Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.i.863.4 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.36522 | + | 1.36556i | −1.36556 | + | 0.788405i | −0.990357 | − | 0.138539i | \(-0.955759\pi\) |
−0.375201 | + | 0.926944i | \(0.622426\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.63213 | + | 2.09701i | −1.62434 | + | 0.937813i | −0.638600 | + | 0.769539i | \(0.720486\pi\) |
−0.985740 | + | 0.168274i | \(0.946181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.517694i | − | 0.195670i | −0.995203 | − | 0.0978349i | \(-0.968808\pi\) | ||
0.995203 | − | 0.0978349i | \(-0.0311917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.22950 | − | 3.86160i | 0.743165 | − | 1.28720i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.15654 | 1.55475 | 0.777377 | − | 0.629035i | \(-0.216550\pi\) | ||||
0.777377 | + | 0.629035i | \(0.216550\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.67164 | − | 2.89536i | 0.463629 | − | 0.803030i | −0.535509 | − | 0.844529i | \(-0.679880\pi\) |
0.999139 | + | 0.0414999i | \(0.0132136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.72719 | − | 9.91978i | 1.47875 | − | 2.56128i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.818251 | − | 1.41725i | −0.198455 | − | 0.343734i | 0.749573 | − | 0.661922i | \(-0.230259\pi\) |
−0.948028 | + | 0.318188i | \(0.896926\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.66388 | + | 2.36135i | 0.840551 | + | 0.541732i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.706940 | + | 1.22446i | 0.154267 | + | 0.267198i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.72719 | + | 3.30659i | 1.19420 | + | 0.689472i | 0.959257 | − | 0.282537i | \(-0.0911759\pi\) |
0.234944 | + | 0.972009i | \(0.424509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.29493 | − | 10.9031i | 1.25899 | − | 2.18063i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.98467i | 0.766850i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.01997 | + | 5.23074i | −0.560795 | + | 0.971325i | 0.436633 | + | 0.899640i | \(0.356171\pi\) |
−0.997427 | + | 0.0716849i | \(0.977162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.896671 | −0.161047 | −0.0805235 | − | 0.996753i | \(-0.525659\pi\) | ||||
−0.0805235 | + | 0.996753i | \(0.525659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.1963 | + | 7.04155i | −2.12311 | + | 1.22578i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08561 | + | 1.88033i | 0.183502 | + | 0.317834i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65178 | −0.929148 | −0.464574 | − | 0.885534i | \(-0.653792\pi\) | ||||
−0.464574 | + | 0.885534i | \(0.653792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.13088i | 1.46211i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.18849 | + | 2.99557i | −0.810305 | + | 0.467830i | −0.847062 | − | 0.531494i | \(-0.821631\pi\) |
0.0367566 | + | 0.999324i | \(0.488297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.89536 | − | 5.01492i | −0.441539 | − | 0.764768i | 0.556265 | − | 0.831005i | \(-0.312234\pi\) |
−0.997804 | + | 0.0662372i | \(0.978901\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.7011i | 2.78780i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.89268 | + | 1.67009i | 0.421941 | + | 0.243608i | 0.695907 | − | 0.718131i | \(-0.255002\pi\) |
−0.273966 | + | 0.961739i | \(0.588336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.73199 | 0.961713 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87068 | + | 2.23474i | 0.542003 | + | 0.312926i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.40275 | − | 7.62579i | 0.604765 | − | 1.04748i | −0.387324 | − | 0.921944i | \(-0.626600\pi\) |
0.992089 | − | 0.125540i | \(-0.0400662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.7292 | + | 10.8133i | −2.52545 | + | 1.45807i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.8904 | − | 0.581873i | −1.57493 | − | 0.0770709i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.109010 | − | 0.0629372i | 0.0141919 | − | 0.00819372i | −0.492887 | − | 0.870093i | \(-0.664058\pi\) |
0.507079 | + | 0.861899i | \(0.330725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1584 | − | 5.86494i | −1.30065 | − | 0.750928i | −0.320131 | − | 0.947373i | \(-0.603727\pi\) |
−0.980515 | + | 0.196445i | \(0.937060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.99912 | − | 1.15420i | −0.251866 | − | 0.145415i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.0218i | 1.73919i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6302 | + | 6.13733i | 1.29868 | + | 0.749794i | 0.980176 | − | 0.198127i | \(-0.0634858\pi\) |
0.318505 | + | 0.947921i | \(0.396819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.0614 | −2.17433 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.44347 | + | 7.69632i | 0.527343 | + | 0.913385i | 0.999492 | + | 0.0318662i | \(0.0101451\pi\) |
−0.472149 | + | 0.881519i | \(0.656522\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.88369 | + | 4.99470i | 0.337510 | + | 0.584585i | 0.983964 | − | 0.178368i | \(-0.0570818\pi\) |
−0.646453 | + | 0.762953i | \(0.723749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 34.3844i | 3.97037i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.66951i | − | 0.304218i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.712296 | − | 1.23373i | −0.0801396 | − | 0.138806i | 0.823170 | − | 0.567795i | \(-0.192203\pi\) |
−0.903310 | + | 0.428989i | \(0.858870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.24719 | + | 2.16019i | 0.138577 | + | 0.240022i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.864719 | 0.0949153 | 0.0474576 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474576 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.94399 | + | 3.43177i | 0.644717 | + | 0.372227i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.4958i | − | 1.76853i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8317 | + | 7.40840i | 1.36016 | + | 0.785289i | 0.989645 | − | 0.143538i | \(-0.0458479\pi\) |
0.370515 | + | 0.928826i | \(0.379181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.49891 | − | 0.865397i | −0.157129 | − | 0.0907182i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.12082 | − | 1.22446i | 0.219919 | − | 0.126970i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.2595 | − | 0.893551i | −1.87338 | − | 0.0916764i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0530805 | − | 0.0306461i | 0.00538951 | − | 0.00311164i | −0.497303 | − | 0.867577i | \(-0.665676\pi\) |
0.502692 | + | 0.864465i | \(0.332343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4965 | − | 19.9125i | 1.15544 | − | 2.00128i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.63213 | + | 2.09701i | 0.361411 | + | 0.208661i | 0.669699 | − | 0.742632i | \(-0.266423\pi\) |
−0.308289 | + | 0.951293i | \(0.599756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.13540 | − | 2.96493i | −0.501164 | − | 0.289347i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.7529i | − | 1.52289i | −0.648231 | − | 0.761443i | \(-0.724491\pi\) | ||
0.648231 | − | 0.761443i | \(-0.275509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.59263 | + | 9.68672i | 0.535677 | + | 0.927819i | 0.999130 | + | 0.0416982i | \(0.0132768\pi\) |
−0.463453 | + | 0.886121i | \(0.653390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3677 | − | 7.71784i | 1.26880 | − | 0.732545i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.82565i | − | 0.830247i | −0.909765 | − | 0.415124i | \(-0.863738\pi\) | ||
0.909765 | − | 0.415124i | \(-0.136262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.7359 | −2.58638 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.45382 | − | 12.9104i | −0.689106 | − | 1.19357i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.733702 | + | 0.423603i | −0.0672584 | + | 0.0388316i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.5899 | 1.41726 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.18126 | − | 14.1704i | 0.737679 | − | 1.27770i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.8321i | 2.84715i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.01975 | − | 1.76627i | 0.0904886 | − | 0.156731i | −0.817228 | − | 0.576314i | \(-0.804490\pi\) |
0.907717 | + | 0.419583i | \(0.137824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.6963 | + | 7.90757i | 1.20589 | + | 0.696223i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.13314 | + | 10.6229i | 0.535855 | + | 0.928127i | 0.999121 | + | 0.0419086i | \(0.0133438\pi\) |
−0.463267 | + | 0.886219i | \(0.653323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22246 | − | 1.89677i | 0.106001 | − | 0.164470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.35591 | − | 14.4729i | −0.719162 | − | 1.24563i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.11319 | + | 14.0524i | −0.693156 | + | 1.20058i | 0.277642 | + | 0.960685i | \(0.410447\pi\) |
−0.970798 | + | 0.239897i | \(0.922886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.91442 | + | 5.04793i | −0.247198 | + | 0.428160i | −0.962747 | − | 0.270403i | \(-0.912843\pi\) |
0.715549 | + | 0.698562i | \(0.246177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.12242 | −0.768247 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.61987 | − | 14.9301i | 0.720830 | − | 1.24851i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 25.3317i | − | 2.10368i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.9226 | + | 9.19292i | −1.31327 | + | 0.758220i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5635 | − | 7.25355i | 1.02924 | − | 0.594234i | 0.112476 | − | 0.993654i | \(-0.464122\pi\) |
0.916768 | + | 0.399420i | \(0.130789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.56743 | −0.208935 | −0.104467 | − | 0.994528i | \(-0.533314\pi\) | ||||
−0.104467 | + | 0.994528i | \(0.533314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.29714 | −0.589939 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.25683 | − | 1.88033i | 0.261595 | − | 0.151032i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.08584 | + | 2.35896i | −0.326086 | + | 0.188266i | −0.654102 | − | 0.756406i | \(-0.726953\pi\) |
0.328016 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0489i | 1.90720i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.71180 | − | 2.96493i | 0.134909 | − | 0.233669i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7652 | 1.07817 | 0.539086 | − | 0.842251i | \(-0.318770\pi\) | ||||
0.539086 | + | 0.842251i | \(0.318770\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29.5324 | − | 51.1517i | 2.29910 | − | 3.98215i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.63962 | + | 16.6963i | −0.745936 | + | 1.29200i | 0.203819 | + | 0.979008i | \(0.434664\pi\) |
−0.949756 | + | 0.312991i | \(0.898669\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.911244 | + | 1.57832i | 0.0700957 | + | 0.121409i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.2872 | − | 8.88380i | 1.32199 | − | 0.679361i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.24935 | + | 3.89599i | 0.171015 | + | 0.296207i | 0.938775 | − | 0.344531i | \(-0.111962\pi\) |
−0.767760 | + | 0.640738i | \(0.778629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.64449 | − | 3.25885i | −0.426683 | − | 0.246346i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.171889 | + | 0.297720i | −0.0129199 | + | 0.0223780i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2232i | 1.36206i | 0.732253 | + | 0.681032i | \(0.238469\pi\) | ||||
−0.732253 | + | 0.681032i | \(0.761531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.85614 | + | 6.67903i | −0.286625 | + | 0.496448i | −0.973002 | − | 0.230797i | \(-0.925867\pi\) |
0.686377 | + | 0.727246i | \(0.259200\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.0356 | 2.36814 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.5280 | − | 11.8519i | 1.50925 | − | 0.871367i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.21934 | − | 7.30811i | −0.308549 | − | 0.534422i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.06284 | 0.150049 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.22637i | − | 0.0887371i | −0.999015 | − | 0.0443685i | \(-0.985872\pi\) | ||
0.999015 | − | 0.0443685i | \(-0.0141276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.83172 | + | 3.94430i | −0.491758 | + | 0.283917i | −0.725304 | − | 0.688429i | \(-0.758301\pi\) |
0.233545 | + | 0.972346i | \(0.424967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.1476 | − | 33.1646i | −1.37119 | − | 2.37496i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5206i | 1.24829i | 0.781308 | + | 0.624146i | \(0.214553\pi\) | ||||
−0.781308 | + | 0.624146i | \(0.785447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.44435 | − | 1.41124i | −0.173275 | − | 0.100040i | 0.410854 | − | 0.911701i | \(-0.365231\pi\) |
−0.584129 | + | 0.811661i | \(0.698564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.5235 | −2.36457 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.70792 | + | 1.56342i | 0.190059 | + | 0.109731i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5635 | − | 21.7607i | 0.877474 | − | 1.51983i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.5375 | − | 14.7441i | 1.77498 | − | 1.02478i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.8929 | + | 12.1764i | 1.30685 | + | 0.842260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.03972 | + | 5.21909i | −0.622320 | + | 0.359297i | −0.777772 | − | 0.628547i | \(-0.783650\pi\) |
0.155452 | + | 0.987844i | \(0.450317\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.0195 | − | 12.1356i | −1.44023 | − | 0.831520i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.0327 | + | 12.1432i | 1.43442 | + | 0.828162i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.464201i | 0.0315120i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6411 | − | 7.87569i | −0.921780 | − | 0.532190i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.47128 | −0.368038 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.571419 | − | 0.989727i | −0.0382651 | − | 0.0662770i | 0.846259 | − | 0.532772i | \(-0.178850\pi\) |
−0.884524 | + | 0.466495i | \(0.845516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −28.0691 | − | 48.6170i | −1.87127 | − | 3.24113i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9989i | 1.12825i | 0.825688 | + | 0.564127i | \(0.190787\pi\) | ||||
−0.825688 | + | 0.564127i | \(0.809213\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.6533i | − | 1.16657i | −0.812269 | − | 0.583283i | \(-0.801768\pi\) | ||
0.812269 | − | 0.583283i | \(-0.198232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.64536 | + | 6.31395i | 0.239847 | + | 0.415428i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.84830 | − | 13.5937i | −0.514159 | − | 0.890550i | −0.999865 | − | 0.0164278i | \(-0.994771\pi\) |
0.485706 | − | 0.874122i | \(-0.338563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0088 | −0.913834 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.36947 | + | 1.94536i | 0.218870 | + | 0.126365i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.1331i | 1.75509i | 0.479490 | + | 0.877547i | \(0.340822\pi\) | ||||
−0.479490 | + | 0.877547i | \(0.659178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6511 | − | 11.9229i | −1.33025 | − | 0.768022i | −0.344914 | − | 0.938634i | \(-0.612092\pi\) |
−0.985338 | + | 0.170613i | \(0.945425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.2522 | − | 9.38322i | −1.04258 | − | 0.601934i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.4515 | + | 14.1171i | −1.56215 | + | 0.901907i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.9617 | − | 6.66093i | 0.824731 | − | 0.423825i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.04525 | + | 1.18082i | −0.129612 | + | 0.0748317i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.232112 | − | 0.402030i | 0.0146508 | − | 0.0253759i | −0.858607 | − | 0.512634i | \(-0.828670\pi\) |
0.873258 | + | 0.487258i | \(0.162003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.5324 | + | 17.0506i | 1.85669 | + | 1.07196i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.7451 | −1.17386 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.74157 | − | 5.62430i | −0.607662 | − | 0.350834i | 0.164388 | − | 0.986396i | \(-0.447435\pi\) |
−0.772050 | + | 0.635562i | \(0.780769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.92589i | 0.181806i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4660 | + | 23.3238i | 0.833526 | + | 1.44371i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.49962 | − | 4.32991i | 0.462447 | − | 0.266994i | −0.250626 | − | 0.968084i | \(-0.580636\pi\) |
0.713072 | + | 0.701090i | \(0.247303\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.9305i | 2.26863i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.4664 | −2.47650 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.91647 | + | 6.78352i | 0.238791 | + | 0.413598i | 0.960368 | − | 0.278736i | \(-0.0899155\pi\) |
−0.721577 | + | 0.692335i | \(0.756582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.19216 | − | 4.15240i | 0.436893 | − | 0.252240i | −0.265386 | − | 0.964142i | \(-0.585499\pi\) |
0.702279 | + | 0.711902i | \(0.252166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.72700 | 0.286091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.4601 | − | 56.2225i | 1.95742 | − | 3.39034i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.2241i | − | 1.45549i | −0.685850 | − | 0.727743i | \(-0.740570\pi\) | ||
0.685850 | − | 0.727743i | \(-0.259430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.99912 | + | 3.46259i | −0.119684 | + | 0.207300i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.5811 | − | 11.8825i | −1.22777 | − | 0.708851i | −0.261205 | − | 0.965283i | \(-0.584120\pi\) |
−0.966562 | + | 0.256432i | \(0.917453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.48644 | − | 9.50279i | −0.326135 | − | 0.564882i | 0.655607 | − | 0.755103i | \(-0.272413\pi\) |
−0.981741 | + | 0.190221i | \(0.939080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 44.4078 | − | 22.8209i | 2.63049 | − | 1.35180i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.55079 | + | 2.68605i | 0.0915402 | + | 0.158552i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.16093 | − | 12.4031i | 0.421231 | − | 0.729594i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0836979 | + | 0.144969i | −0.00490646 | + | 0.00849824i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5459 | 1.02504 | 0.512520 | − | 0.858675i | \(-0.328712\pi\) | ||||
0.512520 | + | 0.858675i | \(0.328712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.263960 | + | 0.457193i | −0.0153684 | + | 0.0266188i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.5471i | 1.19226i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.1476 | − | 11.0549i | 1.10733 | − | 0.639319i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.59619 | + | 1.49891i | −0.149642 | + | 0.0863958i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4544 | −0.658037 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 49.1954 | 2.81692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8230 | − | 12.0222i | 1.18843 | − | 0.686142i | 0.230482 | − | 0.973077i | \(-0.425970\pi\) |
0.957950 | + | 0.286935i | \(0.0926364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3867 | − | 9.46086i | 0.932206 | − | 0.538210i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.7795i | − | 0.838066i | −0.907971 | − | 0.419033i | \(-0.862369\pi\) | ||
0.907971 | − | 0.419033i | \(-0.137631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.22387 | + | 15.9762i | −0.521364 | + | 0.903029i | 0.478327 | + | 0.878182i | \(0.341243\pi\) |
−0.999691 | + | 0.0248474i | \(0.992090\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.68145 | 0.545488 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6670 | − | 20.2079i | 0.655285 | − | 1.13499i | −0.326537 | − | 0.945184i | \(-0.605882\pi\) |
0.981822 | − | 0.189803i | \(-0.0607849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5726 | + | 26.9725i | −0.871898 | + | 1.51017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5114 | + | 37.2589i | 1.20065 | + | 2.07959i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.348662 | − | 7.12482i | 0.0194001 | − | 0.396436i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0457 | − | 36.4523i | −1.16741 | − | 2.02201i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.4555 | − | 15.2741i | −1.46300 | − | 0.844661i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.864595 | − | 1.49752i | 0.0476667 | − | 0.0825611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7128i | 1.24841i | 0.781261 | + | 0.624205i | \(0.214577\pi\) | ||||
−0.781261 | + | 0.624205i | \(0.785423\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6006 | + | 21.8249i | −0.690510 | + | 1.19600i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −51.4803 | −2.81267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0531 | + | 8.69090i | −0.819994 | + | 0.473423i | −0.850414 | − | 0.526114i | \(-0.823649\pi\) |
0.0304207 | + | 0.999537i | \(0.490315\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0519 | + | 20.8746i | 0.654571 | + | 1.13375i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.62372 | −0.250388 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.10896i | − | 0.383848i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 65.6013 | − | 37.8749i | 3.53186 | − | 2.03912i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.10782 | + | 10.5791i | 0.327885 | + | 0.567914i | 0.982092 | − | 0.188402i | \(-0.0603308\pi\) |
−0.654207 | + | 0.756316i | \(0.726997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8033i | 0.738874i | 0.929256 | + | 0.369437i | \(0.120449\pi\) | ||||
−0.929256 | + | 0.369437i | \(0.879551\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.5371 | + | 6.66093i | 0.615803 | + | 0.355534i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.84663 | 0.311185 | 0.155592 | − | 0.987821i | \(-0.450271\pi\) | ||||
0.155592 | + | 0.987821i | \(0.450271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.2786 | − | 18.6360i | −1.71317 | − | 0.989098i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.15691 | − | 2.00383i | 0.0612301 | − | 0.106054i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.3471 | − | 8.28328i | 0.757209 | − | 0.437175i | −0.0710840 | − | 0.997470i | \(-0.522646\pi\) |
0.828293 | + | 0.560296i | \(0.189313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.84802 | + | 17.3034i | 0.413053 | + | 0.910707i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −36.8734 | + | 21.2889i | −1.93535 | + | 1.11738i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.9479 | − | 12.0943i | −1.09646 | − | 0.633043i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.2106 | + | 15.1327i | 1.36818 | + | 0.789919i | 0.990696 | − | 0.136097i | \(-0.0434557\pi\) |
0.377485 | + | 0.926016i | \(0.376789\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.7145i | 1.39070i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.94782 | − | 2.27928i | −0.204961 | − | 0.118334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1762 | −0.578682 | −0.289341 | − | 0.957226i | \(-0.593436\pi\) | ||||
−0.289341 | + | 0.957226i | \(0.593436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −43.4686 | − | 75.2898i | −2.24471 | − | 3.88795i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0966 | + | 17.4878i | 0.520002 | + | 0.900669i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.728987i | − | 0.0374456i | −0.999825 | − | 0.0187228i | \(-0.994040\pi\) | ||
0.999825 | − | 0.0187228i | \(-0.00595999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.57014i | 0.285367i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.531034 | − | 0.919778i | −0.0271346 | − | 0.0469985i | 0.852139 | − | 0.523315i | \(-0.175305\pi\) |
−0.879274 | + | 0.476317i | \(0.841972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.59799 | + | 9.69600i | 0.285300 | + | 0.494154i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.8208 | −1.31255 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.3980 | + | 15.8183i | 1.38914 | + | 0.802018i | 0.993218 | − | 0.116268i | \(-0.0370930\pi\) |
0.395918 | + | 0.918286i | \(0.370426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.8225i | − | 0.547317i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.0124 | − | 16.7503i | −1.46348 | − | 0.844941i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.17431 | + | 2.98739i | 0.260348 | + | 0.150312i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.05761 | − | 0.610610i | 0.0530798 | − | 0.0306456i | −0.473225 | − | 0.880941i | \(-0.656910\pi\) |
0.526305 | + | 0.850296i | \(0.323577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.301232 | + | 6.15560i | −0.0150804 | + | 0.308165i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3396 | + | 14.0524i | −1.21546 | + | 0.701746i | −0.963943 | − | 0.266107i | \(-0.914262\pi\) |
−0.251516 | + | 0.967853i | \(0.580929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.49891 | + | 2.59619i | −0.0746661 | + | 0.129325i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.05991 | − | 5.23074i | −0.450191 | − | 0.259918i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.1436 | −1.44460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1185 | + | 11.6154i | 0.994798 | + | 0.574347i | 0.906705 | − | 0.421766i | \(-0.138589\pi\) |
0.0880927 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 44.3161i | − | 2.18595i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0325822 | − | 0.0564340i | −0.00160326 | − | 0.00277693i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.14078 | + | 1.81333i | −0.154175 | + | 0.0890128i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 15.9193i | − | 0.779569i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.85347 | 0.139401 | 0.0697005 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0697005 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04634 | − | 10.4726i | −0.294680 | − | 0.510401i | 0.680230 | − | 0.732999i | \(-0.261880\pi\) |
−0.974911 | + | 0.222597i | \(0.928547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.8984 | − | 7.44692i | 0.627144 | − | 0.362082i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.6033 | −0.999409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.03624 | + | 5.25892i | −0.146934 | + | 0.254497i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 47.0837i | 2.27322i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.94883 | − | 10.3037i | 0.286545 | − | 0.496311i | −0.686438 | − | 0.727189i | \(-0.740826\pi\) |
0.972983 | + | 0.230878i | \(0.0741598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3848 | − | 8.30507i | −0.691290 | − | 0.399116i | 0.112805 | − | 0.993617i | \(-0.464016\pi\) |
−0.804095 | + | 0.594501i | \(0.797350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 34.5919 | + | 59.9149i | 1.65855 | + | 2.87270i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1757 | + | 25.6389i | 0.630278 | + | 1.22647i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5028 | + | 33.7799i | 0.930819 | + | 1.61223i | 0.781925 | + | 0.623373i | \(0.214238\pi\) |
0.148894 | + | 0.988853i | \(0.452429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.0089 | − | 25.9963i | 0.714712 | − | 1.23792i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.38865 | − | 9.33341i | 0.256022 | − | 0.443444i | −0.709150 | − | 0.705057i | \(-0.750921\pi\) |
0.965173 | + | 0.261613i | \(0.0842546\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −62.1421 | −2.94582 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.8103 | + | 34.3124i | −0.936994 | + | 1.62292i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.4665i | 0.682718i | 0.939933 | + | 0.341359i | \(0.110887\pi\) | ||||
−0.939933 | + | 0.341359i | \(0.889113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.7546 | + | 15.4468i | −1.25983 | + | 0.727361i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.07252 | − | 3.50597i | 0.285312 | − | 0.164725i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.25900 | 0.340307 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5191 | 1.42762 | 0.713812 | − | 0.700338i | \(-0.246967\pi\) | ||||
0.713812 | + | 0.700338i | \(0.246967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.64728 | − | 3.26046i | 0.263593 | − | 0.152185i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.5484 | − | 10.7089i | 0.863883 | − | 0.498763i | −0.00142759 | − | 0.999999i | \(-0.500454\pi\) |
0.865311 | + | 0.501236i | \(0.167121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.2533i | − | 1.08067i | −0.841449 | − | 0.540337i | \(-0.818297\pi\) | ||
0.841449 | − | 0.540337i | \(-0.181703\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.13540 | + | 8.89478i | −0.238149 | + | 0.412486i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.15654 | 0.238616 | 0.119308 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119308 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.17726 | − | 5.50317i | 0.146712 | − | 0.254113i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.44260 | − | 11.1589i | 0.296859 | − | 0.514175i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.9301 | − | 25.8596i | −0.686484 | − | 1.18903i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.8101 | − | 25.0832i | 2.23956 | − | 1.15090i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.6318 | − | 34.0033i | −0.898880 | − | 1.55691i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3508 | − | 6.55337i | −0.518630 | − | 0.299431i | 0.217744 | − | 0.976006i | \(-0.430130\pi\) |
−0.736374 | + | 0.676575i | \(0.763464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.44774 | + | 16.3640i | −0.430780 | + | 0.746133i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.35025i | 0.425451i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.128530 | + | 0.222621i | −0.00583627 | + | 0.0101087i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.2172 | 0.825499 | 0.412750 | − | 0.910845i | \(-0.364568\pi\) | ||||
0.412750 | + | 0.910845i | \(0.364568\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.5576 | + | 18.7972i | −1.47231 | + | 0.850037i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.46771 | + | 11.2024i | 0.291884 | + | 0.505557i | 0.974255 | − | 0.225448i | \(-0.0723847\pi\) |
−0.682372 | + | 0.731005i | \(0.739051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.88438 | 0.445170 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 96.4331i | 4.33434i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.98433 | − | 2.30036i | 0.178722 | − | 0.103185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.73102 | + | 2.99822i | 0.0774912 | + | 0.134219i | 0.902167 | − | 0.431387i | \(-0.141976\pi\) |
−0.824676 | + | 0.565606i | \(0.808642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 52.6538i | − | 2.35240i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.56977 | + | 0.906306i | 0.0699925 | + | 0.0404102i | 0.534588 | − | 0.845113i | \(-0.320467\pi\) |
−0.464595 | + | 0.885523i | \(0.653800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.5899 | −0.782739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.31058 | − | 2.48871i | −0.191439 | − | 0.110528i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.7070 | + | 30.6694i | −0.784847 | + | 1.35940i | 0.144243 | + | 0.989542i | \(0.453925\pi\) |
−0.929090 | + | 0.369853i | \(0.879408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.58572 | − | 1.49287i | 0.114386 | − | 0.0660406i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.40922 | + | 14.5993i | −0.415427 | + | 0.644577i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.1642 | − | 14.5285i | 1.10887 | − | 0.640204i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9162 | + | 8.61189i | 0.656015 | + | 0.378750i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.6404 | − | 6.14324i | −0.467062 | − | 0.269658i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.3979i | − | 0.981271i | −0.871365 | − | 0.490636i | \(-0.836765\pi\) | ||
0.871365 | − | 0.490636i | \(-0.163235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.06121 | + | 4.07679i | 0.308765 | + | 0.178266i | 0.646374 | − | 0.763021i | \(-0.276285\pi\) |
−0.337609 | + | 0.941287i | \(0.609618\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.8006 | 0.776881 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.733702 | + | 1.27081i | 0.0319606 | + | 0.0553573i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.3671 | + | 17.9564i | 0.450744 | + | 0.780711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.561272i | − | 0.0243571i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.0301i | 0.867599i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.0340 | + | 57.2165i | 1.42818 | + | 2.47369i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.8848 | − | 43.1017i | −1.07386 | − | 1.85998i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.7138 | 1.49523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.9988 | + | 15.5877i | 1.16077 | + | 0.670169i | 0.951488 | − | 0.307686i | \(-0.0995548\pi\) |
0.209280 | + | 0.977856i | \(0.432888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 21.0631i | − | 0.903905i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.6264 | − | 23.4556i | −1.74024 | − | 1.00473i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.5877 | − | 8.99959i | −0.666484 | − | 0.384795i | 0.128259 | − | 0.991741i | \(-0.459061\pi\) |
−0.794743 | + | 0.606946i | \(0.792394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −45.2961 | + | 26.1517i | −1.93319 | + | 1.11613i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.4164 | + | 12.0336i | −0.997574 | + | 0.512648i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.638695 | + | 0.368751i | −0.0271601 | + | 0.0156809i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.3688 | + | 56.0644i | −1.37398 | + | 2.37980i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.2517 | − | 5.91880i | −0.434377 | − | 0.250788i | 0.266833 | − | 0.963743i | \(-0.414023\pi\) |
−0.701209 | + | 0.712955i | \(0.747356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3600 | −0.818842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9593 | + | 11.5235i | 0.842682 | + | 0.486523i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7445i | 1.08500i | 0.840055 | + | 0.542501i | \(0.182522\pi\) | ||||
−0.840055 | + | 0.542501i | \(0.817478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5075 | + | 32.0560i | 0.778617 | + | 1.34860i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.11832 | − | 0.645661i | 0.0469650 | − | 0.0271152i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.17502i | − | 0.258870i | −0.991588 | − | 0.129435i | \(-0.958684\pi\) | ||
0.991588 | − | 0.129435i | \(-0.0413164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7592 | −0.952445 | −0.476222 | − | 0.879325i | \(-0.657994\pi\) | ||||
−0.476222 | + | 0.879325i | \(0.657994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.67468 | + | 2.90063i | 0.0699607 | + | 0.121176i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 72.1045 | − | 41.6296i | 3.00697 | − | 1.73607i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.49715 | 0.228849 | 0.114425 | − | 0.993432i | \(-0.463498\pi\) | ||||
0.114425 | + | 0.993432i | \(0.463498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.7723 | − | 18.6582i | 0.447683 | − | 0.775409i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.447660i | − | 0.0185721i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.7030 | − | 39.3227i | 0.940261 | − | 1.62858i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 54.1466 | + | 31.2615i | 2.23869 | + | 1.29251i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.79820 | + | 6.57868i | 0.156769 | + | 0.271531i | 0.933702 | − | 0.358052i | \(-0.116559\pi\) |
−0.776933 | + | 0.629583i | \(0.783226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.28530 | − | 2.11736i | −0.135368 | − | 0.0872442i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.9254 | − | 41.4400i | −0.984159 | − | 1.70461i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9545 | + | 18.9737i | −0.449846 | + | 0.779156i | −0.998376 | − | 0.0569751i | \(-0.981854\pi\) |
0.548530 | + | 0.836131i | \(0.315188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.77660 | − | 3.07717i | 0.0728336 | − | 0.126152i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.70854 | 0.315490 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.88383 | + | 15.3872i | −0.362983 | + | 0.628706i | −0.988450 | − | 0.151545i | \(-0.951575\pi\) |
0.625467 | + | 0.780251i | \(0.284909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.6279i | − | 0.841428i | −0.907193 | − | 0.420714i | \(-0.861780\pi\) | ||
0.907193 | − | 0.420714i | \(-0.138220\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 47.3998 | − | 27.3663i | 1.93027 | − | 1.11444i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −56.6245 | + | 32.6922i | −2.30211 | + | 1.32913i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.1800 | 1.87439 | 0.937195 | − | 0.348807i | \(-0.113413\pi\) | ||||
0.937195 | + | 0.348807i | \(0.113413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.53976 | −0.346048 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.67104 | − | 5.58358i | 0.391249 | − | 0.225887i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.0710 | + | 17.9389i | −1.25495 | + | 0.724544i | −0.972088 | − | 0.234617i | \(-0.924616\pi\) |
−0.282859 | + | 0.959161i | \(0.591283\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 68.6248i | 2.76722i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0899 | − | 27.8685i | 0.647754 | − | 1.12194i | −0.335904 | − | 0.941896i | \(-0.609042\pi\) |
0.983658 | − | 0.180046i | \(-0.0576248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.14561 | −0.0862393 | −0.0431197 | − | 0.999070i | \(-0.513730\pi\) | ||||
−0.0431197 | + | 0.999070i | \(0.513730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.1757 | + | 22.8209i | −0.528722 | + | 0.915773i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.83528 | − | 6.64290i | 0.153657 | − | 0.266142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −35.2777 | − | 61.1028i | −1.41111 | − | 2.44411i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −61.3134 | − | 3.00045i | −2.44862 | − | 0.119826i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.62458 | + | 8.01000i | 0.184394 | + | 0.319380i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7086 | + | 20.6164i | 1.42154 | + | 0.820725i | 0.996430 | − | 0.0844176i | \(-0.0269030\pi\) |
0.425107 | + | 0.905143i | \(0.360236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.2539 | − | 24.6885i | 0.566543 | − | 0.981281i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.55376i | 0.339446i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.2535 | − | 19.4916i | 0.445879 | − | 0.772284i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39.6268 | 1.56761 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9918 | + | 10.9649i | −0.750132 | + | 0.433089i | −0.825742 | − | 0.564049i | \(-0.809243\pi\) |
0.0756095 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5674 | + | 33.8918i | 0.771664 | + | 1.33656i | 0.936650 | + | 0.350266i | \(0.113909\pi\) |
−0.164986 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −66.3292 | −2.61171 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.2393i | − | 0.952944i | −0.879190 | − | 0.476472i | \(-0.841915\pi\) | ||
0.879190 | − | 0.476472i | \(-0.158085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.562116 | − | 0.324538i | 0.0220650 | − | 0.0127392i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.633893 | − | 1.09794i | −0.0248442 | − | 0.0430315i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.6718i | 0.965481i | 0.875764 | + | 0.482740i | \(0.160358\pi\) | ||||
−0.875764 | + | 0.482740i | \(0.839642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.5528 | − | 25.7225i | −1.74082 | − | 1.00506i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.7167 | 1.00330 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.66292 | + | 2.69214i | 0.181642 | + | 0.104871i | 0.588064 | − | 0.808815i | \(-0.299890\pi\) |
−0.406422 | + | 0.913685i | \(0.633224\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5097 | − | 18.2034i | 0.408781 | − | 0.708030i | −0.585972 | − | 0.810331i | \(-0.699287\pi\) |
0.994753 | + | 0.102301i | \(0.0326206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9408 | − | 7.47135i | 0.502577 | − | 0.290163i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.462585 | + | 9.45282i | −0.0179383 | + | 0.366565i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.5919 | + | 19.9716i | −1.33940 | + | 0.773305i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.70306 | + | 1.56061i | 0.104506 | + | 0.0603367i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.3820 | − | 30.2428i | −2.02218 | − | 1.16751i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.54322i | 0.175128i | 0.996159 | + | 0.0875641i | \(0.0279083\pi\) | ||||
−0.996159 | + | 0.0875641i | \(0.972092\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43.4454 | + | 25.0832i | 1.67222 | + | 0.965454i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.30681 | −0.165524 | −0.0827620 | − | 0.996569i | \(-0.526374\pi\) | ||||
−0.0827620 | + | 0.996569i | \(0.526374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0158653 | − | 0.0274795i | −0.000608853 | − | 0.00105456i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2129 | − | 40.2059i | −0.889521 | − | 1.54070i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.9152i | 1.18294i | 0.806328 | + | 0.591469i | \(0.201452\pi\) | ||||
−0.806328 | + | 0.591469i | \(0.798548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 68.0538i | − | 2.60020i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.1066 | + | 41.7539i | 0.919726 | + | 1.59301i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.7196 | − | 25.4952i | −0.560773 | − | 0.971288i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3086 | − | 5.95165i | −0.391590 | − | 0.226084i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 24.4463i | − | 0.927303i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.49096 | + | 4.90226i | 0.321618 | + | 0.185686i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.1259 | + | 21.4346i | 1.40423 | + | 0.810732i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.25585 | − | 4.76652i | 0.311819 | − | 0.180029i | −0.335921 | − | 0.941890i | \(-0.609048\pi\) |
0.647740 | + | 0.761861i | \(0.275714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.7075 | − | 13.3459i | −0.780996 | − | 0.503349i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.1339 | − | 19.1298i | 1.24789 | − | 0.720472i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.08561 | − | 1.88033i | 0.0408286 | − | 0.0707172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.08068 | + | 1.77863i | 0.115697 | + | 0.0667979i | 0.556732 | − | 0.830692i | \(-0.312055\pi\) |
−0.441035 | + | 0.897490i | \(0.645388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.35224 | −0.238228 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.13540 | − | 2.96493i | −0.192322 | − | 0.111037i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 72.3039i | 2.70401i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.0518 | − | 64.1756i | −1.38373 | − | 2.39668i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.6518 | − | 25.7797i | 1.66523 | − | 0.961422i | 0.695077 | − | 0.718935i | \(-0.255370\pi\) |
0.970155 | − | 0.242487i | \(-0.0779631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.58669i | 0.133575i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 65.1256 | 2.42205 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.0210 | + | 65.8544i | 1.41207 | + | 2.44577i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0229 | + | 9.25080i | −0.594255 | + | 0.343093i | −0.766778 | − | 0.641912i | \(-0.778141\pi\) |
0.172523 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7702 | 1.62112 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.73827 | + | 8.20692i | −0.175251 | + | 0.303544i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.1522i | − | 0.670468i | −0.942135 | − | 0.335234i | \(-0.891185\pi\) | ||
0.942135 | − | 0.335234i | \(-0.108815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 38.5554 | − | 66.7799i | 1.42214 | − | 2.46321i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.8149 | + | 31.6474i | 2.01913 | + | 1.16575i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.3465 | − | 33.5092i | −0.711674 | − | 1.23266i | −0.964228 | − | 0.265073i | \(-0.914604\pi\) |
0.252554 | − | 0.967583i | \(-0.418729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.5612 | + | 33.4544i | −0.792072 | + | 1.22898i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.7183 | + | 20.2967i | 0.429904 | + | 0.744615i | 0.996864 | − | 0.0791296i | \(-0.0252141\pi\) |
−0.566960 | + | 0.823745i | \(0.691881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.4216 | + | 52.6917i | −1.11456 | + | 1.93048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.92789 | − | 3.33920i | 0.0705377 | − | 0.122175i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.15516 | −0.297983 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1045 | − | 24.4297i | 0.514681 | − | 0.891453i | −0.485174 | − | 0.874417i | \(-0.661244\pi\) |
0.999855 | − | 0.0170354i | \(-0.00542281\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.26785i | 0.0462030i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.32525 | − | 5.38394i | 0.339381 | − | 0.195942i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.9738 | − | 9.22249i | 0.580579 | − | 0.335197i | −0.180785 | − | 0.983523i | \(-0.557864\pi\) |
0.761363 | + | 0.648325i | \(0.224530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −93.1341 | −3.38055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.41232 | 0.0874467 | 0.0437234 | − | 0.999044i | \(-0.486078\pi\) | ||||
0.0437234 | + | 0.999044i | \(0.486078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.01475 | − | 2.89527i | 0.181546 | − | 0.104816i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.5042 | − | 15.3022i | 0.958262 | − | 0.553253i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.420833i | − | 0.0151954i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.86628 | + | 10.1607i | −0.211544 | + | 0.366404i | −0.952198 | − | 0.305482i | \(-0.901182\pi\) |
0.740654 | + | 0.671886i | \(0.234516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.7212 | 1.10640 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.188383 | − | 0.326288i | 0.00677565 | − | 0.0117358i | −0.862618 | − | 0.505856i | \(-0.831177\pi\) |
0.869393 | + | 0.494121i | \(0.164510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.64449 | + | 9.77654i | −0.202756 | + | 0.351184i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.99547 | − | 6.92036i | −0.143337 | − | 0.248267i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.0836 | − | 1.27643i | −0.934542 | − | 0.0457329i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.9129 | + | 39.6863i | 0.819889 | + | 1.42009i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.8428 | − | 12.0336i | −0.744860 | − | 0.430045i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.89355 | − | 17.1361i | 0.353116 | − | 0.611615i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.71274i | − | 0.132345i | −0.997808 | − | 0.0661725i | \(-0.978921\pi\) | ||
0.997808 | − | 0.0661725i | \(-0.0210788\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.8255 | + | 20.4823i | −0.420998 | + | 0.729190i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.56898 | −0.162454 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.9622 | + | 19.6081i | −1.20603 | + | 0.696304i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −50.4308 | − | 87.3487i | −1.78860 | − | 3.09794i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.03774 | 0.0367587 | 0.0183794 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183794 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.46621i | − | 0.193381i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.2165 | − | 33.0340i | 2.02165 | − | 1.16720i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.8699 | + | 25.7553i | 0.524746 | + | 0.908886i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.3587i | 0.506077i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5266 | − | 10.6963i | −0.652166 | − | 0.376528i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8898 | 0.839921 | 0.419961 | − | 0.907542i | \(-0.362044\pi\) | ||||
0.419961 | + | 0.907542i | \(0.362044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1720 | − | 14.5331i | −0.883909 | − | 0.510325i | −0.0119635 | − | 0.999928i | \(-0.503808\pi\) |
−0.871945 | + | 0.489604i | \(0.837142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3407 | + | 19.6426i | −0.397735 | + | 0.688897i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.9970 | + | 28.8658i | −1.75132 | + | 1.01112i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.23373 | − | 25.2110i | 0.0431628 | − | 0.882022i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.68363 | + | 3.85880i | −0.233545 | + | 0.134837i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0386 | + | 17.3428i | 1.04835 | + | 0.605268i | 0.922188 | − | 0.386741i | \(-0.126399\pi\) |
0.126166 | + | 0.992009i | \(0.459733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.7332 | − | 9.66093i | −0.583284 | − | 0.336759i | 0.179154 | − | 0.983821i | \(-0.442664\pi\) |
−0.762437 | + | 0.647062i | \(0.775997\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 177.304i | 6.17294i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.4175 | − | 18.1389i | −1.09249 | − | 0.630752i | −0.158255 | − | 0.987398i | \(-0.550587\pi\) |
−0.934240 | + | 0.356646i | \(0.883920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.8855 | 1.17689 | 0.588446 | − | 0.808537i | \(-0.299740\pi\) | ||||
0.588446 | + | 0.808537i | \(0.299740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.0794 | + | 57.2952i | 1.14751 | + | 1.98755i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.50846 | − | 9.54093i | −0.190857 | − | 0.330574i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 80.8577i | − | 2.79820i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.57294i | − | 0.123499i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.0241 | + | 22.5585i | 0.449643 | + | 0.778805i | 0.998363 | − | 0.0572016i | \(-0.0182178\pi\) |
−0.548719 | + | 0.836007i | \(0.684884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.74045 | − | 6.47865i | −0.128981 | − | 0.223402i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 64.9050 | 2.23545 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.61952 | − | 3.82178i | −0.227719 | − | 0.131473i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.07077i | − | 0.277315i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9532 | + | 14.9841i | 0.890712 | + | 0.514253i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.3688 | − | 18.6881i | −1.10959 | − | 0.640621i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.3566 | + | 20.9905i | −1.24483 | + | 0.718700i | −0.970073 | − | 0.242814i | \(-0.921929\pi\) |
−0.274753 | + | 0.961515i | \(0.588596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −44.1600 | + | 68.5187i | −1.51024 | + | 2.34329i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.3601 | + | 19.8378i | −1.17372 | + | 0.677647i | −0.954553 | − | 0.298041i | \(-0.903667\pi\) |
−0.219166 | + | 0.975688i | \(0.570334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.13531 | + | 5.43052i | −0.106976 | + | 0.185287i | −0.914544 | − | 0.404487i | \(-0.867450\pi\) |
0.807568 | + | 0.589774i | \(0.200783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.33590 | − | 4.23538i | −0.250007 | − | 0.144341i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.41486 | 0.320486 | 0.160243 | − | 0.987078i | \(-0.448772\pi\) | ||||
0.160243 | + | 0.987078i | \(0.448772\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3399 | − | 9.43384i | −0.555573 | − | 0.320760i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.1147i | 1.32840i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.67298 | − | 6.36179i | −0.124597 | − | 0.215809i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5396 | − | 20.5188i | 1.20421 | − | 0.695253i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.273301i | − | 0.00924984i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.4793 | 0.557101 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2475 | − | 48.9261i | −0.953850 | − | 1.65212i | −0.736979 | − | 0.675916i | \(-0.763748\pi\) |
−0.216871 | − | 0.976200i | \(-0.569585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.4997 | + | 23.9599i | −1.39975 | + | 0.808146i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6960 | 0.596194 | 0.298097 | − | 0.954536i | \(-0.403648\pi\) | ||||
0.298097 | + | 0.954536i | \(0.403648\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.9929 | + | 32.8967i | −0.639162 | + | 1.10706i | 0.346455 | + | 0.938067i | \(0.387385\pi\) |
−0.985617 | + | 0.168995i | \(0.945948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 1.44181i | − | 0.0484660i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.86641 | + | 11.8930i | −0.230552 | + | 0.399327i | −0.957971 | − | 0.286867i | \(-0.907386\pi\) |
0.727419 | + | 0.686194i | \(0.240720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.914385 | − | 0.527920i | −0.0306675 | − | 0.0177059i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.43117 | + | 11.1391i | 0.215452 | + | 0.373175i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.65476 | + | 12.9497i | 0.222693 | + | 0.433344i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.2143 | − | 66.1890i | −1.27736 | − | 2.21246i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.1921 | + | 52.2942i | −1.00808 | + | 1.74605i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.70792 | − | 4.69026i | 0.0903143 | − | 0.156429i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4102 | −0.480074 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.09370 | − | 7.09050i | 0.136230 | − | 0.235957i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 32.3455i | − | 1.07520i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4366 | − | 9.48966i | 0.545767 | − | 0.315099i | −0.201646 | − | 0.979459i | \(-0.564629\pi\) |
0.747413 | + | 0.664360i | \(0.231296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1957 | − | 9.35056i | 0.537176 | − | 0.310139i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.4639 | −0.677999 | −0.339000 | − | 0.940787i | \(-0.610089\pi\) | ||||
−0.339000 | + | 0.940787i | \(0.610089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.45896 | 0.147570 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −116.358 | + | 67.1792i | −3.84667 | + | 2.22087i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.49941 | − | 3.17509i | 0.181606 | − | 0.104851i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.78362i | − | 0.289745i | −0.989450 | − | 0.144872i | \(-0.953723\pi\) | ||
0.989450 | − | 0.144872i | \(-0.0462772\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.8339 | + | 56.8700i | −1.08191 | + | 1.87393i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7115 | 0.977967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.5776 | + | 61.6222i | −1.16978 | + | 2.02613i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.4464 | + | 26.7539i | −0.507326 | + | 0.878715i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7264 | − | 25.5068i | −0.483157 | − | 0.836852i | 0.516656 | − | 0.856193i | \(-0.327176\pi\) |
−0.999813 | + | 0.0193411i | \(0.993843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6652 | + | 15.8966i | 0.808370 | + | 0.520991i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.1822 | + | 34.9566i | 0.660735 | + | 1.14443i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.6504 | + | 17.6960i | 1.00238 | + | 0.578722i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0966 | − | 17.4878i | 0.329841 | − | 0.571302i | −0.652639 | − | 0.757669i | \(-0.726338\pi\) |
0.982480 | + | 0.186367i | \(0.0596715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 50.3829i | − | 1.64418i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.1773 | − | 34.9481i | 0.657761 | − | 1.13927i | −0.323433 | − | 0.946251i | \(-0.604837\pi\) |
0.981194 | − | 0.193024i | \(-0.0618295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.6206 | −1.29022 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.49250 | + | 4.32580i | −0.243731 | + | 0.140718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.63893 | − | 14.9631i | −0.280727 | − | 0.486234i | 0.690837 | − | 0.723011i | \(-0.257242\pi\) |
−0.971564 | + | 0.236777i | \(0.923909\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.2820 | 0.625919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 63.7280i | 2.06652i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.4050 | + | 15.2449i | −0.855342 | + | 0.493832i | −0.862450 | − | 0.506143i | \(-0.831071\pi\) |
0.00710753 | + | 0.999975i | \(0.497738\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.57172 | + | 4.45434i | 0.0832188 | + | 0.144139i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 85.0611i | − | 2.74963i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.27486 | + | 4.20014i | 0.234918 | + | 0.135630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1960 | −0.974064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60.8312 | − | 35.1209i | −1.96026 | − | 1.13176i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5425 | − | 28.6524i | 0.532522 | − | 0.922355i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7891 | + | 10.2705i | −0.572058 | + | 0.330278i | −0.757971 | − | 0.652289i | \(-0.773809\pi\) |
0.185913 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.90469 | + | 17.3278i | 0.286060 | + | 0.556651i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.6910 | − | 27.5344i | 1.53048 | − | 0.883621i | 0.531138 | − | 0.847286i | \(-0.321765\pi\) |
0.999340 | − | 0.0363358i | \(-0.0115686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.61328 | + | 1.50878i | 0.0837779 | + | 0.0483692i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 99.5553 | + | 57.4783i | 3.18832 | + | 1.84078i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.44407i | 0.0461999i | 0.999733 | + | 0.0230999i | \(0.00735359\pi\) | ||||
−0.999733 | + | 0.0230999i | \(0.992646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.1672 | + | 38.2017i | 2.11471 | + | 1.22093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 49.8750 | 1.59239 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.04964 | − | 13.9424i | −0.256743 | − | 0.444693i | 0.708624 | − | 0.705586i | \(-0.249316\pi\) |
−0.965368 | + | 0.260893i | \(0.915983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.7409 | − | 63.6372i | −1.17066 | − | 2.02765i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.72262i | 0.150323i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 38.2952i | − | 1.21772i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.11258 | + | 12.3193i | 0.225939 | + | 0.391337i | 0.956601 | − | 0.291402i | \(-0.0941218\pi\) |
−0.730662 | + | 0.682739i | \(0.760788\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.0157 | − | 53.7207i | −0.984253 | − | 1.70478i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8376 | 0.375277 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6169 | + | 16.5220i | 0.906308 | + | 0.523257i | 0.879241 | − | 0.476377i | \(-0.158050\pi\) |
0.0270664 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 22.5205i | − | 0.712517i |
(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 | 1216.2.s.i.31.4 | yes | 32 | |
4.3 | odd | 2 | inner | 1216.2.s.i.31.14 | yes | 32 | |
8.3 | odd | 2 | inner | 1216.2.s.i.31.3 | ✓ | 32 | |
8.5 | even | 2 | inner | 1216.2.s.i.31.13 | yes | 32 | |
19.8 | odd | 6 | inner | 1216.2.s.i.863.3 | yes | 32 | |
76.27 | even | 6 | inner | 1216.2.s.i.863.13 | yes | 32 | |
152.27 | even | 6 | inner | 1216.2.s.i.863.4 | yes | 32 | |
152.141 | odd | 6 | inner | 1216.2.s.i.863.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.i.31.3 | ✓ | 32 | 8.3 | odd | 2 | inner | |
1216.2.s.i.31.4 | yes | 32 | 1.1 | even | 1 | trivial | |
1216.2.s.i.31.13 | yes | 32 | 8.5 | even | 2 | inner | |
1216.2.s.i.31.14 | yes | 32 | 4.3 | odd | 2 | inner | |
1216.2.s.i.863.3 | yes | 32 | 19.8 | odd | 6 | inner | |
1216.2.s.i.863.4 | yes | 32 | 152.27 | even | 6 | inner | |
1216.2.s.i.863.13 | yes | 32 | 76.27 | even | 6 | inner | |
1216.2.s.i.863.14 | yes | 32 | 152.141 | odd | 6 | inner |