Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(385,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.385");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.8528759163648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 385.5 | ||
Root | \(-1.41743 + 0.995434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.385 |
Dual form | 1152.2.i.e.769.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.57079 | − | 0.729814i | 0.906894 | − | 0.421358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.115851 | + | 0.200661i | 0.0518103 | + | 0.0897381i | 0.890767 | − | 0.454459i | \(-0.150168\pi\) |
−0.838957 | + | 0.544198i | \(0.816834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.230793 | + | 0.399745i | −0.0872315 | + | 0.151089i | −0.906340 | − | 0.422549i | \(-0.861135\pi\) |
0.819108 | + | 0.573639i | \(0.194469\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.93474 | − | 2.29277i | 0.644914 | − | 0.764255i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.749014 | − | 1.29733i | 0.225836 | − | 0.391160i | −0.730734 | − | 0.682663i | \(-0.760822\pi\) |
0.956570 | + | 0.291503i | \(0.0941552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07079 | − | 1.85466i | −0.296983 | − | 0.514389i | 0.678461 | − | 0.734636i | \(-0.262647\pi\) |
−0.975444 | + | 0.220247i | \(0.929314\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.328423 | + | 0.230645i | 0.0847984 | + | 0.0595523i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.03644 | 0.251374 | 0.125687 | − | 0.992070i | \(-0.459886\pi\) | ||||
0.125687 | + | 0.992070i | \(0.459886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94631 | 0.675931 | 0.337965 | − | 0.941159i | \(-0.390261\pi\) | ||||
0.337965 | + | 0.941159i | \(0.390261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0707868 | + | 0.796350i | −0.0154470 | + | 0.173778i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.364866 | − | 0.631966i | −0.0760798 | − | 0.131774i | 0.825476 | − | 0.564438i | \(-0.190907\pi\) |
−0.901555 | + | 0.432664i | \(0.857574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.47316 | − | 4.28363i | 0.494631 | − | 0.856727i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.36578 | − | 5.01345i | 0.262844 | − | 0.964838i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.33711 | − | 4.04800i | 0.433991 | − | 0.751694i | −0.563222 | − | 0.826306i | \(-0.690438\pi\) |
0.997213 | + | 0.0746115i | \(0.0237717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.73632 | + | 4.73945i | 0.491458 | + | 0.851230i | 0.999952 | − | 0.00983556i | \(-0.00313081\pi\) |
−0.508494 | + | 0.861066i | \(0.669797\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.229731 | − | 2.58447i | 0.0399911 | − | 0.449899i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.106951 | −0.0180780 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.30039 | −0.378182 | −0.189091 | − | 0.981960i | \(-0.560554\pi\) | ||||
−0.189091 | + | 0.981960i | \(0.560554\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.03553 | − | 2.13180i | −0.486074 | − | 0.341361i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.84151 | − | 3.18959i | −0.287596 | − | 0.498131i | 0.685639 | − | 0.727941i | \(-0.259523\pi\) |
−0.973235 | + | 0.229811i | \(0.926189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41968 | − | 4.19101i | 0.368998 | − | 0.639123i | −0.620411 | − | 0.784277i | \(-0.713034\pi\) |
0.989409 | + | 0.145153i | \(0.0463676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.684210 | + | 0.122606i | 0.101996 | + | 0.0182771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.40881 | + | 9.36833i | −0.788956 | + | 1.36651i | 0.137651 | + | 0.990481i | \(0.456045\pi\) |
−0.926607 | + | 0.376031i | \(0.877289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.39347 | + | 5.87766i | 0.484781 | + | 0.839666i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.62803 | − | 0.756411i | 0.227970 | − | 0.105919i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0430 | 1.37951 | 0.689756 | − | 0.724042i | \(-0.257718\pi\) | ||||
0.689756 | + | 0.724042i | \(0.257718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.347097 | 0.0468026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.62803 | − | 2.15026i | 0.612998 | − | 0.284809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.71613 | − | 4.70447i | −0.353610 | − | 0.612470i | 0.633269 | − | 0.773932i | \(-0.281713\pi\) |
−0.986879 | + | 0.161461i | \(0.948379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.86526 | − | 11.8910i | 0.879007 | − | 1.52248i | 0.0265746 | − | 0.999647i | \(-0.491540\pi\) |
0.852432 | − | 0.522838i | \(-0.175127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.469996 | + | 1.30256i | 0.0592140 | + | 0.164107i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.248104 | − | 0.429729i | 0.0307736 | − | 0.0533014i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.58388 | + | 9.67156i | 0.682179 | + | 1.18157i | 0.974314 | + | 0.225192i | \(0.0723009\pi\) |
−0.292135 | + | 0.956377i | \(0.594366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.03434 | − | 0.726400i | −0.124520 | − | 0.0874482i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2942 | −1.57773 | −0.788866 | − | 0.614565i | \(-0.789331\pi\) | ||||
−0.788866 | + | 0.614565i | \(0.789331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24276 | 0.496578 | 0.248289 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248289 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.758546 | − | 8.53362i | 0.0875893 | − | 0.985378i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.345734 | + | 0.598829i | 0.0394001 | + | 0.0682429i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.23617 | + | 10.8014i | −0.701624 | + | 1.21525i | 0.266272 | + | 0.963898i | \(0.414208\pi\) |
−0.967896 | + | 0.251351i | \(0.919125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.51354 | − | 8.87182i | −0.168171 | − | 0.985758i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.62651 | + | 6.28130i | −0.398061 | + | 0.689463i | −0.993487 | − | 0.113948i | \(-0.963650\pi\) |
0.595425 | + | 0.803411i | \(0.296984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.120073 | + | 0.207973i | 0.0130238 | + | 0.0225579i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.716820 | − | 8.06420i | 0.0768511 | − | 0.864573i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8627 | −1.25745 | −0.628724 | − | 0.777628i | \(-0.716423\pi\) | ||||
−0.628724 | + | 0.777628i | \(0.716423\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.988520 | 0.103625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.75710 | + | 5.44766i | 0.804373 | + | 0.564896i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.341335 | + | 0.591209i | 0.0350202 | + | 0.0606567i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.21479 | + | 3.83613i | −0.224878 | + | 0.389500i | −0.956283 | − | 0.292444i | \(-0.905532\pi\) |
0.731405 | + | 0.681943i | \(0.238865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.52532 | − | 4.22731i | −0.153301 | − | 0.424861i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.47401 | − | 12.9454i | 0.743692 | − | 1.28811i | −0.207112 | − | 0.978317i | \(-0.566406\pi\) |
0.950804 | − | 0.309794i | \(-0.100260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0310319 | + | 0.0537488i | 0.00305766 | + | 0.00529603i | 0.867550 | − | 0.497350i | \(-0.165693\pi\) |
−0.864493 | + | 0.502646i | \(0.832360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.167997 | + | 0.0780541i | −0.0163948 | + | 0.00761730i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9297 | −1.15329 | −0.576645 | − | 0.816995i | \(-0.695638\pi\) | ||||
−0.576645 | + | 0.816995i | \(0.695638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1328 | −0.970544 | −0.485272 | − | 0.874363i | \(-0.661279\pi\) | ||||
−0.485272 | + | 0.874363i | \(0.661279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.61342 | + | 1.67886i | −0.342971 | + | 0.159350i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.743274 | − | 1.28739i | −0.0699213 | − | 0.121107i | 0.828945 | − | 0.559330i | \(-0.188941\pi\) |
−0.898866 | + | 0.438223i | \(0.855608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0845404 | − | 0.146428i | 0.00788343 | − | 0.0136545i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.32399 | − | 1.13322i | −0.584653 | − | 0.104766i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.239204 | + | 0.414313i | −0.0219278 | + | 0.0379800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.37796 | + | 7.58284i | 0.397996 | + | 0.689349i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.22043 | − | 3.66621i | −0.470711 | − | 0.330571i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.30459 | 0.206129 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5663 | 1.47002 | 0.735010 | − | 0.678056i | \(-0.237177\pi\) | ||||
0.735010 | + | 0.678056i | \(0.237177\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.742144 | − | 8.34910i | 0.0653422 | − | 0.735098i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.43125 | + | 2.47900i | 0.125049 | + | 0.216591i | 0.921752 | − | 0.387780i | \(-0.126758\pi\) |
−0.796703 | + | 0.604371i | \(0.793424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.679988 | + | 1.17777i | −0.0589624 | + | 0.102126i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.16423 | − | 0.306758i | 0.100201 | − | 0.0264015i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.27650 | + | 14.3353i | −0.707109 | + | 1.22475i | 0.258816 | + | 0.965927i | \(0.416668\pi\) |
−0.965925 | + | 0.258822i | \(0.916666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.68545 | + | 6.38339i | 0.312596 | + | 0.541432i | 0.978923 | − | 0.204227i | \(-0.0654682\pi\) |
−0.666328 | + | 0.745659i | \(0.732135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.65894 | + | 18.6631i | −0.139708 | + | 1.57171i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.20814 | −0.268278 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.08303 | 0.0899408 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.62002 | + | 6.75595i | 0.793446 | + | 0.557221i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.06052 | + | 1.83688i | 0.0868814 | + | 0.150483i | 0.906191 | − | 0.422868i | \(-0.138977\pi\) |
−0.819310 | + | 0.573351i | \(0.805643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.97197 | + | 3.41555i | −0.160476 | + | 0.277953i | −0.935040 | − | 0.354543i | \(-0.884636\pi\) |
0.774563 | + | 0.632497i | \(0.217970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00525 | − | 2.37632i | 0.162115 | − | 0.192114i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.634013 | + | 1.09814i | −0.0509252 | + | 0.0882050i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.77046 | − | 9.99472i | −0.460532 | − | 0.797666i | 0.538455 | − | 0.842654i | \(-0.319008\pi\) |
−0.998987 | + | 0.0449886i | \(0.985675\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.7754 | − | 7.32952i | 1.25107 | − | 0.581269i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.336834 | 0.0265462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.716550 | −0.0561245 | −0.0280623 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280623 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.545216 | − | 0.253317i | 0.0424450 | − | 0.0197207i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.36210 | − | 7.55538i | −0.337550 | − | 0.584653i | 0.646422 | − | 0.762980i | \(-0.276265\pi\) |
−0.983971 | + | 0.178327i | \(0.942931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.20683 | − | 7.28645i | 0.323602 | − | 0.560496i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.70036 | − | 6.75521i | 0.435917 | − | 0.516583i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.96809 | + | 15.5332i | −0.681832 | + | 1.18097i | 0.292590 | + | 0.956238i | \(0.405483\pi\) |
−0.974421 | + | 0.224729i | \(0.927850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.14157 | + | 1.97726i | 0.0862949 | + | 0.149467i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.69985 | − | 5.40746i | −0.578756 | − | 0.406449i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.66578 | −0.498224 | −0.249112 | − | 0.968475i | \(-0.580139\pi\) | ||||
−0.249112 | + | 0.968475i | \(0.580139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.1119 | −1.42058 | −0.710290 | − | 0.703909i | \(-0.751436\pi\) | ||||
−0.710290 | + | 0.703909i | \(0.751436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.10566 | − | 23.6886i | 0.155655 | − | 1.75111i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.266503 | − | 0.461598i | −0.0195937 | − | 0.0339373i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.776311 | − | 1.34461i | 0.0567695 | − | 0.0983276i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.68889 | + | 1.70303i | 0.122849 | + | 0.123877i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.03948 | + | 1.80042i | −0.0752138 | + | 0.130274i | −0.901179 | − | 0.433447i | \(-0.857297\pi\) |
0.825965 | + | 0.563721i | \(0.190631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1978 | + | 17.6632i | 0.734057 | + | 1.27142i | 0.955136 | + | 0.296168i | \(0.0957089\pi\) |
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0760965 | − | 0.856083i | 0.00544938 | − | 0.0613054i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5458 | 1.17884 | 0.589419 | − | 0.807828i | \(-0.299357\pi\) | ||||
0.589419 | + | 0.807828i | \(0.299357\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2942 | 1.50951 | 0.754753 | − | 0.656009i | \(-0.227757\pi\) | ||||
0.754753 | + | 0.656009i | \(0.227757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.8295 | + | 11.1168i | 1.11653 | + | 0.784116i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.07878 | + | 1.86850i | 0.0757153 | + | 0.131143i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.426684 | − | 0.739038i | 0.0298009 | − | 0.0516166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.15487 | − | 0.386140i | −0.149774 | − | 0.0268386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.20683 | − | 3.82234i | 0.152650 | − | 0.264397i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1986 | + | 17.6645i | 0.702101 | + | 1.21607i | 0.967728 | + | 0.251999i | \(0.0810879\pi\) |
−0.265627 | + | 0.964076i | \(0.585579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.8824 | + | 9.70230i | −1.43084 | + | 0.664791i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.12129 | 0.0764716 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.52609 | −0.171482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.66447 | − | 3.09643i | 0.450343 | − | 0.209237i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.10981 | − | 1.92225i | −0.0746539 | − | 0.129304i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.52026 | − | 4.36522i | 0.168769 | − | 0.292317i | −0.769218 | − | 0.638986i | \(-0.779354\pi\) |
0.937987 | + | 0.346669i | \(0.112687\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.03644 | − | 13.9581i | −0.335763 | − | 0.930540i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.12047 | + | 14.0651i | −0.538975 | + | 0.933531i | 0.459985 | + | 0.887927i | \(0.347855\pi\) |
−0.998960 | + | 0.0456047i | \(0.985479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.92453 | + | 5.06544i | 0.193259 | + | 0.334734i | 0.946328 | − | 0.323207i | \(-0.104761\pi\) |
−0.753070 | + | 0.657941i | \(0.771428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.980109 | + | 0.688311i | 0.0644864 | + | 0.0452876i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.7492 | −1.35932 | −0.679662 | − | 0.733526i | \(-0.737873\pi\) | ||||
−0.679662 | + | 0.733526i | \(0.737873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.50647 | −0.163504 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.91271 | + | 21.5179i | −0.124244 | + | 1.39774i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.09672 | − | 3.63163i | −0.135626 | − | 0.234910i | 0.790211 | − | 0.612835i | \(-0.209971\pi\) |
−0.925836 | + | 0.377925i | \(0.876638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.03921 | + | 12.1923i | −0.453435 | + | 0.785373i | −0.998597 | − | 0.0529581i | \(-0.983135\pi\) |
0.545161 | + | 0.838331i | \(0.316468\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.85223 | − | 12.8311i | −0.567871 | − | 0.823118i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.786276 | + | 1.36187i | −0.0502334 | + | 0.0870067i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.15487 | − | 5.46440i | −0.200740 | − | 0.347692i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.11229 | + | 12.5133i | −0.0704887 | + | 0.792996i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.3752 | −0.970476 | −0.485238 | − | 0.874382i | \(-0.661267\pi\) | ||||
−0.485238 | + | 0.874382i | \(0.661267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.09316 | −0.0687263 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.340391 | + | 0.239050i | 0.0213161 | + | 0.0149699i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.51288 | + | 6.08448i | 0.219127 | + | 0.379540i | 0.954541 | − | 0.298078i | \(-0.0963456\pi\) |
−0.735414 | + | 0.677618i | \(0.763012\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.530914 | − | 0.919569i | 0.0329894 | − | 0.0571393i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.75940 | − | 13.1903i | −0.294599 | − | 0.816458i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.62093 | − | 9.73573i | 0.346601 | − | 0.600331i | −0.639042 | − | 0.769172i | \(-0.720669\pi\) |
0.985643 | + | 0.168841i | \(0.0540024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.16350 | + | 2.01523i | 0.0714730 | + | 0.123795i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.6338 | + | 8.65760i | −1.14037 | + | 0.529836i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.5678 | −1.25404 | −0.627019 | − | 0.779004i | \(-0.715725\pi\) | ||||
−0.627019 | + | 0.779004i | \(0.715725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.25314 | 0.501343 | 0.250671 | − | 0.968072i | \(-0.419349\pi\) | ||||
0.250671 | + | 0.968072i | \(0.419349\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.55275 | − | 0.721436i | 0.0939769 | − | 0.0436633i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.70486 | − | 6.41701i | −0.223411 | − | 0.386960i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.49837 | + | 11.2555i | −0.390449 | + | 0.676278i | −0.992509 | − | 0.122174i | \(-0.961014\pi\) |
0.602060 | + | 0.798451i | \(0.294347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.1605 | + | 2.89587i | 0.967505 | + | 0.173371i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.29955 | + | 16.1073i | −0.554765 | + | 0.960880i | 0.443157 | + | 0.896444i | \(0.353858\pi\) |
−0.997922 | + | 0.0644365i | \(0.979475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.30074 | + | 14.3773i | 0.493428 | + | 0.854642i | 0.999971 | − | 0.00757254i | \(-0.00241044\pi\) |
−0.506544 | + | 0.862214i | \(0.669077\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.967636 | + | 0.679552i | 0.0573178 | + | 0.0402532i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.70003 | 0.100350 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9258 | −0.936811 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.679301 | + | 7.64212i | −0.0398214 | + | 0.447989i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.33729 | + | 10.9765i | 0.370228 | + | 0.641254i | 0.989601 | − | 0.143843i | \(-0.0459461\pi\) |
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.629335 | − | 1.09004i | 0.0366413 | − | 0.0634646i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.48111 | − | 5.52701i | −0.318047 | − | 0.320709i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.781387 | + | 1.35340i | −0.0451888 | + | 0.0782692i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11689 | + | 1.93451i | 0.0643765 | + | 0.111503i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.29236 | − | 25.7890i | 0.131693 | − | 1.48154i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.18140 | 0.182167 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4097 | −0.879479 | −0.439740 | − | 0.898125i | \(-0.644929\pi\) | ||||
−0.439740 | + | 0.898125i | \(0.644929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0879711 | + | 0.0617804i | 0.00500450 | + | 0.00351457i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7683 | + | 22.1153i | 0.724022 | + | 1.25404i | 0.959375 | + | 0.282133i | \(0.0910419\pi\) |
−0.235354 | + | 0.971910i | \(0.575625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.13328 | − | 15.8193i | 0.516244 | − | 0.894160i | −0.483579 | − | 0.875301i | \(-0.660663\pi\) |
0.999822 | − | 0.0188591i | \(-0.00600341\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.206922 | + | 0.245213i | −0.0116587 | + | 0.0138162i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.22172 | − | 9.04428i | 0.293281 | − | 0.507977i | −0.681303 | − | 0.732002i | \(-0.738586\pi\) |
0.974584 | + | 0.224024i | \(0.0719195\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.50106 | − | 6.06402i | −0.196022 | − | 0.339520i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7391 | + | 8.70649i | −1.04591 | + | 0.485949i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.05369 | 0.169912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5929 | −0.587588 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.9164 | + | 7.39504i | −0.880181 | + | 0.408947i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.49663 | − | 4.32429i | −0.137644 | − | 0.238406i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.37887 | + | 4.12032i | −0.130754 | + | 0.226473i | −0.923968 | − | 0.382471i | \(-0.875073\pi\) |
0.793213 | + | 0.608944i | \(0.208407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.45066 | + | 5.27425i | −0.243895 | + | 0.289027i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.29380 | + | 2.24093i | −0.0706878 | + | 0.122435i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7810 | + | 23.8694i | 0.750700 | + | 1.30025i | 0.947484 | + | 0.319804i | \(0.103617\pi\) |
−0.196783 | + | 0.980447i | \(0.563050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.10708 | − | 1.47976i | −0.114441 | − | 0.0803696i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.19818 | 0.443956 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.36385 | −0.343616 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0259295 | − | 0.291706i | 0.00139600 | − | 0.0157049i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.5341 | + | 18.2457i | 0.565502 | + | 0.979478i | 0.997003 | + | 0.0773655i | \(0.0246508\pi\) |
−0.431501 | + | 0.902113i | \(0.642016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7897 | − | 30.8126i | 0.952258 | − | 1.64936i | 0.211738 | − | 0.977327i | \(-0.432088\pi\) |
0.740521 | − | 0.672033i | \(-0.234579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.7607 | + | 2.83529i | −0.574363 | + | 0.151336i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.52544 | − | 4.37420i | 0.134416 | − | 0.232815i | −0.790958 | − | 0.611870i | \(-0.790418\pi\) |
0.925374 | + | 0.379055i | \(0.123751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.54015 | − | 2.66762i | −0.0817428 | − | 0.141583i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0733665 | + | 0.825371i | −0.00388297 | + | 0.0436833i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1271 | −0.956709 | −0.478355 | − | 0.878167i | \(-0.658767\pi\) | ||||
−0.478355 | + | 0.878167i | \(0.658767\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3192 | −0.543118 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.4109 | + | 8.71593i | 0.651403 | + | 0.457468i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.491530 | + | 0.851355i | 0.0257278 | + | 0.0445619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.83039 | + | 8.36649i | −0.252145 | + | 0.436727i | −0.964116 | − | 0.265481i | \(-0.914469\pi\) |
0.711972 | + | 0.702208i | \(0.247803\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.8758 | − | 1.94889i | −0.566174 | − | 0.101455i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.31785 | + | 4.01464i | −0.120337 | + | 0.208430i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0300 | + | 27.7647i | 0.830001 | + | 1.43760i | 0.898037 | + | 0.439921i | \(0.144993\pi\) |
−0.0680357 | + | 0.997683i | \(0.521673\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.62002 | − | 1.68192i | 0.186937 | − | 0.0868541i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0102 | −0.515551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0684 | −0.825377 | −0.412689 | − | 0.910872i | \(-0.635410\pi\) | ||||
−0.412689 | + | 0.910872i | \(0.635410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.0221 | − | 12.0903i | 1.33315 | − | 0.619406i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.3129 | − | 26.5228i | −0.782454 | − | 1.35525i | −0.930509 | − | 0.366270i | \(-0.880635\pi\) |
0.148055 | − | 0.988979i | \(-0.452699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0801076 | + | 0.138750i | −0.00408266 | + | 0.00707138i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.92754 | − | 13.6563i | −0.250481 | − | 0.694188i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.37823 | − | 12.7795i | 0.374091 | − | 0.647945i | −0.616099 | − | 0.787669i | \(-0.711288\pi\) |
0.990191 | + | 0.139723i | \(0.0446213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.378162 | − | 0.654997i | −0.0191245 | − | 0.0331246i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.05740 | + | 2.84944i | 0.204669 | + | 0.143735i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.88988 | −0.145405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.7032 | −0.687746 | −0.343873 | − | 0.939016i | \(-0.611739\pi\) | ||||
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.208560 | + | 2.34630i | −0.0104411 | + | 0.117462i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.83939 | + | 6.65002i | 0.191730 | + | 0.332086i | 0.945824 | − | 0.324681i | \(-0.105257\pi\) |
−0.754094 | + | 0.656767i | \(0.771924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.86004 | − | 10.1499i | 0.291909 | − | 0.505601i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.60488 | − | 1.33152i | 0.0797470 | − | 0.0661638i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.72303 | + | 2.98437i | −0.0854072 | + | 0.147930i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.73882 | − | 11.6720i | −0.333213 | − | 0.577142i | 0.649927 | − | 0.759997i | \(-0.274800\pi\) |
−0.983140 | + | 0.182855i | \(0.941466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.53850 | + | 28.5580i | −0.125215 | + | 1.40866i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.50745 | 0.123384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.68055 | −0.0824948 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.4477 | + | 7.33724i | 0.511628 | + | 0.359306i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0380 | − | 31.2427i | −0.881213 | − | 1.52630i | −0.849994 | − | 0.526792i | \(-0.823395\pi\) |
−0.0312184 | − | 0.999513i | \(-0.509939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.57726 | − | 4.46394i | 0.125608 | − | 0.217559i | −0.796362 | − | 0.604820i | \(-0.793245\pi\) |
0.921970 | + | 0.387260i | \(0.126579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.0147 | + | 30.5264i | 0.535555 | + | 1.48425i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.56329 | − | 4.43974i | 0.124338 | − | 0.215359i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.16891 | + | 5.48871i | 0.153354 | + | 0.265617i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.03930 | + | 2.34134i | −0.243300 | + | 0.113041i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7200 | 0.998045 | 0.499022 | − | 0.866589i | \(-0.333693\pi\) | ||||
0.499022 | + | 0.866589i | \(0.333693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.3719 | −1.12318 | −0.561592 | − | 0.827414i | \(-0.689811\pi\) | ||||
−0.561592 | + | 0.827414i | \(0.689811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70121 | − | 0.790411i | 0.0815668 | − | 0.0378973i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.07501 | − | 1.86197i | −0.0514246 | − | 0.0890701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.0107 | + | 32.9274i | −0.907330 | + | 1.57154i | −0.0895708 | + | 0.995980i | \(0.528550\pi\) |
−0.817759 | + | 0.575561i | \(0.804784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.0416 | + | 3.59133i | 0.954361 | + | 0.171016i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.30811 | − | 14.3901i | 0.394730 | − | 0.683693i | −0.598336 | − | 0.801245i | \(-0.704171\pi\) |
0.993067 | + | 0.117552i | \(0.0375047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.37432 | − | 2.38038i | −0.0651488 | − | 0.112841i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.00644 | + | 2.11136i | 0.142200 | + | 0.0998640i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9085 | 0.609192 | 0.304596 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304596 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.51728 | −0.259798 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.604825 | + | 6.80427i | −0.0284172 | + | 0.319692i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.114521 | + | 0.198357i | 0.00536884 | + | 0.00929911i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4943 | − | 23.3728i | 0.631237 | − | 1.09333i | −0.356063 | − | 0.934462i | \(-0.615881\pi\) |
0.987299 | − | 0.158872i | \(-0.0507856\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.41555 | − | 5.19615i | 0.0660721 | − | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0800 | + | 17.4591i | −0.469474 | + | 0.813152i | −0.999391 | − | 0.0348972i | \(-0.988890\pi\) |
0.529917 | + | 0.848049i | \(0.322223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2220 | − | 29.8293i | −0.800373 | − | 1.38629i | −0.919371 | − | 0.393391i | \(-0.871302\pi\) |
0.118999 | − | 0.992894i | \(-0.462032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.194459 | + | 2.18766i | −0.00901783 | + | 0.101450i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.6194 | 1.46317 | 0.731585 | − | 0.681750i | \(-0.238781\pi\) | ||||
0.731585 | + | 0.681750i | \(0.238781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.15487 | −0.238030 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.3584 | − | 11.4882i | −0.753757 | − | 0.529349i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.62475 | − | 6.27825i | −0.166666 | − | 0.288674i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.28670 | − | 12.6209i | 0.334337 | − | 0.579088i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.4306 | − | 23.0262i | 0.889667 | − | 1.05430i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.72976 | + | 6.46014i | −0.170417 | + | 0.295171i | −0.938566 | − | 0.345100i | \(-0.887845\pi\) |
0.768149 | + | 0.640272i | \(0.221178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.46323 | + | 4.26644i | 0.112314 | + | 0.194533i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.529094 | − | 0.245826i | 0.0240746 | − | 0.0111855i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.02635 | −0.0466039 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4254 | 1.33339 | 0.666697 | − | 0.745329i | \(-0.267707\pi\) | ||||
0.666697 | + | 0.745329i | \(0.267707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.12555 | + | 0.522948i | −0.0508990 | + | 0.0236485i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4326 | + | 24.9979i | 0.651332 | + | 1.12814i | 0.982800 | + | 0.184674i | \(0.0591229\pi\) |
−0.331467 | + | 0.943467i | \(0.607544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.42228 | − | 4.19552i | 0.109094 | − | 0.188957i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.671544 | − | 0.795813i | 0.0301837 | − | 0.0357691i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.06821 | − | 5.31429i | 0.137628 | − | 0.238379i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8470 | − | 22.2517i | −0.575111 | − | 0.996122i | −0.996030 | − | 0.0890236i | \(-0.971625\pi\) |
0.420918 | − | 0.907099i | \(-0.361708\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.3660 | − | 8.68437i | −0.552470 | − | 0.387989i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7071 | 0.923286 | 0.461643 | − | 0.887066i | \(-0.347260\pi\) | ||||
0.461643 | + | 0.887066i | \(0.347260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.46350 | 0.154124 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.29028 | − | 14.5157i | 0.0573035 | − | 0.644663i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.7631 | − | 18.6421i | −0.477064 | − | 0.826299i | 0.522591 | − | 0.852584i | \(-0.324966\pi\) |
−0.999654 | + | 0.0262850i | \(0.991632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.979199 | + | 1.69602i | −0.0433172 | + | 0.0750276i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.02400 | − | 14.7712i | 0.177664 | − | 0.652164i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.00719018 | + | 0.0124538i | −0.000316837 | + | 0.000548778i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.10255 | + | 14.0340i | 0.356350 | + | 0.617216i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.75062 | + | 30.9444i | −0.120739 | + | 1.35831i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2984 | 0.976911 | 0.488455 | − | 0.872589i | \(-0.337560\pi\) | ||||
0.488455 | + | 0.872589i | \(0.337560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.92665 | 0.215427 | 0.107714 | − | 0.994182i | \(-0.465647\pi\) | ||||
0.107714 | + | 0.994182i | \(0.465647\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.23620 | + | 2.27272i | 0.141240 | + | 0.0991898i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.83604 | + | 4.91217i | 0.123540 | + | 0.213977i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2337 | − | 19.4574i | 0.488424 | − | 0.845975i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.0413 | − | 2.87450i | −0.696132 | − | 0.124743i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.94373 | + | 6.83075i | −0.170822 | + | 0.295873i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.38208 | − | 2.39383i | −0.0597523 | − | 0.103494i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.4705 | + | 4.86478i | −0.451836 | + | 0.209931i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1670 | 0.437925 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0179 | 0.946622 | 0.473311 | − | 0.880895i | \(-0.343059\pi\) | ||||
0.473311 | + | 0.880895i | \(0.343059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.0208 | + | 13.9482i | −1.28832 | + | 0.598573i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.17390 | − | 2.03325i | −0.0502842 | − | 0.0870948i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2563 | − | 26.4247i | 0.652311 | − | 1.12984i | −0.330249 | − | 0.943894i | \(-0.607133\pi\) |
0.982561 | − | 0.185943i | \(-0.0595339\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.9807 | − | 38.7464i | −0.596682 | − | 1.65366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.88587 | − | 11.9267i | 0.293348 | − | 0.508093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.87853 | − | 4.98575i | −0.122407 | − | 0.212016i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.755501 | − | 0.530573i | −0.0320692 | − | 0.0225216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.8358 | −1.47604 | −0.738021 | − | 0.674778i | \(-0.764239\pi\) | ||||
−0.738021 | + | 0.674778i | \(0.764239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.3639 | −0.438344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.238103 | − | 2.67866i | 0.0100527 | − | 0.113093i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.86229 | − | 11.8858i | −0.289211 | − | 0.500928i | 0.684411 | − | 0.729097i | \(-0.260060\pi\) |
−0.973622 | + | 0.228169i | \(0.926726\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.172219 | − | 0.298292i | 0.00724529 | − | 0.0125492i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.89578 | + | 1.44252i | 0.163607 | + | 0.0605802i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6770 | − | 25.4213i | 0.615291 | − | 1.06572i | −0.375042 | − | 0.927008i | \(-0.622372\pi\) |
0.990333 | − | 0.138708i | \(-0.0442950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.60926 | + | 2.78732i | 0.0673455 | + | 0.116646i | 0.897732 | − | 0.440542i | \(-0.145214\pi\) |
−0.830387 | + | 0.557188i | \(0.811880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.318819 | + | 3.58671i | −0.0133189 | + | 0.149837i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.60948 | −0.150526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.782693 | 0.0325839 | 0.0162920 | − | 0.999867i | \(-0.494814\pi\) | ||||
0.0162920 | + | 0.999867i | \(0.494814\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.9095 | + | 20.3026i | 1.20144 | + | 0.843746i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.67395 | − | 2.89936i | −0.0694470 | − | 0.120286i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.52235 | − | 13.0291i | 0.311544 | − | 0.539610i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.505250 | − | 1.40026i | −0.0208895 | − | 0.0578936i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.7201 | − | 22.0318i | 0.525014 | − | 0.909350i | −0.474562 | − | 0.880222i | \(-0.657394\pi\) |
0.999576 | − | 0.0291282i | \(-0.00927309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.06206 | + | 13.9639i | 0.332192 | + | 0.575373i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.9899 | − | 12.0753i | 1.06908 | − | 0.496713i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.4583 | 1.82569 | 0.912843 | − | 0.408311i | \(-0.133882\pi\) | ||||
0.912843 | + | 0.408311i | \(0.133882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.110848 | −0.00454434 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.4487 | − | 15.5408i | 1.36896 | − | 0.636043i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.7554 | + | 41.1455i | 0.970618 | + | 1.68116i | 0.693696 | + | 0.720268i | \(0.255981\pi\) |
0.276922 | + | 0.960892i | \(0.410686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.61527 | − | 6.26183i | 0.147470 | − | 0.255425i | −0.782822 | − | 0.622246i | \(-0.786220\pi\) |
0.930292 | + | 0.366821i | \(0.119554\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.9780 | + | 5.90946i | 1.34297 | + | 0.240652i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.01438 | + | 1.75697i | −0.0412406 | + | 0.0714308i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.00711 | − | 12.1367i | −0.284410 | − | 0.492612i | 0.688056 | − | 0.725658i | \(-0.258464\pi\) |
−0.972466 | + | 0.233045i | \(0.925131\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.05819 | + | 2.14770i | 0.123924 | + | 0.0870294i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.1667 | 0.937225 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2357 | 0.494194 | 0.247097 | − | 0.968991i | \(-0.420523\pi\) | ||||
0.247097 | + | 0.968991i | \(0.420523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.130869 | − | 1.47227i | 0.00527714 | − | 0.0593677i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.07716 | + | 1.86569i | 0.0433647 | + | 0.0751099i | 0.886893 | − | 0.461975i | \(-0.152859\pi\) |
−0.843528 | + | 0.537085i | \(0.819526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.94519 | − | 10.2974i | 0.238957 | − | 0.413886i | −0.721458 | − | 0.692458i | \(-0.756528\pi\) |
0.960415 | + | 0.278572i | \(0.0898611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.66665 | + | 0.966111i | −0.147138 | + | 0.0387687i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.73784 | − | 4.74207i | 0.109689 | − | 0.189987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0988 | − | 20.9557i | −0.483952 | − | 0.838229i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.676861 | − | 7.61466i | 0.0270312 | − | 0.304100i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.38422 | −0.0950652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.3492 | −1.64609 | −0.823043 | − | 0.567979i | \(-0.807725\pi\) | ||||
−0.823043 | + | 0.567979i | \(0.807725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.9116 | + | 20.3041i | 1.14913 | + | 0.807015i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.91923 | + | 3.32420i | 0.0761623 | + | 0.131917i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.26736 | − | 12.5874i | 0.287943 | − | 0.498733i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.7209 | + | 30.4805i | −1.01750 | + | 1.20579i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6110 | − | 21.8429i | 0.498106 | − | 0.862744i | −0.501892 | − | 0.864930i | \(-0.667362\pi\) |
0.999998 | + | 0.00218592i | \(0.000695802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.87820 | − | 13.6454i | −0.310686 | − | 0.538124i | 0.667825 | − | 0.744318i | \(-0.267225\pi\) |
−0.978511 | + | 0.206194i | \(0.933892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.76131 | − | 0.818336i | 0.0693517 | − | 0.0322220i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.8197 | −0.857823 | −0.428911 | − | 0.903347i | \(-0.641103\pi\) | ||||
−0.428911 | + | 0.903347i | \(0.641103\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.13768 | −0.319432 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.96796 | + | 1.84358i | −0.155516 | + | 0.0722556i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5168 | + | 21.6797i | 0.489819 | + | 0.848392i | 0.999931 | − | 0.0117162i | \(-0.00372948\pi\) |
−0.510112 | + | 0.860108i | \(0.670396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.331625 | + | 0.574392i | −0.0129577 | + | 0.0224433i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.20865 | − | 9.72766i | 0.320250 | − | 0.379512i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5079 | − | 25.1285i | 0.565149 | − | 0.978867i | −0.431887 | − | 0.901928i | \(-0.642152\pi\) |
0.997036 | − | 0.0769388i | \(-0.0245146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.99232 | + | 8.64694i | 0.194179 | + | 0.336327i | 0.946631 | − | 0.322320i | \(-0.104463\pi\) |
−0.752452 | + | 0.658647i | \(0.771129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.14616 | − | 2.20948i | −0.122187 | − | 0.0858093i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.315110 | −0.0122195 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.41093 | −0.132072 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.772993 | − | 8.69615i | 0.0298856 | − | 0.336213i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.2844 | − | 17.8130i | −0.397023 | − | 0.687665i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.42824 | − | 4.20584i | 0.0936019 | − | 0.162123i | −0.815422 | − | 0.578866i | \(-0.803495\pi\) |
0.909024 | + | 0.416743i | \(0.136829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0980 | − | 18.2495i | −0.696592 | − | 0.702425i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.10559 | − | 12.3072i | 0.273090 | − | 0.473006i | −0.696562 | − | 0.717497i | \(-0.745288\pi\) |
0.969651 | + | 0.244491i | \(0.0786210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.02231 | − | 1.77070i | −0.0392328 | − | 0.0679533i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.49064 | + | 28.0197i | −0.0954416 | + | 1.07372i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.7153 | 0.792648 | 0.396324 | − | 0.918111i | \(-0.370286\pi\) | ||||
0.396324 | + | 0.918111i | \(0.370286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.83538 | −0.146542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.29065 | + | 5.82236i | 0.316308 | + | 0.222137i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.7539 | − | 18.6263i | −0.409691 | − | 0.709606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.56378 | − | 11.3688i | 0.249698 | − | 0.432489i | −0.713744 | − | 0.700407i | \(-0.753002\pi\) |
0.963442 | + | 0.267917i | \(0.0863353\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.04188 | + | 0.365893i | 0.0775647 | + | 0.0138991i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.853929 | + | 1.47905i | −0.0323914 | + | 0.0561035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.90862 | − | 3.30583i | −0.0722942 | − | 0.125217i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.5925 | + | 15.1430i | −1.23276 | + | 0.572762i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3554 | 0.504426 | 0.252213 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252213 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.77767 | −0.255625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.93713 | + | 1.82926i | −0.148281 | + | 0.0688939i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.44989 | + | 5.97539i | 0.129747 | + | 0.224728i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5083 | − | 23.3971i | 0.507316 | − | 0.878697i | −0.492648 | − | 0.870229i | \(-0.663971\pi\) |
0.999964 | − | 0.00846836i | \(-0.00269560\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6996 | + | 35.1959i | 0.476272 | + | 1.31995i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.99678 | − | 3.45852i | 0.0747800 | − | 0.129523i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.371667 | − | 0.643747i | −0.0138996 | − | 0.0240748i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.94391 | − | 4.17429i | −0.221979 | − | 0.155892i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.5794 | 1.73712 | 0.868559 | − | 0.495585i | \(-0.165046\pi\) | ||||
0.868559 | + | 0.495585i | \(0.165046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0286478 | −0.00106690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.15901 | + | 24.2888i | −0.0802943 | + | 0.903309i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.5601 | − | 20.0227i | −0.429331 | − | 0.743623i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.5353 | + | 21.7119i | −0.464910 | + | 0.805248i | −0.999197 | − | 0.0400549i | \(-0.987247\pi\) |
0.534287 | + | 0.845303i | \(0.320580\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.2693 | − | 13.6945i | −0.861826 | − | 0.507203i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50786 | − | 4.34374i | 0.0927566 | − | 0.160659i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8288 | + | 20.4881i | 0.436907 | + | 0.756746i | 0.997449 | − | 0.0713803i | \(-0.0227404\pi\) |
−0.560542 | + | 0.828126i | \(0.689407\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.241160 | + | 2.71304i | −0.00889532 | + | 0.100072i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.7296 | 0.616243 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.9834 | −1.21332 | −0.606658 | − | 0.794963i | \(-0.707490\pi\) | ||||
−0.606658 | + | 0.794963i | \(0.707490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.94363 | − | 6.28094i | −0.328553 | − | 0.230736i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.16854 | − | 8.95218i | −0.189615 | − | 0.328424i | 0.755507 | − | 0.655141i | \(-0.227391\pi\) |
−0.945122 | + | 0.326717i | \(0.894057\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.245726 | + | 0.425610i | −0.00900271 | + | 0.0155931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.38519 | + | 20.4674i | 0.270210 | + | 0.748865i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.75330 | − | 4.76885i | 0.100603 | − | 0.174250i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5268 | − | 19.9650i | −0.420620 | − | 0.728535i | 0.575381 | − | 0.817886i | \(-0.304854\pi\) |
−0.996000 | + | 0.0893513i | \(0.971521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.1512 | + | 11.2211i | −0.880119 | + | 0.408918i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.913821 | −0.0332573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.86572 | 0.176848 | 0.0884239 | − | 0.996083i | \(-0.471817\pi\) | ||||
0.0884239 | + | 0.996083i | \(0.471817\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.71712 | + | 0.797803i | −0.0623275 | + | 0.0289584i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3733 | + | 33.5556i | 0.702283 | + | 1.21639i | 0.967663 | + | 0.252246i | \(0.0811694\pi\) |
−0.265380 | + | 0.964144i | \(0.585497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.33857 | − | 4.05052i | 0.0846620 | − | 0.146639i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.709145 | + | 0.127075i | 0.0256392 | + | 0.00459439i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.81679 | + | 10.0750i | −0.210032 | + | 0.363786i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0001 | − | 24.2489i | −0.504858 | − | 0.874439i | −0.999984 | − | 0.00561822i | \(-0.998212\pi\) |
0.495127 | − | 0.868821i | \(-0.335122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.95853 | + | 6.99368i | 0.358648 | + | 0.251871i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.9662 | −1.11378 | −0.556888 | − | 0.830588i | \(-0.688005\pi\) | ||||
−0.556888 | + | 0.830588i | \(0.688005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.0694 | 0.972362 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.162837 | − | 1.83192i | 0.00584176 | − | 0.0657196i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.42567 | − | 9.39754i | −0.194395 | − | 0.336702i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.95755 | + | 17.2470i | −0.356309 | + | 0.617146i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.1025 | − | 17.2456i | −0.611192 | − | 0.616309i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.33703 | − | 2.31580i | 0.0477207 | − | 0.0826546i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.48755 | + | 14.7009i | 0.302549 | + | 0.524030i | 0.976713 | − | 0.214552i | \(-0.0688292\pi\) |
−0.674164 | + | 0.738582i | \(0.735496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.72400 | − | 19.3950i | 0.0613762 | − | 0.690480i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.686169 | 0.0243974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.4049 | −1.04420 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.29835 | + | 2.31637i | 0.116980 | + | 0.0821531i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.5688 | − | 21.7698i | −0.445210 | − | 0.771127i | 0.552857 | − | 0.833276i | \(-0.313538\pi\) |
−0.998067 | + | 0.0621496i | \(0.980204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.60592 | + | 9.70974i | −0.198323 | + | 0.343506i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.9514 | + | 27.1985i | −0.810946 | + | 0.961011i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.17789 | − | 5.50427i | 0.112145 | − | 0.194241i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0390226 | + | 0.0675892i | 0.00137537 | + | 0.00238221i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.3076 | + | 15.0106i | −1.13728 | + | 0.528400i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.441024 | −0.0155056 | −0.00775279 | − | 0.999970i | \(-0.502468\pi\) | ||||
−0.00775279 | + | 0.999970i | \(0.502468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.8442 | −1.57469 | −0.787346 | − | 0.616511i | \(-0.788545\pi\) | ||||
−0.787346 | + | 0.616511i | \(0.788545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9639 | − | 6.02326i | 0.454665 | − | 0.211245i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0830133 | − | 0.143783i | −0.00290783 | − | 0.00503651i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.12914 | − | 12.3480i | 0.249417 | − | 0.432003i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.91253 | − | 2.26644i | 0.0668292 | − | 0.0791959i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.3775 | + | 23.1705i | −0.466878 | + | 0.808656i | −0.999284 | − | 0.0378328i | \(-0.987955\pi\) |
0.532406 | + | 0.846489i | \(0.321288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.2608 | − | 36.8247i | −0.741104 | − | 1.28363i | −0.951993 | − | 0.306119i | \(-0.900969\pi\) |
0.210889 | − | 0.977510i | \(-0.432364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.5028 | − | 7.37589i | −0.365659 | − | 0.256795i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.4800 | −0.607839 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7798 | 0.374399 | 0.187200 | − | 0.982322i | \(-0.440059\pi\) | ||||
0.187200 | + | 0.982322i | \(0.440059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.99312 | + | 22.4226i | −0.0691407 | + | 0.777831i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.51714 | + | 6.09186i | 0.121862 | + | 0.211070i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.01071 | − | 1.75060i | 0.0349771 | − | 0.0605821i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.4982 | − | 7.24538i | 0.950476 | − | 0.250437i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8649 | − | 34.4070i | 0.685811 | − | 1.18786i | −0.287370 | − | 0.957820i | \(-0.592781\pi\) |
0.973181 | − | 0.230040i | \(-0.0738859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.57581 | + | 6.19348i | 0.123304 | + | 0.213568i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.85228 | + | 32.0881i | −0.0982377 | + | 1.10517i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.94947 | 0.0670638 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.04160 | −0.138871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.5314 | + | 16.5257i | 0.807597 | + | 0.567160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.839334 | + | 1.45377i | 0.0287720 | + | 0.0498345i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.26964 | + | 3.93113i | −0.0777110 | + | 0.134599i | −0.902262 | − | 0.431188i | \(-0.858094\pi\) |
0.824551 | + | 0.565788i | \(0.191428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.01590 | + | 0.361237i | 0.0689422 | + | 0.0123540i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.41586 | + | 2.45234i | −0.0483648 | + | 0.0837702i | −0.889194 | − | 0.457530i | \(-0.848734\pi\) |
0.840830 | + | 0.541300i | \(0.182068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6443 | − | 20.1684i | −0.397297 | − | 0.688138i | 0.596095 | − | 0.802914i | \(-0.296718\pi\) |
−0.993391 | + | 0.114776i | \(0.963385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.67039 | − | 1.24071i | 0.0910065 | − | 0.0422832i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.111891 | −0.00380882 | −0.00190441 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190441 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.15586 | −0.141304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.0160 | + | 11.6229i | −0.849588 | + | 0.394733i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.34196 | + | 16.1808i | 0.316904 | + | 0.548894i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9583 | − | 20.7124i | 0.405191 | − | 0.701811i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.51029 | + | 12.4999i | 0.152650 | + | 0.423058i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.531882 | + | 0.921248i | −0.0179809 | + | 0.0311439i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1933 | + | 22.8515i | 0.445506 | + | 0.771639i | 0.998087 | − | 0.0618200i | \(-0.0196905\pi\) |
−0.552581 | + | 0.833459i | \(0.686357\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.9653 | + | 12.6167i | 0.605956 | + | 0.425551i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.5296 | −1.56762 | −0.783812 | − | 0.620999i | \(-0.786727\pi\) | ||||
−0.783812 | + | 0.620999i | \(0.786727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.7129 | −0.898959 | −0.449480 | − | 0.893291i | \(-0.648391\pi\) | ||||
−0.449480 | + | 0.893291i | \(0.648391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.193024 | − | 2.17152i | 0.00648844 | − | 0.0729948i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.6389 | + | 35.7476i | 0.692986 | + | 1.20029i | 0.970855 | + | 0.239668i | \(0.0770387\pi\) |
−0.277869 | + | 0.960619i | \(0.589628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.82338 | + | 6.62229i | −0.128232 | + | 0.222105i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6434 | − | 4.68155i | −0.423568 | − | 0.156838i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.9360 | + | 27.6020i | −0.533280 | + | 0.923667i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.772240 | − | 1.33756i | −0.0258131 | − | 0.0447097i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.239660 | + | 2.69617i | −0.00800203 | + | 0.0900226i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.5804 | 0.853153 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.4090 | 0.346774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.16623 | + | 2.22358i | 0.105366 | + | 0.0739962i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.21415 | − | 3.83501i | −0.0736007 | − | 0.127480i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.75080 | − | 16.8889i | 0.323770 | − | 0.560786i | −0.657493 | − | 0.753461i | \(-0.728383\pi\) |
0.981263 | + | 0.192675i | \(0.0617163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.2204 | − | 42.1821i | −0.504828 | − | 1.39909i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.88772 | + | 6.73373i | −0.128806 | + | 0.223098i | −0.923214 | − | 0.384286i | \(-0.874448\pi\) |
0.794408 | + | 0.607384i | \(0.207781\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.43262 | + | 9.40957i | 0.179793 | + | 0.311411i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.99730 | − | 2.32183i | 0.165206 | − | 0.0767574i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.32129 | −0.0436329 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.9999 | −1.48441 | −0.742205 | − | 0.670172i | \(-0.766220\pi\) | ||||
−0.742205 | + | 0.670172i | \(0.766220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.2054 | + | 11.2462i | −0.797595 | + | 0.370576i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.2353 | + | 24.6562i | 0.468559 | + | 0.811569i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.68923 | + | 9.85403i | −0.187061 | + | 0.323999i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.183272 | + | 0.0328413i | 0.00601945 | + | 0.00107865i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.77838 | + | 3.08024i | −0.0583467 | + | 0.101059i | −0.893723 | − | 0.448618i | \(-0.851916\pi\) |
0.835377 | + | 0.549678i | \(0.185250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.99823 | + | 17.3174i | 0.327679 | + | 0.567556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.1963 | + | 25.4199i | 1.18501 | + | 0.832211i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.359747 | 0.0117650 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.3496 | −0.795467 | −0.397734 | − | 0.917501i | \(-0.630203\pi\) | ||||
−0.397734 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.80128 | − | 31.5144i | 0.0914164 | − | 1.02843i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.01758 | + | 13.8869i | 0.261366 | + | 0.452699i | 0.966605 | − | 0.256271i | \(-0.0824938\pi\) |
−0.705239 | + | 0.708969i | \(0.749160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.34381 | + | 2.32755i | −0.0437604 | + | 0.0757953i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.146071 | + | 0.536192i | −0.00475168 | + | 0.0174423i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.6766 | + | 42.7412i | −0.801882 | + | 1.38890i | 0.116493 | + | 0.993191i | \(0.462835\pi\) |
−0.918376 | + | 0.395710i | \(0.870499\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.54309 | − | 7.86887i | −0.147475 | − | 0.255434i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.60156 | − | 18.0175i | 0.0519342 | − | 0.584258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4970 | 1.40900 | 0.704502 | − | 0.709702i | \(-0.251170\pi\) | ||||
0.704502 | + | 0.709702i | \(0.251170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.481699 | −0.0155874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.92503 | − | 6.97015i | −0.320831 | − | 0.225313i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.82031 | − | 6.61697i | −0.123364 | − | 0.213673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.525082 | − | 0.909469i | 0.0169381 | − | 0.0293377i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.0810 | + | 27.3521i | −0.743773 | + | 0.881408i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.36287 | + | 4.09261i | −0.0760635 | + | 0.131746i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.36451 | − | 5.82750i | −0.108195 | − | 0.187400i | 0.806844 | − | 0.590765i | \(-0.201174\pi\) |
−0.915039 | + | 0.403365i | \(0.867841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.79669 | − | 2.22862i | 0.154092 | − | 0.0715937i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9519 | −0.544013 | −0.272007 | − | 0.962295i | \(-0.587687\pi\) | ||||
−0.272007 | + | 0.962295i | \(0.587687\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.40230 | −0.109073 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.6392 | + | 7.73085i | −0.532880 | + | 0.247585i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4250 | + | 33.6451i | 0.621461 | + | 1.07640i | 0.989214 | + | 0.146479i | \(0.0467939\pi\) |
−0.367753 | + | 0.929924i | \(0.619873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.88536 | + | 15.3899i | −0.283977 | + | 0.491863i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.6043 | + | 23.2321i | −0.625917 | + | 0.741743i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.4036 | − | 38.8041i | 0.714563 | − | 1.23766i | −0.248565 | − | 0.968615i | \(-0.579959\pi\) |
0.963128 | − | 0.269044i | \(-0.0867077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.91685 | + | 3.32008i | 0.0610759 | + | 0.105787i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.07760 | − | 4.97046i | −0.225282 | − | 0.158211i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.53144 | −0.112293 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.1824 | 0.672882 | 0.336441 | − | 0.941705i | \(-0.390777\pi\) | ||||
0.336441 | + | 0.941705i | \(0.390777\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.729626 | + | 8.20827i | −0.0231540 | + | 0.260481i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.46696 | + | 4.27291i | 0.0782080 | + | 0.135460i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.90517 | + | 11.9601i | −0.218689 | + | 0.378780i | −0.954407 | − | 0.298507i | \(-0.903511\pi\) |
0.735719 | + | 0.677287i | \(0.236845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.14182 | + | 11.5329i | −0.0994027 | + | 0.364884i |
(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 | 1152.2.i.e.385.5 | ✓ | 10 | |
3.2 | odd | 2 | 3456.2.i.e.1153.3 | 10 | |||
4.3 | odd | 2 | 1152.2.i.h.385.1 | yes | 10 | ||
8.3 | odd | 2 | 1152.2.i.f.385.5 | yes | 10 | ||
8.5 | even | 2 | 1152.2.i.g.385.1 | yes | 10 | ||
9.4 | even | 3 | inner | 1152.2.i.e.769.5 | yes | 10 | |
9.5 | odd | 6 | 3456.2.i.e.2305.3 | 10 | |||
12.11 | even | 2 | 3456.2.i.h.1153.3 | 10 | |||
24.5 | odd | 2 | 3456.2.i.f.1153.3 | 10 | |||
24.11 | even | 2 | 3456.2.i.g.1153.3 | 10 | |||
36.23 | even | 6 | 3456.2.i.h.2305.3 | 10 | |||
36.31 | odd | 6 | 1152.2.i.h.769.1 | yes | 10 | ||
72.5 | odd | 6 | 3456.2.i.f.2305.3 | 10 | |||
72.13 | even | 6 | 1152.2.i.g.769.1 | yes | 10 | ||
72.59 | even | 6 | 3456.2.i.g.2305.3 | 10 | |||
72.67 | odd | 6 | 1152.2.i.f.769.5 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.e.385.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1152.2.i.e.769.5 | yes | 10 | 9.4 | even | 3 | inner | |
1152.2.i.f.385.5 | yes | 10 | 8.3 | odd | 2 | ||
1152.2.i.f.769.5 | yes | 10 | 72.67 | odd | 6 | ||
1152.2.i.g.385.1 | yes | 10 | 8.5 | even | 2 | ||
1152.2.i.g.769.1 | yes | 10 | 72.13 | even | 6 | ||
1152.2.i.h.385.1 | yes | 10 | 4.3 | odd | 2 | ||
1152.2.i.h.769.1 | yes | 10 | 36.31 | odd | 6 | ||
3456.2.i.e.1153.3 | 10 | 3.2 | odd | 2 | |||
3456.2.i.e.2305.3 | 10 | 9.5 | odd | 6 | |||
3456.2.i.f.1153.3 | 10 | 24.5 | odd | 2 | |||
3456.2.i.f.2305.3 | 10 | 72.5 | odd | 6 | |||
3456.2.i.g.1153.3 | 10 | 24.11 | even | 2 | |||
3456.2.i.g.2305.3 | 10 | 72.59 | even | 6 | |||
3456.2.i.h.1153.3 | 10 | 12.11 | even | 2 | |||
3456.2.i.h.2305.3 | 10 | 36.23 | even | 6 |