Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.o (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 95.7 | ||
Character | \(\chi\) | \(=\) | 768.95 |
Dual form | 768.2.o.b.671.7 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 | ||||||||
\(3\) | −0.0499748 | + | 1.73133i | −0.0288530 | + | 0.999584i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.06973 | − | 0.443098i | 0.478400 | − | 0.198160i | −0.130435 | − | 0.991457i | \(-0.541637\pi\) |
0.608834 | + | 0.793297i | \(0.291637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37247 | + | 2.37247i | 0.896708 | + | 0.896708i | 0.995143 | − | 0.0984354i | \(-0.0313838\pi\) |
−0.0984354 | + | 0.995143i | \(0.531384\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99501 | − | 0.173046i | −0.998335 | − | 0.0576820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.50127 | + | 2.27870i | −1.65869 | + | 0.687054i | −0.997977 | − | 0.0635809i | \(-0.979748\pi\) |
−0.660718 | + | 0.750635i | \(0.729748\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.346353 | + | 0.836171i | −0.0960612 | + | 0.231912i | −0.964604 | − | 0.263701i | \(-0.915057\pi\) |
0.868543 | + | 0.495613i | \(0.165057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.713689 | + | 1.87421i | 0.184274 | + | 0.483918i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.685064 | −0.166152 | −0.0830762 | − | 0.996543i | \(-0.526474\pi\) | ||||
−0.0830762 | + | 0.996543i | \(0.526474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.35074 | + | 1.38792i | 0.768712 | + | 0.318411i | 0.732351 | − | 0.680928i | \(-0.238423\pi\) |
0.0363614 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.22609 | + | 3.98896i | −0.922207 | + | 0.870462i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.05133 | + | 2.05133i | 0.427732 | + | 0.427732i | 0.887855 | − | 0.460123i | \(-0.152195\pi\) |
−0.460123 | + | 0.887855i | \(0.652195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.58754 | + | 2.58754i | −0.517508 | + | 0.517508i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.449274 | − | 5.17669i | 0.0864629 | − | 0.996255i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.98869 | − | 4.80112i | 0.369291 | − | 0.891546i | −0.624576 | − | 0.780964i | \(-0.714728\pi\) |
0.993867 | − | 0.110582i | \(-0.0352716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.36503i | 1.14319i | 0.820535 | + | 0.571596i | \(0.193676\pi\) | ||||
−0.820535 | + | 0.571596i | \(0.806324\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.67025 | − | 9.63838i | −0.638909 | − | 1.67783i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.58914 | + | 1.48667i | 0.606676 | + | 0.251293i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.112738 | − | 0.272172i | −0.0185339 | − | 0.0447449i | 0.914342 | − | 0.404944i | \(-0.132709\pi\) |
−0.932876 | + | 0.360199i | \(0.882709\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.43038 | − | 0.641440i | −0.229044 | − | 0.102713i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.26585 | + | 3.26585i | −0.510040 | + | 0.510040i | −0.914539 | − | 0.404499i | \(-0.867446\pi\) |
0.404499 | + | 0.914539i | \(0.367446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.993018 | + | 2.39736i | 0.151434 | + | 0.365594i | 0.981332 | − | 0.192321i | \(-0.0616016\pi\) |
−0.829898 | + | 0.557915i | \(0.811602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.28053 | + | 1.14197i | −0.489033 | + | 0.170235i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.7975i | − | 1.72084i | −0.509589 | − | 0.860418i | \(-0.670203\pi\) | ||
0.509589 | − | 0.860418i | \(-0.329797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.25719i | 0.608171i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0342360 | − | 1.18607i | 0.00479399 | − | 0.166083i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.56192 | + | 3.77080i | 0.214546 | + | 0.517959i | 0.994112 | − | 0.108361i | \(-0.0345602\pi\) |
−0.779566 | + | 0.626320i | \(0.784560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.87520 | + | 4.87520i | −0.657372 | + | 0.657372i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.57040 | + | 5.73187i | −0.340458 | + | 0.759205i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.20815 | + | 5.33094i | 0.287476 | + | 0.694029i | 0.999971 | − | 0.00764882i | \(-0.00243472\pi\) |
−0.712495 | + | 0.701678i | \(0.752435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.53549 | + | 0.636020i | 0.196599 | + | 0.0814341i | 0.478811 | − | 0.877918i | \(-0.341068\pi\) |
−0.282212 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.69500 | − | 7.51609i | −0.843491 | − | 0.946939i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04795i | 0.129982i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.69605 | + | 11.3373i | −0.573714 | + | 1.38507i | 0.324657 | + | 0.945832i | \(0.394751\pi\) |
−0.898371 | + | 0.439237i | \(0.855249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.65405 | + | 3.44902i | −0.439895 | + | 0.415213i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.99150 | + | 7.99150i | −0.948416 | + | 0.948416i | −0.998733 | − | 0.0503173i | \(-0.983977\pi\) |
0.0503173 | + | 0.998733i | \(0.483977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.34760 | − | 2.34760i | −0.274766 | − | 0.274766i | 0.556250 | − | 0.831015i | \(-0.312240\pi\) |
−0.831015 | + | 0.556250i | \(0.812240\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.35057 | − | 4.60920i | −0.502361 | − | 0.532224i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.4577 | − | 7.64543i | −2.10345 | − | 0.871278i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.91043 | 1.00250 | 0.501251 | − | 0.865302i | \(-0.332873\pi\) | ||||
0.501251 | + | 0.865302i | \(0.332873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94011 | + | 1.03655i | 0.993346 | + | 0.115172i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.06920 | − | 7.40970i | 0.336888 | − | 0.813320i | −0.661123 | − | 0.750278i | \(-0.729920\pi\) |
0.998011 | − | 0.0630420i | \(-0.0200802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.732836 | + | 0.303551i | −0.0794872 | + | 0.0329247i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.21294 | + | 3.68301i | 0.880520 | + | 0.394861i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.99332 | − | 1.99332i | −0.211291 | − | 0.211291i | 0.593525 | − | 0.804816i | \(-0.297736\pi\) |
−0.804816 | + | 0.593525i | \(0.797736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.80550 | + | 1.16208i | −0.294096 | + | 0.121819i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0200 | − | 0.318091i | −1.14272 | − | 0.0329845i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19938 | 0.430848 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.66510 | 0.879807 | 0.439904 | − | 0.898045i | \(-0.355013\pi\) | ||||
0.439904 | + | 0.898045i | \(0.355013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.8706 | − | 5.87274i | 1.69556 | − | 0.590233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6920 | − | 6.49983i | 1.56141 | − | 0.646758i | 0.576077 | − | 0.817395i | \(-0.304583\pi\) |
0.985334 | + | 0.170637i | \(0.0545827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.39788 | − | 5.39788i | −0.531869 | − | 0.531869i | 0.389259 | − | 0.921128i | \(-0.372731\pi\) |
−0.921128 | + | 0.389259i | \(0.872731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.75329 | + | 6.13969i | −0.268693 | + | 0.599173i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0169596 | + | 0.00702491i | −0.00163955 | + | 0.000679124i | −0.383503 | − | 0.923540i | \(-0.625282\pi\) |
0.381864 | + | 0.924219i | \(0.375282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.94357 | − | 11.9348i | 0.473508 | − | 1.14315i | −0.489094 | − | 0.872231i | \(-0.662672\pi\) |
0.962602 | − | 0.270919i | \(-0.0873276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.476854 | − | 0.181584i | 0.0452610 | − | 0.0172352i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4984 | 0.987609 | 0.493804 | − | 0.869573i | \(-0.335606\pi\) | ||||
0.493804 | + | 0.869573i | \(0.335606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.10332 | + | 1.28544i | 0.289386 | + | 0.119868i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.18203 | − | 2.44440i | 0.109278 | − | 0.225985i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62529 | − | 1.62529i | −0.148990 | − | 0.148990i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.2933 | − | 17.2933i | 1.57212 | − | 1.57212i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.49105 | − | 5.81747i | −0.495112 | − | 0.524544i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.83694 | + | 9.26318i | −0.343186 | + | 0.828524i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.793212i | − | 0.0703862i | −0.999381 | − | 0.0351931i | \(-0.988795\pi\) | ||
0.999381 | − | 0.0351931i | \(-0.0112046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.20024 | + | 1.59943i | −0.369811 | + | 0.140822i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.39267 | − | 3.89057i | −0.820641 | − | 0.339921i | −0.0674502 | − | 0.997723i | \(-0.521486\pi\) |
−0.753191 | + | 0.657802i | \(0.771486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.65672 | + | 11.2423i | 0.403789 | + | 0.974832i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.81318 | − | 5.73676i | −0.156054 | − | 0.493741i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.95969 | − | 2.95969i | 0.252863 | − | 0.252863i | −0.569280 | − | 0.822144i | \(-0.692778\pi\) |
0.822144 | + | 0.569280i | \(0.192778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.91155 | + | 4.61488i | 0.162135 | + | 0.391429i | 0.983979 | − | 0.178284i | \(-0.0570545\pi\) |
−0.821844 | + | 0.569713i | \(0.807054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.4253 | + | 0.589576i | 1.72012 | + | 0.0496512i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.38924i | − | 0.450671i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.01711i | − | 0.499694i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.37061 | − | 0.212753i | −0.607917 | − | 0.0175475i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.53451 | + | 13.3615i | 0.453405 | + | 1.09462i | 0.971019 | + | 0.239002i | \(0.0768202\pi\) |
−0.517614 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.96063 | − | 2.96063i | 0.240932 | − | 0.240932i | −0.576303 | − | 0.817236i | \(-0.695505\pi\) |
0.817236 | + | 0.576303i | \(0.195505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.05177 | + | 0.118548i | 0.165876 | + | 0.00958400i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82033 | + | 6.80889i | 0.226535 | + | 0.546903i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1213 | + | 6.67768i | 1.28662 | + | 0.532937i | 0.917977 | − | 0.396633i | \(-0.129822\pi\) |
0.368646 | + | 0.929570i | \(0.379822\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.60656 | + | 2.51575i | −0.523934 | + | 0.199512i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.73343i | 0.767102i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62172 | − | 11.1578i | 0.362001 | − | 0.873949i | −0.633006 | − | 0.774147i | \(-0.718179\pi\) |
0.995007 | − | 0.0998018i | \(-0.0318209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.19695 | − | 8.68422i | −0.638131 | − | 0.676066i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.28603 | + | 1.28603i | −0.0995157 | + | 0.0995157i | −0.755112 | − | 0.655596i | \(-0.772417\pi\) |
0.655596 | + | 0.755112i | \(0.272417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.61317 | + | 8.61317i | 0.662551 | + | 0.662551i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.79530 | − | 4.73666i | −0.749065 | − | 0.362222i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0565964 | − | 0.0234430i | −0.00430295 | − | 0.00178234i | 0.380531 | − | 0.924768i | \(-0.375741\pi\) |
−0.384834 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2777 | −0.928107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.33996 | + | 3.55662i | −0.702034 | + | 0.267332i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.17461 | + | 2.83576i | −0.0877946 | + | 0.211955i | −0.961678 | − | 0.274180i | \(-0.911594\pi\) |
0.873884 | + | 0.486135i | \(0.161594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8334 | − | 8.62949i | 1.54854 | − | 0.641425i | 0.565485 | − | 0.824758i | \(-0.308689\pi\) |
0.983051 | + | 0.183334i | \(0.0586889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.17790 | + | 2.62665i | −0.0870726 | + | 0.194168i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.241198 | − | 0.241198i | −0.0177333 | − | 0.0177333i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.76872 | − | 1.56105i | 0.275596 | − | 0.114156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.3474 | − | 11.2156i | 0.970882 | − | 0.815818i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.0566 | 1.66832 | 0.834158 | − | 0.551525i | \(-0.185954\pi\) | ||||
0.834158 | + | 0.551525i | \(0.185954\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.52832 | 0.541900 | 0.270950 | − | 0.962593i | \(-0.412662\pi\) | ||||
0.270950 | + | 0.962593i | \(0.412662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.81435 | − | 0.0523711i | −0.129928 | − | 0.00375037i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.14750 | + | 0.889524i | −0.153003 | + | 0.0633760i | −0.457871 | − | 0.889019i | \(-0.651388\pi\) |
0.304868 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.46994 | + | 7.46994i | 0.529530 | + | 0.529530i | 0.920432 | − | 0.390902i | \(-0.127837\pi\) |
−0.390902 | + | 0.920432i | \(0.627837\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.3939 | − | 8.69699i | −1.36794 | − | 0.613439i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1086 | − | 6.67240i | 1.13060 | − | 0.468311i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.04650 | + | 4.94068i | −0.142934 | + | 0.345072i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.78877 | − | 6.49872i | −0.402348 | − | 0.451692i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.5960 | −1.49382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9819 | − | 6.61994i | −1.10024 | − | 0.455735i | −0.242676 | − | 0.970107i | \(-0.578025\pi\) |
−0.857567 | + | 0.514372i | \(0.828025\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.4365 | − | 14.2353i | −0.920657 | − | 0.975386i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.12453 | + | 2.12453i | 0.144892 | + | 0.144892i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1008 | + | 15.1008i | −1.02511 | + | 1.02511i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.18179 | − | 3.94715i | 0.282579 | − | 0.266723i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.237274 | − | 0.572831i | 0.0159608 | − | 0.0385328i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.2244i | − | 1.22040i | −0.792248 | − | 0.610199i | \(-0.791090\pi\) | ||
0.792248 | − | 0.610199i | \(-0.208910\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.19746 | − | 7.30193i | 0.546497 | − | 0.486795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.8455 | − | 4.49234i | −0.719840 | − | 0.298167i | −0.00747022 | − | 0.999972i | \(-0.502378\pi\) |
−0.712369 | + | 0.701805i | \(0.752378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.20986 | − | 12.5777i | −0.344277 | − | 0.831159i | −0.997273 | − | 0.0737978i | \(-0.976488\pi\) |
0.652996 | − | 0.757362i | \(-0.273512\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.1592 | − | 31.5743i | 0.931606 | − | 2.07744i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7233 | − | 11.7233i | 0.768016 | − | 0.768016i | −0.209741 | − | 0.977757i | \(-0.567262\pi\) |
0.977757 | + | 0.209741i | \(0.0672620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.22743 | − | 12.6201i | −0.341000 | − | 0.823247i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.445297 | + | 15.4269i | −0.0289252 | + | 1.00208i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.5949i | 1.39685i | 0.715681 | + | 0.698427i | \(0.246117\pi\) | ||||
−0.715681 | + | 0.698427i | \(0.753883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.6095i | − | 0.941078i | −0.882379 | − | 0.470539i | \(-0.844059\pi\) | ||
0.882379 | − | 0.470539i | \(-0.155941\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.24138 | + | 15.4265i | −0.143785 | + | 0.989609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.88636 | + | 4.55406i | 0.120515 | + | 0.290949i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.32108 | + | 2.32108i | −0.147687 | + | 0.147687i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6752 | + | 5.68409i | 0.803261 | + | 0.360215i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.08581 | − | 2.62137i | −0.0685355 | − | 0.165459i | 0.885900 | − | 0.463876i | \(-0.153542\pi\) |
−0.954436 | + | 0.298416i | \(0.903542\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.9593 | − | 6.61055i | −1.00335 | − | 0.415602i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.488923 | − | 1.28395i | −0.0306175 | − | 0.0804041i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.35436i | 0.0844827i | 0.999107 | + | 0.0422414i | \(0.0134498\pi\) | ||||
−0.999107 | + | 0.0422414i | \(0.986550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.378254 | − | 0.913186i | 0.0235036 | − | 0.0567426i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.78695 | + | 14.0353i | −0.420102 | + | 0.868760i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.52372 | + | 3.52372i | −0.217282 | + | 0.217282i | −0.807352 | − | 0.590070i | \(-0.799100\pi\) |
0.590070 | + | 0.807352i | \(0.299100\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.34167 | + | 3.34167i | 0.205277 | + | 0.205277i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.55070 | − | 3.35147i | 0.217299 | − | 0.205107i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4741 | + | 6.82380i | 1.00444 | + | 0.416055i | 0.823425 | − | 0.567425i | \(-0.192060\pi\) |
0.181020 | + | 0.983479i | \(0.442060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.50293 | −0.516516 | −0.258258 | − | 0.966076i | \(-0.583149\pi\) | ||||
−0.258258 | + | 0.966076i | \(0.583149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.87173 | − | 4.91532i | −0.113282 | − | 0.297489i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.33852 | − | 20.1310i | 0.502832 | − | 1.21394i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2028 | + | 8.36828i | −1.21387 | + | 0.502801i | −0.895456 | − | 0.445150i | \(-0.853150\pi\) |
−0.318414 | + | 0.947952i | \(0.603150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.10144 | − | 19.0633i | 0.0659416 | − | 1.14129i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3342 | − | 10.3342i | −0.616487 | − | 0.616487i | 0.328142 | − | 0.944629i | \(-0.393578\pi\) |
−0.944629 | + | 0.328142i | \(0.893578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.67342 | + | 3.59265i | −0.515581 | + | 0.213561i | −0.625275 | − | 0.780405i | \(-0.715013\pi\) |
0.109694 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.209864 | + | 7.27052i | −0.0124312 | + | 0.430668i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4962 | −0.914714 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5307 | −0.972393 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.433037 | + | 15.0021i | −0.0253851 | + | 0.879441i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3816 | + | 4.71442i | −0.664922 | + | 0.275420i | −0.689508 | − | 0.724278i | \(-0.742173\pi\) |
0.0245862 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.72426 | + | 4.72426i | 0.275057 | + | 0.275057i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.32455 | + | 29.5021i | 0.541065 | + | 1.71189i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.42575 | + | 1.00478i | −0.140285 | + | 0.0581078i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.33175 | + | 8.04355i | −0.192039 | + | 0.463623i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.4692 | + | 27.4928i | 0.601437 | + | 1.57942i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.92438 | 0.110190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6145 | + | 5.22511i | 0.719950 | + | 0.298213i | 0.712415 | − | 0.701759i | \(-0.247601\pi\) |
0.00753514 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.61527 | − | 9.07575i | 0.546994 | − | 0.516302i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8020 | − | 18.8020i | −1.06617 | − | 1.06617i | −0.997650 | − | 0.0685162i | \(-0.978174\pi\) |
−0.0685162 | − | 0.997650i | \(-0.521826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30835 | − | 4.30835i | 0.243522 | − | 0.243522i | −0.574783 | − | 0.818306i | \(-0.694914\pi\) |
0.818306 | + | 0.574783i | \(0.194914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.4922 | − | 5.07368i | −0.591171 | − | 0.285869i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.543402 | + | 1.31189i | −0.0305205 | + | 0.0736830i | −0.938405 | − | 0.345538i | \(-0.887697\pi\) |
0.907884 | + | 0.419221i | \(0.137697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.9439i | 1.73252i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0113149 | − | 0.0297138i | −0.000631535 | − | 0.00165846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.29547 | − | 0.950815i | −0.127723 | − | 0.0529047i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.26742 | − | 3.05983i | −0.0703040 | − | 0.169729i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.4161 | + | 9.15540i | 1.12901 | + | 0.506295i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.9891 | − | 27.9891i | 1.54309 | − | 1.54309i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.18815 | + | 12.5253i | 0.285167 | + | 0.688453i | 0.999941 | − | 0.0109024i | \(-0.00347041\pi\) |
−0.714774 | + | 0.699356i | \(0.753470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.290551 | + | 0.834667i | 0.0159221 | + | 0.0457395i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2087i | 0.776303i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9878i | 1.08881i | 0.838824 | + | 0.544403i | \(0.183244\pi\) | ||||
−0.838824 | + | 0.544403i | \(0.816756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.524657 | + | 18.1762i | −0.0284955 | + | 0.987197i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.5040 | − | 35.0157i | −0.785435 | − | 1.89621i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.50721 | − | 6.50721i | 0.351357 | − | 0.351357i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.38060 | + | 5.30863i | −0.128167 | + | 0.285807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.84634 | + | 14.1143i | 0.313848 | + | 0.757696i | 0.999555 | + | 0.0298187i | \(0.00949299\pi\) |
−0.685707 | + | 0.727877i | \(0.740507\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.90170 | − | 3.27299i | −0.422969 | − | 0.175199i | 0.161038 | − | 0.986948i | \(-0.448516\pi\) |
−0.584007 | + | 0.811749i | \(0.698516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.17299 | + | 2.16864i | 0.222738 | + | 0.115753i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4566i | 1.51459i | 0.653072 | + | 0.757296i | \(0.273480\pi\) | ||||
−0.653072 | + | 0.757296i | \(0.726520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00776 | + | 12.0898i | −0.265784 | + | 0.641659i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.89514 | − | 2.73269i | 0.153227 | − | 0.144629i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.48589 | + | 3.48589i | −0.183978 | + | 0.183978i | −0.793087 | − | 0.609109i | \(-0.791527\pi\) |
0.609109 | + | 0.793087i | \(0.291527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.13391 | − | 4.13391i | −0.217574 | − | 0.217574i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.0762 | + | 30.8046i | 1.52610 | + | 1.61682i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.55152 | − | 1.47109i | −0.185895 | − | 0.0770003i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.37411 | 0.384925 | 0.192463 | − | 0.981304i | \(-0.438353\pi\) | ||||
0.192463 | + | 0.981304i | \(0.438353\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3464 | − | 9.21609i | 0.538611 | − | 0.479771i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.24050 | + | 12.6517i | −0.272073 | + | 0.656843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.72861 | − | 3.20130i | 0.400172 | − | 0.165757i | −0.173515 | − | 0.984831i | \(-0.555512\pi\) |
0.573687 | + | 0.819074i | \(0.305512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.8459 | − | 7.10593i | −0.818277 | − | 0.366948i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.32577 | + | 3.32577i | 0.171286 | + | 0.171286i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6759 | − | 9.39268i | 1.16478 | − | 0.482470i | 0.285319 | − | 0.958433i | \(-0.407900\pi\) |
0.879465 | + | 0.475963i | \(0.157900\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37331 | + | 0.0396406i | 0.0703569 | + | 0.00203085i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3729 | −0.581129 | −0.290565 | − | 0.956855i | \(-0.593843\pi\) | ||||
−0.290565 | + | 0.956855i | \(0.593843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.1325 | −1.17894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.55924 | − | 7.35194i | −0.130094 | − | 0.373720i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.2635 | + | 4.66550i | −0.571083 | + | 0.236550i | −0.649489 | − | 0.760371i | \(-0.725017\pi\) |
0.0784059 | + | 0.996922i | \(0.475017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.40529 | − | 1.40529i | −0.0710687 | − | 0.0710687i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.20526 | − | 16.0674i | 0.363457 | − | 0.810492i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.53179 | − | 3.94820i | 0.479596 | − | 0.198655i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.65241 | + | 8.81769i | −0.183309 | + | 0.442547i | −0.988645 | − | 0.150272i | \(-0.951985\pi\) |
0.805336 | + | 0.592819i | \(0.201985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.6969 | + | 7.50048i | −0.986076 | + | 0.375494i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.46170 | 0.272744 | 0.136372 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136372 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.32225 | − | 2.20455i | −0.265120 | − | 0.109816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0228 | − | 2.85252i | 0.498038 | − | 0.141743i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.24040 | + | 1.24040i | 0.0614843 | + | 0.0614843i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.6474 | + | 21.6474i | −1.07039 | + | 1.07039i | −0.0730670 | + | 0.997327i | \(0.523279\pi\) |
−0.997327 | + | 0.0730670i | \(0.976721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.97629 | + | 5.27211i | 0.245462 | + | 0.260054i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.40871 | + | 17.8862i | −0.364559 | + | 0.880123i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.28636i | − | 0.455849i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.08541 | + | 3.07889i | −0.395944 | + | 0.150774i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.1057 | − | 6.67119i | −0.786814 | − | 0.325909i | −0.0471519 | − | 0.998888i | \(-0.515014\pi\) |
−0.739662 | + | 0.672979i | \(0.765014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0865 | − | 26.7651i | −0.540321 | − | 1.30445i | −0.924497 | − | 0.381190i | \(-0.875514\pi\) |
0.384176 | − | 0.923260i | \(-0.374486\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.04150 | + | 35.3334i | −0.0992612 | + | 1.71797i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.77263 | − | 1.77263i | 0.0859852 | − | 0.0859852i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.13396 | + | 5.15183i | 0.103270 | + | 0.249315i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.33055 | + | 0.269326i | 0.450483 | + | 0.0130032i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.4774i | − | 0.986361i | −0.869927 | − | 0.493180i | \(-0.835834\pi\) | ||
0.869927 | − | 0.493180i | \(-0.164166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6756i | 0.705262i | 0.935762 | + | 0.352631i | \(0.114713\pi\) | ||||
−0.935762 | + | 0.352631i | \(0.885287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4176 | + | 0.300704i | 0.499486 | + | 0.0144177i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.02639 | + | 9.72056i | 0.192608 | + | 0.464997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.86825 | − | 4.86825i | 0.232349 | − | 0.232349i | −0.581324 | − | 0.813672i | \(-0.697465\pi\) |
0.813672 | + | 0.581324i | \(0.197465\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.736690 | − | 12.7503i | 0.0350805 | − | 0.607158i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00738 | + | 14.5031i | 0.285419 | + | 0.689063i | 0.999944 | − | 0.0105468i | \(-0.00335721\pi\) |
−0.714525 | + | 0.699610i | \(0.753357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.01555 | − | 1.24908i | −0.142951 | − | 0.0592122i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.4097 | + | 8.91432i | −1.10724 | + | 0.421633i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.76611i | 0.0833480i | 0.999131 | + | 0.0416740i | \(0.0132691\pi\) | ||||
−0.999131 | + | 0.0416740i | \(0.986731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5244 | − | 25.4082i | 0.495576 | − | 1.19643i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.97787 | + | 5.27378i | 0.233881 | + | 0.247784i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.48622 | + | 2.48622i | −0.116556 | + | 0.116556i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.3579 | − | 22.3579i | −1.04586 | − | 1.04586i | −0.998897 | − | 0.0469601i | \(-0.985047\pi\) |
−0.0469601 | − | 0.998897i | \(-0.514953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.307782 | + | 3.54637i | −0.0143660 | + | 0.165530i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.811938 | − | 0.336316i | −0.0378157 | − | 0.0156638i | 0.363695 | − | 0.931518i | \(-0.381515\pi\) |
−0.401511 | + | 0.915854i | \(0.631515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0009 | 0.650678 | 0.325339 | − | 0.945597i | \(-0.394522\pi\) | ||||
0.325339 | + | 0.945597i | \(0.394522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.9294 | + | 4.54265i | −0.553211 | + | 0.210661i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.94695 | + | 14.3572i | −0.275192 | + | 0.664373i | −0.999690 | − | 0.0249045i | \(-0.992072\pi\) |
0.724498 | + | 0.689277i | \(0.242072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.0385 | + | 15.7561i | −1.75646 | + | 0.727548i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3669 | + | 27.5776i | −0.569838 | + | 1.27071i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.9257 | − | 10.9257i | −0.502365 | − | 0.502365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.2615 | + | 5.07887i | −0.562595 | + | 0.233034i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.02543 | − | 11.5639i | −0.184312 | − | 0.529473i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4708 | 1.57501 | 0.787505 | − | 0.616309i | \(-0.211373\pi\) | ||||
0.787505 | + | 0.616309i | \(0.211373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.266630 | 0.0121573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.8518 | − | 0.486427i | −0.766782 | − | 0.0221332i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.26935 | − | 3.83949i | 0.420899 | − | 0.174342i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6710 | − | 13.6710i | −0.619490 | − | 0.619490i | 0.325911 | − | 0.945401i | \(-0.394329\pi\) |
−0.945401 | + | 0.325911i | \(0.894329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0869 | + | 8.55934i | 0.863140 | + | 0.387067i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0034 | − | 6.62882i | 0.722223 | − | 0.299154i | 0.00887095 | − | 0.999961i | \(-0.497176\pi\) |
0.713352 | + | 0.700806i | \(0.247176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.36238 | + | 3.28908i | −0.0613585 | + | 0.148133i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.4449 | − | 13.7576i | 0.694196 | − | 0.618359i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.9191 | −1.70090 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.36166 | + | 2.63509i | 0.284787 | + | 0.117963i | 0.520504 | − | 0.853859i | \(-0.325744\pi\) |
−0.235717 | + | 0.971822i | \(0.575744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.16227 | − | 2.29080i | −0.0966029 | − | 0.102346i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8510 | + | 16.8510i | 0.751350 | + | 0.751350i | 0.974731 | − | 0.223381i | \(-0.0717095\pi\) |
−0.223381 | + | 0.974731i | \(0.571709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9062 | − | 13.9062i | 0.618817 | − | 0.618817i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3427 | + | 14.4818i | −0.681392 | + | 0.643159i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.71610 | − | 16.2141i | 0.297686 | − | 0.718678i | −0.702291 | − | 0.711890i | \(-0.747839\pi\) |
0.999977 | − | 0.00678764i | \(-0.00216059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 11.1392i | − | 0.492769i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.69024 | − | 16.7222i | 0.383684 | − | 0.738302i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.16609 | − | 3.38250i | −0.359841 | − | 0.149051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.8828 | + | 64.9009i | 1.18231 | + | 2.85434i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0434160 | − | 0.0968155i | 0.00190575 | − | 0.00424973i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2126 | + | 18.2126i | −0.797908 | + | 0.797908i | −0.982765 | − | 0.184858i | \(-0.940818\pi\) |
0.184858 | + | 0.982765i | \(0.440818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.472480 | + | 1.14067i | 0.0206601 | + | 0.0498779i | 0.933873 | − | 0.357605i | \(-0.116407\pi\) |
−0.913213 | + | 0.407483i | \(0.866407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.613576 | − | 21.2567i | 0.0267787 | − | 0.927721i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.36045i | − | 0.189944i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.5841i | − | 0.634090i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.69091 | − | 16.3483i | −0.246965 | − | 0.709455i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.59967 | − | 3.86195i | −0.0692895 | − | 0.167280i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0150296 | + | 0.0150296i | −0.000649785 | + | 0.000649785i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.85094 | − | 2.17536i | −0.209333 | − | 0.0938735i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.70087 | − | 23.4200i | −0.417846 | − | 1.00877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2297 | − | 5.89412i | −0.611781 | − | 0.253408i | 0.0552087 | − | 0.998475i | \(-0.482418\pi\) |
−0.666990 | + | 0.745067i | \(0.732418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8993 | + | 36.5008i | 0.596478 | + | 1.56640i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 14.9576i | − | 0.640713i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.24323 | − | 15.0725i | 0.266941 | − | 0.644453i | −0.732395 | − | 0.680880i | \(-0.761598\pi\) |
0.999336 | + | 0.0364266i | \(0.0115975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.48874 | − | 2.17059i | −0.191575 | − | 0.0926387i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3272 | − | 13.3272i | 0.567756 | − | 0.567756i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.1397 | + | 21.1397i | 0.898952 | + | 0.898952i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.429648 | − | 0.405540i | 0.0182375 | − | 0.0172142i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.09223 | − | 2.93770i | −0.300507 | − | 0.124474i | 0.227335 | − | 0.973817i | \(-0.426999\pi\) |
−0.527842 | + | 0.849342i | \(0.676999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.34854 | −0.0993325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.51436 | + | 6.60291i | 0.106156 | + | 0.278775i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.517007 | + | 1.24817i | −0.0217892 | + | 0.0526039i | −0.934400 | − | 0.356226i | \(-0.884063\pi\) |
0.912610 | + | 0.408830i | \(0.134063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2305 | − | 4.65183i | 0.472471 | − | 0.195704i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.7509 | + | 23.6693i | 0.787465 | + | 0.994016i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.40004 | + | 4.40004i | 0.184459 | + | 0.184459i | 0.793296 | − | 0.608836i | \(-0.208363\pi\) |
−0.608836 | + | 0.793296i | \(0.708363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9135 | + | 9.90528i | −1.00075 | + | 0.414523i | −0.822071 | − | 0.569385i | \(-0.807181\pi\) |
−0.178676 | + | 0.983908i | \(0.557181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.15225 | + | 39.9186i | −0.0481359 | + | 1.66762i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.6158 | −0.442709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.45244 | −0.310249 | −0.155124 | − | 0.987895i | \(-0.549578\pi\) | ||||
−0.155124 | + | 0.987895i | \(0.549578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.376226 | + | 13.0340i | −0.0156354 | + | 0.541675i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.8608 | − | 10.2977i | 1.03140 | − | 0.427220i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.1850 | − | 17.1850i | −0.711732 | − | 0.711732i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.181343 | − | 3.13861i | 0.00749762 | − | 0.129766i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.1257 | + | 16.2064i | −1.61489 | + | 0.668910i | −0.993420 | − | 0.114526i | \(-0.963465\pi\) |
−0.621472 | + | 0.783436i | \(0.713465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.83416 | + | 21.3275i | −0.364005 | + | 0.878786i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.43274 | − | 3.76249i | −0.0589350 | − | 0.154768i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.7694 | 1.75633 | 0.878164 | − | 0.478359i | \(-0.158768\pi\) | ||||
0.878164 | + | 0.478359i | \(0.158768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.45879 | − | 1.01847i | −0.100801 | − | 0.0417530i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.3062 | + | 12.5596i | −0.544588 | + | 0.514031i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3145 | − | 21.3145i | −0.870885 | − | 0.870885i | 0.121684 | − | 0.992569i | \(-0.461171\pi\) |
−0.992569 | + | 0.121684i | \(0.961171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.26621 | + | 4.26621i | −0.174022 | + | 0.174022i | −0.788744 | − | 0.614722i | \(-0.789268\pi\) |
0.614722 | + | 0.788744i | \(0.289268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.0266 | − | 33.1426i | 0.652652 | − | 1.34967i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8366 | − | 26.1618i | 0.440570 | − | 1.06363i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 30.5562i | − | 1.24024i | −0.784508 | − | 0.620118i | \(-0.787085\pi\) | ||
0.784508 | − | 0.620118i | \(-0.212915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7471 | + | 28.2228i | 0.435495 | + | 1.14364i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.86469 | + | 4.08609i | 0.399083 | + | 0.165305i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.4587 | − | 32.4921i | −0.543590 | − | 1.31234i | −0.922174 | − | 0.386775i | \(-0.873589\pi\) |
0.378584 | − | 0.925567i | \(-0.376411\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.45168 | − | 3.79007i | −0.340804 | − | 0.152830i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1395 | + | 32.1395i | −1.29389 | + | 1.29389i | −0.361524 | + | 0.932363i | \(0.617743\pi\) |
−0.932363 | + | 0.361524i | \(0.882257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9456 | − | 36.0820i | −0.600716 | − | 1.45026i | −0.872846 | − | 0.487996i | \(-0.837728\pi\) |
0.272129 | − | 0.962261i | \(-0.412272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5407 | − | 9.69750i | 0.463113 | − | 0.389147i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 9.45815i | − | 0.378933i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 6.68739i | − | 0.267496i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.07925 | − | 37.3897i | 0.0431013 | − | 1.49320i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0772324 | + | 0.186456i | 0.00307946 | + | 0.00743447i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5960 | − | 20.5960i | 0.819912 | − | 0.819912i | −0.166183 | − | 0.986095i | \(-0.553144\pi\) |
0.986095 | + | 0.166183i | \(0.0531442\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2600 | − | 27.3392i | 0.487291 | − | 1.08664i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.351471 | − | 0.848526i | −0.0139477 | − | 0.0336727i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.55974 | − | 1.47449i | −0.141042 | − | 0.0584216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.3175 | − | 22.5517i | 1.00154 | − | 0.892130i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6916i | 0.501289i | 0.968079 | + | 0.250645i | \(0.0806426\pi\) | ||||
−0.968079 | + | 0.250645i | \(0.919357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.974363 | + | 2.35232i | −0.0384251 | + | 0.0927665i | −0.941927 | − | 0.335818i | \(-0.890987\pi\) |
0.903502 | + | 0.428584i | \(0.140987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.78444 | + | 3.57209i | −0.149012 | + | 0.140651i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.3823 | − | 22.3823i | 0.879941 | − | 0.879941i | −0.113587 | − | 0.993528i | \(-0.536234\pi\) |
0.993528 | + | 0.113587i | \(0.0362341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.2952 | − | 24.2952i | −0.953670 | − | 0.953670i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.3898 | − | 26.8992i | −0.995106 | − | 1.05426i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.02663 | + | 0.839459i | 0.0793083 | + | 0.0328506i | 0.421985 | − | 0.906603i | \(-0.361334\pi\) |
−0.342677 | + | 0.939453i | \(0.611334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7716 | −0.459953 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.62483 | + | 7.43731i | 0.258459 | + | 0.290157i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.65284 | + | 11.2330i | −0.181249 | + | 0.437574i | −0.988224 | − | 0.153011i | \(-0.951103\pi\) |
0.806975 | + | 0.590585i | \(0.201103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0472 | − | 9.13226i | 0.857538 | − | 0.355204i | 0.0897938 | − | 0.995960i | \(-0.471379\pi\) |
0.767744 | + | 0.640757i | \(0.221379\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.979901 | + | 0.439427i | 0.0380562 | + | 0.0170659i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.96289 | + | 9.96289i | 0.386344 | + | 0.386344i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.9282 | − | 5.76923i | 0.539300 | − | 0.223386i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.5525 | + | 0.910763i | 1.21989 | + | 0.0352121i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.89643 | −0.382048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.77155 | 0.0682883 | 0.0341441 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341441 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.2324 | + | 14.5574i | 0.470825 | + | 0.560315i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1005 | − | 12.8822i | 1.19529 | − | 0.495105i | 0.305815 | − | 0.952091i | \(-0.401071\pi\) |
0.889474 | + | 0.456986i | \(0.151071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.5577 | + | 20.5577i | 0.788930 | + | 0.788930i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.31973 | − | 18.5526i | 0.318813 | − | 0.710937i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.51740 | − | 1.04274i | 0.0963256 | − | 0.0398994i | −0.334000 | − | 0.942573i | \(-0.608399\pi\) |
0.430326 | + | 0.902674i | \(0.358399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.85465 | − | 4.47752i | 0.0708624 | − | 0.171077i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.0365 | − | 8.39142i | 0.840747 | − | 0.320153i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.69401 | −0.140731 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0335 | − | 14.9256i | −1.37078 | − | 0.567795i | −0.428779 | − | 0.903409i | \(-0.641056\pi\) |
−0.942000 | + | 0.335614i | \(0.891056\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 53.9579 | + | 26.0921i | 2.04969 | + | 0.991158i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.08969 | + | 4.08969i | 0.155131 | + | 0.155131i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.23732 | − | 2.23732i | 0.0847444 | − | 0.0847444i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7110 | + | 20.8827i | 0.745537 | + | 0.789856i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39440 | + | 3.36638i | −0.0526658 | + | 0.127147i | −0.948023 | − | 0.318203i | \(-0.896921\pi\) |
0.895357 | + | 0.445350i | \(0.146921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.06845i | − | 0.0402973i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.1109 | − | 8.41972i | 0.832743 | − | 0.317105i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 52.6494 | + | 21.8081i | 1.98008 | + | 0.820177i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.10175 | − | 21.9736i | −0.341824 | − | 0.825235i | −0.997531 | − | 0.0702205i | \(-0.977630\pi\) |
0.655708 | − | 0.755015i | \(-0.272370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.6868 | − | 1.54191i | −1.00083 | − | 0.0578263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.0568 | + | 13.0568i | −0.488980 | + | 0.488980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.38796 | − | 5.76505i | −0.0893047 | − | 0.215601i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.3878 | − | 1.07920i | −1.39627 | − | 0.0403034i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5450i | 0.728907i | 0.931222 | + | 0.364453i | \(0.118744\pi\) | ||||
−0.931222 | + | 0.364453i | \(0.881256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 25.6126i | − | 0.953863i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.2938 | + | 0.730106i | 0.940686 | + | 0.0271529i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.27728 | + | 17.5689i | 0.270271 | + | 0.652493i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.8914 | + | 20.8914i | −0.774821 | + | 0.774821i | −0.978945 | − | 0.204124i | \(-0.934565\pi\) |
0.204124 | + | 0.978945i | \(0.434565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5963 | − | 4.65151i | −0.985048 | − | 0.172278i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.680281 | − | 1.64234i | −0.0251611 | − | 0.0607443i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.09957 | + | 3.76916i | 0.336100 | + | 0.139217i | 0.544350 | − | 0.838859i | \(-0.316777\pi\) |
−0.208249 | + | 0.978076i | \(0.566777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.97886 | + | 3.03831i | −0.294305 | + | 0.112070i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 73.0703i | − | 2.69158i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.03797 | + | 19.4054i | −0.295682 | + | 0.713839i | 0.704311 | + | 0.709892i | \(0.251256\pi\) |
−0.999992 | + | 0.00394665i | \(0.998744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.90256 | − | 4.13455i | −0.143364 | − | 0.151886i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.8827 | + | 14.8827i | −0.545995 | + | 0.545995i | −0.925280 | − | 0.379285i | \(-0.876170\pi\) |
0.379285 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8409 | + | 11.8409i | 0.433817 | + | 0.433817i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.4745 | + | 21.6610i | −0.383241 | + | 0.792533i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0569026 | − | 0.0235698i | −0.00207917 | − | 0.000861222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.9945 | −1.75135 | −0.875673 | − | 0.482905i | \(-0.839582\pi\) | ||||
−0.875673 | + | 0.482905i | \(0.839582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.59272 | − | 1.74889i | 0.167368 | − | 0.0637330i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.85523 | − | 4.47893i | 0.0675189 | − | 0.163005i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.61422 | − | 1.91127i | 0.167707 | − | 0.0694663i | −0.297251 | − | 0.954799i | \(-0.596070\pi\) |
0.464957 | + | 0.885333i | \(0.346070\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.2426 | − | 27.3004i | 0.444379 | − | 0.990943i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.4112 | + | 35.4112i | 1.28365 | + | 1.28365i | 0.938573 | + | 0.345081i | \(0.112149\pi\) |
0.345081 | + | 0.938573i | \(0.387851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0435 | − | 16.5865i | 1.44967 | − | 0.600473i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.24738 | − | 0.782322i | 0.0812541 | − | 0.0282849i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.22237 | −0.188569 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.1306 | 1.77169 | 0.885847 | − | 0.463978i | \(-0.153578\pi\) | ||||
0.885847 | + | 0.463978i | \(0.153578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.34485 | − | 0.0676840i | −0.0844476 | − | 0.00243758i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9331 | + | 20.2688i | −1.76000 | + | 0.729017i | −0.763467 | + | 0.645847i | \(0.776504\pi\) |
−0.996535 | + | 0.0831696i | \(0.973496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.4698 | − | 16.4698i | −0.591611 | − | 0.591611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.56212 | + | 0.700519i | 0.0560408 | + | 0.0251310i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4757 | + | 6.41026i | −0.554476 | + | 0.229672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.7531 | − | 62.1736i | 0.921520 | − | 2.22474i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.9605 | − | 12.4519i | −0.856277 | − | 0.444993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.2044 | 0.721126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.3943 | + | 18.3887i | 1.58249 | + | 0.655487i | 0.988805 | − | 0.149214i | \(-0.0476743\pi\) |
0.593681 | + | 0.804701i | \(0.297674\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.92462 | − | 6.27681i | −0.210922 | − | 0.223460i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.9072 | + | 24.9072i | 0.885597 | + | 0.885597i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.06364 | + | 1.06364i | −0.0377711 | + | 0.0377711i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.95253 | + | 5.61854i | −0.211115 | + | 0.199269i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5848 | + | 25.5539i | −0.374931 | + | 0.905164i | 0.617968 | + | 0.786203i | \(0.287956\pi\) |
−0.992899 | + | 0.118961i | \(0.962044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.08201i | 0.285921i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.62505 | + | 6.31492i | 0.198752 | + | 0.223127i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.2642 | + | 7.56530i | 0.644531 | + | 0.266974i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.31287 | + | 10.4122i | 0.152009 | + | 0.366981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.6375 | + | 28.1811i | −0.444863 | + | 0.992022i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4258 | + | 26.4258i | −0.929083 | + | 0.929083i | −0.997647 | − | 0.0685638i | \(-0.978158\pi\) |
0.0685638 | + | 0.997647i | \(0.478158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.2190 | − | 24.6709i | −0.358838 | − | 0.866311i | −0.995464 | − | 0.0951387i | \(-0.969671\pi\) |
0.636626 | − | 0.771173i | \(-0.280329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.424933 | − | 14.7214i | 0.0149030 | − | 0.516301i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 13.9838i | − | 0.489831i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.41115i | 0.329254i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.60358 | − | 2.99494i | 0.300633 | − | 0.104652i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.9273 | + | 38.4519i | 0.555866 | + | 1.34198i | 0.913013 | + | 0.407932i | \(0.133750\pi\) |
−0.357146 | + | 0.934048i | \(0.616250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.1818 | + | 27.1818i | −0.947499 | + | 0.947499i | −0.998689 | − | 0.0511904i | \(-0.983698\pi\) |
0.0511904 | + | 0.998689i | \(0.483698\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.4366 | + | 15.4428i | 1.19893 | + | 0.537648i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.6297 | − | 30.4907i | −0.439176 | − | 1.06027i | −0.976234 | − | 0.216720i | \(-0.930464\pi\) |
0.537058 | − | 0.843546i | \(-0.319536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6568 | + | 14.3553i | 1.20368 | + | 0.498581i | 0.892187 | − | 0.451667i | \(-0.149171\pi\) |
0.311494 | + | 0.950248i | \(0.399171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4786 | − | 35.3960i | −0.467568 | − | 1.22787i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.91645i | − | 0.101049i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.805870 | + | 1.94554i | −0.0278883 | + | 0.0673282i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.9498 | + | 2.85964i | 1.13891 | + | 0.0988438i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.13731 | − | 5.13731i | 0.177360 | − | 0.177360i | −0.612844 | − | 0.790204i | \(-0.709975\pi\) |
0.790204 | + | 0.612844i | \(0.209975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.41020 | + | 1.41020i | 0.0486277 | + | 0.0486277i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.4084 | − | 17.3755i | 0.634018 | − | 0.598443i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0303 | + | 5.39732i | 0.448255 | + | 0.185673i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 82.0555 | 2.81946 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.78660 | − | 15.1961i | −0.198596 | − | 0.521528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.327054 | − | 0.789578i | 0.0112113 | − | 0.0270664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7734 | + | 11.5041i | −0.950943 | + | 0.393893i | −0.803585 | − | 0.595190i | \(-0.797077\pi\) |
−0.147358 | + | 0.989083i | \(0.547077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.5772 | − | 0.726686i | −0.430130 | − | 0.0248521i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.9037 | + | 23.9037i | 0.816536 | + | 0.816536i | 0.985604 | − | 0.169069i | \(-0.0540760\pi\) |
−0.169069 | + | 0.985604i | \(0.554076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.4970 | + | 15.1176i | −1.24526 | + | 0.515805i | −0.905356 | − | 0.424654i | \(-0.860396\pi\) |
−0.339907 | + | 0.940459i | \(0.610396\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.774422 | − | 26.8291i | 0.0263922 | − | 0.914333i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.7809 | −1.66052 | −0.830260 | − | 0.557377i | \(-0.811808\pi\) | ||||
−0.830260 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0709307 | −0.00241172 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.826119 | − | 28.6201i | 0.0280565 | − | 0.971989i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.0187 | + | 20.3042i | −1.66284 | + | 0.688773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.85341 | − | 7.85341i | −0.266103 | − | 0.266103i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.9520 | − | 1.49946i | −0.878342 | − | 0.0507490i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.0796 | + | 12.8736i | −1.05068 | + | 0.435207i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.45430 | − | 20.4105i | 0.285481 | − | 0.689213i | −0.714464 | − | 0.699672i | \(-0.753329\pi\) |
0.999945 | + | 0.0104591i | \(0.00332930\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.59343 | − | 19.9410i | −0.256120 | − | 0.672592i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.8223 | 0.869976 | 0.434988 | − | 0.900436i | \(-0.356753\pi\) | ||||
0.434988 | + | 0.900436i | \(0.356753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3809 | − | 13.8268i | −1.12336 | − | 0.465310i | −0.257839 | − | 0.966188i | \(-0.583010\pi\) |
−0.865518 | + | 0.500878i | \(0.833010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.41534 | + | 7.94315i | −0.282879 | + | 0.267006i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.6997 | + | 34.6997i | 1.16510 | + | 1.16510i | 0.983343 | + | 0.181760i | \(0.0581796\pi\) |
0.181760 | + | 0.983343i | \(0.441820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88187 | − | 1.88187i | 0.0631158 | − | 0.0631158i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −51.5439 | + | 14.6695i | −1.72679 | + | 0.491447i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.3739 | − | 39.5302i | 0.547933 | − | 1.32283i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.55398i | 0.118796i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.61838 | − | 4.24999i | −0.0540360 | − | 0.141903i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.5593 | + | 12.6581i | 1.01921 | + | 0.422170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.07001 | − | 2.58324i | −0.0356473 | − | 0.0860602i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.7595 | − | 6.17033i | −0.457889 | − | 0.205336i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.4625 | − | 18.4625i | 0.613715 | − | 0.613715i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.42403 | + | 17.9232i | 0.246511 | + | 0.595130i | 0.997903 | − | 0.0647258i | \(-0.0206173\pi\) |
−0.751392 | + | 0.659856i | \(0.770617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −48.1224 | + | 16.7516i | −1.59612 | + | 0.555616i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.5930i | − | 1.24551i | −0.782416 | − | 0.622756i | \(-0.786013\pi\) | ||
0.782416 | − | 0.622756i | \(-0.213987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.7565i | 1.58051i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0961708 | + | 3.33174i | −0.00317931 | + | 0.110144i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.0535 | − | 31.5140i | −0.431066 | − | 1.04069i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.3220 | − | 28.3220i | 0.934258 | − | 0.934258i | −0.0637109 | − | 0.997968i | \(-0.520294\pi\) |
0.997968 | + | 0.0637109i | \(0.0202936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.67681 | + | 21.5788i | −0.318862 | + | 0.711046i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.91438 | − | 9.45014i | −0.128843 | − | 0.311055i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.995970 | + | 0.412544i | 0.0327473 | + | 0.0135644i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2326 | + | 17.1008i | 0.500304 | + | 0.561663i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 14.6297i | − | 0.479986i | −0.970775 | − | 0.239993i | \(-0.922855\pi\) | ||
0.970775 | − | 0.239993i | \(-0.0771452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.90865 | + | 14.2647i | −0.193648 | + | 0.467508i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.4922 | − | 31.6129i | 1.09648 | − | 1.03496i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.33983 | − | 3.33983i | 0.109224 | − | 0.109224i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.60824 | + | 5.60824i | 0.183213 | + | 0.183213i | 0.792754 | − | 0.609541i | \(-0.208646\pi\) |
−0.609541 | + | 0.792754i | \(0.708646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.24386 | + | 7.67448i | 0.236395 | + | 0.250447i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5273 | − | 4.36054i | −0.343180 | − | 0.142150i | 0.204435 | − | 0.978880i | \(-0.434464\pi\) |
−0.547615 | + | 0.836730i | \(0.684464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3987 | −0.436321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.30855 | − | 17.9120i | 0.302807 | − | 0.582676i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.3491 | − | 53.9555i | 0.726248 | − | 1.75332i | 0.0715370 | − | 0.997438i | \(-0.477210\pi\) |
0.654711 | − | 0.755879i | \(-0.272790\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.77609 | − | 1.14990i | 0.0901158 | − | 0.0373272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.24416 | − | 1.00637i | −0.0727718 | − | 0.0326338i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.8805 | − | 32.8805i | −1.06510 | − | 1.06510i | −0.997728 | − | 0.0673750i | \(-0.978538\pi\) |
−0.0673750 | − | 0.997728i | \(-0.521462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6644 | − | 10.2163i | 0.798122 | − | 0.330593i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −53.5741 | − | 1.54642i | −1.73180 | − | 0.0499885i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0435 | 0.453489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.51359 | −0.306890 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0520098 | − | 0.0181049i | 0.00167599 | − | 0.000583421i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.05330 | − | 3.33578i | 0.259245 | − | 0.107383i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.6204 | + | 14.6204i | 0.470160 | + | 0.470160i | 0.901966 | − | 0.431807i | \(-0.142124\pi\) |
−0.431807 | + | 0.901966i | \(0.642124\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.76089 | − | 3.92670i | 0.0565679 | − | 0.126144i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9825 | − | 16.5613i | 1.28310 | − | 0.531477i | 0.366178 | − | 0.930545i | \(-0.380666\pi\) |
0.916921 | + | 0.399068i | \(0.130666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.41357 | + | 15.4837i | −0.205610 | + | 0.496386i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.36091 | − | 2.04141i | 0.171687 | − | 0.0653775i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.1567 | −0.452912 | −0.226456 | − | 0.974021i | \(-0.572714\pi\) | ||||
−0.226456 | + | 0.974021i | \(0.572714\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5079 | + | 6.42359i | 0.495635 | + | 0.205299i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8713 | + | 34.8894i | −0.538659 | + | 1.11393i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5590 | − | 27.5590i | −0.878995 | − | 0.878995i | 0.114436 | − | 0.993431i | \(-0.463494\pi\) |
−0.993431 | + | 0.114436i | \(0.963494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.90311 | + | 1.90311i | −0.0606381 | + | 0.0606381i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.0595 | + | 49.8570i | 1.49792 | + | 1.58697i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.88077 | + | 6.95478i | −0.0916030 | + | 0.221149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.9042i | − | 0.473446i | −0.971577 | − | 0.236723i | \(-0.923927\pi\) | ||
0.971577 | − | 0.236723i | \(-0.0760734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.9447 | + | 8.35645i | −0.696395 | + | 0.265184i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3008 | + | 4.68093i | 0.358258 | + | 0.148395i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.66402 | + | 11.2599i | 0.147711 | + | 0.356606i | 0.980366 | − | 0.197186i | \(-0.0631804\pi\) |
−0.832655 | + | 0.553792i | \(0.813180\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.45960 | + | 0.461327i | −0.0461798 | + | 0.0145958i |
(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 | 768.2.o.b.95.7 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.95.4 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.95.8 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.47.7 | 56 | |||
8.5 | even | 2 | 96.2.o.a.35.9 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.95.11 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.35.6 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.47.4 | 56 | |||
32.5 | even | 8 | 384.2.o.a.335.4 | 56 | |||
32.11 | odd | 8 | inner | 768.2.o.b.671.4 | 56 | ||
32.21 | even | 8 | 768.2.o.a.671.11 | 56 | |||
32.27 | odd | 8 | 96.2.o.a.11.6 | ✓ | 56 | ||
96.5 | odd | 8 | 384.2.o.a.335.7 | 56 | |||
96.11 | even | 8 | inner | 768.2.o.b.671.7 | 56 | ||
96.53 | odd | 8 | 768.2.o.a.671.8 | 56 | |||
96.59 | even | 8 | 96.2.o.a.11.9 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.6 | ✓ | 56 | 32.27 | odd | 8 | ||
96.2.o.a.11.9 | yes | 56 | 96.59 | even | 8 | ||
96.2.o.a.35.6 | yes | 56 | 24.5 | odd | 2 | ||
96.2.o.a.35.9 | yes | 56 | 8.5 | even | 2 | ||
384.2.o.a.47.4 | 56 | 24.11 | even | 2 | |||
384.2.o.a.47.7 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.335.4 | 56 | 32.5 | even | 8 | |||
384.2.o.a.335.7 | 56 | 96.5 | odd | 8 | |||
768.2.o.a.95.8 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.95.11 | 56 | 12.11 | even | 2 | |||
768.2.o.a.671.8 | 56 | 96.53 | odd | 8 | |||
768.2.o.a.671.11 | 56 | 32.21 | even | 8 | |||
768.2.o.b.95.4 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.95.7 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.671.4 | 56 | 32.11 | odd | 8 | inner | ||
768.2.o.b.671.7 | 56 | 96.11 | even | 8 | inner |