 0.829161 | − | 0.559010i | \(-0.188819\pi\) | ||||
0.829161 | + | 0.559010i | \(0.188819\pi\) | |||||||
\(440\) | −10.6319 | − | 18.9582i | −0.506854 | − | 0.903795i | ||||
\(441\) | 4.74304 | 0.225859 | ||||||||
\(442\) | − | 6.31032i | − | 0.300151i | ||||||
\(443\) | 12.7539i | 0.605956i | 0.952998 | + | 0.302978i | \(0.0979809\pi\) | ||||
−0.952998 | + | 0.302978i | \(0.902019\pi\) | |||||||
\(444\) | −5.96233 | −0.282960 | ||||||||
\(445\) | −6.65131 | + | 3.73009i | −0.315302 | + | 0.176823i | ||||
\(446\) | 2.44627 | 0.115834 | ||||||||
\(447\) | 13.8729i | 0.656166i | ||||||||
\(448\) | − | 5.06073i | − | 0.239097i | ||||||
\(449\) | 10.3766 | 0.489703 | 0.244851 | − | 0.969561i | \(-0.421261\pi\) | ||||
0.244851 | + | 0.969561i | \(0.421261\pi\) | |||||||
\(450\) | 3.78652 | + | 2.31421i | 0.178498 | + | 0.109093i | ||||
\(451\) | 33.7421 | 1.58885 | ||||||||
\(452\) | − | 6.91934i | − | 0.325458i | ||||||
\(453\) | − | 8.45328i | − | 0.397170i | ||||||
\(454\) | −9.00188 | −0.422479 | ||||||||
\(455\) | 2.52869 | − | 1.41811i | 0.118547 | − | 0.0664818i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.0961i | 1.78206i | 0.453945 | + | 0.891030i | \(0.350016\pi\) | ||||
−0.453945 | + | 0.891030i | \(0.649984\pi\) | |||||||
\(458\) | 21.8621i | 1.02155i | ||||||||
\(459\) | −12.4355 | −0.580439 | ||||||||
\(460\) | 0.00488435 | + | 0.00870952i | 0.000227734 | + | 0.000406084i | ||||
\(461\) | −11.7738 | −0.548359 | −0.274179 | − | 0.961679i | \(-0.588406\pi\) | ||||
−0.274179 | + | 0.961679i | \(0.588406\pi\) | |||||||
\(462\) | − | 3.42888i | − | 0.159526i | ||||||
\(463\) | 10.4282i | 0.484639i | 0.970197 | + | 0.242319i | \(0.0779082\pi\) | ||||
−0.970197 | + | 0.242319i | \(0.922092\pi\) | |||||||
\(464\) | 3.35256 | 0.155639 | ||||||||
\(465\) | 15.0947 | + | 26.9161i | 0.700000 | + | 1.24820i | ||||
\(466\) | −4.74282 | −0.219707 | ||||||||
\(467\) | − | 5.69440i | − | 0.263505i | −0.991283 | − | 0.131753i | \(-0.957940\pi\) | ||
0.991283 | − | 0.131753i | \(-0.0420605\pi\) | |||||||
\(468\) | 0.711203i | 0.0328754i | ||||||||
\(469\) | −1.99728 | −0.0922259 | ||||||||
\(470\) | −30.5662 | + | 17.1417i | −1.40991 | + | 0.790689i | ||||
\(471\) | 25.3125 | 1.16634 | ||||||||
\(472\) | − | 25.8059i | − | 1.18781i | ||||||
\(473\) | 25.2408i | 1.16057i | ||||||||
\(474\) | −15.0770 | −0.692507 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.552927 | −0.0253434 | ||||||||
\(477\) | − | 5.28487i | − | 0.241978i | ||||||
\(478\) | − | 13.0881i | − | 0.598637i | ||||||
\(479\) | 24.3790 | 1.11391 | 0.556954 | − | 0.830544i | \(-0.311970\pi\) | ||||
0.556954 | + | 0.830544i | \(0.311970\pi\) | |||||||
\(480\) | 7.18583 | − | 4.02985i | 0.327987 | − | 0.183937i | ||||
\(481\) | −20.4654 | −0.933144 | ||||||||
\(482\) | 3.58531i | 0.163306i | ||||||||
\(483\) | 0.00875112i | 0.000398190i | ||||||||
\(484\) | −0.362002 | −0.0164546 | ||||||||
\(485\) | −3.30068 | − | 5.88560i | −0.149876 | − | 0.267251i | ||||
\(486\) | −9.01194 | −0.408790 | ||||||||
\(487\) | 5.30022i | 0.240176i | 0.992763 | + | 0.120088i | \(0.0383176\pi\) | ||||
−0.992763 | + | 0.120088i | \(0.961682\pi\) | |||||||
\(488\) | − | 22.4395i | − | 1.01579i | ||||||
\(489\) | −36.8197 | −1.66505 | ||||||||
\(490\) | −9.12378 | − | 16.2690i | −0.412170 | − | 0.734960i | ||||
\(491\) | −11.7908 | −0.532109 | −0.266055 | − | 0.963958i | \(-0.585720\pi\) | ||||
−0.266055 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(492\) | 7.02719i | 0.316810i | ||||||||
\(493\) | − | 2.53511i | − | 0.114175i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.41953 | + | 2.47850i | −0.198643 | + | 0.111400i | ||||
\(496\) | 26.7159 | 1.19958 | ||||||||
\(497\) | 2.59723i | 0.116501i | ||||||||
\(498\) | 25.9746i | 1.16395i | ||||||||
\(499\) | 33.7253 | 1.50975 | 0.754877 | − | 0.655867i | \(-0.227697\pi\) | ||||
0.754877 | + | 0.655867i | \(0.227697\pi\) | |||||||
\(500\) | −0.183988 | + | 4.90519i | −0.00822820 | + | 0.219367i | ||||
\(501\) | 5.99552 | 0.267860 | ||||||||
\(502\) | − | 23.9167i | − | 1.06745i | ||||||
\(503\) | − | 4.11086i | − | 0.183294i | −0.995792 | − | 0.0916471i | \(-0.970787\pi\) | ||
0.995792 | − | 0.0916471i | \(-0.0292132\pi\) | |||||||
\(504\) | −1.23086 | −0.0548267 | ||||||||
\(505\) | 28.1165 | − | 15.7679i | 1.25117 | − | 0.701662i | ||||
\(506\) | 0.0405375 | 0.00180211 | ||||||||
\(507\) | 11.8029i | 0.524183i | ||||||||
\(508\) | 0.596223i | 0.0264531i | ||||||||
\(509\) | 16.7776 | 0.743656 | 0.371828 | − | 0.928302i | \(-0.378731\pi\) | ||||
0.371828 | + | 0.928302i | \(0.378731\pi\) | |||||||
\(510\) | 4.57990 | + | 8.16665i | 0.202802 | + | 0.361625i | ||||
\(511\) | 5.49264 | 0.242980 | ||||||||
\(512\) | − | 24.9844i | − | 1.10416i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.7820 | 0.563789 | ||||||||
\(515\) | −4.82787 | − | 8.60880i | −0.212741 | − | 0.379349i | ||||
\(516\) | −5.25671 | −0.231414 | ||||||||
\(517\) | − | 40.0147i | − | 1.75984i | ||||||
\(518\) | − | 6.37562i | − | 0.280129i | ||||||
\(519\) | −33.9870 | −1.49186 | ||||||||
\(520\) | 13.5523 | − | 7.60020i | 0.594307 | − | 0.333291i | ||||
\(521\) | 35.3846 | 1.55023 | 0.775114 | − | 0.631822i | \(-0.217693\pi\) | ||||
0.775114 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(522\) | − | 1.01583i | − | 0.0444619i | ||||||
\(523\) | 19.9927i | 0.874221i | 0.899408 | + | 0.437110i | \(0.143998\pi\) | ||||
−0.899408 | + | 0.437110i | \(0.856002\pi\) | |||||||
\(524\) | 6.11396 | 0.267090 | ||||||||
\(525\) | −2.24333 | + | 3.67055i | −0.0979070 | + | 0.160196i | ||||
\(526\) | −8.28139 | −0.361086 | ||||||||
\(527\) | − | 20.2018i | − | 0.880003i | ||||||
\(528\) | − | 14.1384i | − | 0.615296i | ||||||
\(529\) | 22.9999 | 0.999996 | ||||||||
\(530\) | −18.1276 | + | 10.1661i | −0.787412 | + | 0.441585i | ||||
\(531\) | −6.01586 | −0.261066 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.1206i | 1.04478i | ||||||||
\(534\) | −6.44733 | −0.279003 | ||||||||
\(535\) | 15.1955 | + | 27.0958i | 0.656959 | + | 1.17145i | ||||
\(536\) | −10.7042 | −0.462352 | ||||||||
\(537\) | 12.9653i | 0.559493i | ||||||||
\(538\) | − | 16.0721i | − | 0.692917i | ||||||
\(539\) | 21.2980 | 0.917371 | ||||||||
\(540\) | −2.69602 | − | 4.80741i | −0.116018 | − | 0.206878i | ||||
\(541\) | 4.66775 | 0.200682 | 0.100341 | − | 0.994953i | \(-0.468007\pi\) | ||||
0.100341 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(542\) | 11.5708i | 0.497009i | ||||||||
\(543\) | − | 32.6757i | − | 1.40225i | ||||||
\(544\) | −5.39330 | −0.231236 | ||||||||
\(545\) | 7.02000 | − | 3.93686i | 0.300704 | − | 0.168637i | ||||
\(546\) | 2.45114 | 0.104899 | ||||||||
\(547\) | − | 35.9629i | − | 1.53766i | −0.639451 | − | 0.768832i | \(-0.720838\pi\) | ||
0.639451 | − | 0.768832i | \(-0.279162\pi\) | |||||||
\(548\) | 7.30101i | 0.311884i | ||||||||
\(549\) | −5.23108 | −0.223257 | ||||||||
\(550\) | 17.0029 | + | 10.3917i | 0.725007 | + | 0.443103i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.0469008i | 0.00199623i | ||||||||
\(553\) | 4.53456i | 0.192829i | ||||||||
\(554\) | 15.8389 | 0.672932 | ||||||||
\(555\) | 26.4858 | − | 14.8534i | 1.12426 | − | 0.630492i | ||||
\(556\) | 1.87326 | 0.0794441 | ||||||||
\(557\) | − | 2.43899i | − | 0.103343i | −0.998664 | − | 0.0516716i | \(-0.983545\pi\) | ||
0.998664 | − | 0.0516716i | \(-0.0164549\pi\) | |||||||
\(558\) | − | 8.09499i | − | 0.342688i | ||||||
\(559\) | −18.0434 | −0.763156 | ||||||||
\(560\) | 1.82162 | + | 3.24822i | 0.0769775 | + | 0.137262i | ||||
\(561\) | −10.6911 | −0.451377 | ||||||||
\(562\) | 35.8542i | 1.51242i | ||||||||
\(563\) | − | 37.5088i | − | 1.58081i | −0.612586 | − | 0.790404i | \(-0.709871\pi\) | ||
0.612586 | − | 0.790404i | \(-0.290129\pi\) | |||||||
\(564\) | 8.33354 | 0.350905 | ||||||||
\(565\) | 17.2375 | + | 30.7371i | 0.725188 | + | 1.29312i | ||||
\(566\) | 17.4567 | 0.733760 | ||||||||
\(567\) | − | 3.61861i | − | 0.151967i | ||||||
\(568\) | 13.9196i | 0.584052i | ||||||||
\(569\) | −8.58058 | −0.359717 | −0.179858 | − | 0.983693i | \(-0.557564\pi\) | ||||
−0.179858 | + | 0.983693i | \(0.557564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8947 | −0.623324 | −0.311662 | − | 0.950193i | \(-0.600886\pi\) | ||||
−0.311662 | + | 0.950193i | \(0.600886\pi\) | |||||||
\(572\) | 3.19357i | 0.133530i | ||||||||
\(573\) | 7.95885i | 0.332486i | ||||||||
\(574\) | −7.51430 | −0.313641 | ||||||||
\(575\) | −0.0433945 | − | 0.0265215i | −0.00180968 | − | 0.00110602i | ||||
\(576\) | −6.32279 | −0.263450 | ||||||||
\(577\) | 31.7203i | 1.32054i | 0.751030 | + | 0.660268i | \(0.229557\pi\) | ||||
−0.751030 | + | 0.660268i | \(0.770443\pi\) | |||||||
\(578\) | 15.1101i | 0.628496i | ||||||||
\(579\) | −10.3828 | −0.431494 | ||||||||
\(580\) | 0.980041 | − | 0.549613i | 0.0406940 | − | 0.0228214i | ||||
\(581\) | 7.81216 | 0.324103 | ||||||||
\(582\) | − | 5.70510i | − | 0.236484i | ||||||
\(583\) | − | 23.7311i | − | 0.982841i | ||||||
\(584\) | 29.4373 | 1.21812 | ||||||||
\(585\) | −1.77176 | − | 3.15930i | −0.0732531 | − | 0.130621i | ||||
\(586\) | −7.21184 | −0.297918 | ||||||||
\(587\) | 6.36781i | 0.262828i | 0.991328 | + | 0.131414i | \(0.0419516\pi\) | ||||
−0.991328 | + | 0.131414i | \(0.958048\pi\) | |||||||
\(588\) | 4.43558i | 0.182920i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.5722 | + | 20.6349i | 0.476420 | + | 0.849527i | ||||
\(591\) | −6.01111 | −0.247264 | ||||||||
\(592\) | − | 26.2888i | − | 1.08046i | ||||||
\(593\) | 15.9159i | 0.653590i | 0.945095 | + | 0.326795i | \(0.105969\pi\) | ||||
−0.945095 | + | 0.326795i | \(0.894031\pi\) | |||||||
\(594\) | −22.3755 | −0.918079 | ||||||||
\(595\) | 2.45621 | − | 1.37746i | 0.100695 | − | 0.0564703i | ||||
\(596\) | 4.02525 | 0.164881 | ||||||||
\(597\) | 20.9353i | 0.856825i | ||||||||
\(598\) | 0.0289783i | 0.00118501i | ||||||||
\(599\) | 43.2212 | 1.76597 | 0.882985 | − | 0.469401i | \(-0.155530\pi\) | ||||
0.882985 | + | 0.469401i | \(0.155530\pi\) | |||||||
\(600\) | −12.0229 | + | 19.6719i | −0.490833 | + | 0.803103i | ||||
\(601\) | −31.4293 | −1.28203 | −0.641015 | − | 0.767528i | \(-0.721486\pi\) | ||||
−0.641015 | + | 0.767528i | \(0.721486\pi\) | |||||||
\(602\) | − | 5.62109i | − | 0.229098i | ||||||
\(603\) | 2.49537i | 0.101619i | ||||||||
\(604\) | −2.45273 | −0.0998004 | ||||||||
\(605\) | 1.60808 | − | 0.901823i | 0.0653779 | − | 0.0366643i | ||||
\(606\) | 27.2542 | 1.10713 | ||||||||
\(607\) | − | 29.2401i | − | 1.18682i | −0.804900 | − | 0.593410i | \(-0.797781\pi\) | ||
0.804900 | − | 0.593410i | \(-0.202219\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.984721 | 0.0399029 | ||||||||
\(610\) | 10.0626 | + | 17.9431i | 0.407422 | + | 0.726494i | ||||
\(611\) | 28.6046 | 1.15722 | ||||||||
\(612\) | 0.690818i | 0.0279247i | ||||||||
\(613\) | − | 29.0513i | − | 1.17337i | −0.809815 | − | 0.586685i | \(-0.800433\pi\) | ||
0.809815 | − | 0.586685i | \(-0.199567\pi\) | |||||||
\(614\) | 12.9248 | 0.521604 | ||||||||
\(615\) | −17.5062 | − | 31.2162i | −0.705919 | − | 1.25876i | ||||
\(616\) | −5.52702 | −0.222690 | ||||||||
\(617\) | − | 11.6592i | − | 0.469383i | −0.972070 | − | 0.234691i | \(-0.924592\pi\) | ||
0.972070 | − | 0.234691i | \(-0.0754080\pi\) | |||||||
\(618\) | − | 8.34479i | − | 0.335677i | ||||||
\(619\) | −6.40765 | −0.257545 | −0.128773 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128773 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(620\) | 7.80975 | − | 4.37976i | 0.313647 | − | 0.175895i | ||||
\(621\) | 0.0571063 | 0.00229160 | ||||||||
\(622\) | − | 18.5153i | − | 0.742395i | ||||||
\(623\) | 1.93911i | 0.0776886i | ||||||||
\(624\) | 10.1069 | 0.404599 | ||||||||
\(625\) | −11.4026 | − | 22.2482i | −0.456102 | − | 0.889927i | ||||
\(626\) | −22.9844 | −0.918641 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7.34447i | − | 0.293076i | ||||||
\(629\) | −19.8788 | −0.792621 | ||||||||
\(630\) | 0.984221 | − | 0.551957i | 0.0392123 | − | 0.0219905i | ||||
\(631\) | −36.4184 | −1.44979 | −0.724896 | − | 0.688858i | \(-0.758112\pi\) | ||||
−0.724896 | + | 0.688858i | \(0.758112\pi\) | |||||||
\(632\) | 24.3025i | 0.966703i | ||||||||
\(633\) | 17.5460i | 0.697392i | ||||||||
\(634\) | −0.604925 | −0.0240246 | ||||||||
\(635\) | −1.48532 | − | 2.64854i | −0.0589430 | − | 0.105104i | ||||
\(636\) | 4.94229 | 0.195974 | ||||||||
\(637\) | 15.2249i | 0.603234i | ||||||||
\(638\) | − | 4.56149i | − | 0.180591i | ||||||
\(639\) | 3.24493 | 0.128367 | ||||||||
\(640\) | 6.83617 | + | 12.1899i | 0.270223 | + | 0.481848i | ||||
\(641\) | −8.52575 | −0.336747 | −0.168373 | − | 0.985723i | \(-0.553851\pi\) | ||||
−0.168373 | + | 0.985723i | \(0.553851\pi\) | |||||||
\(642\) | 26.2648i | 1.03659i | ||||||||
\(643\) | 2.82522i | 0.111416i | 0.998447 | + | 0.0557079i | \(0.0177416\pi\) | ||||
−0.998447 | + | 0.0557079i | \(0.982258\pi\) | |||||||
\(644\) | 0.00253915 | 0.000100057 | ||||||||
\(645\) | 23.3513 | − | 13.0956i | 0.919458 | − | 0.515637i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 20.7093i | − | 0.814168i | −0.913391 | − | 0.407084i | \(-0.866546\pi\) | ||
0.913391 | − | 0.407084i | \(-0.133454\pi\) | |||||||
\(648\) | − | 19.3936i | − | 0.761853i | ||||||
\(649\) | −27.0135 | −1.06037 | ||||||||
\(650\) | −7.42852 | + | 12.1546i | −0.291371 | + | 0.476741i | ||||
\(651\) | 7.84705 | 0.307550 | ||||||||
\(652\) | 10.6833i | 0.418391i | ||||||||
\(653\) | − | 18.4680i | − | 0.722709i | −0.932428 | − | 0.361355i | \(-0.882314\pi\) | ||
0.932428 | − | 0.361355i | \(-0.117686\pi\) | |||||||
\(654\) | 6.80471 | 0.266085 | ||||||||
\(655\) | −27.1594 | + | 15.2312i | −1.06121 | + | 0.595131i | ||||
\(656\) | −30.9840 | −1.20972 | ||||||||
\(657\) | − | 6.86241i | − | 0.267728i | ||||||
\(658\) | 8.91120i | 0.347395i | ||||||||
\(659\) | −19.0672 | −0.742754 | −0.371377 | − | 0.928482i | \(-0.621114\pi\) | ||||
−0.371377 | + | 0.928482i | \(0.621114\pi\) | |||||||
\(660\) | −2.31783 | − | 4.13304i | −0.0902215 | − | 0.160878i | ||||
\(661\) | −34.5435 | −1.34359 | −0.671793 | − | 0.740739i | \(-0.734476\pi\) | ||||
−0.671793 | + | 0.740739i | \(0.734476\pi\) | |||||||
\(662\) | − | 34.5839i | − | 1.34414i | ||||||
\(663\) | − | 7.64253i | − | 0.296811i | ||||||
\(664\) | 41.8685 | 1.62481 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.96559 | −0.308660 | ||||||||
\(667\) | 0.0116417i | 0.000450769i | ||||||||
\(668\) | − | 1.73961i | − | 0.0673076i | ||||||
\(669\) | 2.96271 | 0.114545 | ||||||||
\(670\) | 8.55934 | − | 4.80013i | 0.330676 | − | 0.185445i | ||||
\(671\) | −23.4896 | −0.906804 | ||||||||
\(672\) | − | 2.09494i | − | 0.0808140i | ||||||
\(673\) | − | 35.7304i | − | 1.37731i | −0.725091 | − | 0.688653i | \(-0.758202\pi\) | ||
0.725091 | − | 0.688653i | \(-0.241798\pi\) | |||||||
\(674\) | −12.4615 | −0.479999 | ||||||||
\(675\) | 23.9525 | + | 14.6391i | 0.921933 | + | 0.563459i | ||||
\(676\) | 3.42462 | 0.131716 | ||||||||
\(677\) | 22.3529i | 0.859090i | 0.903045 | + | 0.429545i | \(0.141326\pi\) | ||||
−0.903045 | + | 0.429545i | \(0.858674\pi\) | |||||||
\(678\) | 29.7944i | 1.14425i | ||||||||
\(679\) | −1.71587 | −0.0658492 | ||||||||
\(680\) | 13.1638 | − | 7.38235i | 0.504809 | − | 0.283100i | ||||
\(681\) | −10.9023 | −0.417778 | ||||||||
\(682\) | − | 36.3496i | − | 1.39190i | ||||||
\(683\) | 16.4252i | 0.628492i | 0.949342 | + | 0.314246i | \(0.101752\pi\) | ||||
−0.949342 | + | 0.314246i | \(0.898248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.1883 | − | 32.4325i | −0.694941 | − | 1.23918i | ||||
\(686\) | −9.71574 | −0.370949 | ||||||||
\(687\) | 26.4776i | 1.01018i | ||||||||
\(688\) | − | 23.1776i | − | 0.883639i | ||||||
\(689\) | 16.9642 | 0.646284 | ||||||||
\(690\) | −0.0210318 | − | 0.0375029i | −0.000800669 | − | 0.00142771i | ||||
\(691\) | 4.36093 | 0.165898 | 0.0829489 | − | 0.996554i | \(-0.473566\pi\) | ||||
0.0829489 | + | 0.996554i | \(0.473566\pi\) | |||||||
\(692\) | 9.86139i | 0.374874i | ||||||||
\(693\) | 1.28846i | 0.0489445i | ||||||||
\(694\) | −36.3365 | −1.37932 | ||||||||
\(695\) | −8.32140 | + | 4.66669i | −0.315649 | + | 0.177018i | ||||
\(696\) | 5.27752 | 0.200044 | ||||||||
\(697\) | 23.4292i | 0.887443i | ||||||||
\(698\) | 35.6116i | 1.34792i | ||||||||
\(699\) | −5.74411 | −0.217262 | ||||||||
\(700\) | 1.06502 | + | 0.650907i | 0.0402538 | + | 0.0246020i | ||||
\(701\) | 27.8728 | 1.05274 | 0.526371 | − | 0.850255i | \(-0.323552\pi\) | ||||
0.526371 | + | 0.850255i | \(0.323552\pi\) | |||||||
\(702\) | − | 15.9952i | − | 0.603699i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −28.3917 | −1.07005 | ||||||||
\(705\) | −37.0192 | + | 20.7606i | −1.39422 | + | 0.781890i | ||||
\(706\) | 7.51049 | 0.282661 | ||||||||
\(707\) | − | 8.19701i | − | 0.308280i | ||||||
\(708\) | − | 5.62589i | − | 0.211434i | ||||||
\(709\) | 19.8448 | 0.745288 | 0.372644 | − | 0.927974i | \(-0.378451\pi\) | ||||
0.372644 | + | 0.927974i | \(0.378451\pi\) | |||||||
\(710\) | −6.24199 | − | 11.1304i | −0.234258 | − | 0.417716i | ||||
\(711\) | 5.66541 | 0.212469 | ||||||||
\(712\) | 10.3924i | 0.389473i | ||||||||
\(713\) | 0.0927706i | 0.00347429i | ||||||||
\(714\) | 2.38088 | 0.0891023 | ||||||||
\(715\) | −7.95586 | − | 14.1865i | −0.297532 | − | 0.530544i | ||||
\(716\) | 3.76190 | 0.140589 | ||||||||
\(717\) | − | 15.8512i | − | 0.591975i | ||||||
\(718\) | 13.1844i | 0.492039i | ||||||||
\(719\) | −25.9216 | −0.966713 | −0.483357 | − | 0.875424i | \(-0.660583\pi\) | ||||
−0.483357 | + | 0.875424i | \(0.660583\pi\) | |||||||
\(720\) | 4.05827 | − | 2.27590i | 0.151243 | − | 0.0848179i | ||||
\(721\) | −2.50979 | −0.0934694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.34223i | 0.161489i | ||||||||
\(724\) | −9.48091 | −0.352355 | ||||||||
\(725\) | −2.98433 | + | 4.88297i | −0.110835 | + | 0.181349i | ||||
\(726\) | 1.55877 | 0.0578513 | ||||||||
\(727\) | 15.0074i | 0.556595i | 0.960495 | + | 0.278297i | \(0.0897701\pi\) | ||||
−0.960495 | + | 0.278297i | \(0.910230\pi\) | |||||||
\(728\) | − | 3.95100i | − | 0.146434i | ||||||
\(729\) | −30.0071 | −1.11137 | ||||||||
\(730\) | −23.5387 | + | 13.2006i | −0.871206 | + | 0.488577i | ||||
\(731\) | −17.5263 | −0.648232 | ||||||||
\(732\) | − | 4.89198i | − | 0.180813i | ||||||
\(733\) | 35.9465i | 1.32771i | 0.747859 | + | 0.663857i | \(0.231082\pi\) | ||||
−0.747859 | + | 0.663857i | \(0.768918\pi\) | |||||||
\(734\) | −5.24820 | −0.193715 | ||||||||
\(735\) | −11.0499 | − | 19.7037i | −0.407583 | − | 0.726782i | ||||
\(736\) | 0.0247671 | 0.000912927 | ||||||||
\(737\) | 11.2052i | 0.412747i | ||||||||
\(738\) | 9.38823i | 0.345586i | ||||||||
\(739\) | −25.5211 | −0.938811 | −0.469405 | − | 0.882983i | \(-0.655532\pi\) | ||||
−0.469405 | + | 0.882983i | \(0.655532\pi\) | |||||||
\(740\) | −4.30974 | − | 7.68491i | −0.158429 | − | 0.282503i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.28487i | 0.194014i | ||||||||
\(743\) | − | 46.9698i | − | 1.72315i | −0.507627 | − | 0.861577i | \(-0.669477\pi\) | ||
0.507627 | − | 0.861577i | \(-0.330523\pi\) | |||||||
\(744\) | 42.0555 | 1.54183 | ||||||||
\(745\) | −17.8809 | + | 10.0277i | −0.655107 | + | 0.367388i | ||||
\(746\) | −25.8523 | −0.946521 | ||||||||
\(747\) | − | 9.76038i | − | 0.357114i | ||||||
\(748\) | 3.10203i | 0.113422i | ||||||||
\(749\) | 7.89945 | 0.288640 | ||||||||
\(750\) | 0.792246 | − | 21.1216i | 0.0289287 | − | 0.771251i | ||||
\(751\) | −15.4684 | −0.564450 | −0.282225 | − | 0.959348i | \(-0.591073\pi\) | ||||
−0.282225 | + | 0.959348i | \(0.591073\pi\) | |||||||
\(752\) | 36.7438i | 1.33991i | ||||||||
\(753\) | − | 28.9659i | − | 1.05558i | ||||||
\(754\) | 3.26078 | 0.118751 | ||||||||
\(755\) | 10.8955 | − | 6.11028i | 0.396529 | − | 0.222376i | ||||
\(756\) | −1.40154 | −0.0509735 | ||||||||
\(757\) | − | 21.7345i | − | 0.789953i | −0.918691 | − | 0.394976i | \(-0.870753\pi\) | ||
0.918691 | − | 0.394976i | \(-0.129247\pi\) | |||||||
\(758\) | − | 5.94063i | − | 0.215773i | ||||||
\(759\) | 0.0490956 | 0.00178206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2697 | 0.771026 | 0.385513 | − | 0.922703i | \(-0.374025\pi\) | ||||
0.385513 | + | 0.922703i | \(0.374025\pi\) | |||||||
\(762\) | − | 2.56731i | − | 0.0930039i | ||||||
\(763\) | − | 2.04659i | − | 0.0740917i | ||||||
\(764\) | 2.30927 | 0.0835466 | ||||||||
\(765\) | −1.72097 | − | 3.06875i | −0.0622219 | − | 0.110951i | ||||
\(766\) | 10.4374 | 0.377120 | ||||||||
\(767\) | − | 19.3106i | − | 0.697267i | ||||||
\(768\) | − | 15.1195i | − | 0.545578i | ||||||
\(769\) | −12.9195 | −0.465888 | −0.232944 | − | 0.972490i | \(-0.574836\pi\) | ||||
−0.232944 | + | 0.972490i | \(0.574836\pi\) | |||||||
\(770\) | 4.41953 | − | 2.47850i | 0.159269 | − | 0.0893188i | ||||
\(771\) | 15.4805 | 0.557515 | ||||||||
\(772\) | 3.01259i | 0.108425i | ||||||||
\(773\) | − | 47.4575i | − | 1.70693i | −0.521151 | − | 0.853464i | \(-0.674497\pi\) | ||
0.521151 | − | 0.853464i | \(-0.325503\pi\) | |||||||
\(774\) | −7.02289 | −0.252433 | ||||||||
\(775\) | −23.7816 | + | 38.9115i | −0.854259 | + | 1.39774i | ||||
\(776\) | −9.19605 | −0.330119 | ||||||||
\(777\) | − | 7.72161i | − | 0.277011i | ||||||
\(778\) | 47.8688i | 1.71618i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 2.95451 | − | 1.65690i | 0.105788 | − | 0.0593267i | ||||
\(781\) | 14.5710 | 0.521390 | ||||||||
\(782\) | 0.0281476i | 0.00100656i | ||||||||
\(783\) | − | 6.42590i | − | 0.229643i | ||||||
\(784\) | −19.5571 | −0.698469 | ||||||||
\(785\) | 18.2966 | + | 32.6256i | 0.653034 | + | 1.16446i | ||||
\(786\) | −26.3265 | −0.939035 | ||||||||
\(787\) | − | 41.7297i | − | 1.48750i | −0.668456 | − | 0.743752i | \(-0.733045\pi\) | ||
0.668456 | − | 0.743752i | \(-0.266955\pi\) | |||||||
\(788\) | 1.74414i | 0.0621322i | ||||||||
\(789\) | −10.0297 | −0.357067 | ||||||||
\(790\) | −10.8981 | − | 19.4329i | −0.387736 | − | 0.691390i | ||||
\(791\) | 8.96101 | 0.318617 | ||||||||
\(792\) | 6.90536i | 0.245371i | ||||||||
\(793\) | − | 16.7915i | − | 0.596285i | ||||||
\(794\) | −38.2819 | −1.35857 | ||||||||
\(795\) | −21.9546 | + | 12.3123i | −0.778649 | + | 0.436671i | ||||
\(796\) | 6.07442 | 0.215302 | ||||||||
\(797\) | 19.5110i | 0.691117i | 0.938397 | + | 0.345558i | \(0.112310\pi\) | ||||
−0.938397 | + | 0.345558i | \(0.887690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7846 | 0.982950 | ||||||||
\(800\) | 10.3882 | + | 6.34900i | 0.367280 | + | 0.224471i | ||||
\(801\) | 2.42269 | 0.0856014 | ||||||||
\(802\) | 12.2326i | 0.431949i | ||||||||
\(803\) | − | 30.8148i | − | 1.08743i | ||||||
\(804\) | −2.33361 | −0.0823001 | ||||||||
\(805\) | −0.0112794 | + | 0.00632556i | −0.000397547 | + | 0.000222947i | ||||
\(806\) | 25.9846 | 0.915267 | ||||||||
\(807\) | − | 19.4652i | − | 0.685206i | ||||||
\(808\) | − | 43.9311i | − | 1.54549i | ||||||
\(809\) | 6.34419 | 0.223050 | 0.111525 | − | 0.993762i | \(-0.464427\pi\) | ||||
0.111525 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(810\) | 8.69673 | + | 15.5076i | 0.305572 | + | 0.544880i | ||||
\(811\) | 44.8038 | 1.57327 | 0.786637 | − | 0.617416i | \(-0.211821\pi\) | ||||
0.786637 | + | 0.617416i | \(0.211821\pi\) | |||||||
\(812\) | − | 0.285719i | − | 0.0100268i | ||||||
\(813\) | 14.0136i | 0.491478i | ||||||||
\(814\) | −35.7685 | −1.25369 | ||||||||
\(815\) | −26.6144 | − | 47.4574i | −0.932261 | − | 1.66236i | ||||
\(816\) | 9.81718 | 0.343670 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 13.9915i | − | 0.489201i | ||||||
\(819\) | −0.921056 | −0.0321843 | ||||||||
\(820\) | −9.05743 | + | 5.07946i | −0.316299 | + | 0.177382i | ||||
\(821\) | 44.2814 | 1.54543 | 0.772716 | − | 0.634752i | \(-0.218898\pi\) | ||||
0.772716 | + | 0.634752i | \(0.218898\pi\) | |||||||
\(822\) | − | 31.4379i | − | 1.09652i | ||||||
\(823\) | − | 20.6550i | − | 0.719988i | −0.932955 | − | 0.359994i | \(-0.882779\pi\) | ||
0.932955 | − | 0.359994i | \(-0.117221\pi\) | |||||||
\(824\) | −13.4510 | −0.468587 | ||||||||
\(825\) | 20.5925 | + | 12.5855i | 0.716939 | + | 0.438173i | ||||
\(826\) | 6.01586 | 0.209319 | ||||||||
\(827\) | − | 44.6161i | − | 1.55145i | −0.631068 | − | 0.775727i | \(-0.717383\pi\) | ||
0.631068 | − | 0.775727i | \(-0.282617\pi\) | |||||||
\(828\) | − | 0.00317237i | − | 0.000110248i | ||||||
\(829\) | 28.3748 | 0.985496 | 0.492748 | − | 0.870172i | \(-0.335992\pi\) | ||||
0.492748 | + | 0.870172i | \(0.335992\pi\) | |||||||
\(830\) | −33.4790 | + | 18.7752i | −1.16207 | + | 0.651697i | ||||
\(831\) | 19.1828 | 0.665443 | ||||||||
\(832\) | − | 20.2959i | − | 0.703633i | ||||||
\(833\) | 14.7885i | 0.512392i | ||||||||
\(834\) | −8.06620 | −0.279310 | ||||||||
\(835\) | 4.33374 | + | 7.72770i | 0.149975 | + | 0.267428i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 51.2067i | − | 1.76996i | ||||||
\(838\) | − | 5.48208i | − | 0.189375i | ||||||
\(839\) | 13.5641 | 0.468283 | 0.234142 | − | 0.972203i | \(-0.424772\pi\) | ||||
0.234142 | + | 0.972203i | \(0.424772\pi\) | |||||||
\(840\) | 2.86755 | + | 5.11327i | 0.0989400 | + | 0.176425i | ||||
\(841\) | −27.6900 | −0.954828 | ||||||||
\(842\) | − | 22.9494i | − | 0.790889i | ||||||
\(843\) | 43.4236i | 1.49559i | ||||||||
\(844\) | 5.09101 | 0.175240 | ||||||||
\(845\) | −15.2128 | + | 8.53145i | −0.523337 | + | 0.293491i | ||||
\(846\) | 11.1335 | 0.382778 | ||||||||
\(847\) | − | 0.468817i | − | 0.0161087i | ||||||
\(848\) | 21.7913i | 0.748316i | ||||||||
\(849\) | 21.1421 | 0.725595 | ||||||||
\(850\) | −7.21559 | + | 11.8062i | −0.247493 | + | 0.404949i | ||||
\(851\) | 0.0912876 | 0.00312930 | ||||||||
\(852\) | 3.03458i | 0.103963i | ||||||||
\(853\) | 39.4266i | 1.34994i | 0.737844 | + | 0.674971i | \(0.235844\pi\) | ||||
−0.737844 | + | 0.674971i | \(0.764156\pi\) | |||||||
\(854\) | 5.23108 | 0.179004 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.3363 | 1.44703 | ||||||||
\(857\) | − | 39.4383i | − | 1.34719i | −0.739102 | − | 0.673594i | \(-0.764750\pi\) | ||
0.739102 | − | 0.673594i | \(-0.235250\pi\) | |||||||
\(858\) | − | 13.7514i | − | 0.469465i | ||||||
\(859\) | −42.4044 | −1.44682 | −0.723410 | − | 0.690419i | \(-0.757426\pi\) | ||||
−0.723410 | + | 0.690419i | \(0.757426\pi\) | |||||||
\(860\) | −3.79970 | − | 6.77543i | −0.129569 | − | 0.231040i | ||||
\(861\) | −9.10068 | −0.310150 | ||||||||
\(862\) | − | 8.62178i | − | 0.293659i | ||||||
\(863\) | − | 17.5670i | − | 0.597986i | −0.954255 | − | 0.298993i | \(-0.903349\pi\) | ||
0.954255 | − | 0.298993i | \(-0.0966508\pi\) | |||||||
\(864\) | −13.6707 | −0.465088 | ||||||||
\(865\) | −24.5668 | − | 43.8062i | −0.835296 | − | 1.48946i | ||||
\(866\) | 9.64524 | 0.327759 | ||||||||
\(867\) | 18.3000i | 0.621502i | ||||||||
\(868\) | − | 2.27684i | − | 0.0772809i | ||||||
\(869\) | 25.4398 | 0.862987 | ||||||||
\(870\) | −4.22002 | + | 2.36661i | −0.143072 | + | 0.0802356i | ||||
\(871\) | −8.01002 | −0.271409 | ||||||||
\(872\) | − | 10.9685i | − | 0.371441i | ||||||
\(873\) | 2.14378i | 0.0725561i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.35255 | − | 0.238277i | −0.214756 | − | 0.00805523i | ||||
\(876\) | 6.41756 | 0.216829 | ||||||||
\(877\) | 23.3460i | 0.788339i | 0.919038 | + | 0.394170i | \(0.128968\pi\) | ||||
−0.919038 | + | 0.394170i | \(0.871032\pi\) | |||||||
\(878\) | 43.4107i | 1.46504i | ||||||||
\(879\) | −8.73437 | −0.294603 | ||||||||
\(880\) | 18.2232 | − | 10.2197i | 0.614303 | − | 0.344505i | ||||
\(881\) | −32.9857 | −1.11132 | −0.555659 | − | 0.831410i | \(-0.687534\pi\) | ||||
−0.555659 | + | 0.831410i | \(0.687534\pi\) | |||||||
\(882\) | 5.92587i | 0.199534i | ||||||||
\(883\) | − | 39.9863i | − | 1.34565i | −0.739803 | − | 0.672823i | \(-0.765081\pi\) | ||
0.739803 | − | 0.672823i | \(-0.234919\pi\) | |||||||
\(884\) | −2.21749 | −0.0745824 | ||||||||
\(885\) | 14.0153 | + | 24.9913i | 0.471118 | + | 0.840074i | ||||
\(886\) | −15.9345 | −0.535330 | ||||||||
\(887\) | − | 32.2412i | − | 1.08255i | −0.840844 | − | 0.541277i | \(-0.817941\pi\) | ||
0.840844 | − | 0.541277i | \(-0.182059\pi\) | |||||||
\(888\) | − | 41.3832i | − | 1.38873i | ||||||
\(889\) | −0.772148 | −0.0258970 | ||||||||
\(890\) | −4.66032 | − | 8.31003i | −0.156214 | − | 0.278553i | ||||
\(891\) | −20.3012 | −0.680114 | ||||||||
\(892\) | − | 0.859636i | − | 0.0287827i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −17.3326 | −0.579688 | ||||||||
\(895\) | −16.7111 | + | 9.37168i | −0.558590 | + | 0.313261i | ||||
\(896\) | 3.55381 | 0.118725 | ||||||||
\(897\) | 0.0350960i | 0.00117182i | ||||||||
\(898\) | 12.9644i | 0.432626i | ||||||||
\(899\) | 10.4390 | 0.348161 | ||||||||
\(900\) | 0.813232 | − | 1.33061i | 0.0271077 | − | 0.0443538i | ||||
\(901\) | 16.4779 | 0.548960 | ||||||||
\(902\) | 42.1567i | 1.40367i | ||||||||
\(903\) | − | 6.80779i | − | 0.226549i | ||||||
\(904\) | 48.0256 | 1.59731 | ||||||||
\(905\) | 42.1160 | − | 23.6189i | 1.39998 | − | 0.785120i | ||||
\(906\) | 10.5614 | 0.350878 | ||||||||
\(907\) | 23.6201i | 0.784294i | 0.919903 | + | 0.392147i | \(0.128268\pi\) | ||||
−0.919903 | + | 0.392147i | \(0.871732\pi\) | |||||||
\(908\) | 3.16333i | 0.104979i | ||||||||
\(909\) | −10.2412 | −0.339679 | ||||||||
\(910\) | 1.77176 | + | 3.15930i | 0.0587332 | + | 0.104730i | ||||
\(911\) | 31.5189 | 1.04427 | 0.522135 | − | 0.852863i | \(-0.325136\pi\) | ||||
0.522135 | + | 0.852863i | \(0.325136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 43.8278i | − | 1.45049i | ||||||
\(914\) | −47.5966 | −1.57436 | ||||||||
\(915\) | 12.1870 | + | 21.7312i | 0.402888 | + | 0.718410i | ||||
\(916\) | 7.68252 | 0.253838 | ||||||||
\(917\) | 7.91799i | 0.261475i | ||||||||
\(918\) | − | 15.5367i | − | 0.512787i | ||||||
\(919\) | −9.34643 | −0.308310 | −0.154155 | − | 0.988047i | \(-0.549266\pi\) | ||||
−0.154155 | + | 0.988047i | \(0.549266\pi\) | |||||||
\(920\) | −0.0604509 | + | 0.0339012i | −0.00199301 | + | 0.00111769i | ||||
\(921\) | 15.6535 | 0.515799 | ||||||||
\(922\) | − | 14.7099i | − | 0.484446i | ||||||
\(923\) | 10.4161i | 0.342849i | ||||||||
\(924\) | −1.20494 | −0.0396395 | ||||||||
\(925\) | 38.2894 | + | 23.4014i | 1.25895 | + | 0.769433i | ||||
\(926\) | −13.0288 | −0.428153 | ||||||||
\(927\) | 3.13569i | 0.102989i | ||||||||
\(928\) | − | 2.78692i | − | 0.0914852i | ||||||
\(929\) | 19.7560 | 0.648172 | 0.324086 | − | 0.946028i | \(-0.394943\pi\) | ||||
0.324086 | + | 0.946028i | \(0.394943\pi\) | |||||||
\(930\) | −33.6285 | + | 18.8591i | −1.10272 | + | 0.618413i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.66666i | 0.0545934i | ||||||||
\(933\) | − | 22.4241i | − | 0.734133i | ||||||
\(934\) | 7.11448 | 0.232793 | ||||||||
\(935\) | −7.72782 | − | 13.7798i | −0.252727 | − | 0.450649i | ||||
\(936\) | −4.93631 | −0.161348 | ||||||||
\(937\) | 10.9310i | 0.357099i | 0.983931 | + | 0.178550i | \(0.0571405\pi\) | ||||
−0.983931 | + | 0.178550i | \(0.942859\pi\) | |||||||
\(938\) | − | 2.49537i | − | 0.0814767i | ||||||
\(939\) | −27.8368 | −0.908418 | ||||||||
\(940\) | 6.02373 | + | 10.7412i | 0.196472 | + | 0.350339i | ||||
\(941\) | −4.48898 | −0.146337 | −0.0731683 | − | 0.997320i | \(-0.523311\pi\) | ||||
−0.0731683 | + | 0.997320i | \(0.523311\pi\) | |||||||
\(942\) | 31.6250i | 1.03040i | ||||||||
\(943\) | − | 0.107592i | − | 0.00350366i | ||||||
\(944\) | 24.8054 | 0.807347 | ||||||||
\(945\) | 6.22591 | − | 3.49153i | 0.202529 | − | 0.113579i | ||||
\(946\) | −31.5355 | −1.02531 | ||||||||
\(947\) | 21.4661i | 0.697554i | 0.937206 | + | 0.348777i | \(0.113403\pi\) | ||||
−0.937206 | + | 0.348777i | \(0.886597\pi\) | |||||||
\(948\) | 5.29815i | 0.172076i | ||||||||
\(949\) | 22.0280 | 0.715060 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.732634 | −0.0237573 | ||||||||
\(952\) | − | 3.83775i | − | 0.124382i | ||||||
\(953\) | − | 17.6118i | − | 0.570502i | −0.958453 | − | 0.285251i | \(-0.907923\pi\) | ||
0.958453 | − | 0.285251i | \(-0.0920770\pi\) | |||||||
\(954\) | 6.60283 | 0.213774 | ||||||||
\(955\) | −10.2582 | + | 5.75289i | −0.331949 | + | 0.186159i | ||||
\(956\) | −4.59926 | −0.148751 | ||||||||
\(957\) | − | 5.52449i | − | 0.178581i | ||||||
\(958\) | 30.4588i | 0.984078i | ||||||||
\(959\) | −9.45529 | −0.305327 | ||||||||
\(960\) | 14.7303 | + | 26.2664i | 0.475420 | + | 0.847744i | ||||
\(961\) | 52.1866 | 1.68344 | ||||||||
\(962\) | − | 25.5692i | − | 0.824383i | ||||||
\(963\) | − | 9.86944i | − | 0.318038i | ||||||
\(964\) | 1.25991 | 0.0405788 | ||||||||
\(965\) | −7.50499 | − | 13.3825i | −0.241594 | − | 0.430798i | ||||
\(966\) | −0.0109335 | −0.000351780 | ||||||||
\(967\) | − | 18.1535i | − | 0.583777i | −0.956452 | − | 0.291888i | \(-0.905716\pi\) | ||
0.956452 | − | 0.291888i | \(-0.0942836\pi\) | |||||||
\(968\) | − | 2.51258i | − | 0.0807573i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.35337 | − | 4.12381i | 0.236102 | − | 0.132408i | ||||
\(971\) | −26.8785 | −0.862571 | −0.431286 | − | 0.902215i | \(-0.641940\pi\) | ||||
−0.431286 | + | 0.902215i | \(0.641940\pi\) | |||||||
\(972\) | 3.16686i | 0.101577i | ||||||||
\(973\) | 2.42600i | 0.0777740i | ||||||||
\(974\) | −6.62200 | −0.212183 | ||||||||
\(975\) | −8.99680 | + | 14.7206i | −0.288128 | + | 0.471436i | ||||
\(976\) | 21.5695 | 0.690423 | ||||||||
\(977\) | 25.0326i | 0.800863i | 0.916327 | + | 0.400431i | \(0.131140\pi\) | ||||
−0.916327 | + | 0.400431i | \(0.868860\pi\) | |||||||
\(978\) | − | 46.0019i | − | 1.47098i | ||||||
\(979\) | 10.8788 | 0.347687 | ||||||||
\(980\) | −5.71706 | + | 3.20616i | −0.182625 | + | 0.102417i | ||||
\(981\) | −2.55698 | −0.0816381 | ||||||||
\(982\) | − | 14.7312i | − | 0.470090i | ||||||
\(983\) | − | 34.3362i | − | 1.09516i | −0.836755 | − | 0.547578i | \(-0.815550\pi\) | ||
0.836755 | − | 0.547578i | \(-0.184450\pi\) | |||||||
\(984\) | −48.7742 | −1.55487 | ||||||||
\(985\) | −4.34501 | − | 7.74779i | −0.138443 | − | 0.246865i | ||||
\(986\) | 3.16732 | 0.100868 | ||||||||
\(987\) | 10.7925i | 0.343529i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0804841 | 0.00255925 | ||||||||
\(990\) | −3.09659 | − | 5.52168i | −0.0984161 | − | 0.175490i | ||||
\(991\) | 24.3932 | 0.774875 | 0.387438 | − | 0.921896i | \(-0.373360\pi\) | ||||
0.387438 | + | 0.921896i | \(0.373360\pi\) | |||||||
\(992\) | − | 22.2084i | − | 0.705119i | ||||||
\(993\) | − | 41.8851i | − | 1.32918i | ||||||
\(994\) | −3.24493 | −0.102923 | ||||||||
\(995\) | −26.9837 | + | 15.1326i | −0.855442 | + | 0.479737i | ||||
\(996\) | 9.12768 | 0.289221 | ||||||||
\(997\) | 39.4701i | 1.25003i | 0.780613 | + | 0.625015i | \(0.214907\pi\) | ||||
−0.780613 | + | 0.625015i | \(0.785093\pi\) | |||||||
\(998\) | 42.1359i | 1.33379i | ||||||||
\(999\) | −50.3881 | −1.59421 |
(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 | 1805.2.b.j.1084.12 | yes | 16 | |
5.2 | odd | 4 | 9025.2.a.ck.1.5 | 16 | |||
5.3 | odd | 4 | 9025.2.a.ck.1.12 | 16 | |||
5.4 | even | 2 | inner | 1805.2.b.j.1084.5 | yes | 16 | |
19.18 | odd | 2 | 1805.2.b.i.1084.5 | ✓ | 16 | ||
95.18 | even | 4 | 9025.2.a.cl.1.5 | 16 | |||
95.37 | even | 4 | 9025.2.a.cl.1.12 | 16 | |||
95.94 | odd | 2 | 1805.2.b.i.1084.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.5 | ✓ | 16 | 19.18 | odd | 2 | ||
1805.2.b.i.1084.12 | yes | 16 | 95.94 | odd | 2 | ||
1805.2.b.j.1084.5 | yes | 16 | 5.4 | even | 2 | inner | |
1805.2.b.j.1084.12 | yes | 16 | 1.1 | even | 1 | trivial | |
9025.2.a.ck.1.5 | 16 | 5.2 | odd | 4 | |||
9025.2.a.ck.1.12 | 16 | 5.3 | odd | 4 | |||
9025.2.a.cl.1.5 | 16 | 95.18 | even | 4 | |||
9025.2.a.cl.1.12 | 16 | 95.37 | even | 4 |