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: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 1094 x^{8} - 12883 x^{7} + 1063781 x^{6} - 7555708 x^{5} + 199315216 x^{4} + \cdots + 37456183296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.5 | ||
Root | \(-4.79197 + 8.29994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.6.q.m.289.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 22.2576 | + | 38.5514i | 0.398157 | + | 0.689628i | 0.993499 | − | 0.113845i | \(-0.0363167\pi\) |
−0.595342 | + | 0.803473i | \(0.702983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.29943 | + | 129.376i | 0.0640182 | + | 0.997949i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 131.614 | − | 227.962i | 0.327960 | − | 0.568043i | −0.654147 | − | 0.756367i | \(-0.726972\pi\) |
0.982107 | + | 0.188324i | \(0.0603057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −208.220 | −0.341716 | −0.170858 | − | 0.985296i | \(-0.554654\pi\) | ||||
−0.170858 | + | 0.985296i | \(0.554654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 400.637 | 0.459752 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −750.577 | + | 1300.04i | −0.629902 | + | 1.09102i | 0.357669 | + | 0.933848i | \(0.383572\pi\) |
−0.987571 | + | 0.157174i | \(0.949762\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 567.347 | + | 982.673i | 0.360549 | + | 0.624490i | 0.988051 | − | 0.154125i | \(-0.0492559\pi\) |
−0.627502 | + | 0.778615i | \(0.715923\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1045.73 | + | 517.504i | 0.517455 | + | 0.256074i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 609.477 | + | 1055.64i | 0.240236 | + | 0.416100i | 0.960781 | − | 0.277307i | \(-0.0894419\pi\) |
−0.720546 | + | 0.693407i | \(0.756109\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 571.695 | − | 990.205i | 0.182942 | − | 0.316866i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −350.738 | −0.0774440 | −0.0387220 | − | 0.999250i | \(-0.512329\pi\) | ||||
−0.0387220 | + | 0.999250i | \(0.512329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2181.24 | + | 3778.02i | −0.407662 | + | 0.706091i | −0.994627 | − | 0.103521i | \(-0.966989\pi\) |
0.586966 | + | 0.809612i | \(0.300322\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1184.53 | − | 2051.66i | −0.189348 | − | 0.327960i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4802.89 | + | 3199.56i | −0.662724 | + | 0.441489i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6436.97 | − | 11149.2i | −0.772996 | − | 1.33887i | −0.935914 | − | 0.352229i | \(-0.885424\pi\) |
0.162918 | − | 0.986640i | \(-0.447909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −936.992 | + | 1622.92i | −0.0986449 | + | 0.170858i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18581.8 | −1.72635 | −0.863176 | − | 0.504903i | \(-0.831528\pi\) | ||||
−0.863176 | + | 0.504903i | \(0.831528\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −268.381 | −0.0221351 | −0.0110675 | − | 0.999939i | \(-0.503523\pi\) | ||||
−0.0110675 | + | 0.999939i | \(0.503523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1802.87 | − | 3122.66i | 0.132719 | − | 0.229876i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4850.78 | + | 8401.80i | 0.320307 | + | 0.554789i | 0.980551 | − | 0.196263i | \(-0.0628805\pi\) |
−0.660244 | + | 0.751051i | \(0.729547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16669.2 | + | 2147.49i | −0.991803 | + | 0.127774i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6755.19 | + | 11700.3i | 0.363674 | + | 0.629902i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7861.76 | − | 13617.0i | 0.384441 | − | 0.665872i | −0.607250 | − | 0.794511i | \(-0.707727\pi\) |
0.991692 | + | 0.128639i | \(0.0410608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11717.7 | 0.522317 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10212.2 | 0.416326 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16752.8 | + | 29016.7i | −0.626553 | + | 1.08522i | 0.361685 | + | 0.932300i | \(0.382201\pi\) |
−0.988238 | + | 0.152921i | \(0.951132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −866.770 | − | 1501.29i | −0.0298249 | − | 0.0516583i | 0.850728 | − | 0.525607i | \(-0.176162\pi\) |
−0.880553 | + | 0.473948i | \(0.842828\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8739.34 | − | 5821.91i | 0.277413 | − | 0.184805i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4634.50 | − | 8027.18i | −0.136056 | − | 0.235657i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16991.4 | + | 29430.0i | −0.462427 | + | 0.800947i | −0.999081 | − | 0.0428550i | \(-0.986355\pi\) |
0.536654 | + | 0.843802i | \(0.319688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10970.6 | 0.277400 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15371.3 | 0.361880 | 0.180940 | − | 0.983494i | \(-0.442086\pi\) | ||||
0.180940 | + | 0.983494i | \(0.442086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38204.0 | + | 66171.3i | −0.839078 | + | 1.45333i | 0.0515890 | + | 0.998668i | \(0.483571\pi\) |
−0.890667 | + | 0.454657i | \(0.849762\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5145.26 | − | 8911.85i | −0.105622 | − | 0.182942i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30585.1 | + | 15135.7i | 0.587873 | + | 0.290922i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41761.4 | + | 72333.0i | 0.752849 | + | 1.30397i | 0.946437 | + | 0.322890i | \(0.104654\pi\) |
−0.193588 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14703.1 | −0.234268 | −0.117134 | − | 0.993116i | \(-0.537371\pi\) | ||||
−0.117134 | + | 0.993116i | \(0.537371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66824.3 | −1.00320 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1578.32 | + | 2733.73i | −0.0223562 | + | 0.0387220i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13261.5 | + | 22969.6i | 0.177467 | + | 0.307381i | 0.941012 | − | 0.338373i | \(-0.109876\pi\) |
−0.763545 | + | 0.645754i | \(0.776543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1728.11 | − | 26938.7i | −0.0218760 | − | 0.341015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19631.2 | + | 34002.2i | 0.235364 | + | 0.407662i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25255.6 | + | 43744.0i | −0.287110 | + | 0.497289i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −23955.2 | −0.258506 | −0.129253 | − | 0.991612i | \(-0.541258\pi\) | ||||
−0.129253 | + | 0.991612i | \(0.541258\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21321.5 | −0.218640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −35494.3 | + | 61478.0i | −0.346223 | + | 0.599675i | −0.985575 | − | 0.169239i | \(-0.945869\pi\) |
0.639352 | + | 0.768914i | \(0.279202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −835.673 | − | 1447.43i | −0.00776146 | − | 0.0134432i | 0.862119 | − | 0.506707i | \(-0.169137\pi\) |
−0.869880 | + | 0.493263i | \(0.835804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3325.06 | + | 51832.8i | 0.0294325 | + | 0.458809i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14629.8 | + | 25339.5i | 0.123532 | + | 0.213963i | 0.921158 | − | 0.389189i | \(-0.127245\pi\) |
−0.797626 | + | 0.603152i | \(0.793911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −25366.4 | + | 43935.9i | −0.204500 | + | 0.354204i | −0.949973 | − | 0.312331i | \(-0.898890\pi\) |
0.745474 | + | 0.666535i | \(0.232223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −115865. | −0.892579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 76231.0 | 0.561611 | 0.280805 | − | 0.959765i | \(-0.409398\pi\) | ||||
0.280805 | + | 0.959765i | \(0.409398\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27131.0 | + | 46992.3i | −0.191303 | + | 0.331346i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8432.93 | + | 14606.3i | 0.0569526 | + | 0.0986449i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −174423. | − | 86317.0i | −1.12911 | − | 0.558765i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45881.0 | + | 79468.2i | 0.284885 | + | 0.493435i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83618.3 | + | 144831.i | −0.498355 | + | 0.863176i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 190009. | 1.08767 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22686.7 | 0.124814 | 0.0624068 | − | 0.998051i | \(-0.480122\pi\) | ||||
0.0624068 | + | 0.998051i | \(0.480122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1207.71 | + | 2091.82i | −0.00638984 | + | 0.0110675i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −135441. | − | 234590.i | −0.689558 | − | 1.19435i | −0.971981 | − | 0.235060i | \(-0.924471\pi\) |
0.282423 | − | 0.959290i | \(-0.408862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −122426. | + | 81556.6i | −0.600127 | + | 0.399788i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16225.8 | − | 28103.9i | −0.0766253 | − | 0.132719i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −199041. | + | 344749.i | −0.906026 | + | 1.56928i | −0.0864917 | + | 0.996253i | \(0.527566\pi\) |
−0.819534 | + | 0.573030i | \(0.805768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 155651. | 0.683306 | 0.341653 | − | 0.939826i | \(-0.389013\pi\) | ||||
0.341653 | + | 0.939826i | \(0.389013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 87314.0 | 0.369859 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27404.7 | + | 47466.4i | −0.112069 | + | 0.194109i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7806.60 | − | 13521.4i | −0.0308349 | − | 0.0534076i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −58273.5 | + | 139588.i | −0.222422 | + | 0.532787i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −76353.8 | − | 132249.i | −0.281751 | − | 0.488006i | 0.690065 | − | 0.723747i | \(-0.257582\pi\) |
−0.971816 | + | 0.235741i | \(0.924248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 204779. | − | 354688.i | 0.730876 | − | 1.26591i | −0.225633 | − | 0.974212i | \(-0.572445\pi\) |
0.956509 | − | 0.291702i | \(-0.0942215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 121593. | 0.419935 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −194197. | −0.649253 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −263267. | + | 455991.i | −0.852406 | + | 1.47641i | 0.0266241 | + | 0.999646i | \(0.491524\pi\) |
−0.879030 | + | 0.476766i | \(0.841809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −70755.8 | − | 122553.i | −0.221957 | − | 0.384441i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −131517. | + | 87612.8i | −0.399867 | + | 0.266381i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 198694. | + | 344148.i | 0.585755 | + | 1.01456i | 0.994781 | + | 0.102035i | \(0.0325353\pi\) |
−0.409026 | + | 0.912523i | \(0.634131\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 52729.5 | − | 91330.2i | 0.150780 | − | 0.261159i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −519557. | −1.44159 | −0.720795 | − | 0.693148i | \(-0.756223\pi\) | ||||
−0.720795 | + | 0.693148i | \(0.756223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −327937. | −0.883230 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 45955.1 | − | 79596.5i | 0.120183 | − | 0.208163i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −289019. | − | 500596.i | −0.734195 | − | 1.27166i | −0.955075 | − | 0.296363i | \(-0.904226\pi\) |
0.220880 | − | 0.975301i | \(-0.429107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 132853. | + | 65745.4i | 0.327927 | + | 0.162282i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 150775. | + | 261151.i | 0.361740 | + | 0.626553i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 131661. | − | 228043.i | 0.307130 | − | 0.531966i | −0.670603 | − | 0.741817i | \(-0.733965\pi\) |
0.977733 | + | 0.209851i | \(0.0672979\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 456567. | 1.03588 | 0.517938 | − | 0.855418i | \(-0.326700\pi\) | ||||
0.517938 | + | 0.855418i | \(0.326700\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15601.9 | −0.0344389 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 286544. | − | 496308.i | 0.615547 | − | 1.06616i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 197573. | + | 342206.i | 0.413165 | + | 0.715623i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6050.29 | − | 94315.0i | −0.0123203 | − | 0.192055i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 110601. | + | 191566.i | 0.219369 | + | 0.379958i | 0.954615 | − | 0.297842i | \(-0.0962668\pi\) |
−0.735246 | + | 0.677800i | \(0.762933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 139948. | − | 242397.i | 0.270442 | − | 0.468419i | −0.698533 | − | 0.715578i | \(-0.746164\pi\) |
0.968975 | + | 0.247159i | \(0.0794970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −83420.9 | −0.157104 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257685. | 0.473068 | 0.236534 | − | 0.971623i | \(-0.423989\pi\) | ||||
0.236534 | + | 0.971623i | \(0.423989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −75572.4 | + | 130895.i | −0.135279 | + | 0.234310i | −0.925704 | − | 0.378249i | \(-0.876526\pi\) |
0.790425 | + | 0.612559i | \(0.209860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 152923. | + | 264870.i | 0.266982 | + | 0.462427i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2910.93 | − | 45377.1i | −0.00495783 | − | 0.0772852i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −413588. | − | 716355.i | −0.687358 | − | 1.19054i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 49367.6 | − | 85507.2i | 0.0800786 | − | 0.138700i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 298683. | 0.472982 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.06807e6 | 1.65155 | 0.825776 | − | 0.563998i | \(-0.190737\pi\) | ||||
0.825776 | + | 0.563998i | \(0.190737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 69170.7 | − | 119807.i | 0.104466 | − | 0.180940i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5973.53 | − | 10346.5i | −0.00881322 | − | 0.0152649i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −506888. | − | 250845.i | −0.730740 | − | 0.361623i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 343836. | + | 595542.i | 0.484442 | + | 0.839078i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 156286. | − | 270694.i | 0.215247 | − | 0.372820i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 587032. | 0.790496 | 0.395248 | − | 0.918574i | \(-0.370659\pi\) | ||||
0.395248 | + | 0.918574i | \(0.370659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −92614.6 | −0.121962 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 82623.5 | − | 143108.i | 0.106424 | − | 0.184332i | −0.807895 | − | 0.589326i | \(-0.799393\pi\) |
0.914319 | + | 0.404995i | \(0.132727\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 121458. | + | 210372.i | 0.153052 | + | 0.265094i | 0.932348 | − | 0.361562i | \(-0.117757\pi\) |
−0.779296 | + | 0.626656i | \(0.784423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 255604. | − | 170277.i | 0.315165 | − | 0.209955i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −456035. | − | 789875.i | −0.550311 | − | 0.953166i | −0.998252 | − | 0.0591032i | \(-0.981176\pi\) |
0.447941 | − | 0.894063i | \(-0.352157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −215934. | + | 374008.i | −0.255065 | + | 0.441786i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 751706. | 0.869315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.06926e6 | −1.21085 | −0.605423 | − | 0.795904i | \(-0.706996\pi\) | ||||
−0.605423 | + | 0.795904i | \(0.706996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 387365. | − | 670936.i | 0.429613 | − | 0.744112i | −0.567225 | − | 0.823563i | \(-0.691983\pi\) |
0.996839 | + | 0.0794503i | \(0.0253165\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | + | 51137.9i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −453807. | − | 594824.i | −0.483009 | − | 0.633101i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −118133. | − | 204613.i | −0.123205 | − | 0.213398i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −66164.0 | + | 114599.i | −0.0676275 | + | 0.117134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.16719e6 | 1.16938 | 0.584691 | − | 0.811256i | \(-0.301216\pi\) | ||||
0.584691 | + | 0.811256i | \(0.301216\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 320863. | 0.315150 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −300709. | + | 520844.i | −0.289599 | + | 0.501599i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −427023. | − | 739625.i | −0.403291 | − | 0.698520i | 0.590830 | − | 0.806796i | \(-0.298800\pi\) |
−0.994121 | + | 0.108276i | \(0.965467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.38901e6 | − | 925321.i | 1.28664 | − | 0.857122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14204.9 | + | 24603.6i | 0.0129073 | + | 0.0223562i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.09823e6 | − | 1.90219e6i | 0.979047 | − | 1.69576i | 0.313172 | − | 0.949696i | \(-0.398608\pi\) |
0.665875 | − | 0.746063i | \(-0.268058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 699937. | 0.612272 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 238707. | 0.204921 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 689235. | − | 1.19379e6i | 0.580746 | − | 1.00588i | −0.414645 | − | 0.909983i | \(-0.636094\pi\) |
0.995391 | − | 0.0958989i | \(-0.0305726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −903523. | − | 1.56495e6i | −0.747336 | − | 1.29442i | −0.949095 | − | 0.314989i | \(-0.897999\pi\) |
0.201759 | − | 0.979435i | \(-0.435334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −217743. | − | 107755.i | −0.176822 | − | 0.0875045i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −150486. | − | 260650.i | −0.119996 | − | 0.207838i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −828234. | + | 1.43454e6i | −0.648565 | + | 1.12335i | 0.334901 | + | 0.942253i | \(0.391297\pi\) |
−0.983466 | + | 0.181094i | \(0.942036\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 353361. | 0.271774 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −552799. | −0.417640 | −0.208820 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208820 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.10043e6 | + | 1.90599e6i | −0.816760 | + | 1.41467i | 0.0912972 | + | 0.995824i | \(0.470899\pi\) |
−0.908057 | + | 0.418846i | \(0.862435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 227300. | + | 393696.i | 0.165763 | + | 0.287110i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −154219. | − | 2.40404e6i | −0.110518 | − | 1.72281i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −416803. | − | 721925.i | −0.293553 | − | 0.508449i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −107799. | + | 186713.i | −0.0746243 | + | 0.129253i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 626936. | 0.426633 | 0.213316 | − | 0.976983i | \(-0.431574\pi\) | ||||
0.213316 | + | 0.976983i | \(0.431574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.49151e6 | −0.997865 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −95946.6 | + | 166184.i | −0.0631159 | + | 0.109320i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −126906. | − | 219807.i | −0.0820923 | − | 0.142188i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2227.41 | − | 34722.0i | −0.00141705 | − | 0.0220897i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 319449. | + | 553302.i | 0.199892 | + | 0.346223i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 38584.5 | − | 66830.3i | 0.0237500 | − | 0.0411362i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.71449e6 | −1.03822 | −0.519109 | − | 0.854708i | \(-0.673736\pi\) | ||||
−0.519109 | + | 0.854708i | \(0.673736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15042.1 | −0.00896216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 586169. | − | 1.01527e6i | 0.343654 | − | 0.595226i | −0.641454 | − | 0.767161i | \(-0.721669\pi\) |
0.985108 | + | 0.171935i | \(0.0550019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.30942e6 | + | 2.26798e6i | 0.755470 | + | 1.30851i | 0.945140 | + | 0.326665i | \(0.105925\pi\) |
−0.189670 | + | 0.981848i | \(0.560742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 418960. | + | 207331.i | 0.237901 | + | 0.117730i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −242986. | − | 420864.i | −0.135811 | − | 0.235231i | 0.790096 | − | 0.612983i | \(-0.210031\pi\) |
−0.925907 | + | 0.377752i | \(0.876697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46162.1 | + | 79955.0i | −0.0253985 | + | 0.0439915i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 263336. | 0.142642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.70335e6 | −0.908443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −119039. | + | 206181.i | −0.0625143 | + | 0.108278i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 228298. | + | 395423.i | 0.118068 | + | 0.204500i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.04673e6 | + | 697304.i | −0.533145 | + | 0.355167i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.33773e6 | + | 2.31702e6i | 0.671120 | + | 1.16241i | 0.977587 | + | 0.210532i | \(0.0675196\pi\) |
−0.306467 | + | 0.951881i | \(0.599147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −521395. | + | 903082.i | −0.257665 | + | 0.446289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.51276e6 | −0.736474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.92637e6 | 1.88328 | 0.941642 | − | 0.336615i | \(-0.109282\pi\) | ||||
0.941642 | + | 0.336615i | \(0.109282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 343039. | − | 594162.i | 0.162123 | − | 0.280805i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 574164. | + | 994482.i | 0.267393 | + | 0.463138i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −416179. | − | 2.13877e6i | −0.191005 | − | 0.981589i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 244179. | + | 422931.i | 0.110449 | + | 0.191303i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 717045. | − | 1.24196e6i | 0.319685 | − | 0.553711i | −0.660737 | − | 0.750618i | \(-0.729756\pi\) |
0.980422 | + | 0.196906i | \(0.0630894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.10644e6 | 0.486255 | 0.243128 | − | 0.969994i | \(-0.421827\pi\) | ||||
0.243128 | + | 0.969994i | \(0.421827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 151793. | 0.0657632 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 513012. | − | 888563.i | 0.219124 | − | 0.379535i | −0.735416 | − | 0.677616i | \(-0.763013\pi\) |
0.954541 | + | 0.298081i | \(0.0963466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 342128. | + | 592583.i | 0.144085 | + | 0.249562i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.45768e6 | + | 971065.i | −0.605328 | + | 0.403253i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 413510. | + | 716221.i | 0.169336 | + | 0.293299i | 0.938187 | − | 0.346130i | \(-0.112504\pi\) |
−0.768850 | + | 0.639429i | \(0.779171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 594285. | − | 1.02933e6i | 0.240009 | − | 0.415707i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 825858. | 0.328957 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.40133e6 | −1.33634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −132027. | + | 228677.i | −0.0511677 | + | 0.0886251i | −0.890475 | − | 0.455032i | \(-0.849628\pi\) |
0.839307 | + | 0.543658i | \(0.182961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 752565. | + | 1.30348e6i | 0.287725 | + | 0.498355i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.82696e6 | + | 904109.i | 0.689117 | + | 0.341025i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 557515. | + | 965645.i | 0.207484 | + | 0.359373i | 0.950921 | − | 0.309433i | \(-0.100139\pi\) |
−0.743437 | + | 0.668806i | \(0.766806\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 855039. | − | 1.48097e6i | 0.313984 | − | 0.543836i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 73030.9 | 0.0264639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.68943e6 | −0.604145 | −0.302073 | − | 0.953285i | \(-0.597678\pi\) | ||||
−0.302073 | + | 0.953285i | \(0.597678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 102090. | − | 176825.i | 0.0360306 | − | 0.0624068i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.73368e6 | − | 3.00282e6i | −0.603910 | − | 1.04600i | −0.992223 | − | 0.124475i | \(-0.960275\pi\) |
0.388313 | − | 0.921528i | \(-0.373058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 97250.0 | + | 1.51598e6i | 0.0334378 | + | 0.521246i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10869.4 | + | 18826.4i | 0.00368918 | + | 0.00638984i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −934501. | + | 1.61860e6i | −0.313116 | + | 0.542333i | −0.979035 | − | 0.203691i | \(-0.934706\pi\) |
0.665919 | + | 0.746024i | \(0.268040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.82984e6 | −0.605300 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.43793e6 | −0.796233 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.85902e6 | + | 3.21992e6i | −0.599504 | + | 1.03837i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.15146e6 | + | 3.72644e6i | 0.685106 | + | 1.18664i | 0.973403 | + | 0.229097i | \(0.0735775\pi\) |
−0.288298 | + | 0.957541i | \(0.593089\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 84755.8 | + | 1.32122e6i | 0.0266525 | + | 0.415472i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.40533e6 | − | 4.16616e6i | −0.746989 | − | 1.29382i | −0.949260 | − | 0.314493i | \(-0.898165\pi\) |
0.202271 | − | 0.979330i | \(-0.435168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 454179. | − | 786662.i | 0.139304 | − | 0.241282i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −292065. | −0.0884793 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.38878e6 | −1.01405 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 199699. | − | 345889.i | 0.0590293 | − | 0.102242i | −0.835001 | − | 0.550249i | \(-0.814533\pi\) |
0.894030 | + | 0.448007i | \(0.147866\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79137e6 | + | 3.10274e6i | 0.523094 | + | 0.906026i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.89310e6 | − | 1.92659e6i | −1.12311 | − | 0.555794i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −327256. | − | 566824.i | −0.0932755 | − | 0.161558i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 700430. | − | 1.21318e6i | 0.197253 | − | 0.341653i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.24119e6 | −0.901922 | −0.450961 | − | 0.892544i | \(-0.648919\pi\) | ||||
−0.450961 | + | 0.892544i | \(0.648919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.17199e6 | 0.322268 | 0.161134 | − | 0.986933i | \(-0.448485\pi\) | ||||
0.161134 | + | 0.986933i | \(0.448485\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 392913. | − | 680546.i | 0.106769 | − | 0.184930i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 858203. | + | 1.48645e6i | 0.230472 | + | 0.399189i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 187037. | − | 124599.i | 0.0496430 | − | 0.0330708i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 246643. | + | 427198.i | 0.0647031 | + | 0.112069i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.10370e6 | − | 3.64372e6i | 0.545495 | − | 0.944826i | −0.453080 | − | 0.891470i | \(-0.649675\pi\) |
0.998576 | − | 0.0533561i | \(-0.0169918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.35252e6 | 0.602994 | 0.301497 | − | 0.953467i | \(-0.402514\pi\) | ||||
0.301497 | + | 0.953467i | \(0.402514\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −140519. | −0.0356050 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −691569. | + | 1.19783e6i | −0.173234 | + | 0.300049i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.79766e6 | + | 4.84570e6i | 0.692842 | + | 1.20004i | 0.970903 | + | 0.239474i | \(0.0769751\pi\) |
−0.278060 | + | 0.960564i | \(0.589692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 825747. | + | 1.08234e6i | 0.202186 | + | 0.265013i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.54479e6 | + | 6.13976e6i | 0.858186 | + | 1.48642i | 0.873657 | + | 0.486542i | \(0.161742\pi\) |
−0.0154711 | + | 0.999880i | \(0.504925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −590338. | + | 1.02250e6i | −0.141319 | + | 0.244772i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.37437e6 | −0.325338 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.81355e6 | −1.82908 | −0.914540 | − | 0.404495i | \(-0.867447\pi\) | ||||
−0.914540 | + | 0.404495i | \(0.867447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.44563e6 | + | 4.23596e6i | −0.566174 | + | 0.980642i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.84301e6 | − | 3.19219e6i | −0.421971 | − | 0.730876i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00006e6 | − | 666213.i | 0.226463 | − | 0.150864i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.32148e6 | − | 2.28887e6i | −0.295985 | − | 0.512661i | 0.679229 | − | 0.733927i | \(-0.262314\pi\) |
−0.975213 | + | 0.221266i | \(0.928981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 547171. | − | 947727.i | 0.121225 | − | 0.209967i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.51119e6 | 1.20780 | 0.603898 | − | 0.797062i | \(-0.293614\pi\) | ||||
0.603898 | + | 0.797062i | \(0.293614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −263372. | −0.0570975 | −0.0285488 | − | 0.999592i | \(-0.509089\pi\) | ||||
−0.0285488 | + | 0.999592i | \(0.509089\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −873888. | + | 1.51362e6i | −0.187423 | + | 0.324626i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.55469e6 | + | 6.15691e6i | 0.754241 | + | 1.30638i | 0.945751 | + | 0.324893i | \(0.105328\pi\) |
−0.191510 | + | 0.981491i | \(0.561338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.94856e6 | − | 1.95403e6i | −0.828908 | − | 0.410203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.36940e6 | + | 4.10392e6i | 0.492137 | + | 0.852406i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35322.7 | + | 61180.7i | −0.00725941 | + | 0.0125737i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.29740e6 | 0.263839 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.27361e6 | −0.256294 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 435791. | − | 754812.i | 0.0867839 | − | 0.150314i | −0.819366 | − | 0.573271i | \(-0.805674\pi\) |
0.906150 | + | 0.422956i | \(0.139008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.34031e6 | + | 2.32148e6i | 0.264145 | + | 0.457512i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 91049.6 | + | 1.41933e6i | 0.0177587 | + | 0.276831i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −533187. | − | 923507.i | −0.102926 | − | 0.178273i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52122e6 | + | 2.63482e6i | −0.290649 | + | 0.503418i | −0.973963 | − | 0.226706i | \(-0.927204\pi\) |
0.683315 | + | 0.730124i | \(0.260538\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.57649e6 | 0.676372 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.70685e6 | 0.881104 | 0.440552 | − | 0.897727i | \(-0.354783\pi\) | ||||
0.440552 | + | 0.897727i | \(0.354783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 263256. | − | 455973.i | 0.0487822 | − | 0.0844932i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −474566. | − | 821972.i | −0.0870529 | − | 0.150780i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 127573. | + | 1.98867e6i | 0.0231669 | + | 0.361137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.89328e6 | + | 8.47541e6i | 0.879729 | + | 1.52373i | 0.851639 | + | 0.524129i | \(0.175609\pi\) |
0.0280897 | + | 0.999605i | \(0.491058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.33801e6 | + | 4.04955e6i | −0.416151 | + | 0.720795i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.16799e6 | −0.910756 | −0.455378 | − | 0.890298i | \(-0.650496\pi\) | ||||
−0.455378 | + | 0.890298i | \(0.650496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.16008e6 | −0.551403 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.47572e6 | + | 2.55602e6i | −0.254967 | + | 0.441615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 550457. | + | 953419.i | 0.0941735 | + | 0.163113i | 0.909263 | − | 0.416221i | \(-0.136646\pi\) |
−0.815090 | + | 0.579335i | \(0.803312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.87805e6 | − | 4.39350e6i | −1.50406 | − | 0.744317i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −413596. | − | 716369.i | −0.0693877 | − | 0.120183i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37200.2 | − | 64432.7i | 0.00618055 | − | 0.0107050i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.55372e6 | 0.420192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.20235e6 | −0.847776 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.16154e6 | + | 2.01185e6i | −0.187473 | + | 0.324714i | −0.944407 | − | 0.328778i | \(-0.893363\pi\) |
0.756934 | + | 0.653492i | \(0.226697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.65323e6 | + | 2.86347e6i | 0.264288 | + | 0.457761i | 0.967377 | − | 0.253341i | \(-0.0815296\pi\) |
−0.703089 | + | 0.711102i | \(0.748196\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.11028e6 | − | 739636.i | 0.175806 | − | 0.117117i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.27438e6 | − | 5.67140e6i | −0.513574 | − | 0.889536i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.47525e6 | − | 4.28726e6i | 0.384574 | − | 0.666101i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.71396e6 | 0.417702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.86912e6 | 0.589922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −651248. | + | 1.12800e6i | −0.0983699 | + | 0.170382i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.18494e6 | − | 2.05238e6i | −0.177322 | − | 0.307130i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.70436e6 | + | 4.08260e6i | −0.252691 | + | 0.605291i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.63443e6 | − | 8.02707e6i | −0.680774 | − | 1.17914i | −0.974745 | − | 0.223321i | \(-0.928310\pi\) |
0.293971 | − | 0.955814i | \(-0.405023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.05455e6 | − | 3.55858e6i | 0.299032 | − | 0.517938i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.25838e6 | −0.325692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.75237e6 | −0.679113 | −0.339557 | − | 0.940586i | \(-0.610277\pi\) | ||||
−0.339557 | + | 0.940586i | \(0.610277\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −70208.4 | + | 121605.i | −0.00994164 | + | 0.0172194i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −198990. | − | 344661.i | −0.0279224 | − | 0.0483630i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.01154e6 | + | 6.00325e6i | −1.25310 | + | 0.834783i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.57889e6 | − | 4.46677e6i | −0.355386 | − | 0.615547i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.81393e6 | − | 8.33797e6i | 0.657449 | − | 1.13873i | −0.323825 | − | 0.946117i | \(-0.604969\pi\) |
0.981274 | − | 0.192617i | \(-0.0616976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55882.4 | 0.00756390 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.55631e6 | 0.477082 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.97613e6 | − | 3.42275e6i | 0.262751 | − | 0.455098i | −0.704221 | − | 0.709981i | \(-0.748704\pi\) |
0.966972 | + | 0.254883i | \(0.0820370\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.69672e6 | + | 2.93881e6i | 0.223609 | + | 0.387302i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −762339. | − | 377260.i | −0.0995842 | − | 0.0492814i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.58941e6 | + | 2.75295e6i | 0.205805 | + | 0.356465i | 0.950389 | − | 0.311064i | \(-0.100685\pi\) |
−0.744584 | + | 0.667529i | \(0.767352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.53900e6 | − | 1.30579e7i | 0.967662 | − | 1.67604i | 0.265376 | − | 0.964145i | \(-0.414504\pi\) |
0.702286 | − | 0.711895i | \(-0.252163\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.99082e6 | 0.253306 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.39374e6 | 0.175797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.39207e6 | + | 9.33934e6i | −0.674242 | + | 1.16782i | 0.302447 | + | 0.953166i | \(0.402196\pi\) |
−0.976690 | + | 0.214656i | \(0.931137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.25953e6 | − | 2.18157e6i | −0.156140 | − | 0.270442i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −122027. | − | 1.90223e6i | −0.0149974 | − | 0.233788i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.06944e6 | − | 3.58437e6i | −0.252163 | − | 0.436758i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −375394. | + | 650202.i | −0.0453521 | + | 0.0785522i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.07522e6 | 0.368367 | 0.184183 | − | 0.982892i | \(-0.441036\pi\) | ||||
0.184183 | + | 0.982892i | \(0.441036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.95008e6 | −0.587928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.15958e6 | − | 2.00846e6i | 0.136563 | − | 0.236534i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.78728e6 | + | 4.82772e6i | 0.325495 | + | 0.563774i | 0.981612 | − | 0.190885i | \(-0.0611357\pi\) |
−0.656117 | + | 0.754659i | \(0.727802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −554604. | − | 8.64545e6i | −0.0642229 | − | 1.00114i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 680152. | + | 1.17806e6i | 0.0781034 | + | 0.135279i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.61959e6 | − | 2.80521e6i | 0.184433 | − | 0.319447i | −0.758952 | − | 0.651146i | \(-0.774289\pi\) |
0.943385 | + | 0.331699i | \(0.107622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.58656e7 | −1.79172 | −0.895858 | − | 0.444340i | \(-0.853438\pi\) | ||||
−0.895858 | + | 0.444340i | \(0.853438\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.75261e6 | 0.308285 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.04241e6 | + | 3.53755e6i | −0.226858 | + | 0.392929i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.90510e6 | − | 8.49589e6i | −0.540352 | − | 0.935916i | −0.998884 | − | 0.0472386i | \(-0.984958\pi\) |
0.458532 | − | 0.888678i | \(-0.348375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −366778. | − | 181508.i | −0.0400738 | − | 0.0198314i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.01003e6 | − | 1.74943e6i | −0.109454 | − | 0.189580i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.49079e6 | − | 1.12424e7i | 0.697664 | − | 1.20839i | −0.271611 | − | 0.962407i | \(-0.587556\pi\) |
0.969274 | − | 0.245982i | \(-0.0791104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.44458e6 | −0.793693 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.80430e6 | 0.931069 | 0.465534 | − | 0.885030i | \(-0.345862\pi\) | ||||
0.465534 | + | 0.885030i | \(0.345862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.44030e6 | + | 4.22672e6i | −0.255986 | + | 0.443381i | −0.965163 | − | 0.261650i | \(-0.915733\pi\) |
0.709177 | + | 0.705031i | \(0.249067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −444309. | − | 769565.i | −0.0462334 | − | 0.0800786i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.86164e6 | + | 1.90635e6i | −0.295390 | + | 0.196781i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.44259e6 | + | 4.23070e6i | 0.250122 | + | 0.433223i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.34407e6 | − | 2.32800e6i | 0.136538 | − | 0.236491i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.93258e7 | 1.94765 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.20644e7 | 1.20624 | 0.603120 | − | 0.797650i | \(-0.293924\pi\) | ||||
0.603120 | + | 0.797650i | \(0.293924\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.80630e6 | − | 8.32476e6i | 0.476762 | − | 0.825776i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 504952. | + | 874602.i | 0.0496953 | + | 0.0860749i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.47088e6 | − | 447152.i | 0.338915 | − | 0.0436623i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −622537. | − | 1.07827e6i | −0.0603133 | − | 0.104466i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.18280e6 | − | 1.07089e7i | 0.594347 | − | 1.02944i | −0.399292 | − | 0.916824i | \(-0.630744\pi\) |
0.993639 | − | 0.112615i | \(-0.0359228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.43574e7 | 1.36945 | 0.684727 | − | 0.728799i | \(-0.259921\pi\) | ||||
0.684727 | + | 0.728799i | \(0.259921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −107524. | −0.0101766 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −220051. | + | 381140.i | −0.0206663 | + | 0.0357952i | −0.876174 | − | 0.481996i | \(-0.839912\pi\) |
0.855507 | + | 0.517791i | \(0.173245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.40981e6 | + | 7.63802e6i | 0.410968 | + | 0.711818i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.23614e6 | + | 2.82200e6i | −0.391758 | + | 0.260978i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.57819e6 | + | 1.31258e7i | 0.695477 | + | 1.20460i | 0.970020 | + | 0.243026i | \(0.0781401\pi\) |
−0.274543 | + | 0.961575i | \(0.588527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.02918e6 | − | 1.04428e7i | 0.549104 | − | 0.951077i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.18906e6 | 0.559385 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.07235e7 | −0.961883 | −0.480941 | − | 0.876753i | \(-0.659705\pi\) | ||||
−0.480941 | + | 0.876753i | \(0.659705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.22900e6 | − | 3.86075e6i | 0.198430 | − | 0.343691i | −0.749590 | − | 0.661903i | \(-0.769749\pi\) |
0.948019 | + | 0.318212i | \(0.103082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.40657e6 | − | 2.43625e6i | −0.124273 | − | 0.215247i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.86902e6 | − | 2.90441e6i | −0.514650 | − | 0.254686i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −213767. | − | 370255.i | −0.0186048 | − | 0.0322245i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.64165e6 | − | 4.57546e6i | 0.228197 | − | 0.395248i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −456316. | −0.0391255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.73680e7 | 1.47813 | 0.739064 | − | 0.673635i | \(-0.235268\pi\) | ||||
0.739064 | + | 0.673635i | \(0.235268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −416766. | + | 721860.i | −0.0352073 | + | 0.0609808i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.98147e6 | + | 1.38243e7i | 0.669285 | + | 1.15924i | 0.978104 | + | 0.208115i | \(0.0667328\pi\) |
−0.308819 | + | 0.951121i | \(0.599934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −198815. | − | 3.09923e6i | −0.0165491 | − | 0.257976i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −743612. | − | 1.28797e6i | −0.0614439 | − | 0.106424i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.44780e6 | − | 4.23971e6i | 0.200782 | − | 0.347764i | −0.747999 | − | 0.663700i | \(-0.768985\pi\) |
0.948780 | + | 0.315936i | \(0.102318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.77207e7 | −1.44296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.18625e6 | 0.176729 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.63698e6 | + | 2.83533e6i | −0.131370 | + | 0.227539i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.28107e6 | + | 3.95093e6i | 0.181737 | + | 0.314778i | 0.942472 | − | 0.334285i | \(-0.108495\pi\) |
−0.760735 | + | 0.649062i | \(0.775161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −176956. | − | 2.75848e6i | −0.0139969 | − | 0.218191i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.46443e6 | + | 6.00056e6i | 0.272063 | + | 0.471227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39471e7 | − | 2.41571e7i | 1.08743 | − | 1.88349i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.20862e6 | −0.635444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.19910e7 | −0.921640 | −0.460820 | − | 0.887494i | \(-0.652445\pi\) | ||||
−0.460820 | + | 0.887494i | \(0.652445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.30399e6 | − | 1.26509e7i | 0.557406 | − | 0.965456i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.94340e6 | + | 3.36607e6i | 0.147262 | + | 0.255065i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.24835e6 | − | 4.08188e6i | −0.620610 | − | 0.307122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.84550e6 | − | 8.39266e6i | −0.362012 | − | 0.627024i | 0.626280 | − | 0.779598i | \(-0.284577\pi\) |
−0.988292 | + | 0.152575i | \(0.951243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.38268e6 | − | 5.85897e6i | 0.250950 | − | 0.434658i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.31767e6 | −0.391739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.43986e6 | −0.178484 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.81167e6 | + | 8.33406e6i | −0.349541 | + | 0.605423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.29116e7 | + | 2.23636e7i | 0.931448 | + | 1.61332i | 0.780848 | + | 0.624721i | \(0.214787\pi\) |
0.150600 | + | 0.988595i | \(0.451879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 180327. | − | 120129.i | 0.0129188 | − | 0.00860615i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.48629e6 | − | 6.03842e6i | −0.248037 | − | 0.429613i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −200515. | + | 347303.i | −0.0141678 | + | 0.0245394i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.52983e7 | 1.77523 | 0.887617 | − | 0.460582i | \(-0.152359\pi\) | ||||
0.887617 | + | 0.460582i | \(0.152359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 201441. | − | 348905.i | 0.0139429 | − | 0.0241498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.07195e6 | − | 8.78488e6i | −0.348671 | − | 0.603915i | 0.637343 | − | 0.770580i | \(-0.280033\pi\) |
−0.986014 | + | 0.166665i | \(0.946700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.67832e6 | + | 860366.i | −0.455983 | + | 0.0587442i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.47262e6 | + | 7.74681e6i | 0.303315 | + | 0.525357i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −902329. | + | 1.56288e6i | −0.0607790 | + | 0.105272i | −0.894814 | − | 0.446439i | \(-0.852692\pi\) |
0.834035 | + | 0.551712i | \(0.186025\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.12640e6 | −0.142265 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.19536e6 | −0.145893 | −0.0729464 | − | 0.997336i | \(-0.523240\pi\) | ||||
−0.0729464 | + | 0.997336i | \(0.523240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.39891e6 | − | 5.88708e6i | 0.224362 | − | 0.388606i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 595476. | + | 1.03139e6i | 0.0390447 | + | 0.0676275i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.15690e6 | + | 2.10304e6i | −0.205616 | + | 0.136976i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 990979. | + | 1.71643e6i | 0.0641157 | + | 0.111052i | 0.896301 | − | 0.443445i | \(-0.146244\pi\) |
−0.832186 | + | 0.554497i | \(0.812911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.25234e6 | − | 9.09732e6i | 0.337571 | − | 0.584691i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.82316e7 | 1.16401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.57770e7 | −1.00066 | −0.500328 | − | 0.865836i | \(-0.666787\pi\) | ||||
−0.500328 | + | 0.865836i | \(0.666787\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.44388e6 | − | 2.50088e6i | 0.0909761 | − | 0.157575i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.69391e6 | + | 2.93394e6i | 0.106030 | + | 0.183649i | 0.914159 | − | 0.405357i | \(-0.132853\pi\) |
−0.808129 | + | 0.589006i | \(0.799519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.89477e6 | − | 2.91716e6i | −0.366569 | − | 0.181405i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.70638e6 | + | 4.68759e6i | 0.167200 | + | 0.289599i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.48828e6 | − | 6.04188e6i | 0.214103 | − | 0.370837i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.57463e7 | −0.960203 | −0.480102 | − | 0.877213i | \(-0.659400\pi\) | ||||
−0.480102 | + | 0.877213i | \(0.659400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.68641e6 | −0.465680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.92274e6 | − | 1.37226e7i | 0.476899 | − | 0.826014i | −0.522750 | − | 0.852486i | \(-0.675094\pi\) |
0.999650 | + | 0.0264719i | \(0.00842725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.49401e6 | + | 4.31976e6i | 0.149157 | + | 0.258348i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −961618. | − | 1.49902e7i | −0.0571413 | − | 0.890748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.05424e7 | − | 1.82599e7i | −0.622435 | − | 1.07809i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.02308e6 | − | 3.50407e6i | 0.118682 | − | 0.205563i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 255688. | 0.0149041 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.34388e7 | −1.35757 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.46781e6 | + | 1.46667e7i | −0.487343 | + | 0.844102i | −0.999894 | − | 0.0145542i | \(-0.995367\pi\) |
0.512551 | + | 0.858657i | \(0.328700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.88406e6 | − | 1.71197e7i | −0.565253 | − | 0.979047i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 632674. | + | 9.86245e6i | 0.0359533 | + | 0.560459i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 180479. | + | 312599.i | 0.0101917 | + | 0.0176525i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.14972e6 | − | 5.45547e6i | 0.176748 | − | 0.306136i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.91866e7 | 1.06992 | 0.534960 | − | 0.844878i | \(-0.320327\pi\) | ||||
0.534960 | + | 0.844878i | \(0.320327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45635e7 | −0.807049 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.07418e6 | − | 1.86053e6i | 0.0591556 | − | 0.102460i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.00564e7 | + | 1.74182e7i | 0.550367 | + | 0.953264i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.30484e6 | − | 3.12009e6i | −0.342914 | − | 0.169698i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.20311e6 | − | 1.07441e7i | −0.335294 | − | 0.580746i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.88270e6 | + | 6.72503e6i | −0.208575 | + | 0.361262i | −0.951266 | − | 0.308372i | \(-0.900216\pi\) |
0.742691 | + | 0.669634i | \(0.233549\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.53666e7 | 1.35428 | 0.677141 | − | 0.735853i | \(-0.263219\pi\) | ||||
0.677141 | + | 0.735853i | \(0.263219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.62634e7 | −0.862949 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.84492e6 | + | 1.53199e7i | −0.466445 | + | 0.807906i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −152265. | − | 263731.i | −0.00798078 | − | 0.0138231i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.81971e6 | + | 1.21224e6i | −0.0947965 | + | 0.0631509i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.12996e6 | + | 1.58136e7i | 0.472728 | + | 0.818788i | 0.999513 | − | 0.0312102i | \(-0.00993613\pi\) |
−0.526785 | + | 0.849998i | \(0.676603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.54570e7 | + | 2.67724e7i | −0.795476 | + | 1.37780i | 0.127061 | + | 0.991895i | \(0.459446\pi\) |
−0.922537 | + | 0.385909i | \(0.873888\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.70875e6 | −0.138559 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.22844e7 | −0.624584 | −0.312292 | − | 0.949986i | \(-0.601097\pi\) | ||||
−0.312292 | + | 0.949986i | \(0.601097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.14441e6 | + | 1.41065e7i | −0.411598 | + | 0.712908i | −0.995065 | − | 0.0992286i | \(-0.968362\pi\) |
0.583467 | + | 0.812137i | \(0.301696\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.45411e6 | + | 1.29109e7i | 0.374449 | + | 0.648565i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.71973e6 | − | 2.32825e7i | 0.485335 | − | 1.16256i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.15641e7 | − | 2.00296e7i | −0.573979 | − | 0.994161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.59013e6 | − | 2.75418e6i | 0.0784545 | − | 0.135887i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.04940e6 | 0.149558 | 0.0747790 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747790 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03881e7 | −0.994002 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.48760e6 | + | 4.30865e6i | −0.120562 | + | 0.208820i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.29911e6 | − | 1.26424e7i | −0.351664 | − | 0.609100i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.90049e6 | + | 6.59544e6i | −0.474185 | + | 0.315889i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.90383e6 | + | 1.71539e7i | 0.471557 | + | 0.816760i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.84637e6 | − | 1.35903e7i | 0.371402 | − | 0.643288i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.35001e6 | 0.0635278 | 0.0317639 | − | 0.999495i | \(-0.489888\pi\) | ||||
0.0317639 | + | 0.999495i | \(0.489888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.09141e6 | 0.191407 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.32888e6 | + | 7.49784e6i | −0.201337 | + | 0.348726i | −0.948959 | − | 0.315398i | \(-0.897862\pi\) |
0.747623 | + | 0.664124i | \(0.231195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.31907e6 | − | 1.61411e7i | −0.430913 | − | 0.746364i | 0.566039 | − | 0.824378i | \(-0.308475\pi\) |
−0.996952 | + | 0.0780149i | \(0.975142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.94316e7 | − | 9.61618e6i | −0.893309 | − | 0.442074i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.79236e7 | + | 3.10446e7i | 0.819215 | + | 1.41892i | 0.906261 | + | 0.422718i | \(0.138924\pi\) |
−0.0870457 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.28658e7 | − | 2.22842e7i | 0.584650 | − | 1.01264i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.50246e6 | −0.338966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.19856e7 | 0.987616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.53797e6 | − | 6.12794e6i | 0.158019 | − | 0.273696i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 970187. | + | 1.68041e6i | 0.0430844 | + | 0.0746243i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.57696e6 | + | 2.45825e7i | 0.0696308 | + | 1.08544i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.35730e7 | + | 2.35091e7i | 0.595905 | + | 1.03214i | 0.993418 | + | 0.114542i | \(0.0365400\pi\) |
−0.397513 | + | 0.917596i | \(0.630127\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.82121e6 | − | 4.88648e6i | 0.123158 | − | 0.213316i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.96350e7 | −1.28637 | −0.643183 | − | 0.765712i | \(-0.722387\pi\) | ||||
−0.643183 | + | 0.765712i | \(0.722387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.33752e7 | −1.00891 | −0.504456 | − | 0.863438i | \(-0.668307\pi\) | ||||
−0.504456 | + | 0.863438i | \(0.668307\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.71180e6 | + | 1.16252e7i | −0.288059 | + | 0.498932i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.19794e7 | + | 3.80694e7i | 0.938008 | + | 1.62468i | 0.769180 | + | 0.639032i | \(0.220665\pi\) |
0.168828 | + | 0.985646i | \(0.446002\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 188287. | + | 2.93511e6i | 0.00799033 | + | 0.124558i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 863520. | + | 1.49566e6i | 0.0364400 | + | 0.0631159i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.50415e6 | + | 9.53346e6i | −0.230973 | + | 0.400057i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.17218e7 | 0.489144 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.28430e6 | −0.0947921 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 765045. | − | 1.32510e6i | 0.0315710 | − | 0.0546825i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.18017e7 | + | 2.04412e7i | 0.484321 | + | 0.838868i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −280655. | − | 138888.i | −0.0114539 | − | 0.00566821i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.01621e7 | + | 1.76013e7i | 0.412441 | + | 0.714368i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.22045e6 | + | 1.59703e7i | −0.372164 | + | 0.644606i | −0.989898 | − | 0.141780i | \(-0.954717\pi\) |
0.617735 | + | 0.786387i | \(0.288051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.75008e6 | 0.230815 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.78981e7 | 0.714515 | 0.357257 | − | 0.934006i | \(-0.383712\pi\) | ||||
0.357257 | + | 0.934006i | \(0.383712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.93513e6 | + | 3.35175e6i | −0.0768306 | + | 0.133074i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −347261. | − | 601473.i | −0.0137121 | − | 0.0237500i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.92262e7 | − | 1.94697e7i | 1.14776 | − | 0.764604i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.06153e7 | + | 1.83862e7i | 0.414613 | + | 0.718131i | 0.995388 | − | 0.0959335i | \(-0.0305836\pi\) |
−0.580775 | + | 0.814064i | \(0.697250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.71520e6 | + | 1.33631e7i | −0.299708 | + | 0.519109i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.20061e6 | −0.123660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.47199e7 | −0.565655 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −67689.5 | + | 117242.i | −0.00258715 | + | 0.00448108i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.23910e7 | + | 2.14618e7i | 0.471050 | + | 0.815882i | 0.999452 | − | 0.0331122i | \(-0.0105419\pi\) |
−0.528402 | + | 0.848994i | \(0.677209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.15675e7 | − | 1.51620e7i | −0.437387 | − | 0.573302i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.27552e6 | − | 9.13747e6i | −0.198409 | − | 0.343654i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.79501e6 | + | 1.52334e7i | −0.329009 | + | 0.569860i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.29071e7 | 0.852357 | 0.426179 | − | 0.904639i | \(-0.359859\pi\) | ||||
0.426179 | + | 0.904639i | \(0.359859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.35695e7 | 0.872342 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.11502e7 | + | 3.66333e7i | −0.778648 | + | 1.34866i | 0.154073 | + | 0.988059i | \(0.450761\pi\) |
−0.932721 | + | 0.360599i | \(0.882572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.13252e7 | − | 1.96158e7i | −0.414731 | − | 0.718336i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.50131e6 | − | 2.33248e6i | 0.127541 | − | 0.0849645i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.25484e7 | − | 3.90550e7i | −0.817036 | − | 1.41515i | −0.907857 | − | 0.419281i | \(-0.862282\pi\) |
0.0908205 | − | 0.995867i | \(-0.471051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.95486e6 | − | 1.37782e7i | 0.286726 | − | 0.496624i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.37375e6 | −0.156821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.78979e7 | −1.70838 | −0.854189 | − | 0.519962i | \(-0.825946\pi\) | ||||
−0.854189 | + | 0.519962i | \(0.825946\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.92343e6 | + | 8.52763e6i | −0.174687 | + | 0.302566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 415459. | + | 719595.i | 0.0146638 | + | 0.0253985i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.62541e7 | − | 2.28899e7i | −1.62407 | − | 0.803705i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.79893e6 | + | 8.31200e6i | 0.167624 | + | 0.290333i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.18501e6 | − | 2.05250e6i | 0.0411772 | − | 0.0713210i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.24596e7 | 0.430713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.86466e7 | −1.32906 | −0.664531 | − | 0.747261i | \(-0.731368\pi\) | ||||
−0.664531 | + | 0.747261i | \(0.731368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.66507e6 | + | 1.32763e7i | −0.262245 | + | 0.454221i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.65267e7 | + | 2.86250e7i | 0.562519 | + | 0.974312i | 0.997276 | + | 0.0737638i | \(0.0235011\pi\) |
−0.434757 | + | 0.900548i | \(0.643166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.29182e6 | + | 2.01375e7i | 0.0437440 | + | 0.681904i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.07135e6 | + | 1.85563e6i | 0.0360927 | + | 0.0625143i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.34603e7 | + | 2.33139e7i | −0.451147 | + | 0.781409i | −0.998458 | − | 0.0555203i | \(-0.982318\pi\) |
0.547311 | + | 0.836929i | \(0.315652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.98159e6 | 0.232808 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.10936e6 | 0.136333 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.77826e7 | − | 3.08004e7i | 0.586964 | − | 1.01665i | −0.407663 | − | 0.913132i | \(-0.633656\pi\) |
0.994627 | − | 0.103519i | \(-0.0330103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.73546e6 | + | 9.93411e6i | 0.188355 | + | 0.326241i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 724657. | + | 1.12963e7i | 0.0236777 | + | 0.369100i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −163572. | − | 283315.i | −0.00531763 | − | 0.00921041i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.13709e7 | + | 3.70154e7i | −0.691254 | + | 1.19729i | 0.280173 | + | 0.959950i | \(0.409608\pi\) |
−0.971427 | + | 0.237338i | \(0.923725\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.40792e7 | 0.774942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.72825e6 | −0.215449 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.89893e6 | − | 3.28904e6i | 0.0605022 | − | 0.104793i | −0.834188 | − | 0.551480i | \(-0.814063\pi\) |
0.894690 | + | 0.446688i | \(0.147396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.69255e6 | + | 8.12774e6i | 0.148763 | + | 0.257665i |
(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.m.193.5 | 10 | ||
4.3 | odd | 2 | 168.6.q.b.25.5 | ✓ | 10 | ||
7.2 | even | 3 | inner | 336.6.q.m.289.5 | 10 | ||
12.11 | even | 2 | 504.6.s.e.361.1 | 10 | |||
28.23 | odd | 6 | 168.6.q.b.121.5 | yes | 10 | ||
84.23 | even | 6 | 504.6.s.e.289.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.q.b.25.5 | ✓ | 10 | 4.3 | odd | 2 | ||
168.6.q.b.121.5 | yes | 10 | 28.23 | odd | 6 | ||
336.6.q.m.193.5 | 10 | 1.1 | even | 1 | trivial | ||
336.6.q.m.289.5 | 10 | 7.2 | even | 3 | inner | ||
504.6.s.e.289.1 | 10 | 84.23 | even | 6 | |||
504.6.s.e.361.1 | 10 | 12.11 | even | 2 |