Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
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([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (of order \(6\), 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: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 440.15 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.15 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.850109 | + | 0.490811i | 0.601118 | + | 0.347056i | 0.769481 | − | 0.638669i | \(-0.220515\pi\) |
−0.168363 | + | 0.985725i | \(0.553848\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.518210 | − | 0.897565i | −0.259105 | − | 0.448783i | ||||
\(5\) | 0.940599 | + | 1.62916i | 0.420648 | + | 0.728585i | 0.996003 | − | 0.0893196i | \(-0.0284692\pi\) |
−0.575355 | + | 0.817904i | \(0.695136\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.98061i | − | 1.05381i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.84662i | 0.583954i | ||||||||
\(11\) | −3.54040 | − | 2.04405i | −1.06747 | − | 0.616304i | −0.139980 | − | 0.990154i | \(-0.544704\pi\) |
−0.927489 | + | 0.373850i | \(0.878037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.51415 | − | 2.02890i | 0.974651 | − | 0.562715i | 0.0739997 | − | 0.997258i | \(-0.476424\pi\) |
0.900651 | + | 0.434544i | \(0.143090\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.426498 | − | 0.738716i | 0.106625 | − | 0.184679i | ||||
\(17\) | −1.62145 | −0.393260 | −0.196630 | − | 0.980478i | \(-0.563000\pi\) | ||||
−0.196630 | + | 0.980478i | \(0.563000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.12588i | − | 1.86421i | −0.362194 | − | 0.932103i | \(-0.617972\pi\) | ||
0.362194 | − | 0.932103i | \(-0.382028\pi\) | |||||||
\(20\) | 0.974855 | − | 1.68850i | 0.217984 | − | 0.377560i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00648 | − | 3.47533i | −0.427783 | − | 0.740943i | ||||
\(23\) | −3.73318 | + | 2.15535i | −0.778423 | + | 0.449423i | −0.835871 | − | 0.548926i | \(-0.815037\pi\) |
0.0574484 | + | 0.998348i | \(0.481704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.730548 | − | 1.26535i | 0.146110 | − | 0.253069i | ||||
\(26\) | 3.98322 | 0.781173 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.542317 | + | 0.313107i | 0.100706 | + | 0.0581425i | 0.549507 | − | 0.835489i | \(-0.314816\pi\) |
−0.448801 | + | 0.893632i | \(0.648149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69833 | − | 2.13523i | 0.664240 | − | 0.383499i | −0.129650 | − | 0.991560i | \(-0.541385\pi\) |
0.793891 | + | 0.608060i | \(0.208052\pi\) | |||||||
\(32\) | −4.43744 | + | 2.56195i | −0.784435 | + | 0.452894i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.37841 | − | 0.795827i | −0.236396 | − | 0.136483i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.94153 | 1.30558 | 0.652790 | − | 0.757539i | \(-0.273599\pi\) | ||||
0.652790 | + | 0.757539i | \(0.273599\pi\) | |||||||
\(38\) | 3.98827 | − | 6.90789i | 0.646983 | − | 1.12061i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.85591 | − | 2.80356i | 0.767787 | − | 0.443282i | ||||
\(41\) | −0.912023 | − | 1.57967i | −0.142434 | − | 0.246703i | 0.785979 | − | 0.618254i | \(-0.212160\pi\) |
−0.928413 | + | 0.371551i | \(0.878826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.53614 | + | 6.12477i | −0.539256 | + | 0.934019i | 0.459688 | + | 0.888080i | \(0.347961\pi\) |
−0.998944 | + | 0.0459387i | \(0.985372\pi\) | |||||||
\(44\) | 4.23698i | 0.638749i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.23148 | −0.623898 | ||||||||
\(47\) | 3.96868 | − | 6.87396i | 0.578891 | − | 1.00267i | −0.416715 | − | 0.909037i | \(-0.636819\pi\) |
0.995607 | − | 0.0936324i | \(-0.0298478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.24209 | − | 0.717122i | 0.175658 | − | 0.101416i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.64214 | − | 2.10279i | −0.505073 | − | 0.291604i | ||||
\(53\) | − | 8.37133i | − | 1.14989i | −0.818192 | − | 0.574945i | \(-0.805023\pi\) | ||
0.818192 | − | 0.574945i | \(-0.194977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.69052i | − | 1.03699i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.307352 | + | 0.532350i | 0.0403573 | + | 0.0699009i | ||||
\(59\) | 4.08715 | + | 7.07915i | 0.532101 | + | 0.921627i | 0.999298 | + | 0.0374731i | \(0.0119308\pi\) |
−0.467196 | + | 0.884154i | \(0.654736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24253 | + | 1.87208i | 0.415164 | + | 0.239695i | 0.693006 | − | 0.720932i | \(-0.256286\pi\) |
−0.277842 | + | 0.960627i | \(0.589619\pi\) | |||||||
\(62\) | 4.19198 | 0.532382 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.73573 | −0.841966 | ||||||||
\(65\) | 6.61081 | + | 3.81676i | 0.819971 | + | 0.473410i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.26559 | − | 10.8523i | −0.765464 | − | 1.32582i | −0.940001 | − | 0.341171i | \(-0.889176\pi\) |
0.174537 | − | 0.984651i | \(-0.444157\pi\) | |||||||
\(68\) | 0.840253 | + | 1.45536i | 0.101896 | + | 0.176489i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4969i | − | 1.72047i | −0.509898 | − | 0.860235i | \(-0.670317\pi\) | ||
0.509898 | − | 0.860235i | \(-0.329683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.78935i | − | 0.443510i | −0.975102 | − | 0.221755i | \(-0.928821\pi\) | ||
0.975102 | − | 0.221755i | \(-0.0711785\pi\) | |||||||
\(74\) | 6.75117 | + | 3.89779i | 0.784807 | + | 0.453109i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.29351 | + | 4.21091i | −0.836623 | + | 0.483025i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.18066 | + | 7.24112i | −0.470361 | + | 0.814690i | −0.999426 | − | 0.0338919i | \(-0.989210\pi\) |
0.529064 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(80\) | 1.60465 | 0.179406 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1.79052i | − | 0.197730i | ||||||
\(83\) | −4.38300 | + | 7.59159i | −0.481097 | + | 0.833285i | −0.999765 | − | 0.0216912i | \(-0.993095\pi\) |
0.518668 | + | 0.854976i | \(0.326428\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.52514 | − | 2.64162i | −0.165424 | − | 0.286524i | ||||
\(86\) | −6.01221 | + | 3.47115i | −0.648313 | + | 0.374304i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.09252 | + | 10.5526i | −0.649465 | + | 1.12491i | ||||
\(89\) | 9.80759 | 1.03960 | 0.519801 | − | 0.854287i | \(-0.326006\pi\) | ||||
0.519801 | + | 0.854287i | \(0.326006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.86914 | + | 2.23385i | 0.403386 | + | 0.232895i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.74762 | − | 3.89574i | 0.695964 | − | 0.401815i | ||||
\(95\) | 13.2384 | − | 7.64320i | 1.35823 | − | 0.784175i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4579 | + | 6.61525i | 1.16338 | + | 0.671677i | 0.952111 | − | 0.305752i | \(-0.0989077\pi\) |
0.211267 | + | 0.977428i | \(0.432241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.51431 | −0.151431 | ||||||||
\(101\) | 0.524900 | − | 0.909154i | 0.0522295 | − | 0.0904642i | −0.838729 | − | 0.544550i | \(-0.816701\pi\) |
0.890958 | + | 0.454085i | \(0.150034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41937 | + | 0.819472i | −0.139854 | + | 0.0807449i | −0.568295 | − | 0.822825i | \(-0.692397\pi\) |
0.428440 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(104\) | −6.04736 | − | 10.4743i | −0.592992 | − | 1.02709i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.10874 | − | 7.11654i | 0.399076 | − | 0.691220i | ||||
\(107\) | − | 3.43549i | − | 0.332122i | −0.986116 | − | 0.166061i | \(-0.946895\pi\) | ||
0.986116 | − | 0.166061i | \(-0.0531048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.69058 | 0.353494 | 0.176747 | − | 0.984256i | \(-0.443443\pi\) | ||||
0.176747 | + | 0.984256i | \(0.443443\pi\) | |||||||
\(110\) | 3.77459 | − | 6.53778i | 0.359893 | − | 0.623353i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0858 | + | 8.70977i | −1.41915 | + | 0.819346i | −0.996224 | − | 0.0868183i | \(-0.972330\pi\) |
−0.422925 | + | 0.906165i | \(0.638997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.02285 | − | 4.05465i | −0.654885 | − | 0.378098i | ||||
\(116\) | − | 0.649020i | − | 0.0602600i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.02407i | 0.738675i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.85627 | + | 4.94720i | 0.259661 | + | 0.449746i | ||||
\(122\) | 1.83767 | + | 3.18294i | 0.166375 | + | 0.288170i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.83303 | − | 2.21300i | −0.344216 | − | 0.198733i | ||||
\(125\) | 12.1546 | 1.08714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1288 | −0.898783 | −0.449391 | − | 0.893335i | \(-0.648359\pi\) | ||||
−0.449391 | + | 0.893335i | \(0.648359\pi\) | |||||||
\(128\) | 3.14876 | + | 1.81794i | 0.278314 | + | 0.160685i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.74661 | + | 6.48932i | 0.328599 | + | 0.569151i | ||||
\(131\) | 2.48851 | + | 4.31022i | 0.217422 | + | 0.376586i | 0.954019 | − | 0.299746i | \(-0.0969019\pi\) |
−0.736597 | + | 0.676332i | \(0.763569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 12.3009i | − | 1.06263i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.83293i | 0.414420i | ||||||||
\(137\) | −0.728035 | − | 0.420331i | −0.0622003 | − | 0.0359113i | 0.468577 | − | 0.883422i | \(-0.344767\pi\) |
−0.530778 | + | 0.847511i | \(0.678100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.74392 | + | 3.31626i | −0.487193 | + | 0.281281i | −0.723409 | − | 0.690419i | \(-0.757426\pi\) |
0.236216 | + | 0.971701i | \(0.424093\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.11525 | − | 12.3240i | 0.597098 | − | 1.03420i | ||||
\(143\) | −16.5887 | −1.38721 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.17803i | 0.0978301i | ||||||||
\(146\) | 1.85985 | − | 3.22136i | 0.153923 | − | 0.266602i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.11538 | − | 7.12804i | −0.338282 | − | 0.585921i | ||||
\(149\) | 14.7023 | − | 8.48838i | 1.20446 | − | 0.695395i | 0.242916 | − | 0.970047i | \(-0.421896\pi\) |
0.961544 | + | 0.274652i | \(0.0885627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.975709 | + | 1.68998i | −0.0794021 | + | 0.137528i | −0.902992 | − | 0.429657i | \(-0.858634\pi\) |
0.823590 | + | 0.567186i | \(0.191968\pi\) | |||||||
\(152\) | −24.2201 | −1.96451 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.95730 | + | 4.01680i | 0.558823 | + | 0.322637i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24558 | + | 4.76059i | −0.658069 | + | 0.379936i | −0.791541 | − | 0.611116i | \(-0.790721\pi\) |
0.133472 | + | 0.991053i | \(0.457387\pi\) | |||||||
\(158\) | −7.10804 | + | 4.10383i | −0.565485 | + | 0.326483i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.34769 | − | 4.81954i | −0.659943 | − | 0.381018i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.11021 | 0.0869585 | 0.0434793 | − | 0.999054i | \(-0.486156\pi\) | ||||
0.0434793 | + | 0.999054i | \(0.486156\pi\) | |||||||
\(164\) | −0.945238 | + | 1.63720i | −0.0738107 | + | 0.127844i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.45206 | + | 4.30245i | −0.578392 | + | 0.333935i | ||||
\(167\) | 7.00830 | + | 12.1387i | 0.542319 | + | 0.939324i | 0.998770 | + | 0.0495754i | \(0.0157868\pi\) |
−0.456452 | + | 0.889748i | \(0.650880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.73285 | − | 3.00138i | 0.133296 | − | 0.230875i | ||||
\(170\) | − | 2.99422i | − | 0.229646i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.32985 | 0.558896 | ||||||||
\(173\) | −3.55884 | + | 6.16410i | −0.270574 | + | 0.468647i | −0.969009 | − | 0.247026i | \(-0.920547\pi\) |
0.698435 | + | 0.715673i | \(0.253880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.01994 | + | 1.74357i | −0.227637 | + | 0.131426i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.33752 | + | 4.81367i | 0.624924 | + | 0.360800i | ||||
\(179\) | 6.00265i | 0.448659i | 0.974513 | + | 0.224330i | \(0.0720192\pi\) | ||||
−0.974513 | + | 0.224330i | \(0.927981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.30283i | − | 0.0968385i | −0.998827 | − | 0.0484192i | \(-0.984582\pi\) | ||
0.998827 | − | 0.0484192i | \(-0.0154184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.42428 | + | 11.1272i | 0.473604 | + | 0.820307i | ||||
\(185\) | 7.46979 | + | 12.9381i | 0.549190 | + | 0.951225i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.74059 | + | 3.31433i | 0.419794 | + | 0.242368i | ||||
\(188\) | −8.22643 | −0.599974 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.0054 | 1.08861 | ||||||||
\(191\) | −4.96482 | − | 2.86644i | −0.359242 | − | 0.207408i | 0.309506 | − | 0.950897i | \(-0.399836\pi\) |
−0.668748 | + | 0.743489i | \(0.733170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.779518 | − | 1.35016i | −0.0561109 | − | 0.0971869i | 0.836606 | − | 0.547806i | \(-0.184537\pi\) |
−0.892716 | + | 0.450619i | \(0.851203\pi\) | |||||||
\(194\) | 6.49367 | + | 11.2474i | 0.466218 | + | 0.807514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.5504i | 1.39291i | 0.717602 | + | 0.696454i | \(0.245240\pi\) | ||||
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.976403i | 0.0692154i | 0.999401 | + | 0.0346077i | \(0.0110182\pi\) | ||||
−0.999401 | + | 0.0346077i | \(0.988982\pi\) | |||||||
\(200\) | −3.77151 | − | 2.17748i | −0.266686 | − | 0.153971i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.892445 | − | 0.515253i | 0.0627922 | − | 0.0362531i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.71570 | − | 2.97167i | 0.119829 | − | 0.207551i | ||||
\(206\) | −1.60882 | −0.112092 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.46128i | − | 0.239997i | ||||||
\(209\) | −16.6097 | + | 28.7688i | −1.14892 | + | 1.98998i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9752 | + | 20.7417i | 0.824408 | + | 1.42792i | 0.902371 | + | 0.430961i | \(0.141825\pi\) |
−0.0779625 | + | 0.996956i | \(0.524841\pi\) | |||||||
\(212\) | −7.51382 | + | 4.33810i | −0.516051 | + | 0.297942i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.68618 | − | 2.92054i | 0.115265 | − | 0.199644i | ||||
\(215\) | −13.3044 | −0.907349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.13740 | + | 1.81138i | 0.212491 | + | 0.122682i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.90274 | + | 3.98530i | −0.465383 | + | 0.268689i | ||||
\(221\) | −5.69804 | + | 3.28976i | −0.383292 | + | 0.221293i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.68394 | − | 1.54957i | −0.179730 | − | 0.103767i | 0.407436 | − | 0.913234i | \(-0.366423\pi\) |
−0.587166 | + | 0.809467i | \(0.699756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.0994 | −1.13743 | ||||||||
\(227\) | 10.8991 | − | 18.8779i | 0.723401 | − | 1.25297i | −0.236228 | − | 0.971698i | \(-0.575911\pi\) |
0.959629 | − | 0.281269i | \(-0.0907554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1810 | + | 6.45536i | −0.738862 | + | 0.426582i | −0.821655 | − | 0.569985i | \(-0.806949\pi\) |
0.0827937 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(230\) | −3.98013 | − | 6.89378i | −0.262442 | − | 0.454563i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.933250 | − | 1.61644i | 0.0612709 | − | 0.106124i | ||||
\(233\) | 0.808011i | 0.0529345i | 0.999650 | + | 0.0264673i | \(0.00842578\pi\) | ||||
−0.999650 | + | 0.0264673i | \(0.991574\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.9317 | 0.974039 | ||||||||
\(236\) | 4.23600 | − | 7.33697i | 0.275740 | − | 0.477596i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2032 | + | 7.04552i | −0.789360 | + | 0.455737i | −0.839737 | − | 0.542993i | \(-0.817291\pi\) |
0.0503775 | + | 0.998730i | \(0.483958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0205 | + | 9.24943i | 1.03197 | + | 0.595808i | 0.917549 | − | 0.397624i | \(-0.130165\pi\) |
0.114422 | + | 0.993432i | \(0.463498\pi\) | |||||||
\(242\) | 5.60755i | 0.360467i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.88051i | − | 0.248424i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4866 | − | 28.5556i | −1.04902 | − | 1.81695i | ||||
\(248\) | −6.36431 | − | 11.0233i | −0.404134 | − | 0.699981i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.3327 | + | 5.96561i | 0.653499 | + | 0.377298i | ||||
\(251\) | 22.1733 | 1.39957 | 0.699783 | − | 0.714355i | \(-0.253280\pi\) | ||||
0.699783 | + | 0.714355i | \(0.253280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.6226 | 1.10792 | ||||||||
\(254\) | −8.61056 | − | 4.97131i | −0.540274 | − | 0.311928i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.52026 | + | 14.7575i | 0.532516 | + | 0.922345i | ||||
\(257\) | 2.02896 | + | 3.51427i | 0.126563 | + | 0.219214i | 0.922343 | − | 0.386372i | \(-0.126272\pi\) |
−0.795780 | + | 0.605586i | \(0.792939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 7.91152i | − | 0.490652i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.88554i | 0.301830i | ||||||||
\(263\) | 8.62617 | + | 4.98032i | 0.531913 | + | 0.307100i | 0.741795 | − | 0.670627i | \(-0.233975\pi\) |
−0.209882 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6383 | − | 7.87406i | 0.837793 | − | 0.483700i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.49378 | + | 11.2476i | −0.396671 | + | 0.687054i | ||||
\(269\) | −9.96799 | −0.607759 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0320i | 1.15611i | 0.815997 | + | 0.578057i | \(0.196189\pi\) | ||||
−0.815997 | + | 0.578057i | \(0.803811\pi\) | |||||||
\(272\) | −0.691547 | + | 1.19780i | −0.0419312 | + | 0.0726270i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.412606 | − | 0.714655i | −0.0249265 | − | 0.0431739i | ||||
\(275\) | −5.17286 | + | 2.98655i | −0.311935 | + | 0.180096i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.81184 | − | 13.5305i | 0.469368 | − | 0.812969i | −0.530019 | − | 0.847986i | \(-0.677815\pi\) |
0.999387 | + | 0.0350166i | \(0.0111484\pi\) | |||||||
\(278\) | −6.51062 | −0.390481 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.8780 | + | 12.0539i | 1.24547 | + | 0.719075i | 0.970203 | − | 0.242292i | \(-0.0778991\pi\) |
0.275271 | + | 0.961367i | \(0.411232\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.61349 | + | 1.50890i | −0.155356 | + | 0.0896946i | −0.575662 | − | 0.817687i | \(-0.695256\pi\) |
0.420307 | + | 0.907382i | \(0.361922\pi\) | |||||||
\(284\) | −13.0119 | + | 7.51245i | −0.772117 | + | 0.445782i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.1022 | − | 8.14189i | −0.833879 | − | 0.481440i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3709 | −0.845346 | ||||||||
\(290\) | −0.578190 | + | 1.00145i | −0.0339525 | + | 0.0588074i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.40119 | + | 1.96368i | −0.199040 | + | 0.114916i | ||||
\(293\) | −14.9237 | − | 25.8485i | −0.871849 | − | 1.51009i | −0.860082 | − | 0.510156i | \(-0.829588\pi\) |
−0.0117671 | − | 0.999931i | \(-0.503746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.68873 | + | 13.3173i | −0.447655 | + | 0.775362i | ||||
\(296\) | − | 23.6706i | − | 1.37583i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.6648 | 0.965363 | ||||||||
\(299\) | −8.74598 | + | 15.1485i | −0.505793 | + | 0.876060i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.65892 | + | 0.957777i | −0.0954600 | + | 0.0551139i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00272 | − | 3.46567i | −0.344280 | − | 0.198770i | ||||
\(305\) | 7.04349i | 0.403309i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.68853i | 0.153442i | 0.997053 | + | 0.0767212i | \(0.0244451\pi\) | ||||
−0.997053 | + | 0.0767212i | \(0.975555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.94297 | + | 6.82943i | 0.223946 | + | 0.387886i | ||||
\(311\) | −5.53763 | − | 9.59145i | −0.314010 | − | 0.543881i | 0.665217 | − | 0.746650i | \(-0.268339\pi\) |
−0.979227 | + | 0.202769i | \(0.935006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4970 | − | 8.36987i | −0.819421 | − | 0.473093i | 0.0307957 | − | 0.999526i | \(-0.490196\pi\) |
−0.850217 | + | 0.526433i | \(0.823529\pi\) | |||||||
\(314\) | −9.34619 | −0.527436 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.66584 | 0.487492 | ||||||||
\(317\) | 2.54774 | + | 1.47094i | 0.143095 | + | 0.0826160i | 0.569838 | − | 0.821757i | \(-0.307006\pi\) |
−0.426743 | + | 0.904373i | \(0.640339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28001 | − | 2.21704i | −0.0716668 | − | 0.124131i | ||||
\(320\) | −6.33562 | − | 10.9736i | −0.354172 | − | 0.613444i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1758i | 0.733118i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.92883i | − | 0.328872i | ||||||
\(326\) | 0.943801 | + | 0.544904i | 0.0522723 | + | 0.0301794i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.70839 | + | 2.71839i | −0.259977 | + | 0.150098i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.44077 | + | 4.22753i | −0.134157 | + | 0.232366i | −0.925275 | − | 0.379297i | \(-0.876166\pi\) |
0.791118 | + | 0.611663i | \(0.209499\pi\) | |||||||
\(332\) | 9.08526 | 0.498618 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.7590i | 0.752859i | ||||||||
\(335\) | 11.7868 | − | 20.4154i | 0.643982 | − | 1.11541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.51421 | + | 11.2830i | 0.354852 | + | 0.614621i | 0.987093 | − | 0.160151i | \(-0.0511980\pi\) |
−0.632241 | + | 0.774772i | \(0.717865\pi\) | |||||||
\(338\) | 2.94622 | − | 1.70100i | 0.160253 | − | 0.0925221i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.58068 | + | 2.73782i | −0.0857245 | + | 0.148479i | ||||
\(341\) | −17.4581 | −0.945409 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.2556 | + | 10.5399i | 0.984275 | + | 0.568272i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.05081 | + | 3.49344i | −0.325293 | + | 0.187808i | ||||
\(347\) | 1.86351 | − | 1.07590i | 0.100039 | − | 0.0577573i | −0.449146 | − | 0.893458i | \(-0.648272\pi\) |
0.549185 | + | 0.835701i | \(0.314938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.2919 | + | 14.6023i | 1.35384 | + | 0.781642i | 0.988785 | − | 0.149343i | \(-0.0477159\pi\) |
0.365058 | + | 0.930985i | \(0.381049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.9470 | 1.11648 | ||||||||
\(353\) | −5.41764 | + | 9.38362i | −0.288352 | + | 0.499440i | −0.973416 | − | 0.229042i | \(-0.926441\pi\) |
0.685065 | + | 0.728482i | \(0.259774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.6179 | − | 13.6358i | 1.25351 | − | 0.723713i | ||||
\(356\) | −5.08239 | − | 8.80295i | −0.269366 | − | 0.466556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.94617 | + | 5.10291i | −0.155710 | + | 0.269697i | ||||
\(359\) | − | 20.9492i | − | 1.10566i | −0.833295 | − | 0.552829i | \(-0.813548\pi\) | ||
0.833295 | − | 0.552829i | \(-0.186452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −47.0300 | −2.47526 | ||||||||
\(362\) | 0.639442 | − | 1.10755i | 0.0336083 | − | 0.0582113i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.17348 | − | 3.56426i | 0.323135 | − | 0.186562i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.97835 | − | 2.87425i | −0.259868 | − | 0.150035i | 0.364407 | − | 0.931240i | \(-0.381272\pi\) |
−0.624274 | + | 0.781205i | \(0.714605\pi\) | |||||||
\(368\) | 3.67702i | 0.191678i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.6650i | 0.762398i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4467 | − | 25.0224i | −0.748023 | − | 1.29561i | −0.948769 | − | 0.315970i | \(-0.897670\pi\) |
0.200747 | − | 0.979643i | \(-0.435663\pi\) | |||||||
\(374\) | 3.25342 | + | 5.63509i | 0.168230 | + | 0.291383i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.4886 | − | 11.8291i | −1.05662 | − | 0.610039i | ||||
\(377\) | 2.54104 | 0.130870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.411434 | −0.0211339 | −0.0105670 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105670 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(380\) | −13.7205 | − | 7.92156i | −0.703849 | − | 0.406367i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.81376 | − | 4.87358i | −0.143965 | − | 0.249354i | ||||
\(383\) | −12.4007 | − | 21.4787i | −0.633648 | − | 1.09751i | −0.986800 | − | 0.161944i | \(-0.948223\pi\) |
0.353152 | − | 0.935566i | \(-0.385110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.53038i | − | 0.0778944i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 13.7123i | − | 0.696139i | ||||||
\(389\) | −3.82694 | − | 2.20948i | −0.194033 | − | 0.112025i | 0.399836 | − | 0.916587i | \(-0.369067\pi\) |
−0.593869 | + | 0.804561i | \(0.702400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.05319 | − | 3.49481i | 0.306123 | − | 0.176740i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.59554 | + | 16.6200i | −0.483416 | + | 0.837302i | ||||
\(395\) | −15.7293 | −0.791427 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2603i | 1.11721i | 0.829434 | + | 0.558605i | \(0.188663\pi\) | ||||
−0.829434 | + | 0.558605i | \(0.811337\pi\) | |||||||
\(398\) | −0.479229 | + | 0.830049i | −0.0240216 | + | 0.0416066i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.623155 | − | 1.07934i | −0.0311578 | − | 0.0539668i | ||||
\(401\) | 5.31899 | − | 3.07092i | 0.265617 | − | 0.153354i | −0.361277 | − | 0.932459i | \(-0.617659\pi\) |
0.626894 | + | 0.779104i | \(0.284326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.66434 | − | 15.0071i | 0.431602 | − | 0.747556i | ||||
\(404\) | −1.08803 | −0.0541317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.1162 | − | 16.2329i | −1.39367 | − | 0.804633i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.765886 | − | 0.442185i | 0.0378706 | − | 0.0218646i | −0.480945 | − | 0.876751i | \(-0.659706\pi\) |
0.518816 | + | 0.854886i | \(0.326373\pi\) | |||||||
\(410\) | 2.91706 | − | 1.68416i | 0.144063 | − | 0.0831749i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.47106 | + | 0.849316i | 0.0724739 | + | 0.0418428i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4906 | −0.809491 | ||||||||
\(416\) | −10.3959 | + | 18.0062i | −0.509700 | + | 0.882827i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −28.2401 | + | 16.3044i | −1.38127 | + | 0.797476i | ||||
\(419\) | 7.59365 | + | 13.1526i | 0.370974 | + | 0.642546i | 0.989716 | − | 0.143049i | \(-0.0456905\pi\) |
−0.618742 | + | 0.785595i | \(0.712357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3318 | − | 23.0914i | 0.649753 | − | 1.12541i | −0.333428 | − | 0.942775i | \(-0.608206\pi\) |
0.983182 | − | 0.182630i | \(-0.0584611\pi\) | |||||||
\(422\) | 23.5103i | 1.14446i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24.9517 | −1.21176 | ||||||||
\(425\) | −1.18455 | + | 2.05170i | −0.0574592 | + | 0.0995222i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.08358 | + | 1.78031i | −0.149050 | + | 0.0860543i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.3102 | − | 6.52992i | −0.545424 | − | 0.314901i | ||||
\(431\) | 4.69715i | 0.226254i | 0.993581 | + | 0.113127i | \(0.0360866\pi\) | ||||
−0.993581 | + | 0.113127i | \(0.963913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.97714i | − | 0.431414i | −0.976458 | − | 0.215707i | \(-0.930794\pi\) | ||
0.976458 | − | 0.215707i | \(-0.0692056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.91250 | − | 3.31254i | −0.0915919 | − | 0.158642i | ||||
\(437\) | 17.5142 | + | 30.3354i | 0.837816 | + | 1.45114i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3012 | + | 8.25679i | 0.682558 | + | 0.394075i | 0.800818 | − | 0.598907i | \(-0.204398\pi\) |
−0.118260 | + | 0.992983i | \(0.537732\pi\) | |||||||
\(440\) | −22.9225 | −1.09279 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.45861 | −0.307205 | ||||||||
\(443\) | −0.921171 | − | 0.531838i | −0.0437661 | − | 0.0252684i | 0.477957 | − | 0.878383i | \(-0.341377\pi\) |
−0.521723 | + | 0.853115i | \(0.674711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.22500 | + | 15.9782i | 0.437307 | + | 0.757438i | ||||
\(446\) | −1.52110 | − | 2.63461i | −0.0720260 | − | 0.124753i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.9081i | − | 0.750749i | −0.926873 | − | 0.375374i | \(-0.877514\pi\) | ||
0.926873 | − | 0.375374i | \(-0.122486\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.45688i | 0.351131i | ||||||||
\(452\) | 15.6352 | + | 9.02697i | 0.735417 | + | 0.424593i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.5309 | − | 10.6988i | 0.869698 | − | 0.502121i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3963 | − | 28.3992i | 0.766985 | − | 1.32846i | −0.172206 | − | 0.985061i | \(-0.555090\pi\) |
0.939191 | − | 0.343395i | \(-0.111577\pi\) | |||||||
\(458\) | −12.6734 | −0.592191 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.40463i | 0.391868i | ||||||||
\(461\) | 9.23690 | − | 15.9988i | 0.430205 | − | 0.745138i | −0.566685 | − | 0.823934i | \(-0.691774\pi\) |
0.996891 | + | 0.0787967i | \(0.0251078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.201921 | − | 0.349738i | −0.00938408 | − | 0.0162537i | 0.861295 | − | 0.508105i | \(-0.169654\pi\) |
−0.870679 | + | 0.491851i | \(0.836320\pi\) | |||||||
\(464\) | 0.462594 | − | 0.267079i | 0.0214754 | − | 0.0123988i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.396580 | + | 0.686897i | −0.0183712 | + | 0.0318199i | ||||
\(467\) | 15.0257 | 0.695304 | 0.347652 | − | 0.937624i | \(-0.386979\pi\) | ||||
0.347652 | + | 0.937624i | \(0.386979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.6936 | + | 7.32866i | 0.585512 | + | 0.338046i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.1002 | − | 12.1822i | 0.971216 | − | 0.560732i | ||||
\(473\) | 25.0387 | − | 14.4561i | 1.15128 | − | 0.664691i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.2821 | − | 5.93635i | −0.471773 | − | 0.272379i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.8321 | −0.632664 | ||||||||
\(479\) | 15.5400 | − | 26.9161i | 0.710041 | − | 1.22983i | −0.254800 | − | 0.966994i | \(-0.582010\pi\) |
0.964841 | − | 0.262833i | \(-0.0846569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.9077 | − | 16.1125i | 1.27248 | − | 0.734669i | ||||
\(482\) | 9.07944 | + | 15.7261i | 0.413557 | + | 0.716302i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.96029 | − | 5.12738i | 0.134559 | − | 0.233063i | ||||
\(485\) | 24.8892i | 1.13016i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4956 | 0.611546 | 0.305773 | − | 0.952104i | \(-0.401085\pi\) | ||||
0.305773 | + | 0.952104i | \(0.401085\pi\) | |||||||
\(488\) | 5.57994 | − | 9.66474i | 0.252592 | − | 0.437502i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.07098 | − | 4.08243i | 0.319109 | − | 0.184238i | −0.331886 | − | 0.943319i | \(-0.607685\pi\) |
0.650995 | + | 0.759082i | \(0.274352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.879342 | − | 0.507688i | −0.0396036 | − | 0.0228651i | ||||
\(494\) | − | 32.3672i | − | 1.45627i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.64269i | − | 0.163562i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0097 | + | 24.2655i | 0.627159 | + | 1.08627i | 0.988119 | + | 0.153690i | \(0.0491158\pi\) |
−0.360960 | + | 0.932581i | \(0.617551\pi\) | |||||||
\(500\) | −6.29863 | − | 10.9095i | −0.281683 | − | 0.487890i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.8497 | + | 10.8829i | 0.841305 | + | 0.485727i | ||||
\(503\) | 5.89656 | 0.262915 | 0.131457 | − | 0.991322i | \(-0.458034\pi\) | ||||
0.131457 | + | 0.991322i | \(0.458034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.97488 | 0.0878811 | ||||||||
\(506\) | 14.9811 | + | 8.64936i | 0.665992 | + | 0.384511i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.24883 | + | 9.09123i | 0.232879 | + | 0.403358i | ||||
\(509\) | 7.01957 | + | 12.1582i | 0.311137 | + | 0.538905i | 0.978609 | − | 0.205730i | \(-0.0659569\pi\) |
−0.667472 | + | 0.744635i | \(0.732624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9.45558i | 0.417882i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.98335i | 0.175698i | ||||||||
\(515\) | −2.67011 | − | 1.54159i | −0.117659 | − | 0.0679305i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.1014 | + | 16.2243i | −1.23590 | + | 0.713546i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11.3763 | − | 19.7043i | 0.498883 | − | 0.864090i | ||||
\(521\) | 38.4458 | 1.68434 | 0.842170 | − | 0.539213i | \(-0.181278\pi\) | ||||
0.842170 | + | 0.539213i | \(0.181278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10.4932i | − | 0.458834i | −0.973328 | − | 0.229417i | \(-0.926318\pi\) | ||
0.973328 | − | 0.229417i | \(-0.0736819\pi\) | |||||||
\(524\) | 2.57914 | − | 4.46720i | 0.112670 | − | 0.195150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.88879 | + | 8.46764i | 0.213161 | + | 0.369207i | ||||
\(527\) | −5.99668 | + | 3.46219i | −0.261220 | + | 0.150815i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.20889 | + | 3.82591i | −0.0960388 | + | 0.166344i | ||||
\(530\) | 15.4587 | 0.671483 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.40998 | − | 3.70080i | −0.277647 | − | 0.160300i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.59698 | − | 3.23142i | 0.241979 | − | 0.139706i | ||||
\(536\) | −32.3466 | + | 18.6753i | −1.39716 | + | 0.806650i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.47388 | − | 4.89240i | −0.365335 | − | 0.210926i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.1565 | 1.94143 | 0.970715 | − | 0.240232i | \(-0.0772235\pi\) | ||||
0.970715 | + | 0.240232i | \(0.0772235\pi\) | |||||||
\(542\) | −9.34112 | + | 16.1793i | −0.401236 | + | 0.694960i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.19510 | − | 4.15409i | 0.308487 | − | 0.178105i | ||||
\(545\) | 3.47136 | + | 6.01257i | 0.148697 | + | 0.257550i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.05733 | + | 7.02751i | −0.173479 | + | 0.300475i | −0.939634 | − | 0.342181i | \(-0.888834\pi\) |
0.766155 | + | 0.642656i | \(0.222168\pi\) | |||||||
\(548\) | 0.871279i | 0.0372192i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.86333 | −0.250013 | ||||||||
\(551\) | 2.54427 | − | 4.40680i | 0.108389 | − | 0.187736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.2818 | − | 7.66827i | 0.564291 | − | 0.325794i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.95311 | + | 3.43703i | 0.252468 | + | 0.145763i | ||||
\(557\) | 16.2727i | 0.689494i | 0.938696 | + | 0.344747i | \(0.112035\pi\) | ||||
−0.938696 | + | 0.344747i | \(0.887965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.6978i | 1.21379i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.8324 | + | 20.4942i | 0.499118 | + | 0.864498i | ||||
\(563\) | −5.13594 | − | 8.89572i | −0.216454 | − | 0.374910i | 0.737267 | − | 0.675601i | \(-0.236116\pi\) |
−0.953721 | + | 0.300692i | \(0.902783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.3793 | − | 16.3848i | −1.19393 | − | 0.689314i | ||||
\(566\) | −2.96233 | −0.124516 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.2098 | −1.81304 | ||||||||
\(569\) | 17.8537 | + | 10.3079i | 0.748468 | + | 0.432128i | 0.825140 | − | 0.564928i | \(-0.191096\pi\) |
−0.0766722 | + | 0.997056i | \(0.524429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.12828 | − | 3.68628i | −0.0890656 | − | 0.154266i | 0.818051 | − | 0.575146i | \(-0.195055\pi\) |
−0.907116 | + | 0.420880i | \(0.861721\pi\) | |||||||
\(572\) | 8.59640 | + | 14.8894i | 0.359434 | + | 0.622557i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.29836i | 0.262660i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9289i | 0.704760i | 0.935857 | + | 0.352380i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352380i | \(0.885372\pi\) | |||||||
\(578\) | −12.2168 | − | 7.05338i | −0.508153 | − | 0.293382i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.05736 | − | 0.610467i | 0.0439045 | − | 0.0253483i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.1114 | + | 29.6378i | −0.708682 | + | 1.22747i | ||||
\(584\) | −11.2946 | −0.467374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 29.2988i | − | 1.21032i | ||||||
\(587\) | −12.0558 | + | 20.8812i | −0.497594 | + | 0.861858i | −0.999996 | − | 0.00277589i | \(-0.999116\pi\) |
0.502402 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.3507 | − | 30.0522i | −0.714922 | − | 1.23828i | ||||
\(590\) | −13.0725 | + | 7.54743i | −0.538187 | + | 0.310723i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.38705 | − | 5.86654i | 0.139207 | − | 0.241113i | ||||
\(593\) | 38.5816 | 1.58436 | 0.792178 | − | 0.610290i | \(-0.208947\pi\) | ||||
0.792178 | + | 0.610290i | \(0.208947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.2378 | − | 8.79752i | −0.624163 | − | 0.360360i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.8701 | + | 8.58525i | −0.608083 | + | 0.351077i | ||||
\(599\) | 29.2921 | − | 16.9118i | 1.19684 | − | 0.690997i | 0.236992 | − | 0.971511i | \(-0.423838\pi\) |
0.959850 | + | 0.280514i | \(0.0905050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.4855 | − | 15.8688i | −1.12116 | − | 0.647300i | −0.179461 | − | 0.983765i | \(-0.557435\pi\) |
−0.941696 | + | 0.336465i | \(0.890769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.02249 | 0.0822939 | ||||||||
\(605\) | −5.37320 | + | 9.30666i | −0.218452 | + | 0.378370i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.169355 | + | 0.0977772i | −0.00687391 | + | 0.00396865i | −0.503433 | − | 0.864034i | \(-0.667930\pi\) |
0.496559 | + | 0.868003i | \(0.334597\pi\) | |||||||
\(608\) | 20.8181 | + | 36.0581i | 0.844287 | + | 1.46235i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.45702 | + | 5.98774i | −0.139971 | + | 0.242436i | ||||
\(611\) | − | 32.2082i | − | 1.30300i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.93328 | 0.118474 | 0.0592370 | − | 0.998244i | \(-0.481133\pi\) | ||||
0.0592370 | + | 0.998244i | \(0.481133\pi\) | |||||||
\(614\) | −1.31956 | + | 2.28554i | −0.0532530 | + | 0.0922370i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.86982 | − | 4.54365i | 0.316827 | − | 0.182920i | −0.333150 | − | 0.942874i | \(-0.608112\pi\) |
0.649977 | + | 0.759953i | \(0.274778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8586 | + | 14.3521i | 0.999152 | + | 0.576861i | 0.907997 | − | 0.418976i | \(-0.137611\pi\) |
0.0911550 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(620\) | − | 8.32617i | − | 0.334387i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.8717i | − | 0.435916i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.77986 | + | 13.4751i | 0.311194 | + | 0.539004i | ||||
\(626\) | −8.21604 | − | 14.2306i | −0.328379 | − | 0.568769i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.54588 | + | 4.93397i | 0.341018 | + | 0.196887i | ||||
\(629\) | −12.8768 | −0.513433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7691 | −0.826805 | −0.413403 | − | 0.910548i | \(-0.635660\pi\) | ||||
−0.413403 | + | 0.910548i | \(0.635660\pi\) | |||||||
\(632\) | 21.5830 | + | 12.4609i | 0.858525 | + | 0.495670i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.44390 | + | 2.50091i | 0.0573447 | + | 0.0993240i | ||||
\(635\) | −9.52711 | − | 16.5014i | −0.378072 | − | 0.654839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.51297i | − | 0.0994895i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.83981i | 0.270367i | ||||||||
\(641\) | −39.7733 | − | 22.9632i | −1.57095 | − | 0.906990i | −0.996052 | − | 0.0887664i | \(-0.971708\pi\) |
−0.574900 | − | 0.818224i | \(-0.694959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.15428 | − | 5.28523i | 0.361010 | − | 0.208429i | −0.308514 | − | 0.951220i | \(-0.599832\pi\) |
0.669524 | + | 0.742791i | \(0.266498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.46680 | + | 11.2008i | −0.254433 | + | 0.440691i | ||||
\(647\) | 38.5123 | 1.51408 | 0.757038 | − | 0.653371i | \(-0.226646\pi\) | ||||
0.757038 | + | 0.653371i | \(0.226646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 33.4173i | − | 1.31174i | ||||||
\(650\) | 2.90993 | − | 5.04015i | 0.114137 | − | 0.197691i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.575323 | − | 0.996488i | −0.0225314 | − | 0.0390255i | ||||
\(653\) | 11.0867 | − | 6.40089i | 0.433855 | − | 0.250486i | −0.267133 | − | 0.963660i | \(-0.586076\pi\) |
0.700988 | + | 0.713173i | \(0.252743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.68137 | + | 8.10837i | −0.182916 | + | 0.316820i | ||||
\(656\) | −1.55590 | −0.0607479 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.5777 | − | 24.0049i | −1.61964 | − | 0.935097i | −0.987014 | − | 0.160636i | \(-0.948645\pi\) |
−0.632622 | − | 0.774461i | \(-0.718021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.38011 | + | 5.41561i | −0.364844 | + | 0.210643i | −0.671204 | − | 0.741273i | \(-0.734222\pi\) |
0.306360 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(662\) | −4.14983 | + | 2.39591i | −0.161288 | + | 0.0931196i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.6276 | + | 13.0640i | 0.878121 | + | 0.506983i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.69942 | −0.104522 | ||||||||
\(668\) | 7.26354 | − | 12.5808i | 0.281035 | − | 0.486767i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.0402 | − | 11.5702i | 0.774219 | − | 0.446995i | ||||
\(671\) | −7.65323 | − | 13.2558i | −0.295450 | − | 0.511734i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.19553 | + | 10.7310i | −0.238820 | + | 0.413649i | −0.960376 | − | 0.278707i | \(-0.910094\pi\) |
0.721556 | + | 0.692356i | \(0.243427\pi\) | |||||||
\(674\) | 12.7890i | 0.492613i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.59191 | −0.138150 | ||||||||
\(677\) | −14.4947 | + | 25.1056i | −0.557078 | + | 0.964888i | 0.440660 | + | 0.897674i | \(0.354744\pi\) |
−0.997739 | + | 0.0672139i | \(0.978589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.87364 | + | 4.54585i | −0.301940 | + | 0.174325i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.8413 | − | 8.56862i | −0.568302 | − | 0.328109i | ||||
\(683\) | − | 0.152476i | − | 0.00583433i | −0.999996 | − | 0.00291717i | \(-0.999071\pi\) | ||
0.999996 | − | 0.00291717i | \(-0.000928564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.58145i | − | 0.0604242i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.01631 | + | 5.22441i | 0.114996 | + | 0.199179i | ||||
\(689\) | −16.9846 | − | 29.4181i | −0.647060 | − | 1.12074i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.4428 | − | 21.6176i | −1.42439 | − | 0.822373i | −0.427722 | − | 0.903910i | \(-0.640684\pi\) |
−0.996670 | + | 0.0815369i | \(0.974017\pi\) | |||||||
\(692\) | 7.37691 | 0.280428 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.11225 | 0.0801799 | ||||||||
\(695\) | −10.8055 | − | 6.23853i | −0.409874 | − | 0.236641i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.47880 | + | 2.56136i | 0.0560137 | + | 0.0970186i | ||||
\(698\) | 14.3339 | + | 24.8271i | 0.542546 | + | 0.939718i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5821i | 0.437451i | 0.975786 | + | 0.218726i | \(0.0701900\pi\) | ||||
−0.975786 | + | 0.218726i | \(0.929810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 64.5319i | − | 2.43387i | ||||||
\(704\) | 23.8472 | + | 13.7682i | 0.898774 | + | 0.518907i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.21116 | + | 5.31807i | −0.346667 | + | 0.200148i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.9474 | − | 32.8178i | 0.711584 | − | 1.23250i | −0.252678 | − | 0.967550i | \(-0.581311\pi\) |
0.964262 | − | 0.264949i | \(-0.0853552\pi\) | |||||||
\(710\) | 26.7704 | 1.00467 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 29.2326i | − | 1.09554i | ||||||
\(713\) | −9.20437 | + | 15.9424i | −0.344707 | + | 0.597049i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.6033 | − | 27.0256i | −0.583529 | − | 1.01070i | ||||
\(716\) | 5.38777 | − | 3.11063i | 0.201351 | − | 0.116250i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.2821 | − | 17.8091i | 0.383724 | − | 0.664630i | ||||
\(719\) | 46.6317 | 1.73907 | 0.869534 | − | 0.493873i | \(-0.164419\pi\) | ||||
0.869534 | + | 0.493873i | \(0.164419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −39.9806 | − | 23.0828i | −1.48792 | − | 0.859054i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.16937 | + | 0.675138i | −0.0434594 | + | 0.0250913i | ||||
\(725\) | 0.792377 | − | 0.457479i | 0.0294282 | − | 0.0169904i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.72659 | − | 2.15155i | −0.138212 | − | 0.0797965i | 0.429300 | − | 0.903162i | \(-0.358760\pi\) |
−0.567511 | + | 0.823366i | \(0.692094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.99751 | 0.258989 | ||||||||
\(731\) | 5.73369 | − | 9.93104i | 0.212068 | − | 0.367313i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1337 | − | 7.00539i | 0.448168 | − | 0.258750i | −0.258888 | − | 0.965907i | \(-0.583356\pi\) |
0.707056 | + | 0.707157i | \(0.250023\pi\) | |||||||
\(734\) | −2.82143 | − | 4.88685i | −0.104141 | − | 0.180377i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.0438 | − | 19.1285i | 0.407081 | − | 0.705086i | ||||
\(737\) | 51.2287i | 1.88703i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.8627 | 1.39280 | 0.696401 | − | 0.717653i | \(-0.254784\pi\) | ||||
0.696401 | + | 0.717653i | \(0.254784\pi\) | |||||||
\(740\) | 7.74184 | − | 13.4093i | 0.284596 | − | 0.492934i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0489 | − | 13.8847i | 0.882269 | − | 0.509378i | 0.0108634 | − | 0.999941i | \(-0.496542\pi\) |
0.871406 | + | 0.490563i | \(0.163209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.6579 | + | 15.9683i | 1.01331 | + | 0.585034i | ||||
\(746\) | − | 28.3624i | − | 1.03842i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 6.87007i | − | 0.251195i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.67540 | + | 15.0262i | 0.316570 | + | 0.548315i | 0.979770 | − | 0.200127i | \(-0.0641355\pi\) |
−0.663200 | + | 0.748442i | \(0.730802\pi\) | |||||||
\(752\) | −3.38527 | − | 5.86346i | −0.123448 | − | 0.213818i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.16017 | + | 1.24717i | 0.0786686 | + | 0.0454193i | ||||
\(755\) | −3.67100 | −0.133601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8111 | 0.683701 | 0.341850 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341850 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(758\) | −0.349764 | − | 0.201936i | −0.0127040 | − | 0.00733465i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.7814 | − | 39.4586i | −0.826369 | − | 1.43131i | ||||
\(761\) | −4.22520 | − | 7.31825i | −0.153163 | − | 0.265286i | 0.779225 | − | 0.626744i | \(-0.215613\pi\) |
−0.932389 | + | 0.361457i | \(0.882279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.94167i | 0.214962i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 24.3457i | − | 0.879644i | ||||||
\(767\) | 28.7257 | + | 16.5848i | 1.03723 | + | 0.598843i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.8100 | − | 11.4373i | 0.714366 | − | 0.412440i | −0.0983092 | − | 0.995156i | \(-0.531343\pi\) |
0.812676 | + | 0.582716i | \(0.198010\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.807907 | + | 1.39934i | −0.0290772 | + | 0.0503632i | ||||
\(773\) | −37.6747 | −1.35507 | −0.677533 | − | 0.735492i | \(-0.736951\pi\) | ||||
−0.677533 | + | 0.735492i | \(0.736951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.23957i | − | 0.224132i | ||||||
\(776\) | 19.7175 | − | 34.1517i | 0.707817 | − | 1.22598i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.16888 | − | 3.75660i | −0.0777579 | − | 0.134681i | ||||
\(779\) | −12.8362 | + | 7.41099i | −0.459905 | + | 0.265526i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.6324 | + | 51.3249i | −1.06033 | + | 1.83655i | ||||
\(782\) | 6.86116 | 0.245355 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.5116 | − | 8.95561i | −0.553632 | − | 0.319639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.3222 | + | 11.7330i | −0.724408 | + | 0.418237i | −0.816373 | − | 0.577525i | \(-0.804019\pi\) |
0.0919648 | + | 0.995762i | \(0.470685\pi\) | |||||||
\(788\) | 17.5478 | − | 10.1312i | 0.625113 | − | 0.360909i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.3716 | − | 7.72011i | −0.475741 | − | 0.274669i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1930 | 0.539519 | ||||||||
\(794\) | −10.9256 | + | 18.9237i | −0.387734 | + | 0.671575i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.876386 | − | 0.505981i | 0.0310627 | − | 0.0179340i | ||||
\(797\) | 22.8856 | + | 39.6390i | 0.810648 | + | 1.40408i | 0.912411 | + | 0.409275i | \(0.134218\pi\) |
−0.101763 | + | 0.994809i | \(0.532448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.43503 | + | 11.1458i | −0.227655 | + | 0.394310i | ||||
\(800\) | 7.48653i | 0.264689i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.02896 | 0.212890 | ||||||||
\(803\) | −7.74562 | + | 13.4158i | −0.273337 | + | 0.473433i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.7313 | − | 8.50510i | 0.518887 | − | 0.299579i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.70984 | − | 1.56453i | −0.0953317 | − | 0.0550398i | ||||
\(809\) | 13.2408i | 0.465522i | 0.972534 | + | 0.232761i | \(0.0747761\pi\) | ||||
−0.972534 | + | 0.232761i | \(0.925224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 56.0437i | − | 1.96796i | −0.178275 | − | 0.983981i | \(-0.557052\pi\) | ||
0.178275 | − | 0.983981i | \(-0.442948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.9345 | − | 27.5994i | −0.558505 | − | 0.967359i | ||||
\(815\) | 1.04426 | + | 1.80872i | 0.0365790 | + | 0.0633566i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.7692 | + | 28.7343i | 1.74120 | + | 1.00528i | ||||
\(818\) | 0.868116 | 0.0303530 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.55636 | −0.124193 | ||||||||
\(821\) | −48.7766 | − | 28.1612i | −1.70232 | − | 0.982833i | −0.943407 | − | 0.331636i | \(-0.892399\pi\) |
−0.758909 | − | 0.651197i | \(-0.774267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.52180 | − | 14.7602i | −0.297051 | − | 0.514508i | 0.678409 | − | 0.734685i | \(-0.262670\pi\) |
−0.975460 | + | 0.220177i | \(0.929337\pi\) | |||||||
\(824\) | 2.44253 | + | 4.23058i | 0.0850895 | + | 0.147379i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.7715i | − | 1.59163i | −0.605539 | − | 0.795816i | \(-0.707042\pi\) | ||
0.605539 | − | 0.795816i | \(-0.292958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.2839i | 1.22546i | 0.790293 | + | 0.612730i | \(0.209929\pi\) | ||||
−0.790293 | + | 0.612730i | \(0.790071\pi\) | |||||||
\(830\) | −14.0188 | − | 8.09376i | −0.486600 | − | 0.280938i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.6704 | + | 13.6661i | −0.820623 | + | 0.473787i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1840 | + | 22.8354i | −0.456251 | + | 0.790250i | ||||
\(836\) | 34.4292 | 1.19076 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.9082i | 0.514995i | ||||||||
\(839\) | 22.3195 | − | 38.6585i | 0.770555 | − | 1.33464i | −0.166704 | − | 0.986007i | \(-0.553312\pi\) |
0.937259 | − | 0.348634i | \(-0.113354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3039 | − | 24.7751i | −0.493239 | − | 0.854315i | ||||
\(842\) | 22.6670 | − | 13.0868i | 0.781157 | − | 0.451001i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.4114 | − | 21.4971i | 0.427216 | − | 0.739960i | ||||
\(845\) | 6.51965 | 0.224283 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.18404 | − | 3.57036i | −0.212361 | − | 0.122607i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.01400 | + | 1.16278i | −0.0690795 | + | 0.0398831i | ||||
\(851\) | −29.6472 | + | 17.1168i | −1.01629 | + | 0.586757i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.7652 | + | 27.5772i | 1.63545 | + | 0.944227i | 0.982372 | + | 0.186935i | \(0.0598554\pi\) |
0.653077 | + | 0.757292i | \(0.273478\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.2399 | −0.349992 | ||||||||
\(857\) | −19.0771 | + | 33.0425i | −0.651660 | + | 1.12871i | 0.331059 | + | 0.943610i | \(0.392594\pi\) |
−0.982720 | + | 0.185099i | \(0.940739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0465 | + | 20.2341i | −1.19577 | + | 0.690378i | −0.959609 | − | 0.281336i | \(-0.909222\pi\) |
−0.236160 | + | 0.971714i | \(0.575889\pi\) | |||||||
\(860\) | 6.89444 | + | 11.9415i | 0.235099 | + | 0.407203i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.30541 | + | 3.99309i | −0.0785226 | + | 0.136005i | ||||
\(863\) | 36.2021i | 1.23233i | 0.787616 | + | 0.616167i | \(0.211315\pi\) | ||||
−0.787616 | + | 0.616167i | \(0.788685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.3898 | −0.455266 | ||||||||
\(866\) | 4.40608 | − | 7.63155i | 0.149725 | − | 0.259331i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.6024 | − | 17.0910i | 1.00419 | − | 0.579771i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.0365 | − | 25.4245i | −1.49212 | − | 0.861475i | ||||
\(872\) | − | 11.0002i | − | 0.372514i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34.3846i | 1.16307i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.53439 | + | 9.58584i | 0.186883 | + | 0.323691i | 0.944209 | − | 0.329346i | \(-0.106828\pi\) |
−0.757326 | + | 0.653036i | \(0.773495\pi\) | |||||||
\(878\) | 8.10505 | + | 14.0384i | 0.273532 | + | 0.473771i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.68111 | − | 3.27999i | −0.191510 | − | 0.110568i | ||||
\(881\) | −8.87036 | −0.298850 | −0.149425 | − | 0.988773i | \(-0.547742\pi\) | ||||
−0.149425 | + | 0.988773i | \(0.547742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.1903 | −0.477540 | −0.238770 | − | 0.971076i | \(-0.576744\pi\) | ||||
−0.238770 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(884\) | 5.90556 | + | 3.40958i | 0.198625 | + | 0.114676i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.522064 | − | 0.904241i | −0.0175391 | − | 0.0303786i | ||||
\(887\) | −19.5180 | − | 33.8062i | −0.655350 | − | 1.13510i | −0.981806 | − | 0.189887i | \(-0.939188\pi\) |
0.326456 | − | 0.945213i | \(-0.394146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.1109i | 0.607080i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.21202i | 0.107546i | ||||||||
\(893\) | −55.8570 | − | 32.2490i | −1.86918 | − | 1.07917i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.77931 | + | 5.64609i | −0.326886 | + | 0.188728i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.80786 | − | 13.5236i | 0.260552 | − | 0.451288i | ||||
\(899\) | 2.67422 | 0.0891904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5737i | 0.452207i | ||||||||
\(902\) | −3.65992 | + | 6.33916i | −0.121862 | + | 0.211071i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.9605 | + | 44.9648i | 0.863432 | + | 1.49551i | ||||
\(905\) | 2.12252 | − | 1.22544i | 0.0705550 | − | 0.0407350i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.93487 | + | 8.54745i | −0.163860 | + | 0.283813i | −0.936250 | − | 0.351335i | \(-0.885728\pi\) |
0.772390 | + | 0.635148i | \(0.219061\pi\) | |||||||
\(908\) | −22.5921 | −0.749747 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.6335 | + | 26.9239i | 1.54504 | + | 0.892028i | 0.998509 | + | 0.0545881i | \(0.0173846\pi\) |
0.546529 | + | 0.837440i | \(0.315949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.0351 | − | 17.9181i | 1.02711 | − | 0.593004i | ||||
\(914\) | 27.8772 | − | 16.0949i | 0.922096 | − | 0.532373i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.5882 | + | 6.69046i | 0.382885 | + | 0.221059i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1799 | 0.731647 | 0.365824 | − | 0.930684i | \(-0.380787\pi\) | ||||
0.365824 | + | 0.930684i | \(0.380787\pi\) | |||||||
\(920\) | −12.0853 | + | 20.9324i | −0.398442 | + | 0.690122i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.7047 | − | 9.06714i | 0.517208 | − | 0.298610i | ||||
\(923\) | −29.4128 | − | 50.9444i | −0.968133 | − | 1.67686i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.80167 | − | 10.0488i | 0.190758 | − | 0.330402i | ||||
\(926\) | − | 0.396421i | − | 0.0130272i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.20866 | −0.105329 | ||||||||
\(929\) | 27.4954 | − | 47.6234i | 0.902093 | − | 1.56247i | 0.0773215 | − | 0.997006i | \(-0.475363\pi\) |
0.824772 | − | 0.565466i | \(-0.191303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.725243 | − | 0.418719i | 0.0237561 | − | 0.0137156i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.7734 | + | 7.37475i | 0.417960 | + | 0.241309i | ||||
\(935\) | 12.4698i | 0.407807i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3132i | 0.957622i | 0.877918 | + | 0.478811i | \(0.158932\pi\) | ||||
−0.877918 | + | 0.478811i | \(0.841068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.73777 | − | 13.4022i | −0.252378 | − | 0.437132i | ||||
\(941\) | 7.58758 | + | 13.1421i | 0.247348 | + | 0.428419i | 0.962789 | − | 0.270254i | \(-0.0871076\pi\) |
−0.715441 | + | 0.698673i | \(0.753774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.80950 | + | 3.93147i | 0.221748 | + | 0.128026i | ||||
\(944\) | 6.97265 | 0.226940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.3808 | 0.922739 | ||||||||
\(947\) | −2.27478 | − | 1.31335i | −0.0739206 | − | 0.0426781i | 0.462584 | − | 0.886575i | \(-0.346922\pi\) |
−0.536505 | + | 0.843897i | \(0.680256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.68820 | − | 13.3164i | −0.249570 | − | 0.432267i | ||||
\(950\) | −5.82725 | − | 10.0931i | −0.189061 | − | 0.327463i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5520i | 1.31361i | 0.754061 | + | 0.656805i | \(0.228092\pi\) | ||||
−0.754061 | + | 0.656805i | \(0.771908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.7847i | − | 0.348984i | ||||||
\(956\) | 12.6476 | + | 7.30212i | 0.409054 | + | 0.236167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.4214 | − | 15.2544i | 0.853637 | − | 0.492847i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.38155 | + | 11.0532i | −0.205856 | + | 0.356554i | ||||
\(962\) | 31.6328 | 1.01988 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 19.1726i | − | 0.617507i | ||||||
\(965\) | 1.46643 | − | 2.53993i | 0.0472059 | − | 0.0817631i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.47468 | + | 11.2145i | 0.208212 | + | 0.360633i | 0.951151 | − | 0.308725i | \(-0.0999023\pi\) |
−0.742939 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(968\) | 14.7457 | − | 8.51343i | 0.473945 | − | 0.273632i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.2159 | + | 21.1585i | −0.392228 | + | 0.679359i | ||||
\(971\) | 16.5215 | 0.530202 | 0.265101 | − | 0.964221i | \(-0.414595\pi\) | ||||
0.265101 | + | 0.964221i | \(0.414595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.4728 | + | 6.62381i | 0.367611 | + | 0.212240i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76587 | − | 1.59687i | 0.0885333 | − | 0.0511147i | ||||
\(977\) | −5.50730 | + | 3.17964i | −0.176194 | + | 0.101726i | −0.585503 | − | 0.810670i | \(-0.699103\pi\) |
0.409309 | + | 0.912396i | \(0.365770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.7227 | − | 20.0472i | −1.10974 | − | 0.640711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.01481 | 0.255763 | ||||||||
\(983\) | 1.11487 | − | 1.93102i | 0.0355590 | − | 0.0615899i | −0.847698 | − | 0.530479i | \(-0.822012\pi\) |
0.883257 | + | 0.468889i | \(0.155346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.8508 | + | 18.3891i | −1.01485 | + | 0.585924i | ||||
\(986\) | −0.498358 | − | 0.863181i | −0.0158709 | − | 0.0274893i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.0870 | + | 29.5956i | −0.543610 | + | 0.941561i | ||||
\(989\) | − | 30.4865i | − | 0.969415i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.4570 | −1.57105 | −0.785527 | − | 0.618828i | \(-0.787608\pi\) | ||||
−0.785527 | + | 0.618828i | \(0.787608\pi\) | |||||||
\(992\) | −10.9407 | + | 18.9499i | −0.347369 | + | 0.601661i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59072 | + | 0.918403i | −0.0504293 | + | 0.0291153i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.28219 | + | 4.20437i | 0.230629 | + | 0.133154i | 0.610862 | − | 0.791737i | \(-0.290823\pi\) |
−0.380233 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(998\) | 27.5044i | 0.870636i | ||||||||
\(999\) | 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.o.e.440.15 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.10 | yes | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.18 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.10 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.9 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.8 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.16 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.9 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.16 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.15 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.16 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.16 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.15 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.9 | ✓ | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.10 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.9 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.10 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.10 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.9 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.8 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.16 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.15 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.15 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.9 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.68.10 | 48 | 63.4 | even | 3 | |||
441.2.i.d.227.15 | 48 | 21.2 | odd | 6 | |||
441.2.i.d.227.16 | 48 | 21.5 | even | 6 | |||
441.2.o.e.146.9 | ✓ | 48 | 21.20 | even | 2 | ||
441.2.o.e.146.10 | yes | 48 | 3.2 | odd | 2 | ||
441.2.o.e.293.9 | yes | 48 | 9.4 | even | 3 | ||
441.2.o.e.293.10 | yes | 48 | 63.13 | odd | 6 | ||
441.2.s.d.362.15 | 48 | 21.17 | even | 6 | |||
441.2.s.d.362.16 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.374.15 | 48 | 63.58 | even | 3 | |||
441.2.s.d.374.16 | 48 | 63.40 | odd | 6 | |||
1323.2.i.d.521.8 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.521.18 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.1097.8 | 48 | 63.32 | odd | 6 | |||
1323.2.i.d.1097.18 | 48 | 63.59 | even | 6 | |||
1323.2.o.e.440.15 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.440.16 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.15 | 48 | 63.41 | even | 6 | inner | ||
1323.2.o.e.881.16 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.s.d.656.9 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.656.10 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.962.9 | 48 | 63.5 | even | 6 | |||
1323.2.s.d.962.10 | 48 | 63.23 | odd | 6 |