Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 802.5 | ||
Root | \(0.474636 - 0.274031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.802 |
Dual form | 1323.2.h.g.226.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.69963 | 1.20182 | 0.600909 | − | 0.799317i | \(-0.294805\pi\) | ||||
0.600909 | + | 0.799317i | \(0.294805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.888736 | 0.444368 | ||||||||
\(5\) | −0.474636 | + | 0.822093i | −0.212263 | + | 0.367651i | −0.952423 | − | 0.304781i | \(-0.901417\pi\) |
0.740159 | + | 0.672432i | \(0.234750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.88874 | −0.667769 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.806704 | + | 1.39725i | −0.255102 | + | 0.441850i | ||||
\(11\) | −0.294182 | − | 0.509538i | −0.0886992 | − | 0.153632i | 0.818262 | − | 0.574845i | \(-0.194938\pi\) |
−0.906962 | + | 0.421213i | \(0.861604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50987 | + | 4.34722i | 0.696112 | + | 1.20570i | 0.969804 | + | 0.243885i | \(0.0784218\pi\) |
−0.273692 | + | 0.961817i | \(0.588245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98762 | −1.24691 | ||||||||
\(17\) | −3.79121 | + | 6.56657i | −0.919503 | + | 1.59263i | −0.119332 | + | 0.992854i | \(0.538075\pi\) |
−0.800171 | + | 0.599772i | \(0.795258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.23061 | + | 3.86353i | 0.511737 | + | 0.886355i | 0.999907 | + | 0.0136063i | \(0.00433116\pi\) |
−0.488170 | + | 0.872748i | \(0.662336\pi\) | |||||||
\(20\) | −0.421826 | + | 0.730623i | −0.0943231 | + | 0.163372i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 1.23855 | − | 2.14523i | 0.258256 | − | 0.447312i | −0.707519 | − | 0.706694i | \(-0.750186\pi\) |
0.965775 | + | 0.259382i | \(0.0835190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.04944 | + | 3.54974i | 0.409888 | + | 0.709948i | ||||
\(26\) | 4.26584 | + | 7.38866i | 0.836601 | + | 1.44904i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.73855 | − | 4.74331i | 0.508536 | − | 0.880810i | −0.491415 | − | 0.870925i | \(-0.663520\pi\) |
0.999951 | − | 0.00988468i | \(-0.00314644\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.07463 | −1.09104 | −0.545518 | − | 0.838099i | \(-0.683667\pi\) | ||||
−0.545518 | + | 0.838099i | \(0.683667\pi\) | |||||||
\(32\) | −4.69963 | −0.830785 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.44364 | + | 11.1607i | −1.10508 | + | 1.91405i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.49381 | + | 6.05146i | 0.574379 | + | 0.994853i | 0.996109 | + | 0.0881319i | \(0.0280897\pi\) |
−0.421730 | + | 0.906721i | \(0.638577\pi\) | |||||||
\(38\) | 3.79121 | + | 6.56657i | 0.615015 | + | 1.06524i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.896461 | − | 1.55272i | 0.141743 | − | 0.245506i | ||||
\(41\) | −0.527445 | − | 0.913562i | −0.0823731 | − | 0.142674i | 0.821896 | − | 0.569638i | \(-0.192917\pi\) |
−0.904269 | + | 0.426964i | \(0.859583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.49381 | + | 6.05146i | −0.532801 | + | 0.922838i | 0.466465 | + | 0.884540i | \(0.345527\pi\) |
−0.999266 | + | 0.0382990i | \(0.987806\pi\) | |||||||
\(44\) | −0.261450 | − | 0.452845i | −0.0394151 | − | 0.0682689i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.10507 | − | 3.64610i | 0.310376 | − | 0.537587i | ||||
\(47\) | 7.47680 | 1.09060 | 0.545301 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545301 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.48329 | + | 6.03323i | 0.492612 | + | 0.853228i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.23061 | + | 3.86353i | 0.309330 | + | 0.535775i | ||||
\(53\) | 3.46108 | − | 5.99476i | 0.475416 | − | 0.823444i | −0.524188 | − | 0.851603i | \(-0.675631\pi\) |
0.999603 | + | 0.0281586i | \(0.00896435\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.558517 | 0.0753104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.65452 | − | 8.06186i | 0.611168 | − | 1.05857i | ||||
\(59\) | −10.4302 | −1.35790 | −0.678950 | − | 0.734184i | \(-0.737565\pi\) | ||||
−0.678950 | + | 0.734184i | \(0.737565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6529 | 1.49200 | 0.745999 | − | 0.665947i | \(-0.231972\pi\) | ||||
0.745999 | + | 0.665947i | \(0.231972\pi\) | |||||||
\(62\) | −10.3246 | −1.31123 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98762 | 0.248453 | ||||||||
\(65\) | −4.76509 | −0.591037 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8640 | −1.44942 | −0.724708 | − | 0.689056i | \(-0.758025\pi\) | ||||
−0.724708 | + | 0.689056i | \(0.758025\pi\) | |||||||
\(68\) | −3.36938 | + | 5.83594i | −0.408598 | + | 0.707712i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.30037 | −0.510360 | −0.255180 | − | 0.966894i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.23061 | + | 3.86353i | −0.261073 | + | 0.452192i | −0.966527 | − | 0.256563i | \(-0.917410\pi\) |
0.705454 | + | 0.708756i | \(0.250743\pi\) | |||||||
\(74\) | 5.93818 | + | 10.2852i | 0.690299 | + | 1.19563i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.98242 | + | 3.43366i | 0.227400 | + | 0.393868i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33379 | −0.150063 | −0.0750317 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750317 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(80\) | 2.36730 | − | 4.10029i | 0.264672 | − | 0.458426i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.896461 | − | 1.55272i | −0.0989976 | − | 0.171469i | ||||
\(83\) | −2.84194 | + | 4.92238i | −0.311943 | + | 0.540301i | −0.978783 | − | 0.204900i | \(-0.934313\pi\) |
0.666840 | + | 0.745201i | \(0.267647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.59888 | − | 6.23345i | −0.390354 | − | 0.676113i | ||||
\(86\) | −5.93818 | + | 10.2852i | −0.640330 | + | 1.10908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.555632 | + | 0.962383i | 0.0592306 | + | 0.102590i | ||||
\(89\) | 0.421826 | + | 0.730623i | 0.0447134 | + | 0.0774459i | 0.887516 | − | 0.460777i | \(-0.152429\pi\) |
−0.842803 | + | 0.538223i | \(0.819096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.10074 | − | 1.90654i | 0.114760 | − | 0.198771i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.7078 | 1.31071 | ||||||||
\(95\) | −4.23491 | −0.434492 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.70317 | − | 2.94997i | 0.172930 | − | 0.299524i | −0.766513 | − | 0.642229i | \(-0.778010\pi\) |
0.939443 | + | 0.342705i | \(0.111343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.82141 | + | 3.15478i | 0.182141 | + | 0.315478i | ||||
\(101\) | −4.79329 | − | 8.30222i | −0.476950 | − | 0.826102i | 0.522701 | − | 0.852516i | \(-0.324924\pi\) |
−0.999651 | + | 0.0264143i | \(0.991591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.82644 | − | 10.0917i | 0.574096 | − | 0.994364i | −0.422043 | − | 0.906576i | \(-0.638687\pi\) |
0.996139 | − | 0.0877882i | \(-0.0279799\pi\) | |||||||
\(104\) | −4.74048 | − | 8.21075i | −0.464842 | − | 0.805130i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.88255 | − | 10.1889i | 0.571363 | − | 0.989630i | ||||
\(107\) | −1.89926 | − | 3.28961i | −0.183608 | − | 0.318018i | 0.759499 | − | 0.650509i | \(-0.225444\pi\) |
−0.943107 | + | 0.332491i | \(0.892111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.43199 | − | 11.1405i | 0.616073 | − | 1.06707i | −0.374123 | − | 0.927379i | \(-0.622056\pi\) |
0.990195 | − | 0.139690i | \(-0.0446106\pi\) | |||||||
\(110\) | 0.949271 | 0.0905094 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.51052 | + | 7.81245i | 0.424314 | + | 0.734934i | 0.996356 | − | 0.0852908i | \(-0.0271819\pi\) |
−0.572042 | + | 0.820224i | \(0.693849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17572 | + | 2.03641i | 0.109636 | + | 0.189896i | ||||
\(116\) | 2.43385 | − | 4.21555i | 0.225977 | − | 0.391404i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.7275 | −1.63195 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32691 | − | 9.22649i | 0.484265 | − | 0.838771i | ||||
\(122\) | 19.8056 | 1.79311 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.39874 | −0.484821 | ||||||||
\(125\) | −8.63731 | −0.772544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.43268 | 0.570808 | 0.285404 | − | 0.958407i | \(-0.407872\pi\) | ||||
0.285404 | + | 0.958407i | \(0.407872\pi\) | |||||||
\(128\) | 12.7775 | 1.12938 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.09888 | −0.710319 | ||||||||
\(131\) | 3.31657 | − | 5.74447i | 0.289770 | − | 0.501897i | −0.683984 | − | 0.729497i | \(-0.739754\pi\) |
0.973755 | + | 0.227600i | \(0.0730877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.1643 | −1.74193 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.16059 | − | 12.4025i | 0.614016 | − | 1.06351i | ||||
\(137\) | 7.01671 | + | 12.1533i | 0.599478 | + | 1.03833i | 0.992898 | + | 0.118968i | \(0.0379585\pi\) |
−0.393420 | + | 0.919359i | \(0.628708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.40254 | − | 7.62541i | −0.373418 | − | 0.646779i | 0.616671 | − | 0.787221i | \(-0.288481\pi\) |
−0.990089 | + | 0.140442i | \(0.955148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.30903 | −0.613360 | ||||||||
\(143\) | 1.47672 | − | 2.55775i | 0.123489 | − | 0.213890i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.59963 | + | 4.50268i | 0.215887 | + | 0.373928i | ||||
\(146\) | −3.79121 | + | 6.56657i | −0.313763 | + | 0.543453i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.10507 | + | 5.37815i | 0.255236 | + | 0.442081i | ||||
\(149\) | −2.18292 | + | 3.78092i | −0.178832 | + | 0.309745i | −0.941481 | − | 0.337067i | \(-0.890565\pi\) |
0.762649 | + | 0.646813i | \(0.223898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.32691 | + | 10.9585i | 0.514877 | + | 0.891793i | 0.999851 | + | 0.0172645i | \(0.00549573\pi\) |
−0.484974 | + | 0.874529i | \(0.661171\pi\) | |||||||
\(152\) | −4.21303 | − | 7.29719i | −0.341722 | − | 0.591880i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.88323 | − | 4.99391i | 0.231587 | − | 0.401120i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2739 | 0.899754 | 0.449877 | − | 0.893091i | \(-0.351468\pi\) | ||||
0.449877 | + | 0.893091i | \(0.351468\pi\) | |||||||
\(158\) | −2.26695 | −0.180349 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.23061 | − | 3.86353i | 0.176345 | − | 0.305439i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.833104 | + | 1.44298i | 0.0652537 | + | 0.113023i | 0.896807 | − | 0.442423i | \(-0.145881\pi\) |
−0.831553 | + | 0.555446i | \(0.812548\pi\) | |||||||
\(164\) | −0.468760 | − | 0.811916i | −0.0366040 | − | 0.0634000i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.83024 | + | 8.36622i | −0.374899 | + | 0.649344i | ||||
\(167\) | 1.95135 | + | 3.37984i | 0.151000 | + | 0.261540i | 0.931595 | − | 0.363497i | \(-0.118417\pi\) |
−0.780595 | + | 0.625037i | \(0.785084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09888 | + | 10.5636i | −0.469145 | + | 0.812583i | ||||
\(170\) | −6.11677 | − | 10.5945i | −0.469134 | − | 0.812565i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.10507 | + | 5.37815i | −0.236760 | + | 0.410080i | ||||
\(173\) | −16.1141 | −1.22513 | −0.612566 | − | 0.790419i | \(-0.709863\pi\) | ||||
−0.612566 | + | 0.790419i | \(0.709863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.46727 | + | 2.54138i | 0.110599 | + | 0.191564i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.716947 | + | 1.24179i | 0.0537374 | + | 0.0930760i | ||||
\(179\) | 7.14400 | − | 12.3738i | 0.533967 | − | 0.924859i | −0.465245 | − | 0.885182i | \(-0.654034\pi\) |
0.999213 | − | 0.0396767i | \(-0.0126328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8873 | 0.957905 | 0.478952 | − | 0.877841i | \(-0.341017\pi\) | ||||
0.478952 | + | 0.877841i | \(0.341017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.33929 | + | 4.05178i | −0.172455 | + | 0.298701i | ||||
\(185\) | −6.63315 | −0.487679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.46122 | 0.326237 | ||||||||
\(188\) | 6.64490 | 0.484629 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.19777 | −0.522181 | ||||||||
\(191\) | 2.16435 | 0.156607 | 0.0783034 | − | 0.996930i | \(-0.475050\pi\) | ||||
0.0783034 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4313 | 0.750861 | 0.375431 | − | 0.926850i | \(-0.377495\pi\) | ||||
0.375431 | + | 0.926850i | \(0.377495\pi\) | |||||||
\(194\) | 2.89475 | − | 5.01385i | 0.207831 | − | 0.359973i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7848 | 1.33836 | 0.669179 | − | 0.743101i | \(-0.266646\pi\) | ||||
0.669179 | + | 0.743101i | \(0.266646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.21303 | + | 7.29719i | −0.298654 | + | 0.517284i | −0.975828 | − | 0.218539i | \(-0.929871\pi\) |
0.677174 | + | 0.735823i | \(0.263204\pi\) | |||||||
\(200\) | −3.87085 | − | 6.70452i | −0.273711 | − | 0.474081i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.14681 | − | 14.1107i | −0.573208 | − | 0.992825i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00138 | 0.0699392 | ||||||||
\(206\) | 9.90278 | − | 17.1521i | 0.689960 | − | 1.19505i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.5183 | − | 21.6823i | −0.867986 | − | 1.50340i | ||||
\(209\) | 1.31241 | − | 2.27316i | 0.0907814 | − | 0.157238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.61126 | − | 9.71899i | −0.386295 | − | 0.669083i | 0.605653 | − | 0.795729i | \(-0.292912\pi\) |
−0.991948 | + | 0.126646i | \(0.959579\pi\) | |||||||
\(212\) | 3.07598 | − | 5.32776i | 0.211259 | − | 0.365912i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.22803 | − | 5.59111i | −0.220664 | − | 0.382200i | ||||
\(215\) | −3.31657 | − | 5.74447i | −0.226188 | − | 0.391770i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.9320 | − | 18.9348i | 0.740408 | − | 1.28242i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.496374 | 0.0334655 | ||||||||
\(221\) | −38.0617 | −2.56031 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3774 | − | 17.9742i | 0.694923 | − | 1.20364i | −0.275283 | − | 0.961363i | \(-0.588772\pi\) |
0.970206 | − | 0.242279i | \(-0.0778951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.66621 | + | 13.2783i | 0.509949 | + | 0.883257i | ||||
\(227\) | −5.21512 | − | 9.03284i | −0.346139 | − | 0.599531i | 0.639421 | − | 0.768857i | \(-0.279174\pi\) |
−0.985560 | + | 0.169326i | \(0.945841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.52961 | + | 13.0417i | −0.497570 | + | 0.861817i | −0.999996 | − | 0.00280316i | \(-0.999108\pi\) |
0.502426 | + | 0.864620i | \(0.332441\pi\) | |||||||
\(230\) | 1.99829 | + | 3.46113i | 0.131763 | + | 0.228220i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.17240 | + | 8.95886i | −0.339585 | + | 0.588178i | ||||
\(233\) | 2.19344 | + | 3.79915i | 0.143697 | + | 0.248890i | 0.928886 | − | 0.370366i | \(-0.120768\pi\) |
−0.785189 | + | 0.619256i | \(0.787434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.54875 | + | 6.14662i | −0.231495 | + | 0.400961i | ||||
\(236\) | −9.26972 | −0.603407 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.77561 | − | 8.27160i | −0.308909 | − | 0.535046i | 0.669215 | − | 0.743069i | \(-0.266630\pi\) |
−0.978124 | + | 0.208023i | \(0.933297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.26792 | − | 9.12431i | −0.339337 | − | 0.587749i | 0.644971 | − | 0.764207i | \(-0.276869\pi\) |
−0.984308 | + | 0.176458i | \(0.943536\pi\) | |||||||
\(242\) | 9.05377 | − | 15.6816i | 0.581999 | − | 1.00805i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3563 | 0.662996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1971 | + | 19.3939i | −0.712453 | + | 1.23401i | ||||
\(248\) | 11.4734 | 0.728560 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.6802 | −0.928458 | ||||||||
\(251\) | 24.4346 | 1.54230 | 0.771148 | − | 0.636656i | \(-0.219683\pi\) | ||||
0.771148 | + | 0.636656i | \(0.219683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.45744 | −0.0916282 | ||||||||
\(254\) | 10.9332 | 0.686007 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.7417 | 1.10886 | ||||||||
\(257\) | 2.00416 | − | 3.47131i | 0.125016 | − | 0.216534i | −0.796723 | − | 0.604345i | \(-0.793435\pi\) |
0.921739 | + | 0.387810i | \(0.126768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.23491 | −0.262638 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.63694 | − | 9.76347i | 0.348251 | − | 0.603189i | ||||
\(263\) | 8.84362 | + | 15.3176i | 0.545321 | + | 0.944524i | 0.998587 | + | 0.0531485i | \(0.0169257\pi\) |
−0.453265 | + | 0.891376i | \(0.649741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.28550 | + | 5.69066i | 0.201827 | + | 0.349574i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5439 | −0.644074 | ||||||||
\(269\) | −7.11366 | + | 12.3212i | −0.433727 | + | 0.751238i | −0.997191 | − | 0.0749032i | \(-0.976135\pi\) |
0.563463 | + | 0.826141i | \(0.309469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69937 | + | 4.67545i | 0.163975 | + | 0.284013i | 0.936291 | − | 0.351226i | \(-0.114235\pi\) |
−0.772316 | + | 0.635239i | \(0.780902\pi\) | |||||||
\(272\) | 18.9091 | − | 32.7515i | 1.14653 | − | 1.98585i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9258 | + | 20.6561i | 0.720464 | + | 1.24788i | ||||
\(275\) | 1.20582 | − | 2.08854i | 0.0727136 | − | 0.125944i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83310 | − | 6.63913i | −0.230309 | − | 0.398907i | 0.727590 | − | 0.686012i | \(-0.240640\pi\) |
−0.957899 | + | 0.287105i | \(0.907307\pi\) | |||||||
\(278\) | −7.48267 | − | 12.9604i | −0.448781 | − | 0.777311i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.3312 | + | 19.6263i | −0.675965 | + | 1.17081i | 0.300220 | + | 0.953870i | \(0.402940\pi\) |
−0.976186 | + | 0.216936i | \(0.930394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.8492 | −1.89324 | −0.946619 | − | 0.322353i | \(-0.895526\pi\) | ||||
−0.946619 | + | 0.322353i | \(0.895526\pi\) | |||||||
\(284\) | −3.82189 | −0.226788 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.50987 | − | 4.34722i | 0.148412 | − | 0.257057i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.2465 | − | 35.0680i | −1.19097 | − | 2.06282i | ||||
\(290\) | 4.41840 | + | 7.65289i | 0.259457 | + | 0.449393i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.98242 | + | 3.43366i | −0.116013 | + | 0.200940i | ||||
\(293\) | 13.7468 | + | 23.8102i | 0.803097 | + | 1.39100i | 0.917568 | + | 0.397578i | \(0.130149\pi\) |
−0.114472 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.95056 | − | 8.57462i | 0.288233 | − | 0.499234i | ||||
\(296\) | −6.59888 | − | 11.4296i | −0.383552 | − | 0.664332i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.71015 | + | 6.42617i | −0.214923 | + | 0.372258i | ||||
\(299\) | 12.4344 | 0.719099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.7534 | + | 18.6254i | 0.618789 | + | 1.07177i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.1254 | − | 19.2698i | −0.638088 | − | 1.10520i | ||||
\(305\) | −5.53087 | + | 9.57975i | −0.316697 | + | 0.548535i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8176 | 0.845683 | 0.422841 | − | 0.906204i | \(-0.361033\pi\) | ||||
0.422841 | + | 0.906204i | \(0.361033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.90043 | − | 8.48779i | 0.278326 | − | 0.482074i | ||||
\(311\) | −29.0635 | −1.64804 | −0.824021 | − | 0.566559i | \(-0.808274\pi\) | ||||
−0.824021 | + | 0.566559i | \(0.808274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4780 | −1.38358 | −0.691790 | − | 0.722099i | \(-0.743178\pi\) | ||||
−0.691790 | + | 0.722099i | \(0.743178\pi\) | |||||||
\(314\) | 19.1614 | 1.08134 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.18539 | −0.0666834 | ||||||||
\(317\) | 7.38688 | 0.414888 | 0.207444 | − | 0.978247i | \(-0.433485\pi\) | ||||
0.207444 | + | 0.978247i | \(0.433485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22253 | −0.180427 | ||||||||
\(320\) | −0.943395 | + | 1.63401i | −0.0527374 | + | 0.0913438i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8268 | −1.88218 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.2877 | + | 17.8188i | −0.570657 | + | 0.988407i | ||||
\(326\) | 1.41597 | + | 2.45253i | 0.0784231 | + | 0.135833i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.996205 | + | 1.72548i | 0.0550062 | + | 0.0952736i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0617 | 1.10269 | 0.551347 | − | 0.834276i | \(-0.314114\pi\) | ||||
0.551347 | + | 0.834276i | \(0.314114\pi\) | |||||||
\(332\) | −2.52573 | + | 4.37470i | −0.138618 | + | 0.240093i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.31657 | + | 5.74447i | 0.181475 | + | 0.314324i | ||||
\(335\) | 5.63106 | − | 9.75329i | 0.307658 | − | 0.532879i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.20327 | − | 5.54823i | −0.174493 | − | 0.302231i | 0.765493 | − | 0.643445i | \(-0.222495\pi\) |
−0.939986 | + | 0.341214i | \(0.889162\pi\) | |||||||
\(338\) | −10.3658 | + | 17.9542i | −0.563827 | + | 0.976577i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.19846 | − | 5.53989i | −0.173461 | − | 0.300443i | ||||
\(341\) | 1.78705 | + | 3.09526i | 0.0967740 | + | 0.167617i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.59888 | − | 11.4296i | 0.355788 | − | 0.616243i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.3880 | −1.47239 | ||||||||
\(347\) | 29.1927 | 1.56714 | 0.783572 | − | 0.621300i | \(-0.213395\pi\) | ||||
0.783572 | + | 0.621300i | \(0.213395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.17192 | − | 3.76188i | 0.116260 | − | 0.201369i | −0.802022 | − | 0.597294i | \(-0.796243\pi\) |
0.918283 | + | 0.395925i | \(0.129576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.38255 | + | 2.39464i | 0.0736899 | + | 0.127635i | ||||
\(353\) | 12.8503 | + | 22.2574i | 0.683955 | + | 1.18464i | 0.973764 | + | 0.227560i | \(0.0730747\pi\) |
−0.289809 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.04111 | − | 3.53530i | 0.108331 | − | 0.187635i | ||||
\(356\) | 0.374892 | + | 0.649331i | 0.0198692 | + | 0.0344145i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.1421 | − | 21.0308i | 0.641732 | − | 1.11151i | ||||
\(359\) | 10.3436 | + | 17.9157i | 0.545916 | + | 0.945554i | 0.998549 | + | 0.0538567i | \(0.0171514\pi\) |
−0.452633 | + | 0.891697i | \(0.649515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.451246 | + | 0.781582i | −0.0237498 | + | 0.0411359i | ||||
\(362\) | 21.9036 | 1.15123 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.11745 | − | 3.66754i | −0.110833 | − | 0.191968i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.42391 | + | 2.46628i | 0.0743273 | + | 0.128739i | 0.900794 | − | 0.434248i | \(-0.142986\pi\) |
−0.826466 | + | 0.562986i | \(0.809652\pi\) | |||||||
\(368\) | −6.17742 | + | 10.6996i | −0.322020 | + | 0.557755i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.2739 | −0.586101 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7163 | + | 18.5612i | −0.554871 | + | 0.961065i | 0.443043 | + | 0.896501i | \(0.353899\pi\) |
−0.997914 | + | 0.0645641i | \(0.979434\pi\) | |||||||
\(374\) | 7.58242 | 0.392077 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.1217 | −0.728271 | ||||||||
\(377\) | 27.4936 | 1.41599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0494 | 1.38943 | 0.694716 | − | 0.719284i | \(-0.255530\pi\) | ||||
0.694716 | + | 0.719284i | \(0.255530\pi\) | |||||||
\(380\) | −3.76371 | −0.193074 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.67859 | 0.188213 | ||||||||
\(383\) | −7.21340 | + | 12.4940i | −0.368588 | + | 0.638412i | −0.989345 | − | 0.145590i | \(-0.953492\pi\) |
0.620757 | + | 0.784003i | \(0.286825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.7293 | 0.902399 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.51366 | − | 2.62174i | 0.0768446 | − | 0.133099i | ||||
\(389\) | −3.05377 | − | 5.28929i | −0.154832 | − | 0.268178i | 0.778166 | − | 0.628059i | \(-0.216150\pi\) |
−0.932998 | + | 0.359882i | \(0.882817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.39120 | + | 16.2660i | 0.474933 | + | 0.822609i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.9271 | 1.60846 | ||||||||
\(395\) | 0.633065 | − | 1.09650i | 0.0318530 | − | 0.0551710i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.44364 | + | 11.1607i | 0.323397 | + | 0.560140i | 0.981187 | − | 0.193061i | \(-0.0618417\pi\) |
−0.657789 | + | 0.753202i | \(0.728508\pi\) | |||||||
\(398\) | −7.16059 | + | 12.4025i | −0.358928 | + | 0.621682i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.2218 | − | 17.7047i | −0.511092 | − | 0.885237i | ||||
\(401\) | 4.19530 | − | 7.26647i | 0.209503 | − | 0.362870i | −0.742055 | − | 0.670339i | \(-0.766149\pi\) |
0.951558 | + | 0.307469i | \(0.0994820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.2465 | − | 26.4078i | −0.759483 | − | 1.31546i | ||||
\(404\) | −4.25997 | − | 7.37848i | −0.211941 | − | 0.367093i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.05563 | − | 3.56046i | 0.101894 | − | 0.176485i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.81266 | 0.336864 | 0.168432 | − | 0.985713i | \(-0.446130\pi\) | ||||
0.168432 | + | 0.985713i | \(0.446130\pi\) | |||||||
\(410\) | 1.70197 | 0.0840543 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.17817 | − | 8.96885i | 0.255110 | − | 0.441864i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.69777 | − | 4.67267i | −0.132428 | − | 0.229372i | ||||
\(416\) | −11.7955 | − | 20.4303i | −0.578320 | − | 1.00168i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.23061 | − | 3.86353i | 0.109103 | − | 0.188971i | ||||
\(419\) | −5.16231 | − | 8.94137i | −0.252195 | − | 0.436815i | 0.711935 | − | 0.702246i | \(-0.247819\pi\) |
−0.964130 | + | 0.265431i | \(0.914486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.56801 | + | 2.71588i | −0.0764202 | + | 0.132364i | −0.901703 | − | 0.432356i | \(-0.857682\pi\) |
0.825283 | + | 0.564720i | \(0.191016\pi\) | |||||||
\(422\) | −9.53706 | − | 16.5187i | −0.464257 | − | 0.804117i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.53706 | + | 11.3225i | −0.317468 | + | 0.549870i | ||||
\(425\) | −31.0795 | −1.50757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.68794 | − | 2.92359i | −0.0815895 | − | 0.141317i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.63694 | − | 9.76347i | −0.271837 | − | 0.470836i | ||||
\(431\) | 15.9363 | − | 27.6025i | 0.767625 | − | 1.32957i | −0.171222 | − | 0.985233i | \(-0.554771\pi\) |
0.938847 | − | 0.344334i | \(-0.111895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.48855 | 0.359877 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.71634 | − | 9.90099i | 0.273763 | − | 0.474171i | ||||
\(437\) | 11.0509 | 0.528636 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.28930 | 0.109262 | 0.0546311 | − | 0.998507i | \(-0.482602\pi\) | ||||
0.0546311 | + | 0.998507i | \(0.482602\pi\) | |||||||
\(440\) | −1.05489 | −0.0502900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −64.6908 | −3.07703 | ||||||||
\(443\) | −37.3497 | −1.77454 | −0.887270 | − | 0.461251i | \(-0.847401\pi\) | ||||
−0.887270 | + | 0.461251i | \(0.847401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.800854 | −0.0379641 | ||||||||
\(446\) | 17.6378 | − | 30.5495i | 0.835172 | − | 1.44656i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20286 | 0.292731 | 0.146366 | − | 0.989231i | \(-0.453242\pi\) | ||||
0.146366 | + | 0.989231i | \(0.453242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.310330 | + | 0.537507i | −0.0146129 | + | 0.0253102i | ||||
\(452\) | 4.00866 | + | 6.94320i | 0.188552 | + | 0.326581i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.86376 | − | 15.3525i | −0.415997 | − | 0.720527i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1716 | 0.943589 | 0.471795 | − | 0.881709i | \(-0.343606\pi\) | ||||
0.471795 | + | 0.881709i | \(0.343606\pi\) | |||||||
\(458\) | −12.7975 | + | 22.1660i | −0.597989 | + | 1.03575i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.04490 | + | 1.80983i | 0.0487189 | + | 0.0843836i | ||||
\(461\) | −11.2680 | + | 19.5168i | −0.524803 | + | 0.908986i | 0.474780 | + | 0.880105i | \(0.342528\pi\) |
−0.999583 | + | 0.0288813i | \(0.990806\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8145 | + | 23.9275i | 0.642016 | + | 1.11200i | 0.984982 | + | 0.172656i | \(0.0552350\pi\) |
−0.342966 | + | 0.939348i | \(0.611432\pi\) | |||||||
\(464\) | −13.6588 | + | 23.6578i | −0.634096 | + | 1.09829i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.72803 | + | 6.45714i | 0.172698 | + | 0.299121i | ||||
\(467\) | 10.0612 | + | 17.4265i | 0.465577 | + | 0.806404i | 0.999227 | − | 0.0393016i | \(-0.0125133\pi\) |
−0.533650 | + | 0.845705i | \(0.679180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.03156 | + | 10.4470i | −0.278215 | + | 0.481883i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.6999 | 0.906764 | ||||||||
\(473\) | 4.11126 | 0.189036 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.14301 | + | 15.8362i | −0.419510 | + | 0.726613i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.11677 | − | 14.0586i | −0.371252 | − | 0.643028i | ||||
\(479\) | −4.79329 | − | 8.30222i | −0.219011 | − | 0.379338i | 0.735495 | − | 0.677530i | \(-0.236950\pi\) |
−0.954506 | + | 0.298192i | \(0.903616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5380 | + | 30.3767i | −0.799664 | + | 1.38506i | ||||
\(482\) | −8.95351 | − | 15.5079i | −0.407821 | − | 0.706367i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.73422 | − | 8.19991i | 0.215192 | − | 0.372723i | ||||
\(485\) | 1.61677 | + | 2.80032i | 0.0734135 | + | 0.127156i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.53706 | + | 11.3225i | −0.296223 | + | 0.513073i | −0.975269 | − | 0.221023i | \(-0.929060\pi\) |
0.679046 | + | 0.734096i | \(0.262394\pi\) | |||||||
\(488\) | −22.0092 | −0.996311 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.67054 | + | 13.2858i | 0.346167 | + | 0.599578i | 0.985565 | − | 0.169298i | \(-0.0541499\pi\) |
−0.639398 | + | 0.768876i | \(0.720817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.7648 | + | 35.9657i | 0.935201 | + | 1.61982i | ||||
\(494\) | −19.0309 | + | 32.9624i | −0.856239 | + | 1.48305i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2979 | 1.36042 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.43268 | + | 4.21352i | −0.108902 | + | 0.188623i | −0.915326 | − | 0.402715i | \(-0.868067\pi\) |
0.806424 | + | 0.591338i | \(0.201400\pi\) | |||||||
\(500\) | −7.67628 | −0.343294 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.5297 | 1.85356 | ||||||||
\(503\) | −16.0085 | −0.713783 | −0.356892 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356892 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.10026 | 0.404956 | ||||||||
\(506\) | −2.47710 | −0.110121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.71695 | 0.253649 | ||||||||
\(509\) | −15.5925 | + | 27.0071i | −0.691127 | + | 1.19707i | 0.280342 | + | 0.959900i | \(0.409552\pi\) |
−0.971469 | + | 0.237167i | \(0.923781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.59937 | 0.203265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.40633 | − | 5.89994i | 0.150247 | − | 0.260235i | ||||
\(515\) | 5.53087 | + | 9.57975i | 0.243719 | + | 0.422134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.19954 | − | 3.80971i | −0.0967356 | − | 0.167551i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | 10.4830 | − | 18.1572i | 0.459270 | − | 0.795480i | −0.539652 | − | 0.841888i | \(-0.681444\pi\) |
0.998923 | + | 0.0464085i | \(0.0147776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.7821 | − | 37.7277i | −0.952465 | − | 1.64972i | −0.740064 | − | 0.672536i | \(-0.765205\pi\) |
−0.212401 | − | 0.977183i | \(-0.568128\pi\) | |||||||
\(524\) | 2.94756 | − | 5.10532i | 0.128765 | − | 0.223027i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.0309 | + | 26.0342i | 0.655377 | + | 1.13515i | ||||
\(527\) | 23.0302 | − | 39.8894i | 1.00321 | − | 1.73761i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.43199 | + | 14.6046i | 0.366608 | + | 0.634984i | ||||
\(530\) | 5.58413 | + | 9.67200i | 0.242559 | + | 0.420125i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.64764 | − | 4.58584i | 0.114682 | − | 0.198635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.60582 | 0.155893 | ||||||||
\(536\) | 22.4079 | 0.967875 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.0906 | + | 20.9415i | −0.521262 | + | 0.902852i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.93268 | − | 8.54365i | −0.212072 | − | 0.367320i | 0.740291 | − | 0.672287i | \(-0.234688\pi\) |
−0.952363 | + | 0.304967i | \(0.901355\pi\) | |||||||
\(542\) | 4.58793 | + | 7.94652i | 0.197068 | + | 0.341332i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.8173 | − | 30.8604i | 0.763909 | − | 1.32313i | ||||
\(545\) | 6.10570 | + | 10.5754i | 0.261539 | + | 0.453000i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.284350 | + | 0.492509i | −0.0121579 | + | 0.0210582i | −0.872040 | − | 0.489434i | \(-0.837203\pi\) |
0.859882 | + | 0.510492i | \(0.170537\pi\) | |||||||
\(548\) | 6.23600 | + | 10.8011i | 0.266389 | + | 0.461399i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.04944 | − | 3.54974i | 0.0873885 | − | 0.151361i | ||||
\(551\) | 24.4346 | 1.04095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.51485 | − | 11.2841i | −0.276789 | − | 0.479413i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.91269 | − | 6.77698i | −0.165935 | − | 0.287408i | ||||
\(557\) | −1.29349 | + | 2.24040i | −0.0548071 | + | 0.0949286i | −0.892127 | − | 0.451784i | \(-0.850788\pi\) |
0.837320 | + | 0.546713i | \(0.184121\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.0760 | −1.48356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.2589 | + | 33.3574i | −0.812388 | + | 1.40710i | ||||
\(563\) | 33.2831 | 1.40272 | 0.701358 | − | 0.712809i | \(-0.252578\pi\) | ||||
0.701358 | + | 0.712809i | \(0.252578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.56341 | −0.360265 | ||||||||
\(566\) | −54.1318 | −2.27533 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.12227 | 0.340803 | ||||||||
\(569\) | 5.35346 | 0.224429 | 0.112214 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112214 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.90112 | 0.205105 | 0.102553 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102553 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(572\) | 1.31241 | − | 2.27316i | 0.0548747 | − | 0.0950457i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.1533 | 0.423424 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0378 | − | 31.2425i | 0.750925 | − | 1.30064i | −0.196450 | − | 0.980514i | \(-0.562941\pi\) |
0.947375 | − | 0.320127i | \(-0.103725\pi\) | |||||||
\(578\) | −34.4116 | − | 59.6026i | −1.43133 | − | 2.47914i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.31038 | + | 4.00170i | 0.0959333 | + | 0.166161i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.07275 | −0.168676 | ||||||||
\(584\) | 4.21303 | − | 7.29719i | 0.174337 | − | 0.301960i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.3645 | + | 40.4684i | 0.965177 | + | 1.67174i | ||||
\(587\) | 0.527445 | − | 0.913562i | 0.0217700 | − | 0.0377068i | −0.854935 | − | 0.518735i | \(-0.826403\pi\) |
0.876705 | + | 0.481028i | \(0.159737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.5501 | − | 23.4695i | −0.558323 | − | 0.967045i | ||||
\(590\) | 8.41411 | − | 14.5737i | 0.346403 | − | 0.599988i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.4258 | − | 30.1824i | −0.716196 | − | 1.24049i | ||||
\(593\) | −7.53548 | − | 13.0518i | −0.309445 | − | 0.535975i | 0.668796 | − | 0.743446i | \(-0.266810\pi\) |
−0.978241 | + | 0.207471i | \(0.933477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.94004 | + | 3.36024i | −0.0794670 | + | 0.137641i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.1338 | 0.864227 | ||||||||
\(599\) | −42.0566 | −1.71839 | −0.859194 | − | 0.511650i | \(-0.829035\pi\) | ||||
−0.859194 | + | 0.511650i | \(0.829035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.44989 | + | 16.3677i | −0.385469 | + | 0.667652i | −0.991834 | − | 0.127534i | \(-0.959294\pi\) |
0.606365 | + | 0.795186i | \(0.292627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.62296 | + | 9.73924i | 0.228795 | + | 0.396284i | ||||
\(605\) | 5.05669 | + | 8.75844i | 0.205583 | + | 0.356081i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7213 | − | 25.4980i | 0.597518 | − | 1.03493i | −0.395668 | − | 0.918393i | \(-0.629487\pi\) |
0.993186 | − | 0.116538i | \(-0.0371796\pi\) | |||||||
\(608\) | −10.4830 | − | 18.1572i | −0.425143 | − | 0.736370i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.40043 | + | 16.2820i | −0.380612 | + | 0.659240i | ||||
\(611\) | 18.7658 | + | 32.5033i | 0.759182 | + | 1.31494i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.83379 | − | 10.1044i | 0.235625 | − | 0.408114i | −0.723829 | − | 0.689979i | \(-0.757620\pi\) |
0.959454 | + | 0.281865i | \(0.0909531\pi\) | |||||||
\(614\) | 25.1843 | 1.01636 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4054 | − | 28.4151i | −0.660458 | − | 1.14395i | −0.980495 | − | 0.196542i | \(-0.937029\pi\) |
0.320037 | − | 0.947405i | \(-0.396305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0806 | + | 20.9242i | 0.485560 | + | 0.841014i | 0.999862 | − | 0.0165947i | \(-0.00528250\pi\) |
−0.514303 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(620\) | 2.56243 | − | 4.43827i | 0.102910 | − | 0.178245i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −49.3972 | −1.98065 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.14764 | + | 10.6480i | −0.245906 | + | 0.425921i | ||||
\(626\) | −41.6035 | −1.66281 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0195 | 0.399822 | ||||||||
\(629\) | −52.9830 | −2.11257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1003 | −0.441894 | −0.220947 | − | 0.975286i | \(-0.570915\pi\) | ||||
−0.220947 | + | 0.975286i | \(0.570915\pi\) | |||||||
\(632\) | 2.51918 | 0.100208 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.5549 | 0.498620 | ||||||||
\(635\) | −3.05318 | + | 5.28826i | −0.121162 | + | 0.209858i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.47710 | −0.216840 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.06464 | + | 10.5043i | −0.239726 | + | 0.415218i | ||||
\(641\) | 3.65019 | + | 6.32231i | 0.144174 | + | 0.249716i | 0.929064 | − | 0.369918i | \(-0.120614\pi\) |
−0.784891 | + | 0.619634i | \(0.787281\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6256 | − | 18.4041i | −0.419033 | − | 0.725787i | 0.576809 | − | 0.816879i | \(-0.304298\pi\) |
−0.995842 | + | 0.0910922i | \(0.970964\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −57.4930 | −2.26203 | ||||||||
\(647\) | 8.47300 | − | 14.6757i | 0.333108 | − | 0.576960i | −0.650011 | − | 0.759924i | \(-0.725236\pi\) |
0.983120 | + | 0.182964i | \(0.0585693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.06839 | + | 5.31460i | 0.120445 | + | 0.208616i | ||||
\(650\) | −17.4852 | + | 30.2853i | −0.685826 | + | 1.18789i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.740409 | + | 1.28243i | 0.0289967 | + | 0.0502237i | ||||
\(653\) | −1.86652 | + | 3.23292i | −0.0730427 | + | 0.126514i | −0.900233 | − | 0.435408i | \(-0.856604\pi\) |
0.827191 | + | 0.561921i | \(0.189938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.14833 | + | 5.45306i | 0.123015 | + | 0.213069i | ||||
\(656\) | 2.63070 | + | 4.55650i | 0.102711 | + | 0.177902i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7992 | + | 20.4368i | −0.459632 | + | 0.796105i | −0.998941 | − | 0.0460022i | \(-0.985352\pi\) |
0.539310 | + | 0.842107i | \(0.318685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5175 | 1.34258 | 0.671288 | − | 0.741197i | \(-0.265742\pi\) | ||||
0.671288 | + | 0.741197i | \(0.265742\pi\) | |||||||
\(662\) | 34.0975 | 1.32524 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.36767 | − | 9.29708i | 0.208306 | − | 0.360796i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.78366 | − | 11.7496i | −0.262664 | − | 0.454948i | ||||
\(668\) | 1.73424 | + | 3.00379i | 0.0670996 | + | 0.116220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.57072 | − | 16.5770i | 0.369749 | − | 0.640424i | ||||
\(671\) | −3.42807 | − | 5.93759i | −0.132339 | − | 0.229218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2287 | − | 21.1808i | 0.471382 | − | 0.816458i | −0.528082 | − | 0.849194i | \(-0.677088\pi\) |
0.999464 | + | 0.0327353i | \(0.0104218\pi\) | |||||||
\(674\) | −5.44437 | − | 9.42992i | −0.209709 | − | 0.363227i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.42030 | + | 9.38823i | −0.208473 | + | 0.361086i | ||||
\(677\) | 8.32045 | 0.319781 | 0.159890 | − | 0.987135i | \(-0.448886\pi\) | ||||
0.159890 | + | 0.987135i | \(0.448886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.79734 | + | 11.7733i | 0.260666 | + | 0.451487i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.03731 | + | 5.26078i | 0.116305 | + | 0.201446i | ||||
\(683\) | −21.2312 | + | 36.7735i | −0.812389 | + | 1.40710i | 0.0987988 | + | 0.995107i | \(0.468500\pi\) |
−0.911188 | + | 0.411991i | \(0.864833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3215 | −0.508989 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.4258 | − | 30.1824i | 0.664352 | − | 1.15069i | ||||
\(689\) | 34.7474 | 1.32377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3929 | 1.34641 | 0.673204 | − | 0.739456i | \(-0.264917\pi\) | ||||
0.673204 | + | 0.739456i | \(0.264917\pi\) | |||||||
\(692\) | −14.3212 | −0.544410 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 49.6167 | 1.88342 | ||||||||
\(695\) | 8.35840 | 0.317052 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.99862 | 0.302969 | ||||||||
\(698\) | 3.69146 | − | 6.39380i | 0.139724 | − | 0.242009i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.00372 | 0.264527 | 0.132263 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132263 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.5867 | + | 26.9969i | −0.587862 | + | 1.01821i | ||||
\(704\) | −0.584722 | − | 1.01277i | −0.0220375 | − | 0.0381701i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.8408 | + | 37.8294i | 0.821989 | + | 1.42373i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.22253 | −0.0834688 | −0.0417344 | − | 0.999129i | \(-0.513288\pi\) | ||||
−0.0417344 | + | 0.999129i | \(0.513288\pi\) | |||||||
\(710\) | 3.46913 | − | 6.00870i | 0.130194 | − | 0.225503i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.796717 | − | 1.37995i | −0.0298582 | − | 0.0517160i | ||||
\(713\) | −7.52373 | + | 13.0315i | −0.281766 | + | 0.488033i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40180 | + | 2.42800i | 0.0524245 | + | 0.0908019i | ||||
\(716\) | 6.34913 | − | 10.9970i | 0.237278 | − | 0.410977i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.5803 | + | 30.4500i | 0.656092 | + | 1.13638i | ||||
\(719\) | 13.0088 | + | 22.5319i | 0.485145 | + | 0.840296i | 0.999854 | − | 0.0170686i | \(-0.00543337\pi\) |
−0.514709 | + | 0.857365i | \(0.672100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.766951 | + | 1.32840i | −0.0285430 | + | 0.0494379i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.4534 | 0.425662 | ||||||||
\(725\) | 22.4500 | 0.833772 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.685875 | − | 1.18797i | 0.0254377 | − | 0.0440594i | −0.853026 | − | 0.521868i | \(-0.825235\pi\) |
0.878464 | + | 0.477809i | \(0.158569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.59888 | − | 6.23345i | −0.133201 | − | 0.230710i | ||||
\(731\) | −26.4915 | − | 45.8847i | −0.979824 | − | 1.69711i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.400087 | − | 0.692971i | 0.0147776 | − | 0.0255955i | −0.858542 | − | 0.512743i | \(-0.828629\pi\) |
0.873320 | + | 0.487148i | \(0.161963\pi\) | |||||||
\(734\) | 2.42011 | + | 4.19176i | 0.0893280 | + | 0.154721i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.82072 | + | 10.0818i | −0.214555 | + | 0.371620i | ||||
\(737\) | 3.49017 | + | 6.04515i | 0.128562 | + | 0.222676i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.68547 | + | 4.65136i | −0.0987865 | + | 0.171103i | −0.911183 | − | 0.412003i | \(-0.864829\pi\) |
0.812396 | + | 0.583106i | \(0.198163\pi\) | |||||||
\(740\) | −5.89511 | −0.216709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.63162 | − | 11.4863i | −0.243290 | − | 0.421391i | 0.718359 | − | 0.695672i | \(-0.244893\pi\) |
−0.961650 | + | 0.274281i | \(0.911560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.07218 | − | 3.58912i | −0.0759188 | − | 0.131495i | ||||
\(746\) | −18.2138 | + | 31.5472i | −0.666854 | + | 1.15503i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.96485 | 0.144969 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.77816 | + | 4.81191i | −0.101377 | + | 0.175589i | −0.912252 | − | 0.409629i | \(-0.865658\pi\) |
0.810875 | + | 0.585219i | \(0.198991\pi\) | |||||||
\(752\) | −37.2914 | −1.35988 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.7289 | 1.70177 | ||||||||
\(755\) | −12.0119 | −0.437158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3942 | −0.486819 | −0.243410 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243410 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(758\) | 45.9739 | 1.66985 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.99862 | 0.290141 | ||||||||
\(761\) | −6.42191 | + | 11.1231i | −0.232794 | + | 0.403211i | −0.958629 | − | 0.284658i | \(-0.908120\pi\) |
0.725835 | + | 0.687868i | \(0.241453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.92353 | 0.0695910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.2601 | + | 21.2351i | −0.442975 | + | 0.767256i | ||||
\(767\) | −26.1785 | − | 45.3425i | −0.945251 | − | 1.63722i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.48259 | − | 2.56793i | −0.0534636 | − | 0.0926018i | 0.838055 | − | 0.545586i | \(-0.183693\pi\) |
−0.891519 | + | 0.452984i | \(0.850359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.27067 | 0.333659 | ||||||||
\(773\) | −9.63939 | + | 16.6959i | −0.346705 | + | 0.600510i | −0.985662 | − | 0.168732i | \(-0.946033\pi\) |
0.638957 | + | 0.769242i | \(0.279366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.4496 | − | 21.5633i | −0.447203 | − | 0.774578i | ||||
\(776\) | −3.21683 | + | 5.57171i | −0.115477 | + | 0.200013i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.19028 | − | 8.98983i | −0.186080 | − | 0.322301i | ||||
\(779\) | 2.35305 | − | 4.07560i | 0.0843068 | − | 0.146024i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.26509 | + | 2.19120i | 0.0452685 | + | 0.0784074i | ||||
\(782\) | 15.9616 | + | 27.6462i | 0.570784 | + | 0.988627i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.35098 | + | 9.26818i | −0.190985 | + | 0.330795i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6453 | 0.486402 | 0.243201 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243201 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(788\) | 16.6947 | 0.594724 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.07598 | − | 1.86364i | 0.0382815 | − | 0.0663055i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.2472 | + | 50.6577i | 1.03860 | + | 1.79891i | ||||
\(794\) | 10.9518 | + | 18.9691i | 0.388665 | + | 0.673187i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.74427 | + | 6.48527i | −0.132712 | + | 0.229864i | ||||
\(797\) | −11.4792 | − | 19.8826i | −0.406616 | − | 0.704279i | 0.587892 | − | 0.808939i | \(-0.299958\pi\) |
−0.994508 | + | 0.104660i | \(0.966625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.3461 | + | 49.0969i | −1.00281 | + | 1.73692i | ||||
\(800\) | −9.63162 | − | 16.6824i | −0.340529 | − | 0.589814i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.13045 | − | 12.3503i | 0.251785 | − | 0.436104i | ||||
\(803\) | 2.62482 | 0.0926279 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.9134 | − | 44.8834i | −0.912761 | − | 1.58095i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.05326 | + | 15.6807i | 0.318492 | + | 0.551645i | ||||
\(809\) | 19.7291 | − | 34.1718i | 0.693639 | − | 1.20142i | −0.276998 | − | 0.960870i | \(-0.589340\pi\) |
0.970637 | − | 0.240548i | \(-0.0773270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.496374 | −0.0174300 | −0.00871502 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871502 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.49381 | − | 6.05146i | 0.122458 | − | 0.212103i | ||||
\(815\) | −1.58168 | −0.0554039 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.1733 | −1.09062 | ||||||||
\(818\) | 11.5790 | 0.404850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.889960 | 0.0310788 | ||||||||
\(821\) | −47.1038 | −1.64393 | −0.821967 | − | 0.569534i | \(-0.807124\pi\) | ||||
−0.821967 | + | 0.569534i | \(0.807124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.19777 | −0.0766094 | −0.0383047 | − | 0.999266i | \(-0.512196\pi\) | ||||
−0.0383047 | + | 0.999266i | \(0.512196\pi\) | |||||||
\(824\) | −11.0046 | + | 19.0605i | −0.383364 | + | 0.664005i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.3360 | 1.92422 | 0.962110 | − | 0.272661i | \(-0.0879036\pi\) | ||||
0.962110 | + | 0.272661i | \(0.0879036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1603 | − | 17.5982i | 0.352882 | − | 0.611209i | −0.633871 | − | 0.773439i | \(-0.718535\pi\) |
0.986753 | + | 0.162229i | \(0.0518684\pi\) | |||||||
\(830\) | −4.58520 | − | 7.94181i | −0.159155 | − | 0.275664i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.98867 | + | 8.64062i | 0.172951 | + | 0.299560i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.70472 | −0.128207 | ||||||||
\(836\) | 1.16639 | − | 2.02024i | 0.0403403 | − | 0.0698715i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.77400 | − | 15.1970i | −0.303093 | − | 0.524972i | ||||
\(839\) | 12.2760 | − | 21.2626i | 0.423813 | − | 0.734066i | −0.572496 | − | 0.819908i | \(-0.694025\pi\) |
0.996309 | + | 0.0858417i | \(0.0273579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.499311 | − | 0.864833i | −0.0172176 | − | 0.0298218i | ||||
\(842\) | −2.66504 | + | 4.61598i | −0.0918432 | + | 0.159077i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.98693 | − | 8.63762i | −0.171657 | − | 0.297319i | ||||
\(845\) | −5.78949 | − | 10.0277i | −0.199165 | − | 0.344963i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.2625 | + | 29.8996i | −0.592798 | + | 1.02676i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −52.8235 | −1.81183 | ||||||||
\(851\) | 17.3090 | 0.593346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.7708 | + | 46.3684i | −0.916614 | + | 1.58762i | −0.112093 | + | 0.993698i | \(0.535756\pi\) |
−0.804521 | + | 0.593925i | \(0.797578\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.58719 | + | 6.21320i | 0.122608 | + | 0.212363i | ||||
\(857\) | 27.0777 | + | 46.8999i | 0.924955 | + | 1.60207i | 0.791633 | + | 0.610996i | \(0.209231\pi\) |
0.133322 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.896461 | − | 1.55272i | 0.0305869 | − | 0.0529780i | −0.850327 | − | 0.526255i | \(-0.823596\pi\) |
0.880914 | + | 0.473277i | \(0.156929\pi\) | |||||||
\(860\) | −2.94756 | − | 5.10532i | −0.100511 | − | 0.174090i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.0858 | − | 46.9140i | 0.922547 | − | 1.59790i | ||||
\(863\) | −16.2854 | − | 28.2072i | −0.554363 | − | 0.960185i | −0.997953 | − | 0.0639549i | \(-0.979629\pi\) |
0.443590 | − | 0.896230i | \(-0.353705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.64833 | − | 13.2473i | 0.260051 | − | 0.450421i | ||||
\(866\) | 12.7277 | 0.432506 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.392378 | + | 0.679618i | 0.0133105 | + | 0.0230545i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7770 | − | 51.5753i | −1.00896 | − | 1.74756i | ||||
\(872\) | −12.1483 | + | 21.0415i | −0.411394 | + | 0.712556i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.7824 | 0.635324 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3647 | − | 31.8085i | 0.620131 | − | 1.07410i | −0.369330 | − | 0.929298i | \(-0.620413\pi\) |
0.989461 | − | 0.144800i | \(-0.0462538\pi\) | |||||||
\(878\) | 3.89095 | 0.131313 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.78567 | −0.0939049 | ||||||||
\(881\) | 25.3721 | 0.854807 | 0.427403 | − | 0.904061i | \(-0.359428\pi\) | ||||
0.427403 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9381 | −0.570012 | −0.285006 | − | 0.958526i | \(-0.591996\pi\) | ||||
−0.285006 | + | 0.958526i | \(0.591996\pi\) | |||||||
\(884\) | −33.8268 | −1.13772 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −63.4807 | −2.13267 | ||||||||
\(887\) | 24.0069 | − | 41.5811i | 0.806071 | − | 1.39616i | −0.109494 | − | 0.993987i | \(-0.534923\pi\) |
0.915566 | − | 0.402169i | \(-0.131744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.36115 | −0.0456260 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.22279 | − | 15.9743i | 0.308802 | − | 0.534860i | ||||
\(893\) | 16.6778 | + | 28.8868i | 0.558102 | + | 0.966661i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.78159 | + | 11.7461i | 0.226684 | + | 0.392627i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.5426 | 0.351810 | ||||||||
\(899\) | −16.6357 | + | 28.8138i | −0.554831 | + | 0.960995i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.2433 | + | 45.4548i | 0.874292 | + | 1.51432i | ||||
\(902\) | −0.527445 | + | 0.913562i | −0.0175620 | + | 0.0304183i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.51918 | − | 14.7557i | −0.283344 | − | 0.490766i | ||||
\(905\) | −6.11677 | + | 10.5945i | −0.203328 | + | 0.352175i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3887 | + | 21.4579i | 0.411361 | + | 0.712499i | 0.995039 | − | 0.0994869i | \(-0.0317201\pi\) |
−0.583678 | + | 0.811985i | \(0.698387\pi\) | |||||||
\(908\) | −4.63486 | − | 8.02781i | −0.153813 | − | 0.266412i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7916 | − | 27.3519i | 0.523200 | − | 0.906209i | −0.476435 | − | 0.879210i | \(-0.658071\pi\) |
0.999635 | − | 0.0269997i | \(-0.00859533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.34419 | 0.110676 | ||||||||
\(914\) | 34.2843 | 1.13402 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.69183 | + | 11.5906i | −0.221104 | + | 0.382964i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.796041 | − | 1.37878i | −0.0262590 | − | 0.0454819i | 0.852597 | − | 0.522569i | \(-0.175026\pi\) |
−0.878856 | + | 0.477087i | \(0.841693\pi\) | |||||||
\(920\) | −2.22062 | − | 3.84623i | −0.0732118 | − | 0.126807i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1514 | + | 33.1712i | −0.630718 | + | 1.09244i | ||||
\(923\) | −10.7934 | − | 18.6947i | −0.355268 | − | 0.615342i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3207 | + | 24.8042i | −0.470863 | + | 0.815558i | ||||
\(926\) | 23.4796 | + | 40.6678i | 0.771587 | + | 1.33643i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.8702 | + | 22.2918i | −0.422484 | + | 0.731764i | ||||
\(929\) | −27.0711 | −0.888175 | −0.444087 | − | 0.895983i | \(-0.646472\pi\) | ||||
−0.444087 | + | 0.895983i | \(0.646472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.94939 | + | 3.37644i | 0.0638543 | + | 0.110599i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.1003 | + | 29.6186i | 0.559540 | + | 0.969151i | ||||
\(935\) | −2.11745 | + | 3.66754i | −0.0692482 | + | 0.119941i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6624 | 1.06704 | 0.533518 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533518 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.15390 | + | 5.46272i | −0.102869 | + | 0.178174i | ||||
\(941\) | −4.72285 | −0.153961 | −0.0769803 | − | 0.997033i | \(-0.524528\pi\) | ||||
−0.0769803 | + | 0.997033i | \(0.524528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.61307 | −0.0850933 | ||||||||
\(944\) | 52.0220 | 1.69317 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.98762 | 0.227187 | ||||||||
\(947\) | −56.7810 | −1.84514 | −0.922568 | − | 0.385835i | \(-0.873913\pi\) | ||||
−0.922568 | + | 0.385835i | \(0.873913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.3942 | −0.726945 | ||||||||
\(950\) | −15.5397 | + | 26.9156i | −0.504175 | + | 0.873257i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.1693 | 1.52796 | 0.763982 | − | 0.645238i | \(-0.223242\pi\) | ||||
0.763982 | + | 0.645238i | \(0.223242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.02728 | + | 1.77930i | −0.0332419 | + | 0.0575766i | ||||
\(956\) | −4.24426 | − | 7.35127i | −0.137269 | − | 0.237757i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.14681 | − | 14.1107i | −0.263211 | − | 0.455896i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.90112 | 0.190359 | ||||||||
\(962\) | −29.8081 | + | 51.6291i | −0.961052 | + | 1.66459i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.68179 | − | 8.10910i | −0.150790 | − | 0.261177i | ||||
\(965\) | −4.95107 | + | 8.57550i | −0.159380 | + | 0.276055i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.6985 | − | 41.0469i | −0.762091 | − | 1.31998i | −0.941771 | − | 0.336255i | \(-0.890840\pi\) |
0.179680 | − | 0.983725i | \(-0.442494\pi\) | |||||||
\(968\) | −10.0611 | + | 17.4264i | −0.323377 | + | 0.560106i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.74790 | + | 4.75950i | 0.0882297 | + | 0.152818i | ||||
\(971\) | 11.3736 | + | 19.6997i | 0.364997 | + | 0.632193i | 0.988776 | − | 0.149408i | \(-0.0477367\pi\) |
−0.623779 | + | 0.781601i | \(0.714403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.1106 | + | 19.2441i | −0.356006 | + | 0.616620i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −58.1202 | −1.86038 | ||||||||
\(977\) | −35.6849 | −1.14166 | −0.570831 | − | 0.821068i | \(-0.693379\pi\) | ||||
−0.570831 | + | 0.821068i | \(0.693379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.248187 | − | 0.429872i | 0.00793209 | − | 0.0137388i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.0371 | + | 22.5809i | 0.416029 | + | 0.720584i | ||||
\(983\) | 12.0067 | + | 20.7962i | 0.382954 | + | 0.663296i | 0.991483 | − | 0.130236i | \(-0.0415735\pi\) |
−0.608529 | + | 0.793532i | \(0.708240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.91591 | + | 15.4428i | −0.284085 | + | 0.492049i | ||||
\(986\) | 35.2925 | + | 61.1284i | 1.12394 | + | 1.94672i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.95125 | + | 17.2361i | −0.316591 | + | 0.548352i | ||||
\(989\) | 8.65452 | + | 14.9901i | 0.275198 | + | 0.476656i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.2095 | − | 38.4679i | 0.705507 | − | 1.22197i | −0.261002 | − | 0.965338i | \(-0.584053\pi\) |
0.966508 | − | 0.256635i | \(-0.0826139\pi\) | |||||||
\(992\) | 28.5485 | 0.906416 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.99931 | − | 6.92701i | −0.126787 | − | 0.219601i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.52336 | − | 7.83470i | −0.143256 | − | 0.248127i | 0.785465 | − | 0.618906i | \(-0.212424\pi\) |
−0.928721 | + | 0.370779i | \(0.879091\pi\) | |||||||
\(998\) | −4.13465 | + | 7.16142i | −0.130880 | + | 0.226691i | ||||
\(999\) | 0 | 0 |
(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 | 1323.2.h.g.802.5 | 12 | ||
3.2 | odd | 2 | 441.2.h.g.214.2 | 12 | |||
7.2 | even | 3 | 1323.2.g.g.667.2 | 12 | |||
7.3 | odd | 6 | 1323.2.f.g.883.2 | 12 | |||
7.4 | even | 3 | 1323.2.f.g.883.1 | 12 | |||
7.5 | odd | 6 | 1323.2.g.g.667.1 | 12 | |||
7.6 | odd | 2 | inner | 1323.2.h.g.802.6 | 12 | ||
9.4 | even | 3 | 1323.2.g.g.361.2 | 12 | |||
9.5 | odd | 6 | 441.2.g.g.67.5 | 12 | |||
21.2 | odd | 6 | 441.2.g.g.79.5 | 12 | |||
21.5 | even | 6 | 441.2.g.g.79.6 | 12 | |||
21.11 | odd | 6 | 441.2.f.g.295.6 | yes | 12 | ||
21.17 | even | 6 | 441.2.f.g.295.5 | yes | 12 | ||
21.20 | even | 2 | 441.2.h.g.214.1 | 12 | |||
63.4 | even | 3 | 1323.2.f.g.442.1 | 12 | |||
63.5 | even | 6 | 441.2.h.g.373.1 | 12 | |||
63.11 | odd | 6 | 3969.2.a.be.1.1 | 6 | |||
63.13 | odd | 6 | 1323.2.g.g.361.1 | 12 | |||
63.23 | odd | 6 | 441.2.h.g.373.2 | 12 | |||
63.25 | even | 3 | 3969.2.a.bd.1.6 | 6 | |||
63.31 | odd | 6 | 1323.2.f.g.442.2 | 12 | |||
63.32 | odd | 6 | 441.2.f.g.148.6 | yes | 12 | ||
63.38 | even | 6 | 3969.2.a.be.1.2 | 6 | |||
63.40 | odd | 6 | inner | 1323.2.h.g.226.6 | 12 | ||
63.41 | even | 6 | 441.2.g.g.67.6 | 12 | |||
63.52 | odd | 6 | 3969.2.a.bd.1.5 | 6 | |||
63.58 | even | 3 | inner | 1323.2.h.g.226.5 | 12 | ||
63.59 | even | 6 | 441.2.f.g.148.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.5 | ✓ | 12 | 63.59 | even | 6 | ||
441.2.f.g.148.6 | yes | 12 | 63.32 | odd | 6 | ||
441.2.f.g.295.5 | yes | 12 | 21.17 | even | 6 | ||
441.2.f.g.295.6 | yes | 12 | 21.11 | odd | 6 | ||
441.2.g.g.67.5 | 12 | 9.5 | odd | 6 | |||
441.2.g.g.67.6 | 12 | 63.41 | even | 6 | |||
441.2.g.g.79.5 | 12 | 21.2 | odd | 6 | |||
441.2.g.g.79.6 | 12 | 21.5 | even | 6 | |||
441.2.h.g.214.1 | 12 | 21.20 | even | 2 | |||
441.2.h.g.214.2 | 12 | 3.2 | odd | 2 | |||
441.2.h.g.373.1 | 12 | 63.5 | even | 6 | |||
441.2.h.g.373.2 | 12 | 63.23 | odd | 6 | |||
1323.2.f.g.442.1 | 12 | 63.4 | even | 3 | |||
1323.2.f.g.442.2 | 12 | 63.31 | odd | 6 | |||
1323.2.f.g.883.1 | 12 | 7.4 | even | 3 | |||
1323.2.f.g.883.2 | 12 | 7.3 | odd | 6 | |||
1323.2.g.g.361.1 | 12 | 63.13 | odd | 6 | |||
1323.2.g.g.361.2 | 12 | 9.4 | even | 3 | |||
1323.2.g.g.667.1 | 12 | 7.5 | odd | 6 | |||
1323.2.g.g.667.2 | 12 | 7.2 | even | 3 | |||
1323.2.h.g.226.5 | 12 | 63.58 | even | 3 | inner | ||
1323.2.h.g.226.6 | 12 | 63.40 | odd | 6 | inner | ||
1323.2.h.g.802.5 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.h.g.802.6 | 12 | 7.6 | odd | 2 | inner | ||
3969.2.a.bd.1.5 | 6 | 63.52 | odd | 6 | |||
3969.2.a.bd.1.6 | 6 | 63.25 | even | 3 | |||
3969.2.a.be.1.1 | 6 | 63.11 | odd | 6 | |||
3969.2.a.be.1.2 | 6 | 63.38 | even | 6 |