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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.9 | ||
Character | \(\chi\) | \(=\) | 1323.226 |
Dual form | 1323.2.h.h.802.9 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72661 | 1.22090 | 0.610449 | − | 0.792056i | \(-0.290989\pi\) | ||||
0.610449 | + | 0.792056i | \(0.290989\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.981184 | 0.490592 | ||||||||
\(5\) | 1.75616 | + | 3.04175i | 0.785377 | + | 1.36031i | 0.928774 | + | 0.370647i | \(0.120864\pi\) |
−0.143397 | + | 0.989665i | \(0.545803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.75910 | −0.621935 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.03220 | + | 5.25192i | 0.958865 | + | 1.66080i | ||||
\(11\) | −3.04532 | + | 5.27465i | −0.918199 | + | 1.59037i | −0.116049 | + | 0.993244i | \(0.537023\pi\) |
−0.802150 | + | 0.597123i | \(0.796310\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.560139 | − | 0.970190i | 0.155355 | − | 0.269082i | −0.777833 | − | 0.628471i | \(-0.783681\pi\) |
0.933188 | + | 0.359388i | \(0.117015\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99965 | −1.24991 | ||||||||
\(17\) | 0.601978 | + | 1.04266i | 0.146001 | + | 0.252881i | 0.929746 | − | 0.368202i | \(-0.120026\pi\) |
−0.783745 | + | 0.621083i | \(0.786693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.10269 | − | 1.90991i | 0.252974 | − | 0.438163i | −0.711370 | − | 0.702818i | \(-0.751925\pi\) |
0.964343 | + | 0.264655i | \(0.0852581\pi\) | |||||||
\(20\) | 1.72311 | + | 2.98452i | 0.385300 | + | 0.667359i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25808 | + | 9.10727i | −1.12103 | + | 1.94168i | ||||
\(23\) | −0.636695 | − | 1.10279i | −0.132760 | − | 0.229947i | 0.791980 | − | 0.610548i | \(-0.209051\pi\) |
−0.924740 | + | 0.380601i | \(0.875717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66817 | + | 6.35345i | −0.733633 | + | 1.27069i | ||||
\(26\) | 0.967143 | − | 1.67514i | 0.189672 | − | 0.328522i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.10262 | + | 5.37390i | 0.576142 | + | 0.997907i | 0.995917 | + | 0.0902789i | \(0.0287758\pi\) |
−0.419774 | + | 0.907628i | \(0.637891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.188404 | −0.0338383 | −0.0169192 | − | 0.999857i | \(-0.505386\pi\) | ||||
−0.0169192 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(32\) | −5.11425 | −0.904079 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.03938 | + | 1.80026i | 0.178252 | + | 0.308742i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.78835 | + | 3.09752i | −0.294003 | + | 0.509228i | −0.974753 | − | 0.223288i | \(-0.928321\pi\) |
0.680749 | + | 0.732516i | \(0.261654\pi\) | |||||||
\(38\) | 1.90391 | − | 3.29767i | 0.308855 | − | 0.534953i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.08925 | − | 5.35074i | −0.488453 | − | 0.846026i | ||||
\(41\) | −1.68320 | + | 2.91538i | −0.262871 | + | 0.455307i | −0.967004 | − | 0.254762i | \(-0.918003\pi\) |
0.704132 | + | 0.710069i | \(0.251336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90276 | − | 3.29567i | −0.290168 | − | 0.502585i | 0.683681 | − | 0.729781i | \(-0.260378\pi\) |
−0.973849 | + | 0.227195i | \(0.927044\pi\) | |||||||
\(44\) | −2.98802 | + | 5.17540i | −0.450461 | + | 0.780221i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.09932 | − | 1.90408i | −0.162086 | − | 0.280742i | ||||
\(47\) | 5.72070 | 0.834449 | 0.417225 | − | 0.908803i | \(-0.363003\pi\) | ||||
0.417225 | + | 0.908803i | \(0.363003\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.33349 | + | 10.9699i | −0.895691 | + | 1.55138i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.549600 | − | 0.951935i | 0.0762158 | − | 0.132010i | ||||
\(53\) | −4.16913 | − | 7.22115i | −0.572675 | − | 0.991901i | −0.996290 | − | 0.0860593i | \(-0.972573\pi\) |
0.423615 | − | 0.905842i | \(-0.360761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.3922 | −2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.35702 | + | 9.27862i | 0.703411 | + | 1.21834i | ||||
\(59\) | 11.2685 | 1.46704 | 0.733519 | − | 0.679669i | \(-0.237877\pi\) | ||||
0.733519 | + | 0.679669i | \(0.237877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0022 | 1.53672 | 0.768361 | − | 0.640017i | \(-0.221073\pi\) | ||||
0.768361 | + | 0.640017i | \(0.221073\pi\) | |||||||
\(62\) | −0.325300 | −0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | 3.93477 | 0.488048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.91303 | −0.966731 | −0.483366 | − | 0.875419i | \(-0.660586\pi\) | ||||
−0.483366 | + | 0.875419i | \(0.660586\pi\) | |||||||
\(68\) | 0.590651 | + | 1.02304i | 0.0716270 | + | 0.124062i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2052 | 1.44850 | 0.724248 | − | 0.689540i | \(-0.242187\pi\) | ||||
0.724248 | + | 0.689540i | \(0.242187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.65737 | + | 4.60269i | 0.311021 | + | 0.538704i | 0.978584 | − | 0.205849i | \(-0.0659957\pi\) |
−0.667563 | + | 0.744554i | \(0.732662\pi\) | |||||||
\(74\) | −3.08779 | + | 5.34820i | −0.358948 | + | 0.621716i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.08194 | − | 1.87397i | 0.124107 | − | 0.214959i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.21711 | 1.03701 | 0.518503 | − | 0.855076i | \(-0.326490\pi\) | ||||
0.518503 | + | 0.855076i | \(0.326490\pi\) | |||||||
\(80\) | −8.78016 | − | 15.2077i | −0.981651 | − | 1.70027i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.90623 | + | 5.03373i | −0.320939 | + | 0.555883i | ||||
\(83\) | −0.624950 | − | 1.08245i | −0.0685972 | − | 0.118814i | 0.829687 | − | 0.558229i | \(-0.188519\pi\) |
−0.898284 | + | 0.439415i | \(0.855186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11433 | + | 3.66213i | −0.229332 | + | 0.397214i | ||||
\(86\) | −3.28532 | − | 5.69034i | −0.354265 | − | 0.613605i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.35702 | − | 9.27862i | 0.571060 | − | 0.989105i | ||||
\(89\) | 2.77066 | − | 4.79892i | 0.293689 | − | 0.508684i | −0.680990 | − | 0.732293i | \(-0.738450\pi\) |
0.974679 | + | 0.223608i | \(0.0717837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.624715 | − | 1.08204i | −0.0651310 | − | 0.112810i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.87741 | 1.01878 | ||||||||
\(95\) | 7.74596 | 0.794718 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.24277 | + | 14.2769i | 0.836926 | + | 1.44960i | 0.892452 | + | 0.451142i | \(0.148983\pi\) |
−0.0555261 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.59915 | + | 6.23391i | −0.359915 | + | 0.623391i | ||||
\(101\) | −6.48192 | + | 11.2270i | −0.644975 | + | 1.11713i | 0.339332 | + | 0.940667i | \(0.389799\pi\) |
−0.984307 | + | 0.176463i | \(0.943534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.35091 | − | 2.33984i | −0.133109 | − | 0.230552i | 0.791765 | − | 0.610826i | \(-0.209163\pi\) |
−0.924873 | + | 0.380275i | \(0.875829\pi\) | |||||||
\(104\) | −0.985340 | + | 1.70666i | −0.0966205 | + | 0.167352i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.19847 | − | 12.4681i | −0.699177 | − | 1.21101i | ||||
\(107\) | −0.0892402 | + | 0.154569i | −0.00862718 | + | 0.0149427i | −0.870307 | − | 0.492510i | \(-0.836079\pi\) |
0.861680 | + | 0.507453i | \(0.169413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.67927 | − | 8.10473i | −0.448192 | − | 0.776292i | 0.550076 | − | 0.835115i | \(-0.314599\pi\) |
−0.998268 | + | 0.0588226i | \(0.981265\pi\) | |||||||
\(110\) | −36.9360 | −3.52171 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.21019 | + | 7.29226i | −0.396061 | + | 0.685998i | −0.993236 | − | 0.116113i | \(-0.962957\pi\) |
0.597175 | + | 0.802111i | \(0.296290\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.23627 | − | 3.87333i | 0.208533 | − | 0.361190i | ||||
\(116\) | 3.04424 | + | 5.27278i | 0.282651 | + | 0.489565i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.4564 | 1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0479 | − | 22.5997i | −1.18618 | − | 2.05452i | ||||
\(122\) | 20.7231 | 1.87618 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.184859 | −0.0166008 | ||||||||
\(125\) | −8.20593 | −0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | 12.2469 | 1.08248 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.79381 | 0.595857 | ||||||||
\(131\) | −7.62335 | − | 13.2040i | −0.666055 | − | 1.15364i | −0.978998 | − | 0.203870i | \(-0.934648\pi\) |
0.312943 | − | 0.949772i | \(-0.398685\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.6627 | −1.18028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.05894 | − | 1.83413i | −0.0908032 | − | 0.157276i | ||||
\(137\) | 3.07350 | − | 5.32346i | 0.262587 | − | 0.454814i | −0.704342 | − | 0.709861i | \(-0.748758\pi\) |
0.966929 | + | 0.255047i | \(0.0820910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.438687 | − | 0.759829i | 0.0372090 | − | 0.0644478i | −0.846821 | − | 0.531878i | \(-0.821487\pi\) |
0.884030 | + | 0.467430i | \(0.154820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.0737 | 1.76847 | ||||||||
\(143\) | 3.41161 | + | 5.90908i | 0.285293 | + | 0.494142i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8974 | + | 18.8748i | −0.904977 | + | 1.56747i | ||||
\(146\) | 4.58824 | + | 7.94706i | 0.379725 | + | 0.657703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.75470 | + | 3.03923i | −0.144236 | + | 0.249823i | ||||
\(149\) | 2.88776 | + | 5.00175i | 0.236575 | + | 0.409760i | 0.959729 | − | 0.280927i | \(-0.0906418\pi\) |
−0.723154 | + | 0.690686i | \(0.757308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01321 | − | 1.75494i | 0.0824541 | − | 0.142815i | −0.821849 | − | 0.569705i | \(-0.807058\pi\) |
0.904304 | + | 0.426890i | \(0.140391\pi\) | |||||||
\(152\) | −1.93973 | + | 3.35972i | −0.157333 | + | 0.272509i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.330866 | − | 0.573077i | −0.0265758 | − | 0.0460307i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.04756 | −0.243222 | −0.121611 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121611 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(158\) | 15.9144 | 1.26608 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.98141 | − | 15.5563i | −0.710043 | − | 1.22983i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.69445 | − | 4.66693i | 0.211046 | − | 0.365542i | −0.740996 | − | 0.671509i | \(-0.765646\pi\) |
0.952042 | + | 0.305967i | \(0.0989797\pi\) | |||||||
\(164\) | −1.65153 | + | 2.86053i | −0.128963 | + | 0.223370i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.07905 | − | 1.86896i | −0.0837502 | − | 0.145060i | ||||
\(167\) | 8.30480 | − | 14.3843i | 0.642645 | − | 1.11309i | −0.342196 | − | 0.939629i | \(-0.611171\pi\) |
0.984840 | − | 0.173464i | \(-0.0554961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87249 | + | 10.1714i | 0.451730 | + | 0.782419i | ||||
\(170\) | −3.65063 | + | 6.32308i | −0.279991 | + | 0.484958i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.86696 | − | 3.23366i | −0.142354 | − | 0.246564i | ||||
\(173\) | 17.6503 | 1.34193 | 0.670965 | − | 0.741489i | \(-0.265880\pi\) | ||||
0.670965 | + | 0.741489i | \(0.265880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.2255 | − | 26.3714i | 1.14767 | − | 1.98782i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.78384 | − | 8.28586i | 0.358564 | − | 0.621051i | ||||
\(179\) | 1.31422 | + | 2.27630i | 0.0982294 | + | 0.170138i | 0.910952 | − | 0.412513i | \(-0.135349\pi\) |
−0.812722 | + | 0.582651i | \(0.802015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.97391 | 0.295378 | 0.147689 | − | 0.989034i | \(-0.452816\pi\) | ||||
0.147689 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.12001 | + | 1.93991i | 0.0825681 | + | 0.143012i | ||||
\(185\) | −12.5625 | −0.923613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.33286 | −0.536232 | ||||||||
\(188\) | 5.61306 | 0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | 18.2059 | 1.31733 | 0.658666 | − | 0.752435i | \(-0.271121\pi\) | ||||
0.658666 | + | 0.752435i | \(0.271121\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.202385 | −0.0145680 | −0.00728401 | − | 0.999973i | \(-0.502319\pi\) | ||||
−0.00728401 | + | 0.999973i | \(0.502319\pi\) | |||||||
\(194\) | 14.2321 | + | 24.6506i | 1.02180 | + | 1.76981i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.63136 | 0.116229 | 0.0581147 | − | 0.998310i | \(-0.481491\pi\) | ||||
0.0581147 | + | 0.998310i | \(0.481491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.14605 | − | 5.44912i | −0.223018 | − | 0.386278i | 0.732705 | − | 0.680546i | \(-0.238257\pi\) |
−0.955723 | + | 0.294268i | \(0.904924\pi\) | |||||||
\(200\) | 6.45266 | − | 11.1763i | 0.456272 | − | 0.790287i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.1918 | + | 19.3847i | −0.787449 | + | 1.36390i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8238 | −0.825812 | ||||||||
\(206\) | −2.33249 | − | 4.04000i | −0.162512 | − | 0.281480i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.80050 | + | 4.85061i | −0.194180 | + | 0.336329i | ||||
\(209\) | 6.71607 | + | 11.6326i | 0.464560 | + | 0.804642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14368 | − | 14.1053i | 0.560634 | − | 0.971046i | −0.436807 | − | 0.899555i | \(-0.643891\pi\) |
0.997441 | − | 0.0714912i | \(-0.0227758\pi\) | |||||||
\(212\) | −4.09069 | − | 7.08528i | −0.280950 | − | 0.486619i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.154083 | + | 0.266880i | −0.0105329 | + | 0.0182435i | ||||
\(215\) | 6.68308 | − | 11.5754i | 0.455782 | − | 0.789438i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.07927 | − | 13.9937i | −0.547197 | − | 0.947773i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −20.9897 | −1.41513 | ||||||||
\(221\) | 1.34877 | 0.0907278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.98472 | − | 17.2940i | −0.668626 | − | 1.15809i | −0.978288 | − | 0.207248i | \(-0.933549\pi\) |
0.309662 | − | 0.950847i | \(-0.399784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.26936 | + | 12.5909i | −0.483551 | + | 0.837534i | ||||
\(227\) | 1.80642 | − | 3.12880i | 0.119896 | − | 0.207666i | −0.799830 | − | 0.600226i | \(-0.795077\pi\) |
0.919726 | + | 0.392560i | \(0.128411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.85733 | − | 11.8772i | −0.453145 | − | 0.784870i | 0.545435 | − | 0.838153i | \(-0.316365\pi\) |
−0.998579 | + | 0.0532835i | \(0.983031\pi\) | |||||||
\(230\) | 3.86117 | − | 6.68774i | 0.254598 | − | 0.440976i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45781 | − | 9.45321i | −0.358323 | − | 0.620634i | ||||
\(233\) | −12.6271 | + | 21.8707i | −0.827227 | + | 1.43280i | 0.0729776 | + | 0.997334i | \(0.476750\pi\) |
−0.900205 | + | 0.435466i | \(0.856583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0464 | + | 17.4009i | 0.655357 | + | 1.13511i | ||||
\(236\) | 11.0565 | 0.719717 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.49495 | − | 7.78549i | 0.290754 | − | 0.503601i | −0.683234 | − | 0.730200i | \(-0.739427\pi\) |
0.973988 | + | 0.226598i | \(0.0727604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.62862 | + | 8.01701i | −0.298156 | + | 0.516421i | −0.975714 | − | 0.219048i | \(-0.929705\pi\) |
0.677558 | + | 0.735469i | \(0.263038\pi\) | |||||||
\(242\) | −22.5287 | − | 39.0209i | −1.44820 | − | 2.50836i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.7763 | 0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23532 | − | 2.13963i | −0.0786013 | − | 0.136141i | ||||
\(248\) | 0.331421 | 0.0210452 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.1684 | −0.896091 | ||||||||
\(251\) | −20.6517 | −1.30353 | −0.651763 | − | 0.758422i | \(-0.725970\pi\) | ||||
−0.651763 | + | 0.758422i | \(0.725970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | −17.1355 | −1.07518 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.8076 | 1.17548 | ||||||||
\(257\) | −1.22289 | − | 2.11811i | −0.0762819 | − | 0.132124i | 0.825361 | − | 0.564605i | \(-0.190972\pi\) |
−0.901643 | + | 0.432481i | \(0.857638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.86073 | 0.239432 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1626 | − | 22.7982i | −0.813186 | − | 1.40848i | ||||
\(263\) | −12.2814 | + | 21.2720i | −0.757302 | + | 1.31169i | 0.186919 | + | 0.982375i | \(0.440150\pi\) |
−0.944222 | + | 0.329311i | \(0.893184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6433 | − | 25.3629i | 0.899531 | − | 1.55803i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.76415 | −0.474271 | ||||||||
\(269\) | −14.7851 | − | 25.6086i | −0.901466 | − | 1.56139i | −0.825592 | − | 0.564268i | \(-0.809158\pi\) |
−0.0758746 | − | 0.997117i | \(-0.524175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3958 | − | 21.4701i | 0.752989 | − | 1.30421i | −0.193380 | − | 0.981124i | \(-0.561945\pi\) |
0.946368 | − | 0.323090i | \(-0.104722\pi\) | |||||||
\(272\) | −3.00968 | − | 5.21291i | −0.182488 | − | 0.316079i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30674 | − | 9.19154i | 0.320592 | − | 0.555281i | ||||
\(275\) | −22.3415 | − | 38.6966i | −1.34724 | − | 2.33349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.939249 | + | 1.62683i | −0.0564340 | + | 0.0977466i | −0.892862 | − | 0.450330i | \(-0.851306\pi\) |
0.836428 | + | 0.548076i | \(0.184640\pi\) | |||||||
\(278\) | 0.757442 | − | 1.31193i | 0.0454284 | − | 0.0786842i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.03965 | − | 10.4610i | −0.360295 | − | 0.624049i | 0.627714 | − | 0.778444i | \(-0.283991\pi\) |
−0.988009 | + | 0.154395i | \(0.950657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.9719 | −1.66276 | −0.831378 | − | 0.555708i | \(-0.812447\pi\) | ||||
−0.831378 | + | 0.555708i | \(0.812447\pi\) | |||||||
\(284\) | 11.9756 | 0.710620 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.89052 | + | 10.2027i | 0.348314 | + | 0.603297i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.77524 | − | 13.4671i | 0.457367 | − | 0.792183i | ||||
\(290\) | −18.8155 | + | 32.5894i | −1.10488 | + | 1.91372i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.60736 | + | 4.51609i | 0.152584 | + | 0.264284i | ||||
\(293\) | 4.41163 | − | 7.64117i | 0.257730 | − | 0.446402i | −0.707903 | − | 0.706309i | \(-0.750359\pi\) |
0.965634 | + | 0.259908i | \(0.0836921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7893 | + | 34.2761i | 1.15218 | + | 1.99563i | ||||
\(296\) | 3.14589 | − | 5.44883i | 0.182851 | − | 0.316707i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.98604 | + | 8.63608i | 0.288834 | + | 0.500275i | ||||
\(299\) | −1.42655 | −0.0824996 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.74942 | − | 3.03009i | 0.100668 | − | 0.174362i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.51304 | + | 9.54887i | −0.316195 | + | 0.547665i | ||||
\(305\) | 21.0777 | + | 36.5076i | 1.20691 | + | 2.09042i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.05532 | 0.0602304 | 0.0301152 | − | 0.999546i | \(-0.490413\pi\) | ||||
0.0301152 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.571277 | − | 0.989481i | −0.0324464 | − | 0.0561988i | ||||
\(311\) | −3.07215 | −0.174206 | −0.0871029 | − | 0.996199i | \(-0.527761\pi\) | ||||
−0.0871029 | + | 0.996199i | \(0.527761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.1621 | 1.59181 | 0.795907 | − | 0.605419i | \(-0.206994\pi\) | ||||
0.795907 | + | 0.605419i | \(0.206994\pi\) | |||||||
\(314\) | −5.26196 | −0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | −12.8465 | −0.721530 | −0.360765 | − | 0.932657i | \(-0.617484\pi\) | ||||
−0.360765 | + | 0.932657i | \(0.617484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7939 | −2.11605 | ||||||||
\(320\) | 2.05291 | + | 3.55575i | 0.114761 | + | 0.198772i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.65517 | 0.147738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.10937 | + | 7.11763i | 0.227947 | + | 0.394815i | ||||
\(326\) | 4.65227 | − | 8.05797i | 0.257665 | − | 0.446290i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.96091 | − | 5.12845i | 0.163489 | − | 0.283171i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.5560 | −1.18483 | −0.592413 | − | 0.805634i | \(-0.701825\pi\) | ||||
−0.592413 | + | 0.805634i | \(0.701825\pi\) | |||||||
\(332\) | −0.613191 | − | 1.06208i | −0.0336532 | − | 0.0582891i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.3392 | − | 24.8361i | 0.784604 | − | 1.35897i | ||||
\(335\) | −13.8965 | − | 24.0695i | −0.759248 | − | 1.31506i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30340 | − | 10.9178i | 0.343368 | − | 0.594731i | −0.641688 | − | 0.766966i | \(-0.721766\pi\) |
0.985056 | + | 0.172235i | \(0.0550989\pi\) | |||||||
\(338\) | 10.1395 | + | 17.5621i | 0.551516 | + | 0.955254i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.07455 | + | 3.59323i | −0.112508 | + | 0.194870i | ||||
\(341\) | 0.573750 | − | 0.993764i | 0.0310703 | − | 0.0538153i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.34714 | + | 5.79741i | 0.180466 | + | 0.312575i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.4752 | 1.63836 | ||||||||
\(347\) | −23.1366 | −1.24204 | −0.621020 | − | 0.783795i | \(-0.713281\pi\) | ||||
−0.621020 | + | 0.783795i | \(0.713281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.24346 | + | 14.2781i | 0.441262 | + | 0.764289i | 0.997783 | − | 0.0665448i | \(-0.0211975\pi\) |
−0.556521 | + | 0.830833i | \(0.687864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.5745 | − | 26.9759i | 0.830124 | − | 1.43782i | ||||
\(353\) | −12.2438 | + | 21.2068i | −0.651669 | + | 1.12872i | 0.331049 | + | 0.943614i | \(0.392598\pi\) |
−0.982718 | + | 0.185110i | \(0.940736\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.4343 | + | 37.1253i | 1.13761 | + | 1.97041i | ||||
\(356\) | 2.71852 | − | 4.70862i | 0.144081 | − | 0.249556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.26915 | + | 3.93028i | 0.119928 | + | 0.207722i | ||||
\(359\) | 10.2389 | − | 17.7342i | 0.540386 | − | 0.935977i | −0.458495 | − | 0.888697i | \(-0.651611\pi\) |
0.998882 | − | 0.0472797i | \(-0.0150552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.06816 | + | 12.2424i | 0.372009 | + | 0.644338i | ||||
\(362\) | 6.86139 | 0.360627 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.33349 | + | 16.1661i | −0.488537 | + | 0.846172i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1269 | + | 19.2724i | −0.580821 | + | 1.00601i | 0.414561 | + | 0.910021i | \(0.363935\pi\) |
−0.995382 | + | 0.0959900i | \(0.969398\pi\) | |||||||
\(368\) | 3.18325 | + | 5.51355i | 0.165938 | + | 0.287414i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.6905 | −1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2684 | + | 28.1777i | 0.842347 | + | 1.45899i | 0.887905 | + | 0.460027i | \(0.152160\pi\) |
−0.0455576 | + | 0.998962i | \(0.514506\pi\) | |||||||
\(374\) | −12.6610 | −0.654685 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0633 | −0.518973 | ||||||||
\(377\) | 6.95160 | 0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | 7.60021 | 0.389883 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 31.4345 | 1.60833 | ||||||||
\(383\) | 15.8147 | + | 27.3919i | 0.808093 | + | 1.39966i | 0.914183 | + | 0.405302i | \(0.132834\pi\) |
−0.106090 | + | 0.994357i | \(0.533833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.349441 | −0.0177861 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.08767 | + | 14.0083i | 0.410589 | + | 0.711162i | ||||
\(389\) | −2.62313 | + | 4.54340i | −0.132998 | + | 0.230359i | −0.924831 | − | 0.380378i | \(-0.875794\pi\) |
0.791833 | + | 0.610738i | \(0.209127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.766552 | − | 1.32771i | 0.0387662 | − | 0.0671451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.81672 | 0.141904 | ||||||||
\(395\) | 16.1867 | + | 28.0362i | 0.814440 | + | 1.41065i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0138175 | + | 0.0239325i | −0.000693478 | + | 0.00120114i | −0.866372 | − | 0.499399i | \(-0.833554\pi\) |
0.865678 | + | 0.500600i | \(0.166887\pi\) | |||||||
\(398\) | −5.43201 | − | 9.40851i | −0.272282 | − | 0.471606i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3395 | − | 31.7650i | 0.916977 | − | 1.58825i | ||||
\(401\) | 6.06885 | + | 10.5115i | 0.303064 | + | 0.524922i | 0.976828 | − | 0.214024i | \(-0.0686572\pi\) |
−0.673765 | + | 0.738946i | \(0.735324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.105532 | + | 0.182787i | −0.00525694 | + | 0.00910529i | ||||
\(404\) | −6.35996 | + | 11.0158i | −0.316420 | + | 0.548055i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.8922 | − | 18.8659i | −0.539907 | − | 0.935146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3453 | 1.54993 | 0.774963 | − | 0.632007i | \(-0.217769\pi\) | ||||
0.774963 | + | 0.632007i | \(0.217769\pi\) | |||||||
\(410\) | −20.4152 | −1.00823 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.32549 | − | 2.29582i | −0.0653022 | − | 0.113107i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.19502 | − | 3.80189i | 0.107749 | − | 0.186627i | ||||
\(416\) | −2.86469 | + | 4.96179i | −0.140453 | + | 0.243272i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.5960 | + | 20.0849i | 0.567181 | + | 0.982385i | ||||
\(419\) | −7.44319 | + | 12.8920i | −0.363623 | + | 0.629814i | −0.988554 | − | 0.150866i | \(-0.951794\pi\) |
0.624931 | + | 0.780680i | \(0.285127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.54213 | − | 7.86721i | −0.221370 | − | 0.383424i | 0.733854 | − | 0.679307i | \(-0.237720\pi\) |
−0.955224 | + | 0.295883i | \(0.904386\pi\) | |||||||
\(422\) | 14.0610 | − | 24.3543i | 0.684477 | − | 1.18555i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.33392 | + | 12.7027i | 0.356166 | + | 0.616898i | ||||
\(425\) | −8.83262 | −0.428445 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.0875611 | + | 0.151660i | −0.00423243 | + | 0.00733078i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.5391 | − | 19.9863i | 0.556463 | − | 0.963823i | ||||
\(431\) | −8.31776 | − | 14.4068i | −0.400652 | − | 0.693950i | 0.593152 | − | 0.805090i | \(-0.297883\pi\) |
−0.993805 | + | 0.111140i | \(0.964550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7423 | 0.948756 | 0.474378 | − | 0.880321i | \(-0.342673\pi\) | ||||
0.474378 | + | 0.880321i | \(0.342673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.59122 | − | 7.95223i | −0.219880 | − | 0.380843i | ||||
\(437\) | −2.80830 | −0.134339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.73514 | −0.321451 | −0.160725 | − | 0.986999i | \(-0.551383\pi\) | ||||
−0.160725 | + | 0.986999i | \(0.551383\pi\) | |||||||
\(440\) | 37.6310 | 1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | −28.6403 | −1.36074 | −0.680372 | − | 0.732867i | \(-0.738182\pi\) | ||||
−0.680372 | + | 0.732867i | \(0.738182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.4628 | 0.922626 | ||||||||
\(446\) | −17.2397 | − | 29.8601i | −0.816324 | − | 1.41392i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.66872 | 0.314716 | 0.157358 | − | 0.987542i | \(-0.449702\pi\) | ||||
0.157358 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2518 | − | 17.7566i | −0.482736 | − | 0.836124i | ||||
\(452\) | −4.13097 | + | 7.15505i | −0.194305 | + | 0.336545i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.11898 | − | 5.40223i | 0.146381 | − | 0.253539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6573 | −1.34053 | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(458\) | −11.8399 | − | 20.5074i | −0.553244 | − | 0.958246i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.19419 | − | 3.80045i | 0.102305 | − | 0.177197i | ||||
\(461\) | 10.0087 | + | 17.3355i | 0.466150 | + | 0.807395i | 0.999253 | − | 0.0386554i | \(-0.0123075\pi\) |
−0.533103 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95789 | + | 8.58731i | −0.230413 | + | 0.399086i | −0.957930 | − | 0.287003i | \(-0.907341\pi\) |
0.727517 | + | 0.686090i | \(0.240674\pi\) | |||||||
\(464\) | −15.5120 | − | 26.8676i | −0.720127 | − | 1.24730i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.8020 | + | 37.7623i | −1.00996 | + | 1.74930i | ||||
\(467\) | −8.04035 | + | 13.9263i | −0.372063 | + | 0.644432i | −0.989883 | − | 0.141888i | \(-0.954683\pi\) |
0.617820 | + | 0.786320i | \(0.288016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.3463 | + | 30.0446i | 0.800124 | + | 1.38586i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.8225 | −0.912402 | ||||||||
\(473\) | 23.1780 | 1.06573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.08967 | + | 14.0117i | 0.371180 | + | 0.642902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.76103 | − | 13.4425i | 0.354981 | − | 0.614846i | ||||
\(479\) | 4.10128 | − | 7.10362i | 0.187392 | − | 0.324573i | −0.756988 | − | 0.653429i | \(-0.773330\pi\) |
0.944380 | + | 0.328856i | \(0.106663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00345 | + | 3.47008i | 0.0913496 | + | 0.158222i | ||||
\(482\) | −7.99183 | + | 13.8423i | −0.364018 | + | 0.630497i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8024 | − | 22.1745i | −0.581929 | − | 1.00793i | ||||
\(485\) | −28.9512 | + | 50.1449i | −1.31460 | + | 2.27696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36840 | − | 2.37014i | −0.0620081 | − | 0.107401i | 0.833355 | − | 0.552738i | \(-0.186417\pi\) |
−0.895363 | + | 0.445337i | \(0.853084\pi\) | |||||||
\(488\) | −21.1130 | −0.955741 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.85482 | + | 17.0690i | −0.444742 | + | 0.770315i | −0.998034 | − | 0.0626719i | \(-0.980038\pi\) |
0.553293 | + | 0.832987i | \(0.313371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.73542 | + | 6.46993i | −0.168235 | + | 0.291391i | ||||
\(494\) | −2.13291 | − | 3.69431i | −0.0959642 | − | 0.166215i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.941952 | 0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5480 | + | 28.6619i | 0.740789 | + | 1.28309i | 0.952136 | + | 0.305674i | \(0.0988817\pi\) |
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(500\) | −8.05153 | −0.360075 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −35.6575 | −1.59147 | ||||||||
\(503\) | 12.1860 | 0.543346 | 0.271673 | − | 0.962390i | \(-0.412423\pi\) | ||||
0.271673 | + | 0.962390i | \(0.412423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | 13.3912 | 0.595310 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.73765 | −0.432038 | ||||||||
\(509\) | −6.81965 | − | 11.8120i | −0.302276 | − | 0.523557i | 0.674375 | − | 0.738389i | \(-0.264413\pi\) |
−0.976651 | + | 0.214832i | \(0.931080\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.97968 | 0.352656 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.11146 | − | 3.65715i | −0.0931325 | − | 0.161310i | ||||
\(515\) | 4.74481 | − | 8.21826i | 0.209081 | − | 0.362140i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4214 | + | 30.1747i | −0.766190 | + | 1.32708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.92164 | −0.303534 | ||||||||
\(521\) | 17.7745 | + | 30.7863i | 0.778714 | + | 1.34877i | 0.932683 | + | 0.360697i | \(0.117461\pi\) |
−0.153969 | + | 0.988076i | \(0.549206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3593 | − | 23.1391i | 0.584163 | − | 1.01180i | −0.410816 | − | 0.911718i | \(-0.634756\pi\) |
0.994979 | − | 0.100082i | \(-0.0319105\pi\) | |||||||
\(524\) | −7.47991 | − | 12.9556i | −0.326761 | − | 0.565967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2052 | + | 36.7284i | −0.924589 | + | 1.60143i | ||||
\(527\) | −0.113415 | − | 0.196440i | −0.00494043 | − | 0.00855708i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6892 | − | 18.5143i | 0.464750 | − | 0.804970i | ||||
\(530\) | 25.2833 | − | 43.7919i | 1.09824 | − | 1.90220i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88565 | + | 3.26604i | 0.0816766 | + | 0.141468i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.626879 | −0.0271023 | ||||||||
\(536\) | 13.9198 | 0.601244 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.5282 | − | 44.2161i | −1.10060 | − | 1.90629i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7927 | + | 32.5500i | −0.807963 | + | 1.39943i | 0.106309 | + | 0.994333i | \(0.466097\pi\) |
−0.914272 | + | 0.405100i | \(0.867237\pi\) | |||||||
\(542\) | 21.4026 | − | 37.0705i | 0.919322 | − | 1.59231i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.07866 | − | 5.33240i | −0.131997 | − | 0.228625i | ||||
\(545\) | 16.4350 | − | 28.4663i | 0.704000 | − | 1.21936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13381 | − | 15.8202i | −0.390533 | − | 0.676424i | 0.601986 | − | 0.798506i | \(-0.294376\pi\) |
−0.992520 | + | 0.122082i | \(0.961043\pi\) | |||||||
\(548\) | 3.01567 | − | 5.22329i | 0.128823 | − | 0.223128i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −38.5750 | − | 66.8139i | −1.64485 | − | 2.84896i | ||||
\(551\) | 13.6849 | 0.582995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.62172 | + | 2.80890i | −0.0689002 | + | 0.119339i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.430433 | − | 0.745532i | 0.0182544 | − | 0.0316176i | ||||
\(557\) | −1.94636 | − | 3.37119i | −0.0824698 | − | 0.142842i | 0.821840 | − | 0.569718i | \(-0.192947\pi\) |
−0.904310 | + | 0.426876i | \(0.859614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.26324 | −0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.4281 | − | 18.0620i | −0.439884 | − | 0.761901i | ||||
\(563\) | −3.32855 | −0.140282 | −0.0701409 | − | 0.997537i | \(-0.522345\pi\) | ||||
−0.0701409 | + | 0.997537i | \(0.522345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.5750 | −1.24423 | ||||||||
\(566\) | −48.2965 | −2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | 36.6244 | 1.53538 | 0.767688 | − | 0.640824i | \(-0.221407\pi\) | ||||
0.767688 | + | 0.640824i | \(0.221407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5824 | −0.945044 | −0.472522 | − | 0.881319i | \(-0.656656\pi\) | ||||
−0.472522 | + | 0.881319i | \(0.656656\pi\) | |||||||
\(572\) | 3.34742 | + | 5.79789i | 0.139962 | + | 0.242422i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.34201 | 0.389589 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2725 | − | 19.5245i | −0.469279 | − | 0.812815i | 0.530104 | − | 0.847932i | \(-0.322153\pi\) |
−0.999383 | + | 0.0351177i | \(0.988819\pi\) | |||||||
\(578\) | 13.4248 | − | 23.2525i | 0.558399 | − | 0.967175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.6923 | + | 18.5197i | −0.443975 | + | 0.768987i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.7854 | 2.10332 | ||||||||
\(584\) | −4.67457 | − | 8.09659i | −0.193435 | − | 0.335039i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.61717 | − | 13.1933i | 0.314662 | − | 0.545011i | ||||
\(587\) | 12.1198 | + | 20.9921i | 0.500237 | + | 0.866436i | 1.00000 | 0.000273884i | \(8.71801e-5\pi\) | |
−0.499763 | + | 0.866162i | \(0.666579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.207750 | + | 0.359834i | −0.00856020 | + | 0.0148267i | ||||
\(590\) | 34.1684 | + | 59.1814i | 1.40669 | + | 2.43646i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.94112 | − | 15.4865i | 0.367478 | − | 0.636490i | ||||
\(593\) | −22.8663 | + | 39.6056i | −0.939007 | + | 1.62641i | −0.171680 | + | 0.985153i | \(0.554919\pi\) |
−0.767328 | + | 0.641255i | \(0.778414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.83343 | + | 4.90764i | 0.116062 | + | 0.201025i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.46310 | −0.100724 | ||||||||
\(599\) | 30.1668 | 1.23258 | 0.616290 | − | 0.787519i | \(-0.288635\pi\) | ||||
0.616290 | + | 0.787519i | \(0.288635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.36933 | + | 12.7641i | 0.300601 | + | 0.520657i | 0.976272 | − | 0.216547i | \(-0.0694794\pi\) |
−0.675671 | + | 0.737203i | \(0.736146\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.994149 | − | 1.72192i | 0.0404513 | − | 0.0700638i | ||||
\(605\) | 45.8285 | − | 79.3772i | 1.86319 | − | 3.22714i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.03918 | + | 5.26401i | 0.123356 | + | 0.213660i | 0.921089 | − | 0.389351i | \(-0.127301\pi\) |
−0.797733 | + | 0.603011i | \(0.793967\pi\) | |||||||
\(608\) | −5.63941 | + | 9.76774i | −0.228708 | + | 0.396134i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.3930 | + | 63.0345i | 1.47351 | + | 2.55219i | ||||
\(611\) | 3.20439 | − | 5.55016i | 0.129636 | − | 0.224535i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.88668 | − | 10.1960i | −0.237761 | − | 0.411814i | 0.722311 | − | 0.691569i | \(-0.243080\pi\) |
−0.960071 | + | 0.279755i | \(0.909747\pi\) | |||||||
\(614\) | 1.82213 | 0.0735352 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0319 | − | 27.7680i | 0.645418 | − | 1.11790i | −0.338786 | − | 0.940863i | \(-0.610016\pi\) |
0.984205 | − | 0.177034i | \(-0.0566503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.27588 | − | 10.8701i | 0.252249 | − | 0.436908i | −0.711896 | − | 0.702285i | \(-0.752163\pi\) |
0.964145 | + | 0.265377i | \(0.0854965\pi\) | |||||||
\(620\) | −0.324641 | − | 0.562294i | −0.0130379 | − | 0.0225823i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.30441 | −0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.92995 | + | 6.80687i | 0.157198 | + | 0.272275i | ||||
\(626\) | 48.6249 | 1.94344 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.99022 | −0.119323 | ||||||||
\(629\) | −4.30619 | −0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | −16.2138 | −0.644950 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.1809 | −0.880915 | ||||||||
\(635\) | −17.4288 | − | 30.1875i | −0.691639 | − | 1.19795i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −65.2553 | −2.58348 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.5074 | + | 37.2519i | 0.850155 | + | 1.47251i | ||||
\(641\) | −9.49183 | + | 16.4403i | −0.374905 | + | 0.649354i | −0.990313 | − | 0.138855i | \(-0.955658\pi\) |
0.615408 | + | 0.788209i | \(0.288991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.81347 | − | 8.33718i | 0.189825 | − | 0.328786i | −0.755367 | − | 0.655302i | \(-0.772541\pi\) |
0.945192 | + | 0.326516i | \(0.105875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.58445 | 0.180373 | ||||||||
\(647\) | −3.90607 | − | 6.76551i | −0.153564 | − | 0.265980i | 0.778972 | − | 0.627059i | \(-0.215742\pi\) |
−0.932535 | + | 0.361079i | \(0.882408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.3163 | + | 59.4375i | −1.34703 | + | 2.33313i | ||||
\(650\) | 7.09528 | + | 12.2894i | 0.278300 | + | 0.482029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64376 | − | 4.57912i | 0.103537 | − | 0.179332i | ||||
\(653\) | 15.8714 | + | 27.4901i | 0.621097 | + | 1.07577i | 0.989282 | + | 0.146019i | \(0.0466461\pi\) |
−0.368185 | + | 0.929753i | \(0.620021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.7756 | − | 46.3767i | 1.04621 | − | 1.81209i | ||||
\(656\) | 8.41540 | − | 14.5759i | 0.328566 | − | 0.569093i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.10685 | − | 5.38122i | −0.121026 | − | 0.209623i | 0.799147 | − | 0.601136i | \(-0.205285\pi\) |
−0.920172 | + | 0.391513i | \(0.871952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5263 | 1.07065 | 0.535324 | − | 0.844647i | \(-0.320190\pi\) | ||||
0.535324 | + | 0.844647i | \(0.320190\pi\) | |||||||
\(662\) | −37.2189 | −1.44655 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.09935 | + | 1.90413i | 0.0426630 | + | 0.0738945i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.95084 | − | 6.84306i | 0.152977 | − | 0.264964i | ||||
\(668\) | 8.14854 | − | 14.1137i | 0.315276 | − | 0.546075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.9939 | − | 41.5586i | −0.926965 | − | 1.60555i | ||||
\(671\) | −36.5505 | + | 63.3073i | −1.41102 | + | 2.44395i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.10894 | − | 14.0451i | −0.312577 | − | 0.541399i | 0.666343 | − | 0.745646i | \(-0.267859\pi\) |
−0.978919 | + | 0.204247i | \(0.934526\pi\) | |||||||
\(674\) | 10.8835 | − | 18.8508i | 0.419217 | − | 0.726106i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.76199 | + | 9.98006i | 0.221615 | + | 0.383849i | ||||
\(677\) | 20.5090 | 0.788225 | 0.394112 | − | 0.919062i | \(-0.371052\pi\) | ||||
0.394112 | + | 0.919062i | \(0.371052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.71932 | − | 6.44205i | 0.142629 | − | 0.247041i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.990642 | − | 1.71584i | 0.0379337 | − | 0.0657030i | ||||
\(683\) | −0.0561542 | − | 0.0972618i | −0.00214868 | − | 0.00372162i | 0.864949 | − | 0.501860i | \(-0.167351\pi\) |
−0.867098 | + | 0.498138i | \(0.834017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5902 | 0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.51311 | + | 16.4772i | 0.362684 | + | 0.628187i | ||||
\(689\) | −9.34118 | −0.355871 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8670 | 0.717735 | 0.358868 | − | 0.933388i | \(-0.383163\pi\) | ||||
0.358868 | + | 0.933388i | \(0.383163\pi\) | |||||||
\(692\) | 17.3182 | 0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | 3.08161 | 0.116892 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.05299 | −0.153518 | ||||||||
\(698\) | 14.2332 | + | 24.6527i | 0.538736 | + | 0.933118i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.16006 | 0.119354 | 0.0596770 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596770 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.94398 | + | 6.83118i | 0.148750 | + | 0.257643i | ||||
\(704\) | −3.55992 | + | 6.16596i | −0.134170 | + | 0.232388i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.1402 | + | 36.6159i | −0.795622 | + | 1.37806i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5211 | −0.808243 | −0.404121 | − | 0.914705i | \(-0.632423\pi\) | ||||
−0.404121 | + | 0.914705i | \(0.632423\pi\) | |||||||
\(710\) | 37.0087 | + | 64.1009i | 1.38891 | + | 2.40567i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.87385 | + | 8.44176i | −0.182655 | + | 0.316368i | ||||
\(713\) | 0.119956 | + | 0.207769i | 0.00449237 | + | 0.00778102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9826 | + | 20.7545i | −0.448125 | + | 0.776175i | ||||
\(716\) | 1.28949 | + | 2.23347i | 0.0481906 | + | 0.0834685i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.6785 | − | 30.6201i | 0.659757 | − | 1.14273i | ||||
\(719\) | −9.41508 | + | 16.3074i | −0.351123 | + | 0.608163i | −0.986447 | − | 0.164083i | \(-0.947533\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.2040 | + | 21.1379i | 0.454185 | + | 0.786671i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.89914 | 0.144910 | ||||||||
\(725\) | −45.5237 | −1.69071 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5426 | − | 33.8489i | −0.724797 | − | 1.25538i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.234261 | − | 0.972174i | \(-0.424733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.1153 | + | 27.9125i | −0.596454 | + | 1.03309i | ||||
\(731\) | 2.29084 | − | 3.96784i | 0.0847296 | − | 0.146756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.29924 | − | 16.1068i | −0.343475 | − | 0.594917i | 0.641600 | − | 0.767039i | \(-0.278271\pi\) |
−0.985076 | + | 0.172123i | \(0.944937\pi\) | |||||||
\(734\) | −19.2119 | + | 33.2759i | −0.709123 | + | 1.22824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.25621 | + | 5.63993i | 0.120026 | + | 0.207890i | ||||
\(737\) | 24.0977 | − | 41.7385i | 0.887651 | − | 1.53746i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.75068 | − | 4.76432i | −0.101185 | − | 0.175258i | 0.810988 | − | 0.585063i | \(-0.198930\pi\) |
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(740\) | −12.3261 | −0.453117 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2326 | + | 17.7234i | −0.375399 | + | 0.650210i | −0.990387 | − | 0.138327i | \(-0.955828\pi\) |
0.614988 | + | 0.788537i | \(0.289161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.1427 | + | 17.5677i | −0.371601 | + | 0.643631i | ||||
\(746\) | 28.0892 | + | 48.6520i | 1.02842 | + | 1.78128i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.19489 | −0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0230 | − | 32.9488i | −0.694159 | − | 1.20232i | −0.970463 | − | 0.241248i | \(-0.922443\pi\) |
0.276305 | − | 0.961070i | \(-0.410890\pi\) | |||||||
\(752\) | −28.6015 | −1.04299 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0027 | 0.437113 | ||||||||
\(755\) | 7.11744 | 0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | 2.66658 | 0.0968546 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.6259 | −0.494263 | ||||||||
\(761\) | −20.0375 | − | 34.7059i | −0.726357 | − | 1.25809i | −0.958413 | − | 0.285385i | \(-0.907878\pi\) |
0.232055 | − | 0.972703i | \(-0.425455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.8633 | 0.646273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.3058 | + | 47.2951i | 0.986599 | + | 1.70884i | ||||
\(767\) | 6.31195 | − | 10.9326i | 0.227911 | − | 0.394754i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4828 | − | 38.9414i | 0.810751 | − | 1.40426i | −0.101587 | − | 0.994827i | \(-0.532392\pi\) |
0.912339 | − | 0.409436i | \(-0.134274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.198577 | −0.00714695 | ||||||||
\(773\) | −12.1781 | − | 21.0930i | −0.438014 | − | 0.758663i | 0.559522 | − | 0.828816i | \(-0.310985\pi\) |
−0.997536 | + | 0.0701524i | \(0.977651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.691096 | − | 1.19701i | 0.0248249 | − | 0.0429980i | ||||
\(776\) | −14.4998 | − | 25.1145i | −0.520514 | − | 0.901556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.52913 | + | 7.84468i | −0.162377 | + | 0.281245i | ||||
\(779\) | 3.71208 | + | 6.42951i | 0.132999 | + | 0.230361i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.1689 | + | 64.3784i | −1.33001 | + | 2.30364i | ||||
\(782\) | 1.32354 | − | 2.29243i | 0.0473296 | − | 0.0819773i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.35200 | − | 9.26993i | −0.191021 | − | 0.330858i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5233 | 1.48015 | 0.740073 | − | 0.672526i | \(-0.234791\pi\) | ||||
0.740073 | + | 0.672526i | \(0.234791\pi\) | |||||||
\(788\) | 1.60066 | 0.0570212 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.9481 | + | 48.4075i | 0.994349 | + | 1.72226i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.72289 | − | 11.6444i | 0.238737 | − | 0.413504i | ||||
\(794\) | −0.0238574 | + | 0.0413222i | −0.000846666 | + | 0.00146647i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.08686 | − | 5.34659i | −0.109411 | − | 0.189505i | ||||
\(797\) | 17.3018 | − | 29.9676i | 0.612861 | − | 1.06151i | −0.377895 | − | 0.925848i | \(-0.623352\pi\) |
0.990756 | − | 0.135657i | \(-0.0433146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44373 | + | 5.96472i | 0.121831 | + | 0.211017i | ||||
\(800\) | 18.7599 | − | 32.4931i | 0.663263 | − | 1.14880i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.4785 | + | 18.1494i | 0.370010 | + | 0.640876i | ||||
\(803\) | −32.3701 | −1.14232 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.182213 | + | 0.315603i | −0.00641819 | + | 0.0111166i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.4023 | − | 19.7494i | 0.401133 | − | 0.694782i | ||||
\(809\) | −5.62597 | − | 9.74446i | −0.197799 | − | 0.342597i | 0.750016 | − | 0.661420i | \(-0.230046\pi\) |
−0.947814 | + | 0.318823i | \(0.896713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6803 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.8066 | − | 32.5740i | −0.659171 | − | 1.14172i | ||||
\(815\) | 18.9275 | 0.663002 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.39258 | −0.293619 | ||||||||
\(818\) | 54.1211 | 1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | −34.6431 | −1.20905 | −0.604526 | − | 0.796585i | \(-0.706638\pi\) | ||||
−0.604526 | + | 0.796585i | \(0.706638\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.3870 | 1.26837 | 0.634186 | − | 0.773180i | \(-0.281335\pi\) | ||||
0.634186 | + | 0.773180i | \(0.281335\pi\) | |||||||
\(824\) | 2.37638 | + | 4.11601i | 0.0827851 | + | 0.143388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.3576 | 0.846997 | 0.423498 | − | 0.905897i | \(-0.360802\pi\) | ||||
0.423498 | + | 0.905897i | \(0.360802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.5851 | − | 33.9224i | −0.680219 | − | 1.17817i | −0.974914 | − | 0.222583i | \(-0.928551\pi\) |
0.294694 | − | 0.955592i | \(-0.404782\pi\) | |||||||
\(830\) | 3.78994 | − | 6.56438i | 0.131551 | − | 0.227853i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.654792 | − | 1.13413i | 0.0227008 | − | 0.0393190i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.3381 | 2.01887 | ||||||||
\(836\) | 6.58970 | + | 11.4137i | 0.227910 | + | 0.394751i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.8515 | + | 22.2594i | −0.443947 | + | 0.768939i | ||||
\(839\) | 17.1739 | + | 29.7460i | 0.592907 | + | 1.02695i | 0.993839 | + | 0.110838i | \(0.0353534\pi\) |
−0.400931 | + | 0.916108i | \(0.631313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.75250 | + | 8.23157i | −0.163879 | + | 0.283847i | ||||
\(842\) | −7.84250 | − | 13.5836i | −0.270270 | − | 0.468122i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.99045 | − | 13.8399i | 0.275043 | − | 0.476388i | ||||
\(845\) | −20.6260 | + | 35.7253i | −0.709556 | + | 1.22899i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.8442 | + | 36.1032i | 0.715793 | + | 1.23979i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.2505 | −0.523088 | ||||||||
\(851\) | 4.55454 | 0.156127 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3371 | − | 28.2967i | −0.559373 | − | 0.968862i | −0.997549 | − | 0.0699730i | \(-0.977709\pi\) |
0.438176 | − | 0.898889i | \(-0.355625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.156982 | − | 0.271901i | 0.00536555 | − | 0.00929340i | ||||
\(857\) | −28.8340 | + | 49.9419i | −0.984950 | + | 1.70598i | −0.342791 | + | 0.939412i | \(0.611372\pi\) |
−0.642159 | + | 0.766571i | \(0.721961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.9884 | − | 25.9607i | −0.511397 | − | 0.885766i | −0.999913 | − | 0.0132108i | \(-0.995795\pi\) |
0.488515 | − | 0.872555i | \(-0.337539\pi\) | |||||||
\(860\) | 6.55733 | − | 11.3576i | 0.223603 | − | 0.387292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3615 | − | 24.8749i | −0.489156 | − | 0.847243i | ||||
\(863\) | −11.5888 | + | 20.0724i | −0.394487 | + | 0.683272i | −0.993036 | − | 0.117815i | \(-0.962411\pi\) |
0.598548 | + | 0.801087i | \(0.295744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.9967 | + | 53.6879i | 1.05392 | + | 1.82544i | ||||
\(866\) | 34.0873 | 1.15833 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0690 | + | 48.6170i | −0.952177 | + | 1.64922i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.43240 | + | 7.67715i | −0.150186 | + | 0.260130i | ||||
\(872\) | 8.23129 | + | 14.2570i | 0.278747 | + | 0.482803i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.84884 | −0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.369978 | + | 0.640820i | 0.0124933 | + | 0.0216390i | 0.872204 | − | 0.489141i | \(-0.162690\pi\) |
−0.859711 | + | 0.510780i | \(0.829357\pi\) | |||||||
\(878\) | −11.6290 | −0.392458 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 106.954 | 3.60540 | ||||||||
\(881\) | 18.0285 | 0.607395 | 0.303697 | − | 0.952769i | \(-0.401779\pi\) | ||||
0.303697 | + | 0.952769i | \(0.401779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | 1.32339 | 0.0445104 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.4507 | −1.66133 | ||||||||
\(887\) | −15.4763 | − | 26.8058i | −0.519645 | − | 0.900051i | −0.999739 | − | 0.0228344i | \(-0.992731\pi\) |
0.480094 | − | 0.877217i | \(-0.340602\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 33.6047 | 1.12643 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.79685 | − | 16.9686i | −0.328023 | − | 0.568152i | ||||
\(893\) | 6.30813 | − | 10.9260i | 0.211094 | − | 0.365625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.61595 | + | 7.99506i | −0.154294 | + | 0.267245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.5143 | 0.384236 | ||||||||
\(899\) | −0.584545 | − | 1.01246i | −0.0194957 | − | 0.0337675i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.01945 | − | 8.69395i | 0.167222 | − | 0.289637i | ||||
\(902\) | −17.7008 | − | 30.6587i | −0.589372 | − | 1.02082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.40614 | − | 12.8278i | 0.246324 | − | 0.426646i | ||||
\(905\) | 6.97880 | + | 12.0876i | 0.231983 | + | 0.401807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4042 | − | 37.0731i | 0.710714 | − | 1.23099i | −0.253876 | − | 0.967237i | \(-0.581706\pi\) |
0.964590 | − | 0.263755i | \(-0.0849611\pi\) | |||||||
\(908\) | 1.77243 | − | 3.06993i | 0.0588200 | − | 0.101879i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.04869 | − | 5.28049i | −0.101008 | − | 0.174950i | 0.811092 | − | 0.584918i | \(-0.198873\pi\) |
−0.912100 | + | 0.409968i | \(0.865540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.61269 | 0.251943 | ||||||||
\(914\) | −49.4800 | −1.63665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.72830 | − | 11.6538i | −0.222309 | − | 0.385051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.4307 | + | 21.5305i | −0.410050 | + | 0.710227i | −0.994895 | − | 0.100918i | \(-0.967822\pi\) |
0.584845 | + | 0.811145i | \(0.301155\pi\) | |||||||
\(920\) | −3.93382 | + | 6.81357i | −0.129694 | + | 0.224637i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.2811 | + | 29.9317i | 0.569121 | + | 0.985747i | ||||
\(923\) | 6.83664 | − | 11.8414i | 0.225031 | − | 0.389764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1199 | − | 22.7244i | −0.431381 | − | 0.747174i | ||||
\(926\) | −8.56034 | + | 14.8269i | −0.281310 | + | 0.487244i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.8676 | − | 27.4834i | −0.520878 | − | 0.902188i | ||||
\(929\) | 41.8402 | 1.37273 | 0.686366 | − | 0.727256i | \(-0.259205\pi\) | ||||
0.686366 | + | 0.727256i | \(0.259205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.3895 | + | 21.4592i | −0.405831 | + | 0.702920i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.8826 | + | 24.0453i | −0.454251 | + | 0.786786i | ||||
\(935\) | −12.8776 | − | 22.3047i | −0.421144 | − | 0.729443i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2537 | −0.955676 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.85740 | + | 17.0735i | 0.321513 | + | 0.556877i | ||||
\(941\) | 3.35737 | 0.109447 | 0.0547236 | − | 0.998502i | \(-0.482572\pi\) | ||||
0.0547236 | + | 0.998502i | \(0.482572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.28673 | 0.139595 | ||||||||
\(944\) | −56.3387 | −1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | −5.26601 | −0.171122 | −0.0855612 | − | 0.996333i | \(-0.527268\pi\) | ||||
−0.0855612 | + | 0.996333i | \(0.527268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.95398 | 0.193274 | ||||||||
\(950\) | 13.9677 | + | 24.1928i | 0.453173 | + | 0.784918i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.2520 | −1.82218 | −0.911090 | − | 0.412208i | \(-0.864758\pi\) | ||||
−0.911090 | + | 0.412208i | \(0.864758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.9724 | + | 55.3778i | 1.03460 | + | 1.79198i | ||||
\(956\) | 4.41038 | − | 7.63900i | 0.142642 | − | 0.247063i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.08131 | − | 12.2652i | 0.228787 | − | 0.396270i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9645 | −0.998855 | ||||||||
\(962\) | 3.45918 | + | 5.99148i | 0.111528 | + | 0.193173i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.54153 | + | 7.86616i | −0.146273 | + | 0.253352i | ||||
\(965\) | −0.355420 | − | 0.615606i | −0.0114414 | − | 0.0198171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.88641 | + | 11.9276i | −0.221452 | + | 0.383566i | −0.955249 | − | 0.295803i | \(-0.904413\pi\) |
0.733797 | + | 0.679369i | \(0.237746\pi\) | |||||||
\(968\) | 22.9526 | + | 39.7551i | 0.737725 | + | 1.27778i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −49.9874 | + | 86.5807i | −1.60500 | + | 2.77994i | ||||
\(971\) | 25.6627 | − | 44.4491i | 0.823555 | − | 1.42644i | −0.0794635 | − | 0.996838i | \(-0.525321\pi\) |
0.903019 | − | 0.429602i | \(-0.141346\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.36269 | − | 4.09230i | −0.0757055 | − | 0.131126i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60.0066 | −1.92077 | ||||||||
\(977\) | −17.6850 | −0.565794 | −0.282897 | − | 0.959150i | \(-0.591296\pi\) | ||||
−0.282897 | + | 0.959150i | \(0.591296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.8751 | + | 29.2285i | 0.539329 | + | 0.934146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.0154 | + | 29.4716i | −0.542984 | + | 0.940476i | ||||
\(983\) | 8.00207 | − | 13.8600i | 0.255226 | − | 0.442065i | −0.709731 | − | 0.704473i | \(-0.751183\pi\) |
0.964957 | + | 0.262408i | \(0.0845166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.86492 | + | 4.96218i | 0.0912839 | + | 0.158108i | ||||
\(986\) | −6.44961 | + | 11.1711i | −0.205397 | + | 0.355759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.21207 | − | 2.09937i | −0.0385612 | − | 0.0667899i | ||||
\(989\) | −2.42295 | + | 4.19667i | −0.0770454 | + | 0.133446i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.43319 | + | 9.41055i | 0.172591 | + | 0.298936i | 0.939325 | − | 0.343029i | \(-0.111453\pi\) |
−0.766734 | + | 0.641965i | \(0.778120\pi\) | |||||||
\(992\) | 0.963543 | 0.0305925 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0499 | − | 19.1390i | 0.350306 | − | 0.606748i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5187 | − | 35.5395i | 0.649835 | − | 1.12555i | −0.333327 | − | 0.942811i | \(-0.608171\pi\) |
0.983162 | − | 0.182736i | \(-0.0584954\pi\) | |||||||
\(998\) | 28.5719 | + | 49.4880i | 0.904428 | + | 1.56652i | ||||
\(999\) | 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.h.226.9 | 24 | ||
3.2 | odd | 2 | 441.2.h.h.373.3 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.442.4 | 24 | |||
7.3 | odd | 6 | 1323.2.g.h.361.4 | 24 | |||
7.4 | even | 3 | 1323.2.g.h.361.3 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.442.3 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.h.h.226.10 | 24 | ||
9.2 | odd | 6 | 441.2.g.h.79.10 | 24 | |||
9.7 | even | 3 | 1323.2.g.h.667.3 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.148.10 | yes | 24 | ||
21.5 | even | 6 | 441.2.f.h.148.9 | ✓ | 24 | ||
21.11 | odd | 6 | 441.2.g.h.67.10 | 24 | |||
21.17 | even | 6 | 441.2.g.h.67.9 | 24 | |||
21.20 | even | 2 | 441.2.h.h.373.4 | 24 | |||
63.2 | odd | 6 | 441.2.f.h.295.10 | yes | 24 | ||
63.5 | even | 6 | 3969.2.a.bh.1.3 | 12 | |||
63.11 | odd | 6 | 441.2.h.h.214.3 | 24 | |||
63.16 | even | 3 | 1323.2.f.h.883.4 | 24 | |||
63.20 | even | 6 | 441.2.g.h.79.9 | 24 | |||
63.23 | odd | 6 | 3969.2.a.bh.1.4 | 12 | |||
63.25 | even | 3 | inner | 1323.2.h.h.802.9 | 24 | ||
63.34 | odd | 6 | 1323.2.g.h.667.4 | 24 | |||
63.38 | even | 6 | 441.2.h.h.214.4 | 24 | |||
63.40 | odd | 6 | 3969.2.a.bi.1.10 | 12 | |||
63.47 | even | 6 | 441.2.f.h.295.9 | yes | 24 | ||
63.52 | odd | 6 | inner | 1323.2.h.h.802.10 | 24 | ||
63.58 | even | 3 | 3969.2.a.bi.1.9 | 12 | |||
63.61 | odd | 6 | 1323.2.f.h.883.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 21.5 | even | 6 | ||
441.2.f.h.148.10 | yes | 24 | 21.2 | odd | 6 | ||
441.2.f.h.295.9 | yes | 24 | 63.47 | even | 6 | ||
441.2.f.h.295.10 | yes | 24 | 63.2 | odd | 6 | ||
441.2.g.h.67.9 | 24 | 21.17 | even | 6 | |||
441.2.g.h.67.10 | 24 | 21.11 | odd | 6 | |||
441.2.g.h.79.9 | 24 | 63.20 | even | 6 | |||
441.2.g.h.79.10 | 24 | 9.2 | odd | 6 | |||
441.2.h.h.214.3 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.214.4 | 24 | 63.38 | even | 6 | |||
441.2.h.h.373.3 | 24 | 3.2 | odd | 2 | |||
441.2.h.h.373.4 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.3 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.442.4 | 24 | 7.2 | even | 3 | |||
1323.2.f.h.883.3 | 24 | 63.61 | odd | 6 | |||
1323.2.f.h.883.4 | 24 | 63.16 | even | 3 | |||
1323.2.g.h.361.3 | 24 | 7.4 | even | 3 | |||
1323.2.g.h.361.4 | 24 | 7.3 | odd | 6 | |||
1323.2.g.h.667.3 | 24 | 9.7 | even | 3 | |||
1323.2.g.h.667.4 | 24 | 63.34 | odd | 6 | |||
1323.2.h.h.226.9 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.h.h.226.10 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.802.9 | 24 | 63.25 | even | 3 | inner | ||
1323.2.h.h.802.10 | 24 | 63.52 | odd | 6 | inner | ||
3969.2.a.bh.1.3 | 12 | 63.5 | even | 6 | |||
3969.2.a.bh.1.4 | 12 | 63.23 | odd | 6 | |||
3969.2.a.bi.1.9 | 12 | 63.58 | even | 3 | |||
3969.2.a.bi.1.10 | 12 | 63.40 | odd | 6 |