Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,2,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(2.25236 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.73 |
Dual form | 76.2.i.a.25.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.456991 | − | 0.166331i | 0.263844 | − | 0.0960313i | −0.206711 | − | 0.978402i | \(-0.566276\pi\) |
0.470555 | + | 0.882371i | \(0.344054\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.485063 | − | 2.75093i | 0.216927 | − | 1.23025i | −0.660605 | − | 0.750734i | \(-0.729700\pi\) |
0.877531 | − | 0.479519i | \(-0.159189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.68285 | + | 2.91479i | 0.636058 | + | 1.10169i | 0.986290 | + | 0.165022i | \(0.0527696\pi\) |
−0.350231 | + | 0.936663i | \(0.613897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.11696 | + | 1.77634i | −0.705653 | + | 0.592113i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.258097 | − | 0.447037i | 0.0778191 | − | 0.134787i | −0.824490 | − | 0.565877i | \(-0.808538\pi\) |
0.902309 | + | 0.431090i | \(0.141871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.37365 | − | 1.59188i | −1.21303 | − | 0.441508i | −0.345278 | − | 0.938500i | \(-0.612215\pi\) |
−0.867755 | + | 0.496993i | \(0.834438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.235896 | − | 1.33783i | −0.0609080 | − | 0.345426i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.735881 | − | 0.617477i | −0.178477 | − | 0.149760i | 0.549173 | − | 0.835709i | \(-0.314943\pi\) |
−0.727650 | + | 0.685949i | \(0.759387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12016 | + | 3.04379i | −0.715813 | + | 0.698292i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.25387 | + | 1.05212i | 0.273616 | + | 0.229591i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.629673 | + | 3.57105i | 0.131296 | + | 0.744616i | 0.977368 | + | 0.211547i | \(0.0678501\pi\) |
−0.846072 | + | 0.533069i | \(0.821039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.63386 | − | 0.958648i | −0.526773 | − | 0.191730i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.40145 | + | 2.42738i | −0.269709 | + | 0.467150i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.21450 | − | 5.21459i | 1.15400 | − | 0.968325i | 0.154199 | − | 0.988040i | \(-0.450720\pi\) |
0.999806 | + | 0.0197150i | \(0.00627588\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.38969 | − | 4.13907i | −0.429202 | − | 0.743399i | 0.567601 | − | 0.823304i | \(-0.307872\pi\) |
−0.996803 | + | 0.0799047i | \(0.974538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0435918 | − | 0.247221i | 0.00758835 | − | 0.0430357i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.83466 | − | 3.21555i | 1.49333 | − | 0.543528i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.13084 | 1.50110 | 0.750550 | − | 0.660813i | \(-0.229789\pi\) | ||||
0.750550 | + | 0.660813i | \(0.229789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.26350 | −0.362450 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.54978 | + | 2.38392i | −1.02290 | + | 0.372306i | −0.798375 | − | 0.602161i | \(-0.794306\pi\) |
−0.224529 | + | 0.974467i | \(0.572084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.817138 | + | 4.63422i | −0.124612 | + | 0.706712i | 0.856925 | + | 0.515441i | \(0.172372\pi\) |
−0.981537 | + | 0.191271i | \(0.938739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.85973 | + | 6.68524i | 0.575374 | + | 0.996577i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4172 | − | 8.74111i | 1.51951 | − | 1.27502i | 0.677562 | − | 0.735466i | \(-0.263037\pi\) |
0.841950 | − | 0.539555i | \(-0.181408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16398 | + | 3.74813i | −0.309141 | + | 0.535447i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.438996 | − | 0.159782i | −0.0614718 | − | 0.0223739i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.20127 | − | 6.81274i | −0.165007 | − | 0.935802i | −0.949057 | − | 0.315104i | \(-0.897960\pi\) |
0.784050 | − | 0.620698i | \(-0.213151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.10457 | − | 0.926847i | −0.148941 | − | 0.124976i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.919606 | + | 1.90996i | −0.121805 | + | 0.252981i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.9602 | − | 9.19667i | −1.42689 | − | 1.19730i | −0.947522 | − | 0.319691i | \(-0.896421\pi\) |
−0.479370 | − | 0.877613i | \(-0.659135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05803 | + | 6.00040i | 0.135467 | + | 0.768272i | 0.974533 | + | 0.224243i | \(0.0719908\pi\) |
−0.839066 | + | 0.544029i | \(0.816898\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.74018 | − | 3.18116i | −1.10116 | − | 0.400789i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.50065 | + | 11.2594i | −0.806306 | + | 1.39656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.38541 | − | 2.84069i | 0.413593 | − | 0.347046i | −0.412126 | − | 0.911127i | \(-0.635214\pi\) |
0.825720 | + | 0.564081i | \(0.190769\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.881732 | + | 1.52720i | 0.106148 | + | 0.183854i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.66206 | + | 9.42601i | −0.197250 | + | 1.11866i | 0.711928 | + | 0.702253i | \(0.247822\pi\) |
−0.909178 | + | 0.416408i | \(0.863289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.65102 | − | 2.05680i | 0.661401 | − | 0.240730i | 0.0105601 | − | 0.999944i | \(-0.496639\pi\) |
0.650841 | + | 0.759214i | \(0.274416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.36310 | −0.157398 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.73735 | 0.197990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.85305 | + | 3.58622i | −1.10856 | + | 0.403481i | −0.830463 | − | 0.557073i | \(-0.811924\pi\) |
−0.278092 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.20293 | − | 6.82213i | 0.133658 | − | 0.758015i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.39066 | + | 4.14075i | 0.262409 | + | 0.454506i | 0.966882 | − | 0.255225i | \(-0.0821497\pi\) |
−0.704472 | + | 0.709731i | \(0.748816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.05558 | + | 1.72484i | −0.222959 | + | 0.187085i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.97262 | − | 3.41669i | 0.211487 | − | 0.366307i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.30245 | − | 3.02185i | −0.880058 | − | 0.320315i | −0.137825 | − | 0.990457i | \(-0.544011\pi\) |
−0.742233 | + | 0.670142i | \(0.766233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.72022 | − | 15.4272i | −0.285157 | − | 1.61721i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.78053 | − | 1.49404i | −0.184632 | − | 0.154925i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.85977 | + | 10.0598i | 0.703797 | + | 1.03211i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.46492 | + | 7.10291i | 0.859482 | + | 0.721191i | 0.961856 | − | 0.273555i | \(-0.0881994\pi\) |
−0.102374 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.247709 | + | 1.40483i | 0.0248956 | + | 0.141190i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.382988 | − | 0.139396i | −0.0381087 | − | 0.0138704i | 0.322895 | − | 0.946435i | \(-0.395344\pi\) |
−0.361004 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.40104 | − | 4.15872i | 0.236581 | − | 0.409770i | −0.723150 | − | 0.690691i | \(-0.757306\pi\) |
0.959731 | + | 0.280921i | \(0.0906398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.50251 | − | 2.93896i | 0.341810 | − | 0.286813i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.53236 | + | 7.85028i | 0.438160 | + | 0.758916i | 0.997548 | − | 0.0699906i | \(-0.0222969\pi\) |
−0.559387 | + | 0.828906i | \(0.688964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35374 | − | 7.67741i | 0.129664 | − | 0.735363i | −0.848763 | − | 0.528773i | \(-0.822652\pi\) |
0.978428 | − | 0.206590i | \(-0.0662366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.17271 | − | 1.51874i | 0.396056 | − | 0.144153i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.07308 | −0.289091 | −0.144546 | − | 0.989498i | \(-0.546172\pi\) | ||||
−0.144546 | + | 0.989498i | \(0.546172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1291 | 0.944547 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0866 | − | 4.39915i | 1.11740 | − | 0.406701i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.561435 | − | 3.18406i | 0.0514667 | − | 0.291882i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.36677 | + | 9.29552i | 0.487888 | + | 0.845047i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.59667 | + | 2.17886i | −0.234134 | + | 0.196461i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.06865 | − | 5.31506i | 0.274469 | − | 0.475394i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.77012 | − | 3.55603i | −0.866958 | − | 0.315547i | −0.130023 | − | 0.991511i | \(-0.541505\pi\) |
−0.736935 | + | 0.675964i | \(0.763727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.397390 | + | 2.25371i | 0.0349882 | + | 0.198428i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.54356 | + | 2.13430i | 0.222232 | + | 0.186475i | 0.747106 | − | 0.664705i | \(-0.231443\pi\) |
−0.524874 | + | 0.851180i | \(0.675887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.1227 | − | 3.97234i | −1.22460 | − | 0.344446i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.99777 | + | 5.03272i | 0.516206 | + | 0.433148i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.738982 | + | 4.19097i | 0.0631355 | + | 0.358059i | 0.999966 | + | 0.00827481i | \(0.00263398\pi\) |
−0.936830 | + | 0.349784i | \(0.886255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.85603 | + | 1.76745i | 0.411883 | + | 0.149913i | 0.539647 | − | 0.841892i | \(-0.318558\pi\) |
−0.127764 | + | 0.991805i | \(0.540780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.30667 | − | 5.72732i | 0.278472 | − | 0.482327i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.84045 | + | 1.54432i | −0.153906 | + | 0.129143i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.3305 | − | 19.6251i | −0.940950 | − | 1.62977i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.365491 | + | 2.07280i | −0.0301451 | + | 0.170962i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.5930 | + | 6.40331i | −1.44127 | + | 0.524580i | −0.940139 | − | 0.340791i | \(-0.889305\pi\) |
−0.501132 | + | 0.865371i | \(0.667083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.08388 | 0.739235 | 0.369618 | − | 0.929184i | \(-0.379489\pi\) | ||||
0.369618 | + | 0.929184i | \(0.379489\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.65468 | 0.214618 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5454 | + | 4.56617i | −1.00767 | + | 0.366764i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.531125 | + | 3.01216i | −0.0423884 | + | 0.240397i | −0.998639 | − | 0.0521517i | \(-0.983392\pi\) |
0.956251 | + | 0.292548i | \(0.0945032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.68214 | − | 2.91355i | −0.133402 | − | 0.231060i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.34920 | + | 7.84491i | −0.736820 | + | 0.618266i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.64442 | + | 13.2405i | −0.598757 | + | 1.03708i | 0.394248 | + | 0.919004i | \(0.371005\pi\) |
−0.993005 | + | 0.118074i | \(0.962328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.658943 | − | 0.239836i | −0.0512987 | − | 0.0186712i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57778 | + | 14.6193i | 0.199475 | + | 1.13128i | 0.905901 | + | 0.423491i | \(0.139195\pi\) |
−0.706426 | + | 0.707787i | \(0.749694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.63618 | + | 5.56842i | 0.510475 | + | 0.428340i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.19844 | − | 11.9860i | 0.0916473 | − | 0.916594i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.06288 | − | 3.40916i | −0.308895 | − | 0.259194i | 0.475140 | − | 0.879910i | \(-0.342397\pi\) |
−0.784035 | + | 0.620716i | \(0.786842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.63815 | − | 9.29041i | −0.123833 | − | 0.702289i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.53839 | − | 2.37978i | −0.491455 | − | 0.178875i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.46494 | + | 9.46556i | −0.408469 | + | 0.707489i | −0.994718 | − | 0.102641i | \(-0.967271\pi\) |
0.586249 | + | 0.810131i | \(0.300604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.57271 | + | 2.15876i | −0.191228 | + | 0.160460i | −0.733375 | − | 0.679824i | \(-0.762056\pi\) |
0.542147 | + | 0.840284i | \(0.317612\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.48156 | + | 2.56614i | 0.109520 | + | 0.189695i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.42903 | − | 25.1183i | 0.325629 | − | 1.84673i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.465963 | + | 0.169597i | −0.0340746 | + | 0.0124021i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.43373 | −0.686203 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6763 | −1.27902 | −0.639508 | − | 0.768785i | \(-0.720862\pi\) | ||||
−0.639508 | + | 0.768785i | \(0.720862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.3296 | − | 8.49127i | 1.67930 | − | 0.611215i | 0.686086 | − | 0.727521i | \(-0.259328\pi\) |
0.993213 | + | 0.116306i | \(0.0371053\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.09794 | + | 6.22672i | −0.0786251 | + | 0.445905i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.599101 | − | 1.03767i | −0.0426842 | − | 0.0739311i | 0.843894 | − | 0.536510i | \(-0.180258\pi\) |
−0.886578 | + | 0.462579i | \(0.846924\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0334 | − | 8.41899i | 0.711246 | − | 0.596806i | −0.213703 | − | 0.976899i | \(-0.568552\pi\) |
0.924948 | + | 0.380093i | \(0.124108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.07460 | − | 1.86127i | 0.0757968 | − | 0.131284i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.6575 | + | 9.33857i | 1.80080 | + | 0.655439i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.38095 | + | 19.1743i | 0.236136 | + | 1.33919i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.67639 | − | 6.44126i | −0.533546 | − | 0.447698i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.555382 | + | 2.18041i | 0.0384166 | + | 0.150822i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.362133 | + | 0.303866i | 0.0249303 | + | 0.0209190i | 0.655168 | − | 0.755484i | \(-0.272598\pi\) |
−0.630237 | + | 0.776403i | \(0.717042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.808292 | + | 4.58405i | 0.0553833 | + | 0.314094i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.3520 | + | 4.49578i | 0.842402 | + | 0.306609i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.04301 | − | 13.9309i | 0.545995 | − | 0.945691i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.24035 | − | 1.87988i | 0.151389 | − | 0.127030i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23554 | + | 3.87206i | 0.150378 | + | 0.260463i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.40576 | + | 19.3150i | −0.228066 | + | 1.29343i | 0.628669 | + | 0.777673i | \(0.283600\pi\) |
−0.856736 | + | 0.515756i | \(0.827511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.27867 | − | 2.64922i | 0.485244 | − | 0.176615i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.929069 | 0.0616645 | 0.0308322 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308322 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.58741 | −0.501390 | −0.250695 | − | 0.968066i | \(-0.580659\pi\) | ||||
−0.250695 | + | 0.968066i | \(0.580659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.793955 | − | 0.288976i | 0.0522384 | − | 0.0190132i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.646394 | − | 3.66588i | 0.0423467 | − | 0.240160i | −0.956286 | − | 0.292433i | \(-0.905535\pi\) |
0.998633 | + | 0.0522725i | \(0.0166464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.9931 | − | 32.8971i | −1.23898 | − | 2.14597i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.90626 | + | 3.27774i | −0.253739 | + | 0.212912i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.65144 | − | 16.7168i | 0.624300 | − | 1.08132i | −0.364376 | − | 0.931252i | \(-0.618718\pi\) |
0.988676 | − | 0.150067i | \(-0.0479490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8080 | + | 4.66174i | 0.825037 | + | 0.300289i | 0.719821 | − | 0.694160i | \(-0.244224\pi\) |
0.105217 | + | 0.994449i | \(0.466446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.04516 | − | 11.5987i | −0.131197 | − | 0.744056i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.26118 | + | 7.77105i | 0.591675 | + | 0.496474i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.4918 | − | 8.34555i | 1.17661 | − | 0.531015i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.78125 | + | 1.49464i | 0.112882 | + | 0.0947191i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.99329 | − | 16.9758i | −0.188935 | − | 1.07150i | −0.920794 | − | 0.390048i | \(-0.872458\pi\) |
0.731859 | − | 0.681456i | \(-0.238653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.75891 | + | 0.640190i | 0.110582 | + | 0.0402484i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.652489 | + | 1.13014i | −0.0408604 | + | 0.0707724i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4154 | + | 8.73957i | −0.649695 | + | 0.545159i | −0.906979 | − | 0.421177i | \(-0.861617\pi\) |
0.257283 | + | 0.966336i | \(0.417173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3659 | + | 26.6144i | 0.954788 | + | 1.65374i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.89297 | + | 22.0781i | −0.240969 | + | 1.36660i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.53896 | + | 2.74396i | −0.464872 | + | 0.169200i | −0.563828 | − | 0.825892i | \(-0.690672\pi\) |
0.0989559 | + | 0.995092i | \(0.468450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.3241 | −1.18707 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.29677 | −0.262958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.158312 | − | 0.0576210i | 0.00965248 | − | 0.00351322i | −0.337189 | − | 0.941437i | \(-0.609476\pi\) |
0.346842 | + | 0.937924i | \(0.387254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.06021 | + | 11.6841i | −0.125149 | + | 0.709756i | 0.856070 | + | 0.516860i | \(0.172899\pi\) |
−0.981219 | + | 0.192896i | \(0.938212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.80913 | − | 6.59761i | −0.230539 | − | 0.399306i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.10834 | + | 0.930010i | −0.0668356 | + | 0.0560817i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.34766 | + | 2.33422i | −0.0809733 | + | 0.140250i | −0.903668 | − | 0.428233i | \(-0.859136\pi\) |
0.822695 | + | 0.568483i | \(0.192470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.4113 | + | 4.51734i | 0.743044 | + | 0.270446i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.33967 | + | 18.9402i | 0.199228 | + | 1.12988i | 0.906267 | + | 0.422705i | \(0.138919\pi\) |
−0.707039 | + | 0.707174i | \(0.749970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2293 | − | 17.8135i | −1.26195 | − | 1.05890i | −0.995471 | − | 0.0950608i | \(-0.969695\pi\) |
−0.266478 | − | 0.963841i | \(-0.585860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.80810 | + | 3.45622i | 0.284807 | + | 0.204729i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.9709 | − | 15.0794i | −1.06079 | − | 0.890109i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.79178 | − | 15.8330i | −0.164222 | − | 0.931350i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.04983 | + | 1.83799i | 0.296026 | + | 0.107745i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.84253 | − | 15.3157i | 0.516586 | − | 0.894754i | −0.483228 | − | 0.875494i | \(-0.660536\pi\) |
0.999815 | − | 0.0192592i | \(-0.00613078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.6158 | + | 25.6897i | −1.78252 | + | 1.49571i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.723419 | + | 1.25300i | 0.0419770 | + | 0.0727064i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.93071 | − | 16.6209i | 0.169488 | − | 0.961211i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8829 | + | 5.41692i | −0.857835 | + | 0.312226i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.198208 | −0.0113868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.0199 | 0.974555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.96657 | + | 3.62753i | −0.568822 | + | 0.207034i | −0.610389 | − | 0.792101i | \(-0.708987\pi\) |
0.0415675 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.405528 | − | 2.29986i | 0.0230697 | − | 0.130835i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1081 | − | 22.7039i | −0.743292 | − | 1.28742i | −0.950989 | − | 0.309226i | \(-0.899930\pi\) |
0.207697 | − | 0.978193i | \(-0.433403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.73987 | + | 5.65542i | −0.380960 | + | 0.319663i | −0.813079 | − | 0.582153i | \(-0.802210\pi\) |
0.432119 | + | 0.901817i | \(0.357766\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.9907 | + | 22.5005i | −0.731943 | + | 1.26776i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.5280 | − | 5.65174i | −0.872140 | − | 0.317433i | −0.133107 | − | 0.991102i | \(-0.542495\pi\) |
−0.739034 | + | 0.673669i | \(0.764718\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.727169 | − | 4.12398i | −0.0407136 | − | 0.230898i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.37700 | + | 2.83364i | 0.188486 | + | 0.158158i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.17553 | − | 0.313238i | 0.232333 | − | 0.0174290i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.99355 | + | 8.38559i | 0.554343 | + | 0.465149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.658348 | − | 3.73368i | −0.0364067 | − | 0.206473i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.0091 | + | 15.6540i | 2.37117 | + | 0.863036i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.22922 | − | 5.59317i | 0.177494 | − | 0.307429i | −0.763528 | − | 0.645775i | \(-0.776534\pi\) |
0.941022 | + | 0.338347i | \(0.109868\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.3296 | + | 16.2195i | −1.05926 | + | 0.888821i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.17241 | − | 10.6909i | −0.337235 | − | 0.584108i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.92728 | + | 10.9302i | −0.104986 | + | 0.595404i | 0.886240 | + | 0.463226i | \(0.153308\pi\) |
−0.991226 | + | 0.132178i | \(0.957803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.40437 | + | 0.511149i | −0.0762750 | + | 0.0277618i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.46709 | −0.133600 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.99327 | 0.485591 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.62893 | − | 1.68479i | 0.249213 | − | 0.0907061i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.526344 | − | 2.98505i | 0.0282556 | − | 0.160246i | −0.967415 | − | 0.253195i | \(-0.918518\pi\) |
0.995671 | + | 0.0929497i | \(0.0296296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.04290 | + | 3.53842i | 0.109354 | + | 0.189407i | 0.915509 | − | 0.402298i | \(-0.131788\pi\) |
−0.806155 | + | 0.591705i | \(0.798455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.99355 | − | 8.38559i | 0.533416 | − | 0.447590i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.04626 | − | 13.9365i | 0.428259 | − | 0.741767i | −0.568459 | − | 0.822711i | \(-0.692460\pi\) |
0.996719 | + | 0.0809447i | \(0.0257937\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.1241 | + | 9.14442i | 1.33345 | + | 0.485335i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.273037 | − | 1.54847i | −0.0144506 | − | 0.0819537i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.4035 | + | 18.7988i | 1.18241 | + | 0.992160i | 0.999960 | + | 0.00894547i | \(0.00284747\pi\) |
0.182451 | + | 0.983215i | \(0.441597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.470738 | − | 18.9942i | 0.0247757 | − | 0.999693i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.99870 | + | 3.35531i | 0.209877 | + | 0.176108i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.91702 | − | 16.5432i | −0.152684 | − | 0.865912i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.57969 | − | 2.75878i | −0.395657 | − | 0.144007i | 0.136527 | − | 0.990636i | \(-0.456406\pi\) |
−0.532183 | + | 0.846629i | \(0.678628\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.63095 | − | 16.6813i | 0.501367 | − | 0.868393i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.8361 | − | 14.9663i | 0.926006 | − | 0.777011i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0909149 | + | 0.157469i | 0.00470740 | + | 0.00815345i | 0.868370 | − | 0.495918i | \(-0.165168\pi\) |
−0.863662 | + | 0.504071i | \(0.831835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.518286 | − | 2.93935i | 0.0267642 | − | 0.151787i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −35.4811 | + | 12.9141i | −1.82737 | + | 0.665108i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.82977 | 0.145355 | 0.0726777 | − | 0.997355i | \(-0.476846\pi\) | ||||
0.0726777 | + | 0.997355i | \(0.476846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.05633 | −0.259044 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.5927 | − | 8.95103i | 1.25663 | − | 0.457376i | 0.373994 | − | 0.927431i | \(-0.377988\pi\) |
0.882637 | + | 0.470055i | \(0.155766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.842727 | − | 4.77934i | 0.0429493 | − | 0.243578i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.50210 | − | 11.2620i | −0.330520 | − | 0.572478i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.7179 | + | 11.5107i | −0.695528 | + | 0.583617i | −0.920497 | − | 0.390749i | \(-0.872216\pi\) |
0.224970 | + | 0.974366i | \(0.427772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.74168 | − | 3.01668i | 0.0880805 | − | 0.152560i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.51739 | + | 0.552283i | 0.0765420 | + | 0.0278590i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.08608 | + | 28.8446i | 0.255909 | + | 1.45133i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05186 | + | 1.72171i | 0.102980 | + | 0.0864103i | 0.692824 | − | 0.721107i | \(-0.256366\pi\) |
−0.589844 | + | 0.807517i | \(0.700811\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.11469 | + | 0.533727i | −0.356180 | + | 0.0267198i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8632 | + | 20.0236i | 1.19167 | + | 0.999929i | 0.999829 | + | 0.0185028i | \(0.00588995\pi\) |
0.191840 | + | 0.981426i | \(0.438554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.86279 | + | 21.9070i | 0.192419 | + | 1.09126i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.1837 | − | 6.61833i | −0.903556 | − | 0.328867i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.35664 | − | 4.08182i | 0.116814 | − | 0.202328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.46492 | − | 7.10291i | 0.418563 | − | 0.351216i | −0.409053 | − | 0.912511i | \(-0.634141\pi\) |
0.827616 | + | 0.561294i | \(0.189696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.03480 | + | 1.79232i | 0.0510428 | + | 0.0884087i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.36198 | − | 47.4232i | 0.411466 | − | 2.33354i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5505 | − | 4.56802i | 0.616081 | − | 0.224235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.51314 | 0.123069 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.02242 | −0.391921 | −0.195960 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195960 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7095 | − | 6.44572i | 0.863107 | − | 0.314145i | 0.127734 | − | 0.991808i | \(-0.459230\pi\) |
0.735372 | + | 0.677663i | \(0.237007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.52571 | + | 37.0091i | −0.317291 | + | 1.79945i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.34627 | + | 2.33180i | 0.0653035 | + | 0.113109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.7094 | + | 13.1817i | −0.760229 | + | 0.637908i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.584201 | + | 1.01187i | −0.0282055 | + | 0.0488534i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3859 | − | 5.23604i | −0.692945 | − | 0.252211i | −0.0285491 | − | 0.999592i | \(-0.509089\pi\) |
−0.664395 | + | 0.747381i | \(0.731311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.647150 | + | 3.67017i | 0.0311000 | + | 0.176377i | 0.996401 | − | 0.0847620i | \(-0.0270130\pi\) |
−0.965301 | + | 0.261139i | \(0.915902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.44221 | − | 7.08386i | −0.404773 | − | 0.339645i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.8342 | − | 9.22565i | −0.613943 | − | 0.441322i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.52228 | − | 5.47284i | −0.311292 | − | 0.261205i | 0.473734 | − | 0.880668i | \(-0.342906\pi\) |
−0.785026 | + | 0.619463i | \(0.787350\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.07689 | − | 11.7786i | −0.0988994 | − | 0.560886i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2321 | + | 3.72417i | 0.486141 | + | 0.176941i | 0.573450 | − | 0.819241i | \(-0.305605\pi\) |
−0.0873095 | + | 0.996181i | \(0.527827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.3401 | + | 21.3737i | −0.584977 | + | 1.01321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.97475 | + | 5.85251i | −0.329894 | + | 0.276814i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.42967 | − | 5.94036i | −0.161856 | − | 0.280343i | 0.773678 | − | 0.633579i | \(-0.218415\pi\) |
−0.935534 | + | 0.353236i | \(0.885081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.624774 | + | 3.54327i | −0.0294195 | + | 0.166846i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.15125 | − | 1.51093i | 0.195043 | − | 0.0709897i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −43.7585 | −2.05143 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.5371 | −1.52202 | −0.761010 | − | 0.648740i | \(-0.775296\pi\) | ||||
−0.761010 | + | 0.648740i | \(0.775296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.53015 | − | 0.920900i | 0.118097 | − | 0.0429839i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.42346 | − | 19.4154i | 0.159446 | − | 0.904265i | −0.795161 | − | 0.606398i | \(-0.792614\pi\) |
0.954608 | − | 0.297867i | \(-0.0962751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5884 | + | 18.3396i | 0.492084 | + | 0.852314i | 0.999958 | − | 0.00911693i | \(-0.00290205\pi\) |
−0.507875 | + | 0.861431i | \(0.669569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.97366 | + | 4.17340i | −0.230648 | + | 0.193537i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.61175 | − | 9.71984i | 0.259681 | − | 0.449781i | −0.706475 | − | 0.707738i | \(-0.749716\pi\) |
0.966156 | + | 0.257957i | \(0.0830492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.9772 | + | 5.08727i | 0.645405 | + | 0.234908i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.258296 | + | 1.46487i | 0.0119017 | + | 0.0674977i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86076 | + | 1.56137i | 0.0855580 | + | 0.0717917i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.1360 | − | 5.02579i | 0.510954 | − | 0.230599i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.6448 | + | 12.2884i | 0.670539 | + | 0.562649i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.86409 | + | 21.9143i | 0.176555 | + | 1.00129i | 0.936334 | + | 0.351110i | \(0.114196\pi\) |
−0.759779 | + | 0.650181i | \(0.774693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.9351 | − | 14.5352i | −1.82088 | − | 0.662748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.96765 | + | 5.14012i | −0.135033 | + | 0.233883i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.6456 | − | 19.8410i | 1.07369 | − | 0.900935i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.74337 | − | 4.75166i | −0.124314 | − | 0.215318i | 0.797151 | − | 0.603781i | \(-0.206340\pi\) |
−0.921465 | + | 0.388462i | \(0.873006\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.29112 | + | 7.32230i | −0.0583865 | + | 0.331126i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4961 | + | 9.27982i | −1.15062 | + | 0.418792i | −0.845739 | − | 0.533597i | \(-0.820840\pi\) |
−0.304884 | + | 0.952390i | \(0.598618\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.79302 | −0.350980 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.98473 | 0.179100 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.2718 | + | 11.0180i | −1.35788 | + | 0.494226i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.79671 | − | 15.8609i | 0.125198 | − | 0.710032i | −0.855992 | − | 0.516988i | \(-0.827053\pi\) |
0.981190 | − | 0.193044i | \(-0.0618359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.60967 | + | 6.25214i | 0.161268 | + | 0.279325i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.2137 | − | 14.4440i | 0.767523 | − | 0.644028i | −0.172550 | − | 0.985001i | \(-0.555201\pi\) |
0.940073 | + | 0.340973i | \(0.110756\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.569243 | + | 0.985957i | −0.0253310 | + | 0.0438745i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.95887 | + | 1.44091i | 0.175820 | + | 0.0639932i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.46194 | + | 19.6336i | 0.153448 | + | 0.870246i | 0.960191 | + | 0.279344i | \(0.0901169\pi\) |
−0.806743 | + | 0.590902i | \(0.798772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5050 | + | 13.0102i | 0.685899 | + | 0.575538i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.01569 | − | 11.8395i | −0.133146 | − | 0.522728i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.2757 | − | 8.62232i | −0.452801 | − | 0.379945i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.21894 | − | 6.91294i | −0.0536088 | − | 0.304031i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.42375 | − | 0.882173i | −0.106391 | − | 0.0387231i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.39608 | + | 14.5424i | −0.367839 | + | 0.637116i | −0.989227 | − | 0.146387i | \(-0.953236\pi\) |
0.621388 | + | 0.783503i | \(0.286569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8256 | + | 9.92282i | −0.517096 | + | 0.433895i | −0.863618 | − | 0.504147i | \(-0.831807\pi\) |
0.346522 | + | 0.938042i | \(0.387363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.29390 | − | 3.97316i | −0.100114 | − | 0.173403i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.797253 | + | 4.52144i | −0.0347289 | + | 0.196957i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.25701 | − | 3.36928i | 0.402479 | − | 0.146490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.5386 | 1.71583 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.4414 | 1.40519 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.7941 | − | 8.66033i | 1.02871 | − | 0.374419i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.923013 | + | 5.23467i | −0.0398309 | + | 0.225892i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.11703 | + | 1.93476i | 0.0481141 | + | 0.0833360i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5437 | − | 8.84722i | 0.453309 | − | 0.380372i | −0.387353 | − | 0.921932i | \(-0.626610\pi\) |
0.840662 | + | 0.541560i | \(0.182166\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.816637 | + | 1.41446i | −0.0350453 | + | 0.0607002i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.4634 | − | 7.44806i | −0.876555 | − | 0.319040i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.60558 | − | 37.4621i | −0.282434 | − | 1.60176i | −0.714310 | − | 0.699830i | \(-0.753259\pi\) |
0.431875 | − | 0.901933i | \(-0.357852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.8985 | − | 10.8232i | −0.550497 | − | 0.461921i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.51813 | + | 35.1859i | −0.149877 | + | 1.49897i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.0343 | − | 22.6845i | −1.14962 | − | 0.964642i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.15393 | − | 12.2155i | −0.0914290 | − | 0.518520i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.8744 | + | 13.0572i | 1.52005 | + | 0.553251i | 0.961160 | − | 0.275993i | \(-0.0890068\pi\) |
0.558886 | + | 0.829245i | \(0.311229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.9510 | − | 18.9677i | 0.463178 | − | 0.802247i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.184732 | + | 0.155008i | −0.00779938 | + | 0.00654446i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.24788 | + | 2.16139i | 0.0525919 | + | 0.0910919i | 0.891123 | − | 0.453762i | \(-0.149918\pi\) |
−0.838531 | + | 0.544854i | \(0.816585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.49064 | + | 8.45384i | −0.0627117 | + | 0.355656i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.9094 | − | 7.97437i | 0.920108 | − | 0.334892i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.7113 | 1.53902 | 0.769509 | − | 0.638636i | \(-0.220501\pi\) | ||||
0.769509 | + | 0.638636i | \(0.220501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9010 | 0.749133 | 0.374567 | − | 0.927200i | \(-0.377792\pi\) | ||||
0.374567 | + | 0.927200i | \(0.377792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.07793 | + | 2.94012i | −0.337460 | + | 0.122825i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.76491 | − | 10.0093i | 0.0736018 | − | 0.417417i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.61207 | + | 11.4524i | 0.275264 | + | 0.476771i | 0.970202 | − | 0.242299i | \(-0.0779014\pi\) |
−0.694938 | + | 0.719070i | \(0.744568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.24904 | − | 7.76087i | 0.384377 | − | 0.322531i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.04626 | + | 13.9365i | −0.333815 | + | 0.578185i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.35559 | − | 1.22133i | −0.138974 | − | 0.0505825i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.23900 | − | 35.3831i | −0.257951 | − | 1.46291i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.65952 | + | 1.39250i | 0.0684957 | + | 0.0574747i | 0.676393 | − | 0.736541i | \(-0.263542\pi\) |
−0.607897 | + | 0.794016i | \(0.707987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0547 | + | 5.64083i | 0.826338 | + | 0.232426i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.446381 | − | 0.374558i | −0.0183617 | − | 0.0154073i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.84333 | + | 44.4818i | 0.322087 | + | 1.82665i | 0.529400 | + | 0.848372i | \(0.322417\pi\) |
−0.207313 | + | 0.978275i | \(0.566472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.48679 | − | 3.08894i | −0.347924 | − | 0.126634i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.18481 | − | 5.51626i | 0.130346 | − | 0.225766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.79340 | + | 6.53944i | −0.318430 | + | 0.267194i | −0.787966 | − | 0.615719i | \(-0.788866\pi\) |
0.469536 | + | 0.882913i | \(0.344421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7570 | + | 29.0241i | 0.683534 | + | 1.18392i | 0.973895 | + | 0.226999i | \(0.0728914\pi\) |
−0.290361 | + | 0.956917i | \(0.593775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.12073 | + | 12.0273i | −0.0863629 | + | 0.489788i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.1745 | − | 10.2547i | 1.14546 | − | 0.416913i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.0948 | −0.693856 | −0.346928 | − | 0.937892i | \(-0.612775\pi\) | ||||
−0.346928 | + | 0.937892i | \(0.612775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.2785 | 0.538074 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −59.4762 | + | 21.6476i | −2.40615 | + | 0.875767i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.92635 | + | 10.9248i | −0.0778043 | + | 0.441250i | 0.920874 | + | 0.389860i | \(0.127476\pi\) |
−0.998679 | + | 0.0513907i | \(0.983635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.73435 | + | 8.20014i | 0.190907 | + | 0.330661i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.39215 | − | 2.00725i | 0.0963042 | − | 0.0808088i | −0.593364 | − | 0.804934i | \(-0.702201\pi\) |
0.689669 | + | 0.724125i | \(0.257756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.214658 | − | 0.371798i | 0.00862783 | − | 0.0149438i | −0.861679 | − | 0.507453i | \(-0.830587\pi\) |
0.870307 | + | 0.492509i | \(0.163920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.55076 | − | 3.47619i | −0.383259 | − | 0.139495i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.16377 | − | 29.2852i | −0.206882 | − | 1.17329i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.8686 | − | 20.0281i | −0.954744 | − | 0.801126i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.616475 | + | 0.904052i | 0.0246196 | + | 0.0361044i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.71921 | − | 5.63808i | −0.267912 | − | 0.224805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.64012 | − | 31.9867i | −0.224530 | − | 1.27337i | −0.863582 | − | 0.504208i | \(-0.831784\pi\) |
0.639052 | − | 0.769163i | \(-0.279327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.216034 | + | 0.0786299i | 0.00858658 | + | 0.00312526i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5215 | + | 25.1520i | −0.576269 | + | 0.998127i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.4311 | − | 12.9482i | 0.611402 | − | 0.513027i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2253 | − | 22.9068i | −0.523184 | − | 0.906181i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.22929 | + | 18.3142i | −0.127549 | + | 0.723368i | 0.852212 | + | 0.523197i | \(0.175261\pi\) |
−0.979761 | + | 0.200171i | \(0.935850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0472 | − | 9.84439i | 1.06664 | − | 0.388225i | 0.251720 | − | 0.967800i | \(-0.419004\pi\) |
0.814919 | + | 0.579575i | \(0.196782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.39256 | 0.251707 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.0213 | −1.41614 | −0.708071 | − | 0.706141i | \(-0.750435\pi\) | ||||
−0.708071 | + | 0.706141i | \(0.750435\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.94003 | + | 2.52596i | −0.272420 | + | 0.0991528i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.35844 | − | 7.70409i | 0.0532414 | − | 0.301947i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.4702 | − | 25.0631i | −0.566262 | − | 0.980795i | −0.996931 | − | 0.0782852i | \(-0.975056\pi\) |
0.430669 | − | 0.902510i | \(-0.358278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.10510 | − | 5.96189i | 0.277619 | − | 0.232950i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.30939 | + | 14.3923i | −0.324180 | + | 0.561497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.1158 | − | 16.4208i | −1.75746 | − | 0.639664i | −0.757550 | − | 0.652778i | \(-0.773604\pi\) |
−0.999914 | + | 0.0131131i | \(0.995826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.64069 | − | 9.30480i | −0.0638154 | − | 0.361915i | −0.999947 | − | 0.0102659i | \(-0.996732\pi\) |
0.936132 | − | 0.351649i | \(-0.114379\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.66566 | + | 1.39766i | 0.0646891 | + | 0.0542806i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.7781 | + | 36.9238i | −0.689403 | + | 1.43185i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.5347 | + | 18.9088i | 0.872546 | + | 0.732153i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.65629 | + | 9.39327i | 0.0640357 | + | 0.363165i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.95547 | + | 1.07570i | 0.114095 | + | 0.0415271i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.60353 | + | 16.6338i | −0.370189 | + | 0.641186i | −0.989594 | − | 0.143885i | \(-0.954040\pi\) |
0.619406 | + | 0.785071i | \(0.287374\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.01823 | − | 5.04990i | 0.231642 | − | 0.194371i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.226932 | − | 0.393058i | −0.00872171 | − | 0.0151064i | 0.861632 | − | 0.507534i | \(-0.169443\pi\) |
−0.870353 | + | 0.492428i | \(0.836110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.45825 | + | 36.6266i | −0.247845 | + | 1.40560i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.424576 | − | 0.154533i | 0.0162698 | − | 0.00592172i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.53688 | 0.250127 | 0.125063 | − | 0.992149i | \(-0.460087\pi\) | ||||
0.125063 | + | 0.992149i | \(0.460087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.8875 | 0.454199 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.46738 | + | 1.26202i | −0.132289 | + | 0.0481491i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.59113 | + | 31.7089i | −0.213005 | + | 1.20801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.9350 | + | 18.9400i | 0.415987 | + | 0.720510i | 0.995531 | − | 0.0944301i | \(-0.0301029\pi\) |
−0.579545 | + | 0.814941i | \(0.696770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.67791 | + | 3.08613i | −0.139712 | + | 0.117232i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.21761 | − | 12.5013i | 0.273779 | − | 0.474200i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.29187 | + | 2.29005i | 0.238322 | + | 0.0867420i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.314354 | − | 1.78279i | −0.0118900 | − | 0.0674314i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.84736 | + | 3.22832i | 0.145313 | + | 0.121932i | 0.712546 | − | 0.701625i | \(-0.247542\pi\) |
−0.567233 | + | 0.823557i | \(0.691986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.4896 | + | 27.7923i | −1.07451 | + | 1.04821i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.1515 | − | 11.8745i | −0.532977 | − | 0.447220i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.238202 | − | 1.35091i | −0.00895851 | − | 0.0508062i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.1948 | − | 17.1775i | −1.77244 | − | 0.645115i | −0.999949 | − | 0.0100871i | \(-0.996789\pi\) |
−0.772489 | − | 0.635028i | \(-0.780989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.4882 | − | 25.0942i | 0.543349 | − | 0.941108i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.2761 | − | 11.1400i | 0.497194 | − | 0.417196i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.35559 | + | 5.81205i | 0.125492 | + | 0.217358i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.63010 | − | 9.24476i | 0.0608772 | − | 0.345252i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.9561 | − | 3.98770i | 0.408594 | − | 0.148716i | −0.129542 | − | 0.991574i | \(-0.541351\pi\) |
0.538136 | + | 0.842858i | \(0.319129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1624 | 0.601918 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.62854 | 0.246518 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.3671 | + | 7.77699i | −0.793555 | + | 0.288830i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.57741 | − | 37.3023i | 0.243942 | − | 1.38347i | −0.578993 | − | 0.815332i | \(-0.696554\pi\) |
0.822936 | − | 0.568134i | \(-0.192335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.52722 | + | 13.0375i | 0.278786 | + | 0.482871i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.46284 | − | 2.90567i | 0.128078 | − | 0.107470i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.45973 | − | 14.6527i | 0.312467 | − | 0.541209i | −0.666429 | − | 0.745569i | \(-0.732178\pi\) |
0.978896 | + | 0.204360i | \(0.0655112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.52484 | + | 2.01088i | 0.203787 | + | 0.0741723i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.396132 | − | 2.24658i | −0.0145917 | − | 0.0827537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.7418 | − | 22.4390i | −0.983712 | − | 0.825432i | 0.000933516 | − | 1.00000i | \(-0.499703\pi\) |
−0.984645 | + | 0.174567i | \(0.944147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.06247 | − | 6.88960i | 0.259446 | − | 0.253096i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.8275 | − | 26.7064i | −1.16764 | − | 0.979765i | −0.167656 | − | 0.985845i | \(-0.553620\pi\) |
−0.999982 | + | 0.00608086i | \(0.998064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.08137 | + | 51.5030i | 0.332716 | + | 1.88692i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.4163 | − | 4.51916i | −0.454289 | − | 0.165348i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.2546 | + | 26.4217i | −0.557391 | + | 0.965429i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.7302 | − | 32.4985i | 1.41328 | − | 1.18589i | 0.458461 | − | 0.888715i | \(-0.348401\pi\) |
0.954824 | − | 0.297172i | \(-0.0960435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.19151 | − | 7.25991i | −0.152747 | − | 0.264566i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.40625 | − | 24.9891i | 0.160360 | − | 0.909447i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3326 | − | 13.2240i | 1.32053 | − | 0.480634i | 0.416902 | − | 0.908951i | \(-0.363116\pi\) |
0.903628 | + | 0.428318i | \(0.140894\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.910288 | 0.0330414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.8058 | −0.826711 | −0.413355 | − | 0.910570i | \(-0.635643\pi\) | ||||
−0.413355 | + | 0.910570i | \(0.635643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.6562 | − | 8.97411i | 0.892613 | − | 0.324884i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.28769 | − | 7.30283i | 0.0465564 | − | 0.264034i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.2960 | + | 57.6703i | 1.20225 | + | 2.08235i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.37493 | − | 4.51010i | 0.193825 | − | 0.162638i | −0.540711 | − | 0.841209i | \(-0.681845\pi\) |
0.734535 | + | 0.678570i | \(0.237400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.30609 | + | 5.72631i | −0.119066 | + | 0.206228i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.2329 | + | 7.36419i | 0.727728 | + | 0.264871i | 0.679203 | − | 0.733950i | \(-0.262326\pi\) |
0.0485254 | + | 0.998822i | \(0.484548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32622 | + | 13.1926i | 0.0835602 | + | 0.473893i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4489 | + | 9.60674i | 0.410726 | + | 0.344640i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.1802 | − | 27.3743i | 0.472228 | − | 0.980787i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.78480 | + | 3.17582i | 0.135431 | + | 0.113640i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.94848 | + | 22.3930i | 0.141107 | + | 0.800259i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.02861 | + | 2.92218i | 0.286553 | + | 0.104297i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7212 | + | 35.8901i | −0.738630 | + | 1.27934i | 0.214483 | + | 0.976728i | \(0.431193\pi\) |
−0.953112 | + | 0.302616i | \(0.902140\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.98883 | + | 2.50793i | −0.106405 | + | 0.0892846i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.17155 | − | 8.95738i | −0.183879 | − | 0.318488i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.92444 | − | 27.9279i | 0.174872 | − | 0.991749i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.83093 | + | 3.21419i | −0.313201 | + | 0.113996i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.8182 | 0.666574 | 0.333287 | − | 0.942825i | \(-0.391842\pi\) | ||||
0.333287 | + | 0.942825i | \(0.391842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.0633 | −0.462146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.9438 | − | 8.35085i | 0.810678 | − | 0.295063i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.539043 | − | 3.05706i | 0.0190224 | − | 0.107881i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.0458 | + | 29.5243i | 0.600787 | + | 1.04059i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0627632 | − | 0.0526646i | 0.00220937 | − | 0.00185388i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.63505 | − | 11.4922i | 0.233276 | − | 0.404046i | −0.725494 | − | 0.688228i | \(-0.758389\pi\) |
0.958770 | + | 0.284183i | \(0.0917222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.9744 | − | 17.0973i | −1.64949 | − | 0.600367i | −0.660833 | − | 0.750533i | \(-0.729797\pi\) |
−0.988661 | + | 0.150166i | \(0.952019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.00192 | + | 5.68218i | 0.0351389 | + | 0.199283i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.7157 | + | 27.4517i | 1.14598 | + | 0.961593i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.5560 | − | 16.9467i | −0.404292 | − | 0.592889i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.1625 | + | 27.8266i | 1.15879 | + | 0.972341i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.94472 | − | 28.0429i | −0.172572 | − | 0.978704i | −0.940909 | − | 0.338659i | \(-0.890027\pi\) |
0.768337 | − | 0.640045i | \(-0.221084\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.2257 | − | 5.17773i | −0.495877 | − | 0.180484i | 0.0819619 | − | 0.996635i | \(-0.473881\pi\) |
−0.577838 | + | 0.816151i | \(0.696104\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.351813 | + | 0.609358i | −0.0122486 | + | 0.0212151i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.8843 | − | 31.7887i | 1.31737 | − | 1.10540i | 0.330511 | − | 0.943802i | \(-0.392779\pi\) |
0.986856 | − | 0.161600i | \(-0.0516654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9838 | − | 38.0771i | −0.763529 | − | 1.32247i | −0.941021 | − | 0.338349i | \(-0.890132\pi\) |
0.177492 | − | 0.984122i | \(-0.443202\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.227617 | + | 1.29088i | −0.00789593 | + | 0.0447801i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.90682 | − | 1.42197i | 0.135363 | − | 0.0492682i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.4671 | 1.43503 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.3961 | 0.463039 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.514663 | − | 0.187322i | 0.0177681 | − | 0.00646708i | −0.333121 | − | 0.942884i | \(-0.608102\pi\) |
0.350889 | + | 0.936417i | \(0.385879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.39234 | − | 36.2528i | 0.220425 | − | 1.25009i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.67655 | + | 8.10002i | 0.161069 | + | 0.278980i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.5373 | − | 15.5546i | 0.637702 | − | 0.535095i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0630 | + | 31.2860i | −0.620651 | + | 1.07500i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.6645 | − | 4.60951i | −0.434645 | − | 0.158198i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.74944 | + | 32.6067i | 0.197088 | + | 1.11774i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.8253 | − | 9.92258i | −0.404890 | − | 0.339743i | 0.417490 | − | 0.908681i | \(-0.362910\pi\) |
−0.822380 | + | 0.568939i | \(0.807354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.3914 | − | 9.11081i | −1.10776 | − | 0.311583i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5748 | − | 21.4598i | −0.873619 | − | 0.733054i | 0.0912378 | − | 0.995829i | \(-0.470918\pi\) |
−0.964857 | + | 0.262776i | \(0.915362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.69049 | + | 26.6011i | 0.160037 | + | 0.907617i | 0.954035 | + | 0.299696i | \(0.0968852\pi\) |
−0.793997 | + | 0.607921i | \(0.792004\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7207 | − | 3.90203i | −0.365361 | − | 0.132981i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.50763 | + | 9.53949i | −0.187482 | + | 0.324728i | −0.944410 | − | 0.328770i | \(-0.893366\pi\) |
0.756928 | + | 0.653498i | \(0.226699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3491 | + | 9.52305i | −0.385882 | + | 0.323793i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.90933 | − | 6.77116i | −0.132768 | − | 0.229961i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.939870 | + | 5.33027i | −0.0318829 | + | 0.180817i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3286 | + | 7.03505i | −0.654926 | + | 0.238374i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.5371 | −1.03352 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.6564 | 0.698313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.08935 | + | 1.85237i | −0.171855 | + | 0.0625502i | −0.426515 | − | 0.904481i | \(-0.640259\pi\) |
0.254660 | + | 0.967031i | \(0.418037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.49348 | − | 8.46993i | 0.0503737 | − | 0.285684i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.50935 | − | 4.34631i | −0.0845420 | − | 0.146431i | 0.820654 | − | 0.571425i | \(-0.193609\pi\) |
−0.905196 | + | 0.424994i | \(0.860276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.3981 | + | 33.8980i | −1.35950 | + | 1.14076i | −0.383370 | + | 0.923595i | \(0.625237\pi\) |
−0.976135 | + | 0.217165i | \(0.930319\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.71813 | + | 16.8323i | −0.326671 | + | 0.565812i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.9355 | + | 5.80006i | 0.535063 | + | 0.194747i | 0.595398 | − | 0.803431i | \(-0.296995\pi\) |
−0.0603347 | + | 0.998178i | \(0.519217\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.07659 | − | 34.4621i | −0.203802 | − | 1.15582i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.73927 | − | 2.29852i | −0.0917690 | − | 0.0770034i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.89737 | + | 58.9815i | −0.197348 | + | 1.97374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3882 | + | 19.6251i | 0.781783 | + | 0.655994i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.42526 | − | 8.08307i | −0.0475882 | − | 0.269886i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.4343 | − | 13.2610i | −1.21515 | − | 0.442279i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.32272 | + | 5.75512i | −0.110696 | + | 0.191731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.90034 | + | 4.95097i | −0.196351 | + | 0.164758i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.69068 | + | 8.12449i | 0.155923 | + | 0.270067i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.93064 | − | 16.6205i | 0.0973104 | − | 0.551875i | −0.896704 | − | 0.442630i | \(-0.854046\pi\) |
0.994015 | − | 0.109245i | \(-0.0348433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.05838 | − | 0.385221i | 0.0351044 | − | 0.0127770i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.57339 | −0.317181 | −0.158590 | − | 0.987344i | \(-0.550695\pi\) | ||||
−0.158590 | + | 0.987344i | \(0.550695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.46809 | 0.0816817 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.77793 | − | 2.83093i | 0.257130 | − | 0.0935878i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.94059 | + | 11.0057i | −0.0640840 | + | 0.363439i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2796 | + | 17.8047i | 0.339091 | + | 0.587323i | 0.984262 | − | 0.176715i | \(-0.0565472\pi\) |
−0.645171 | + | 0.764038i | \(0.723214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.95126 | + | 3.31550i | −0.130198 | + | 0.109249i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.2743 | − | 38.5803i | 0.733169 | − | 1.26989i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0494 | − | 8.75326i | −0.790739 | − | 0.287805i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.30440 | + | 13.0689i | 0.0756863 | + | 0.429238i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.4080 | − | 12.9288i | −0.505519 | − | 0.424181i | 0.354030 | − | 0.935234i | \(-0.384811\pi\) |
−0.859549 | + | 0.511053i | \(0.829255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.65654 | − | 18.2815i | −0.152612 | − | 0.599151i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.76664 | − | 8.19519i | −0.319746 | − | 0.268298i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.240527 | + | 1.36410i | 0.00786608 | + | 0.0446107i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2898 | + | 7.38487i | 0.662838 | + | 0.241253i | 0.651461 | − | 0.758682i | \(-0.274156\pi\) |
0.0113766 | + | 0.999935i | \(0.496379\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.13939 | + | 3.70553i | −0.0698163 | + | 0.120925i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.36721 | + | 3.66452i | −0.142367 | + | 0.119460i | −0.711190 | − | 0.703000i | \(-0.751843\pi\) |
0.568823 | + | 0.822460i | \(0.307399\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.6373 | − | 21.8885i | −0.411528 | − | 0.712787i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.57596 | + | 25.9515i | −0.148856 | + | 0.844203i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.71384 | + | 0.987756i | −0.0881879 | + | 0.0320978i | −0.385737 | − | 0.922609i | \(-0.626053\pi\) |
0.297549 | + | 0.954706i | \(0.403831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.9898 | −0.908586 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.03622 | −0.260592 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.8902 | + | 5.78355i | −0.514733 | + | 0.187348i | −0.586309 | − | 0.810088i | \(-0.699420\pi\) |
0.0715755 | + | 0.997435i | \(0.477197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.57414 | + | 48.6264i | −0.277453 | + | 1.57351i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.01826 | − | 1.76367i | −0.0329155 | − | 0.0570114i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9722 | + | 9.20676i | −0.354311 | + | 0.297302i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.07872 | − | 7.06455i | 0.131572 | − | 0.227889i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.5396 | − | 8.56771i | −0.758553 | − | 0.276091i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.0426 | − | 68.2968i | −0.387664 | − | 2.19855i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.8032 | + | 26.6860i | 1.02272 | + | 0.858165i | 0.989967 | − | 0.141299i | \(-0.0451278\pi\) |
0.0327538 | + | 0.999463i | \(0.489572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.85608 | − | 0.837667i | 0.0596258 | − | 0.0269098i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.7074 | + | 14.0192i | 0.536166 | + | 0.449896i | 0.870224 | − | 0.492656i | \(-0.163974\pi\) |
−0.334059 | + | 0.942552i | \(0.608418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.02024 | + | 17.1286i | 0.0968244 | + | 0.549119i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.96175 | + | 2.16990i | 0.190929 | + | 0.0694924i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.8843 | − | 39.6367i | 0.732132 | − | 1.26809i | −0.223838 | − | 0.974626i | \(-0.571859\pi\) |
0.955970 | − | 0.293464i | \(-0.0948082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.49371 | + | 2.93157i | −0.111659 | + | 0.0936934i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7719 | + | 18.6575i | 0.343920 | + | 0.595687i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.63229 | − | 48.9562i | 0.275327 | − | 1.56146i | −0.462593 | − | 0.886571i | \(-0.653081\pi\) |
0.737920 | − | 0.674888i | \(-0.235808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.14517 | + | 1.14475i | −0.100213 | + | 0.0364747i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.2585 | 0.708497 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0636 | −0.542590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8537 | + | 13.4137i | −1.17070 | + | 0.426099i | −0.852908 | − | 0.522062i | \(-0.825163\pi\) |
−0.317790 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.545406 | − | 3.09315i | 0.0173079 | − | 0.0981581i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.2932 | − | 31.6848i | −0.579934 | − | 1.00448i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4326 | − | 14.6277i | 0.552096 | − | 0.463263i | −0.323554 | − | 0.946210i | \(-0.604878\pi\) |
0.875650 | + | 0.482946i | \(0.160433\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.7964 | + | 22.1640i | −0.404861 | + | 0.701239i |
(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 | 76.2.i.a.73.2 | yes | 12 | |
3.2 | odd | 2 | 684.2.bo.c.73.1 | 12 | |||
4.3 | odd | 2 | 304.2.u.e.225.1 | 12 | |||
19.2 | odd | 18 | 1444.2.e.h.653.3 | 12 | |||
19.3 | odd | 18 | 1444.2.e.h.429.3 | 12 | |||
19.5 | even | 9 | 1444.2.a.h.1.3 | 6 | |||
19.6 | even | 9 | inner | 76.2.i.a.25.2 | ✓ | 12 | |
19.14 | odd | 18 | 1444.2.a.g.1.4 | 6 | |||
19.16 | even | 9 | 1444.2.e.g.429.4 | 12 | |||
19.17 | even | 9 | 1444.2.e.g.653.4 | 12 | |||
57.44 | odd | 18 | 684.2.bo.c.253.1 | 12 | |||
76.43 | odd | 18 | 5776.2.a.bw.1.4 | 6 | |||
76.63 | odd | 18 | 304.2.u.e.177.1 | 12 | |||
76.71 | even | 18 | 5776.2.a.by.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.i.a.25.2 | ✓ | 12 | 19.6 | even | 9 | inner | |
76.2.i.a.73.2 | yes | 12 | 1.1 | even | 1 | trivial | |
304.2.u.e.177.1 | 12 | 76.63 | odd | 18 | |||
304.2.u.e.225.1 | 12 | 4.3 | odd | 2 | |||
684.2.bo.c.73.1 | 12 | 3.2 | odd | 2 | |||
684.2.bo.c.253.1 | 12 | 57.44 | odd | 18 | |||
1444.2.a.g.1.4 | 6 | 19.14 | odd | 18 | |||
1444.2.a.h.1.3 | 6 | 19.5 | even | 9 | |||
1444.2.e.g.429.4 | 12 | 19.16 | even | 9 | |||
1444.2.e.g.653.4 | 12 | 19.17 | even | 9 | |||
1444.2.e.h.429.3 | 12 | 19.3 | odd | 18 | |||
1444.2.e.h.653.3 | 12 | 19.2 | odd | 18 | |||
5776.2.a.bw.1.4 | 6 | 76.43 | odd | 18 | |||
5776.2.a.by.1.3 | 6 | 76.71 | even | 18 |