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 | 385.4 | ||
Root | \(1.72806 + 0.117480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.385 |
Dual form | 1152.2.i.h.769.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.762291 | − | 1.55529i | 0.440109 | − | 0.897945i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.705463 | + | 1.22190i | 0.315493 | + | 0.546449i | 0.979542 | − | 0.201239i | \(-0.0644969\pi\) |
−0.664049 | + | 0.747689i | \(0.731164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.17123 | + | 2.02864i | −0.442685 | + | 0.766753i | −0.997888 | − | 0.0649620i | \(-0.979307\pi\) |
0.555203 | + | 0.831715i | \(0.312641\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83783 | − | 2.37116i | −0.612609 | − | 0.790386i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.30116 | + | 2.25368i | −0.392315 | + | 0.679510i | −0.992754 | − | 0.120161i | \(-0.961659\pi\) |
0.600439 | + | 0.799670i | \(0.294992\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.26229 | + | 2.18635i | 0.350096 | + | 0.606385i | 0.986266 | − | 0.165164i | \(-0.0528155\pi\) |
−0.636170 | + | 0.771549i | \(0.719482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.43817 | − | 0.165755i | 0.629532 | − | 0.0427979i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.94479 | 1.19929 | 0.599644 | − | 0.800267i | \(-0.295309\pi\) | ||||
0.599644 | + | 0.800267i | \(0.295309\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00929 | −0.231546 | −0.115773 | − | 0.993276i | \(-0.536935\pi\) | ||||
−0.115773 | + | 0.993276i | \(0.536935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.26229 | + | 3.36802i | 0.493672 | + | 0.734961i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50663 | + | 2.60955i | 0.314153 | + | 0.544129i | 0.979257 | − | 0.202622i | \(-0.0649461\pi\) |
−0.665104 | + | 0.746751i | \(0.731613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50464 | − | 2.60612i | 0.300929 | − | 0.521224i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.08879 | + | 1.05083i | −0.979337 | + | 0.202233i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0708926 | + | 0.122790i | −0.0131644 | + | 0.0228015i | −0.872533 | − | 0.488556i | \(-0.837524\pi\) |
0.859368 | + | 0.511357i | \(0.170857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.77135 | + | 8.26422i | 0.856960 | + | 1.48430i | 0.874815 | + | 0.484458i | \(0.160983\pi\) |
−0.0178546 | + | 0.999841i | \(0.505684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.51325 | + | 3.74164i | 0.437501 | + | 0.651335i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.30505 | −0.558656 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.00324 | 1.48012 | 0.740062 | − | 0.672539i | \(-0.234796\pi\) | ||||
0.740062 | + | 0.672539i | \(0.234796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.36263 | − | 0.296587i | 0.698580 | − | 0.0474920i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.33084 | + | 7.50123i | 0.676364 | + | 1.17150i | 0.976068 | + | 0.217464i | \(0.0697785\pi\) |
−0.299705 | + | 0.954032i | \(0.596888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.15717 | + | 5.46838i | −0.481464 | + | 0.833920i | −0.999774 | − | 0.0212731i | \(-0.993228\pi\) |
0.518310 | + | 0.855193i | \(0.326561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.60080 | − | 3.91840i | 0.238633 | − | 0.584121i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.24898 | − | 5.62740i | 0.473912 | − | 0.820840i | −0.525642 | − | 0.850706i | \(-0.676175\pi\) |
0.999554 | + | 0.0298661i | \(0.00950808\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.756418 | + | 1.31015i | 0.108060 | + | 0.187165i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.76937 | − | 7.69057i | 0.527817 | − | 1.07689i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.02590 | −0.827721 | −0.413861 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413861 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.67169 | −0.495090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.769369 | + | 1.56973i | −0.101905 | + | 0.207916i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.64142 | − | 9.77123i | −0.734451 | − | 1.27211i | −0.954964 | − | 0.296722i | \(-0.904106\pi\) |
0.220513 | − | 0.975384i | \(-0.429227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45856 | + | 5.99040i | −0.442823 | + | 0.766992i | −0.997898 | − | 0.0648083i | \(-0.979356\pi\) |
0.555075 | + | 0.831801i | \(0.312690\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.96275 | − | 0.951101i | 0.877224 | − | 0.119827i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.78100 | + | 3.08478i | −0.220906 | + | 0.382620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.154962 | + | 0.268402i | 0.0189316 | + | 0.0327905i | 0.875336 | − | 0.483515i | \(-0.160640\pi\) |
−0.856404 | + | 0.516306i | \(0.827307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.20708 | − | 0.353996i | 0.626859 | − | 0.0426161i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.24940 | −0.979023 | −0.489512 | − | 0.871997i | \(-0.662825\pi\) | ||||
−0.489512 | + | 0.871997i | \(0.662825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.78931 | −0.794628 | −0.397314 | − | 0.917683i | \(-0.630058\pi\) | ||||
−0.397314 | + | 0.917683i | \(0.630058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.90628 | − | 4.32677i | −0.335589 | − | 0.499612i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.04793 | − | 5.27917i | −0.347344 | − | 0.601618i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.99530 | − | 8.65211i | 0.562015 | − | 0.973438i | −0.435306 | − | 0.900283i | \(-0.643360\pi\) |
0.997321 | − | 0.0731553i | \(-0.0233069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.24479 | + | 8.71556i | −0.249421 | + | 0.968395i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.47041 | − | 6.01093i | 0.380928 | − | 0.659786i | −0.610268 | − | 0.792195i | \(-0.708938\pi\) |
0.991195 | + | 0.132410i | \(0.0422714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.48837 | + | 6.04203i | 0.378367 | + | 0.655351i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.136932 | + | 0.203860i | 0.0146807 | + | 0.0218561i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8969 | 1.68507 | 0.842535 | − | 0.538642i | \(-0.181062\pi\) | ||||
0.842535 | + | 0.538642i | \(0.181062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.91375 | −0.619930 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.4904 | − | 1.12108i | 1.70997 | − | 0.116250i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.712014 | − | 1.23325i | −0.0730511 | − | 0.126528i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.44449 | − | 12.8942i | 0.755874 | − | 1.30921i | −0.189065 | − | 0.981965i | \(-0.560546\pi\) |
0.944939 | − | 0.327247i | \(-0.106121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.73514 | − | 1.05661i | 0.777411 | − | 0.106193i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.823082 | + | 1.42562i | −0.0818997 | + | 0.141855i | −0.904066 | − | 0.427393i | \(-0.859432\pi\) |
0.822166 | + | 0.569248i | \(0.192765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.40783 | + | 11.0987i | 0.631382 | + | 1.09359i | 0.987269 | + | 0.159057i | \(0.0508454\pi\) |
−0.355887 | + | 0.934529i | \(0.615821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.51941 | + | 5.14030i | −0.245869 | + | 0.501642i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6556 | −1.32014 | −0.660070 | − | 0.751204i | \(-0.729473\pi\) | ||||
−0.660070 | + | 0.751204i | \(0.729473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9953 | −1.24473 | −0.622363 | − | 0.782729i | \(-0.713827\pi\) | ||||
−0.622363 | + | 0.782729i | \(0.713827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.86309 | − | 14.0026i | 0.651415 | − | 1.32907i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.75804 | − | 6.50912i | −0.353527 | − | 0.612326i | 0.633338 | − | 0.773875i | \(-0.281684\pi\) |
−0.986865 | + | 0.161549i | \(0.948351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12574 | + | 3.68189i | −0.198226 | + | 0.343338i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.86432 | − | 7.01123i | 0.264806 | − | 0.648188i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.79151 | + | 10.0312i | −0.530907 | + | 0.919558i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.11395 | + | 3.66148i | 0.192178 | + | 0.332861i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.9679 | − | 1.01757i | 1.34961 | − | 0.0917514i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3005 | 1.01075 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.09832 | 0.186196 | 0.0930981 | − | 0.995657i | \(-0.470323\pi\) | ||||
0.0930981 | + | 0.995657i | \(0.470323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.09821 | + | 9.07879i | 0.536917 | + | 0.799343i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00428 | − | 6.93562i | −0.349856 | − | 0.605968i | 0.636368 | − | 0.771386i | \(-0.280436\pi\) |
−0.986224 | + | 0.165418i | \(0.947103\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.18211 | − | 2.04748i | 0.102502 | − | 0.177539i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.87396 | − | 5.47666i | −0.419484 | − | 0.471355i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.17445 | − | 2.03420i | 0.100340 | − | 0.173793i | −0.811485 | − | 0.584373i | \(-0.801340\pi\) |
0.911825 | + | 0.410580i | \(0.134674\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.62654 | + | 9.74546i | 0.477237 | + | 0.826599i | 0.999660 | − | 0.0260876i | \(-0.00830490\pi\) |
−0.522422 | + | 0.852687i | \(0.674972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.27554 | − | 9.34280i | −0.528496 | − | 0.786806i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.56978 | −0.549392 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.200049 | −0.0166131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.61427 | − | 0.177728i | 0.215622 | − | 0.0146587i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9924 | − | 20.7715i | −0.982458 | − | 1.70167i | −0.652729 | − | 0.757591i | \(-0.726376\pi\) |
−0.329729 | − | 0.944076i | \(-0.606957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.56507 | + | 11.3710i | −0.534258 | + | 0.925362i | 0.464941 | + | 0.885342i | \(0.346076\pi\) |
−0.999199 | + | 0.0400204i | \(0.987258\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.08767 | − | 11.7249i | −0.734695 | − | 0.947901i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.73203 | + | 11.6602i | −0.540729 | + | 0.936571i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6217 | + | 20.1293i | 0.927511 | + | 1.60650i | 0.787473 | + | 0.616350i | \(0.211389\pi\) |
0.140038 | + | 0.990146i | \(0.455278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.59349 | + | 9.37200i | −0.364287 | + | 0.743248i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.05845 | −0.556284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5825 | 1.76879 | 0.884397 | − | 0.466735i | \(-0.154570\pi\) | ||||
0.884397 | + | 0.466735i | \(0.154570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.79889 | + | 5.71052i | −0.217894 | + | 0.444564i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4260 | − | 21.5224i | −0.961549 | − | 1.66545i | −0.718614 | − | 0.695409i | \(-0.755223\pi\) |
−0.242935 | − | 0.970043i | \(-0.578110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.31325 | − | 5.73871i | 0.254865 | − | 0.441439i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.85489 | + | 2.39318i | 0.141847 | + | 0.183011i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.98389 | + | 6.90030i | −0.302890 | + | 0.524620i | −0.976789 | − | 0.214203i | \(-0.931285\pi\) |
0.673900 | + | 0.738823i | \(0.264618\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.52458 | + | 6.10475i | 0.266433 | + | 0.461476i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.4975 | + | 1.32551i | −1.46552 | + | 0.0996312i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.70760 | −0.277119 | −0.138560 | − | 0.990354i | \(-0.544247\pi\) | ||||
−0.138560 | + | 0.990354i | \(0.544247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0683 | −0.971362 | −0.485681 | − | 0.874136i | \(-0.661428\pi\) | ||||
−0.485681 | + | 0.874136i | \(0.661428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.68036 | + | 9.94547i | 0.493826 | + | 0.735191i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.35146 | + | 11.0010i | 0.466968 | + | 0.808813i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43398 | + | 11.1440i | −0.470499 | + | 0.814928i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.82840 | − | 11.5541i | 0.278475 | − | 0.840436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.157984 | − | 0.273636i | 0.0114313 | − | 0.0197996i | −0.860253 | − | 0.509867i | \(-0.829695\pi\) |
0.871684 | + | 0.490068i | \(0.163028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0237 | − | 17.3616i | −0.721522 | − | 1.24971i | −0.960390 | − | 0.278661i | \(-0.910109\pi\) |
0.238867 | − | 0.971052i | \(-0.423224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.44008 | + | 5.12146i | 0.246349 | + | 0.366755i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.5586 | −1.67848 | −0.839240 | − | 0.543761i | \(-0.817000\pi\) | ||||
−0.839240 | + | 0.543761i | \(0.817000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.249396 | 0.0176792 | 0.00883960 | − | 0.999961i | \(-0.497186\pi\) | ||||
0.00883960 | + | 0.999961i | \(0.497186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.535568 | − | 0.0364098i | 0.0377760 | − | 0.00256815i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.166064 | − | 0.287631i | −0.0116554 | − | 0.0201877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.11050 | + | 10.5837i | −0.426776 | + | 0.739197i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.41875 | − | 8.36835i | 0.237619 | − | 0.581641i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.31325 | − | 2.27461i | 0.0908391 | − | 0.157338i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17490 | + | 2.03499i | 0.0808834 | + | 0.140094i | 0.903630 | − | 0.428315i | \(-0.140893\pi\) |
−0.822746 | + | 0.568409i | \(0.807559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.28844 | + | 12.8302i | −0.430877 | + | 0.879108i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.90907 | −0.607593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.3535 | −1.51745 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.17542 | + | 10.5593i | −0.349723 | + | 0.713532i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24177 | + | 10.8111i | 0.419867 | + | 0.727230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.71439 | + | 8.16556i | −0.315699 | + | 0.546806i | −0.979586 | − | 0.201027i | \(-0.935572\pi\) |
0.663887 | + | 0.747833i | \(0.268906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.94479 | + | 1.22185i | −0.596320 | + | 0.0814563i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0231851 | − | 0.0401577i | 0.00153885 | − | 0.00266536i | −0.865255 | − | 0.501332i | \(-0.832844\pi\) |
0.866794 | + | 0.498667i | \(0.166177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.03468 | + | 6.98827i | 0.266619 | + | 0.461798i | 0.967987 | − | 0.251002i | \(-0.0807600\pi\) |
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.5340 | + | 0.716141i | −0.693089 | + | 0.0471186i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.99336 | 0.261614 | 0.130807 | − | 0.991408i | \(-0.458243\pi\) | ||||
0.130807 | + | 0.991408i | \(0.458243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.16814 | 0.598063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.64863 | − | 14.3645i | −0.626746 | − | 0.933076i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.84910 | − | 3.20273i | −0.119608 | − | 0.207167i | 0.800004 | − | 0.599994i | \(-0.204830\pi\) |
−0.919612 | + | 0.392827i | \(0.871497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0879 | − | 22.6689i | 0.843066 | − | 1.46023i | −0.0442246 | − | 0.999022i | \(-0.514082\pi\) |
0.887290 | − | 0.461211i | \(-0.152585\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.8440 | + | 10.1351i | 0.759793 | + | 0.650165i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.06725 | + | 1.84853i | −0.0681841 | + | 0.118098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.27401 | − | 2.20665i | −0.0810635 | − | 0.140406i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.70326 | − | 9.97956i | −0.424802 | − | 0.632429i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7393 | 1.24593 | 0.622967 | − | 0.782248i | \(-0.285927\pi\) | ||||
0.622967 | + | 0.782248i | \(0.285927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.84146 | −0.492988 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0562 | − | 0.819626i | 0.754991 | − | 0.0513270i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.53591 | − | 6.12438i | −0.220564 | − | 0.382028i | 0.734415 | − | 0.678700i | \(-0.237456\pi\) |
−0.954979 | + | 0.296672i | \(0.904123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5449 | + | 18.2643i | −0.655229 | + | 1.13489i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.421442 | − | 0.0575684i | 0.0260866 | − | 0.00356339i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.03211 | − | 6.98383i | 0.248631 | − | 0.430641i | −0.714515 | − | 0.699620i | \(-0.753353\pi\) |
0.963146 | + | 0.268979i | \(0.0866861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.25105 | − | 7.36304i | −0.261140 | − | 0.452308i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1181 | − | 24.7242i | 0.741614 | − | 1.51310i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.76619 | −0.534484 | −0.267242 | − | 0.963629i | \(-0.586112\pi\) | ||||
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.7606 | −1.68634 | −0.843168 | − | 0.537650i | \(-0.819312\pi\) | ||||
−0.843168 | + | 0.537650i | \(0.819312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.50800 | + | 9.19758i | −0.272836 | + | 0.556663i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.91557 | + | 6.78197i | 0.236118 | + | 0.408968i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7727 | − | 23.8551i | 0.827524 | − | 1.43331i | −0.0724506 | − | 0.997372i | \(-0.523082\pi\) |
0.899975 | − | 0.435942i | \(-0.143585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.8269 | − | 26.5018i | 0.648188 | − | 1.58662i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.24109 | − | 5.61373i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.32863 | − | 5.76536i | −0.197866 | − | 0.342715i | 0.749970 | − | 0.661472i | \(-0.230068\pi\) |
−0.947836 | + | 0.318757i | \(0.896735\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.46081 | + | 0.167295i | −0.145766 | + | 0.00990968i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2897 | −1.19766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.45099 | 0.438293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.3794 | − | 21.4075i | −0.842933 | − | 1.25493i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.61375 | − | 4.52714i | −0.152697 | − | 0.264479i | 0.779521 | − | 0.626376i | \(-0.215462\pi\) |
−0.932218 | + | 0.361897i | \(0.882129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.95963 | − | 13.7865i | 0.463428 | − | 0.802681i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.25310 | − | 12.8358i | 0.246790 | − | 0.744808i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.80360 | + | 6.58802i | −0.219968 | + | 0.380995i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.39557 | − | 12.8095i | −0.426274 | − | 0.738328i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.58982 | + | 2.36686i | 0.0913327 | + | 0.135973i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.75955 | −0.558830 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8311 | 0.903531 | 0.451765 | − | 0.892137i | \(-0.350794\pi\) | ||||
0.451765 | + | 0.892137i | \(0.350794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.1463 | − | 1.50558i | 1.25986 | − | 0.0856496i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.40298 | − | 2.43003i | −0.0795557 | − | 0.137794i | 0.823503 | − | 0.567312i | \(-0.192017\pi\) |
−0.903058 | + | 0.429518i | \(0.858683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.35704 | + | 12.7428i | −0.415845 | + | 0.720264i | −0.995517 | − | 0.0945858i | \(-0.969847\pi\) |
0.579672 | + | 0.814850i | \(0.303181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.07411 | + | 7.83680i | 0.342237 | + | 0.441554i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.668345 | − | 1.15761i | 0.0375380 | − | 0.0650178i | −0.846646 | − | 0.532156i | \(-0.821382\pi\) |
0.884184 | + | 0.467139i | \(0.154715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.184486 | − | 0.319538i | −0.0103292 | − | 0.0178907i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4096 | + | 21.2384i | −0.581005 | + | 1.18541i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.99071 | −0.277691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.59719 | 0.421416 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.90620 | + | 20.2114i | −0.547814 | + | 1.11769i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.61063 | + | 13.1820i | 0.419588 | + | 0.726747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.69612 | − | 4.66981i | 0.148192 | − | 0.256676i | −0.782367 | − | 0.622817i | \(-0.785988\pi\) |
0.930559 | + | 0.366141i | \(0.119321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.5464 | − | 21.3481i | −0.906737 | − | 1.16987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.218640 | + | 0.378695i | −0.0119456 | + | 0.0206903i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8198 | + | 20.4725i | 0.643866 | + | 1.11521i | 0.984562 | + | 0.175035i | \(0.0560039\pi\) |
−0.340696 | + | 0.940173i | \(0.610663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9883 | + | 0.882988i | −0.705425 | + | 0.0479573i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.8332 | −1.34479 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9411 | −1.07672 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.10595 | + | 6.11280i | 0.221057 | + | 0.329102i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.649676 | − | 1.12527i | −0.0348764 | − | 0.0604077i | 0.848060 | − | 0.529900i | \(-0.177770\pi\) |
−0.882937 | + | 0.469492i | \(0.844437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.27720 | − | 10.8724i | 0.336011 | − | 0.581988i | −0.647668 | − | 0.761923i | \(-0.724255\pi\) |
0.983678 | + | 0.179935i | \(0.0575888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.72102 | − | 9.79942i | −0.465493 | − | 0.523054i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.71760 | + | 13.3673i | −0.410766 | + | 0.711468i | −0.994974 | − | 0.100136i | \(-0.968072\pi\) |
0.584207 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.81965 | − | 10.0799i | −0.308875 | − | 0.534987i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.1866 | + | 16.6541i | 0.592056 | + | 0.881431i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.8687 | 1.52363 | 0.761817 | − | 0.647792i | \(-0.224308\pi\) | ||||
0.761817 | + | 0.647792i | \(0.224308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9813 | −0.946386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.30609 | − | 0.496694i | 0.383470 | − | 0.0260697i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.78961 | − | 8.29584i | −0.250699 | − | 0.434224i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.959507 | − | 1.66192i | 0.0500859 | − | 0.0867513i | −0.839896 | − | 0.542748i | \(-0.817384\pi\) |
0.889981 | + | 0.455997i | \(0.150717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.82729 | − | 24.0551i | 0.511588 | − | 1.25226i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.05775 | − | 12.2244i | 0.366420 | − | 0.634658i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.71108 | + | 8.15984i | 0.243931 | + | 0.422500i | 0.961830 | − | 0.273646i | \(-0.0882297\pi\) |
−0.717900 | + | 0.696147i | \(0.754896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.61427 | − | 17.5755i | 0.444839 | − | 0.907596i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.357948 | −0.0184353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1191 | 0.827984 | 0.413992 | − | 0.910281i | \(-0.364134\pi\) | ||||
0.413992 | + | 0.910281i | \(0.364134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.59953 | − | 3.26349i | 0.0819465 | − | 0.167194i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.35380 | + | 7.54100i | 0.222469 | + | 0.385327i | 0.955557 | − | 0.294806i | \(-0.0952552\pi\) |
−0.733088 | + | 0.680133i | \(0.761922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.30041 | − | 7.44853i | 0.219169 | − | 0.379612i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.7687 | − | 2.56378i | 0.954068 | − | 0.130324i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1015 | − | 17.4963i | 0.512167 | − | 0.887099i | −0.487734 | − | 0.872993i | \(-0.662176\pi\) |
0.999900 | − | 0.0141065i | \(-0.00449040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.44995 | + | 12.9037i | 0.376760 | + | 0.652568i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8393 | + | 0.940845i | −0.698100 | + | 0.0474593i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0960 | 0.709246 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.3319 | −1.77326 | −0.886628 | − | 0.462483i | \(-0.846959\pi\) | ||||
−0.886628 | + | 0.462483i | \(0.846959\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.28330 | − | 3.39929i | −0.114308 | − | 0.170178i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.03813 | + | 8.72630i | 0.251592 | + | 0.435771i | 0.963964 | − | 0.266031i | \(-0.0857125\pi\) |
−0.712372 | + | 0.701802i | \(0.752379\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0457 | + | 20.8637i | −0.600037 | + | 1.03930i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.2331 | + | 3.40560i | −0.607870 | + | 0.169226i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7147 | + | 20.2904i | −0.580675 | + | 1.00576i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.08466 | + | 3.61073i | 0.103080 | + | 0.178539i | 0.912952 | − | 0.408067i | \(-0.133797\pi\) |
−0.809872 | + | 0.586606i | \(0.800464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.26849 | − | 3.37725i | −0.111897 | − | 0.166588i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.4297 | 1.30052 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.79300 | 0.480719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.4460 | − | 1.32201i | 0.952276 | − | 0.0647392i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.13944 | + | 14.0979i | 0.397638 | + | 0.688729i | 0.993434 | − | 0.114407i | \(-0.0364968\pi\) |
−0.595796 | + | 0.803136i | \(0.703163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.90585 | − | 11.9613i | 0.336570 | − | 0.582957i | −0.647215 | − | 0.762308i | \(-0.724066\pi\) |
0.983785 | + | 0.179351i | \(0.0573996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.3145 | + | 2.63833i | −0.939103 | + | 0.128280i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.44015 | − | 12.8867i | 0.360900 | − | 0.625098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.10157 | − | 14.0323i | −0.392063 | − | 0.679072i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.00808 | + | 10.2179i | −0.241792 | + | 0.493324i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2716 | −0.639268 | −0.319634 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319634 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.32495 | −0.207844 | −0.103922 | − | 0.994585i | \(-0.533139\pi\) | ||||
−0.103922 | + | 0.994585i | \(0.533139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.152495 | + | 0.311133i | −0.00731158 | + | 0.0149177i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.52062 | − | 2.63379i | −0.0727410 | − | 0.125991i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.69938 | − | 16.7998i | 0.462926 | − | 0.801812i | −0.536179 | − | 0.844104i | \(-0.680133\pi\) |
0.999105 | + | 0.0422926i | \(0.0134662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.71642 | − | 4.20142i | 0.0817343 | − | 0.200068i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1280 | − | 26.2025i | 0.718754 | − | 1.24492i | −0.242740 | − | 0.970091i | \(-0.578046\pi\) |
0.961494 | − | 0.274827i | \(-0.0886204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2147 | + | 19.4244i | 0.531627 | + | 0.920806i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −41.4473 | + | 2.81774i | −1.96039 | + | 0.133274i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.49691 | −0.400994 | −0.200497 | − | 0.979694i | \(-0.564256\pi\) | ||||
−0.200497 | + | 0.979694i | \(0.564256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5405 | −1.06139 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.6807 | + | 18.8786i | 0.595792 | + | 0.886994i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.17194 | − | 7.22601i | −0.195583 | − | 0.338760i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.8223 | + | 27.4050i | −0.740136 | + | 1.28195i | 0.212297 | + | 0.977205i | \(0.431906\pi\) |
−0.952433 | + | 0.304748i | \(0.901428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.1630 | + | 5.19615i | −1.17451 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.62685 | − | 16.6742i | 0.448367 | − | 0.776594i | −0.549913 | − | 0.835222i | \(-0.685339\pi\) |
0.998280 | + | 0.0586276i | \(0.0186725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.46981 | + | 12.9381i | 0.347151 | + | 0.601284i | 0.985742 | − | 0.168263i | \(-0.0538157\pi\) |
−0.638591 | + | 0.769546i | \(0.720482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.0032 | + | 19.3587i | 0.603009 | + | 0.897738i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.9590 | −1.84908 | −0.924540 | − | 0.381084i | \(-0.875551\pi\) | ||||
−0.924540 | + | 0.381084i | \(0.875551\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.725987 | −0.0335230 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.1660 | − | 2.73063i | 1.85075 | − | 0.125821i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.21598 | − | 14.2305i | −0.377771 | − | 0.654319i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.51862 | + | 2.63032i | −0.0696789 | + | 0.120687i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0746 | + | 14.2884i | 0.507069 | + | 0.654220i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.1993 | − | 28.0581i | 0.740167 | − | 1.28201i | −0.212252 | − | 0.977215i | \(-0.568080\pi\) |
0.952419 | − | 0.304792i | \(-0.0985869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3647 | + | 19.6843i | 0.518186 | + | 0.897525i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.38059 | + | 10.9779i | −0.244825 | + | 0.499512i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0073 | 0.953891 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.8763 | 1.26320 | 0.631598 | − | 0.775296i | \(-0.282399\pi\) | ||||
0.631598 | + | 0.775296i | \(0.282399\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.2144 | − | 35.1222i | 0.778462 | − | 1.58828i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.12126 | − | 14.0664i | −0.366507 | − | 0.634809i | 0.622510 | − | 0.782612i | \(-0.286113\pi\) |
−0.989017 | + | 0.147803i | \(0.952780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.350549 | + | 0.607170i | −0.0157880 | + | 0.0273455i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.74793 | + | 8.70616i | 0.303297 | + | 0.391313i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.66198 | − | 16.7350i | 0.433399 | − | 0.750669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1826 | − | 31.4932i | −0.813966 | − | 1.40983i | −0.910068 | − | 0.414459i | \(-0.863971\pi\) |
0.0961021 | − | 0.995371i | \(-0.469362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.9456 | + | 2.91960i | −1.91867 | + | 0.130438i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.2509 | 1.92846 | 0.964231 | − | 0.265063i | \(-0.0853929\pi\) | ||||
0.964231 | + | 0.265063i | \(0.0853929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.32262 | −0.103355 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.39968 | − | 9.52761i | −0.284220 | − | 0.423136i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.2885 | + | 36.8728i | 0.943597 | + | 1.63436i | 0.758536 | + | 0.651632i | \(0.225915\pi\) |
0.185062 | + | 0.982727i | \(0.440751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.95187 | − | 13.7730i | 0.351770 | − | 0.609284i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.13604 | − | 1.06059i | 0.226762 | − | 0.0468263i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.04098 | + | 15.6594i | −0.398393 | + | 0.690037i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.45489 | + | 14.6443i | 0.371846 | + | 0.644056i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.69506 | + | 11.4561i | 0.337776 | + | 0.502868i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0544 | 0.922408 | 0.461204 | − | 0.887294i | \(-0.347418\pi\) | ||||
0.461204 | + | 0.887294i | \(0.347418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.0092 | 0.918667 | 0.459333 | − | 0.888264i | \(-0.348088\pi\) | ||||
0.459333 | + | 0.888264i | \(0.348088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1814 | − | 0.828134i | 0.531639 | − | 0.0361427i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.5934 | + | 40.8649i | 1.02774 | + | 1.78010i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.96016 | − | 12.0554i | 0.302616 | − | 0.524146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8012 | + | 31.3345i | −0.555524 | + | 1.35980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9336 | + | 18.9375i | −0.473585 | + | 0.820273i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.63355 | − | 16.6858i | −0.416495 | − | 0.721390i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.82627 | + | 5.76638i | −0.121962 | + | 0.248837i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.93689 | −0.169574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3375 | 0.530429 | 0.265215 | − | 0.964189i | \(-0.414557\pi\) | ||||
0.265215 | + | 0.964189i | \(0.414557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.96187 | + | 20.3250i | −0.427505 | + | 0.872229i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.16772 | − | 15.8790i | −0.392702 | − | 0.680179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.461070 | − | 0.798596i | 0.0197139 | − | 0.0341455i | −0.856000 | − | 0.516976i | \(-0.827058\pi\) |
0.875714 | + | 0.482830i | \(0.160391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.5604 | − | 2.80852i | 0.877498 | − | 0.119865i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0715510 | − | 0.123930i | 0.00304817 | − | 0.00527959i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7013 | + | 20.2673i | 0.497591 | + | 0.861853i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.9514 | − | 1.49234i | 0.931786 | − | 0.0633461i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1352 | −0.810786 | −0.405393 | − | 0.914142i | \(-0.632865\pi\) | ||||
−0.405393 | + | 0.914142i | \(0.632865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.9411 | −0.674235 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.4275 | + | 18.5016i | 0.524690 | + | 0.781139i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9309 | + | 29.3252i | 0.713552 | + | 1.23591i | 0.963515 | + | 0.267653i | \(0.0862482\pi\) |
−0.249963 | + | 0.968255i | \(0.580419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.30232 | − | 9.18388i | 0.223070 | − | 0.386369i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.0515 | − | 14.7618i | −0.632105 | − | 0.619938i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1745 | + | 24.5509i | −0.594225 | + | 1.02923i | 0.399431 | + | 0.916763i | \(0.369208\pi\) |
−0.993656 | + | 0.112465i | \(0.964125\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9901 | − | 20.7674i | −0.501769 | − | 0.869089i | −0.999998 | − | 0.00204345i | \(-0.999350\pi\) |
0.498229 | − | 0.867045i | \(-0.333984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.305153 | − | 0.454300i | −0.0127479 | − | 0.0189787i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.06773 | 0.378151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2508 | 0.426746 | 0.213373 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213373 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.6432 | + | 2.35517i | −1.43972 | + | 0.0978774i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.12934 | + | 14.0804i | 0.337262 | + | 0.584155i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.84068 | − | 13.5805i | 0.324728 | − | 0.562445i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.5877 | − | 1.44626i | 0.437746 | − | 0.0597955i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.15393 | + | 3.73071i | −0.0889021 | + | 0.153983i | −0.907047 | − | 0.421029i | \(-0.861669\pi\) |
0.818145 | + | 0.575012i | \(0.195002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.81566 | − | 8.34097i | −0.198426 | − | 0.343684i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.9585 | + | 36.6403i | −0.738714 | + | 1.50718i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.4046 | −1.12537 | −0.562686 | − | 0.826670i | \(-0.690232\pi\) | ||||
−0.562686 | + | 0.826670i | \(0.690232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.3428 | −0.669990 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.190112 | − | 0.387882i | 0.00778077 | − | 0.0158749i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.5711 | + | 23.5058i | 0.554500 | + | 0.960423i | 0.997942 | + | 0.0641195i | \(0.0204239\pi\) |
−0.443442 | + | 0.896303i | \(0.646243\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7512 | − | 20.3537i | 0.479341 | − | 0.830244i | −0.520378 | − | 0.853936i | \(-0.674209\pi\) |
0.999719 | + | 0.0236923i | \(0.00754221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.351631 | − | 0.860716i | 0.0143195 | − | 0.0350510i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.98263 | + | 5.16607i | −0.121261 | + | 0.210031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.69717 | + | 4.67164i | 0.109475 | + | 0.189616i | 0.915558 | − | 0.402187i | \(-0.131750\pi\) |
−0.806083 | + | 0.591803i | \(0.798416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.573937 | + | 0.0390183i | −0.0232571 | + | 0.00158110i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.4046 | 0.663660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.92486 | −0.239303 | −0.119651 | − | 0.992816i | \(-0.538178\pi\) | ||||
−0.119651 | + | 0.992816i | \(0.538178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.8027 | + | 17.5714i | 0.475930 | + | 0.708548i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.12456 | − | 10.6081i | −0.246566 | − | 0.427064i | 0.716005 | − | 0.698095i | \(-0.245969\pi\) |
−0.962571 | + | 0.271031i | \(0.912635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.656697 | + | 1.13743i | −0.0263949 | + | 0.0457173i | −0.878921 | − | 0.476967i | \(-0.841736\pi\) |
0.852526 | + | 0.522684i | \(0.175069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.4091 | − | 11.6962i | −0.417703 | − | 0.469354i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6190 | + | 32.2491i | −0.745955 | + | 1.29203i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.448881 | + | 0.777485i | 0.0179553 | + | 0.0310994i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.53659 | − | 3.77638i | −0.101302 | − | 0.150814i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.5192 | 1.77510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7173 | −1.14322 | −0.571608 | − | 0.820527i | \(-0.693680\pi\) | ||||
−0.571608 | + | 0.820527i | \(0.693680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.06060 | − | 0.276054i | 0.161394 | − | 0.0109722i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.48029 | + | 2.56394i | 0.0587435 | + | 0.101747i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.90964 | + | 3.30759i | −0.0756626 | + | 0.131052i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1610 | + | 19.5606i | 0.599758 | + | 0.773806i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.67893 | − | 16.7644i | 0.382295 | − | 0.662154i | −0.609095 | − | 0.793097i | \(-0.708467\pi\) |
0.991390 | + | 0.130943i | \(0.0418006\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.415416 | + | 0.719521i | 0.0163824 | + | 0.0283751i | 0.874100 | − | 0.485745i | \(-0.161452\pi\) |
−0.857718 | + | 0.514120i | \(0.828118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.79130 | + | 13.8561i | −0.267407 | + | 0.545585i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.1290 | 0.398211 | 0.199106 | − | 0.979978i | \(-0.436196\pi\) | ||||
0.199106 | + | 0.979978i | \(0.436196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.3616 | 1.15254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.0399 | + | 34.7661i | −0.667845 | + | 1.36259i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0565 | + | 36.4709i | 0.824004 | + | 1.42722i | 0.902678 | + | 0.430317i | \(0.141598\pi\) |
−0.0786734 | + | 0.996900i | \(0.525068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.64975 | − | 9.78565i | 0.220754 | − | 0.382357i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.4776 | + | 16.0985i | 0.486796 | + | 0.628063i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.0094 | − | 22.5329i | 0.506774 | − | 0.877759i | −0.493195 | − | 0.869919i | \(-0.664171\pi\) |
0.999969 | − | 0.00784021i | \(-0.00249564\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6544 | − | 25.3822i | −0.569990 | − | 0.987252i | −0.996566 | − | 0.0828004i | \(-0.973614\pi\) |
0.426576 | − | 0.904452i | \(-0.359720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.5723 | − | 1.46656i | 0.837799 | − | 0.0569566i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.33574 | 0.129355 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.427235 | −0.0165426 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.10605 | + | 13.5568i | 0.352060 | + | 0.524134i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.00029 | − | 15.5890i | −0.347453 | − | 0.601805i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.72976 | + | 13.3883i | −0.297960 | + | 0.516082i | −0.975669 | − | 0.219248i | \(-0.929640\pi\) |
0.677709 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.91821 | + | 14.8431i | −0.189302 | + | 0.571312i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.02467 | + | 5.23889i | −0.116248 | + | 0.201347i | −0.918278 | − | 0.395937i | \(-0.870420\pi\) |
0.802030 | + | 0.597284i | \(0.203753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4385 | + | 30.2044i | 0.669228 | + | 1.15914i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0447830 | − | 0.0666713i | −0.00171609 | − | 0.00255485i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.1518 | 0.962406 | 0.481203 | − | 0.876609i | \(-0.340200\pi\) | ||||
0.481203 | + | 0.876609i | \(0.340200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.31411 | 0.126626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.9444 | − | 0.947988i | 0.532011 | − | 0.0361680i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.60644 | − | 13.1747i | −0.289782 | − | 0.501918i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.8943 | − | 37.9221i | 0.832899 | − | 1.44262i | −0.0628298 | − | 0.998024i | \(-0.520013\pi\) |
0.895729 | − | 0.444600i | \(-0.146654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.91619 | + | 16.9293i | −0.262724 | + | 0.643092i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.93864 | + | 13.7501i | −0.301130 | + | 0.521572i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.4151 | + | 37.0921i | 0.811155 | + | 1.40496i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.04410 | − | 6.21081i | 0.115138 | − | 0.234914i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4594 | 1.41482 | 0.707412 | − | 0.706802i | \(-0.249863\pi\) | ||||
0.707412 | + | 0.706802i | \(0.249863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.08685 | −0.342717 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.98879 | − | 14.2591i | 0.263213 | − | 0.537028i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.92804 | − | 3.33947i | −0.0725116 | − | 0.125594i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.4907 | − | 28.5627i | 0.619321 | − | 1.07269i | −0.370289 | − | 0.928916i | \(-0.620741\pi\) |
0.989610 | − | 0.143778i | \(-0.0459252\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.6960 | + | 4.05643i | −1.11369 | + | 0.152128i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.3773 | + | 24.9022i | −0.538433 | + | 0.932594i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.63474 | − | 8.02760i | −0.173329 | − | 0.300215i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.39070 | + | 0.434463i | −0.238665 | + | 0.0162253i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0397 | 0.449006 | 0.224503 | − | 0.974473i | \(-0.427924\pi\) | ||||
0.224503 | + | 0.974473i | \(0.427924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0203 | −1.11801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.2798 | − | 37.6357i | −0.940168 | − | 1.39969i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.213336 | + | 0.369509i | 0.00792311 | + | 0.0137232i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6359 | − | 27.0822i | 0.579905 | − | 1.00443i | −0.415585 | − | 0.909555i | \(-0.636423\pi\) |
0.995490 | − | 0.0948705i | \(-0.0302437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.7915 | − | 10.6949i | 0.918204 | − | 0.396109i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.6116 | + | 27.0400i | −0.577414 | + | 1.00011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.40335 | − | 4.16273i | −0.0887699 | − | 0.153754i | 0.818222 | − | 0.574903i | \(-0.194960\pi\) |
−0.906991 | + | 0.421149i | \(0.861627\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.06144 | + | 3.06900i | 0.0760374 | + | 0.113202i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.806522 | −0.0297086 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.79606 | −0.286783 | −0.143391 | − | 0.989666i | \(-0.545801\pi\) | ||||
−0.143391 | + | 0.989666i | \(0.545801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.40315 | + | 0.299342i | −0.161754 | + | 0.0109966i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.5475 | − | 40.7855i | −0.863875 | − | 1.49628i | −0.868160 | − | 0.496285i | \(-0.834697\pi\) |
0.00428429 | − | 0.999991i | \(-0.498636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.9204 | − | 29.3071i | 0.619917 | − | 1.07373i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.6309 | + | 2.81815i | −0.754845 | + | 0.103111i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9940 | − | 27.7023i | 0.584406 | − | 1.01222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.25631 | − | 10.8362i | −0.228296 | − | 0.395420i | 0.729007 | − | 0.684506i | \(-0.239982\pi\) |
−0.957303 | + | 0.289086i | \(0.906649\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0471 | − | 30.7002i | 0.548346 | − | 1.11878i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.5257 | −0.674218 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0507 | 0.474337 | 0.237168 | − | 0.971469i | \(-0.423781\pi\) | ||||
0.237168 | + | 0.971469i | \(0.423781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.97747 | + | 12.1957i | −0.216968 | + | 0.442676i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5379 | + | 19.9842i | 0.418249 | + | 0.724428i | 0.995763 | − | 0.0919523i | \(-0.0293107\pi\) |
−0.577515 | + | 0.816380i | \(0.695977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2206 | − | 26.3628i | 0.551021 | − | 0.954397i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.91560 | − | 19.3757i | 0.286189 | − | 0.700530i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.2422 | − | 24.6683i | 0.514257 | − | 0.890720i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7111 | + | 28.9444i | 0.602617 | + | 1.04376i | 0.992423 | + | 0.122866i | \(0.0392085\pi\) |
−0.389807 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.2205 | + | 0.830797i | −0.440112 | + | 0.0299204i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.28916 | −0.334108 | −0.167054 | − | 0.985948i | \(-0.553425\pi\) | ||||
−0.167054 | + | 0.985948i | \(0.553425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.7167 | 1.03154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.3679 | + | 30.3231i | 0.730696 | + | 1.08783i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.37106 | − | 7.57089i | −0.156609 | − | 0.271255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7338 | − | 18.5915i | 0.384086 | − | 0.665256i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.231726 | − | 0.699347i | 0.00828122 | − | 0.0249926i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.3973 | + | 28.4010i | −0.585246 | + | 1.01368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.77105 | + | 8.26370i | 0.170070 | + | 0.294569i | 0.938444 | − | 0.345431i | \(-0.112267\pi\) |
−0.768374 | + | 0.640001i | \(0.778934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.78820 | − | 11.5948i | −0.277267 | − | 0.412786i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6062 | 0.626004 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.4628 | −0.620123 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.6922 | + | 0.998826i | −0.521077 | + | 0.0354247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3400 | − | 19.6415i | −0.401685 | − | 0.695738i | 0.592245 | − | 0.805758i | \(-0.298242\pi\) |
−0.993929 | + | 0.110020i | \(0.964909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0655 | − | 27.8263i | 0.568358 | − | 0.984424i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.2158 | − | 37.6941i | −1.03229 | − | 1.33186i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.83399 | − | 15.3009i | 0.311745 | − | 0.539958i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.97948 | − | 8.62471i | −0.175503 | − | 0.303981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.68238 | + | 13.6339i | −0.235231 | + | 0.479937i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.1636 | −1.13081 | −0.565405 | − | 0.824813i | \(-0.691280\pi\) | ||||
−0.565405 | + | 0.824813i | \(0.691280\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.49576 | 0.122753 | 0.0613764 | − | 0.998115i | \(-0.480451\pi\) | ||||
0.0613764 | + | 0.998115i | \(0.480451\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1616 | + | 43.1757i | −0.742171 | + | 1.51424i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9311 | + | 27.5935i | 0.558042 | + | 0.966557i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.18649 | − | 5.51916i | 0.111481 | − | 0.193091i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.8685 | + | 14.0225i | 0.379775 | + | 0.489984i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.6693 | + | 21.9438i | −0.442160 | + | 0.765844i | −0.997850 | − | 0.0655463i | \(-0.979121\pi\) |
0.555690 | + | 0.831390i | \(0.312454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.8599 | − | 43.0585i | −0.866560 | − | 1.50093i | −0.865490 | − | 0.500926i | \(-0.832993\pi\) |
−0.00107015 | − | 0.999999i | \(-0.500341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5327 | − | 0.920001i | 0.471148 | − | 0.0320303i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.4868 | 1.51218 | 0.756092 | − | 0.654466i | \(-0.227106\pi\) | ||||
0.756092 | + | 0.654466i | \(0.227106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.62272 | −0.0563594 | −0.0281797 | − | 0.999603i | \(-0.508971\pi\) | ||||
−0.0281797 | + | 0.999603i | \(0.508971\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6027 | − | 39.6051i | −0.922836 | − | 1.37388i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.74033 | + | 6.47844i | 0.129595 | + | 0.224465i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.5321 | − | 30.3665i | 0.606724 | − | 1.05088i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.9647 | − | 37.0410i | −1.13943 | − | 1.28032i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9586 | − | 36.3014i | 0.723573 | − | 1.25326i | −0.235986 | − | 0.971756i | \(-0.575832\pi\) |
0.959559 | − | 0.281508i | \(-0.0908348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4899 | + | 25.0973i | 0.499653 | + | 0.865425i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.26030 | − | 9.32011i | −0.215616 | − | 0.321002i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.34949 | 0.321632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.90375 | −0.340297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.5042 | + | 0.782094i | −0.394822 | + | 0.0268414i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.5645 | + | 23.4944i | 0.464986 | + | 0.805379i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.30061 | − | 5.71683i | 0.113011 | − | 0.195741i | −0.803972 | − | 0.594667i | \(-0.797284\pi\) |
0.916983 | + | 0.398927i | \(0.130617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.61566 | + | 3.95479i | −0.0552545 | + | 0.135251i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0909 | − | 20.9421i | 0.413018 | − | 0.715368i | −0.582200 | − | 0.813046i | \(-0.697808\pi\) |
0.995218 | + | 0.0976773i | \(0.0311413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.44631 | − | 16.3615i | −0.322304 | − | 0.558247i | 0.658659 | − | 0.752442i | \(-0.271124\pi\) |
−0.980963 | + | 0.194195i | \(0.937791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.4667 | + | 31.5563i | −0.527102 | + | 1.07544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.37925 | −0.183112 | −0.0915559 | − | 0.995800i | \(-0.529184\pi\) | ||||
−0.0915559 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.2420 | −0.382238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.67982 | − | 11.5884i | 0.192897 | − | 0.393563i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9994 | + | 22.5156i | 0.440974 | + | 0.763789i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.391214 | + | 0.677602i | −0.0132558 | + | 0.0229597i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44.2560 | + | 6.04530i | −1.49784 | + | 0.204602i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.2356 | + | 22.9247i | −0.447443 | + | 0.774995i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.00289 | + | 5.20115i | 0.101400 | + | 0.175630i | 0.912262 | − | 0.409608i | \(-0.134334\pi\) |
−0.810862 | + | 0.585238i | \(0.801001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.03343 | + | 0.614125i | −0.304690 | + | 0.0207139i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3457 | −0.954991 | −0.477496 | − | 0.878634i | \(-0.658455\pi\) | ||||
−0.477496 | + | 0.878634i | \(0.658455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1360 | 0.408409 | 0.204204 | − | 0.978928i | \(-0.434539\pi\) | ||||
0.204204 | + | 0.978928i | \(0.434539\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.3744 | − | 22.8888i | −0.516804 | − | 0.769399i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9032 | + | 39.6696i | 0.769015 | + | 1.33197i | 0.938097 | + | 0.346372i | \(0.112586\pi\) |
−0.169082 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.45763 | + | 4.25674i | −0.0824263 | + | 0.142766i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7212 | − | 16.3994i | −0.560182 | − | 0.549400i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.27915 | + | 5.67965i | −0.109733 | + | 0.190062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.61558 | − | 4.53031i | −0.0874290 | − | 0.151432i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.34681 | + | 10.9377i | 0.245303 | + | 0.365198i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.35301 | −0.0451256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.7968 | −0.992677 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.5600 | + | 1.73766i | −0.850584 | + | 0.0578258i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.21923 | − | 15.9682i | −0.306458 | − | 0.530800i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9721 | + | 19.0043i | −0.364324 | + | 0.631028i | −0.988667 | − | 0.150122i | \(-0.952033\pi\) |
0.624343 | + | 0.781150i | \(0.285367\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.89305 | − | 0.668384i | 0.162292 | − | 0.0221689i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2789 | − | 21.2676i | 0.406817 | − | 0.704628i | −0.587714 | − | 0.809069i | \(-0.699972\pi\) |
0.994531 | + | 0.104441i | \(0.0333053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.03114 | + | 15.6424i | 0.298887 | + | 0.517688i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.43961 | + | 15.1789i | −0.245946 | + | 0.501798i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.7598 | 0.619504 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.9172 | −1.58064 | −0.790322 | − | 0.612692i | \(-0.790087\pi\) | ||||
−0.790322 | + | 0.612692i | \(0.790087\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0679 | − | 24.6219i | 0.397652 | − | 0.811321i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4131 | − | 18.0361i | −0.342752 | − | 0.593665i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5467 | − | 23.4635i | 0.445412 | − | 0.771476i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.5403 | − | 35.5914i | 0.477565 | − | 1.16898i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5376 | − | 26.9120i | 0.509773 | − | 0.882953i | −0.490163 | − | 0.871631i | \(-0.663063\pi\) |
0.999936 | − | 0.0113223i | \(-0.00360408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.763443 | − | 1.32232i | −0.0250208 | − | 0.0433373i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.84887 | + | 0.329644i | −0.158745 | + | 0.0107920i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.1557 | −0.593756 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.1142 | −1.11446 | −0.557232 | − | 0.830357i | \(-0.688137\pi\) | ||||
−0.557232 | + | 0.830357i | \(0.688137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2104 | + | 21.1560i | 0.463740 | + | 0.690400i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.3292 | − | 26.5509i | −0.499716 | − | 0.865534i | 0.500284 | − | 0.865861i | \(-0.333229\pi\) |
−1.00000 | 0.000327806i | \(0.999896\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.0499 | + | 22.6031i | −0.424963 | + | 0.736058i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.8187 | − | 3.47306i | 0.547113 | − | 0.112979i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.01450 | − | 12.1495i | 0.227941 | − | 0.394805i | −0.729257 | − | 0.684240i | \(-0.760134\pi\) |
0.957198 | + | 0.289435i | \(0.0934675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.57008 | − | 14.8438i | −0.278197 | − | 0.481850i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29094 | − | 1.92190i | −0.0418615 | − | 0.0623219i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9957 | −0.680117 | −0.340059 | − | 0.940404i | \(-0.610447\pi\) | ||||
−0.340059 | + | 0.940404i | \(0.610447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.445808 | 0.0144260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.637605 | + | 0.0433467i | −0.0206109 | + | 0.00140120i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.75110 | + | 4.76505i | 0.0888378 | + | 0.153872i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0316 | + | 52.0162i | −0.968761 | + | 1.67794i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.0967 | + | 32.3797i | 0.808729 | + | 1.04342i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1427 | − | 24.4959i | 0.455270 | − | 0.788551i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5923 | + | 30.4708i | 0.565731 | + | 0.979875i | 0.996981 | + | 0.0776429i | \(0.0247394\pi\) |
−0.431250 | + | 0.902233i | \(0.641927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.80437 | + | 7.76198i | −0.122214 | + | 0.249351i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.7300 | 1.37127 | 0.685635 | − | 0.727945i | \(-0.259525\pi\) | ||||
0.685635 | + | 0.727945i | \(0.259525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.3600 | −0.845063 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.79126 | − | 11.8158i | 0.185469 | − | 0.378408i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.84824 | + | 3.20125i | 0.0591305 | + | 0.102417i | 0.894075 | − | 0.447917i | \(-0.147834\pi\) |
−0.834945 | + | 0.550334i | \(0.814501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.6845 | + | 35.8265i | −0.661078 | + | 1.14502i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.8831 | + | 30.8140i | 0.762530 | + | 0.983814i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.7711 | + | 39.4407i | −0.726285 | + | 1.25796i | 0.232158 | + | 0.972678i | \(0.425421\pi\) |
−0.958443 | + | 0.285284i | \(0.907912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.6197 | − | 28.7862i | −0.529548 | − | 0.917205i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.3033 | − | 1.78819i | 0.837243 | − | 0.0569188i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.0267 | −0.605013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1458 | 0.639951 | 0.319976 | − | 0.947426i | \(-0.396325\pi\) | ||||
0.319976 | + | 0.947426i | \(0.396325\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.20766 | − | 7.75298i | −0.165260 | − | 0.246033i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.175940 | + | 0.304736i | 0.00557766 | + | 0.00966079i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3577 | + | 30.0645i | −0.549725 | + | 0.952152i | 0.448568 | + | 0.893749i | \(0.351934\pi\) |
−0.998293 | + | 0.0584029i | \(0.981399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.8156 | + | 9.46090i | −1.44954 | + | 0.299330i |
(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.h.385.4 | yes | 10 | |
3.2 | odd | 2 | 3456.2.i.h.1153.2 | 10 | |||
4.3 | odd | 2 | 1152.2.i.e.385.2 | ✓ | 10 | ||
8.3 | odd | 2 | 1152.2.i.g.385.4 | yes | 10 | ||
8.5 | even | 2 | 1152.2.i.f.385.2 | yes | 10 | ||
9.4 | even | 3 | inner | 1152.2.i.h.769.4 | yes | 10 | |
9.5 | odd | 6 | 3456.2.i.h.2305.2 | 10 | |||
12.11 | even | 2 | 3456.2.i.e.1153.2 | 10 | |||
24.5 | odd | 2 | 3456.2.i.g.1153.4 | 10 | |||
24.11 | even | 2 | 3456.2.i.f.1153.4 | 10 | |||
36.23 | even | 6 | 3456.2.i.e.2305.2 | 10 | |||
36.31 | odd | 6 | 1152.2.i.e.769.2 | yes | 10 | ||
72.5 | odd | 6 | 3456.2.i.g.2305.4 | 10 | |||
72.13 | even | 6 | 1152.2.i.f.769.2 | yes | 10 | ||
72.59 | even | 6 | 3456.2.i.f.2305.4 | 10 | |||
72.67 | odd | 6 | 1152.2.i.g.769.4 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.e.385.2 | ✓ | 10 | 4.3 | odd | 2 | ||
1152.2.i.e.769.2 | yes | 10 | 36.31 | odd | 6 | ||
1152.2.i.f.385.2 | yes | 10 | 8.5 | even | 2 | ||
1152.2.i.f.769.2 | yes | 10 | 72.13 | even | 6 | ||
1152.2.i.g.385.4 | yes | 10 | 8.3 | odd | 2 | ||
1152.2.i.g.769.4 | yes | 10 | 72.67 | odd | 6 | ||
1152.2.i.h.385.4 | yes | 10 | 1.1 | even | 1 | trivial | |
1152.2.i.h.769.4 | yes | 10 | 9.4 | even | 3 | inner | |
3456.2.i.e.1153.2 | 10 | 12.11 | even | 2 | |||
3456.2.i.e.2305.2 | 10 | 36.23 | even | 6 | |||
3456.2.i.f.1153.4 | 10 | 24.11 | even | 2 | |||
3456.2.i.f.2305.4 | 10 | 72.59 | even | 6 | |||
3456.2.i.g.1153.4 | 10 | 24.5 | odd | 2 | |||
3456.2.i.g.2305.4 | 10 | 72.5 | odd | 6 | |||
3456.2.i.h.1153.2 | 10 | 3.2 | odd | 2 | |||
3456.2.i.h.2305.2 | 10 | 9.5 | odd | 6 |