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 | 257.4 | ||
Root | \(0.339489 + 2.98073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.e.17.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.588012 | − | 5.16277i | −0.113163 | − | 0.993576i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.27911 | − | 7.41164i | 0.382736 | − | 0.662917i | −0.608717 | − | 0.793388i | \(-0.708315\pi\) |
0.991452 | + | 0.130470i | \(0.0416487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.41772 | − | 17.3728i | 0.346524 | − | 0.938041i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.3085 | + | 6.07155i | −0.974388 | + | 0.224872i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −53.8609 | + | 31.0966i | −1.47633 | + | 0.852361i | −0.999643 | − | 0.0267105i | \(-0.991497\pi\) |
−0.476690 | + | 0.879072i | \(0.658163\pi\) | |||||||
\(12\) | 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 | 0.755070 | − | 0.655644i | \(-0.227603\pi\) |
−0.945340 | + | 0.326088i | \(0.894270\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | −93.4654 | − | 22.9178i | −0.971229 | − | 0.238147i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −45.8287 | − | 26.4592i | −0.415476 | − | 0.239875i | 0.277664 | − | 0.960678i | \(-0.410440\pi\) |
−0.693140 | + | 0.720803i | \(0.743773\pi\) | |||||||
\(24\) | 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 | \(-0.943539\pi\) | ||
0.984310 | − | 0.176448i | \(-0.0564606\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 192.216 | + | 259.786i | 1.01395 | + | 1.37039i | ||||
\(34\) | 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 | ||||||||
\(39\) | −318.575 | + | 36.2840i | −1.30802 | + | 0.148976i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −210.211 | −0.800719 | −0.400360 | − | 0.916358i | \(-0.631115\pi\) | ||||
−0.400360 | + | 0.916358i | \(0.631115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −351.939 | −1.24815 | −0.624073 | − | 0.781366i | \(-0.714523\pi\) | ||||
−0.624073 | + | 0.781366i | \(0.714523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −67.5768 | + | 220.970i | −0.223861 | + | 0.732006i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 115.819 | − | 200.605i | 0.359446 | − | 0.622579i | −0.628422 | − | 0.777872i | \(-0.716299\pi\) |
0.987868 | + | 0.155294i | \(0.0496324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −260.626 | − | 222.987i | −0.759842 | − | 0.650108i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −111.416 | + | 82.4363i | −0.305908 | + | 0.226341i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −232.890 | + | 134.459i | −0.603583 | + | 0.348479i | −0.770450 | − | 0.637500i | \(-0.779968\pi\) |
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(54\) | 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 | 0.875935 | − | 0.482429i | \(-0.160245\pi\) |
−0.855763 | + | 0.517367i | \(0.826912\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −63.3607 | + | 496.017i | −0.126710 | + | 0.991940i | ||||
\(64\) | 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 | \(0.234737\pi\) | ||||
−0.740186 | + | 0.672402i | \(0.765263\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 216.192 | − | 159.961i | 0.332850 | − | 0.246275i | ||||
\(76\) | 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 | ||||||||
\(81\) | 655.273 | − | 319.467i | 0.898865 | − | 0.438226i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1371.18 | −1.81333 | −0.906663 | − | 0.421855i | \(-0.861379\pi\) | ||||
−0.906663 | + | 0.421855i | \(0.861379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −228.274 | −0.291292 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −284.529 | + | 32.4063i | −0.350628 | + | 0.0399347i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 386.840 | − | 670.026i | 0.460729 | − | 0.798007i | −0.538268 | − | 0.842774i | \(-0.680921\pi\) |
0.998997 | + | 0.0447669i | \(0.0142545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1072.01 | − | 396.012i | −1.23491 | − | 0.456191i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −478.495 | − | 646.704i | −0.533523 | − | 0.721076i | ||||
\(94\) | 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 | \(-0.998140\pi\) |
0.494930 | − | 0.868933i | \(-0.335194\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | −569.808 | + | 594.664i | −0.529595 | + | 0.552698i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 117.848 | + | 68.0393i | 0.106474 | + | 0.0614730i | 0.552292 | − | 0.833651i | \(-0.313754\pi\) |
−0.445817 | + | 0.895124i | \(0.647087\pi\) | |||||||
\(108\) | 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 | \(0.0623105\pi\) | ||||
−0.980901 | + | 0.194506i | \(0.937690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −392.212 | + | 226.444i | −0.318035 | + | 0.183617i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 374.652 | + | 1623.39i | 0.296039 | + | 1.28276i | ||||
\(118\) | 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 | ||||||||
\(123\) | 123.607 | + | 1085.27i | 0.0906119 | + | 0.795576i | ||||
\(124\) | 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 | ||||||||
\(129\) | 206.945 | + | 1816.98i | 0.141244 | + | 1.24013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1323.92 | − | 2293.10i | 0.882991 | − | 1.52938i | 0.0349910 | − | 0.999388i | \(-0.488860\pi\) |
0.848000 | − | 0.529997i | \(-0.177807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 964.197 | − | 801.206i | 0.628620 | − | 0.522356i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1180.55 | + | 218.951i | 0.752636 | + | 0.139587i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 405.314 | − | 234.008i | 0.252761 | − | 0.145932i | −0.368267 | − | 0.929720i | \(-0.620049\pi\) |
0.621028 | + | 0.783788i | \(0.286715\pi\) | |||||||
\(138\) | 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 | ||||||||
\(147\) | −997.980 | + | 1476.67i | −0.559946 | + | 0.828529i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1570.24 | + | 906.580i | 0.863351 | + | 0.498456i | 0.865133 | − | 0.501543i | \(-0.167234\pi\) |
−0.00178220 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(150\) | 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 | ||||||||
\(159\) | 831.125 | + | 1123.30i | 0.414544 | + | 0.560271i | ||||
\(160\) | 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 | ||||||||
\(165\) | 2747.96 | − | 312.977i | 1.29653 | − | 0.147668i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −303.672 | −0.140712 | −0.0703559 | − | 0.997522i | \(-0.522414\pi\) | ||||
−0.0703559 | + | 0.997522i | \(0.522414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1610.64 | −0.733110 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1747.73 | − | 534.489i | −0.781592 | − | 0.239026i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1308.97 | − | 2267.21i | 0.575256 | − | 0.996373i | −0.420758 | − | 0.907173i | \(-0.638236\pi\) |
0.996014 | − | 0.0891996i | \(-0.0284309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 944.774 | − | 161.920i | 0.408104 | − | 0.0699428i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 76.3701 | − | 56.5061i | 0.0324312 | − | 0.0239958i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2395.77 | − | 1383.20i | 1.00038 | − | 0.577569i | 0.0920191 | − | 0.995757i | \(-0.470668\pi\) |
0.908361 | + | 0.418188i | \(0.137335\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | 2598.08 | + | 35.4533i | 0.999907 | + | 0.0136447i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2764.63 | + | 1596.16i | 1.04734 | + | 0.604680i | 0.921903 | − | 0.387422i | \(-0.126634\pi\) |
0.125434 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(192\) | 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 | \(-0.860529\pi\) | ||
0.905534 | − | 0.424274i | \(-0.139471\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 540.810 | − | 400.145i | 0.189780 | − | 0.140418i | ||||
\(202\) | 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 | ||||||||
\(207\) | 1366.33 | + | 417.850i | 0.458776 | + | 0.140302i | ||||
\(208\) | 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 | ||||||||
\(213\) | 4153.65 | − | 473.078i | 1.33616 | − | 0.152182i | ||||
\(214\) | 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 | ||||||||
\(219\) | −1321.78 | − | 1786.43i | −0.407842 | − | 0.551214i | ||||
\(220\) | 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 | 0.667615 | − | 0.744506i | \(-0.267315\pi\) |
−0.978569 | + | 0.205919i | \(0.933982\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 5746.79 | − | 1672.08i | 1.63684 | − | 0.476254i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3641.17 | + | 2102.23i | 1.02378 | + | 0.591081i | 0.915197 | − | 0.403007i | \(-0.132035\pi\) |
0.108585 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(234\) | 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 | \(-0.827235\pi\) | ||
0.856288 | − | 0.516498i | \(-0.172765\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −2034.64 | − | 3195.17i | −0.537129 | − | 0.843500i | ||||
\(244\) | 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 | ||||||||
\(249\) | 806.268 | + | 7079.07i | 0.205202 | + | 1.80168i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5269.47 | −1.32512 | −0.662562 | − | 0.749007i | \(-0.730531\pi\) | ||||
−0.662562 | + | 0.749007i | \(0.730531\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3291.16 | 0.817841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 134.228 | + | 1178.53i | 0.0329635 | + | 0.289421i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 570.595 | − | 988.300i | 0.138493 | − | 0.239877i | −0.788433 | − | 0.615120i | \(-0.789107\pi\) |
0.926926 | + | 0.375243i | \(0.122441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3738.88 | + | 4499.48i | 0.896998 | + | 1.07948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 334.613 | + | 1449.90i | 0.0793564 | + | 0.343857i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1978.91 | + | 1142.53i | −0.463974 | + | 0.267875i | −0.713714 | − | 0.700438i | \(-0.752988\pi\) |
0.249740 | + | 0.968313i | \(0.419655\pi\) | |||||||
\(264\) | 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 | 0.740050 | − | 0.672552i | \(-0.234802\pi\) |
−0.952472 | + | 0.304626i | \(0.901468\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −1414.17 | + | 5767.38i | −0.313514 | + | 1.27860i | ||||
\(274\) | 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 | \(-0.813203\pi\) | ||
0.832695 | − | 0.553733i | \(-0.186797\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −1790.42 | − | 2419.82i | −0.372124 | − | 0.502939i | ||||
\(286\) | 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 | ||||||||
\(291\) | 4382.00 | − | 499.086i | 0.882740 | − | 0.100539i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6408.45 | −1.27777 | −0.638884 | − | 0.769303i | \(-0.720603\pi\) | ||||
−0.638884 | + | 0.769303i | \(0.720603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 156.471 | 0.0308817 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6634.20 | − | 5667.54i | −1.29615 | − | 1.10729i | ||||
\(298\) | 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 | ||||||||
\(303\) | −4282.75 | + | 3168.80i | −0.812005 | + | 0.600801i | ||||
\(304\) | 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 | 0.883923 | − | 0.467633i | \(-0.154893\pi\) |
−0.846943 | + | 0.531683i | \(0.821560\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 3405.17 | + | 2592.12i | 0.609078 | + | 0.463649i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5714.50 | + | 3299.27i | 1.01249 | + | 0.584559i | 0.911919 | − | 0.410371i | \(-0.134601\pi\) |
0.100568 | + | 0.994930i | \(0.467934\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −5873.64 | + | 4345.90i | −0.993313 | + | 0.734950i | ||||
\(328\) | 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 | ||||||||
\(333\) | 2494.22 | − | 8155.88i | 0.410458 | − | 1.34216i | ||||
\(334\) | 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 | ||||||||
\(339\) | 2412.48 | − | 274.769i | 0.386514 | − | 0.0440219i | ||||
\(340\) | 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 | ||||||||
\(345\) | 1399.70 | + | 1891.75i | 0.218428 | + | 0.295213i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2098.92 | + | 1211.81i | −0.324715 | + | 0.187474i | −0.653492 | − | 0.756933i | \(-0.726697\pi\) |
0.328777 | + | 0.944407i | \(0.393363\pi\) | |||||||
\(348\) | 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 | \(0.0397325\pi\) |
−0.388290 | + | 0.921537i | \(0.626934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5962.94 | + | 3442.71i | 0.891494 | + | 0.514704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 717.112 | + | 2464.65i | 0.106313 | + | 0.365387i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9906.07 | + | 5719.27i | 1.45633 | + | 0.840813i | 0.998828 | − | 0.0483961i | \(-0.0154110\pi\) |
0.457502 | + | 0.889209i | \(0.348744\pi\) | |||||||
\(360\) | 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 | ||||||||
\(369\) | 5530.34 | − | 1276.31i | 0.780212 | − | 0.180060i | ||||
\(370\) | 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 | ||||||||
\(375\) | −889.501 | − | 7809.86i | −0.122490 | − | 1.07546i | ||||
\(376\) | 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 | ||||||||
\(381\) | 152.393 | + | 1338.01i | 0.0204916 | + | 0.179918i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 618.611 | − | 1071.47i | 0.0825314 | − | 0.142949i | −0.821805 | − | 0.569769i | \(-0.807033\pi\) |
0.904337 | + | 0.426820i | \(0.140366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9246.88 | + | 3415.91i | 1.22406 | + | 0.452185i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9258.99 | − | 2136.82i | 1.21618 | − | 0.280673i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2602.51 | − | 1502.56i | 0.339209 | − | 0.195842i | −0.320713 | − | 0.947176i | \(-0.603923\pi\) |
0.659922 | + | 0.751334i | \(0.270589\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −4703.41 | − | 4506.81i | −0.590138 | − | 0.565470i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2993.97 | − | 1728.57i | −0.372848 | − | 0.215264i | 0.301854 | − | 0.953354i | \(-0.402394\pi\) |
−0.674702 | + | 0.738090i | \(0.735728\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | −1446.46 | − | 1954.94i | −0.173598 | − | 0.234623i | ||||
\(412\) | 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 | ||||||||
\(417\) | −15092.2 | + | 1718.92i | −1.77235 | + | 0.201861i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2968.51 | 0.346112 | 0.173056 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173056 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8733.67 | −1.01105 | −0.505526 | − | 0.862811i | \(-0.668702\pi\) | ||||
−0.505526 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1829.04 | + | 5980.81i | −0.210239 | + | 0.687463i | ||||
\(424\) | 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 | ||||||||
\(429\) | 16030.4 | − | 11860.9i | 1.80409 | − | 1.33484i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 51.3171 | − | 29.6279i | 0.00573517 | − | 0.00331120i | −0.497130 | − | 0.867676i | \(-0.665613\pi\) |
0.502865 | + | 0.864365i | \(0.332279\pi\) | |||||||
\(432\) | 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 | ||||||||
\(441\) | 8210.55 | + | 4284.04i | 0.886572 | + | 0.462590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13052.4 | + | 7535.83i | 1.39986 | + | 0.808212i | 0.994378 | − | 0.105889i | \(-0.0337687\pi\) |
0.405487 | + | 0.914101i | \(0.367102\pi\) | |||||||
\(444\) | 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 | \(-0.909229\pi\) | ||
0.959615 | − | 0.281316i | \(-0.0907709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11322.2 | − | 6536.86i | 1.18213 | − | 0.682502i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6910.19 | + | 5112.84i | −0.716709 | + | 0.530292i | ||||
\(454\) | 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 | ||||||||
\(459\) | 2430.66 | − | 2845.24i | 0.247175 | − | 0.289334i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −987.346 | −0.0997512 | −0.0498756 | − | 0.998755i | \(-0.515882\pi\) | ||||
−0.0498756 | + | 0.998755i | \(0.515882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17023.3 | 1.70872 | 0.854362 | − | 0.519678i | \(-0.173948\pi\) | ||||
0.854362 | + | 0.519678i | \(0.173948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6840.67 | + | 779.116i | −0.682212 | + | 0.0777003i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6858.57 | − | 11879.4i | 0.679608 | − | 1.17712i | −0.295491 | − | 0.955345i | \(-0.595483\pi\) |
0.975099 | − | 0.221770i | \(-0.0711834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2363.37 | − | 405.046i | 0.232687 | − | 0.0398791i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4283.53 | + | 5789.35i | 0.419054 | + | 0.566367i | ||||
\(472\) | 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 | 0.908767 | − | 0.417303i | \(-0.137025\pi\) |
−0.815779 | + | 0.578364i | \(0.803691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16880.3 | + | 9745.85i | 1.60016 | + | 0.923851i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3677.01 | + | 3523.31i | 0.346397 | + | 0.331918i | ||||
\(484\) | 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 | \(0.288231\pi\) | ||||
−0.617289 | + | 0.786737i | \(0.711769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1273.05 | + | 734.997i | −0.116299 | + | 0.0671452i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3231.66 | − | 14003.0i | −0.293439 | − | 1.27149i | ||||
\(496\) | 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 | ||||||||
\(501\) | 178.563 | + | 1567.79i | 0.0159234 | + | 0.139808i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13477.7 | −1.19471 | −0.597356 | − | 0.801976i | \(-0.703782\pi\) | ||||
−0.597356 | + | 0.801976i | \(0.703782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8774.71 | −0.773207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 947.078 | + | 8315.39i | 0.0829610 | + | 0.728401i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7065.77 | − | 12238.3i | 0.615294 | − | 1.06572i | −0.375039 | − | 0.927009i | \(-0.622371\pi\) |
0.990333 | − | 0.138711i | \(-0.0442961\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1337.97 | − | 7806.81i | −0.115828 | − | 0.675837i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1731.76 | + | 9337.42i | −0.149043 | + | 0.803620i | ||||
\(514\) | 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 | 0.999213 | − | 0.0396697i | \(-0.0126306\pi\) |
−0.533961 | + | 0.845509i | \(0.679297\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −1391.49 | − | 4782.44i | −0.115676 | − | 0.397567i | ||||
\(526\) | 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 | ||||||||
\(537\) | −8549.87 | − | 11555.5i | −0.687065 | − | 0.928594i | ||||
\(538\) | 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 | ||||||||
\(543\) | −2785.87 | + | 317.296i | −0.220172 | + | 0.0250764i | ||||
\(544\) | 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 | ||||||||
\(549\) | 2156.50 | + | 659.498i | 0.167645 | + | 0.0512690i | ||||
\(550\) | 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 | ||||||||
\(555\) | 11292.2 | − | 8355.09i | 0.863653 | − | 0.639016i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7314.84 | − | 4223.22i | 0.556445 | − | 0.321263i | −0.195273 | − | 0.980749i | \(-0.562559\pi\) |
0.751717 | + | 0.659486i | \(0.229226\pi\) | |||||||
\(558\) | 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 | \(0.139234\pi\) |
−0.0860755 | + | 0.996289i | \(0.527433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3463.35 | + | 1999.56i | 0.257883 | + | 0.148889i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1344.66 | − | 13434.1i | −0.0995955 | − | 0.995028i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8724.86 | − | 5037.30i | −0.642821 | − | 0.371133i | 0.142879 | − | 0.989740i | \(-0.454364\pi\) |
−0.785700 | + | 0.618607i | \(0.787697\pi\) | |||||||
\(570\) | 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 | ||||||||
\(579\) | −6004.02 | + | 4442.36i | −0.430947 | + | 0.318857i | ||||
\(580\) | 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 | ||||||||
\(585\) | 13635.2 | + | 4169.90i | 0.963668 | + | 0.294708i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3318.05 | −0.233306 | −0.116653 | − | 0.993173i | \(-0.537217\pi\) | ||||
−0.116653 | + | 0.993173i | \(0.537217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10479.9 | 0.733135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12113.2 | + | 1379.63i | −0.843097 | + | 0.0960243i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12126.5 | + | 21003.6i | −0.839754 | + | 1.45450i | 0.0503470 | + | 0.998732i | \(0.483967\pi\) |
−0.890101 | + | 0.455764i | \(0.849366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1465.00 | + | 3965.75i | −0.100940 | + | 0.273244i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5660.57 | − | 7650.47i | −0.388060 | − | 0.524477i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9619.77 | − | 5553.97i | 0.656182 | − | 0.378847i | −0.134639 | − | 0.990895i | \(-0.542987\pi\) |
0.790821 | + | 0.612048i | \(0.209654\pi\) | |||||||
\(600\) | 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 | ||||||||
\(609\) | −1263.04 | + | 5151.02i | −0.0840408 | + | 0.342742i | ||||
\(610\) | 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 | \(-0.901933\pi\) | ||
0.952915 | − | 0.303237i | \(-0.0980672\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 1353.85 | − | 7299.76i | 0.0874847 | − | 0.471706i | ||||
\(622\) | 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 | ||||||||
\(627\) | 2475.45 | + | 21734.6i | 0.157671 | + | 1.38436i | ||||
\(628\) | 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 | ||||||||
\(633\) | 2523.45 | + | 22156.0i | 0.158449 | + | 1.39119i | ||||
\(634\) | 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 | ||||||||
\(639\) | −4884.79 | − | 21166.2i | −0.302409 | − | 1.31036i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21346.3 | + | 12324.3i | −1.31533 | + | 0.759409i | −0.982974 | − | 0.183744i | \(-0.941178\pi\) |
−0.332360 | + | 0.943153i | \(0.607845\pi\) | |||||||
\(642\) | 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 | \(-0.977018\pi\) |
0.436225 | − | 0.899837i | \(-0.356315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −984.743 | − | 568.542i | −0.0595602 | − | 0.0343871i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14305.9 | + | 4162.42i | −0.861277 | + | 0.250596i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11414.2 | − | 6589.99i | −0.684030 | − | 0.394925i | 0.117341 | − | 0.993092i | \(-0.462563\pi\) |
−0.801372 | + | 0.598166i | \(0.795896\pi\) | |||||||
\(654\) | 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 | \(0.102432\pi\) | ||||
−0.948668 | + | 0.316275i | \(0.897568\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 5086.82 | + | 6875.03i | 0.297973 | + | 0.402721i | ||||
\(664\) | 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 | ||||||||
\(669\) | 6044.98 | − | 688.491i | 0.349346 | − | 0.0397886i | ||||
\(670\) | 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 | ||||||||
\(675\) | −4716.49 | + | 5520.94i | −0.268945 | + | 0.314817i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1368.23 | − | 2369.84i | 0.0776739 | − | 0.134535i | −0.824572 | − | 0.565757i | \(-0.808584\pi\) |
0.902246 | + | 0.431222i | \(0.141917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14745.4 | + | 5447.15i | 0.833399 | + | 0.307868i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8884.61 | + | 6573.71i | −0.499940 | + | 0.369905i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7977.54 | − | 4605.84i | 0.446928 | − | 0.258034i | −0.259604 | − | 0.965715i | \(-0.583592\pi\) |
0.706532 | + | 0.707681i | \(0.250259\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | −12011.8 | − | 28686.2i | −0.658426 | − | 1.57244i | ||||
\(694\) | 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 | \(-0.832967\pi\) | ||
0.865450 | − | 0.500996i | \(-0.167033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18517.3 | + | 10691.0i | −0.993446 | + | 0.573566i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8280.71 | + | 6126.89i | −0.442368 | + | 0.327308i | ||||
\(706\) | 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 | ||||||||
\(711\) | −9621.96 | + | 31462.9i | −0.507527 | + | 1.65957i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8192.92 | −0.430333 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32843.9 | 1.71789 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19705.1 | + | 2244.31i | −1.02636 | + | 0.116897i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8305.93 | + | 14386.3i | −0.430819 | + | 0.746200i | −0.996944 | − | 0.0781192i | \(-0.975109\pi\) |
0.566125 | + | 0.824319i | \(0.308442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4577.54 | + | 3803.74i | −0.236445 | + | 0.196475i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5059.29 | + | 6837.82i | 0.260245 | + | 0.351730i | ||||
\(724\) | 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 | ||||||||
\(735\) | 6674.09 | + | 13715.5i | 0.334935 | + | 0.688305i | ||||
\(736\) | 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 | \(-0.932178\pi\) | ||
0.977387 | − | 0.211460i | \(-0.0678218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13438.5 | − | 7758.72i | 0.660870 | − | 0.381553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36073.6 | − | 8325.16i | 1.76688 | − | 0.407767i | ||||
\(748\) | 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 | ||||||||
\(753\) | 3098.51 | + | 27205.1i | 0.149955 | + | 1.31661i | ||||
\(754\) | 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 | ||||||||
\(759\) | −1935.25 | − | 16991.5i | −0.0925493 | − | 0.812587i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19166.3 | − | 33197.0i | 0.912980 | − | 1.58133i | 0.103147 | − | 0.994666i | \(-0.467109\pi\) |
0.809833 | − | 0.586661i | \(-0.199558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25668.2 | + | 4399.13i | −1.21789 | + | 0.208728i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6005.54 | − | 1385.98i | 0.283831 | − | 0.0655034i | ||||
\(766\) | 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 | 0.696665 | − | 0.717396i | \(-0.254666\pi\) |
−0.969616 | + | 0.244632i | \(0.921333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6939.52 | + | 4006.53i | 0.321645 | + | 0.185702i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21031.3 | − | 21948.7i | 0.971034 | − | 1.01339i | ||||
\(778\) | 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 | ||||||||
\(789\) | 7062.23 | + | 9544.87i | 0.318659 | + | 0.430680i | ||||
\(790\) | 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 | ||||||||
\(795\) | 11881.9 | − | 1353.29i | 0.530074 | − | 0.0603726i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33773.5 | 1.50103 | 0.750513 | − | 0.660856i | \(-0.229807\pi\) | ||||
0.750513 | + | 0.660856i | \(0.229807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6178.50 | −0.273567 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6109.07 | + | 19976.1i | −0.269480 | + | 0.881174i | ||||
\(802\) | 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 | ||||||||
\(807\) | −7829.45 | + | 5793.00i | −0.341524 | + | 0.252693i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30723.2 | + | 17738.1i | −1.33519 | + | 0.770874i | −0.986090 | − | 0.166210i | \(-0.946847\pi\) |
−0.349103 | + | 0.937084i | \(0.613514\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | 30607.2 | + | 3909.74i | 1.30587 | + | 0.166810i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4221.32 | + | 2437.18i | 0.179446 | + | 0.103603i | 0.587032 | − | 0.809563i | \(-0.300296\pi\) |
−0.407586 | + | 0.913167i | \(0.633629\pi\) | |||||||
\(822\) | 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 | \(0.125012\pi\) | ||||
−0.923865 | + | 0.382719i | \(0.874988\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 2216.98 | − | 1640.34i | 0.0925467 | − | 0.0684752i | ||||
\(832\) | 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 | ||||||||
\(837\) | 16515.0 | + | 14108.6i | 0.682008 | + | 0.582633i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19529.4 | 0.803612 | 0.401806 | − | 0.915725i | \(-0.368383\pi\) | ||||
0.401806 | + | 0.915725i | \(0.368383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21351.7 | 0.875465 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26932.3 | + | 3067.44i | −1.10035 | + | 0.125324i | ||||
\(844\) | 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 | ||||||||
\(849\) | −3239.82 | − | 4378.74i | −0.130966 | − | 0.177006i | ||||
\(850\) | 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 | 0.690376 | − | 0.723450i | \(-0.257445\pi\) |
−0.971715 | + | 0.236158i | \(0.924112\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 19647.5 | + | 4817.59i | 0.777682 | + | 0.190689i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9357.24 | + | 5402.41i | 0.369090 | + | 0.213094i | 0.673061 | − | 0.739587i | \(-0.264979\pi\) |
−0.303971 | + | 0.952681i | \(0.598313\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −5153.34 | − | 22329.8i | −0.199787 | − | 0.865692i | ||||
\(874\) | 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 | ||||||||
\(879\) | 3768.25 | + | 33085.4i | 0.144596 | + | 1.26956i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47633.6 | 1.82158 | 0.910792 | − | 0.412865i | \(-0.135472\pi\) | ||||
0.910792 | + | 0.412865i | \(0.135472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42383.1 | 1.61530 | 0.807648 | − | 0.589665i | \(-0.200740\pi\) | ||||
0.807648 | + | 0.589665i | \(0.200740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92.0068 | − | 807.824i | −0.00349466 | − | 0.0306833i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8634.30 | − | 14955.0i | 0.326845 | − | 0.566112i | −0.655039 | − | 0.755595i | \(-0.727348\pi\) |
0.981884 | + | 0.189483i | \(0.0606812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1663.25 | + | 4502.43i | −0.0627488 | + | 0.169861i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25359.2 | + | 37583.5i | −0.953497 | + | 1.41312i | ||||
\(892\) | 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 | ||||||||
\(903\) | 32894.1 | + | 8065.68i | 1.21223 | + | 0.297241i | ||||
\(904\) | 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 | \(-0.932435\pi\) | ||
0.977557 | − | 0.210671i | \(-0.0675648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73852.7 | − | 42638.9i | 2.67707 | − | 1.54561i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2209.17 | + | 2985.78i | 0.0798174 | + | 0.107876i | ||||
\(916\) | 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 | ||||||||
\(921\) | 19194.8 | − | 2186.19i | 0.686744 | − | 0.0782164i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49644.9 | 1.77040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16348.9 | −0.581134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8297.38 | + | 2537.50i | 0.293982 | + | 0.0899055i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4965.04 | − | 8599.69i | 0.175347 | − | 0.303710i | −0.764934 | − | 0.644108i | \(-0.777229\pi\) |
0.940281 | + | 0.340398i | \(0.110562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7731.23 | − | 21892.7i | −0.272160 | − | 0.770680i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1694.36 | − | 1253.65i | 0.0594542 | − | 0.0439901i | ||||
\(934\) | 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 | 0.812409 | − | 0.583088i | \(-0.198156\pi\) |
−0.911174 | + | 0.412023i | \(0.864822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9633.71 | + | 5562.03i | 0.332680 | + | 0.192073i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11380.2 | − | 19104.3i | 0.391745 | − | 0.657633i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14842.2 | − | 8569.15i | −0.509299 | − | 0.294044i | 0.223246 | − | 0.974762i | \(-0.428335\pi\) |
−0.732546 | + | 0.680718i | \(0.761668\pi\) | |||||||
\(948\) | 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 | \(-0.690464\pi\) | ||
0.563287 | − | 0.826261i | \(-0.309536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23660.3 | − | 13660.3i | 0.801706 | − | 0.462865i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14317.2 | − | 10593.3i | 0.483605 | − | 0.357819i | ||||
\(958\) | 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 | ||||||||
\(963\) | −3513.49 | − | 1074.49i | −0.117571 | − | 0.0359554i | ||||
\(964\) | 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 | ||||||||
\(969\) | −9321.39 | + | 1061.66i | −0.309026 | + | 0.0351964i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1364.94 | + | 2364.14i | −0.0451111 | + | 0.0781348i | −0.887699 | − | 0.460424i | \(-0.847698\pi\) |
0.842588 | + | 0.538558i | \(0.181031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50785.3 | − | 18760.7i | −1.67328 | − | 0.618131i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9870.54 | − | 13340.4i | −0.324216 | − | 0.438189i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49381.0 | + | 28510.2i | −1.61703 | + | 0.933593i | −0.629348 | + | 0.777123i | \(0.716678\pi\) |
−0.987683 | + | 0.156470i | \(0.949989\pi\) | |||||||
\(978\) | 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 | \(0.163865\pi\) |
−0.00880172 | + | 0.999961i | \(0.502802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17389.6 | − | 10039.9i | −0.562517 | − | 0.324770i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15422.5 | + | 16095.3i | −0.497369 | + | 0.519066i | ||||
\(988\) | 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 | ||||||||
\(999\) | −43573.6 | − | 8081.36i | −1.37999 | − | 0.255939i |
(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.257.4 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.257.7 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.5.7 | yes | 16 | ||
7.3 | odd | 6 | inner | 336.4.bc.e.17.7 | 16 | ||
12.11 | even | 2 | 42.4.f.a.5.1 | ✓ | 16 | ||
21.17 | even | 6 | inner | 336.4.bc.e.17.4 | 16 | ||
28.3 | even | 6 | 42.4.f.a.17.1 | yes | 16 | ||
28.11 | odd | 6 | 294.4.f.a.227.4 | 16 | |||
28.19 | even | 6 | 294.4.d.a.293.8 | 16 | |||
28.23 | odd | 6 | 294.4.d.a.293.1 | 16 | |||
28.27 | even | 2 | 294.4.f.a.215.6 | 16 | |||
84.11 | even | 6 | 294.4.f.a.227.6 | 16 | |||
84.23 | even | 6 | 294.4.d.a.293.16 | 16 | |||
84.47 | odd | 6 | 294.4.d.a.293.9 | 16 | |||
84.59 | odd | 6 | 42.4.f.a.17.7 | yes | 16 | ||
84.83 | odd | 2 | 294.4.f.a.215.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.1 | ✓ | 16 | 12.11 | even | 2 | ||
42.4.f.a.5.7 | yes | 16 | 4.3 | odd | 2 | ||
42.4.f.a.17.1 | yes | 16 | 28.3 | even | 6 | ||
42.4.f.a.17.7 | yes | 16 | 84.59 | odd | 6 | ||
294.4.d.a.293.1 | 16 | 28.23 | odd | 6 | |||
294.4.d.a.293.8 | 16 | 28.19 | even | 6 | |||
294.4.d.a.293.9 | 16 | 84.47 | odd | 6 | |||
294.4.d.a.293.16 | 16 | 84.23 | even | 6 | |||
294.4.f.a.215.4 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.215.6 | 16 | 28.27 | even | 2 | |||
294.4.f.a.227.4 | 16 | 28.11 | odd | 6 | |||
294.4.f.a.227.6 | 16 | 84.11 | even | 6 | |||
336.4.bc.e.17.4 | 16 | 21.17 | even | 6 | inner | ||
336.4.bc.e.17.7 | 16 | 7.3 | odd | 6 | inner | ||
336.4.bc.e.257.4 | 16 | 1.1 | even | 1 | trivial | ||
336.4.bc.e.257.7 | 16 | 3.2 | odd | 2 | inner |