Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
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, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), 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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.a.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −43.0000 | + | 74.4782i | −0.769207 | + | 1.33231i | 0.168786 | + | 0.985653i | \(0.446015\pi\) |
−0.937993 | + | 0.346654i | \(0.887318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.5000 | − | 127.306i | −0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.0000 | + | 29.4449i | 0.0423611 | + | 0.0733716i | 0.886429 | − | 0.462865i | \(-0.153179\pi\) |
−0.844067 | + | 0.536237i | \(0.819845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | −0.00492337 | −0.00246169 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246169 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 774.000 | 0.888204 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 952.000 | + | 1648.91i | 0.798941 | + | 1.38381i | 0.920306 | + | 0.391198i | \(0.127939\pi\) |
−0.121366 | + | 0.992608i | \(0.538727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −744.500 | + | 1289.51i | −0.473130 | + | 0.819486i | −0.999527 | − | 0.0307534i | \(-0.990209\pi\) |
0.526397 | + | 0.850239i | \(0.323543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −882.000 | + | 763.834i | −0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −112.000 | + | 193.990i | −0.0441467 | + | 0.0764644i | −0.887254 | − | 0.461280i | \(-0.847390\pi\) |
0.843108 | + | 0.537745i | \(0.180724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2135.50 | − | 3698.79i | −0.683360 | − | 1.18361i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6508.00 | −1.43699 | −0.718493 | − | 0.695534i | \(-0.755168\pi\) | ||||
−0.718493 | + | 0.695534i | \(0.755168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 865.500 | + | 1499.09i | 0.161757 | + | 0.280171i | 0.935499 | − | 0.353330i | \(-0.114951\pi\) |
−0.773742 | + | 0.633501i | \(0.781617\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 153.000 | − | 265.004i | 0.0244572 | − | 0.0423611i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10535.0 | + | 3649.43i | 1.45367 | + | 0.503564i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3816.50 | − | 6610.37i | 0.458312 | − | 0.793819i | −0.540560 | − | 0.841305i | \(-0.681788\pi\) |
0.998872 | + | 0.0474862i | \(0.0151210\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.5000 | + | 23.3827i | 0.00142126 | + | 0.00246169i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15414.0 | 1.43204 | 0.716021 | − | 0.698079i | \(-0.245961\pi\) | ||||
0.716021 | + | 0.698079i | \(0.245961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18491.0 | −1.52507 | −0.762534 | − | 0.646948i | \(-0.776045\pi\) | ||||
−0.762534 | + | 0.646948i | \(0.776045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3483.00 | − | 6032.73i | −0.256402 | − | 0.444102i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9231.00 | − | 15988.6i | 0.609543 | − | 1.05576i | −0.381773 | − | 0.924256i | \(-0.624686\pi\) |
0.991316 | − | 0.131503i | \(-0.0419802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15606.5 | + | 6237.98i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8568.00 | − | 14840.2i | 0.461269 | − | 0.798941i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9978.00 | + | 17282.4i | 0.487926 | + | 0.845112i | 0.999904 | − | 0.0138864i | \(-0.00442031\pi\) |
−0.511978 | + | 0.858999i | \(0.671087\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2924.00 | −0.130338 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13401.0 | 0.546324 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15914.0 | − | 27563.9i | −0.595181 | − | 1.03088i | −0.993521 | − | 0.113646i | \(-0.963747\pi\) |
0.398340 | − | 0.917238i | \(-0.369586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28827.0 | − | 49929.8i | 0.991916 | − | 1.71805i | 0.386062 | − | 0.922473i | \(-0.373835\pi\) |
0.605854 | − | 0.795576i | \(-0.292832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9922.50 | + | 3437.25i | 0.314970 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 129.000 | − | 223.435i | 0.00378710 | − | 0.00655944i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −30281.5 | − | 52449.1i | −0.824120 | − | 1.42742i | −0.902590 | − | 0.430501i | \(-0.858337\pi\) |
0.0784702 | − | 0.996916i | \(-0.474996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2016.00 | 0.0509762 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 44834.0 | 1.05551 | 0.527754 | − | 0.849397i | \(-0.323034\pi\) | ||||
0.527754 | + | 0.849397i | \(0.323034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10410.5 | − | 18031.5i | −0.228646 | − | 0.396027i | 0.728761 | − | 0.684768i | \(-0.240097\pi\) |
−0.957407 | + | 0.288741i | \(0.906763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19219.5 | + | 33289.2i | −0.394538 | + | 0.683360i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3332.00 | − | 2885.60i | 0.0640440 | − | 0.0554637i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15265.5 | + | 26440.6i | −0.275197 | + | 0.476655i | −0.970185 | − | 0.242367i | \(-0.922076\pi\) |
0.694988 | + | 0.719021i | \(0.255410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −110602. | −1.76225 | −0.881125 | − | 0.472883i | \(-0.843213\pi\) | ||||
−0.881125 | + | 0.472883i | \(0.843213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −163744. | −2.45820 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29286.0 | + | 50724.8i | 0.414822 | + | 0.718493i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 29496.0 | − | 51088.6i | 0.394719 | − | 0.683673i | −0.598346 | − | 0.801238i | \(-0.704175\pi\) |
0.993065 | + | 0.117564i | \(0.0375086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 73.5000 | + | 381.917i | 0.000930430 | + | 0.00483466i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7789.50 | − | 13491.8i | 0.0933904 | − | 0.161757i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −64027.0 | − | 110898.i | −0.727871 | − | 1.26071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −119846. | −1.29328 | −0.646642 | − | 0.762793i | \(-0.723827\pi\) | ||||
−0.646642 | + | 0.762793i | \(0.723827\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2754.00 | −0.0282407 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50005.0 | − | 86611.2i | −0.487764 | − | 0.844833i | 0.512137 | − | 0.858904i | \(-0.328854\pi\) |
−0.999901 | + | 0.0140714i | \(0.995521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 60845.5 | − | 105387.i | 0.565113 | − | 0.978805i | −0.431926 | − | 0.901909i | \(-0.642166\pi\) |
0.997039 | − | 0.0768956i | \(-0.0245008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18963.0 | − | 98534.6i | −0.167855 | − | 0.872199i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −24324.0 | + | 42130.4i | −0.205388 | + | 0.355743i | −0.950256 | − | 0.311469i | \(-0.899179\pi\) |
0.744868 | + | 0.667212i | \(0.232512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 76037.5 | + | 131701.i | 0.613002 | + | 1.06175i | 0.990732 | + | 0.135834i | \(0.0433714\pi\) |
−0.377730 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −68697.0 | −0.529213 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −60886.0 | −0.448561 | −0.224280 | − | 0.974525i | \(-0.572003\pi\) | ||||
−0.224280 | + | 0.974525i | \(0.572003\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9632.00 | − | 16683.1i | −0.0679160 | − | 0.117634i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 121.500 | − | 210.444i | 0.000820562 | − | 0.00142126i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186592. | − | 161593.i | 1.20789 | − | 1.04606i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 79947.5 | − | 138473.i | 0.496411 | − | 0.859809i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −69363.0 | − | 120140.i | −0.413395 | − | 0.716021i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 98556.0 | 0.564167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 151965. | 0.836054 | 0.418027 | − | 0.908435i | \(-0.362722\pi\) | ||||
0.418027 | + | 0.908435i | \(0.362722\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 83209.5 | + | 144123.i | 0.440249 | + | 0.762534i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 117751. | − | 203951.i | 0.599496 | − | 1.03836i | −0.393399 | − | 0.919368i | \(-0.628701\pi\) |
0.992895 | − | 0.118990i | \(-0.0379657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 182402. | + | 63186.1i | 0.894132 | + | 0.309736i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −31347.0 | + | 54294.6i | −0.148034 | + | 0.256402i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −162754. | − | 281898.i | −0.740850 | − | 1.28319i | −0.952109 | − | 0.305760i | \(-0.901090\pi\) |
0.211259 | − | 0.977430i | \(-0.432244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3211.00 | −0.0140962 | −0.00704812 | − | 0.999975i | \(-0.502244\pi\) | ||||
−0.00704812 | + | 0.999975i | \(0.502244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −166158. | −0.703839 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −51.0000 | − | 88.3346i | −0.000208560 | − | 0.000361236i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 279844. | − | 484704.i | 1.10534 | − | 1.91451i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 118850. | + | 93569.7i | 0.453632 | + | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 75942.0 | − | 131535.i | 0.280231 | − | 0.485375i | −0.691210 | − | 0.722654i | \(-0.742922\pi\) |
0.971442 | + | 0.237279i | \(0.0762556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 38324.0 | + | 66379.1i | 0.136782 | + | 0.236913i | 0.926277 | − | 0.376844i | \(-0.122991\pi\) |
−0.789495 | + | 0.613757i | \(0.789657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −154224. | −0.532627 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −148866. | −0.497698 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 194855. | + | 337499.i | 0.630903 | + | 1.09276i | 0.987368 | + | 0.158447i | \(0.0506487\pi\) |
−0.356465 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 89802.0 | − | 155542.i | 0.281704 | − | 0.487926i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27440.0 | + | 9505.49i | 0.0834295 | + | 0.0289008i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −56186.0 | + | 97317.0i | −0.165638 | + | 0.286893i | −0.936882 | − | 0.349647i | \(-0.886302\pi\) |
0.771244 | + | 0.636540i | \(0.219635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13158.0 | + | 22790.3i | 0.0376253 | + | 0.0651689i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −52550.0 | −0.145808 | −0.0729040 | − | 0.997339i | \(-0.523227\pi\) | ||||
−0.0729040 | + | 0.997339i | \(0.523227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −371284. | −0.999976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −60304.5 | − | 104450.i | −0.157710 | − | 0.273162i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 67628.0 | − | 117135.i | 0.171795 | − | 0.297558i | −0.767252 | − | 0.641345i | \(-0.778377\pi\) |
0.939048 | + | 0.343787i | \(0.111710\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −418558. | + | 362482.i | −1.03314 | + | 0.894728i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −143226. | + | 248075.i | −0.343628 | + | 0.595181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 125319. | + | 217059.i | 0.292337 | + | 0.506343i | 0.974362 | − | 0.224986i | \(-0.0722336\pi\) |
−0.682025 | + | 0.731329i | \(0.738900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 199233. | 0.452027 | 0.226014 | − | 0.974124i | \(-0.427431\pi\) | ||||
0.226014 | + | 0.974124i | \(0.427431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −518886. | −1.14537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 328219. | + | 568492.i | 0.705074 | + | 1.22122i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32368.0 | + | 56063.0i | −0.0676880 | + | 0.117239i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17860.5 | − | 92805.9i | −0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −119385. | + | 206781.i | −0.236792 | + | 0.410135i | −0.959792 | − | 0.280713i | \(-0.909429\pi\) |
0.723000 | + | 0.690848i | \(0.242763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42845.5 | − | 74210.6i | −0.0827965 | − | 0.143408i | 0.821654 | − | 0.569987i | \(-0.193052\pi\) |
−0.904450 | + | 0.426579i | \(0.859718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2322.00 | −0.00437296 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −71408.0 | −0.131094 | −0.0655468 | − | 0.997849i | \(-0.520879\pi\) | ||||
−0.0655468 | + | 0.997849i | \(0.520879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −355676. | − | 616049.i | −0.636681 | − | 1.10276i | −0.986156 | − | 0.165818i | \(-0.946973\pi\) |
0.349475 | − | 0.936946i | \(-0.386360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −272534. | + | 472042.i | −0.475806 | + | 0.824120i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 159446. | + | 828506.i | 0.271565 | + | 1.41109i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −662802. | + | 1.14801e6i | −1.10154 | + | 1.90792i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9072.00 | − | 15713.2i | −0.0147156 | − | 0.0254881i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −50626.0 | −0.0801693 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 260260. | 0.402440 | 0.201220 | − | 0.979546i | \(-0.435509\pi\) | ||||
0.201220 | + | 0.979546i | \(0.435509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −201753. | − | 349446.i | −0.304699 | − | 0.527754i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 795113. | − | 1.37718e6i | 1.17309 | − | 2.03186i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 169638. | − | 146911.i | 0.244553 | − | 0.211790i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −93694.5 | + | 162284.i | −0.132009 | + | 0.228646i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2856.00 | − | 4946.74i | −0.00393349 | − | 0.00681300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −105656. | −0.142276 | −0.0711381 | − | 0.997466i | \(-0.522663\pi\) | ||||
−0.0711381 | + | 0.997466i | \(0.522663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 345951. | 0.455573 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 327375. | + | 567030.i | 0.421678 | + | 0.730368i | 0.996104 | − | 0.0881890i | \(-0.0281080\pi\) |
−0.574426 | + | 0.818557i | \(0.694775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −278856. | + | 482994.i | −0.351392 | + | 0.608629i | −0.986494 | − | 0.163800i | \(-0.947625\pi\) |
0.635101 | + | 0.772429i | \(0.280958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37485.0 | − | 12985.2i | −0.0462197 | − | 0.0160110i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 623797. | − | 1.08045e6i | 0.752755 | − | 1.30381i | −0.193728 | − | 0.981055i | \(-0.562058\pi\) |
0.946483 | − | 0.322754i | \(-0.104609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 793866. | + | 1.37502e6i | 0.937729 | + | 1.62420i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 274779. | 0.317770 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 496926. | 0.562726 | 0.281363 | − | 0.959601i | \(-0.409214\pi\) | ||||
0.281363 | + | 0.959601i | \(0.409214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 138809. | + | 240424.i | 0.153948 | + | 0.266646i | 0.932676 | − | 0.360716i | \(-0.117468\pi\) |
−0.778727 | + | 0.627363i | \(0.784134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 206486. | − | 1.43058e6i | 0.219774 | − | 1.52264i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2233.50 | − | 3868.54i | 0.00232940 | − | 0.00403463i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 497709. | + | 862057.i | 0.508718 | + | 0.881125i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 308328. | 0.308908 | 0.154454 | − | 0.988000i | \(-0.450638\pi\) | ||||
0.154454 | + | 0.988000i | \(0.450638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7616.00 | −0.00748041 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 736848. | + | 1.27626e6i | 0.709623 | + | 1.22910i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −204381. | + | 353998.i | −0.193022 | + | 0.334325i | −0.946250 | − | 0.323435i | \(-0.895162\pi\) |
0.753228 | + | 0.657759i | \(0.228496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −935042. | − | 323908.i | −0.866128 | − | 0.300035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 263574. | − | 456524.i | 0.239498 | − | 0.414822i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 544062. | + | 942343.i | 0.485019 | + | 0.840078i | 0.999852 | − | 0.0172127i | \(-0.00547924\pi\) |
−0.514833 | + | 0.857291i | \(0.672146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.71622e6 | −1.50126 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −530928. | −0.455782 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 334145. | + | 578756.i | 0.281549 | + | 0.487657i | 0.971766 | − | 0.235945i | \(-0.0758184\pi\) |
−0.690217 | + | 0.723602i | \(0.742485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −415332. | + | 719376.i | −0.343536 | + | 0.595022i | −0.985087 | − | 0.172059i | \(-0.944958\pi\) |
0.641551 | + | 0.767081i | \(0.278291\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2646.00 | − | 2291.50i | 0.00214874 | − | 0.00186086i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 72607.0 | − | 125759.i | 0.0578958 | − | 0.100278i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −462537. | − | 801137.i | −0.362198 | − | 0.627346i | 0.626124 | − | 0.779724i | \(-0.284640\pi\) |
−0.988322 | + | 0.152377i | \(0.951307\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −140211. | −0.107838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.33635e6 | 1.00961 | 0.504805 | − | 0.863233i | \(-0.331564\pi\) | ||||
0.504805 | + | 0.863233i | \(0.331564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −496478. | − | 859926.i | −0.368497 | − | 0.638256i | 0.620833 | − | 0.783942i | \(-0.286794\pi\) |
−0.989331 | + | 0.145686i | \(0.953461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −576243. | + | 998082.i | −0.420236 | + | 0.727871i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −377643. | − | 1.96229e6i | −0.270630 | − | 1.40624i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.10268e6 | + | 1.90990e6i | −0.776613 | + | 1.34513i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 539307. | + | 934107.i | 0.373339 | + | 0.646642i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 563544. | 0.383494 | 0.191747 | − | 0.981444i | \(-0.438585\pi\) | ||||
0.191747 | + | 0.981444i | \(0.438585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.73721e6 | 1.83127 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12393.0 | + | 21465.3i | 0.00815240 | + | 0.0141204i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 336.000 | − | 581.969i | 0.000217351 | − | 0.000376463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 453029. | + | 2.35401e6i | 0.288211 | + | 1.49759i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −450045. | + | 779501.i | −0.281611 | + | 0.487764i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.47912e6 | + | 4.29397e6i | 1.52598 | + | 2.64307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.82703e6 | −1.71193 | −0.855963 | − | 0.517037i | \(-0.827035\pi\) | ||||
−0.855963 | + | 0.517037i | \(0.827035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.09522e6 | −0.652536 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −563657. | − | 976283.i | −0.330456 | − | 0.572367i | 0.652145 | − | 0.758094i | \(-0.273869\pi\) |
−0.982601 | + | 0.185727i | \(0.940536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.18006e6 | − | 2.04393e6i | 0.680840 | − | 1.17925i | −0.293885 | − | 0.955841i | \(-0.594948\pi\) |
0.974725 | − | 0.223408i | \(-0.0717183\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −682668. | + | 591208.i | −0.387644 | + | 0.335710i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.11210e6 | − | 1.92621e6i | 0.621578 | − | 1.07660i | −0.367614 | − | 0.929979i | \(-0.619825\pi\) |
0.989192 | − | 0.146626i | \(-0.0468415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −110636. | − | 191627.i | −0.0608723 | − | 0.105434i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 437832. | 0.237162 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.83506e6 | −1.51201 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6406.50 | + | 11096.4i | 0.00336444 | + | 0.00582738i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 684338. | − | 1.18531e6i | 0.353917 | − | 0.613002i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.26160e6 | − | 783439.i | −1.15193 | − | 0.399039i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.85152e6 | + | 3.20693e6i | −0.928877 | + | 1.60886i | −0.143673 | + | 0.989625i | \(0.545891\pi\) |
−0.785204 | + | 0.619237i | \(0.787442\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 309136. | + | 535440.i | 0.152771 | + | 0.264606i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.20842e6 | 2.53568 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21432e6 | 0.582452 | 0.291226 | − | 0.956654i | \(-0.405937\pi\) | ||||
0.291226 | + | 0.956654i | \(0.405937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 273987. | + | 474559.i | 0.129488 | + | 0.224280i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29427.0 | + | 50969.1i | −0.0137044 | + | 0.0237367i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.17649e6 | + | 1.83397e6i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −86688.0 | + | 150148.i | −0.0392113 | + | 0.0679160i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −488952. | − | 846890.i | −0.217993 | − | 0.377575i | 0.736201 | − | 0.676763i | \(-0.236618\pi\) |
−0.954194 | + | 0.299188i | \(0.903284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 511282. | 0.224697 | 0.112348 | − | 0.993669i | \(-0.464163\pi\) | ||||
0.112348 | + | 0.993669i | \(0.464163\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2187.00 | −0.000947504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.51376e6 | − | 2.62191e6i | −0.646577 | − | 1.11990i | −0.983935 | − | 0.178528i | \(-0.942866\pi\) |
0.337357 | − | 0.941377i | \(-0.390467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.92786e6 | + | 3.33915e6i | −0.811905 | + | 1.40626i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.09916e6 | − | 727170.i | −0.871716 | − | 0.301971i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.29728e6 | − | 3.97900e6i | 0.940757 | − | 1.62944i | 0.176725 | − | 0.984260i | \(-0.443450\pi\) |
0.764032 | − | 0.645179i | \(-0.223217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129489. | + | 224282.i | 0.0522956 | + | 0.0905786i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.43906e6 | −0.573206 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.79061e6 | 0.703506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −556365. | − | 963653.i | −0.215623 | − | 0.373470i | 0.737842 | − | 0.674973i | \(-0.235845\pi\) |
−0.953465 | + | 0.301503i | \(0.902512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −624267. | + | 1.08126e6i | −0.238674 | + | 0.413395i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.95569e6 | − | 1.69368e6i | 0.737675 | − | 0.638845i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.22947e6 | − | 2.12951e6i | 0.457559 | − | 0.792516i | −0.541272 | − | 0.840848i | \(-0.682057\pi\) |
0.998831 | + | 0.0483315i | \(0.0153904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −443502. | − | 768168.i | −0.162861 | − | 0.282084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19524.0 | 0.00707482 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.10130e6 | 1.46664 | 0.733320 | − | 0.679884i | \(-0.237970\pi\) | ||||
0.733320 | + | 0.679884i | \(0.237970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −683842. | − | 1.18445e6i | −0.241348 | − | 0.418027i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.29707e6 | + | 2.24658e6i | −0.451820 | + | 0.782575i | −0.998499 | − | 0.0547673i | \(-0.982558\pi\) |
0.546679 | + | 0.837342i | \(0.315892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 71638.0 | + | 372242.i | 0.0246315 | + | 0.127989i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 748886. | − | 1.29711e6i | 0.254178 | − | 0.440249i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.11703e6 | − | 1.93476e6i | −0.374276 | − | 0.648265i | 0.615942 | − | 0.787791i | \(-0.288775\pi\) |
−0.990218 | + | 0.139526i | \(0.955442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −426496. | −0.141082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.11952e6 | −0.692238 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.31283e6 | − | 2.27389e6i | −0.423367 | − | 0.733293i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.03200e6 | − | 1.78747e6i | 0.328627 | − | 0.569198i | −0.653613 | − | 0.756829i | \(-0.726748\pi\) |
0.982240 | + | 0.187631i | \(0.0600809\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −328324. | − | 1.70602e6i | −0.103245 | − | 0.536479i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −576414. | + | 998378.i | −0.179008 | + | 0.310052i | −0.941541 | − | 0.336898i | \(-0.890622\pi\) |
0.762533 | + | 0.646950i | \(0.223956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2596.50 | − | 4497.27i | −0.000796390 | − | 0.00137939i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 564246. | 0.170935 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 259522. | 0.0776583 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.96706e6 | − | 5.13910e6i | −0.877038 | − | 1.51907i | −0.854576 | − | 0.519327i | \(-0.826183\pi\) |
−0.0224623 | − | 0.999748i | \(-0.507151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.46479e6 | + | 2.53708e6i | −0.427730 | + | 0.740850i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.11914e6 | + | 2.70126e6i | −0.899830 | + | 0.779275i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.75589e6 | − | 8.23744e6i | 1.35554 | − | 2.34786i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14449.5 | + | 25027.3i | 0.00406923 | + | 0.00704812i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −771666. | −0.214731 | −0.107365 | − | 0.994220i | \(-0.534241\pi\) | ||||
−0.107365 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.87542e6 | −0.790671 | −0.395336 | − | 0.918537i | \(-0.629372\pi\) | ||||
−0.395336 | + | 0.918537i | \(0.629372\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 747711. | + | 1.29507e6i | 0.203181 | + | 0.351920i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.06599e6 | − | 7.04250e6i | 1.09193 | − | 1.89128i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.06261e6 | − | 2.44656e6i | −1.87454 | − | 0.649361i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −459.000 | + | 795.011i | −0.000120412 | + | 0.000208560i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −68931.0 | − | 119392.i | −0.0178740 | − | 0.0309587i | 0.856950 | − | 0.515399i | \(-0.172356\pi\) |
−0.874824 | + | 0.484441i | \(0.839023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.56526e6 | 0.401204 | 0.200602 | − | 0.979673i | \(-0.435710\pi\) | ||||
0.200602 | + | 0.979673i | \(0.435710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.03719e6 | −1.27634 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −166768. | − | 288851.i | −0.0417743 | − | 0.0723552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.44079e6 | − | 4.22757e6i | 0.604462 | − | 1.04696i | −0.387675 | − | 0.921796i | \(-0.626722\pi\) |
0.992136 | − | 0.125162i | \(-0.0399451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | − | 1.34740e6i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −650758. | + | 1.12715e6i | −0.157547 | + | 0.272879i | −0.933984 | − | 0.357316i | \(-0.883692\pi\) |
0.776437 | + | 0.630195i | \(0.217025\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.53666e6 | + | 4.39362e6i | 0.607242 | + | 1.05177i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.36696e6 | −0.323583 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.13141e6 | −0.733034 | −0.366517 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366517 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 262038. | + | 453863.i | 0.0606629 | + | 0.105071i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 344916. | − | 597412.i | 0.0789710 | − | 0.136782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31605.0 | − | 10948.3i | −0.00715694 | − | 0.00247924i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.24634e6 | + | 5.62283e6i | −0.727116 | + | 1.25940i | 0.230981 | + | 0.972958i | \(0.425807\pi\) |
−0.958097 | + | 0.286444i | \(0.907527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 694008. | + | 1.20206e6i | 0.153756 | + | 0.266314i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.34717e6 | 1.17185 | 0.585925 | − | 0.810365i | \(-0.300731\pi\) | ||||
0.585925 | + | 0.810365i | \(0.300731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.37285e6 | −0.731215 | −0.365607 | − | 0.930769i | \(-0.619139\pi\) | ||||
−0.365607 | + | 0.930769i | \(0.619139\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 669897. | + | 1.16030e6i | 0.143673 | + | 0.248849i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.11726e6 | − | 1.93515e6i | 0.237062 | − | 0.410604i | −0.722808 | − | 0.691049i | \(-0.757149\pi\) |
0.959870 | + | 0.280445i | \(0.0904821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.93517e6 | + | 5.14001e6i | −1.24595 | + | 1.07903i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.75369e6 | − | 3.03749e6i | 0.364252 | − | 0.630903i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −314347. | − | 544465.i | −0.0646036 | − | 0.111897i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.35952e6 | 1.29327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.61644e6 | −0.325284 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.26068e6 | − | 2.18357e6i | −0.251054 | − | 0.434838i | 0.712762 | − | 0.701406i | \(-0.247444\pi\) |
−0.963816 | + | 0.266568i | \(0.914110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11449.5 | + | 19831.1i | −0.00225644 | + | 0.00390827i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −49392.0 | − | 256648.i | −0.00963360 | − | 0.0500577i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.15338e6 | − | 8.92591e6i | 0.994804 | − | 1.72305i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 958358. | + | 1.65993e6i | 0.183107 | + | 0.317151i | 0.942937 | − | 0.332971i | \(-0.108051\pi\) |
−0.759830 | + | 0.650122i | \(0.774718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.01135e6 | 0.191262 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.82875e6 | −1.09112 | −0.545559 | − | 0.838073i | \(-0.683683\pi\) | ||||
−0.545559 | + | 0.838073i | \(0.683683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.19562e6 | − | 1.07311e7i | −1.14807 | − | 1.98851i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 118422. | − | 205113.i | 0.0217230 | − | 0.0376253i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.09843e6 | − | 5.70763e6i | −0.199472 | − | 1.03649i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.00243e6 | + | 8.66446e6i | −0.899352 | + | 1.55772i | −0.0710277 | + | 0.997474i | \(0.522628\pi\) |
−0.828324 | + | 0.560249i | \(0.810705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 236475. | + | 409587.i | 0.0420912 | + | 0.0729040i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.13666e6 | −0.200313 | −0.100157 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100157 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.60086e6 | 1.50077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.67078e6 | + | 2.89387e6i | 0.288668 | + | 0.499988i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.00968e6 | + | 3.48088e6i | −0.343822 | + | 0.595517i | −0.985139 | − | 0.171759i | \(-0.945055\pi\) |
0.641317 | + | 0.767276i | \(0.278388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.04046e6 | + | 1.76709e6i | −0.345681 | + | 0.299368i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −542740. | + | 940054.i | −0.0910540 | + | 0.157710i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.23271e6 | + | 9.06332e6i | 0.869378 | + | 1.50581i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 627708. | 0.103284 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.21730e6 | −0.198372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.76014e6 | + | 4.78070e6i | 0.445488 | + | 0.771609i | 0.998086 | − | 0.0618395i | \(-0.0196967\pi\) |
−0.552598 | + | 0.833448i | \(0.686363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.47236e6 | − | 7.74636e6i | 0.714961 | − | 1.23835i | −0.248013 | − | 0.968757i | \(-0.579778\pi\) |
0.962974 | − | 0.269593i | \(-0.0868891\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.70878e6 | + | 1.63117e6i | 0.745607 | + | 0.258286i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.64791e6 | + | 2.85427e6i | −0.258468 | + | 0.447680i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.19308e6 | + | 5.53058e6i | 0.496102 | + | 0.859274i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.57807e6 | 0.396788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46242.0 | −0.00705048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.09186e6 | − | 3.62321e6i | −0.315972 | − | 0.547280i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.12787e6 | − | 1.95353e6i | 0.168781 | − | 0.292337i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −448987. | − | 353486.i | −0.0665674 | − | 0.0524083i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −424528. | + | 735305.i | −0.0623611 | + | 0.108013i | −0.895520 | − | 0.445021i | \(-0.853196\pi\) |
0.833159 | + | 0.553033i | \(0.186530\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −896548. | − | 1.55287e6i | −0.130489 | − | 0.226014i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.30784e7 | −1.88610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.61340e6 | −1.23085 | −0.615426 | − | 0.788194i | \(-0.711016\pi\) | ||||
−0.615426 | + | 0.788194i | \(0.711016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.33499e6 | + | 4.04432e6i | 0.330639 | + | 0.572683i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.84521e6 | − | 8.39214e6i | 0.679882 | − | 1.17759i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.74005e6 | + | 1.29559e6i | 0.520073 | + | 0.180159i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.95397e6 | − | 5.11643e6i | 0.407074 | − | 0.705074i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.89940e6 | − | 6.75395e6i | −0.532549 | − | 0.922401i | −0.999278 | − | 0.0380009i | \(-0.987901\pi\) |
0.466729 | − | 0.884400i | \(-0.345432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55473.0 | 0.00750848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 582624. | 0.0781594 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 536357. | + | 928998.i | 0.0713153 | + | 0.123522i | 0.899478 | − | 0.436966i | \(-0.143947\pi\) |
−0.828163 | + | 0.560488i | \(0.810614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.61810e6 | − | 4.53468e6i | 0.345036 | − | 0.597620i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −642978. | + | 556835.i | −0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 507621. | − | 879225.i | 0.0657293 | − | 0.113846i | −0.831288 | − | 0.555842i | \(-0.812396\pi\) |
0.897017 | + | 0.441996i | \(0.145729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.39047e6 | − | 5.87246e6i | −0.435180 | − | 0.753754i | 0.562130 | − | 0.827049i | \(-0.309982\pi\) |
−0.997310 | + | 0.0732945i | \(0.976649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.14893e6 | 0.273423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 956704. | 0.120672 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.65268e6 | + | 2.86253e6i | 0.206657 | + | 0.357941i | 0.950659 | − | 0.310236i | \(-0.100408\pi\) |
−0.744002 | + | 0.668177i | \(0.767075\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −385610. | + | 667895.i | −0.0478026 | + | 0.0827965i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.70975e6 | + | 1.40803e7i | 0.333034 | + | 1.73050i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −339252. | + | 587602.i | −0.0413381 | + | 0.0715998i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10449.0 | + | 18098.2i | 0.00126237 | + | 0.00218648i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.19833e7 | 1.43543 | 0.717715 | − | 0.696337i | \(-0.245188\pi\) | ||||
0.717715 | + | 0.696337i | \(0.245188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.57746e6 | −0.306128 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 321336. | + | 556570.i | 0.0378434 | + | 0.0655468i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.65510e6 | − | 4.59877e6i | 0.310059 | − | 0.537038i | −0.668316 | − | 0.743877i | \(-0.732985\pi\) |
0.978375 | + | 0.206840i | \(0.0663179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.01173e6 | + | 2.08456e7i | 0.464557 | + | 2.41391i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.20108e6 | + | 5.54444e6i | −0.367588 | + | 0.636681i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21118e6 | + | 2.09782e6i | 0.137924 | + | 0.238892i | 0.926711 | − | 0.375775i | \(-0.122624\pi\) |
−0.788786 | + | 0.614667i | \(0.789290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.10659e6 | −0.802556 | −0.401278 | − | 0.915956i | \(-0.631434\pi\) | ||||
−0.401278 | + | 0.915956i | \(0.631434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.90560e6 | 0.549413 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.87548e6 | + | 1.19087e7i | 0.763686 | + | 1.32274i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.95970e6 | − | 1.55187e7i | 0.987011 | − | 1.70955i | 0.354374 | − | 0.935104i | \(-0.384694\pi\) |
0.632636 | − | 0.774449i | \(-0.281973\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.74006e6 | − | 4.97103e6i | 0.627152 | − | 0.543130i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27693.0 | + | 47965.7i | −0.00300101 | + | 0.00519790i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.98950e6 | − | 1.21062e7i | −0.751269 | − | 1.30124i | −0.947208 | − | 0.320619i | \(-0.896109\pi\) |
0.195940 | − | 0.980616i | \(-0.437224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.19304e7 | 1.27195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.25594e6 | −0.555824 | −0.277912 | − | 0.960606i | \(-0.589642\pi\) | ||||
−0.277912 | + | 0.960606i | \(0.589642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 721506. | + | 1.24969e6i | 0.0756857 | + | 0.131091i | 0.901384 | − | 0.433020i | \(-0.142552\pi\) |
−0.825699 | + | 0.564112i | \(0.809219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −81648.0 | + | 141418.i | −0.00849604 | + | 0.0147156i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.22652e6 | − | 2.50334e6i | −0.745949 | − | 0.258404i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.43553e6 | − | 4.21846e6i | 0.249398 | − | 0.431970i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 227817. | + | 394591.i | 0.0231429 | + | 0.0400846i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.45332e7 | 1.46466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51723e7 | −1.51697 | −0.758487 | − | 0.651688i | \(-0.774061\pi\) | ||||
−0.758487 | + | 0.651688i | \(0.774061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.17117e6 | − | 2.02853e6i | −0.116174 | − | 0.201220i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.53450e6 | + | 1.13181e7i | −0.643099 | + | 1.11388i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46819.5 | − | 18713.9i | 0.00457170 | − | 0.00182733i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.81578e6 | + | 3.14502e6i | −0.175918 | + | 0.304699i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 72424.0 | + | 125442.i | 0.00696205 | + | 0.0120586i | 0.869485 | − | 0.493959i | \(-0.164451\pi\) |
−0.862523 | + | 0.506017i | \(0.831117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27469.0 | 0.00262009 | 0.00131004 | − | 0.999999i | \(-0.499583\pi\) | ||||
0.00131004 | + | 0.999999i | \(0.499583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.43120e7 | −1.35457 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.27892e6 | + | 7.41130e6i | 0.401858 | + | 0.696039i | 0.993950 | − | 0.109831i | \(-0.0350311\pi\) |
−0.592092 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 541076. | − | 937171.i | 0.0504251 | − | 0.0873388i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.90843e6 | − | 661099.i | −0.176491 | − | 0.0611384i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.25152e6 | + | 1.08279e7i | −0.573723 | + | 0.993718i | 0.422456 | + | 0.906384i | \(0.361168\pi\) |
−0.996179 | + | 0.0873343i | \(0.972165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.01266e7 | + | 1.75398e7i | 0.922274 | + | 1.59742i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.68650e6 | 0.152431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.80471e7 | −1.61880 | −0.809400 | − | 0.587258i | \(-0.800207\pi\) | ||||
−0.809400 | + | 0.587258i | \(0.800207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.67072e6 | − | 2.89377e6i | −0.148731 | − | 0.257609i | 0.782028 | − | 0.623243i | \(-0.214185\pi\) |
−0.930759 | + | 0.365634i | \(0.880852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25704.0 | + | 44520.6i | −0.00227100 | + | 0.00393349i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.25493e7 | + | 1.08680e7i | −1.10044 | + | 0.953006i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 728896. | − | 1.26248e6i | 0.0634382 | − | 0.109878i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 475452. | + | 823507.i | 0.0410716 | + | 0.0711381i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.96024e6 | 0.168075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.47066e6 | −0.720907 | −0.360454 | − | 0.932777i | \(-0.617378\pi\) | ||||
−0.360454 | + | 0.932777i | \(0.617378\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.55678e6 | − | 2.69642e6i | −0.131513 | − | 0.227787i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.32764e6 | + | 1.26918e7i | −0.614458 | + | 1.06427i | 0.376021 | + | 0.926611i | \(0.377292\pi\) |
−0.990479 | + | 0.137662i | \(0.956041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.93623e6 | + | 1.52571e7i | 0.244408 | + | 1.26998i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.94638e6 | − | 5.10327e6i | 0.243456 | − | 0.421678i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.88081e6 | + | 1.71141e7i | 0.810477 | + | 1.40379i | 0.912531 | + | 0.409008i | \(0.134125\pi\) |
−0.102054 | + | 0.994779i | \(0.532541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.79937e7 | 2.27947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.01942e6 | 0.405753 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29934.0 | − | 51847.2i | −0.00240224 | − | 0.00416080i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.79162e6 | − | 1.17634e7i | 0.541101 | − | 0.937214i | −0.457740 | − | 0.889086i | \(-0.651341\pi\) |
0.998841 | − | 0.0481282i | \(-0.0153256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 67473.0 | + | 350600.i | 0.00533700 | + | 0.0277318i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 138073. | − | 239149.i | 0.0108429 | − | 0.0187805i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.46741e7 | + | 2.54163e7i | 1.14412 | + | 1.98167i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.12283e7 | −0.869206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29915e7 | −0.998538 | −0.499269 | − | 0.866447i | \(-0.666398\pi\) | ||||
−0.499269 | + | 0.866447i | \(0.666398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.68277e6 | + | 9.84284e6i | 0.433682 | + | 0.751160i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.14479e6 | − | 1.23751e7i | 0.541398 | − | 0.937729i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.80098e6 | + | 8.48790e6i | −0.737430 | + | 0.638633i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −954367. | + | 1.65301e6i | −0.0713017 | + | 0.123498i | −0.899472 | − | 0.436978i | \(-0.856049\pi\) |
0.828170 | + | 0.560476i | \(0.189382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.23651e6 | − | 2.14169e6i | −0.0917323 | − | 0.158885i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −387744. | −0.0285641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8772.00 | 0.000641702 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.23617e6 | − | 3.87315e6i | −0.162445 | − | 0.281363i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.55999e6 | + | 9.63018e6i | −0.401099 | + | 0.694724i | −0.993859 | − | 0.110655i | \(-0.964705\pi\) |
0.592760 | + | 0.805379i | \(0.298038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.49071e7 | − | 5.16399e6i | −1.06796 | − | 0.369953i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.24928e6 | − | 2.16382e6i | 0.0888821 | − | 0.153948i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.38978e7 | + | 2.40718e7i | 0.981979 | + | 1.70084i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.37406e6 | −0.587624 | −0.293812 | − | 0.955863i | \(-0.594924\pi\) | ||||
−0.293812 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.76034e7 | − | 3.04900e7i | −1.21844 | − | 2.11040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.32224e6 | + | 4.02224e6i | −0.159642 | + | 0.276508i | −0.934740 | − | 0.355334i | \(-0.884367\pi\) |
0.775098 | + | 0.631841i | \(0.217701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.20794e7 | + | 4.82820e6i | −0.824761 | + | 0.329660i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.02957e6 | − | 1.78327e6i | 0.0698212 | − | 0.120934i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.53116e6 | − | 9.58026e6i | −0.372568 | − | 0.645307i | 0.617392 | − | 0.786656i | \(-0.288189\pi\) |
−0.989960 | + | 0.141349i | \(0.954856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −40203.0 | −0.00268976 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.97245e6 | −0.131079 | −0.0655395 | − | 0.997850i | \(-0.520877\pi\) | ||||
−0.0655395 | + | 0.997850i | \(0.520877\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.53101e6 | + | 1.13120e7i | 0.431112 | + | 0.746707i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.47938e6 | − | 7.75852e6i | 0.293708 | − | 0.508718i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.95938e6 | + | 2.06439e6i | 0.388147 | + | 0.134458i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.51232e6 | − | 1.30117e7i | 0.486042 | − | 0.841850i | −0.513829 | − | 0.857893i | \(-0.671773\pi\) |
0.999871 | + | 0.0160425i | \(0.00510670\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.38748e6 | − | 2.40318e6i | −0.0891740 | − | 0.154454i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.59173e6 | −0.420854 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.72426e6 | −0.299636 | −0.149818 | − | 0.988714i | \(-0.547869\pi\) | ||||
−0.149818 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 34272.0 | + | 59360.8i | 0.00215941 | + | 0.00374021i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.28918e6 | − | 7.42907e6i | 0.268480 | − | 0.465021i | −0.699989 | − | 0.714153i | \(-0.746812\pi\) |
0.968470 | + | 0.249132i | \(0.0801453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.49034e7 | − | 1.29067e7i | 0.926771 | − | 0.802607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.63163e6 | − | 1.14863e7i | 0.409701 | − | 0.709623i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47742.0 | + | 82691.6i | 0.00293030 | + | 0.00507543i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.76168e7 | 1.07426 | 0.537131 | − | 0.843499i | \(-0.319508\pi\) | ||||
0.537131 | + | 0.843499i | \(0.319508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.67886e6 | 0.222883 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 627101. | + | 1.08617e6i | 0.0377475 | + | 0.0653807i | 0.884282 | − | 0.466953i | \(-0.154648\pi\) |
−0.846534 | + | 0.532334i | \(0.821315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.69655e6 | − | 6.40261e6i | 0.221076 | − | 0.382916i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.68308e6 | + | 8.74552e6i | 0.100012 | + | 0.519677i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.14757e7 | + | 1.98765e7i | −0.677542 | + | 1.17354i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 762178. | + | 1.32013e6i | 0.0447125 | + | 0.0774443i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.74433e6 | −0.276548 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.35151e7 | −1.94118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.54560e6 | + | 6.14117e6i | 0.204058 | + | 0.353439i | 0.949832 | − | 0.312760i | \(-0.101254\pi\) |
−0.745774 | + | 0.666199i | \(0.767920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.89656e6 | − | 8.48109e6i | 0.280026 | − | 0.485019i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.49171e6 | + | 7.75114e6i | 0.0847700 | + | 0.440478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −86481.0 | + | 149789.i | −0.00488357 | + | 0.00845860i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.72297e6 | + | 1.33766e7i | 0.433378 | + | 0.750632i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.71630e6 | −0.151472 | −0.0757358 | − | 0.997128i | \(-0.524131\pi\) | ||||
−0.0757358 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.51516e7 | 1.94795 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.38918e6 | + | 4.13817e6i | 0.131573 | + | 0.227891i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 353957. | − | 613072.i | 0.0193714 | − | 0.0335523i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.88787e6 | + | 1.63495e6i | −0.102679 | + | 0.0889229i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.00730e6 | − | 5.20881e6i | 0.162552 | − | 0.281549i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.09370e7 | + | 1.89434e7i | 0.587524 | + | 1.01762i | 0.994556 | + | 0.104207i | \(0.0332304\pi\) |
−0.407032 | + | 0.913414i | \(0.633436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.72352e7 | 0.920164 | 0.460082 | − | 0.887876i | \(-0.347820\pi\) | ||||
0.460082 | + | 0.887876i | \(0.347820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.47598e6 | 0.396681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.83200e6 | − | 8.36926e6i | −0.254819 | − | 0.441360i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.37665e7 | − | 2.38444e7i | 0.721556 | − | 1.24977i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29767.5 | − | 10311.8i | −0.00155072 | − | 0.000537184i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.13096e7 | − | 1.95887e7i | 0.585582 | − | 1.01426i | −0.409220 | − | 0.912436i | \(-0.634199\pi\) |
0.994803 | − | 0.101823i | \(-0.0324674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 813164. | + | 1.40844e6i | 0.0418484 | + | 0.0724835i | 0.886191 | − | 0.463320i | \(-0.153342\pi\) |
−0.844343 | + | 0.535804i | \(0.820009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.30693e6 | −0.0668523 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.28304e7 | 1.16078 | 0.580391 | − | 0.814338i | \(-0.302900\pi\) | ||||
0.580391 | + | 0.814338i | \(0.302900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.29297e7 | − | 2.23948e7i | −0.653432 | − | 1.13178i | −0.982284 | − | 0.187397i | \(-0.939995\pi\) |
0.328852 | − | 0.944382i | \(-0.393338\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.16283e6 | + | 7.21023e6i | −0.209115 | + | 0.362198i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.51433e7 | − | 1.97952e7i | −1.25548 | − | 0.988433i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.25965e6 | − | 3.91383e6i | 0.112157 | − | 0.194261i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 630950. | + | 1.09284e6i | 0.0311301 | + | 0.0539190i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23061e7 | 0.603554 | 0.301777 | − | 0.953379i | \(-0.402420\pi\) | ||||
0.301777 | + | 0.953379i | \(0.402420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.18429e7 | 1.06493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.01357e6 | − | 1.04158e7i | −0.291449 | − | 0.504805i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.59652e7 | − | 2.76526e7i | 0.769189 | − | 1.33227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.95871e7 | − | 6.78518e6i | −0.938129 | − | 0.324977i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.46831e6 | + | 7.73933e6i | −0.212752 | + | 0.368497i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 854896. | + | 1.48072e6i | 0.0404659 | + | 0.0700890i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.91416e7 | −0.900753 | −0.450377 | − | 0.892839i | \(-0.648710\pi\) | ||||
−0.450377 | + | 0.892839i | \(0.648710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.03724e7 | 0.485247 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.37754e6 | + | 4.11801e6i | 0.110580 | + | 0.191529i | 0.916004 | − | 0.401169i | \(-0.131396\pi\) |
−0.805424 | + | 0.592698i | \(0.798063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.59938e6 | + | 7.96636e6i | −0.212675 | + | 0.368364i | −0.952551 | − | 0.304380i | \(-0.901551\pi\) |
0.739876 | + | 0.672743i | \(0.234884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.35951e7 | + | 1.17737e7i | −0.624994 | + | 0.541261i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.67659e6 | + | 1.50283e7i | −0.396572 | + | 0.686883i | −0.993300 | − | 0.115560i | \(-0.963134\pi\) |
0.596728 | + | 0.802443i | \(0.296467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.81601e6 | + | 1.00736e7i | 0.264292 | + | 0.457768i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.98482e7 | 0.896756 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03805e6 | −0.0466305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 90844.5 | + | 157347.i | 0.00405745 | + | 0.00702771i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.85376e6 | − | 8.40696e6i | 0.215547 | − | 0.373339i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.41462e6 | − | 1.25467e7i | −0.106618 | − | 0.554001i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.77811e7 | − | 3.07978e7i | 0.780655 | − | 1.35213i | −0.150905 | − | 0.988548i | \(-0.548219\pi\) |
0.931560 | − | 0.363587i | \(-0.118448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.53595e6 | − | 4.39239e6i | −0.110705 | − | 0.191747i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.63056e7 | −1.14185 | −0.570923 | − | 0.821003i | \(-0.693415\pi\) | ||||
−0.570923 | + | 0.821003i | \(0.693415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.20394e7 | −0.519642 | −0.259821 | − | 0.965657i | \(-0.583664\pi\) | ||||
−0.259821 | + | 0.965657i | \(0.583664\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.23174e7 | − | 2.13344e7i | −0.528643 | − | 0.915636i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −66795.0 | + | 115692.i | −0.00285059 | + | 0.00493737i | −0.867447 | − | 0.497529i | \(-0.834241\pi\) |
0.864597 | + | 0.502467i | \(0.167574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.72314e6 | − | 1.93460e7i | −0.157999 | − | 0.820989i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 111537. | − | 193188.i | 0.00470679 | − | 0.00815240i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.37450e7 | + | 2.38070e7i | 0.576786 | + | 0.999023i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.15549e7 | −0.899472 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6048.00 | −0.000250975 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.63267e6 | − | 9.75608e6i | −0.232442 | − | 0.402602i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.89981e7 | + | 3.29057e7i | −0.779648 | + | 1.35039i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.63091e7 | − | 1.41241e7i | 0.665594 | − | 0.576422i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.56702e6 | + | 1.48385e7i | −0.347703 | + | 0.602239i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.37379e6 | − | 1.10397e7i | −0.257264 | − | 0.445595i | 0.708244 | − | 0.705968i | \(-0.249488\pi\) |
−0.965508 | + | 0.260373i | \(0.916154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.10081e6 | 0.325176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.43253e7 | −0.971095 | −0.485548 | − | 0.874210i | \(-0.661380\pi\) | ||||
−0.485548 | + | 0.874210i | \(0.661380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.88023e6 | − | 3.25666e6i | −0.0746509 | − | 0.129299i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.23121e7 | − | 3.86457e7i | 0.881024 | − | 1.52598i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.88490e7 | − | 9.99359e6i | −1.13294 | − | 0.392462i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.92402e7 | + | 3.33251e7i | −0.751487 | + | 1.30161i | 0.195615 | + | 0.980681i | \(0.437330\pi\) |
−0.947102 | + | 0.320933i | \(0.896004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27216e7 | + | 2.20345e7i | 0.494190 | + | 0.855963i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −134502. | −0.00519666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.26005e7 | −1.25277 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.92849e6 | + | 8.53639e6i | 0.188371 | + | 0.326268i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.98339e7 | + | 3.43533e7i | −0.753996 | + | 1.30596i | 0.191876 | + | 0.981419i | \(0.438543\pi\) |
−0.945872 | + | 0.324540i | \(0.894791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.57509e6 | − | 2.47689e7i | 0.135180 | − | 0.936555i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.07291e6 | + | 8.78654e6i | −0.190789 | + | 0.330456i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.78365e6 | − | 4.82142e6i | −0.104132 | − | 0.180362i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.48428e7 | 0.552288 | 0.276144 | − | 0.961116i | \(-0.410943\pi\) | ||||
0.276144 | + | 0.961116i | \(0.410943\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.12412e7 | −0.786166 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.33532e7 | − | 4.04488e7i | −0.859748 | − | 1.48913i | −0.872169 | − | 0.489205i | \(-0.837287\pi\) |
0.0124203 | − | 0.999923i | \(-0.496046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.72637e6 | + | 2.99016e6i | −0.0632199 | + | 0.109500i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.68001e6 | + | 2.66044e6i | 0.279758 | + | 0.0969110i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.01190e7 | − | 3.48471e7i | 0.729006 | − | 1.26267i | −0.228298 | − | 0.973591i | \(-0.573316\pi\) |
0.957304 | − | 0.289083i | \(-0.0933505\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31231.5 | + | 54094.5i | 0.00112571 | + | 0.00194979i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.00178e7 | −0.717737 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.45579e7 | 0.875908 | 0.437954 | − | 0.898997i | \(-0.355703\pi\) | ||||
0.437954 | + | 0.898997i | \(0.355703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.02671e7 | − | 1.77832e7i | −0.364284 | − | 0.630958i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −995724. | + | 1.72464e6i | −0.0351446 | + | 0.0608723i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.18998e7 | + | 2.76260e7i | −1.12006 | + | 0.970000i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.28164e7 | − | 2.21986e7i | 0.447669 | − | 0.775386i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.97024e6 | − | 3.41256e6i | −0.0684627 | − | 0.118581i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.36943e6 | 0.254751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.34313e7 | −1.83751 | −0.918754 | − | 0.394830i | \(-0.870803\pi\) | ||||
−0.918754 | + | 0.394830i | \(0.870803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.27578e7 | + | 2.20971e7i | 0.436480 | + | 0.756006i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.40743e6 | + | 2.43773e6i | −0.0479046 | + | 0.0829733i | −0.888983 | − | 0.457939i | \(-0.848588\pi\) |
0.841079 | + | 0.540913i | \(0.181921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 78669.5 | + | 408779.i | 0.00266394 | + | 0.0138422i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57658.5 | − | 99867.5i | 0.00194246 | − | 0.00336444i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.27356e7 | − | 2.20588e7i | −0.426859 | − | 0.739341i | 0.569733 | − | 0.821830i | \(-0.307047\pi\) |
−0.996592 | + | 0.0824885i | \(0.973713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00573e6 | 0.0668829 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.23181e7 | −0.408668 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.45067e6 | − | 2.51264e6i | −0.0478835 | − | 0.0829367i | 0.841090 | − | 0.540895i | \(-0.181914\pi\) |
−0.888974 | + | 0.457958i | \(0.848581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.07054e6 | − | 5.31834e6i | 0.100838 | − | 0.174657i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.07087e6 | + | 2.11529e7i | 0.133013 | + | 0.691156i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.07099e6 | − | 3.58706e6i | 0.0673268 | − | 0.116613i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36892e6 | + | 2.37103e6i | 0.0442785 | + | 0.0766927i | 0.887315 | − | 0.461163i | \(-0.152568\pi\) |
−0.843037 | + | 0.537856i | \(0.819234\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.33274e7 | 1.07258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.11763e7 | 1.95896 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.37040e7 | + | 2.37359e7i | 0.436624 | + | 0.756256i | 0.997427 | − | 0.0716942i | \(-0.0228406\pi\) |
−0.560802 | + | 0.827950i | \(0.689507\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.78223e6 | − | 4.81896e6i | 0.0882021 | − | 0.152771i |
(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 | 336.6.q.a.289.1 | 2 | ||
4.3 | odd | 2 | 42.6.e.b.37.1 | yes | 2 | ||
7.4 | even | 3 | inner | 336.6.q.a.193.1 | 2 | ||
12.11 | even | 2 | 126.6.g.b.37.1 | 2 | |||
28.3 | even | 6 | 294.6.e.m.67.1 | 2 | |||
28.11 | odd | 6 | 42.6.e.b.25.1 | ✓ | 2 | ||
28.19 | even | 6 | 294.6.a.e.1.1 | 1 | |||
28.23 | odd | 6 | 294.6.a.d.1.1 | 1 | |||
28.27 | even | 2 | 294.6.e.m.79.1 | 2 | |||
84.11 | even | 6 | 126.6.g.b.109.1 | 2 | |||
84.23 | even | 6 | 882.6.a.m.1.1 | 1 | |||
84.47 | odd | 6 | 882.6.a.y.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.e.b.25.1 | ✓ | 2 | 28.11 | odd | 6 | ||
42.6.e.b.37.1 | yes | 2 | 4.3 | odd | 2 | ||
126.6.g.b.37.1 | 2 | 12.11 | even | 2 | |||
126.6.g.b.109.1 | 2 | 84.11 | even | 6 | |||
294.6.a.d.1.1 | 1 | 28.23 | odd | 6 | |||
294.6.a.e.1.1 | 1 | 28.19 | even | 6 | |||
294.6.e.m.67.1 | 2 | 28.3 | even | 6 | |||
294.6.e.m.79.1 | 2 | 28.27 | even | 2 | |||
336.6.q.a.193.1 | 2 | 7.4 | even | 3 | inner | ||
336.6.q.a.289.1 | 2 | 1.1 | even | 1 | trivial | ||
882.6.a.m.1.1 | 1 | 84.23 | even | 6 | |||
882.6.a.y.1.1 | 1 | 84.47 | odd | 6 |