Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{11} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-1.62928 - 2.51902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.4.bc.e.257.3 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.82199 | − | 4.36307i | −0.543093 | − | 0.839673i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.24534 | + | 3.88904i | 0.200829 | + | 0.347846i | 0.948796 | − | 0.315890i | \(-0.102303\pi\) |
−0.747967 | + | 0.663736i | \(0.768970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.71288 | − | 15.7690i | 0.524446 | − | 0.851443i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0727 | + | 24.6251i | −0.410101 | + | 0.912040i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.2835 | − | 11.7107i | −0.555974 | − | 0.320992i | 0.195554 | − | 0.980693i | \(-0.437350\pi\) |
−0.751528 | + | 0.659701i | \(0.770683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.91384i | − | 0.126170i | −0.998008 | − | 0.0630848i | \(-0.979906\pi\) | ||
0.998008 | − | 0.0630848i | \(-0.0200939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.6318 | − | 20.7714i | 0.183008 | − | 0.357544i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 58.0418 | − | 100.531i | 0.828071 | − | 1.43426i | −0.0714778 | − | 0.997442i | \(-0.522772\pi\) |
0.899549 | − | 0.436819i | \(-0.143895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.02533 | + | 4.63343i | −0.0969019 | + | 0.0559464i | −0.547668 | − | 0.836696i | \(-0.684484\pi\) |
0.450766 | + | 0.892642i | \(0.351151\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.2107 | + | 2.12191i | −0.999757 | + | 0.0220494i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −107.721 | + | 62.1928i | −0.976583 | + | 0.563830i | −0.901237 | − | 0.433327i | \(-0.857339\pi\) |
−0.0753461 | + | 0.997157i | \(0.524006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.4169 | − | 90.7888i | 0.419335 | − | 0.726310i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 138.688 | − | 21.1808i | 0.988538 | − | 0.150972i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 207.807i | 1.33065i | 0.746555 | + | 0.665324i | \(0.231707\pi\) | ||||
−0.746555 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −122.764 | − | 70.8780i | −0.711262 | − | 0.410647i | 0.100266 | − | 0.994961i | \(-0.468030\pi\) |
−0.811528 | + | 0.584314i | \(0.801364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.14540 | + | 121.546i | 0.0324175 | + | 0.641165i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 83.1348 | + | 2.36716i | 0.401496 | + | 0.0114321i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −149.838 | − | 259.526i | −0.665761 | − | 1.15313i | −0.979078 | − | 0.203483i | \(-0.934774\pi\) |
0.313317 | − | 0.949648i | \(-0.398560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −25.8025 | + | 16.6888i | −0.105941 | + | 0.0685218i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −508.379 | −1.93647 | −0.968237 | − | 0.250032i | \(-0.919559\pi\) | ||||
−0.968237 | + | 0.250032i | \(0.919559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −391.127 | −1.38712 | −0.693562 | − | 0.720397i | \(-0.743959\pi\) | ||||
−0.693562 | + | 0.720397i | \(0.743959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −120.630 | + | 12.2294i | −0.399610 | + | 0.0405123i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.2575 | + | 69.7281i | 0.124940 | + | 0.216402i | 0.921709 | − | 0.387881i | \(-0.126793\pi\) |
−0.796770 | + | 0.604283i | \(0.793460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −154.320 | − | 306.324i | −0.449912 | − | 0.893073i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −602.419 | + | 30.4585i | −1.65403 | + | 0.0836282i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 258.697 | + | 149.359i | 0.670467 | + | 0.387094i | 0.796254 | − | 0.604963i | \(-0.206812\pi\) |
−0.125786 | + | 0.992057i | \(0.540145\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 105.178i | − | 0.257858i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 42.8634 | + | 21.9396i | 0.0996034 | + | 0.0509818i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −102.276 | + | 177.147i | −0.225682 | + | 0.390892i | −0.956524 | − | 0.291655i | \(-0.905794\pi\) |
0.730842 | + | 0.682547i | \(0.239128\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −543.757 | + | 313.939i | −1.14133 | + | 0.658946i | −0.946759 | − | 0.321943i | \(-0.895664\pi\) |
−0.194569 | + | 0.980889i | \(0.562331\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 280.764 | + | 413.786i | 0.561475 | + | 0.827494i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.9992 | − | 13.2786i | 0.0438876 | − | 0.0253385i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51.3894 | + | 89.0091i | −0.0937048 | + | 0.162301i | −0.909067 | − | 0.416649i | \(-0.863204\pi\) |
0.815363 | + | 0.578951i | \(0.196538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 575.340 | + | 294.487i | 1.00381 | + | 0.513798i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.9785i | − | 0.0785256i | −0.999229 | − | 0.0392628i | \(-0.987499\pi\) | ||
0.999229 | − | 0.0392628i | \(-0.0125010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −228.182 | − | 131.741i | −0.365845 | − | 0.211221i | 0.305797 | − | 0.952097i | \(-0.401077\pi\) |
−0.671642 | + | 0.740876i | \(0.734411\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −544.038 | + | 27.5067i | −0.837601 | + | 0.0423493i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −381.677 | + | 206.105i | −0.564885 | + | 0.305038i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −533.634 | − | 924.281i | −0.759981 | − | 1.31633i | −0.942860 | − | 0.333190i | \(-0.891875\pi\) |
0.182878 | − | 0.983136i | \(-0.441459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −483.790 | − | 545.333i | −0.663635 | − | 0.748056i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 270.436 | 0.357642 | 0.178821 | − | 0.983882i | \(-0.442772\pi\) | ||||
0.178821 | + | 0.983882i | \(0.442772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 521.294 | 0.665203 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 906.676 | − | 586.430i | 1.11731 | − | 0.722665i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 443.765 | + | 768.624i | 0.528528 | + | 0.915438i | 0.999447 | + | 0.0332610i | \(0.0105893\pi\) |
−0.470918 | + | 0.882177i | \(0.656077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −93.2551 | − | 57.4405i | −0.107426 | − | 0.0661692i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.1945 | + | 735.646i | 0.0414719 | + | 0.820246i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.0392 | − | 20.8072i | −0.0389215 | − | 0.0224713i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 219.564i | − | 0.229828i | −0.993375 | − | 0.114914i | \(-0.963341\pi\) | ||
0.993375 | − | 0.114914i | \(-0.0366593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 512.971 | − | 369.815i | 0.520763 | − | 0.375432i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 492.533 | − | 853.093i | 0.485237 | − | 0.840455i | −0.514619 | − | 0.857419i | \(-0.672067\pi\) |
0.999856 | + | 0.0169642i | \(0.00540012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1112.87 | − | 642.516i | 1.06461 | − | 0.614650i | 0.137903 | − | 0.990446i | \(-0.455964\pi\) |
0.926703 | + | 0.375796i | \(0.122631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −224.278 | − | 369.403i | −0.208450 | − | 0.343334i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −158.409 | + | 91.4575i | −0.143121 | + | 0.0826311i | −0.569851 | − | 0.821748i | \(-0.692999\pi\) |
0.426729 | + | 0.904379i | \(0.359666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 291.471 | − | 504.843i | 0.256127 | − | 0.443625i | −0.709074 | − | 0.705134i | \(-0.750887\pi\) |
0.965201 | + | 0.261509i | \(0.0842201\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −709.490 | + | 1386.13i | −0.606683 | + | 1.18528i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2283.94i | − | 1.90137i | −0.310152 | − | 0.950687i | \(-0.600380\pi\) | ||
0.310152 | − | 0.950687i | \(-0.399620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −483.741 | − | 279.288i | −0.392253 | − | 0.226467i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 145.629 | + | 65.4823i | 0.115072 | + | 0.0517422i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1021.52 | − | 1891.71i | −0.786914 | − | 1.45725i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −391.219 | − | 677.611i | −0.293928 | − | 0.509099i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1434.64 | + | 2218.09i | 1.05169 | + | 1.62601i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1032.11 | 0.738517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1554.48 | 1.08613 | 0.543064 | − | 0.839692i | \(-0.317264\pi\) | ||||
0.543064 | + | 0.839692i | \(0.317264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1103.76 | + | 1706.51i | 0.753337 | + | 1.16473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1047.46 | + | 1814.26i | 0.698605 | + | 1.21002i | 0.968950 | + | 0.247256i | \(0.0795288\pi\) |
−0.270345 | + | 0.962763i | \(0.587138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.88481 | + | 171.555i | −0.00318471 | + | 0.111847i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 393.775 | + | 491.805i | 0.251042 | + | 0.313540i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 529.002 | + | 305.420i | 0.329896 | + | 0.190465i | 0.655795 | − | 0.754939i | \(-0.272334\pi\) |
−0.325899 | + | 0.945405i | \(0.605667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1806.61i | 1.10241i | 0.834370 | + | 0.551204i | \(0.185831\pi\) | ||||
−0.834370 | + | 0.551204i | \(0.814169\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 190.622 | − | 372.419i | 0.113853 | − | 0.222435i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −69.2553 | + | 119.954i | −0.0404994 | + | 0.0701470i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −808.170 | + | 466.597i | −0.462861 | + | 0.267233i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −901.023 | + | 1537.75i | −0.505545 | + | 0.862800i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2341.75 | + | 1352.01i | −1.28754 | + | 0.743363i | −0.978215 | − | 0.207592i | \(-0.933437\pi\) |
−0.309328 | + | 0.950956i | \(0.600104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 770.352 | − | 1334.29i | 0.415168 | − | 0.719092i | −0.580278 | − | 0.814418i | \(-0.697056\pi\) |
0.995446 | + | 0.0953266i | \(0.0303895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1832.91 | + | 2542.44i | 0.968512 | + | 1.34343i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 636.580i | − | 0.329880i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 477.498 | + | 275.684i | 0.242729 | + | 0.140140i | 0.616430 | − | 0.787409i | \(-0.288578\pi\) |
−0.373701 | + | 0.927549i | \(0.621911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −78.3786 | − | 1550.20i | −0.0390933 | − | 0.773201i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −65.5670 | + | 2302.72i | −0.0320957 | + | 1.12720i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1155.82 | − | 2001.94i | −0.555403 | − | 0.961986i | −0.997872 | − | 0.0652023i | \(-0.979231\pi\) |
0.442469 | − | 0.896784i | \(-0.354103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −458.899 | + | 296.811i | −0.216516 | + | 0.140041i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2580.87 | 1.19589 | 0.597944 | − | 0.801538i | \(-0.295984\pi\) | ||||
0.597944 | + | 0.801538i | \(0.295984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2162.03 | 0.984081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.2364 | − | 248.929i | −0.0112858 | − | 0.111322i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −501.050 | − | 867.845i | −0.220197 | − | 0.381393i | 0.734670 | − | 0.678424i | \(-0.237337\pi\) |
−0.954868 | + | 0.297031i | \(0.904004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −922.524 | − | 1708.38i | −0.398493 | − | 0.737951i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1061.53 | − | 53.6712i | 0.450787 | − | 0.0227919i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2598.36 | − | 1500.17i | −1.08498 | − | 0.626411i | −0.152742 | − | 0.988266i | \(-0.548810\pi\) |
−0.932234 | + | 0.361855i | \(0.882144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 967.850i | − | 0.397457i | −0.980055 | − | 0.198729i | \(-0.936319\pi\) | ||
0.980055 | − | 0.198729i | \(-0.0636812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2904.21 | + | 1486.52i | 1.17315 | + | 0.600473i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 672.872 | − | 1165.45i | 0.267408 | − | 0.463165i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2354.59 | + | 1359.42i | −0.920773 | + | 0.531608i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1013.06 | − | 2392.69i | 0.389891 | − | 0.920861i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −356.214 | + | 205.660i | −0.134946 | + | 0.0779113i | −0.565953 | − | 0.824437i | \(-0.691492\pi\) |
0.431007 | + | 0.902349i | \(0.358158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −408.212 | + | 707.043i | −0.152247 | + | 0.263700i | −0.932053 | − | 0.362321i | \(-0.881984\pi\) |
0.779806 | + | 0.626021i | \(0.215318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −122.839 | − | 62.8749i | −0.0451111 | − | 0.0230901i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 633.331i | − | 0.229051i | −0.993420 | − | 0.114525i | \(-0.963465\pi\) | ||
0.993420 | − | 0.114525i | \(-0.0365347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2964.48 | + | 1711.54i | 1.05601 | + | 0.609688i | 0.924326 | − | 0.381603i | \(-0.124628\pi\) |
0.131685 | + | 0.991292i | \(0.457961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 533.373 | − | 26.9675i | 0.187170 | − | 0.00946339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3276.90 | + | 2018.41i | 1.13297 | + | 0.697854i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1141.48 | − | 1977.11i | −0.388901 | − | 0.673596i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −338.739 | − | 3341.29i | −0.113739 | − | 1.12191i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 217.043 | 0.0718333 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1023.65 | −0.333986 | −0.166993 | − | 0.985958i | \(-0.553406\pi\) | ||||
−0.166993 | + | 0.985958i | \(0.553406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −204.970 | + | 132.573i | −0.0659358 | + | 0.0426467i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −878.212 | − | 1521.11i | −0.278575 | − | 0.482506i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2310.07 | + | 1247.43i | −0.722661 | + | 0.390237i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 69.1334 | + | 1367.35i | 0.0213315 | + | 0.421903i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −594.527 | − | 343.250i | −0.180960 | − | 0.104477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1521.32i | 0.456840i | 0.973563 | + | 0.228420i | \(0.0733559\pi\) | ||||
−0.973563 | + | 0.228420i | \(0.926644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1655.28 | + | 2296.05i | 0.490454 | + | 0.680311i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −729.575 | + | 1263.66i | −0.213320 | + | 0.369481i | −0.952752 | − | 0.303751i | \(-0.901761\pi\) |
0.739432 | + | 0.673232i | \(0.235094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4152.17 | − | 2397.26i | 1.19818 | − | 0.691770i | 0.238031 | − | 0.971257i | \(-0.423498\pi\) |
0.960149 | + | 0.279488i | \(0.0901646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1976.34 | + | 1083.66i | 0.562917 | + | 0.308655i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1445.76 | − | 834.708i | 0.406501 | − | 0.234693i | −0.282784 | − | 0.959183i | \(-0.591258\pi\) |
0.689285 | + | 0.724490i | \(0.257925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −180.784 | + | 313.126i | −0.0501831 | + | 0.0869196i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2526.79 | + | 4936.60i | −0.692543 | + | 1.35302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3529.25i | − | 0.955181i | −0.878583 | − | 0.477590i | \(-0.841510\pi\) | ||
0.878583 | − | 0.477590i | \(-0.158490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4269.15 | − | 2464.80i | −1.14108 | − | 0.658803i | −0.194382 | − | 0.980926i | \(-0.562270\pi\) |
−0.946698 | + | 0.322123i | \(0.895603\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1014.07 | + | 3649.73i | −0.267707 | + | 0.963500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 844.806 | − | 1287.96i | 0.220297 | − | 0.335855i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4014 | + | 47.4605i | 0.00705873 | + | 0.0122261i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −763.170 | − | 1179.93i | −0.194233 | − | 0.300302i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1294.99 | 0.325652 | 0.162826 | − | 0.986655i | \(-0.447939\pi\) | ||||
0.162826 | + | 0.986655i | \(0.447939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2913.29 | 0.723940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1471.09 | − | 2274.44i | −0.361267 | − | 0.558553i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −728.040 | − | 1261.00i | −0.176708 | − | 0.306067i | 0.764043 | − | 0.645165i | \(-0.223211\pi\) |
−0.940751 | + | 0.339098i | \(0.889878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5547.82 | − | 157.967i | −1.33098 | − | 0.0378980i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5117.27 | − | 2300.99i | −1.21360 | − | 0.545700i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1850.30 | − | 1068.27i | −0.433820 | − | 0.250466i | 0.267153 | − | 0.963654i | \(-0.413917\pi\) |
−0.700973 | + | 0.713188i | \(0.747251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1341.44i | 0.310959i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2101.26 | − | 4105.23i | 0.481628 | − | 0.940958i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1443.73 | + | 2500.61i | −0.327233 | + | 0.566784i | −0.981962 | − | 0.189080i | \(-0.939449\pi\) |
0.654729 | + | 0.755864i | \(0.272783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5072.92 | − | 2928.85i | 1.13711 | − | 0.656513i | 0.191400 | − | 0.981512i | \(-0.438697\pi\) |
0.945714 | + | 0.324999i | \(0.105364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.5486 | + | 568.975i | 0.00278197 | + | 0.126139i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2126.40 | + | 1227.68i | −0.466279 | + | 0.269206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1401.52 | − | 2427.50i | 0.304003 | − | 0.526549i | −0.673036 | − | 0.739610i | \(-0.735010\pi\) |
0.977039 | + | 0.213061i | \(0.0683433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3104.71 | − | 2238.27i | 0.666215 | − | 0.480293i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4665.53i | 0.990469i | 0.868759 | + | 0.495235i | \(0.164918\pi\) | ||||
−0.868759 | + | 0.495235i | \(0.835082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4654.53 | − | 2687.29i | −0.977679 | − | 0.564463i | −0.0761103 | − | 0.997099i | \(-0.524250\pi\) |
−0.901569 | + | 0.432636i | \(0.857583\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9190 | + | 215.959i | 0.00226941 | + | 0.0448853i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4937.83 | + | 8016.61i | −1.01558 | + | 1.64880i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4281.21 | − | 7415.27i | −0.871404 | − | 1.50932i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −957.973 | + | 619.608i | −0.192981 | + | 0.124818i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1302.13 | 0.259630 | 0.129815 | − | 0.991538i | \(-0.458562\pi\) | ||||
0.129815 | + | 0.991538i | \(0.458562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −918.578 | −0.181294 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3061.13 | − | 1194.51i | −0.598063 | − | 0.233376i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 367.799 | + | 637.046i | 0.0711383 | + | 0.123215i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3798.97 | + | 6167.66i | −0.727472 | + | 1.18106i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5112.03 | + | 258.465i | −0.969235 | + | 0.0490048i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2441.84 | − | 1409.80i | −0.458424 | − | 0.264671i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 644.894i | − | 0.119889i | −0.998202 | − | 0.0599447i | \(-0.980908\pi\) | ||
0.998202 | − | 0.0599447i | \(-0.0190924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5943.85 | − | 3042.35i | −1.09428 | − | 0.560108i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −668.420 | + | 1157.74i | −0.121873 | + | 0.211091i | −0.920506 | − | 0.390727i | \(-0.872224\pi\) |
0.798633 | + | 0.601818i | \(0.205557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1459.67 | + | 842.739i | −0.263595 | + | 0.152187i | −0.625973 | − | 0.779844i | \(-0.715298\pi\) |
0.362378 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −978.819 | + | 2020.99i | −0.175080 | + | 0.361492i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2609.95 | − | 1506.85i | 0.462427 | − | 0.266982i | −0.250637 | − | 0.968081i | \(-0.580640\pi\) |
0.713064 | + | 0.701099i | \(0.247307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2433.57 | − | 4215.06i | 0.427127 | − | 0.739806i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 846.064 | + | 433.057i | 0.147111 | + | 0.0752987i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1075.73i | 0.185310i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −536.910 | − | 309.985i | −0.0916382 | − | 0.0529074i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3025.19 | + | 152.955i | −0.511601 | + | 0.0258667i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1490.56 | + | 42.4417i | 0.249778 | + | 0.00711211i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −394.460 | − | 683.225i | −0.0655030 | − | 0.113454i | 0.831414 | − | 0.555653i | \(-0.187532\pi\) |
−0.896917 | + | 0.442199i | \(0.854199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8049.97 | − | 816.104i | 1.32473 | − | 0.134301i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −461.547 | −0.0752746 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1906.16 | 0.308116 | 0.154058 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154058 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9964.99 | + | 6445.27i | −1.59653 | + | 1.03262i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1660.06 | + | 2875.31i | 0.263629 | + | 0.456618i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6329.30 | − | 541.828i | −0.996356 | − | 0.0852944i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 146.561 | + | 2898.74i | 0.0228713 | + | 0.452356i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4538.98 | + | 2620.58i | 0.702205 | + | 0.405418i | 0.808168 | − | 0.588952i | \(-0.200459\pi\) |
−0.105963 | + | 0.994370i | \(0.533793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4502.54i | 0.690588i | 0.938495 | + | 0.345294i | \(0.112221\pi\) | ||||
−0.938495 | + | 0.345294i | \(0.887779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −125.260 | − | 820.179i | −0.0190481 | − | 0.124723i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4799.70 | + | 8313.33i | −0.723689 | + | 1.25347i | 0.235822 | + | 0.971796i | \(0.424222\pi\) |
−0.959511 | + | 0.281671i | \(0.909111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 182.701 | − | 105.483i | 0.0273148 | − | 0.0157702i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5370.93 | + | 9795.36i | −0.796245 | + | 1.45217i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8803.94 | − | 5082.96i | 1.29430 | − | 0.747265i | 0.314888 | − | 0.949129i | \(-0.398033\pi\) |
0.979414 | + | 0.201863i | \(0.0646997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3386.56 | + | 5865.70i | −0.493740 | + | 0.855183i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1852.44 | + | 3619.13i | −0.267846 | + | 0.523292i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1183.21i | − | 0.169677i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −332.544 | − | 191.995i | −0.0472988 | − | 0.0273080i | 0.476164 | − | 0.879356i | \(-0.342027\pi\) |
−0.523463 | + | 0.852048i | \(0.675360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5629.14 | − | 12518.9i | 0.794149 | − | 1.76614i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4867.92 | − | 2628.68i | 0.681213 | − | 0.367855i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1481.79 | + | 2566.54i | 0.205695 | + | 0.356275i | 0.950354 | − | 0.311171i | \(-0.100721\pi\) |
−0.744659 | + | 0.667445i | \(0.767388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2912.61 | − | 4503.16i | −0.401083 | − | 0.620113i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1228.94 | 0.167887 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13195.4 | 1.78839 | 0.894195 | − | 0.447677i | \(-0.147749\pi\) | ||||
0.894195 | + | 0.447677i | \(0.147749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4386.74 | − | 6782.32i | −0.589868 | − | 0.911991i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4475.95 | − | 7752.57i | −0.597155 | − | 1.03430i | −0.993239 | − | 0.116088i | \(-0.962964\pi\) |
0.396084 | − | 0.918214i | \(-0.370369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1658.55 | − | 1021.58i | −0.219552 | − | 0.135233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4330.84 | − | 9631.54i | 0.568860 | − | 1.26511i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7594.74 | − | 4384.82i | −0.989893 | − | 0.571515i | −0.0846507 | − | 0.996411i | \(-0.526977\pi\) |
−0.905242 | + | 0.424896i | \(0.860311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14439.1i | 1.86757i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4959.80 | − | 9689.97i | 0.636613 | − | 1.24375i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2396.38 | − | 4150.65i | 0.305253 | − | 0.528713i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1187.30 | + | 685.490i | −0.150098 | + | 0.0866594i | −0.573168 | − | 0.819438i | \(-0.694286\pi\) |
0.423070 | + | 0.906097i | \(0.360953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 762.291 | − | 462.814i | 0.0956448 | − | 0.0580694i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2392.14 | + | 1381.10i | −0.297899 | + | 0.171992i | −0.641499 | − | 0.767124i | \(-0.721687\pi\) |
0.343599 | + | 0.939116i | \(0.388354\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −419.161 | + | 726.008i | −0.0518112 | + | 0.0897396i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1034.55 | − | 3105.94i | 0.126931 | − | 0.381075i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7018.82i | 0.854815i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2310.01 | + | 1333.69i | 0.279273 | + | 0.161239i | 0.633094 | − | 0.774075i | \(-0.281784\pi\) |
−0.353821 | + | 0.935313i | \(0.615118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −160.274 | − | 3169.96i | −0.0192354 | − | 0.380445i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1800.03 | + | 3333.40i | 0.214465 | + | 0.397157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 607.221 | + | 1051.74i | 0.0718249 | + | 0.124404i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7882.37 | − | 5098.24i | 0.925662 | − | 0.598710i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14480.6 | −1.68836 | −0.844179 | − | 0.536061i | \(-0.819912\pi\) | ||||
−0.844179 | + | 0.536061i | \(0.819912\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14248.8 | 1.64951 | 0.824753 | − | 0.565494i | \(-0.191314\pi\) | ||||
0.824753 | + | 0.565494i | \(0.191314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2162.82 | + | 219.266i | −0.248605 | + | 0.0252035i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6084.75 | − | 10539.1i | −0.694479 | − | 1.20287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −330.971 | + | 11623.7i | −0.0375101 | + | 1.31736i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 718.804 | − | 36.3429i | 0.0808955 | − | 0.00409010i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4826.49 | + | 2786.57i | 0.539405 | + | 0.311426i | 0.744838 | − | 0.667246i | \(-0.232527\pi\) |
−0.205433 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2939.93i | 0.326291i | 0.986602 | + | 0.163146i | \(0.0521640\pi\) | ||||
−0.986602 | + | 0.163146i | \(0.947836\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4316.44 | + | 2209.37i | 0.475765 | + | 0.243520i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 576.332 | − | 998.236i | 0.0630885 | − | 0.109273i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8290.73 | − | 4786.66i | 0.901355 | − | 0.520398i | 0.0237157 | − | 0.999719i | \(-0.492450\pi\) |
0.877640 | + | 0.479321i | \(0.159117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9252.00 | − | 408.300i | 0.999028 | − | 0.0440881i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6197.42 | + | 3578.08i | −0.664669 | + | 0.383747i | −0.794054 | − | 0.607848i | \(-0.792033\pi\) |
0.129385 | + | 0.991594i | \(0.458700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1992.81 | + | 3451.64i | −0.212288 | + | 0.367693i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12507.3 | + | 6401.86i | 1.32344 | + | 0.677400i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14839.2i | − | 1.55970i | −0.625964 | − | 0.779852i | \(-0.715294\pi\) | ||
0.625964 | − | 0.779852i | \(-0.284706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10311.7 | + | 5953.48i | 1.07663 | + | 0.621593i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7995.52 | + | 404.256i | −0.829276 | + | 0.0419284i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.9990 | − | 491.646i | 0.00144238 | − | 0.0506565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3787.42 | + | 6560.00i | 0.387676 | + | 0.671474i | 0.992136 | − | 0.125161i | \(-0.0399447\pi\) |
−0.604461 | + | 0.796635i | \(0.706611\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5920.37 | − | 15171.9i | 0.602046 | − | 1.54284i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14850.5 | 1.50034 | 0.750170 | − | 0.661245i | \(-0.229971\pi\) | ||||
0.750170 | + | 0.661245i | \(0.229971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3361.43 | −0.337406 | −0.168703 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168703 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2777.44 | + | 1796.42i | −0.276991 | + | 0.179155i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 115.422 | + | 199.917i | 0.0114371 | + | 0.0198096i | 0.871687 | − | 0.490063i | \(-0.163026\pi\) |
−0.860250 | + | 0.509872i | \(0.829693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 904.441 | + | 1674.89i | 0.0890473 | + | 0.164903i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −144.670 | − | 2861.33i | −0.0141529 | − | 0.279922i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7933.44 | + | 4580.37i | 0.771205 | + | 0.445255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 971.480i | 0.0938411i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6542.45 | + | 4716.63i | −0.628005 | + | 0.452745i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2200.43 | − | 3811.26i | 0.209896 | − | 0.363551i | −0.741786 | − | 0.670637i | \(-0.766021\pi\) |
0.951682 | + | 0.307087i | \(0.0993541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1534.80 | + | 886.116i | −0.145490 | + | 0.0839988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10232.0 | − | 6212.19i | 0.963913 | − | 0.585226i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 853.894 | − | 492.996i | 0.0799450 | − | 0.0461563i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5972.31 | + | 10344.3i | −0.555711 | + | 0.962520i | 0.442137 | + | 0.896948i | \(0.354221\pi\) |
−0.997848 | + | 0.0655721i | \(0.979113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5472.87 | + | 10692.4i | −0.506118 | + | 0.988804i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19916.7i | − | 1.83060i | −0.402768 | − | 0.915302i | \(-0.631952\pi\) | ||
0.402768 | − | 0.915302i | \(-0.368048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20891.1 | + | 12061.5i | 1.90850 | + | 1.10187i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2590.02 | + | 1164.61i | 0.235177 | + | 0.105748i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −740.801 | − | 456.296i | −0.0668601 | − | 0.0411825i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 665.569 | + | 1152.80i | 0.0597093 | + | 0.103420i | 0.894335 | − | 0.447398i | \(-0.147649\pi\) |
−0.834626 | + | 0.550818i | \(0.814316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7283.19 | − | 11260.5i | −0.649479 | − | 1.00416i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10393.2 | 0.921288 | 0.460644 | − | 0.887585i | \(-0.347618\pi\) | ||||
0.460644 | + | 0.887585i | \(0.347618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4423.62 | 0.389799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6101.22 | − | 9433.07i | −0.534447 | − | 0.826306i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5132.02 | + | 8888.91i | 0.446901 | + | 0.774055i | 0.998182 | − | 0.0602640i | \(-0.0191943\pi\) |
−0.551281 | + | 0.834319i | \(0.685861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4293.73 | + | 2318.61i | −0.371709 | + | 0.200723i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1014.88 | + | 812.584i | −0.0873449 | + | 0.0699346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4997.54 | + | 2885.33i | 0.427608 | + | 0.246879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1885.78i | − | 0.160418i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2372.50 | + | 4635.17i | −0.200658 | + | 0.392026i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1549.97 | − | 2684.63i | 0.130337 | − | 0.225750i | −0.793470 | − | 0.608610i | \(-0.791727\pi\) |
0.923806 | + | 0.382860i | \(0.125061\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8265.94 | − | 4772.34i | 0.691098 | − | 0.399005i | −0.112925 | − | 0.993603i | \(-0.536022\pi\) |
0.804023 | + | 0.594598i | \(0.202689\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4850.42 | + | 8846.07i | −0.403219 | + | 0.735380i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14250.9 | + | 8227.77i | −1.17795 | + | 0.680090i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1652.39 | − | 2862.03i | 0.135809 | − | 0.235229i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3229.80 | − | 4480.06i | −0.263957 | − | 0.366136i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3006.47i | 0.244324i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −711.364 | − | 410.706i | −0.0574859 | − | 0.0331895i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 787.238 | + | 15570.3i | 0.0632622 | + | 1.25122i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −457.119 | + | 8020.53i | −0.0365297 | + | 0.640944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3403.83 | + | 5895.60i | 0.270503 | + | 0.468524i | 0.968991 | − | 0.247098i | \(-0.0794768\pi\) |
−0.698488 | + | 0.715622i | \(0.746143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4222.79 | + | 2731.27i | −0.333734 | + | 0.215856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2617.80 | 0.205751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14906.9 | 1.16521 | 0.582606 | − | 0.812754i | \(-0.302033\pi\) | ||||
0.582606 | + | 0.812754i | \(0.302033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1709.89 | − | 16866.2i | −0.132926 | − | 1.31117i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −962.859 | − | 1667.72i | −0.0744449 | − | 0.128942i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19758.1 | − | 562.586i | −1.51935 | − | 0.0432615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6983.77 | + | 353.102i | −0.534135 | + | 0.0270060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10661.9 | − | 6155.67i | −0.811061 | − | 0.468266i | 0.0362634 | − | 0.999342i | \(-0.488454\pi\) |
−0.847324 | + | 0.531076i | \(0.821788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2313.06i | 0.175013i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12575.9 | + | 6436.95i | 0.946442 | + | 0.484435i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 417.925 | − | 723.867i | 0.0312850 | − | 0.0541872i | −0.849959 | − | 0.526849i | \(-0.823373\pi\) |
0.881244 | + | 0.472662i | \(0.156707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8882.34 | − | 5128.22i | 0.661386 | − | 0.381851i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13298.3 | + | 2332.11i | −0.984969 | + | 0.172732i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5291.04 | + | 3054.78i | −0.389828 | + | 0.225067i | −0.682086 | − | 0.731272i | \(-0.738927\pi\) |
0.292258 | + | 0.956340i | \(0.405593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6319.69 | + | 10946.0i | −0.463171 | + | 0.802236i | −0.999117 | − | 0.0420166i | \(-0.986622\pi\) |
0.535946 | + | 0.844252i | \(0.319955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1902.54 | + | 973.814i | 0.138708 | + | 0.0709977i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13039.8i | 0.945736i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15334.7 | − | 8853.51i | −1.10640 | − | 0.638781i | −0.168506 | − | 0.985701i | \(-0.553894\pi\) |
−0.937895 | + | 0.346920i | \(0.887228\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4236.85 | − | 214.216i | 0.304106 | − | 0.0153757i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2626.72 | − | 4264.50i | 0.187564 | − | 0.304512i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3498.19 | − | 6059.05i | −0.248508 | − | 0.430429i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 72.3229 | + | 713.386i | 0.00511143 | + | 0.0504186i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11725.2 | 0.824446 | 0.412223 | − | 0.911083i | \(-0.364752\pi\) | ||||
0.412223 | + | 0.911083i | \(0.364752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1313.63 | 0.0918968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2763.27 | + | 1787.26i | −0.192328 | + | 0.124396i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7523.76 | + | 13031.5i | 0.521018 | + | 0.902430i | 0.999701 | + | 0.0244425i | \(0.00778108\pi\) |
−0.478683 | + | 0.877988i | \(0.658886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5063.27 | − | 8220.26i | 0.348864 | − | 0.566383i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −898.161 | − | 17764.2i | −0.0615734 | − | 1.21782i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5292.70 | − | 3055.74i | −0.361025 | − | 0.208438i | 0.308505 | − | 0.951223i | \(-0.400171\pi\) |
−0.669530 | + | 0.742785i | \(0.733505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7494.08i | 0.508636i | 0.967121 | + | 0.254318i | \(0.0818509\pi\) | ||||
−0.967121 | + | 0.254318i | \(0.918149\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1622.84 | − | 2251.04i | −0.109597 | − | 0.152022i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1756.84 | − | 3042.93i | 0.118059 | − | 0.204484i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17917.1 | + | 10344.5i | −1.19808 | + | 0.691711i | −0.960127 | − | 0.279565i | \(-0.909810\pi\) |
−0.237953 | + | 0.971277i | \(0.576476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −440.947 | − | 19993.3i | −0.0293400 | − | 1.33032i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 412.361 | − | 238.077i | 0.0273033 | − | 0.0157636i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11645.5 | − | 20170.6i | 0.767305 | − | 1.32901i | −0.171714 | − | 0.985147i | \(-0.554931\pi\) |
0.939019 | − | 0.343865i | \(-0.111736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5404.99 | + | 10559.7i | −0.354391 | + | 0.692374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11640.9i | 0.759554i | 0.925078 | + | 0.379777i | \(0.123999\pi\) | ||||
−0.925078 | + | 0.379777i | \(0.876001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13978.4 | + | 8070.44i | 0.907657 | + | 0.524036i | 0.879676 | − | 0.475573i | \(-0.157759\pi\) |
0.0279803 | + | 0.999608i | \(0.491092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13622.3 | + | 10907.0i | −0.880266 | + | 0.704805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16430.6 | + | 467.841i | 1.05663 | + | 0.0300861i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4234.68 | − | 7334.68i | −0.271019 | − | 0.469420i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −612.493 | − | 946.972i | −0.0390121 | − | 0.0603165i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34787.4 | −2.20519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9424.67 | −0.594596 | −0.297298 | − | 0.954785i | \(-0.596086\pi\) | ||||
−0.297298 | + | 0.954785i | \(0.596086\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2888.74 | + | 4466.26i | 0.181385 | + | 0.280439i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3490.34 | + | 6045.45i | 0.218126 | + | 0.377805i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1811.55 | + | 912.623i | −0.112679 | + | 0.0567652i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1156.85 | + | 520.179i | 0.0716185 | + | 0.0322034i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1459.54 | + | 842.666i | 0.0899351 | + | 0.0519241i | 0.544293 | − | 0.838895i | \(-0.316798\pi\) |
−0.454358 | + | 0.890819i | \(0.650131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10186.5i | − | 0.624752i | −0.949958 | − | 0.312376i | \(-0.898875\pi\) | ||
0.949958 | − | 0.312376i | \(-0.101125\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4158.39 | + | 8124.26i | −0.253855 | + | 0.495957i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 163.793 | − | 283.698i | 0.00995266 | − | 0.0172385i | −0.861006 | − | 0.508594i | \(-0.830165\pi\) |
0.870959 | + | 0.491356i | \(0.163499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4149.04 | − | 2395.45i | 0.250946 | − | 0.144884i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11961.6 | + | 6558.72i | 0.720143 | + | 0.394864i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1769.92 | + | 1021.87i | −0.106068 | + | 0.0612384i | −0.552096 | − | 0.833781i | \(-0.686172\pi\) |
0.446028 | + | 0.895019i | \(0.352838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4703.82 | + | 8147.25i | −0.280600 | + | 0.486014i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5770.73 | − | 4160.28i | 0.342675 | − | 0.247044i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27567.4i | − | 1.62955i | −0.579778 | − | 0.814774i | \(-0.696861\pi\) | ||
0.579778 | − | 0.814774i | \(-0.303139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18417.0 | + | 10633.0i | 1.08372 | + | 0.625684i | 0.931897 | − | 0.362724i | \(-0.118153\pi\) |
0.151820 | + | 0.988408i | \(0.451487\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 180.127 | + | 3562.61i | 0.0105513 | + | 0.208688i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −678.152 | + | 366.202i | −0.0395453 | + | 0.0213544i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12924.1 | − | 22385.2i | −0.750260 | − | 1.29949i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6637.64 | − | 4293.16i | 0.383596 | − | 0.248107i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14705.8 | 0.846065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9377.40 | −0.537106 | −0.268553 | − | 0.963265i | \(-0.586545\pi\) | ||||
−0.268553 | + | 0.963265i | \(0.586545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5346.62 | − | 13701.5i | 0.304876 | − | 0.781293i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5342.31 | − | 9253.15i | −0.303282 | − | 0.525299i | 0.673596 | − | 0.739100i | \(-0.264749\pi\) |
−0.976877 | + | 0.213801i | \(0.931416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3462.30 | − | 2132.60i | −0.195686 | − | 0.120533i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7572.30 | − | 382.857i | 0.426096 | − | 0.0215435i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24985.9 | − | 14425.6i | −1.39979 | − | 0.808172i | −0.405424 | − | 0.914129i | \(-0.632876\pi\) |
−0.994371 | + | 0.105957i | \(0.966209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2743.08i | 0.153004i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22176.8 | − | 11351.2i | −1.23158 | − | 0.630384i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 883.284 | − | 1529.89i | 0.0488395 | − | 0.0845926i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1139.99 | − | 658.171i | 0.0627599 | − | 0.0362344i | −0.468292 | − | 0.883574i | \(-0.655130\pi\) |
0.531052 | + | 0.847339i | \(0.321797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −849.162 | − | 11681.0i | −0.0465469 | − | 0.640294i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7025.98 | + | 4056.45i | −0.383469 | + | 0.221396i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29507.3 | + | 51108.1i | −1.60354 | + | 2.77741i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7721.80 | − | 3952.39i | −0.417833 | − | 0.213867i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12811.2i | − | 0.690259i | −0.938555 | − | 0.345129i | \(-0.887835\pi\) | ||
0.938555 | − | 0.345129i | \(-0.112165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2404.99 | + | 1388.52i | 0.129027 | + | 0.0744938i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1876.36 | − | 94.8693i | 0.100238 | − | 0.00506807i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8668.46 | − | 16052.7i | −0.461119 | − | 0.853925i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16482.9 | − | 28549.2i | −0.873101 | − | 1.51226i | −0.858772 | − | 0.512358i | \(-0.828772\pi\) |
−0.0143290 | − | 0.999897i | \(-0.504561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28669.3 | − | 2906.48i | 1.51221 | − | 0.153308i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17632.4 | 0.926141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −622.006 | −0.0325339 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15398.4 | + | 9959.52i | −0.802039 | + | 0.518752i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4307.48 | + | 7460.77i | 0.223424 | + | 0.386982i | 0.955845 | − | 0.293870i | \(-0.0949432\pi\) |
−0.732421 | + | 0.680851i | \(0.761610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 677.375 | − | 23789.5i | 0.0349886 | − | 1.22880i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1293.44 | + | 25582.2i | 0.0665335 | + | 1.31592i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18866.5 | + | 10892.6i | 0.966463 | + | 0.557988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26635.3i | − | 1.35880i | −0.733768 | − | 0.679400i | \(-0.762240\pi\) | ||
0.733768 | − | 0.679400i | \(-0.237760\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18785.7 | − | 5875.05i | 0.954415 | − | 0.298484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22701.7 | + | 39320.5i | −1.14864 | + | 1.98950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5328.35 | + | 3076.33i | −0.268496 | + | 0.155016i | −0.628204 | − | 0.778049i | \(-0.716210\pi\) |
0.359708 | + | 0.933065i | \(0.382876\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8003.48 | − | 51.3415i | −0.401650 | − | 0.00257655i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2084.72 | − | 1203.61i | 0.104195 | − | 0.0601569i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7364.30 | − | 12755.3i | 0.366577 | − | 0.634929i | −0.622451 | − | 0.782659i | \(-0.713863\pi\) |
0.989028 | + | 0.147729i | \(0.0471965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 129.747 | − | 253.487i | 0.00643236 | − | 0.0125669i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27255.1i | 1.34575i | 0.739755 | + | 0.672876i | \(0.234941\pi\) | ||||
−0.739755 | + | 0.672876i | \(0.765059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10516.1 | − | 6071.45i | −0.517152 | − | 0.298578i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2994.47 | + | 6659.52i | −0.146669 | + | 0.326184i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −96.4195 | + | 3386.26i | −0.00470373 | + | 0.165195i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3075.69 | − | 5327.25i | −0.149445 | − | 0.258847i | 0.781577 | − | 0.623809i | \(-0.214415\pi\) |
−0.931023 | + | 0.364961i | \(0.881082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3654.44 | − | 5650.11i | −0.176859 | − | 0.273441i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6918.80 | 0.333511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21107.3 | −1.01342 | −0.506710 | − | 0.862117i | \(-0.669139\pi\) | ||||
−0.506710 | + | 0.862117i | \(0.669139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8221.27 | − | 12710.9i | −0.393166 | − | 0.607873i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7530.97 | − | 13044.0i | −0.358735 | − | 0.621348i | 0.629015 | − | 0.777393i | \(-0.283459\pi\) |
−0.987750 | + | 0.156046i | \(0.950125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5129.82 | − | 9499.67i | −0.243397 | − | 0.450736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5772.14 | + | 12836.9i | −0.272800 | + | 0.606692i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1047.62 | + | 604.845i | 0.0493187 | + | 0.0284742i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26099.2i | − | 1.22387i | −0.790906 | − | 0.611937i | \(-0.790390\pi\) | ||
0.790906 | − | 0.611937i | \(-0.209610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3447.31 | + | 6735.03i | −0.161027 | + | 0.314599i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.84542 | − | 15.3207i | 0.000411575 | − | 0.000712869i | −0.865820 | − | 0.500356i | \(-0.833202\pi\) |
0.866231 | + | 0.499644i | \(0.166536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12869.8 | + | 7430.41i | −0.596514 | + | 0.344398i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14966.7 | + | 24651.3i | 0.691025 | + | 1.13817i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4079.91 | − | 2355.54i | 0.187648 | − | 0.108339i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −550.151 | + | 952.889i | −0.0252061 | + | 0.0436582i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4401.53 | + | 28820.4i | 0.200891 | + | 1.31540i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2476.01i | 0.112577i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2066.21 | − | 1192.93i | −0.0935865 | − | 0.0540322i | 0.452476 | − | 0.891776i | \(-0.350541\pi\) |
−0.546063 | + | 0.837744i | \(0.683874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 560.596 | + | 11087.7i | 0.0252950 | + | 0.500293i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36015.4 | − | 22183.7i | −1.61891 | − | 0.997169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1856.58 | + | 3215.70i | 0.0831390 | + | 0.144001i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5852.81 | − | 3785.54i | 0.261104 | − | 0.168880i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13183.5 | 0.585927 | 0.292964 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292964 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9346.49 | 0.413836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23841.1 | + | 2417.01i | −1.05167 | + | 0.106618i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3085.56 | + | 5344.35i | 0.135600 | + | 0.234867i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9102.59 | + | 4915.39i | −0.398539 | + | 0.215211i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14984.5 | − | 757.621i | 0.653630 | − | 0.0330477i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26645.9 | + | 15384.0i | 1.15800 | + | 0.668570i | 0.950823 | − | 0.309734i | \(-0.100240\pi\) |
0.207174 | + | 0.978304i | \(0.433574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42776.4i | − | 1.85214i | −0.377357 | − | 0.926068i | \(-0.623167\pi\) | ||
0.377357 | − | 0.926068i | \(-0.376833\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27094.5 | − | 13868.3i | −1.16881 | − | 0.598256i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5190.41 | − | 8990.05i | 0.223082 | − | 0.386390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3138.92 | − | 1812.26i | 0.134415 | − | 0.0776045i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2447.06 | − | 1660.39i | 0.104405 | − | 0.0708411i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36141.5 | + | 20866.3i | −1.53635 | + | 0.887014i | −0.537305 | + | 0.843388i | \(0.680558\pi\) |
−0.999048 | + | 0.0436263i | \(0.986109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7822.35 | + | 13548.7i | −0.331312 | + | 0.573850i | −0.982769 | − | 0.184836i | \(-0.940825\pi\) |
0.651457 | + | 0.758685i | \(0.274158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11357.1 | + | 5813.13i | 0.479278 | + | 0.245318i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24395.1i | 1.02576i | 0.858461 | + | 0.512879i | \(0.171421\pi\) | ||||
−0.858461 | + | 0.512879i | \(0.828579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32786.9 | + | 18929.5i | 1.37362 | + | 0.793062i | 0.991382 | − | 0.131000i | \(-0.0418188\pi\) |
0.382242 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14546.4 | + | 735.470i | −0.607231 | + | 0.0307018i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39752.2 | − | 2265.62i | −1.65346 | − | 0.0942367i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5794.92 | + | 10037.1i | 0.240169 | + | 0.415986i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18527.2 | − | 7229.68i | −0.765105 | − | 0.298559i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40533.9 | −1.66792 | −0.833960 | − | 0.551826i | \(-0.813931\pi\) | ||||
−0.833960 | + | 0.551826i | \(0.813931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18794.8 | −0.770625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20356.0 | − | 13166.1i | 0.831670 | − | 0.537917i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4854.48 | + | 8408.21i | 0.197632 | + | 0.342309i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14485.1 | − | 412.444i | −0.587619 | − | 0.0167317i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1410.20 | + | 27891.6i | 0.0570060 | + | 1.12749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32281.4 | + | 18637.6i | 1.30034 | + | 0.750752i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38466.5i | − | 1.54404i | −0.635598 | − | 0.772021i | \(-0.719246\pi\) | ||
0.635598 | − | 0.772021i | \(-0.280754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 911.431 | − | 657.075i | 0.0364565 | − | 0.0262824i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13054.1 | − | 22610.3i | 0.520326 | − | 0.901230i | −0.479395 | − | 0.877599i | \(-0.659144\pi\) |
0.999721 | − | 0.0236312i | \(-0.00752274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21033.3 | + | 12143.6i | −0.835445 | + | 0.482345i | −0.855713 | − | 0.517450i | \(-0.826881\pi\) |
0.0202681 | + | 0.999795i | \(0.493548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48911.5 | − | 1078.73i | 1.93600 | − | 0.0426982i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32475.9 | − | 18750.0i | 1.28099 | − | 0.739579i | 0.303960 | − | 0.952685i | \(-0.401691\pi\) |
0.977029 | + | 0.213106i | \(0.0683579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2250.06 | − | 3897.21i | 0.0884441 | − | 0.153190i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20271.8 | + | 39605.1i | −0.794079 | + | 1.55139i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24996.9i | 0.975791i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 526.386 | + | 303.909i | 0.0204775 | + | 0.0118227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5406.79 | + | 2431.17i | 0.209613 | + | 0.0942528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10024.8 | − | 16275.3i | 0.387313 | − | 0.628806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7420.70 | + | 12853.0i | 0.285723 | + | 0.494887i | 0.972784 | − | 0.231713i | \(-0.0744329\pi\) |
−0.687061 | + | 0.726600i | \(0.741100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3674.61 | − | 5681.30i | −0.141003 | − | 0.218004i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30469.3 | −1.16520 | −0.582598 | − | 0.812760i | \(-0.697964\pi\) | ||||
−0.582598 | + | 0.812760i | \(0.697964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6758.53 | 0.257580 | 0.128790 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128790 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2592.22 | + | 4007.82i | 0.0984593 | + | 0.152227i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17666.5 | + | 30599.4i | 0.668754 | + | 1.15832i | 0.978253 | + | 0.207416i | \(0.0665053\pi\) |
−0.309499 | + | 0.950900i | \(0.600161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15098.5 | − | 24512.6i | 0.569616 | − | 0.924776i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3426.74 | + | 16726.8i | 0.128844 | + | 0.628922i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −646.160 | − | 373.061i | −0.0242138 | − | 0.0139798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13473.5i | − | 0.503207i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1741.55 | − | 3402.47i | 0.0648257 | − | 0.126650i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14728.9 | − | 25511.3i | 0.546427 | − | 0.946439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30030.5 | − | 17338.1i | 1.11039 | − | 0.641084i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37630.6 | − | 829.935i | 1.38679 | − | 0.0305853i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3764.01 | − | 2173.15i | 0.138254 | − | 0.0798210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10481.2 | + | 18153.9i | −0.383706 | + | 0.664598i | −0.991589 | − | 0.129429i | \(-0.958686\pi\) |
0.607883 | + | 0.794027i | \(0.292019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15553.8 | + | 21574.7i | 0.567533 | + | 0.787226i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5419.65i | − | 0.197103i | −0.995132 | − | 0.0985516i | \(-0.968579\pi\) | ||
0.995132 | − | 0.0985516i | \(-0.0314209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5485.41 | − | 3167.00i | −0.198840 | − | 0.114800i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 739.815 | + | 14632.3i | 0.0267296 | + | 0.528667i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38782.8 | + | 1104.29i | 1.39664 | + | 0.0397677i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12706.3 | + | 22007.9i | 0.456084 | + | 0.789961i | 0.998750 | − | 0.0499878i | \(-0.0159183\pi\) |
−0.542666 | + | 0.839949i | \(0.682585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2813.71 | + | 1819.89i | −0.100668 | + | 0.0651110i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −277.823 | −0.00990754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31416.1 | −1.11671 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3499.52 | + | 34518.9i | 0.123991 | + | 1.22303i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 276.744 | + | 479.335i | 0.00977360 | + | 0.0169284i | 0.870871 | − | 0.491512i | \(-0.163556\pi\) |
−0.861097 | + | 0.508440i | \(0.830222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2657.80 | + | 1743.32i | 0.0935615 | + | 0.0613696i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6937.57 | − | 350.765i | 0.243436 | − | 0.0123082i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10573.7 | − | 6104.72i | −0.369836 | − | 0.213525i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18956.6i | − | 0.660923i | −0.943819 | − | 0.330462i | \(-0.892796\pi\) | ||
0.943819 | − | 0.330462i | \(-0.107204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7796.09 | + | 3990.42i | 0.270943 | + | 0.138682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16542.7 | − | 28652.8i | 0.573089 | − | 0.992619i | −0.423157 | − | 0.906056i | \(-0.639078\pi\) |
0.996246 | − | 0.0865632i | \(-0.0275884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54763.2 | − | 31617.5i | 1.89113 | − | 1.09184i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11579.9 | − | 1432.57i | 0.398620 | − | 0.0493137i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11619.3 | − | 6708.40i | 0.398708 | − | 0.230194i | −0.287219 | − | 0.957865i | \(-0.592731\pi\) |
0.685926 | + | 0.727671i | \(0.259397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −779.096 | + | 1349.43i | −0.0266497 | + | 0.0461586i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13939.8 | − | 7135.05i | −0.475319 | − | 0.243291i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36353.5i | − | 1.23568i | −0.786303 | − | 0.617841i | \(-0.788007\pi\) | ||
0.786303 | − | 0.617841i | \(-0.211993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1599.64 | − | 923.554i | −0.0542023 | − | 0.0312937i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25258.1 | + | 1277.06i | −0.853165 | + | 0.0431362i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9954.29 | − | 5375.31i | 0.335183 | − | 0.180999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4848.13 | − | 8397.21i | −0.162738 | − | 0.281871i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −498.131 | − | 4913.52i | −0.0166688 | − | 0.164419i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3666.29 | −0.122303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3453.28 | −0.114840 | −0.0574198 | − | 0.998350i | \(-0.518287\pi\) | ||||
−0.0574198 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4693.48 | − | 3035.70i | 0.155600 | − | 0.100641i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25320.0 | − | 43855.6i | −0.836826 | − | 1.44943i | −0.892535 | − | 0.450978i | \(-0.851075\pi\) |
0.0557091 | − | 0.998447i | \(-0.482258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28488.4 | + | 17547.4i | 0.938638 | + | 0.578154i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 162.670 | + | 3217.35i | 0.00534320 | + | 0.105680i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26914.6 | − | 15539.1i | −0.881344 | − | 0.508844i | −0.0102426 | − | 0.999948i | \(-0.503260\pi\) |
−0.871101 | + | 0.491103i | \(0.836594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20787.2i | − | 0.678613i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9204.42 | + | 12767.5i | 0.299566 | + | 0.415529i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20154.8 | − | 34909.1i | 0.653956 | − | 1.13268i | −0.328199 | − | 0.944609i | \(-0.606442\pi\) |
0.982155 | − | 0.188076i | \(-0.0602251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2463.05 | − | 1422.04i | 0.0796744 | − | 0.0460001i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4021.16 | − | 6623.17i | −0.129681 | − | 0.213594i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42132.6 | − | 24325.3i | 1.35464 | − | 0.782102i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2007.28 | − | 3476.71i | 0.0643425 | − | 0.111444i | −0.832060 | − | 0.554686i | \(-0.812838\pi\) |
0.896402 | + | 0.443242i | \(0.146172\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1867.79 | + | 3649.11i | −0.0596904 | + | 0.116617i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15372.0i | 0.489773i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36113.8 | + | 20850.3i | 1.14718 | + | 0.662323i | 0.948198 | − | 0.317680i | \(-0.102904\pi\) |
0.198980 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26277.7 | − | 32819.5i | −0.832221 | − | 1.03940i |
(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 | 336.4.bc.e.17.3 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.17.1 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.17.3 | yes | 16 | ||
7.5 | odd | 6 | inner | 336.4.bc.e.257.1 | 16 | ||
12.11 | even | 2 | 42.4.f.a.17.8 | yes | 16 | ||
21.5 | even | 6 | inner | 336.4.bc.e.257.3 | 16 | ||
28.3 | even | 6 | 294.4.d.a.293.3 | 16 | |||
28.11 | odd | 6 | 294.4.d.a.293.6 | 16 | |||
28.19 | even | 6 | 42.4.f.a.5.8 | yes | 16 | ||
28.23 | odd | 6 | 294.4.f.a.215.5 | 16 | |||
28.27 | even | 2 | 294.4.f.a.227.2 | 16 | |||
84.11 | even | 6 | 294.4.d.a.293.11 | 16 | |||
84.23 | even | 6 | 294.4.f.a.215.2 | 16 | |||
84.47 | odd | 6 | 42.4.f.a.5.3 | ✓ | 16 | ||
84.59 | odd | 6 | 294.4.d.a.293.14 | 16 | |||
84.83 | odd | 2 | 294.4.f.a.227.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.3 | ✓ | 16 | 84.47 | odd | 6 | ||
42.4.f.a.5.8 | yes | 16 | 28.19 | even | 6 | ||
42.4.f.a.17.3 | yes | 16 | 4.3 | odd | 2 | ||
42.4.f.a.17.8 | yes | 16 | 12.11 | even | 2 | ||
294.4.d.a.293.3 | 16 | 28.3 | even | 6 | |||
294.4.d.a.293.6 | 16 | 28.11 | odd | 6 | |||
294.4.d.a.293.11 | 16 | 84.11 | even | 6 | |||
294.4.d.a.293.14 | 16 | 84.59 | odd | 6 | |||
294.4.f.a.215.2 | 16 | 84.23 | even | 6 | |||
294.4.f.a.215.5 | 16 | 28.23 | odd | 6 | |||
294.4.f.a.227.2 | 16 | 28.27 | even | 2 | |||
294.4.f.a.227.5 | 16 | 84.83 | odd | 2 | |||
336.4.bc.e.17.1 | 16 | 3.2 | odd | 2 | inner | ||
336.4.bc.e.17.3 | 16 | 1.1 | even | 1 | trivial | ||
336.4.bc.e.257.1 | 16 | 7.5 | odd | 6 | inner | ||
336.4.bc.e.257.3 | 16 | 21.5 | even | 6 | inner |