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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 118x^{6} + 555x^{5} + 12174x^{4} + 28215x^{3} + 199593x^{2} - 283824x + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(5.87364 + 10.1734i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.k.193.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 21.8866 | − | 37.9086i | 0.391519 | − | 0.678130i | −0.601131 | − | 0.799150i | \(-0.705283\pi\) |
0.992650 | + | 0.121020i | \(0.0386165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 65.0901 | + | 112.117i | 0.502076 | + | 0.864823i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 167.022 | + | 289.291i | 0.416191 | + | 0.720864i | 0.995553 | − | 0.0942064i | \(-0.0300314\pi\) |
−0.579361 | + | 0.815071i | \(0.696698\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.3608 | 0.0842895 | 0.0421447 | − | 0.999112i | \(-0.486581\pi\) | ||||
0.0421447 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 393.958 | 0.452087 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −45.1772 | − | 78.2492i | −0.0379138 | − | 0.0656685i | 0.846446 | − | 0.532475i | \(-0.178738\pi\) |
−0.884360 | + | 0.466806i | \(0.845405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −127.305 | + | 220.500i | −0.0809027 | + | 0.140128i | −0.903638 | − | 0.428297i | \(-0.859114\pi\) |
0.822735 | + | 0.568425i | \(0.192447\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −580.962 | + | 1011.85i | −0.287475 | + | 0.500691i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −208.044 | + | 360.344i | −0.0820043 | + | 0.142036i | −0.904111 | − | 0.427298i | \(-0.859465\pi\) |
0.822106 | + | 0.569334i | \(0.192799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 604.457 | + | 1046.95i | 0.193426 | + | 0.335024i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3103.97 | −0.685366 | −0.342683 | − | 0.939451i | \(-0.611336\pi\) | ||||
−0.342683 | + | 0.939451i | \(0.611336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.3099 | − | 64.6226i | −0.00697300 | − | 0.0120776i | 0.862518 | − | 0.506027i | \(-0.168886\pi\) |
−0.869491 | + | 0.493949i | \(0.835553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1503.20 | + | 2603.62i | −0.240288 | + | 0.416191i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5674.81 | − | 13.6153i | 0.783035 | − | 0.00187869i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2461.48 | + | 4263.41i | −0.295592 | + | 0.511980i | −0.975122 | − | 0.221667i | \(-0.928850\pi\) |
0.679530 | + | 0.733647i | \(0.262184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 231.124 | + | 400.318i | 0.0243323 | + | 0.0421447i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3568.39 | −0.331522 | −0.165761 | − | 0.986166i | \(-0.553008\pi\) | ||||
−0.165761 | + | 0.986166i | \(0.553008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20365.6 | 1.67967 | 0.839837 | − | 0.542838i | \(-0.182650\pi\) | ||||
0.839837 | + | 0.542838i | \(0.182650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1772.81 | + | 3070.60i | 0.130506 | + | 0.226043i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6721.95 | − | 11642.8i | 0.443865 | − | 0.768797i | −0.554107 | − | 0.832445i | \(-0.686940\pi\) |
0.997972 | + | 0.0636486i | \(0.0202737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8333.56 | + | 14595.4i | −0.495839 | + | 0.868415i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 406.595 | − | 704.243i | 0.0218895 | − | 0.0379138i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3131.01 | + | 5423.06i | 0.153107 | + | 0.265189i | 0.932368 | − | 0.361510i | \(-0.117739\pi\) |
−0.779261 | + | 0.626699i | \(0.784405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14622.2 | 0.651787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2291.50 | −0.0934184 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −561.308 | − | 972.214i | −0.0209928 | − | 0.0363607i | 0.855338 | − | 0.518070i | \(-0.173349\pi\) |
−0.876331 | + | 0.481709i | \(0.840016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15309.5 | + | 26516.9i | −0.526790 | + | 0.912428i | 0.472722 | + | 0.881211i | \(0.343271\pi\) |
−0.999513 | + | 0.0312162i | \(0.990062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10501.0 | + | 25.1944i | −0.333332 | + | 0.000799746i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1124.11 | − | 1947.02i | 0.0330009 | − | 0.0571592i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30650.3 | + | 53087.9i | 0.834157 | + | 1.44480i | 0.894715 | + | 0.446638i | \(0.147379\pi\) |
−0.0605570 | + | 0.998165i | \(0.519288\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3744.80 | −0.0946904 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6112.32 | −0.143900 | −0.0719499 | − | 0.997408i | \(-0.522922\pi\) | ||||
−0.0719499 | + | 0.997408i | \(0.522922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5203.58 | − | 9012.87i | −0.114287 | − | 0.197950i | 0.803208 | − | 0.595699i | \(-0.203125\pi\) |
−0.917494 | + | 0.397749i | \(0.869792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5440.11 | + | 9422.55i | −0.111675 | + | 0.193426i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21563.0 | + | 37556.1i | −0.414460 | + | 0.721861i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −21611.5 | + | 37432.2i | −0.389598 | + | 0.674804i | −0.992395 | − | 0.123090i | \(-0.960720\pi\) |
0.602797 | + | 0.797895i | \(0.294053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −25057.7 | −0.399251 | −0.199625 | − | 0.979872i | \(-0.563972\pi\) | ||||
−0.199625 | + | 0.979872i | \(0.563972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3955.09 | −0.0593758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13967.9 | − | 24193.0i | −0.197848 | − | 0.342683i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −43209.1 | + | 74840.3i | −0.578229 | + | 1.00152i | 0.417453 | + | 0.908698i | \(0.362923\pi\) |
−0.995683 | + | 0.0928239i | \(0.970411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3343.08 | + | 5758.43i | 0.0423197 | + | 0.0728955i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 335.789 | − | 581.604i | 0.00402587 | − | 0.00697300i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5572.56 | + | 9651.96i | 0.0633499 | + | 0.109725i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −59317.2 | −0.640105 | −0.320052 | − | 0.947400i | \(-0.603700\pi\) | ||||
−0.320052 | + | 0.947400i | \(0.603700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −27057.6 | −0.277461 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18971.6 | + | 32859.7i | 0.185055 | + | 0.320524i | 0.943595 | − | 0.331102i | \(-0.107420\pi\) |
−0.758540 | + | 0.651626i | \(0.774087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −61903.9 | + | 107221.i | −0.574943 | + | 0.995830i | 0.421105 | + | 0.907012i | \(0.361642\pi\) |
−0.996048 | + | 0.0888184i | \(0.971691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 25642.8 | + | 44169.5i | 0.226982 | + | 0.390975i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −60880.3 | + | 105448.i | −0.514064 | + | 0.890385i | 0.485803 | + | 0.874068i | \(0.338527\pi\) |
−0.999867 | + | 0.0163163i | \(0.994806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −23898.2 | − | 41392.8i | −0.192663 | − | 0.333702i | 0.753469 | − | 0.657484i | \(-0.228379\pi\) |
−0.946132 | + | 0.323781i | \(0.895046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −44306.7 | −0.341320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 158165. | 1.16523 | 0.582617 | − | 0.812747i | \(-0.302029\pi\) | ||||
0.582617 | + | 0.812747i | \(0.302029\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9106.76 | + | 15773.4i | 0.0642124 | + | 0.111219i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2080.11 | + | 3602.86i | −0.0140482 | + | 0.0243323i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5832.50 | − | 10158.4i | 0.0377561 | − | 0.0657593i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24732.6 | − | 42838.1i | 0.153570 | − | 0.265991i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16057.7 | − | 27812.8i | −0.0957021 | − | 0.165761i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 189709. | 1.08596 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 887.264 | 0.00488139 | 0.00244070 | − | 0.999997i | \(-0.499223\pi\) | ||||
0.00244070 | + | 0.999997i | \(0.499223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 91645.0 | + | 158734.i | 0.484880 | + | 0.839837i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −152395. | + | 263956.i | −0.775877 | + | 1.34386i | 0.158424 | + | 0.987371i | \(0.449359\pi\) |
−0.934300 | + | 0.356487i | \(0.883975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −33008.1 | + | 79.1946i | −0.161805 | + | 0.000388210i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15955.3 | + | 27635.4i | −0.0753478 | + | 0.130506i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 191249. | + | 331254.i | 0.870559 | + | 1.50785i | 0.861419 | + | 0.507895i | \(0.169576\pi\) |
0.00914050 | + | 0.999958i | \(0.497090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 256870. | 1.12765 | 0.563827 | − | 0.825893i | \(-0.309328\pi\) | ||||
0.563827 | + | 0.825893i | \(0.309328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 120995. | 0.512531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8578.40 | + | 14858.2i | 0.0350805 | + | 0.0607613i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −67935.2 | + | 117667.i | −0.268334 | + | 0.464767i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −151261. | + | 725.830i | −0.577344 | + | 0.00277039i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 218803. | − | 378978.i | 0.807398 | − | 1.39845i | −0.107263 | − | 0.994231i | \(-0.534209\pi\) |
0.914661 | − | 0.404223i | \(-0.132458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123625. | + | 214124.i | 0.441227 | + | 0.764228i | 0.997781 | − | 0.0665837i | \(-0.0212099\pi\) |
−0.556554 | + | 0.830812i | \(0.687877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7318.70 | 0.0252758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3266.34 | −0.0109202 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −143559. | − | 248652.i | −0.464817 | − | 0.805086i | 0.534377 | − | 0.845247i | \(-0.320546\pi\) |
−0.999193 | + | 0.0401604i | \(0.987213\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28179.1 | + | 48807.6i | −0.0883962 | + | 0.153107i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −53942.4 | + | 129.421i | −0.164008 | + | 0.000393496i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −207591. | + | 359558.i | −0.611983 | + | 1.05999i | 0.378923 | + | 0.925428i | \(0.376295\pi\) |
−0.990906 | + | 0.134558i | \(0.957039\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 65799.8 | + | 113969.i | 0.188155 | + | 0.325893i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 460536. | 1.27783 | 0.638914 | − | 0.769278i | \(-0.279384\pi\) | ||||
0.638914 | + | 0.769278i | \(0.279384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −368655. | −0.992895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10311.7 | − | 17860.5i | −0.0269676 | − | 0.0467092i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 86491.7 | − | 149808.i | 0.219715 | − | 0.380557i | −0.735006 | − | 0.678061i | \(-0.762821\pi\) |
0.954721 | + | 0.297504i | \(0.0961540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −78037.0 | + | 135916.i | −0.192622 | + | 0.335487i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5051.77 | − | 8749.92i | 0.0121202 | − | 0.0209928i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −335711. | − | 581468.i | −0.783128 | − | 1.35642i | −0.930111 | − | 0.367279i | \(-0.880290\pi\) |
0.146983 | − | 0.989139i | \(-0.453044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −436870. | −0.991187 | −0.495594 | − | 0.868555i | \(-0.665049\pi\) | ||||
−0.495594 | + | 0.868555i | \(0.665049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −275572. | −0.608285 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 107747. | + | 186623.i | 0.231460 | + | 0.400900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15091.2 | − | 26138.7i | 0.0315587 | − | 0.0546613i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −47450.7 | − | 81733.5i | −0.0966246 | − | 0.166435i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 343882. | − | 595622.i | 0.682066 | − | 1.18137i | −0.292283 | − | 0.956332i | \(-0.594415\pi\) |
0.974349 | − | 0.225041i | \(-0.0722517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −127984. | − | 221676.i | −0.247323 | − | 0.428375i | 0.715459 | − | 0.698654i | \(-0.246217\pi\) |
−0.962782 | + | 0.270279i | \(0.912884\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20234.0 | 0.0381062 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −141432. | −0.259647 | −0.129824 | − | 0.991537i | \(-0.541441\pi\) | ||||
−0.129824 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −109813. | − | 190201.i | −0.196571 | − | 0.340472i | 0.750843 | − | 0.660481i | \(-0.229647\pi\) |
−0.947415 | + | 0.320009i | \(0.896314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −275853. | + | 477791.i | −0.481601 | + | 0.834157i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −202038. | − | 348009.i | −0.344106 | − | 0.592720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −78099.7 | + | 135273.i | −0.129797 | + | 0.224815i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16851.6 | − | 29187.8i | −0.0273348 | − | 0.0473452i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −85051.5 | −0.134684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 83847.8 | 0.129654 | 0.0648270 | − | 0.997897i | \(-0.479350\pi\) | ||||
0.0648270 | + | 0.997897i | \(0.479350\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27505.4 | − | 47640.8i | −0.0415403 | − | 0.0719499i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 445732. | − | 772030.i | 0.657624 | − | 1.13904i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4816.81 | − | 8389.38i | 0.00694401 | − | 0.0120943i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 46832.3 | − | 81115.8i | 0.0659834 | − | 0.114287i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2320.34 | − | 4018.94i | −0.00319573 | − | 0.00553517i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35948e6 | 1.83067 | 0.915334 | − | 0.402696i | \(-0.131927\pi\) | ||||
0.915334 | + | 0.402696i | \(0.131927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −97922.0 | −0.128951 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −39.6650 | − | 68.7017i | −5.10908e−5 | − | 8.84918e-5i | 0.866000 | − | 0.500044i | \(-0.166683\pi\) |
−0.866051 | + | 0.499956i | \(0.833350\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −313520. | + | 543033.i | −0.395073 | + | 0.684286i | −0.993110 | − | 0.117182i | \(-0.962614\pi\) |
0.598038 | + | 0.801468i | \(0.295947\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −389754. | + | 935.116i | −0.480575 | + | 0.00115302i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 437020. | − | 756941.i | 0.527365 | − | 0.913423i | −0.472126 | − | 0.881531i | \(-0.656513\pi\) |
0.999491 | − | 0.0318924i | \(-0.0101534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −294241. | − | 509640.i | −0.347563 | − | 0.601996i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −389007. | −0.449870 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.24472e6 | 1.40954 | 0.704768 | − | 0.709438i | \(-0.251051\pi\) | ||||
0.704768 | + | 0.709438i | \(0.251051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −829806. | − | 1.43727e6i | −0.920310 | − | 1.59402i | −0.798935 | − | 0.601417i | \(-0.794603\pi\) |
−0.121375 | − | 0.992607i | \(-0.538730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 370900. | + | 635358.i | 0.394768 | + | 0.676244i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6538.51 | + | 11325.0i | −0.00681925 | + | 0.0118113i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −112760. | − | 195305.i | −0.115254 | − | 0.199625i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 683674. | 0.684959 | 0.342479 | − | 0.939525i | \(-0.388733\pi\) | ||||
0.342479 | + | 0.939525i | \(0.388733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138992. | −0.136518 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17797.9 | − | 30826.9i | −0.0171403 | − | 0.0296879i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 796279. | − | 1.37920e6i | 0.752026 | − | 1.30255i | −0.194814 | − | 0.980840i | \(-0.562410\pi\) |
0.946839 | − | 0.321706i | \(-0.104256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −638221. | + | 1531.25i | −0.591182 | + | 0.00141839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 125711. | − | 217737.i | 0.114228 | − | 0.197848i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −368365. | − | 638026.i | −0.328389 | − | 0.568786i | 0.653803 | − | 0.756664i | \(-0.273172\pi\) |
−0.982192 | + | 0.187878i | \(0.939839\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 274108. | 0.239777 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −777763. | −0.667682 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −782085. | − | 1.35461e6i | −0.658981 | − | 1.14139i | −0.980880 | − | 0.194615i | \(-0.937654\pi\) |
0.321899 | − | 0.946774i | \(-0.395679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 817767. | − | 1.41641e6i | 0.676404 | − | 1.17157i | −0.299652 | − | 0.954048i | \(-0.596871\pi\) |
0.976056 | − | 0.217518i | \(-0.0697960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −29838.7 | + | 51969.7i | −0.0242311 | + | 0.0422030i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −201916. | + | 349728.i | −0.161005 | + | 0.278868i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113434. | + | 196473.i | 0.0888264 | + | 0.153852i | 0.907015 | − | 0.421098i | \(-0.138355\pi\) |
−0.818189 | + | 0.574949i | \(0.805022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6044.20 | 0.00464867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −583971. | −0.441190 | −0.220595 | − | 0.975366i | \(-0.570800\pi\) | ||||
−0.220595 | + | 0.975366i | \(0.570800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −41952.8 | − | 72664.4i | −0.0311383 | − | 0.0539332i | 0.850036 | − | 0.526724i | \(-0.176580\pi\) |
−0.881175 | + | 0.472791i | \(0.843247\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −50153.0 | + | 86867.6i | −0.0365751 | + | 0.0633499i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −232267. | − | 400078.i | −0.166449 | − | 0.286708i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 705847. | − | 1.22256e6i | 0.497125 | − | 0.861046i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −266927. | − | 462331.i | −0.184782 | − | 0.320052i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.25224e6 | 0.852153 | 0.426076 | − | 0.904687i | \(-0.359895\pi\) | ||||
0.426076 | + | 0.904687i | \(0.359895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49140.4 | −0.0328763 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −121759. | − | 210893.i | −0.0800960 | − | 0.138730i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10685.3 | + | 18507.5i | −0.00691210 | + | 0.0119721i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.32560e6 | + | 2.28333e6i | 0.843325 | + | 1.45262i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −170744. | + | 295737.i | −0.106841 | + | 0.185055i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 670147. | + | 1.16073e6i | 0.412497 | + | 0.714465i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47937e6 | −1.50140 | −0.750699 | − | 0.660645i | \(-0.770283\pi\) | ||||
−0.750699 | + | 0.660645i | \(0.770283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.11427e6 | −0.663887 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 790296. | + | 1.36883e6i | 0.463329 | + | 0.802509i | 0.999124 | − | 0.0418390i | \(-0.0133216\pi\) |
−0.535796 | + | 0.844348i | \(0.679988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −56967.7 | + | 98670.9i | −0.0328676 | + | 0.0569283i | −0.881991 | − | 0.471266i | \(-0.843797\pi\) |
0.849124 | + | 0.528194i | \(0.177131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −228875. | + | 398628.i | −0.129964 | + | 0.226356i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.34397e6 | − | 2.32783e6i | 0.751176 | − | 1.30108i | −0.196077 | − | 0.980589i | \(-0.562820\pi\) |
0.947253 | − | 0.320487i | \(-0.103847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −518432. | − | 897951.i | −0.285243 | − | 0.494056i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.09584e6 | −0.593590 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23005.2 | 0.0122693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31045.4 | + | 53772.2i | 0.0163038 | + | 0.0282390i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 215083. | − | 372536.i | 0.111234 | − | 0.192663i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.74289e6 | − | 4181.61i | 0.887727 | − | 0.00212987i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.83147e6 | + | 3.17219e6i | −0.918816 | + | 1.59144i | −0.117601 | + | 0.993061i | \(0.537520\pi\) |
−0.801216 | + | 0.598376i | \(0.795813\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −199380. | − | 345337.i | −0.0985307 | − | 0.170660i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.68332e6 | 1.30635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 431607. | 0.207021 | 0.103510 | − | 0.994628i | \(-0.466993\pi\) | ||||
0.103510 | + | 0.994628i | \(0.466993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 711741. | + | 1.23277e6i | 0.336374 | + | 0.582617i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12463.2 | − | 21586.9i | 0.00580421 | − | 0.0100532i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.17883e6 | + | 15682.9i | −0.999974 | + | 0.00719766i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −81960.8 | + | 141960.i | −0.0370731 | + | 0.0642124i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −171029. | − | 296231.i | −0.0762511 | − | 0.132071i | 0.825379 | − | 0.564580i | \(-0.190962\pi\) |
−0.901630 | + | 0.432509i | \(0.857628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 827018. | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37442.0 | −0.0162215 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −133454. | − | 231149.i | −0.0570026 | − | 0.0987314i | 0.836116 | − | 0.548553i | \(-0.184821\pi\) |
−0.893119 | + | 0.449821i | \(0.851488\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −133778. | + | 231710.i | −0.0563394 | + | 0.0975828i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 105423. | − | 252.936i | 0.0437789 | − | 0.000105036i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 124401. | − | 215469.i | 0.0509434 | − | 0.0882366i | −0.839429 | − | 0.543469i | \(-0.817111\pi\) |
0.890373 | + | 0.455232i | \(0.150444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.20564e6 | + | 2.08822e6i | 0.486909 | + | 0.843352i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 445186. | 0.177327 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −455554. | −0.178981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −329673. | − | 571010.i | −0.127767 | − | 0.221299i | 0.795044 | − | 0.606551i | \(-0.207448\pi\) |
−0.922811 | + | 0.385253i | \(0.874114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 144520. | − | 250315.i | 0.0552536 | − | 0.0957021i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −404221. | + | 704028.i | −0.152470 | + | 0.265555i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 199710. | − | 345907.i | 0.0743236 | − | 0.128732i | −0.826468 | − | 0.562983i | \(-0.809654\pi\) |
0.900792 | + | 0.434251i | \(0.142987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 853690. | + | 1.47863e6i | 0.313489 | + | 0.542979i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −159422. | −0.0577691 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.42582e6 | −1.22509 | −0.612543 | − | 0.790437i | \(-0.709853\pi\) | ||||
−0.612543 | + | 0.790437i | \(0.709853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3992.69 | + | 6915.54i | 0.00140914 | + | 0.00244070i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.34375e6 | − | 4.05949e6i | 0.816421 | − | 1.41408i | −0.0918822 | − | 0.995770i | \(-0.529288\pi\) |
0.908303 | − | 0.418313i | \(-0.137378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 951759. | + | 1.63940e6i | 0.327247 | + | 0.563680i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −824805. | + | 1.42860e6i | −0.279946 | + | 0.484880i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 660449. | + | 1.14393e6i | 0.221292 | + | 0.383289i | 0.955201 | − | 0.295959i | \(-0.0956393\pi\) |
−0.733909 | + | 0.679248i | \(0.762306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37595.4 | 0.0124364 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.74311e6 | −0.895905 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 946003. | + | 1.63853e6i | 0.305070 | + | 0.528397i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 146821. | − | 254301.i | 0.0467531 | − | 0.0809788i | −0.841702 | − | 0.539943i | \(-0.818446\pi\) |
0.888455 | + | 0.458964i | \(0.151779\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −149154. | − | 256917.i | −0.0469032 | − | 0.0807904i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.41600e6 | − | 2.45258e6i | 0.439745 | − | 0.761661i | −0.557925 | − | 0.829892i | \(-0.688402\pi\) |
0.997670 | + | 0.0682310i | \(0.0217355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1916.27 | − | 3319.07i | −0.000587751 | − | 0.00101801i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −287195. | −0.0870042 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.64449e6 | −0.492091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 379369. | + | 657086.i | 0.112138 | + | 0.194229i | 0.916632 | − | 0.399732i | \(-0.130897\pi\) |
−0.804494 | + | 0.593961i | \(0.797563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.72124e6 | + | 2.98128e6i | −0.502618 | + | 0.870559i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 72466.4 | − | 126214.i | 0.0209055 | − | 0.0364109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −548426. | + | 949902.i | −0.156314 | + | 0.270744i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.15591e6 | + | 2.00210e6i | 0.325526 | + | 0.563827i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.52140e6 | 1.53643 | 0.768217 | − | 0.640190i | \(-0.221144\pi\) | ||||
0.768217 | + | 0.640190i | \(0.221144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.49511e6 | −0.686095 | −0.343047 | − | 0.939318i | \(-0.611459\pi\) | ||||
−0.343047 | + | 0.939318i | \(0.611459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 544478. | + | 943064.i | 0.147955 | + | 0.256266i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 54615.3 | − | 94596.5i | 0.0146670 | − | 0.0254040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.96950e6 | + | 9523.81i | −1.05358 | + | 0.00252779i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −77205.6 | + | 133724.i | −0.0202538 | + | 0.0350805i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.27016e6 | + | 2.19999e6i | 0.329357 | + | 0.570463i | 0.982384 | − | 0.186871i | \(-0.0598348\pi\) |
−0.653028 | + | 0.757334i | \(0.726501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.61890e6 | −1.44023 | −0.720114 | − | 0.693855i | \(-0.755911\pi\) | ||||
−0.720114 | + | 0.693855i | \(0.755911\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.22283e6 | −0.309845 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −52970.4 | − | 91747.4i | −0.0132687 | − | 0.0229821i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.88879e6 | − | 3.27147e6i | 0.467758 | − | 0.810181i | −0.531563 | − | 0.847019i | \(-0.678395\pi\) |
0.999321 | + | 0.0368379i | \(0.0117285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −686333. | − | 1.17570e6i | −0.168050 | − | 0.287872i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.79882e6 | + | 3.11565e6i | −0.435491 | + | 0.754292i | −0.997336 | − | 0.0729505i | \(-0.976758\pi\) |
0.561845 | + | 0.827243i | \(0.310092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.89140e6 | + | 3.27599e6i | 0.452775 | + | 0.784229i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.93845e6 | 0.932302 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.97694e6 | −0.696873 | −0.348437 | − | 0.937332i | \(-0.613287\pi\) | ||||
−0.348437 | + | 0.937332i | \(0.613287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −596000. | − | 1.03230e6i | −0.137976 | − | 0.238982i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.11262e6 | + | 1.92712e6i | −0.254743 | + | 0.441227i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 291463. | − | 699.291i | 0.0660016 | − | 0.000158354i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −539924. | + | 935176.i | −0.120932 | + | 0.209461i | −0.920136 | − | 0.391600i | \(-0.871922\pi\) |
0.799203 | + | 0.601061i | \(0.205255\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32934.2 | + | 57043.6i | 0.00729651 | + | 0.0126379i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.35905e6 | −1.17445 | −0.587226 | − | 0.809423i | \(-0.699780\pi\) | ||||
−0.587226 | + | 0.809423i | \(0.699780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.63745e6 | 1.22217 | 0.611083 | − | 0.791567i | \(-0.290734\pi\) | ||||
0.611083 | + | 0.791567i | \(0.290734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14698.5 | − | 25458.6i | −0.00315240 | − | 0.00546012i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 789613. | − | 1.36765e6i | 0.167541 | − | 0.290190i | −0.770013 | − | 0.638028i | \(-0.779751\pi\) |
0.937555 | + | 0.347837i | \(0.113084\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.95704e6 | + | 6.89193e6i | −0.830689 | + | 1.44680i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29203e6 | − | 2.23787e6i | 0.268362 | − | 0.464817i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.40150e6 | + | 5.89158e6i | 0.699066 | + | 1.21082i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −307803. | −0.0625948 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −507223. | −0.102071 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.41132e6 | + | 2.44448e6i | 0.281053 | + | 0.486797i | 0.971644 | − | 0.236447i | \(-0.0759831\pi\) |
−0.690592 | + | 0.723245i | \(0.742650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −126424. | + | 218972.i | −0.0249153 | + | 0.0431545i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −243749. | − | 419857.i | −0.0475418 | − | 0.0818905i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.29825e6 | + | 2.24863e6i | −0.250613 | + | 0.434074i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 232457. | + | 402627.i | 0.0444140 | + | 0.0769273i | 0.887378 | − | 0.461043i | \(-0.152525\pi\) |
−0.842964 | + | 0.537970i | \(0.819191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.73664e6 | −0.706657 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.75237e6 | −1.07682 | −0.538410 | − | 0.842683i | \(-0.680975\pi\) | ||||
−0.538410 | + | 0.842683i | \(0.680975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 140229. | + | 242883.i | 0.0259848 | + | 0.0450070i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −592198. | + | 1.02572e6i | −0.108631 | + | 0.188155i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −397851. | − | 685296.i | −0.0722486 | − | 0.124448i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.25961e6 | + | 3.91376e6i | −0.406240 | + | 0.703628i | −0.994465 | − | 0.105069i | \(-0.966494\pi\) |
0.588225 | + | 0.808697i | \(0.299827\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.07241e6 | + | 3.58952e6i | 0.368877 | + | 0.638914i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.11694e6 | 1.60668 | 0.803340 | − | 0.595521i | \(-0.203054\pi\) | ||||
0.803340 | + | 0.595521i | \(0.203054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.66089e6 | 0.289809 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.65895e6 | − | 2.87338e6i | −0.286624 | − | 0.496448i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1564.91 | − | 2710.50i | 0.000267729 | − | 0.000463719i | −0.865892 | − | 0.500232i | \(-0.833248\pi\) |
0.866159 | + | 0.499768i | \(0.166581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 671797. | − | 1.17006e6i | 0.113811 | − | 0.198224i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 92805.7 | − | 160744.i | 0.0155697 | − | 0.0269676i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.70973e6 | + | 4.69338e6i | 0.450202 | + | 0.779772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.49087e6 | 0.738931 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.55685e6 | 0.253705 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.82812e6 | + | 3.16640e6i | 0.295060 | + | 0.511059i | 0.974999 | − | 0.222210i | \(-0.0713271\pi\) |
−0.679939 | + | 0.733269i | \(0.737994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16664e6 | − | 2.02069e6i | 0.186502 | − | 0.323031i | −0.757580 | − | 0.652743i | \(-0.773618\pi\) |
0.944082 | + | 0.329712i | \(0.106952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.41053e6 | + | 3384.20i | −0.223349 | + | 0.000535868i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3371.11 | + | 5838.94i | −0.000528745 | + | 0.000915814i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.13161e6 | + | 5.42410e6i | 0.486551 | + | 0.842730i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 90931.9 | 0.0139952 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −183275. | −0.0279438 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.66492e6 | + | 4.61578e6i | 0.402531 | + | 0.697205i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.02140e6 | − | 5.23321e6i | 0.452139 | − | 0.783128i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.61422e6 | + | 26940.0i | −0.832373 | + | 0.00399416i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.23089e6 | − | 7.32811e6i | 0.621496 | − | 1.07646i | −0.367712 | − | 0.929940i | \(-0.619859\pi\) |
0.989207 | − | 0.146522i | \(-0.0468081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.96591e6 | − | 3.40506e6i | −0.286131 | − | 0.495594i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.09219e6 | −0.301725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 584951. | 0.0835893 | 0.0417947 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417947 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.24007e6 | − | 2.14787e6i | −0.175597 | − | 0.304143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 395152. | − | 684424.i | 0.0554480 | − | 0.0960387i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.60349e6 | + | 13444.2i | −0.779195 | + | 0.00186948i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −969722. | + | 1.67961e6i | −0.133633 | + | 0.231460i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 617407. | + | 1.06938e6i | 0.0843206 | + | 0.146048i | 0.905101 | − | 0.425196i | \(-0.139795\pi\) |
−0.820781 | + | 0.571243i | \(0.806461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.04599e6 | 0.141579 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 271642. | 0.0364409 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.70627e6 | − | 8.15150e6i | −0.625757 | − | 1.08384i | −0.988394 | − | 0.151913i | \(-0.951457\pi\) |
0.362636 | − | 0.931931i | \(-0.381877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.46168e6 | − | 5.99580e6i | 0.456211 | − | 0.790180i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 423521. | − | 737642.i | 0.0553245 | − | 0.0963581i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −360053. | + | 623630.i | −0.0466215 | + | 0.0807508i | −0.888394 | − | 0.459081i | \(-0.848179\pi\) |
0.841773 | + | 0.539832i | \(0.181512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.18233e6 | + | 1.07081e7i | 0.793528 | + | 1.37443i | 0.923770 | + | 0.382948i | \(0.125091\pi\) |
−0.130242 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.18988e6 | 0.787582 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −503015. | −0.0634471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.95903e6 | − | 5.12519e6i | −0.370007 | − | 0.640871i | 0.619559 | − | 0.784950i | \(-0.287311\pi\) |
−0.989566 | + | 0.144079i | \(0.953978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.15186e6 | − | 1.99508e6i | 0.142792 | − | 0.247323i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.63101e6 | − | 2.80940e6i | −0.200454 | − | 0.345281i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.04590e6 | + | 1.81155e6i | −0.127443 | + | 0.220738i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 91053.0 | + | 157708.i | 0.0110003 | + | 0.0190531i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.99600e6 | −1.19738 | −0.598688 | − | 0.800982i | \(-0.704311\pi\) | ||||
−0.598688 | + | 0.800982i | \(0.704311\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18999.0 | 0.00225654 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −636446. | − | 1.10236e6i | −0.0749537 | − | 0.129824i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.58800e6 | − | 4.48255e6i | 0.302223 | − | 0.523466i | −0.674416 | − | 0.738352i | \(-0.735605\pi\) |
0.976639 | + | 0.214886i | \(0.0689378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −257437. | − | 443434.i | −0.0298112 | − | 0.0513496i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 988316. | − | 1.71181e6i | 0.113491 | − | 0.196571i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 904038. | + | 1.56584e6i | 0.102948 | + | 0.178312i | 0.912898 | − | 0.408187i | \(-0.133839\pi\) |
−0.809950 | + | 0.586499i | \(0.800506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.55217e6 | 0.401151 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.96535e6 | −0.556105 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.08262e6 | − | 1.87516e6i | −0.120251 | − | 0.208281i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.25611e6 | − | 7.37181e6i | 0.468858 | − | 0.812086i | −0.530508 | − | 0.847680i | \(-0.677999\pi\) |
0.999366 | + | 0.0355935i | \(0.0113322\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.80329e6 | − | 3.14077e6i | 0.197025 | − | 0.343157i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 345245. | − | 597981.i | 0.0374131 | − | 0.0648014i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.30029e6 | − | 1.09124e7i | −0.677188 | − | 1.17292i | −0.975824 | − | 0.218557i | \(-0.929865\pi\) |
0.298636 | − | 0.954367i | \(-0.403468\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.40579e6 | −0.149877 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.92514e6 | 0.943848 | 0.471924 | − | 0.881639i | \(-0.343560\pi\) | ||||
0.471924 | + | 0.881639i | \(0.343560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.20749e6 | − | 7.28758e6i | −0.441363 | − | 0.764464i | 0.556428 | − | 0.830896i | \(-0.312172\pi\) |
−0.997791 | + | 0.0664325i | \(0.978838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 151664. | − | 262690.i | 0.0157817 | − | 0.0273348i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.12034e7 | + | 26879.6i | −1.15645 | + | 0.00277462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.26315e6 | − | 3.91989e6i | 0.231746 | − | 0.401397i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −382732. | − | 662911.i | −0.0388799 | − | 0.0673420i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 444812. | 0.0448280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.12046e7 | 1.12027 | 0.560135 | − | 0.828401i | \(-0.310749\pi\) | ||||
0.560135 | + | 0.828401i | \(0.310749\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 377315. | + | 653529.i | 0.0374279 | + | 0.0648270i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19419.2 | − | 33635.0i | 0.00191116 | − | 0.00331022i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −428018. | + | 749634.i | −0.0417940 | + | 0.0731982i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 247549. | − | 428767.i | 0.0239833 | − | 0.0415403i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.97074e6 | + | 5.14547e6i | 0.285574 | + | 0.494629i | 0.972748 | − | 0.231864i | \(-0.0744823\pi\) |
−0.687174 | + | 0.726493i | \(0.741149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.03768e6 | −0.289744 | −0.144872 | − | 0.989450i | \(-0.546277\pi\) | ||||
−0.144872 | + | 0.989450i | \(0.546277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.02318e6 | 0.759359 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.36312e6 | − | 1.10212e7i | −0.597598 | − | 1.03507i | −0.993175 | − | 0.116637i | \(-0.962788\pi\) |
0.395576 | − | 0.918433i | \(-0.370545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 187502. | − | 324763.i | 0.0174741 | − | 0.0302660i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 87064.4 | − | 208.889i | 0.00805171 | − | 1.93180e-5i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.13179e6 | − | 5.42442e6i | 0.287415 | − | 0.497818i | −0.685777 | − | 0.727812i | \(-0.740537\pi\) |
0.973192 | + | 0.229994i | \(0.0738707\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.67081e6 | + | 1.15542e7i | 0.607540 | + | 1.05229i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 842981. | 0.0761911 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.17924e7 | −1.05777 | −0.528884 | − | 0.848694i | \(-0.677389\pi\) | ||||
−0.528884 | + | 0.848694i | \(0.677389\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.26979e6 | − | 1.60557e7i | −0.825213 | − | 1.42931i | −0.901756 | − | 0.432245i | \(-0.857722\pi\) |
0.0765432 | − | 0.997066i | \(-0.475612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20883.0 | − | 36170.5i | 0.00184506 | − | 0.00319573i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −719432. | + | 1.25303e6i | −0.0630864 | + | 0.109877i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 645764. | − | 1.11850e6i | 0.0562029 | − | 0.0973463i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.11764e6 | + | 1.05961e7i | 0.528468 | + | 0.915334i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.02281e7 | −0.876982 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.90083e6 | −0.331985 | −0.165993 | − | 0.986127i | \(-0.553083\pi\) | ||||
−0.165993 | + | 0.986127i | \(0.553083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −440649. | − | 763226.i | −0.0372249 | − | 0.0644754i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.41266e6 | − | 5.91091e6i | 0.286168 | − | 0.495658i | −0.686723 | − | 0.726919i | \(-0.740952\pi\) |
0.972892 | + | 0.231260i | \(0.0742850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.86096e6 | − | 6.65048e6i | −0.321381 | − | 0.553577i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 356.985 | − | 618.316i | 2.94973e−5 | − | 5.10908e-5i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.36231e6 | + | 4.09164e6i | 0.193769 | + | 0.335619i | 0.946496 | − | 0.322714i | \(-0.104595\pi\) |
−0.752727 | + | 0.658333i | \(0.771262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.67432e7 | 1.36336 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.64337e6 | −0.456191 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 160811. | + | 278533.i | 0.0129053 | + | 0.0223526i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.96331e6 | − | 1.37929e7i | 0.634452 | − | 1.09890i | −0.352179 | − | 0.935933i | \(-0.614559\pi\) |
0.986631 | − | 0.162970i | \(-0.0521074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.76118e6 | − | 3.03363e6i | −0.139307 | − | 0.239955i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.62200e6 | − | 9.73758e6i | 0.441498 | − | 0.764697i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 161210. | + | 279223.i | 0.0125692 | + | 0.0217706i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.86636e6 | 0.608949 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.22412e7 | −1.70948 | −0.854738 | − | 0.519060i | \(-0.826282\pi\) | ||||
−0.854738 | + | 0.519060i | \(0.826282\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −626721. | − | 1.08551e6i | −0.0478284 | − | 0.0828412i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.64817e6 | − | 4.58676e6i | 0.200665 | − | 0.347563i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.44928e6 | + | 4.26588e6i | −0.184285 | + | 0.320967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.68408e6 | − | 2.91691e6i | 0.125819 | − | 0.217925i | −0.796234 | − | 0.604989i | \(-0.793177\pi\) |
0.922053 | + | 0.387064i | \(0.126511\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75053e6 | − | 3.03201e6i | −0.129866 | − | 0.224935i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31048.5 | 0.00228726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 751007. | 0.0549387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.60123e6 | + | 9.70162e6i | 0.406898 | + | 0.704768i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.36961e6 | − | 4.10428e6i | 0.170944 | − | 0.296084i | −0.767806 | − | 0.640682i | \(-0.778652\pi\) |
0.938750 | + | 0.344598i | \(0.111985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.60506e7 | + | 38509.3i | −1.14988 | + | 0.00275885i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.46826e6 | − | 1.29354e7i | 0.531341 | − | 0.920310i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.87622e6 | − | 3.24970e6i | −0.132568 | − | 0.229614i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.03003e7 | −1.42451 | −0.712256 | − | 0.701919i | \(-0.752327\pi\) | ||||
−0.712256 | + | 0.701919i | \(0.752327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −920058. | − | 1.59359e6i | −0.0636828 | − | 0.110302i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.26709e6 | − | 2.19466e6i | 0.0871057 | − | 0.150871i | −0.819181 | − | 0.573535i | \(-0.805572\pi\) |
0.906287 | + | 0.422664i | \(0.138905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.28307e6 | + | 5.74999e6i | −0.224162 | + | 0.392599i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.02386e7 | + | 1.77337e7i | −0.694338 | + | 1.20263i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.35597e7 | + | 2.34860e7i | 0.913352 | + | 1.58197i | 0.809296 | + | 0.587401i | \(0.199849\pi\) |
0.104056 | + | 0.994571i | \(0.466818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −117693. | −0.00787419 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.58583e7 | −1.05386 | −0.526932 | − | 0.849908i | \(-0.676658\pi\) | ||||
−0.526932 | + | 0.849908i | \(0.676658\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.57769e6 | − | 1.65890e7i | −0.632223 | − | 1.09504i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.01484e6 | − | 1.75775e6i | 0.0665418 | − | 0.115254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.57852e7 | + | 37872.6i | −1.02812 | + | 0.00246672i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.09937e7 | − | 1.90416e7i | 0.711284 | − | 1.23198i | −0.253091 | − | 0.967442i | \(-0.581447\pi\) |
0.964375 | − | 0.264538i | \(-0.0852194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.07653e6 | + | 5.32871e6i | 0.197731 | + | 0.342479i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.08229e7 | 0.690995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.45560e7 | −0.923213 | −0.461607 | − | 0.887085i | \(-0.652727\pi\) | ||||
−0.461607 | + | 0.887085i | \(0.652727\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −625465. | − | 1.08334e6i | −0.0394093 | − | 0.0682589i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.23612e7 | − | 2.14103e7i | 0.773749 | − | 1.34017i | −0.161745 | − | 0.986833i | \(-0.551712\pi\) |
0.935495 | − | 0.353341i | \(-0.114954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.08532e6 | − | 5.37366e6i | 0.191862 | − | 0.334163i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 160181. | − | 277442.i | 0.00989596 | − | 0.0171403i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28829.2 | − | 49933.7i | −0.00176947 | − | 0.00306482i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.14189e7 | 0.696322 | 0.348161 | − | 0.937435i | \(-0.386806\pi\) | ||||
0.348161 | + | 0.937435i | \(0.386806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.43330e7 | 0.868364 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.52146e6 | − | 7.83141e6i | −0.272164 | − | 0.471402i | 0.697252 | − | 0.716826i | \(-0.254406\pi\) |
−0.969416 | + | 0.245425i | \(0.921073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45104.4 | − | 78123.2i | 0.00269752 | − | 0.00467225i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.88393e6 | − | 4.96755e6i | −0.171369 | − | 0.295182i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 454275. | − | 786828.i | 0.0268210 | − | 0.0464554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.02089e6 | − | 1.76824e6i | −0.0598898 | − | 0.103732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.26279e6 | 0.131899 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.25681e7 | −0.727938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 700700. | + | 1.21365e6i | 0.0403270 | + | 0.0698483i | 0.885484 | − | 0.464669i | \(-0.153827\pi\) |
−0.845157 | + | 0.534517i | \(0.820493\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.31528e6 | − | 5.74223e6i | 0.189595 | − | 0.328389i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.02949e7 | + | 1.77330e7i | 0.585036 | + | 1.00772i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −786310. | + | 1.36193e6i | −0.0444029 | + | 0.0769080i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.23349e6 | + | 2.13646e6i | 0.0692176 | + | 0.119888i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.96609e6 | 0.555750 | 0.277875 | − | 0.960617i | \(-0.410370\pi\) | ||||
0.277875 | + | 0.960617i | \(0.410370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.21472e6 | −0.0673143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.49994e6 | − | 6.06207e6i | −0.192743 | − | 0.333841i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.73823e6 | − | 3.01070e6i | 0.0951302 | − | 0.164770i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.17571e6 | + | 2.04771e6i | −0.0639454 | + | 0.111373i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.03876e6 | − | 1.21915e7i | 0.380463 | − | 0.658981i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.51409e7 | + | 2.62248e7i | 0.813355 | + | 1.40877i | 0.910503 | + | 0.413502i | \(0.135694\pi\) |
−0.0971485 | + | 0.995270i | \(0.530972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.52190e7 | 1.34641 | 0.673203 | − | 0.739458i | \(-0.264918\pi\) | ||||
0.673203 | + | 0.739458i | \(0.264918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.47198e7 | 0.781044 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.08691e6 | + | 1.57390e7i | 0.479206 | + | 0.830009i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.59265e6 | + | 4.49060e6i | −0.135890 | + | 0.235369i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −539337. | + | 1294.00i | −0.0280964 | + | 6.74102e-5i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.38467e7 | + | 2.39832e7i | −0.716950 | + | 1.24179i | 0.245252 | + | 0.969459i | \(0.421129\pi\) |
−0.962203 | + | 0.272335i | \(0.912204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.42671e6 | + | 1.28634e7i | 0.382206 | + | 0.661999i | 0.991377 | − | 0.131039i | \(-0.0418313\pi\) |
−0.609172 | + | 0.793038i | \(0.708498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.63448e6 | −0.185912 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.88266e6 | −0.502470 | −0.251235 | − | 0.967926i | \(-0.580837\pi\) | ||||
−0.251235 | + | 0.967926i | \(0.580837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.71460e7 | + | 2.96978e7i | 0.866516 | + | 1.50085i | 0.865534 | + | 0.500851i | \(0.166979\pi\) |
0.000982496 | 1.00000i | \(0.499687\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.02090e6 | + | 1.76825e6i | −0.0512840 | + | 0.0888264i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.51857e6 | − | 7286.88i | 0.0758266 | − | 0.000363855i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.00796e7 | − | 1.74583e7i | 0.500294 | − | 0.866534i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27198.9 | + | 47109.9i | 0.00134196 | + | 0.00232433i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.40547e7 | −0.689312 | −0.344656 | − | 0.938729i | \(-0.612004\pi\) | ||||
−0.344656 | + | 0.938729i | \(0.612004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.08765e7 | −0.530274 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.62787e6 | − | 4.55160e6i | −0.127361 | − | 0.220595i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.06859e6 | + | 1.39752e7i | −0.388737 | + | 0.673312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.41273e6 | − | 15385.7i | 0.307139 | − | 0.000736901i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 377575. | − | 653980.i | 0.0179777 | − | 0.0311383i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.02420e6 | − | 1.77396e6i | −0.0484796 | − | 0.0839692i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.38937e7 | 1.59495 | 0.797474 | − | 0.603354i | \(-0.206169\pi\) | ||||
0.797474 | + | 0.603354i | \(0.206169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −902755. | −0.0422332 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.56740e7 | + | 2.71482e7i | 0.729002 | + | 1.26267i | 0.957305 | + | 0.289079i | \(0.0933491\pi\) |
−0.228303 | + | 0.973590i | \(0.573318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.78882e6 | − | 1.52227e7i | 0.406394 | − | 0.703896i | −0.588088 | − | 0.808797i | \(-0.700119\pi\) |
0.994483 | + | 0.104901i | \(0.0334526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.07310e6 | − | 3.61069e6i | 0.0953042 | − | 0.165990i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.02906e7 | − | 1.78239e7i | 0.470343 | − | 0.814657i | −0.529082 | − | 0.848571i | \(-0.677464\pi\) |
0.999425 | + | 0.0339134i | \(0.0107970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.78601e6 | − | 6.55756e6i | −0.172045 | − | 0.297990i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27052e7 | 0.574031 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.44384e7 | −0.648590 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.57422e6 | + | 2.72664e6i | 0.0703107 | + | 0.121782i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.40234e6 | − | 4.16098e6i | 0.106684 | − | 0.184782i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.23482e7 | + | 2.12696e7i | 0.545234 | + | 0.939161i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.63733e7 | + | 2.83593e7i | −0.718847 | + | 1.24508i | 0.242610 | + | 0.970124i | \(0.421996\pi\) |
−0.961457 | + | 0.274955i | \(0.911337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.63507e6 | + | 9.76022e6i | 0.245995 | + | 0.426076i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.45099e7 | −1.06390 | −0.531950 | − | 0.846776i | \(-0.678541\pi\) | ||||
−0.531950 | + | 0.846776i | \(0.678541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.49986e7 | −0.647365 | −0.323682 | − | 0.946166i | \(-0.604921\pi\) | ||||
−0.323682 | + | 0.946166i | \(0.604921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −221132. | − | 383011.i | −0.00949058 | − | 0.0164382i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.27679e7 | + | 2.21147e7i | −0.544894 | + | 0.943784i | 0.453720 | + | 0.891144i | \(0.350097\pi\) |
−0.998614 | + | 0.0526394i | \(0.983237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57752.1 | + | 99477.7i | 0.00245083 | + | 0.00422154i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.09583e6 | − | 1.89804e6i | 0.0462435 | − | 0.0800960i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.71148e6 | + | 2.96438e6i | 0.0718198 | + | 0.124395i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.93902e7 | −1.22644 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −192336. | −0.00798140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 115809. | + | 200587.i | 0.00477906 | + | 0.00827757i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 282900. | − | 489997.i | 0.0116097 | − | 0.0201086i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.18316e7 | + | 2.06070e7i | −0.482864 | + | 0.840998i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.56158e6 | + | 1.65611e7i | −0.388068 | + | 0.672154i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.14946e7 | + | 1.99093e7i | 0.463956 | + | 0.803596i | 0.999154 | − | 0.0411313i | \(-0.0130962\pi\) |
−0.535198 | + | 0.844727i | \(0.679763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07339e6 | −0.123370 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.81822e7 | −0.725857 | −0.362928 | − | 0.931817i | \(-0.618223\pi\) | ||||
−0.362928 | + | 0.931817i | \(0.618223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.18519e6 | − | 7.24896e6i | −0.166165 | − | 0.287805i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.03132e6 | + | 1.04466e7i | −0.238155 | + | 0.412497i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.95134e7 | + | 94802.4i | −1.55175 | + | 0.00372303i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.41468e7 | + | 2.45029e7i | −0.552546 | + | 0.957037i | 0.445544 | + | 0.895260i | \(0.353010\pi\) |
−0.998090 | + | 0.0617775i | \(0.980323\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.11572e7 | − | 1.93248e7i | −0.433416 | − | 0.750699i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −313933. | −0.0121292 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.95144e6 | −0.228701 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.01421e6 | − | 8.68487e6i | −0.191648 | − | 0.331943i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.43383e7 | − | 2.48347e7i | 0.545079 | − | 0.944105i | −0.453523 | − | 0.891245i | \(-0.649833\pi\) |
0.998602 | − | 0.0528603i | \(-0.0168338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.15738e6 | − | 3.69563e6i | −0.0815742 | − | 0.139738i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.11267e6 | + | 1.23195e7i | −0.267503 | + | 0.463329i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −660589. | − | 1.14417e6i | −0.0247117 | − | 0.0428019i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.99596e7 | 1.85896 | 0.929479 | − | 0.368875i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368875i | \(0.120257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.02542e6 | −0.0379522 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.77422e6 | − | 1.00012e7i | −0.212578 | − | 0.368196i | 0.739942 | − | 0.672670i | \(-0.234853\pi\) |
−0.952521 | + | 0.304474i | \(0.901519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 742383. | − | 1.28585e6i | 0.0271862 | − | 0.0470879i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.13694e6 | + | 9925.52i | −0.150695 | + | 0.000361555i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.04254e6 | + | 1.04660e7i | −0.218950 | + | 0.379232i | −0.954487 | − | 0.298252i | \(-0.903596\pi\) |
0.735537 | + | 0.677484i | \(0.236930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −267260. | − | 462908.i | −0.00963316 | − | 0.0166851i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.41915e7 | 0.867384 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.34953e6 | 0.190802 | 0.0954011 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0954011 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50528e7 | − | 2.60722e7i | −0.534083 | − | 0.925059i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.66589e6 | − | 8.08156e6i | 0.164685 | − | 0.285243i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.46908e7 | + | 4.30037e7i | −0.866939 | + | 1.50994i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.43118e7 | − | 2.47887e7i | 0.499903 | − | 0.865857i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.93130e6 | − | 8.54126e6i | −0.171355 | − | 0.296795i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.12046e7 | −0.387326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.79471e7 | −1.64891 | −0.824454 | − | 0.565929i | \(-0.808518\pi\) | ||||
−0.824454 | + | 0.565929i | \(0.808518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 103523. | + | 179308.i | 0.00354184 | + | 0.00613465i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.28388e6 | − | 5.68785e6i | 0.111774 | − | 0.193598i | −0.804712 | − | 0.593666i | \(-0.797680\pi\) |
0.916485 | + | 0.400068i | \(0.131014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.67197e7 | + | 2.87995e7i | 0.566169 | + | 0.975222i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −279408. | + | 483950.i | −0.00941300 | + | 0.0163038i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.10448e6 | + | 8.84122e6i | 0.171086 | + | 0.296330i | 0.938800 | − | 0.344463i | \(-0.111939\pi\) |
−0.767714 | + | 0.640793i | \(0.778606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.88675e7 | −0.962616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.87150e6 | 0.128442 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 337772. | + | 585038.i | 0.0111491 | + | 0.0193108i | 0.871546 | − | 0.490314i | \(-0.163118\pi\) |
−0.860397 | + | 0.509624i | \(0.829784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.09547e6 | + | 5.36151e6i | −0.101657 | + | 0.176075i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.87558e6 | + | 1.35656e7i | 0.257330 | + | 0.443249i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.23694e6 | + | 7.33860e6i | −0.137740 | + | 0.238574i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.48979e7 | + | 2.58040e7i | 0.481883 | + | 0.834646i | 0.999784 | − | 0.0207947i | \(-0.00661964\pi\) |
−0.517901 | + | 0.855441i | \(0.673286\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.29664e7 | −1.06096 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.61370e6 | −0.307846 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.52562e7 | + | 4.37449e7i | 0.804691 | + | 1.39377i | 0.916499 | + | 0.400036i | \(0.131002\pi\) |
−0.111808 | + | 0.993730i | \(0.535664\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.79442e6 | − | 3.10803e6i | 0.0568867 | − | 0.0985307i |
(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.k.289.3 | 8 | ||
4.3 | odd | 2 | 168.6.q.a.121.3 | yes | 8 | ||
7.4 | even | 3 | inner | 336.6.q.k.193.3 | 8 | ||
12.11 | even | 2 | 504.6.s.a.289.2 | 8 | |||
28.11 | odd | 6 | 168.6.q.a.25.3 | ✓ | 8 | ||
84.11 | even | 6 | 504.6.s.a.361.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.q.a.25.3 | ✓ | 8 | 28.11 | odd | 6 | ||
168.6.q.a.121.3 | yes | 8 | 4.3 | odd | 2 | ||
336.6.q.k.193.3 | 8 | 7.4 | even | 3 | inner | ||
336.6.q.k.289.3 | 8 | 1.1 | even | 1 | trivial | ||
504.6.s.a.289.2 | 8 | 12.11 | even | 2 | |||
504.6.s.a.361.2 | 8 | 84.11 | even | 6 |