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 | 257.7 | ||
Root | \(2.41164 + 1.78437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.e.17.7 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 4.17709 | + | 3.09062i | 0.803881 | + | 0.594790i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27911 | + | 7.41164i | −0.382736 | + | 0.662917i | −0.991452 | − | 0.130470i | \(-0.958351\pi\) |
0.608717 | + | 0.793388i | \(0.291685\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.41772 | − | 17.3728i | 0.346524 | − | 0.938041i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.89612 | + | 25.8196i | 0.292449 | + | 0.956281i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 53.8609 | − | 31.0966i | 1.47633 | − | 0.852361i | 0.476690 | − | 0.879072i | \(-0.341837\pi\) |
0.999643 | + | 0.0267105i | \(0.00850323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 61.7061i | − | 1.31648i | −0.752810 | − | 0.658238i | \(-0.771302\pi\) | ||
0.752810 | − | 0.658238i | \(-0.228698\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −40.7808 | + | 17.7340i | −0.701971 | + | 0.305259i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.3365 | + | 23.0995i | 0.190270 | + | 0.329557i | 0.945340 | − | 0.326088i | \(-0.105730\pi\) |
−0.755070 | + | 0.655644i | \(0.772397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.6213 | + | 33.8450i | 0.707824 | + | 0.408662i | 0.810255 | − | 0.586078i | \(-0.199329\pi\) |
−0.102431 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 80.5000 | − | 52.7328i | 0.836502 | − | 0.547964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 45.8287 | + | 26.4592i | 0.415476 | + | 0.239875i | 0.693140 | − | 0.720803i | \(-0.256227\pi\) |
−0.277664 | + | 0.960678i | \(0.589560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.8784 | + | 44.8227i | 0.207027 | + | 0.358581i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −46.8158 | + | 132.255i | −0.333693 | + | 0.942682i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 55.1116i | 0.352895i | 0.984310 | + | 0.176448i | \(0.0564606\pi\) | ||||
−0.984310 | + | 0.176448i | \(0.943539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 134.080 | − | 77.4108i | 0.776819 | − | 0.448497i | −0.0584827 | − | 0.998288i | \(-0.518626\pi\) |
0.835302 | + | 0.549792i | \(0.185293\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 321.089 | + | 36.5704i | 1.69377 | + | 0.192912i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 101.299 | + | 121.906i | 0.489217 | + | 0.588739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −157.940 | + | 273.560i | −0.701761 | + | 1.21549i | 0.266087 | + | 0.963949i | \(0.414269\pi\) |
−0.967848 | + | 0.251536i | \(0.919064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 190.710 | − | 257.752i | 0.783027 | − | 1.05829i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.211 | 0.800719 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −351.939 | −1.24815 | −0.624073 | − | 0.781366i | \(-0.714523\pi\) | ||||
−0.624073 | + | 0.781366i | \(0.714523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −225.154 | − | 51.9617i | −0.745866 | − | 0.172133i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −115.819 | + | 200.605i | −0.359446 | + | 0.622579i | −0.987868 | − | 0.155294i | \(-0.950368\pi\) |
0.628422 | + | 0.777872i | \(0.283701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −260.626 | − | 222.987i | −0.759842 | − | 0.650108i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.6841 | + | 137.707i | −0.0430630 | + | 0.378095i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 232.890 | − | 134.459i | 0.603583 | − | 0.348479i | −0.166867 | − | 0.985979i | \(-0.553365\pi\) |
0.770450 | + | 0.637500i | \(0.220032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 532.263i | 1.30492i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 140.264 | + | 322.550i | 0.325938 | + | 0.749522i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.14155 | − | 15.8336i | −0.0201717 | − | 0.0349384i | 0.855763 | − | 0.517367i | \(-0.173088\pi\) |
−0.875935 | + | 0.482429i | \(0.839755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.3320 | − | 41.7609i | −0.151822 | − | 0.0876547i | 0.422164 | − | 0.906519i | \(-0.361271\pi\) |
−0.573987 | + | 0.818865i | \(0.694604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 499.233 | + | 28.5253i | 0.998372 | + | 0.0570452i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 457.344 | + | 264.047i | 0.872715 | + | 0.503862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 64.7354 | + | 112.125i | 0.118040 | + | 0.204451i | 0.918991 | − | 0.394279i | \(-0.129006\pi\) |
−0.800951 | + | 0.598730i | \(0.795672\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 109.655 | + | 252.162i | 0.191318 | + | 0.439952i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 804.537i | − | 1.34480i | −0.740186 | − | 0.672402i | \(-0.765263\pi\) | ||
0.740186 | − | 0.672402i | \(-0.234737\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 370.377 | − | 213.837i | 0.593826 | − | 0.342846i | −0.172783 | − | 0.984960i | \(-0.555276\pi\) |
0.766609 | + | 0.642114i | \(0.221943\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −30.4336 | + | 267.208i | −0.0468556 | + | 0.411394i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −194.570 | − | 1135.28i | −0.287965 | − | 1.68022i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 609.284 | − | 1055.31i | 0.867718 | − | 1.50293i | 0.00339594 | − | 0.999994i | \(-0.498919\pi\) |
0.864322 | − | 0.502938i | \(-0.167748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −604.302 | + | 407.749i | −0.828947 | + | 0.559327i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1371.18 | 1.81333 | 0.906663 | − | 0.421855i | \(-0.138621\pi\) | ||||
0.906663 | + | 0.421855i | \(0.138621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −228.274 | −0.291292 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −170.329 | + | 230.206i | −0.209899 | + | 0.283686i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −386.840 | + | 670.026i | −0.460729 | + | 0.798007i | −0.998997 | − | 0.0447669i | \(-0.985745\pi\) |
0.538268 | + | 0.842774i | \(0.319079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1072.01 | − | 396.012i | −1.23491 | − | 0.456191i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 799.309 | + | 91.0371i | 0.891231 | + | 0.101506i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −501.694 | + | 289.653i | −0.541819 | + | 0.312819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 848.768i | 0.888447i | 0.895916 | + | 0.444223i | \(0.146520\pi\) | ||||
−0.895916 | + | 0.444223i | \(0.853480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1228.19 | + | 1145.12i | 1.24685 | + | 1.16252i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 512.647 | + | 887.931i | 0.505053 | + | 0.874777i | 0.999983 | + | 0.00584430i | \(0.00186031\pi\) |
−0.494930 | + | 0.868933i | \(0.664806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −278.306 | − | 160.680i | −0.266236 | − | 0.153711i | 0.360940 | − | 0.932589i | \(-0.382456\pi\) |
−0.627176 | + | 0.778878i | \(0.715789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 46.3683 | + | 822.287i | 0.0430960 | + | 0.764257i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −117.848 | − | 68.0393i | −0.106474 | − | 0.0614730i | 0.445817 | − | 0.895124i | \(-0.352913\pi\) |
−0.552292 | + | 0.833651i | \(0.686246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −703.079 | − | 1217.77i | −0.617823 | − | 1.07010i | −0.989882 | − | 0.141892i | \(-0.954681\pi\) |
0.372059 | − | 0.928209i | \(-0.378652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1505.20 | + | 654.551i | −1.28709 | + | 0.559705i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 467.285i | − | 0.389013i | −0.980901 | − | 0.194506i | \(-0.937690\pi\) | ||
0.980901 | − | 0.194506i | \(-0.0623105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −392.212 | + | 226.444i | −0.318035 | + | 0.183617i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1593.23 | − | 487.239i | 1.25892 | − | 0.385002i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 486.893 | − | 83.4460i | 0.375071 | − | 0.0642814i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1268.50 | − | 2197.10i | 0.953039 | − | 1.65071i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 878.071 | + | 649.684i | 0.643683 | + | 0.476260i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1512.72 | −1.08242 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −259.166 | −0.181081 | −0.0905404 | − | 0.995893i | \(-0.528859\pi\) | ||||
−0.0905404 | + | 0.995893i | \(0.528859\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1470.08 | − | 1087.71i | −1.00336 | − | 0.742385i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1323.92 | + | 2293.10i | −0.882991 | + | 1.52938i | −0.0349910 | + | 0.999388i | \(0.511140\pi\) |
−0.848000 | + | 0.529997i | \(0.822193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 964.197 | − | 801.206i | 0.628620 | − | 0.522356i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −779.894 | − | 912.914i | −0.497204 | − | 0.582008i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −405.314 | + | 234.008i | −0.252761 | + | 0.145932i | −0.621028 | − | 0.783788i | \(-0.713285\pi\) |
0.368267 | + | 0.929720i | \(0.379951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2923.27i | − | 1.78380i | −0.452229 | − | 0.891902i | \(-0.649371\pi\) | ||
0.452229 | − | 0.891902i | \(-0.350629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1103.78 | + | 479.990i | −0.659256 | + | 0.286684i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1918.85 | − | 3323.54i | −1.12211 | − | 1.94356i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −408.467 | − | 235.829i | −0.233940 | − | 0.135066i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −399.489 | − | 1736.93i | −0.224145 | − | 0.974556i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1570.24 | − | 906.580i | −0.863351 | − | 0.498456i | 0.00178220 | − | 0.999998i | \(-0.499433\pi\) |
−0.865133 | + | 0.501543i | \(0.832766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −827.154 | − | 1432.67i | −0.445780 | − | 0.772114i | 0.552326 | − | 0.833628i | \(-0.313740\pi\) |
−0.998106 | + | 0.0615140i | \(0.980407\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −491.114 | + | 526.740i | −0.259505 | + | 0.278330i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1325.00i | 0.686622i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1200.29 | + | 692.988i | −0.610151 | + | 0.352271i | −0.773024 | − | 0.634376i | \(-0.781257\pi\) |
0.162874 | + | 0.986647i | \(0.447924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1388.36 | + | 158.127i | 0.692481 | + | 0.0788699i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 753.785 | − | 626.363i | 0.368985 | − | 0.306611i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −576.540 | + | 998.597i | −0.277044 | + | 0.479854i | −0.970649 | − | 0.240502i | \(-0.922688\pi\) |
0.693605 | + | 0.720356i | \(0.256021\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1645.02 | + | 2223.31i | −0.776151 | + | 1.04900i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 303.672 | 0.140712 | 0.0703559 | − | 0.997522i | \(-0.477586\pi\) | ||||
0.0703559 | + | 0.997522i | \(0.477586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1610.64 | −0.733110 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −410.984 | + | 1780.82i | −0.183794 | + | 0.796391i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1308.97 | + | 2267.21i | −0.575256 | + | 0.996373i | 0.420758 | + | 0.907173i | \(0.361764\pi\) |
−0.996014 | + | 0.0891996i | \(0.971569\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 944.774 | − | 161.920i | 0.408104 | − | 0.0699428i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7507 | − | 94.3915i | 0.00456537 | − | 0.0400842i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2395.77 | + | 1383.20i | −1.00038 | + | 0.577569i | −0.908361 | − | 0.418188i | \(-0.862665\pi\) |
−0.0920191 | + | 0.995757i | \(0.529332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 539.608i | − | 0.221595i | −0.993843 | − | 0.110798i | \(-0.964659\pi\) | ||
0.993843 | − | 0.110798i | \(-0.0353405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −173.070 | − | 397.990i | −0.0699109 | − | 0.160766i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1351.68 | − | 2341.19i | −0.537178 | − | 0.930419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1436.63 | + | 829.441i | 0.561802 | + | 0.324357i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1997.18 | + | 1662.09i | 0.768642 | + | 0.639679i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2764.63 | − | 1596.16i | −1.04734 | − | 0.604680i | −0.125434 | − | 0.992102i | \(-0.540032\pi\) |
−0.921903 | + | 0.387422i | \(0.873366\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −718.685 | − | 1244.80i | −0.268042 | − | 0.464262i | 0.700314 | − | 0.713835i | \(-0.253043\pi\) |
−0.968356 | + | 0.249573i | \(0.919710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1094.29 | + | 2516.42i | 0.401867 | + | 0.924128i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2346.26i | 0.848548i | 0.905534 | + | 0.424274i | \(0.139471\pi\) | ||||
−0.905534 | + | 0.424274i | \(0.860529\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1586.15 | − | 915.766i | 0.565022 | − | 0.326216i | −0.190137 | − | 0.981758i | \(-0.560893\pi\) |
0.755159 | + | 0.655542i | \(0.227560\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −76.1304 | + | 668.428i | −0.0267155 | + | 0.234564i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 957.440 | + | 353.690i | 0.331030 | + | 0.122287i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −899.518 | + | 1558.01i | −0.306464 | + | 0.530811i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −321.297 | + | 1392.20i | −0.107882 | + | 0.467463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4209.86 | 1.39331 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4291.48 | −1.40018 | −0.700090 | − | 0.714055i | \(-0.746857\pi\) | ||||
−0.700090 | + | 0.714055i | \(0.746857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2486.52 | − | 3360.62i | 0.799876 | − | 1.08106i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1505.99 | − | 2608.45i | 0.477709 | − | 0.827417i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −484.356 | − | 2826.13i | −0.151522 | − | 0.884103i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2207.98 | + | 251.478i | 0.681287 | + | 0.0775949i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1425.38 | − | 822.945i | 0.433853 | − | 0.250485i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1170.88i | 0.351604i | 0.984426 | + | 0.175802i | \(0.0562519\pi\) | ||||
−0.984426 | + | 0.175802i | \(0.943748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −952.964 | + | 1022.09i | −0.282360 | + | 0.302843i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1063.49 | + | 1842.02i | 0.310954 | + | 0.538588i | 0.978569 | − | 0.205919i | \(-0.0660182\pi\) |
−0.667615 | + | 0.744506i | \(0.732685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1124.19 | − | 649.049i | −0.324403 | − | 0.187294i | 0.328950 | − | 0.944347i | \(-0.393305\pi\) |
−0.653354 | + | 0.757053i | \(0.726638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2695.99 | − | 5343.51i | 0.767892 | − | 1.52198i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3641.17 | − | 2102.23i | −1.02378 | − | 0.591081i | −0.108585 | − | 0.994087i | \(-0.534632\pi\) |
−0.915197 | + | 0.403007i | \(0.867965\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −991.207 | − | 1716.82i | −0.275145 | − | 0.476566i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5806.59 | − | 2525.06i | 1.59147 | − | 0.692068i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3816.77i | 1.03300i | 0.856288 | + | 0.516498i | \(0.172765\pi\) | ||||
−0.856288 | + | 0.516498i | \(0.827235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1417.67 | + | 818.491i | −0.378921 | + | 0.218770i | −0.677349 | − | 0.735662i | \(-0.736871\pi\) |
0.298428 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3784.42 | − | 164.465i | −0.999057 | − | 0.0434174i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2767.95 | − | 977.479i | 0.721786 | − | 0.254893i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2088.44 | − | 3617.29i | 0.537994 | − | 0.931833i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5727.52 | + | 4237.78i | 1.45770 | + | 1.07855i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5269.47 | 1.32512 | 0.662562 | − | 0.749007i | \(-0.269469\pi\) | ||||
0.662562 | + | 0.749007i | \(0.269469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3291.16 | 0.817841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −953.521 | − | 705.509i | −0.234164 | − | 0.173257i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −570.595 | + | 988.300i | −0.138493 | + | 0.239877i | −0.926926 | − | 0.375243i | \(-0.877559\pi\) |
0.788433 | + | 0.615120i | \(0.210893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3738.88 | + | 4499.48i | 0.896998 | + | 1.07948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1422.96 | + | 435.168i | −0.337467 | + | 0.103204i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1978.91 | − | 1142.53i | 0.463974 | − | 0.267875i | −0.249740 | − | 0.968313i | \(-0.580345\pi\) |
0.713714 | + | 0.700438i | \(0.247012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2301.46i | 0.533501i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3686.66 | + | 1603.18i | −0.845018 | + | 0.367465i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 937.191 | + | 1623.26i | 0.212422 | + | 0.367926i | 0.952472 | − | 0.304626i | \(-0.0985315\pi\) |
−0.740050 | + | 0.672552i | \(0.765198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2841.71 | − | 1640.66i | −0.636980 | − | 0.367760i | 0.146471 | − | 0.989215i | \(-0.453209\pi\) |
−0.783450 | + | 0.621455i | \(0.786542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3253.94 | − | 4967.34i | −0.721382 | − | 1.10123i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2787.66 | + | 1609.46i | 0.611282 | + | 0.352924i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 265.374 | + | 459.642i | 0.0575625 | + | 0.0997011i | 0.893371 | − | 0.449320i | \(-0.148334\pi\) |
−0.835808 | + | 0.549022i | \(0.815000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3057.42 | + | 2850.63i | 0.656069 | + | 0.611695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5216.62i | 1.10747i | 0.832695 | + | 0.553733i | \(0.186797\pi\) | ||||
−0.832695 | + | 0.553733i | \(0.813203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 907.832 | − | 524.137i | 0.190689 | − | 0.110094i | −0.401616 | − | 0.915808i | \(-0.631551\pi\) |
0.592305 | + | 0.805714i | \(0.298218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2990.83 | − | 340.640i | −0.621619 | − | 0.0707991i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1349.08 | − | 3651.95i | 0.277469 | − | 0.751108i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2100.77 | − | 3638.65i | 0.427595 | − | 0.740616i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2623.22 | + | 3545.38i | −0.528439 | + | 0.714205i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6408.45 | 1.27777 | 0.638884 | − | 0.769303i | \(-0.279397\pi\) | ||||
0.638884 | + | 0.769303i | \(0.279397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 156.471 | 0.0308817 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1591.13 | + | 8579.16i | 0.310864 | + | 1.67614i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1632.69 | − | 2827.91i | 0.315790 | − | 0.546964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2258.65 | + | 6114.16i | −0.432512 | + | 1.17081i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −602.886 | + | 5293.37i | −0.114307 | + | 1.00362i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 619.034 | − | 357.399i | 0.116216 | − | 0.0670971i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3717.93i | 0.691184i | 0.938385 | + | 0.345592i | \(0.112322\pi\) | ||||
−0.938385 | + | 0.345592i | \(0.887678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −665.907 | − | 1531.31i | −0.122596 | − | 0.281920i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −202.816 | − | 351.287i | −0.0369795 | − | 0.0640503i | 0.846943 | − | 0.531683i | \(-0.178440\pi\) |
−0.883923 | + | 0.467633i | \(0.845107\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2640.01 | − | 1524.21i | −0.476748 | − | 0.275251i | 0.242312 | − | 0.970198i | \(-0.422094\pi\) |
−0.719060 | + | 0.694948i | \(0.755427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2347.69 | + | 3578.07i | −0.419929 | + | 0.640005i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5714.50 | − | 3299.27i | −1.01249 | − | 0.584559i | −0.100568 | − | 0.994930i | \(-0.532066\pi\) |
−0.911919 | + | 0.410371i | \(0.865399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1713.78 | + | 2968.36i | 0.300794 | + | 0.520991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −281.976 | − | 648.428i | −0.0490292 | − | 0.112747i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1805.50i | 0.311024i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2765.83 | − | 1596.85i | 0.472064 | − | 0.272546i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 826.838 | − | 7259.67i | 0.139830 | − | 1.22771i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2741.76 | + | 3299.52i | 0.459448 | + | 0.552914i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −184.027 | + | 318.744i | −0.0305591 | + | 0.0529298i | −0.880900 | − | 0.473302i | \(-0.843062\pi\) |
0.850341 | + | 0.526231i | \(0.176395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8310.31 | − | 1917.88i | −1.36757 | − | 0.315613i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1108.04 | −0.180712 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6514.00 | 1.05294 | 0.526469 | − | 0.850194i | \(-0.323516\pi\) | ||||
0.526469 | + | 0.850194i | \(0.323516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1444.20 | − | 1951.89i | 0.231381 | − | 0.312720i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4814.43 | − | 8338.83i | 0.764562 | − | 1.32426i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5546.52 | + | 3096.72i | −0.873131 | + | 0.487485i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2338.16 | − | 266.304i | −0.364876 | − | 0.0415574i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2098.92 | − | 1211.81i | 0.324715 | − | 0.187474i | −0.328777 | − | 0.944407i | \(-0.606637\pi\) |
0.653492 | + | 0.756933i | \(0.273303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10490.9i | 1.60907i | 0.593903 | + | 0.804536i | \(0.297586\pi\) | ||||
−0.593903 | + | 0.804536i | \(0.702414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8160.92 | + | 2888.82i | 1.24102 | + | 0.439298i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4005.42 | − | 6937.60i | −0.603930 | − | 1.04604i | −0.992220 | − | 0.124500i | \(-0.960267\pi\) |
0.388290 | − | 0.921537i | \(-0.373066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5962.94 | + | 3442.71i | 0.891494 | + | 0.514704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2291.69 | + | 1156.24i | 0.339746 | + | 0.171414i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9906.07 | − | 5719.27i | −1.45633 | − | 0.840813i | −0.457502 | − | 0.889209i | \(-0.651256\pi\) |
−0.998828 | + | 0.0483961i | \(0.984589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1138.53 | − | 1971.99i | −0.165990 | − | 0.287504i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12089.0 | − | 5257.03i | 1.74796 | − | 0.760118i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3660.13i | 0.524877i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1259.42 | − | 727.126i | 0.179131 | − | 0.103421i | −0.407753 | − | 0.913092i | \(-0.633688\pi\) |
0.586884 | + | 0.809671i | \(0.300354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1659.85 | + | 5427.57i | 0.234170 | + | 0.765713i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −841.305 | − | 4908.87i | −0.117731 | − | 0.686942i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3990.41 | + | 6911.59i | −0.553929 | + | 0.959433i | 0.444057 | + | 0.895999i | \(0.353539\pi\) |
−0.997986 | + | 0.0634346i | \(0.979795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6318.78 | − | 4675.26i | −0.870135 | − | 0.643811i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3400.72 | 0.464578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5818.85 | −0.788639 | −0.394320 | − | 0.918973i | \(-0.629020\pi\) | ||||
−0.394320 | + | 0.918973i | \(0.629020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1082.56 | − | 800.983i | −0.145567 | − | 0.107705i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −618.611 | + | 1071.47i | −0.0825314 | + | 0.142949i | −0.904337 | − | 0.426820i | \(-0.859634\pi\) |
0.821805 | + | 0.569769i | \(0.192967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9246.88 | + | 3415.91i | 1.22406 | + | 0.452185i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2778.96 | − | 9086.93i | −0.365019 | − | 1.19358i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2602.51 | + | 1502.56i | −0.339209 | + | 0.195842i | −0.659922 | − | 0.751334i | \(-0.729411\pi\) |
0.320713 | + | 0.947176i | \(0.396077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1411.50i | 0.182564i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12617.3 | + | 5486.75i | −1.61948 | + | 0.704249i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5214.39 | + | 9031.58i | 0.664213 | + | 1.15045i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5552.29 | − | 3205.62i | −0.701918 | − | 0.405253i | 0.106143 | − | 0.994351i | \(-0.466150\pi\) |
−0.808061 | + | 0.589098i | \(0.799483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6503.76 | − | 366.743i | 0.816028 | − | 0.0460153i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2993.97 | + | 1728.57i | 0.372848 | + | 0.215264i | 0.674702 | − | 0.738090i | \(-0.264272\pi\) |
−0.301854 | + | 0.953354i | \(0.597606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4776.72 | − | 8273.52i | −0.590435 | − | 1.02266i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −436.213 | − | 6223.68i | −0.0535200 | − | 0.763598i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19645.6i | 2.39261i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13285.6 | − | 7670.42i | 1.60618 | − | 0.927329i | 0.615968 | − | 0.787772i | \(-0.288765\pi\) |
0.990214 | − | 0.139558i | \(-0.0445681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2416.26 | − | 275.199i | −0.289989 | − | 0.0330282i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −333.742 | + | 57.1983i | −0.0397636 | + | 0.00681487i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5867.42 | + | 10162.7i | −0.694024 | + | 1.20209i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9034.73 | − | 12210.8i | 1.06099 | − | 1.43397i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2968.51 | −0.346112 | −0.173056 | − | 0.984912i | \(-0.555364\pi\) | ||||
−0.173056 | + | 0.984912i | \(0.555364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8733.67 | −1.01105 | −0.505526 | − | 0.862811i | \(-0.668702\pi\) | ||||
−0.505526 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6094.05 | − | 1406.40i | −0.700480 | − | 0.161659i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −690.255 | + | 1195.56i | −0.0787819 | + | 0.136454i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1189.71 | + | 988.597i | −0.134834 | + | 0.112041i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2256.61 | − | 19813.2i | 0.253964 | − | 2.22981i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −51.3171 | + | 29.6279i | −0.00573517 | + | 0.00331120i | −0.502865 | − | 0.864365i | \(-0.667721\pi\) |
0.497130 | + | 0.867676i | \(0.334387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3034.66i | 0.336805i | 0.985718 | + | 0.168403i | \(0.0538609\pi\) | ||||
−0.985718 | + | 0.168403i | \(0.946139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −977.347 | − | 2247.49i | −0.107725 | − | 0.247722i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1791.03 | + | 3102.15i | 0.196056 | + | 0.339578i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2155.72 | + | 1244.61i | 0.234367 | + | 0.135312i | 0.612585 | − | 0.790405i | \(-0.290130\pi\) |
−0.378218 | + | 0.925716i | \(0.623463\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3699.50 | − | 8489.98i | 0.399471 | − | 0.916746i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13052.4 | − | 7535.83i | −1.39986 | − | 0.808212i | −0.405487 | − | 0.914101i | \(-0.632898\pi\) |
−0.994378 | + | 0.105889i | \(0.966231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3310.66 | − | 5734.23i | −0.352675 | − | 0.610851i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3757.15 | − | 8639.89i | −0.397555 | − | 0.914212i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5352.96i | 0.562632i | 0.959615 | + | 0.281316i | \(0.0907709\pi\) | ||||
−0.959615 | + | 0.281316i | \(0.909229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11322.2 | − | 6536.86i | 1.18213 | − | 0.682502i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 972.754 | − | 8540.82i | 0.100892 | − | 0.885834i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7522.33 | − | 6250.74i | 0.775060 | − | 0.644042i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1063.05 | + | 1841.25i | −0.108812 | + | 0.188468i | −0.915289 | − | 0.402797i | \(-0.868038\pi\) |
0.806477 | + | 0.591265i | \(0.201371\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3679.38 | + | 682.394i | −0.374159 | + | 0.0693931i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 987.346 | 0.0997512 | 0.0498756 | − | 0.998755i | \(-0.484118\pi\) | ||||
0.0498756 | + | 0.998755i | \(0.484118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17023.3 | 1.70872 | 0.854362 | − | 0.519678i | \(-0.173948\pi\) | ||||
0.854362 | + | 0.519678i | \(0.173948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4095.07 | + | 5534.64i | −0.408396 | + | 0.551963i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6858.57 | + | 11879.4i | −0.679608 | + | 1.17712i | 0.295491 | + | 0.955345i | \(0.404517\pi\) |
−0.975099 | + | 0.221770i | \(0.928817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2363.37 | − | 405.046i | 0.232687 | − | 0.0398791i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7155.48 | − | 814.971i | −0.700015 | − | 0.0797280i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18955.8 | + | 10944.1i | −1.84268 | + | 1.06387i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3503.42i | 0.338416i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5310.61 | + | 4951.42i | 0.509761 | + | 0.475283i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −974.841 | − | 1688.47i | −0.0929887 | − | 0.161061i | 0.815779 | − | 0.578364i | \(-0.196309\pi\) |
−0.908767 | + | 0.417303i | \(0.862975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16880.3 | + | 9745.85i | 1.60016 | + | 0.923851i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5084.48 | − | 286.711i | 0.478989 | − | 0.0270099i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6290.76 | − | 3631.97i | −0.588967 | − | 0.340040i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1269.48 | + | 2198.80i | 0.118122 | + | 0.204594i | 0.919023 | − | 0.394203i | \(-0.128979\pi\) |
−0.800901 | + | 0.598796i | \(0.795646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5494.55 | + | 2389.36i | −0.508123 | + | 0.220962i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17119.1i | − | 1.57347i | −0.617289 | − | 0.786737i | \(-0.711769\pi\) | ||
0.617289 | − | 0.786737i | \(-0.288231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1273.05 | + | 734.997i | −0.116299 | + | 0.0671452i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13742.8 | + | 4202.82i | −1.24787 | + | 0.381621i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13977.0 | − | 5163.29i | −1.26148 | − | 0.466007i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 454.423 | − | 787.084i | 0.0407671 | − | 0.0706107i | −0.844922 | − | 0.534890i | \(-0.820353\pi\) |
0.885689 | + | 0.464279i | \(0.153687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1268.47 | + | 938.536i | 0.113116 | + | 0.0836940i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13477.7 | 1.19471 | 0.597356 | − | 0.801976i | \(-0.296218\pi\) | ||||
0.597356 | + | 0.801976i | \(0.296218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8774.71 | −0.773207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6727.80 | − | 4977.89i | −0.589333 | − | 0.436047i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7065.77 | + | 12238.3i | −0.615294 | + | 1.06572i | 0.375039 | + | 0.927009i | \(0.377629\pi\) |
−0.990333 | + | 0.138711i | \(0.955704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1337.97 | − | 7806.81i | −0.115828 | − | 0.675837i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7220.56 | + | 6168.46i | −0.621434 | + | 0.530885i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2381.80 | − | 1375.14i | 0.203796 | − | 0.117662i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14406.3i | 1.22551i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12474.8 | + | 5424.78i | −1.05507 | + | 0.458808i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5532.79 | − | 9583.08i | −0.465251 | − | 0.805839i | 0.533961 | − | 0.845509i | \(-0.320703\pi\) |
−0.999213 | + | 0.0396697i | \(0.987369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5211.30 | + | 3008.74i | 0.435706 | + | 0.251555i | 0.701774 | − | 0.712399i | \(-0.252391\pi\) |
−0.266069 | + | 0.963954i | \(0.585725\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4446.83 | + | 2243.58i | 0.369668 | + | 0.186511i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3576.31 | + | 2064.78i | 0.295610 | + | 0.170671i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4683.32 | − | 8111.75i | −0.384920 | − | 0.666701i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 336.635 | − | 361.055i | 0.0275117 | − | 0.0295075i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12971.3i | − | 1.05413i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1008.57 | − | 582.296i | 0.0815030 | − | 0.0470558i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14282.3 | − | 1626.67i | −1.14772 | − | 0.130719i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20971.7 | − | 3905.69i | −1.67591 | − | 0.312115i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3477.08 | + | 6022.47i | −0.276324 | + | 0.478607i | −0.970468 | − | 0.241229i | \(-0.922450\pi\) |
0.694145 | + | 0.719836i | \(0.255783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1667.72 | − | 2253.99i | 0.131803 | − | 0.178136i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12034.2 | 0.945852 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14101.3 | −1.10224 | −0.551122 | − | 0.834424i | \(-0.685800\pi\) | ||||
−0.551122 | + | 0.834424i | \(0.685800\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 507.107 | − | 2197.33i | 0.0394222 | − | 0.170819i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1865.25 | + | 3230.71i | −0.144215 | + | 0.249788i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14423.4 | − | 17357.6i | −1.10913 | − | 1.33476i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1589.61 | − | 13956.9i | 0.121577 | − | 1.06745i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7314.84 | + | 4223.22i | −0.556445 | + | 0.321263i | −0.751717 | − | 0.659486i | \(-0.770774\pi\) |
0.195273 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21716.8i | 1.64315i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3437.46 | + | 7904.74i | 0.258698 | + | 0.594899i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10951.1 | − | 18967.8i | −0.819774 | − | 1.41989i | −0.905849 | − | 0.423601i | \(-0.860766\pi\) |
0.0860755 | − | 0.996289i | \(-0.472567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3463.35 | + | 1999.56i | 0.257883 | + | 0.148889i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3205.49 | + | 13115.2i | 0.237422 | + | 0.971407i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8724.86 | + | 5037.30i | 0.642821 | + | 0.371133i | 0.785700 | − | 0.618607i | \(-0.212303\pi\) |
−0.142879 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9133.47 | + | 15819.6i | 0.669394 | + | 1.15942i | 0.978074 | + | 0.208258i | \(0.0667795\pi\) |
−0.308680 | + | 0.951166i | \(0.599887\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6614.97 | − | 15211.7i | −0.482276 | − | 1.10904i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2738.89i | 0.198642i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3379.83 | − | 1951.34i | 0.243855 | − | 0.140789i | −0.373093 | − | 0.927794i | \(-0.621703\pi\) |
0.616947 | + | 0.787005i | \(0.288369\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 845.191 | − | 7420.81i | 0.0606648 | − | 0.532640i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8799.82 | − | 23821.1i | 0.628361 | − | 1.70097i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8362.44 | − | 14484.2i | 0.594060 | − | 1.02894i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3206.35 | + | 13893.4i | −0.226609 | + | 0.981915i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3318.05 | 0.233306 | 0.116653 | − | 0.993173i | \(-0.462783\pi\) | ||||
0.116653 | + | 0.993173i | \(0.462783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10479.9 | 0.733135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7251.39 | + | 9800.53i | −0.504708 | + | 0.682132i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12126.5 | − | 21003.6i | 0.839754 | − | 1.45450i | −0.0503470 | − | 0.998732i | \(-0.516033\pi\) |
0.890101 | − | 0.455764i | \(-0.150634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1465.00 | + | 3965.75i | −0.100940 | + | 0.273244i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9455.78 | + | 1076.96i | 0.648240 | + | 0.0738311i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9619.77 | + | 5553.97i | −0.656182 | + | 0.378847i | −0.790821 | − | 0.612048i | \(-0.790346\pi\) |
0.134639 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13367.3i | − | 0.907258i | −0.891191 | − | 0.453629i | \(-0.850129\pi\) | ||
0.891191 | − | 0.453629i | \(-0.149871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2383.86 | + | 2556.79i | −0.160992 | + | 0.172671i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10856.1 | + | 18803.3i | 0.729524 | + | 1.26357i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10180.8 | − | 5877.90i | −0.680769 | − | 0.393042i | 0.119376 | − | 0.992849i | \(-0.461911\pi\) |
−0.800145 | + | 0.599807i | \(0.795244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2906.19 | + | 4436.48i | 0.193374 | + | 0.295198i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12378.5 | + | 7146.75i | 0.819610 | + | 0.473202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11860.0 | + | 20542.2i | 0.781439 | + | 1.35349i | 0.931103 | + | 0.364755i | \(0.118847\pi\) |
−0.149664 | + | 0.988737i | \(0.547819\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8572.59 | + | 3727.88i | −0.562082 | + | 0.244427i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9294.78i | 0.606473i | 0.952915 | + | 0.303237i | \(0.0980672\pi\) | ||||
−0.952915 | + | 0.303237i | \(0.901933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11638.1 | − | 6719.28i | 0.755696 | − | 0.436301i | −0.0720523 | − | 0.997401i | \(-0.522955\pi\) |
0.827748 | + | 0.561100i | \(0.189622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5644.86 | + | 4822.35i | −0.364767 | + | 0.311617i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9157.58 | + | 11020.5i | 0.588909 | + | 0.708712i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3238.32 | − | 5608.94i | 0.207253 | − | 0.358972i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17584.9 | + | 13011.1i | 1.12006 | + | 0.828728i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8425.47 | −0.534095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11635.5 | −0.734076 | −0.367038 | − | 0.930206i | \(-0.619628\pi\) | ||||
−0.367038 | + | 0.930206i | \(0.619628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17925.9 | − | 13263.4i | −1.12558 | − | 0.832813i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1109.00 | − | 1920.84i | 0.0693060 | − | 0.120042i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13759.7 | + | 16082.2i | −0.855851 | + | 1.00031i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20772.8 | − | 6352.73i | 1.28601 | − | 0.393286i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21346.3 | − | 12324.3i | 1.31533 | − | 0.759409i | 0.332360 | − | 0.943153i | \(-0.392155\pi\) |
0.982974 | + | 0.183744i | \(0.0588218\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5268.28i | − | 0.323111i | −0.986864 | − | 0.161556i | \(-0.948349\pi\) | ||
0.986864 | − | 0.161556i | \(-0.0516511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14352.4 | − | 6241.28i | 0.876161 | − | 0.381008i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9235.29 | + | 15996.0i | 0.561169 | + | 0.971974i | 0.997395 | + | 0.0721365i | \(0.0229817\pi\) |
−0.436225 | + | 0.899837i | \(0.643685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −984.743 | − | 568.542i | −0.0595602 | − | 0.0343871i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6711.31 | − | 13302.0i | 0.404050 | − | 0.800837i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11414.2 | + | 6589.99i | 0.684030 | + | 0.394925i | 0.801372 | − | 0.598166i | \(-0.204104\pi\) |
−0.117341 | + | 0.993092i | \(0.537437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11330.4 | − | 19624.9i | −0.675904 | − | 1.17070i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8445.72 | + | 7874.49i | 0.501521 | + | 0.467600i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10701.0i | − | 0.632549i | −0.948668 | − | 0.316275i | \(-0.897568\pi\) | ||
0.948668 | − | 0.316275i | \(-0.102432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11215.0 | + | 6475.01i | −0.659931 | + | 0.381011i | −0.792251 | − | 0.610196i | \(-0.791091\pi\) |
0.132320 | + | 0.991207i | \(0.457758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8497.36 | + | 967.804i | 0.497753 | + | 0.0566914i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1812.35 | + | 10574.7i | 0.105684 | + | 0.616647i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1458.21 | + | 2525.69i | −0.0846508 | + | 0.146619i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3618.74 | + | 4890.86i | −0.209131 | + | 0.282648i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5194.48 | −0.298854 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3025.28 | 0.173278 | 0.0866389 | − | 0.996240i | \(-0.472387\pi\) | ||||
0.0866389 | + | 0.996240i | \(0.472387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7139.52 | + | 1324.13i | −0.407111 | + | 0.0755047i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1368.23 | + | 2369.84i | −0.0776739 | + | 0.134535i | −0.902246 | − | 0.431222i | \(-0.858083\pi\) |
0.824572 | + | 0.565757i | \(0.191416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14745.4 | + | 5447.15i | 0.833399 | + | 0.307868i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1250.69 | + | 10981.2i | −0.0703770 | + | 0.617913i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7977.54 | + | 4605.84i | −0.446928 | + | 0.258034i | −0.706532 | − | 0.707681i | \(-0.749741\pi\) |
0.259604 | + | 0.965715i | \(0.416408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4005.39i | − | 0.223413i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2689.86 | − | 6185.57i | −0.149381 | − | 0.343514i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8296.95 | − | 14370.7i | −0.458764 | − | 0.794603i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2228.30 | − | 1286.51i | −0.122675 | − | 0.0708264i | 0.437407 | − | 0.899264i | \(-0.355897\pi\) |
−0.560082 | + | 0.828437i | \(0.689230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27776.1 | − | 13988.0i | 1.52255 | − | 0.766755i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21666.2 | + | 12509.0i | 1.18251 | + | 0.682725i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2803.49 | + | 4855.79i | 0.152353 | + | 0.263882i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8712.29 | − | 20034.7i | −0.471430 | − | 1.08409i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18596.9i | 1.00199i | 0.865450 | + | 0.500996i | \(0.167033\pi\) | ||||
−0.865450 | + | 0.500996i | \(0.832967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18517.3 | + | 10691.0i | −0.993446 | + | 0.573566i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1165.68 | − | 10234.8i | 0.0622726 | − | 0.546756i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18715.8 | − | 3207.61i | 0.995590 | − | 0.170629i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12000.1 | − | 20784.8i | 0.635647 | − | 1.10097i | −0.350731 | − | 0.936476i | \(-0.614067\pi\) |
0.986378 | − | 0.164496i | \(-0.0525998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32058.7 | + | 7398.59i | 1.69099 | + | 0.390252i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8192.92 | 0.430333 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32843.9 | 1.71789 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11796.2 | + | 15943.0i | −0.614416 | + | 0.830406i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8305.93 | − | 14386.3i | 0.430819 | − | 0.746200i | −0.566125 | − | 0.824319i | \(-0.691558\pi\) |
0.996944 | + | 0.0781192i | \(0.0248915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4577.54 | + | 3803.74i | −0.236445 | + | 0.196475i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8451.37 | − | 962.565i | −0.434730 | − | 0.0495134i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2470.25 | + | 1426.20i | −0.126542 | + | 0.0730589i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31798.3i | 1.62219i | 0.584912 | + | 0.811097i | \(0.301129\pi\) | ||||
−0.584912 | + | 0.811097i | \(0.698871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15299.6 | − | 12383.2i | −0.777299 | − | 0.629132i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4693.65 | − | 8129.64i | −0.237484 | − | 0.411334i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29412.4 | + | 16981.3i | 1.48209 | + | 0.855686i | 0.999794 | − | 0.0203212i | \(-0.00646890\pi\) |
0.482298 | + | 0.876007i | \(0.339802\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14583.0 | + | 4471.66i | 0.731838 | + | 0.224408i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6973.40 | + | 4026.10i | 0.348533 | + | 0.201225i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14447.3 | − | 25023.5i | −0.719153 | − | 1.24561i | −0.961336 | − | 0.275379i | \(-0.911197\pi\) |
0.242183 | − | 0.970231i | \(-0.422137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19903.3 | − | 8655.16i | 0.986729 | − | 0.429089i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8565.28i | 0.422920i | 0.977387 | + | 0.211460i | \(0.0678218\pi\) | ||||
−0.977387 | + | 0.211460i | \(0.932178\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13438.5 | − | 7758.72i | 0.660870 | − | 0.381553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10827.0 | + | 35403.2i | 0.530306 | + | 1.73405i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1938.34 | + | 1610.68i | −0.0945601 | + | 0.0785754i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7333.06 | + | 12701.2i | −0.356308 | + | 0.617144i | −0.987341 | − | 0.158613i | \(-0.949298\pi\) |
0.631033 | + | 0.775756i | \(0.282631\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22011.0 | + | 16285.9i | 1.06524 | + | 0.788171i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14157.9 | 0.682464 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19962.2 | −0.958439 | −0.479220 | − | 0.877695i | \(-0.659080\pi\) | ||||
−0.479220 | + | 0.877695i | \(0.659080\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13747.5 | + | 10171.7i | 0.657447 | + | 0.486444i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19166.3 | + | 33197.0i | −0.912980 | + | 1.58133i | −0.103147 | + | 0.994666i | \(0.532891\pi\) |
−0.809833 | + | 0.586661i | \(0.800442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25668.2 | + | 4399.13i | −1.21789 | + | 0.208728i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1802.48 | − | 5893.94i | −0.0851880 | − | 0.278557i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −977.032 | + | 564.089i | −0.0459955 | + | 0.0265555i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1797.33i | 0.0842826i | 0.999112 | + | 0.0421413i | \(0.0134180\pi\) | ||||
−0.999112 | + | 0.0421413i | \(0.986582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5437.89 | + | 2364.72i | −0.254009 | + | 0.110458i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5866.15 | + | 10160.5i | 0.272951 | + | 0.472765i | 0.969616 | − | 0.244632i | \(-0.0786671\pi\) |
−0.696665 | + | 0.717396i | \(0.745334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6939.52 | + | 4006.53i | 0.321645 | + | 0.185702i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1711.43 | + | 30350.2i | 0.0790182 | + | 1.40130i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12322.9 | + | 7114.61i | 0.566768 | + | 0.327224i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25018.4 | − | 43333.1i | −1.14626 | − | 1.98538i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7288.76 | − | 2580.09i | −0.332668 | − | 0.117759i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 11861.5i | − | 0.539306i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13313.4 | + | 7686.49i | −0.603013 | + | 0.348150i | −0.770226 | − | 0.637771i | \(-0.779857\pi\) |
0.167213 | + | 0.985921i | \(0.446523\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11797.2 | + | 1343.64i | 0.532309 | + | 0.0606272i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8118.02 | − | 2998.90i | −0.364910 | − | 0.134802i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2576.90 | + | 4463.32i | −0.115395 | + | 0.199871i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7112.95 | + | 9613.42i | −0.317321 | + | 0.428871i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33773.5 | −1.50103 | −0.750513 | − | 0.660856i | \(-0.770193\pi\) | ||||
−0.750513 | + | 0.660856i | \(0.770193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6178.50 | −0.273567 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20354.3 | − | 4697.43i | −0.897859 | − | 0.207211i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13299.2 | − | 23034.9i | 0.584457 | − | 1.01231i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1416.85 | + | 8267.06i | 0.0620340 | + | 0.361957i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1102.16 | + | 9677.01i | −0.0480766 | + | 0.422115i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30723.2 | − | 17738.1i | 1.33519 | − | 0.770874i | 0.349103 | − | 0.937084i | \(-0.386486\pi\) |
0.986090 | + | 0.166210i | \(0.0531530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31038.0i | − | 1.34389i | −0.740603 | − | 0.671943i | \(-0.765460\pi\) | ||
0.740603 | − | 0.671943i | \(-0.234540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6799.40 | − | 15635.8i | −0.293315 | − | 0.674505i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4934.16 | − | 8546.22i | −0.212069 | − | 0.367314i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20631.1 | − | 11911.4i | −0.883467 | − | 0.510070i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1760.19 | − | 30805.7i | 0.0750987 | − | 1.31433i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4221.32 | − | 2437.18i | −0.179446 | − | 0.103603i | 0.407586 | − | 0.913167i | \(-0.366371\pi\) |
−0.587032 | + | 0.809563i | \(0.699704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11051.1 | − | 19141.0i | −0.468064 | − | 0.810710i | 0.531270 | − | 0.847202i | \(-0.321715\pi\) |
−0.999334 | + | 0.0364924i | \(0.988382\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6670.09 | + | 15338.5i | 0.281482 | + | 0.647293i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18204.1i | − | 0.765439i | −0.923865 | − | 0.382719i | \(-0.874988\pi\) | ||
0.923865 | − | 0.382719i | \(-0.125012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27346.1 | + | 15788.3i | −1.14568 | + | 0.661458i | −0.947830 | − | 0.318775i | \(-0.896729\pi\) |
−0.197848 | + | 0.980233i | \(0.563395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −312.087 | + | 2740.14i | −0.0130279 | + | 0.114385i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1675.05 | − | 8994.21i | 0.0696724 | − | 0.374107i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1299.45 | + | 2250.71i | −0.0538554 | + | 0.0932803i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3960.91 | + | 21356.7i | 0.163571 | + | 0.881953i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19529.4 | −0.803612 | −0.401806 | − | 0.915725i | \(-0.631617\pi\) | ||||
−0.401806 | + | 0.915725i | \(0.631617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21351.7 | 0.875465 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16122.6 | + | 21790.3i | −0.658709 | + | 0.890270i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6892.13 | − | 11937.5i | 0.280587 | − | 0.485992i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30028.8 | − | 36137.6i | −1.21818 | − | 1.46600i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5412.01 | + | 616.399i | 0.218775 | + | 0.0249172i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14476.3 | + | 8357.92i | −0.583129 | + | 0.336670i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20178.9i | 0.809979i | 0.914321 | + | 0.404989i | \(0.132725\pi\) | ||||
−0.914321 | + | 0.404989i | \(0.867275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11440.2 | − | 10666.4i | −0.457597 | − | 0.426647i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7058.30 | + | 12225.3i | 0.281338 | + | 0.487292i | 0.971715 | − | 0.236158i | \(-0.0758884\pi\) |
−0.690376 | + | 0.723450i | \(0.742555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16476.7 | + | 9512.82i | 0.654456 | + | 0.377850i | 0.790161 | − | 0.612899i | \(-0.209997\pi\) |
−0.135706 | + | 0.990749i | \(0.543330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16922.0 | − | 11085.0i | 0.669803 | − | 0.438766i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9357.24 | − | 5402.41i | −0.369090 | − | 0.213094i | 0.303971 | − | 0.952681i | \(-0.401687\pi\) |
−0.673061 | + | 0.739587i | \(0.735021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11202.5 | − | 19403.3i | −0.440342 | − | 0.762694i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20020.8 | − | 8706.25i | 0.784247 | − | 0.341038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 75786.5i | − | 2.95844i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6918.79 | − | 3994.57i | 0.269155 | − | 0.155397i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21914.8 | + | 6701.98i | −0.849605 | + | 0.259825i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9708.24 | + | 26280.2i | −0.375084 | + | 1.01535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1795.88 | + | 3110.55i | −0.0691476 | + | 0.119767i | −0.898526 | − | 0.438920i | \(-0.855361\pi\) |
0.829379 | + | 0.558687i | \(0.188695\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26768.7 | + | 19806.1i | 1.02717 | + | 0.760004i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47633.6 | −1.82158 | −0.910792 | − | 0.412865i | \(-0.864528\pi\) | ||||
−0.910792 | + | 0.412865i | \(0.864528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42383.1 | 1.61530 | 0.807648 | − | 0.589665i | \(-0.200740\pi\) | ||||
0.807648 | + | 0.589665i | \(0.200740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 653.593 | + | 483.592i | 0.0248252 | + | 0.0183681i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8634.30 | + | 14955.0i | −0.326845 | + | 0.566112i | −0.981884 | − | 0.189483i | \(-0.939319\pi\) |
0.655039 | + | 0.755595i | \(0.272652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1663.25 | + | 4502.43i | −0.0627488 | + | 0.169861i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19868.6 | + | 40753.5i | −0.747053 | + | 1.53232i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13578.9 | + | 7839.81i | −0.508849 | + | 0.293784i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 23675.4i | − | 0.884225i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15559.9 | − | 6766.39i | 0.579186 | − | 0.251865i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4266.23 | + | 7389.33i | 0.158272 | + | 0.274136i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6211.89 | + | 3586.44i | 0.229687 | + | 0.132610i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28331.1 | + | 18558.8i | −1.04408 | + | 0.683939i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3999.38 | + | 2309.04i | 0.146899 | + | 0.0848124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2270.97 | + | 3933.44i | 0.0831383 | + | 0.144000i | 0.904596 | − | 0.426269i | \(-0.140172\pi\) |
−0.821458 | + | 0.570269i | \(0.806839\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18878.1 | + | 20247.6i | −0.688831 | + | 0.738800i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11585.4i | 0.421342i | 0.977557 | + | 0.210671i | \(0.0675648\pi\) | ||||
−0.977557 | + | 0.210671i | \(0.932435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73852.7 | − | 42638.9i | 2.67707 | − | 1.54561i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3690.34 | + | 420.310i | 0.133332 | + | 0.0151858i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31341.0 | + | 37716.7i | 1.12865 | + | 1.35825i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2666.17 | + | 4617.93i | −0.0957004 | + | 0.165758i | −0.909901 | − | 0.414826i | \(-0.863842\pi\) |
0.814200 | + | 0.580584i | \(0.197176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11490.7 | + | 15530.1i | −0.411109 | + | 0.555629i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49644.9 | −1.77040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16348.9 | −0.581134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1951.15 | − | 8454.49i | 0.0691308 | − | 0.299549i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4965.04 | + | 8599.69i | −0.175347 | + | 0.303710i | −0.940281 | − | 0.340398i | \(-0.889438\pi\) |
0.764934 | + | 0.644108i | \(0.222771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7731.23 | − | 21892.7i | −0.272160 | − | 0.770680i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 238.516 | − | 2094.18i | 0.00836942 | − | 0.0734839i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12295.0 | + | 7098.54i | −0.430044 | + | 0.248286i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28533.5i | − | 0.994821i | −0.867515 | − | 0.497411i | \(-0.834284\pi\) | ||
0.867515 | − | 0.497411i | \(-0.165716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6316.79 | − | 14526.0i | −0.219532 | − | 0.504834i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2850.92 | + | 4937.95i | 0.0987646 | + | 0.171065i | 0.911174 | − | 0.412023i | \(-0.135178\pi\) |
−0.812409 | + | 0.583088i | \(0.801844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9633.71 | + | 5562.03i | 0.332680 | + | 0.192073i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20865.0 | + | 7690.09i | −0.718241 | + | 0.264718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14842.2 | + | 8569.15i | 0.509299 | + | 0.294044i | 0.732546 | − | 0.680718i | \(-0.238332\pi\) |
−0.223246 | + | 0.974762i | \(0.571665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13195.0 | − | 22854.5i | −0.451348 | − | 0.781758i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13673.2 | − | 31442.7i | −0.466228 | − | 1.07213i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48616.8i | 1.65252i | 0.563287 | + | 0.826261i | \(0.309536\pi\) | ||||
−0.563287 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23660.3 | − | 13660.3i | 0.801706 | − | 0.462865i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2015.45 | + | 17695.7i | −0.0680776 | + | 0.597724i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1464.18 | + | 8543.21i | 0.0493021 | + | 0.287669i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2910.62 | + | 5041.35i | −0.0977015 | + | 0.169224i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 826.208 | − | 3580.02i | 0.0276471 | − | 0.119797i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12301.3 | 0.410356 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14811.1 | 0.492547 | 0.246273 | − | 0.969200i | \(-0.420794\pi\) | ||||
0.246273 | + | 0.969200i | \(0.420794\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5580.12 | + | 7541.73i | −0.184994 | + | 0.250026i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1364.94 | − | 2364.14i | 0.0451111 | − | 0.0781348i | −0.842588 | − | 0.538558i | \(-0.818969\pi\) |
0.887699 | + | 0.460424i | \(0.152302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50785.3 | − | 18760.7i | −1.67328 | − | 0.618131i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16488.4 | + | 1877.94i | 0.541591 | + | 0.0616843i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49381.0 | − | 28510.2i | 1.61703 | − | 0.933593i | 0.629348 | − | 0.777123i | \(-0.283322\pi\) |
0.987683 | − | 0.156470i | \(-0.0500114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48117.6i | 1.57083i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25890.7 | − | 27768.9i | 0.842636 | − | 0.903763i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26554.1 | − | 45993.0i | −0.861591 | − | 1.49232i | −0.870393 | − | 0.492358i | \(-0.836135\pi\) |
0.00880172 | − | 0.999961i | \(-0.497198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17389.6 | − | 10039.9i | −0.562517 | − | 0.324770i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1255.01 | + | 22256.1i | 0.0404736 | + | 0.717752i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16128.9 | − | 9312.03i | −0.518574 | − | 0.299399i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9561.35 | − | 16560.7i | −0.306485 | − | 0.530847i | 0.671106 | − | 0.741361i | \(-0.265820\pi\) |
−0.977591 | + | 0.210514i | \(0.932486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1753.82 | + | 762.665i | −0.0560480 | + | 0.0243731i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15674.7i | 0.499417i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18152.4 | − | 10480.3i | 0.576623 | − | 0.332914i | −0.183167 | − | 0.983082i | \(-0.558635\pi\) |
0.759790 | + | 0.650168i | \(0.225302\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28785.5 | − | 33695.2i | −0.911644 | − | 1.06714i |
(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.257.7 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.257.4 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.5.1 | ✓ | 16 | ||
7.3 | odd | 6 | inner | 336.4.bc.e.17.4 | 16 | ||
12.11 | even | 2 | 42.4.f.a.5.7 | yes | 16 | ||
21.17 | even | 6 | inner | 336.4.bc.e.17.7 | 16 | ||
28.3 | even | 6 | 42.4.f.a.17.7 | yes | 16 | ||
28.11 | odd | 6 | 294.4.f.a.227.6 | 16 | |||
28.19 | even | 6 | 294.4.d.a.293.9 | 16 | |||
28.23 | odd | 6 | 294.4.d.a.293.16 | 16 | |||
28.27 | even | 2 | 294.4.f.a.215.4 | 16 | |||
84.11 | even | 6 | 294.4.f.a.227.4 | 16 | |||
84.23 | even | 6 | 294.4.d.a.293.1 | 16 | |||
84.47 | odd | 6 | 294.4.d.a.293.8 | 16 | |||
84.59 | odd | 6 | 42.4.f.a.17.1 | yes | 16 | ||
84.83 | odd | 2 | 294.4.f.a.215.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.1 | ✓ | 16 | 4.3 | odd | 2 | ||
42.4.f.a.5.7 | yes | 16 | 12.11 | even | 2 | ||
42.4.f.a.17.1 | yes | 16 | 84.59 | odd | 6 | ||
42.4.f.a.17.7 | yes | 16 | 28.3 | even | 6 | ||
294.4.d.a.293.1 | 16 | 84.23 | even | 6 | |||
294.4.d.a.293.8 | 16 | 84.47 | odd | 6 | |||
294.4.d.a.293.9 | 16 | 28.19 | even | 6 | |||
294.4.d.a.293.16 | 16 | 28.23 | odd | 6 | |||
294.4.f.a.215.4 | 16 | 28.27 | even | 2 | |||
294.4.f.a.215.6 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.227.4 | 16 | 84.11 | even | 6 | |||
294.4.f.a.227.6 | 16 | 28.11 | odd | 6 | |||
336.4.bc.e.17.4 | 16 | 7.3 | odd | 6 | inner | ||
336.4.bc.e.17.7 | 16 | 21.17 | even | 6 | inner | ||
336.4.bc.e.257.4 | 16 | 3.2 | odd | 2 | inner | ||
336.4.bc.e.257.7 | 16 | 1.1 | even | 1 | trivial |