Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.6.q.b.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −5.50000 | − | 9.52628i | −0.0983870 | − | 0.170411i | 0.812630 | − | 0.582780i | \(-0.198035\pi\) |
−0.911017 | + | 0.412368i | \(0.864702\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −129.500 | + | 6.06218i | −0.998906 | + | 0.0467610i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 134.500 | − | 232.961i | 0.335151 | − | 0.580499i | −0.648363 | − | 0.761332i | \(-0.724546\pi\) |
0.983514 | + | 0.180833i | \(0.0578793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −308.000 | −0.505466 | −0.252733 | − | 0.967536i | \(-0.581329\pi\) | ||||
−0.252733 | + | 0.967536i | \(0.581329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 99.0000 | 0.113608 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −948.000 | + | 1641.98i | −0.795584 | + | 1.37799i | 0.126884 | + | 0.991918i | \(0.459502\pi\) |
−0.922468 | + | 0.386074i | \(0.873831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −82.0000 | − | 142.028i | −0.0521111 | − | 0.0902590i | 0.838793 | − | 0.544450i | \(-0.183262\pi\) |
−0.890904 | + | 0.454191i | \(0.849928\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 535.500 | − | 1036.63i | 0.264979 | − | 0.512952i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1632.00 | − | 2826.71i | −0.643281 | − | 1.11419i | −0.984696 | − | 0.174282i | \(-0.944239\pi\) |
0.341415 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1502.00 | − | 2601.54i | 0.480640 | − | 0.832493i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2417.00 | 0.533681 | 0.266840 | − | 0.963741i | \(-0.414020\pi\) | ||||
0.266840 | + | 0.963741i | \(0.414020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1420.50 | − | 2460.38i | 0.265483 | − | 0.459830i | −0.702207 | − | 0.711973i | \(-0.747802\pi\) |
0.967690 | + | 0.252143i | \(0.0811352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1210.50 | + | 2096.65i | 0.193500 | + | 0.335151i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 770.000 | + | 1200.31i | 0.106248 | + | 0.165624i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5664.00 | + | 9810.34i | 0.680172 | + | 1.17809i | 0.974928 | + | 0.222520i | \(0.0714284\pi\) |
−0.294756 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1386.00 | − | 2400.62i | 0.145916 | − | 0.252733i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −16856.0 | −1.56601 | −0.783006 | − | 0.622015i | \(-0.786314\pi\) | ||||
−0.783006 | + | 0.622015i | \(0.786314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7894.00 | 0.651067 | 0.325534 | − | 0.945530i | \(-0.394456\pi\) | ||||
0.325534 | + | 0.945530i | \(0.394456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −445.500 | + | 771.629i | −0.0327957 | + | 0.0568038i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10551.0 | + | 18274.9i | 0.696705 | + | 1.20673i | 0.969603 | + | 0.244685i | \(0.0786847\pi\) |
−0.272897 | + | 0.962043i | \(0.587982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16733.5 | − | 1570.10i | 0.995627 | − | 0.0934196i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8532.00 | − | 14777.9i | −0.459331 | − | 0.795584i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14845.5 | − | 25713.2i | 0.725947 | − | 1.25738i | −0.232635 | − | 0.972564i | \(-0.574735\pi\) |
0.958583 | − | 0.284814i | \(-0.0919318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2959.00 | −0.131898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1476.00 | 0.0601727 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4081.50 | + | 7069.37i | −0.152648 | + | 0.264393i | −0.932200 | − | 0.361944i | \(-0.882113\pi\) |
0.779552 | + | 0.626337i | \(0.215447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7583.00 | − | 13134.1i | −0.260925 | − | 0.451936i | 0.705563 | − | 0.708648i | \(-0.250694\pi\) |
−0.966488 | + | 0.256711i | \(0.917361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5670.00 | + | 8838.66i | 0.179983 | + | 0.280566i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1694.00 | + | 2934.09i | 0.0497313 | + | 0.0861372i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16039.0 | + | 27780.4i | −0.436506 | + | 0.756051i | −0.997417 | − | 0.0718253i | \(-0.977118\pi\) |
0.560911 | + | 0.827876i | \(0.310451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 29376.0 | 0.742797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38274.0 | 0.901069 | 0.450534 | − | 0.892759i | \(-0.351233\pi\) | ||||
0.450534 | + | 0.892759i | \(0.351233\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17433.0 | + | 30194.8i | −0.382882 | + | 0.663171i | −0.991473 | − | 0.130313i | \(-0.958402\pi\) |
0.608591 | + | 0.793484i | \(0.291735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13518.0 | + | 23413.9i | 0.277498 | + | 0.480640i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16005.5 | + | 30983.8i | −0.307640 | + | 0.595536i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6764.50 | + | 11716.5i | 0.121946 | + | 0.211217i | 0.920535 | − | 0.390660i | \(-0.127753\pi\) |
−0.798589 | + | 0.601877i | \(0.794420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 68103.0 | 1.08510 | 0.542552 | − | 0.840023i | \(-0.317458\pi\) | ||||
0.542552 | + | 0.840023i | \(0.317458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20856.0 | 0.313100 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10876.5 | + | 18838.7i | −0.154060 | + | 0.266840i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 57461.0 | + | 99525.4i | 0.768950 | + | 1.33186i | 0.938133 | + | 0.346276i | \(0.112554\pi\) |
−0.169183 | + | 0.985585i | \(0.554113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39886.0 | − | 1867.15i | 0.504914 | − | 0.0236361i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12784.5 | + | 22143.4i | 0.153277 | + | 0.265483i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −902.000 | + | 1562.31i | −0.0102541 | + | 0.0177606i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 154959. | 1.67220 | 0.836099 | − | 0.548579i | \(-0.184831\pi\) | ||||
0.836099 | + | 0.548579i | \(0.184831\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21789.0 | −0.223434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 53785.0 | − | 93158.4i | 0.524636 | − | 0.908695i | −0.474953 | − | 0.880011i | \(-0.657535\pi\) |
0.999589 | − | 0.0286843i | \(-0.00913174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4468.00 | + | 7738.80i | 0.0414973 | + | 0.0718755i | 0.886028 | − | 0.463632i | \(-0.153454\pi\) |
−0.844531 | + | 0.535507i | \(0.820121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12820.5 | + | 600.156i | −0.113483 | + | 0.00531240i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 96833.5 | + | 167721.i | 0.817648 | + | 1.41621i | 0.907411 | + | 0.420244i | \(0.138056\pi\) |
−0.0897634 | + | 0.995963i | \(0.528611\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −102555. | + | 177630.i | −0.826781 | + | 1.43203i | 0.0737692 | + | 0.997275i | \(0.476497\pi\) |
−0.900550 | + | 0.434752i | \(0.856836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −101952. | −0.785395 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 46664.0 | 0.343784 | 0.171892 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171892 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17952.0 | + | 31093.8i | −0.126581 | + | 0.219245i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12474.0 | + | 21605.6i | 0.0842444 | + | 0.145916i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112812. | − | 218384.i | 0.730277 | − | 1.41369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 44345.0 | + | 76807.8i | 0.275348 | + | 0.476916i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 75852.0 | − | 131380.i | 0.452069 | − | 0.783006i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −67419.0 | −0.385929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 304365. | 1.67450 | 0.837250 | − | 0.546820i | \(-0.184162\pi\) | ||||
0.837250 | + | 0.546820i | \(0.184162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −35523.0 | + | 61527.6i | −0.187947 | + | 0.325534i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6651.50 | − | 11520.7i | −0.0338642 | − | 0.0586546i | 0.848597 | − | 0.529041i | \(-0.177448\pi\) |
−0.882461 | + | 0.470386i | \(0.844115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11480.0 | + | 17895.5i | 0.0562746 | + | 0.0877235i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4009.50 | − | 6944.66i | −0.0189346 | − | 0.0327957i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 199131. | − | 344905.i | 0.906437 | − | 1.56999i | 0.0874596 | − | 0.996168i | \(-0.472125\pi\) |
0.818977 | − | 0.573826i | \(-0.194542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −230286. | −1.01095 | −0.505476 | − | 0.862841i | \(-0.668683\pi\) | ||||
−0.505476 | + | 0.862841i | \(0.668683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −189918. | −0.804486 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −41426.0 | + | 71751.9i | −0.169408 | + | 0.293423i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13293.5 | − | 23025.0i | −0.0525073 | − | 0.0909452i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −63063.0 | + | 137490.i | −0.240703 | + | 0.524781i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 48567.0 | + | 84120.5i | 0.179216 | + | 0.310410i | 0.941612 | − | 0.336700i | \(-0.109311\pi\) |
−0.762397 | + | 0.647110i | \(0.775977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14523.5 | + | 25155.4i | −0.0518357 | + | 0.0897821i | −0.890779 | − | 0.454437i | \(-0.849841\pi\) |
0.838943 | + | 0.544219i | \(0.183174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 153576. | 0.530389 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31251.0 | −0.104480 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 288250. | − | 499264.i | 0.933298 | − | 1.61652i | 0.155656 | − | 0.987811i | \(-0.450251\pi\) |
0.777642 | − | 0.628708i | \(-0.216416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 133610. | + | 231418.i | 0.419126 | + | 0.725947i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 228480. | + | 356165.i | 0.694678 | + | 1.08290i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −132616. | − | 229698.i | −0.390955 | − | 0.677154i | 0.601621 | − | 0.798782i | \(-0.294522\pi\) |
−0.992576 | + | 0.121628i | \(0.961189\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13315.5 | − | 23063.1i | 0.0380757 | − | 0.0659490i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 363790. | 1.00939 | 0.504696 | − | 0.863297i | \(-0.331605\pi\) | ||||
0.504696 | + | 0.863297i | \(0.331605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −276429. | −0.744504 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6642.00 | + | 11504.3i | −0.0173704 | + | 0.0300863i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 82423.0 | + | 142761.i | 0.209379 | + | 0.362655i | 0.951519 | − | 0.307590i | \(-0.0995224\pi\) |
−0.742140 | + | 0.670245i | \(0.766189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −178738. | + | 346005.i | −0.441186 | + | 0.854057i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −36733.5 | − | 63624.3i | −0.0881311 | − | 0.152648i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15314.0 | − | 26524.6i | 0.0357237 | − | 0.0618752i | −0.847611 | − | 0.530618i | \(-0.821960\pi\) |
0.883334 | + | 0.468743i | \(0.155293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −651392. | −1.47790 | −0.738952 | − | 0.673759i | \(-0.764679\pi\) | ||||
−0.738952 | + | 0.673759i | \(0.764679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 136494. | 0.301291 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 62304.0 | − | 107914.i | 0.133840 | − | 0.231818i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 255012. | + | 441694.i | 0.533282 | + | 0.923671i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −94405.5 | + | 4419.33i | −0.192240 | + | 0.00899915i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −378680. | − | 655893.i | −0.751085 | − | 1.30092i | −0.947297 | − | 0.320356i | \(-0.896198\pi\) |
0.196213 | − | 0.980561i | \(-0.437136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 80169.5 | − | 138858.i | 0.154923 | − | 0.268335i | −0.778108 | − | 0.628131i | \(-0.783820\pi\) |
0.933031 | + | 0.359796i | \(0.117154\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −30492.0 | −0.0574248 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −61738.0 | −0.113341 | −0.0566705 | − | 0.998393i | \(-0.518048\pi\) | ||||
−0.0566705 | + | 0.998393i | \(0.518048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 185454. | − | 321216.i | 0.331974 | − | 0.574995i | −0.650925 | − | 0.759142i | \(-0.725619\pi\) |
0.982899 | + | 0.184147i | \(0.0589522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −144351. | − | 250023.i | −0.252017 | − | 0.436506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −313001. | + | 14652.3i | −0.533097 | + | 0.0249554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 92708.0 | + | 160575.i | 0.154075 | + | 0.266866i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −132192. | + | 228963.i | −0.214427 | + | 0.371398i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −44116.0 | −0.0698603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −217450. | −0.336243 | −0.168122 | − | 0.985766i | \(-0.553770\pi\) | ||||
−0.168122 | + | 0.985766i | \(0.553770\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −172233. | + | 298316.i | −0.260116 | + | 0.450534i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −43417.0 | − | 75200.4i | −0.0640566 | − | 0.110949i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −169040. | + | 327230.i | −0.243691 | + | 0.471742i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −156897. | − | 271754.i | −0.221057 | − | 0.382882i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 291984. | − | 505731.i | 0.402141 | − | 0.696529i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −589771. | −0.794184 | −0.397092 | − | 0.917779i | \(-0.629981\pi\) | ||||
−0.397092 | + | 0.917779i | \(0.629981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −243324. | −0.320427 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −193522. | + | 335191.i | −0.249268 | + | 0.431745i | −0.963323 | − | 0.268345i | \(-0.913523\pi\) |
0.714055 | + | 0.700090i | \(0.246857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 116366. | + | 201552.i | 0.146635 | + | 0.253979i | 0.929982 | − | 0.367606i | \(-0.119822\pi\) |
−0.783347 | + | 0.621585i | \(0.786489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −169470. | − | 264178.i | −0.208960 | − | 0.325736i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21048.0 | − | 36456.2i | −0.0253993 | − | 0.0439928i | 0.853046 | − | 0.521835i | \(-0.174752\pi\) |
−0.878446 | + | 0.477842i | \(0.841419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 116061. | − | 201024.i | 0.137093 | − | 0.237453i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −121761. | −0.140811 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 313416. | 0.354917 | 0.177458 | − | 0.984128i | \(-0.443212\pi\) | ||||
0.177458 | + | 0.984128i | \(0.443212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −428904. | + | 742883.i | −0.475682 | + | 0.823906i | −0.999612 | − | 0.0278556i | \(-0.991132\pi\) |
0.523930 | + | 0.851762i | \(0.324465\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −106992. | − | 150772.i | −0.113876 | − | 0.160475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25256.0 | + | 43744.7i | 0.0263404 | + | 0.0456229i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −306464. | + | 530810.i | −0.313242 | + | 0.542552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −454517. | −0.455371 | −0.227686 | − | 0.973735i | \(-0.573116\pi\) | ||||
−0.227686 | + | 0.973735i | \(0.573116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −878016. | −0.862385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −93852.0 | + | 162556.i | −0.0903843 | + | 0.156550i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −439091. | − | 760528.i | −0.414688 | − | 0.718261i | 0.580707 | − | 0.814112i | \(-0.302776\pi\) |
−0.995396 | + | 0.0958512i | \(0.969443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −792960. | − | 1.23610e6i | −0.734517 | − | 1.14500i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −97888.5 | − | 169548.i | −0.0889468 | − | 0.154060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 980467. | − | 1.69822e6i | 0.874065 | − | 1.51392i | 0.0163091 | − | 0.999867i | \(-0.494808\pi\) |
0.857756 | − | 0.514058i | \(-0.171858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −326601. | −0.285695 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.03430e6 | −0.887907 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 526898. | − | 912613.i | 0.443962 | − | 0.768964i | −0.554018 | − | 0.832505i | \(-0.686906\pi\) |
0.997979 | + | 0.0635408i | \(0.0202393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −52529.5 | − | 90983.8i | −0.0434490 | − | 0.0752559i | 0.843483 | − | 0.537156i | \(-0.180501\pi\) |
−0.886932 | + | 0.461900i | \(0.847168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −164934. | + | 319283.i | −0.133938 | + | 0.259280i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −404038. | − | 699814.i | −0.322174 | − | 0.558022i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 213796. | − | 370306.i | 0.167417 | − | 0.289975i | −0.770094 | − | 0.637931i | \(-0.779791\pi\) |
0.937511 | + | 0.347955i | \(0.113124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −230121. | −0.176989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 638878. | 0.482672 | 0.241336 | − | 0.970442i | \(-0.422414\pi\) | ||||
0.241336 | + | 0.970442i | \(0.422414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.22571e6 | + | 2.12299e6i | −0.909750 | + | 1.57573i | −0.0953386 | + | 0.995445i | \(0.530393\pi\) |
−0.814411 | + | 0.580288i | \(0.802940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8118.00 | − | 14060.8i | −0.00592021 | − | 0.0102541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.18285e6 | − | 102184.i | 1.56430 | − | 0.0732282i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.08748e6 | − | 1.88357e6i | −0.765908 | − | 1.32659i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −697316. | + | 1.20779e6i | −0.482722 | + | 0.836099i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.71617e6 | 1.16786 | 0.583930 | − | 0.811804i | \(-0.301514\pi\) | ||||
0.583930 | + | 0.811804i | \(0.301514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 89793.0 | 0.0600741 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 98050.5 | − | 169828.i | 0.0644998 | − | 0.111717i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 502656. | + | 870626.i | 0.325157 | + | 0.563188i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.02227e6 | + | 47854.8i | −0.650355 | + | 0.0304445i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 484065. | + | 838425.i | 0.302898 | + | 0.524636i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −83413.0 | + | 144476.i | −0.0513433 | + | 0.0889293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.80897e6 | −1.09543 | −0.547715 | − | 0.836665i | \(-0.684502\pi\) | ||||
−0.547715 | + | 0.836665i | \(0.684502\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −80424.0 | −0.0479170 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 760728. | − | 1.31762e6i | 0.445993 | − | 0.772483i | −0.552127 | − | 0.833760i | \(-0.686184\pi\) |
0.998121 | + | 0.0612765i | \(0.0195171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 674200. | + | 1.16775e6i | 0.388980 | + | 0.673734i | 0.992313 | − | 0.123756i | \(-0.0394941\pi\) |
−0.603332 | + | 0.797490i | \(0.706161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 53014.5 | − | 102627.i | 0.0301036 | − | 0.0582752i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24847.5 | + | 43037.1i | 0.0138878 | + | 0.0240544i | 0.872886 | − | 0.487925i | \(-0.162246\pi\) |
−0.858998 | + | 0.511979i | \(0.828913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 325086. | − | 563066.i | 0.178864 | − | 0.309801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.74300e6 | −0.944138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 310944. | 0.165835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −462616. | + | 801274.i | −0.242947 | + | 0.420797i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −922995. | − | 1.59867e6i | −0.477342 | − | 0.826781i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.47714e6 | − | 2.30263e6i | −0.752371 | − | 1.17283i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 793918. | + | 1.37511e6i | 0.398296 | + | 0.689868i | 0.993516 | − | 0.113694i | \(-0.0362684\pi\) |
−0.595220 | + | 0.803563i | \(0.702935\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 458784. | − | 794637.i | 0.226724 | − | 0.392698i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 352858. | 0.171786 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 214825. | 0.103041 | 0.0515205 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515205 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −209988. | + | 363710.i | −0.0992419 | + | 0.171892i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −382114. | − | 661842.i | −0.177954 | − | 0.308225i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.15747e6 | + | 304770.i | −0.990169 | + | 0.139874i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −161568. | − | 279844.i | −0.0730815 | − | 0.126581i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.29430e6 | − | 2.24179e6i | 0.577046 | − | 0.999473i | −0.418770 | − | 0.908092i | \(-0.637539\pi\) |
0.995816 | − | 0.0913809i | \(-0.0291281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24878.0 | −0.0109333 | −0.00546666 | − | 0.999985i | \(-0.501740\pi\) | ||||
−0.00546666 | + | 0.999985i | \(0.501740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −224532. | −0.0972771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 868004. | − | 1.50343e6i | 0.370753 | − | 0.642163i | −0.618928 | − | 0.785447i | \(-0.712433\pi\) |
0.989682 | + | 0.143284i | \(0.0457662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −210507. | − | 364609.i | −0.0886535 | − | 0.153552i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.19448e6 | + | 1.86201e6i | 0.496030 | + | 0.773235i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 431213. | + | 746883.i | 0.176586 | + | 0.305856i | 0.940709 | − | 0.339215i | \(-0.110161\pi\) |
−0.764123 | + | 0.645070i | \(0.776828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.22460e6 | − | 2.12107e6i | 0.494569 | − | 0.856618i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −798210. | −0.317944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 383526. | 0.150682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.55771e6 | − | 2.69803e6i | 0.603700 | − | 1.04564i | −0.388555 | − | 0.921425i | \(-0.627026\pi\) |
0.992255 | − | 0.124214i | \(-0.0396409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 682668. | + | 1.18242e6i | 0.261002 | + | 0.452069i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.76661e6 | + | 3.41985e6i | −0.666357 | + | 1.28995i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 898472. | + | 1.55620e6i | 0.334374 | + | 0.579153i | 0.983364 | − | 0.181644i | \(-0.0581418\pi\) |
−0.648990 | + | 0.760797i | \(0.724808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 303386. | − | 525479.i | 0.111408 | − | 0.192964i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −744436. | −0.269758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.45466e6 | −1.23540 | −0.617699 | − | 0.786415i | \(-0.711935\pi\) | ||||
−0.617699 | + | 0.786415i | \(0.711935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.36964e6 | + | 2.37229e6i | −0.483387 | + | 0.837250i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.07752e6 | + | 1.86632e6i | 0.375343 | + | 0.650113i | 0.990378 | − | 0.138387i | \(-0.0441917\pi\) |
−0.615036 | + | 0.788499i | \(0.710858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 383191. | − | 17938.0i | 0.131754 | − | 0.00616768i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −319707. | − | 553749.i | −0.108511 | − | 0.187947i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 231387. | − | 400774.i | 0.0775291 | − | 0.134284i | −0.824654 | − | 0.565637i | \(-0.808630\pi\) |
0.902183 | + | 0.431353i | \(0.141964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.18854e6 | 2.04714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 119727. | 0.0391031 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 74409.5 | − | 128881.i | 0.0239958 | − | 0.0415620i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.03311e6 | + | 3.52144e6i | 0.647416 | + | 1.12136i | 0.983738 | + | 0.179611i | \(0.0574839\pi\) |
−0.336321 | + | 0.941747i | \(0.609183\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −191142. | + | 8947.77i | −0.0601068 | + | 0.00281373i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.53432e6 | + | 4.38956e6i | 0.787045 | + | 1.36320i | 0.927769 | + | 0.373154i | \(0.121724\pi\) |
−0.140724 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −437514. | + | 757796.i | −0.134193 | + | 0.232429i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 72171.0 | 0.0218638 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.04723e6 | 0.911842 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.43867e6 | + | 2.49185e6i | −0.425258 | + | 0.736568i | −0.996444 | − | 0.0842522i | \(-0.973150\pi\) |
0.571187 | + | 0.820820i | \(0.306483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79218e6 | + | 3.10415e6i | 0.523331 | + | 0.906437i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 485698. | − | 940226.i | 0.140117 | − | 0.271242i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −374567. | − | 648768.i | −0.106760 | − | 0.184914i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.03629e6 | − | 1.79490e6i | 0.291837 | − | 0.505476i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.41342e6 | 0.949850 | 0.474925 | − | 0.880026i | \(-0.342475\pi\) | ||||
0.474925 | + | 0.880026i | \(0.342475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.30737e6 | −0.359496 | −0.179748 | − | 0.983713i | \(-0.557528\pi\) | ||||
−0.179748 | + | 0.983713i | \(0.557528\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 854631. | − | 1.48026e6i | 0.232235 | − | 0.402243i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.84779e6 | + | 4.93252e6i | 0.764779 | + | 1.32464i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.06162e6 | + | 1.65490e6i | 0.281773 | + | 0.439241i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −372834. | − | 645767.i | −0.0978075 | − | 0.169408i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 967734. | − | 1.67616e6i | 0.250936 | − | 0.434634i | −0.712848 | − | 0.701319i | \(-0.752595\pi\) |
0.963784 | + | 0.266685i | \(0.0859283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 516670. | 0.132432 | 0.0662161 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662161 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 239283. | 0.0606302 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −267648. | + | 463580.i | −0.0670441 | + | 0.116124i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.45765e6 | + | 2.52472e6i | 0.360987 | + | 0.625249i | 0.988124 | − | 0.153661i | \(-0.0491064\pi\) |
−0.627136 | + | 0.778910i | \(0.715773\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −787846. | − | 1.11023e6i | −0.192906 | − | 0.271843i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −891896. | − | 1.54481e6i | −0.215926 | − | 0.373995i | 0.737633 | − | 0.675202i | \(-0.235944\pi\) |
−0.953559 | + | 0.301208i | \(0.902610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 632071. | − | 1.09478e6i | 0.151309 | − | 0.262076i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −874206. | −0.206940 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.00158e6 | 0.936733 | 0.468366 | − | 0.883534i | \(-0.344843\pi\) | ||||
0.468366 | + | 0.883534i | \(0.344843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.26713e6 | + | 3.92679e6i | −0.524850 | + | 0.909067i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −130712. | − | 226399.i | −0.0299274 | − | 0.0518357i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −237160. | − | 369696.i | −0.0537048 | − | 0.0837175i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 583832. | + | 1.01123e6i | 0.130767 | + | 0.226495i | 0.923972 | − | 0.382459i | \(-0.124923\pi\) |
−0.793206 | + | 0.608954i | \(0.791589\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −691092. | + | 1.19701e6i | −0.153110 | + | 0.265195i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.61358e6 | 0.791928 | 0.395964 | − | 0.918266i | \(-0.370411\pi\) | ||||
0.395964 | + | 0.918266i | \(0.370411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.80111e6 | 0.390471 | 0.195235 | − | 0.980756i | \(-0.437453\pi\) | ||||
0.195235 | + | 0.980756i | \(0.437453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 140630. | − | 243577.i | 0.0301609 | − | 0.0522402i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.18487e6 | − | 2.05226e6i | −0.251409 | − | 0.435452i | 0.712505 | − | 0.701667i | \(-0.247560\pi\) |
−0.963914 | + | 0.266214i | \(0.914227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.90864e6 | − | 3.69479e6i | 0.400675 | − | 0.775635i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.59425e6 | + | 4.49337e6i | 0.538840 | + | 0.933298i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.06174e6 | − | 1.83899e6i | 0.218206 | − | 0.377944i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −492656. | −0.100187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.40497e6 | −0.483965 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 259073. | − | 448728.i | 0.0515921 | − | 0.0893602i | −0.839076 | − | 0.544014i | \(-0.816904\pi\) |
0.890668 | + | 0.454654i | \(0.150237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.74451e6 | − | 3.02158e6i | −0.343804 | − | 0.595486i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.80419e6 | + | 178083.i | −0.741984 | + | 0.0347339i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −852274. | − | 1.47618e6i | −0.164522 | − | 0.284961i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.41306e6 | − | 2.44750e6i | 0.269985 | − | 0.467627i | −0.698873 | − | 0.715246i | \(-0.746315\pi\) |
0.968858 | + | 0.247619i | \(0.0796480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.38709e6 | 0.451436 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.34747e6 | −1.74981 | −0.874904 | − | 0.484296i | \(-0.839076\pi\) | ||||
−0.874904 | + | 0.484296i | \(0.839076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.29132e6 | + | 3.96868e6i | −0.424588 | + | 0.735408i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 119840. | + | 207568.i | 0.0219830 | + | 0.0380757i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.95648e6 | + | 232024.i | −0.900083 | + | 0.0421349i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.08593e6 | + | 7.07703e6i | 0.734580 | + | 1.27233i | 0.954907 | + | 0.296904i | \(0.0959542\pi\) |
−0.220327 | + | 0.975426i | \(0.570712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.63706e6 | + | 2.83546e6i | −0.291386 | + | 0.504696i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.37713e6 | 1.30007 | 0.650036 | − | 0.759903i | \(-0.274754\pi\) | ||||
0.650036 | + | 0.759903i | \(0.274754\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.18327e6 | −0.206469 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.24393e6 | − | 2.15455e6i | 0.214920 | − | 0.372252i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 163158. | + | 282597.i | 0.0279134 | + | 0.0483474i | 0.879645 | − | 0.475631i | \(-0.157780\pi\) |
−0.851731 | + | 0.523979i | \(0.824447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.07453e6 | − | 4.01591e6i | 0.351453 | − | 0.680350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59778.0 | − | 103539.i | −0.0100288 | − | 0.0173704i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49148.0 | − | 85126.8i | 0.00816559 | − | 0.0141432i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.67644e6 | 0.934006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.48361e6 | −0.241770 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.08351e6 | − | 1.87670e6i | 0.174880 | − | 0.302901i | −0.765240 | − | 0.643745i | \(-0.777380\pi\) |
0.940120 | + | 0.340844i | \(0.110713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −361702. | − | 626486.i | −0.0578225 | − | 0.100151i | 0.835665 | − | 0.549239i | \(-0.185082\pi\) |
−0.893488 | + | 0.449088i | \(0.851749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.89252e6 | − | 2.95015e6i | −0.299669 | − | 0.467138i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.69327e6 | + | 4.66488e6i | 0.422428 | + | 0.731667i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.10868e6 | + | 3.65233e6i | −0.327620 | + | 0.567455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 661203. | 0.101765 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.19165e6 | 0.791566 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.06517e6 | − | 1.84493e6i | 0.160892 | − | 0.278673i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 137826. | + | 238722.i | 0.0206251 | + | 0.0357237i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.88488e6 | − | 4.10943e6i | 0.279455 | − | 0.609270i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.99982e6 | − | 5.19584e6i | −0.440659 | − | 0.763243i | 0.557080 | − | 0.830459i | \(-0.311922\pi\) |
−0.997738 | + | 0.0672159i | \(0.978588\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.93126e6 | − | 5.07710e6i | 0.426634 | − | 0.738952i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.25621e6 | 0.325378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.01570e6 | −1.00254 | −0.501271 | − | 0.865290i | \(-0.667134\pi\) | ||||
−0.501271 | + | 0.865290i | \(0.667134\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −614223. | + | 1.06387e6i | −0.0869752 | + | 0.150645i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −198194. | − | 343282.i | −0.0278107 | − | 0.0481695i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −947030. | − | 1.47627e6i | −0.131689 | − | 0.205284i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 560736. | + | 971223.i | 0.0772727 | + | 0.133840i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.45936e6 | − | 7.72384e6i | 0.609025 | − | 1.05486i | −0.382377 | − | 0.924006i | \(-0.624894\pi\) |
0.991402 | − | 0.130855i | \(-0.0417722\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.43135e6 | −0.329093 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.59022e6 | −0.615781 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.67412e6 | + | 1.15599e7i | −0.887407 | + | 1.53703i | −0.0444767 | + | 0.999010i | \(0.514162\pi\) |
−0.842930 | + | 0.538023i | \(0.819171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −256652. | − | 444534.i | −0.0338239 | − | 0.0585847i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 390380. | − | 755705.i | 0.0509952 | − | 0.0987176i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −551074. | − | 954488.i | −0.0713558 | − | 0.123592i | 0.828140 | − | 0.560521i | \(-0.189399\pi\) |
−0.899496 | + | 0.436930i | \(0.856066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 946741. | − | 1.63980e6i | 0.121518 | − | 0.210475i | −0.798848 | − | 0.601532i | \(-0.794557\pi\) |
0.920367 | + | 0.391057i | \(0.127890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.81624e6 | 0.867278 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.80506e6 | −1.23675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.41476e6 | + | 2.45043e6i | −0.176906 | + | 0.306410i | −0.940819 | − | 0.338909i | \(-0.889942\pi\) |
0.763913 | + | 0.645319i | \(0.223275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 721526. | + | 1.24972e6i | 0.0894448 | + | 0.154923i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.81934e6 | + | 412852.i | −1.08392 | + | 0.0507405i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.99344e6 | − | 6.91684e6i | −0.486604 | − | 0.842823i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 137214. | − | 237662.i | 0.0165771 | − | 0.0287124i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.06799e7 | 1.27930 | 0.639649 | − | 0.768667i | \(-0.279080\pi\) | ||||
0.639649 | + | 0.768667i | \(0.279080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −465924. | −0.0553384 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 277821. | − | 481200.i | 0.0327187 | − | 0.0566705i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.34984e6 | + | 1.27303e7i | 0.858304 | + | 1.48663i | 0.873545 | + | 0.486743i | \(0.161815\pi\) |
−0.0152406 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.70085e6 | + | 126433.i | −0.312758 | + | 0.0146409i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.66909e6 | + | 2.89094e6i | 0.191665 | + | 0.331974i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.24581e6 | − | 7.35396e6i | 0.483497 | − | 0.837441i | −0.516323 | − | 0.856394i | \(-0.672700\pi\) |
0.999820 | + | 0.0189523i | \(0.00603306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.62947e6 | 0.974536 | 0.487268 | − | 0.873253i | \(-0.337994\pi\) | ||||
0.487268 | + | 0.873253i | \(0.337994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.59832e6 | 0.291004 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 487795. | − | 844886.i | 0.0541812 | − | 0.0938447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.29037e6 | + | 9.16319e6i | 0.582793 | + | 1.00943i | 0.995147 | + | 0.0984029i | \(0.0313734\pi\) |
−0.412354 | + | 0.911024i | \(0.635293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.29430e6 | − | 2.50554e6i | 0.141414 | − | 0.273753i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.24971e6 | − | 5.62866e6i | −0.352161 | − | 0.609961i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.92392e6 | + | 3.33233e6i | −0.206793 | + | 0.358176i | −0.950703 | − | 0.310104i | \(-0.899636\pi\) |
0.743910 | + | 0.668280i | \(0.232969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66874e6 | −0.177911 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.51001e7 | −1.59686 | −0.798428 | − | 0.602090i | \(-0.794335\pi\) | ||||
−0.798428 | + | 0.602090i | \(0.794335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.96551e6 | − | 8.60051e6i | 0.520879 | − | 0.902190i | −0.478826 | − | 0.877910i | \(-0.658937\pi\) |
0.999705 | − | 0.0242796i | \(-0.00772920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.18973e6 | − | 2.06067e6i | −0.123799 | − | 0.214427i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.04454e6 | − | 1.25402e7i | −0.830388 | − | 1.29445i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.32295e6 | − | 7.48756e6i | −0.442670 | − | 0.766726i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 198522. | − | 343850.i | 0.0201669 | − | 0.0349301i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.14779e7 | −2.16454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.25224e6 | 0.925068 | 0.462534 | − | 0.886602i | \(-0.346940\pi\) | ||||
0.462534 | + | 0.886602i | \(0.346940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 978525. | − | 1.69486e6i | 0.0970650 | − | 0.168122i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.67401e6 | − | 2.89947e6i | −0.164749 | − | 0.285354i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.15392e6 | + | 483592.i | −0.503256 | + | 0.0472205i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.55010e6 | − | 2.68485e6i | −0.150178 | − | 0.260116i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.50214e6 | + | 4.33384e6i | −0.240529 | + | 0.416608i | −0.960865 | − | 0.277017i | \(-0.910654\pi\) |
0.720336 | + | 0.693625i | \(0.243987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.26137e7 | −1.20314 | −0.601569 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601569 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 781506. | 0.0739662 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.26916e6 | + | 1.08585e7i | −0.588774 | + | 1.01979i | 0.405620 | + | 0.914042i | \(0.367056\pi\) |
−0.994393 | + | 0.105744i | \(0.966278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.09792e6 | + | 1.90166e6i | 0.102320 | + | 0.177223i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.78983e6 | − | 2.79007e6i | −0.165523 | − | 0.258025i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.33033e6 | + | 7.50035e6i | 0.397409 | + | 0.688333i | 0.993405 | − | 0.114654i | \(-0.0365760\pi\) |
−0.595996 | + | 0.802987i | \(0.703243\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −73166.5 | + | 126728.i | −0.00666360 | + | 0.0115417i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.82415e6 | 0.255255 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.94177e6 | −0.712367 | −0.356183 | − | 0.934416i | \(-0.615922\pi\) | ||||
−0.356183 | + | 0.934416i | \(0.615922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.05708e6 | − | 1.83092e6i | 0.0941032 | − | 0.162992i | −0.815131 | − | 0.579277i | \(-0.803335\pi\) |
0.909234 | + | 0.416285i | \(0.136668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.62786e6 | + | 4.55158e6i | 0.232176 | + | 0.402141i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 107338. | − | 207787.i | 0.00941238 | − | 0.0182207i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.94454e6 | − | 6.83215e6i | −0.343307 | − | 0.594625i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.65397e6 | − | 4.59681e6i | 0.229261 | − | 0.397092i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.07965e6 | −0.349798 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −442307. | −0.0376432 | −0.0188216 | − | 0.999823i | \(-0.505991\pi\) | ||||
−0.0188216 | + | 0.999823i | \(0.505991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09496e6 | − | 1.89652e6i | 0.0924992 | − | 0.160213i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.37804e6 | − | 9.31503e6i | −0.450975 | − | 0.781111i | 0.547472 | − | 0.836824i | \(-0.315590\pi\) |
−0.998447 | + | 0.0557130i | \(0.982257\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00672e7 | + | 939389.i | −1.67037 | + | 0.0781936i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.74170e6 | − | 3.01672e6i | −0.143915 | − | 0.249268i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.74430e6 | + | 9.94941e6i | −0.471178 | + | 0.816104i | −0.999456 | − | 0.0329669i | \(-0.989504\pi\) |
0.528278 | + | 0.849071i | \(0.322838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.38088e6 | −0.356726 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.09459e6 | −0.169319 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.57241e6 | + | 7.91965e6i | −0.366942 | + | 0.635562i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.06942e6 | + | 8.78049e6i | 0.403890 | + | 0.699558i | 0.994192 | − | 0.107625i | \(-0.0343246\pi\) |
−0.590302 | + | 0.807183i | \(0.700991\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.82168e6 | − | 132089.i | 0.223190 | − | 0.0104480i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.26657e6 | + | 2.19377e6i | 0.0994645 | + | 0.172278i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.59795e7 | − | 2.76773e7i | 1.24589 | − | 2.15795i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 378864. | 0.0293285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.96839e7 | −1.51292 | −0.756459 | − | 0.654041i | \(-0.773073\pi\) | ||||
−0.756459 | + | 0.654041i | \(0.773073\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 928896. | − | 1.60890e6i | 0.0708890 | − | 0.122783i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.04455e6 | + | 1.80921e6i | 0.0791509 | + | 0.137093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.40042e6 | + | 1.23901e7i | −0.481570 | + | 0.932234i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00859e7 | + | 1.74692e7i | 0.753524 | + | 1.30514i | 0.946105 | + | 0.323861i | \(0.104981\pi\) |
−0.192581 | + | 0.981281i | \(0.561686\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 547924. | − | 949033.i | 0.0406487 | − | 0.0704056i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.27302e6 | −0.683121 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 911372. | 0.0666700 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.41037e6 | + | 2.44284e6i | −0.102456 | + | 0.177458i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.07867e6 | + | 3.60037e6i | 0.149956 | + | 0.259731i | 0.931211 | − | 0.364481i | \(-0.118753\pi\) |
−0.781255 | + | 0.624212i | \(0.785420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −625520. | − | 975089.i | −0.0448129 | − | 0.0698564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.86013e6 | − | 6.68594e6i | −0.274635 | − | 0.475682i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.63033e6 | − | 6.28792e6i | 0.256508 | − | 0.444286i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.54433e7 | 1.08369 | 0.541845 | − | 0.840479i | \(-0.317726\pi\) | ||||
0.541845 | + | 0.840479i | \(0.317726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.48351e6 | + | 1.29618e7i | −0.517979 | + | 0.897166i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.10207e6 | + | 5.37294e6i | 0.213251 | + | 0.369362i | 0.952730 | − | 0.303818i | \(-0.0982614\pi\) |
−0.739479 | + | 0.673180i | \(0.764928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.65662e6 | − | 155440.i | 0.113111 | − | 0.0106132i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.31449e6 | + | 7.47292e6i | 0.292591 | + | 0.506782i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.09492e7 | − | 1.89646e7i | 0.737517 | − | 1.27742i | −0.216093 | − | 0.976373i | \(-0.569331\pi\) |
0.953610 | − | 0.301045i | \(-0.0973353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −454608. | −0.0304153 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.75483e6 | 0.183073 | 0.0915363 | − | 0.995802i | \(-0.470822\pi\) | ||||
0.0915363 | + | 0.995802i | \(0.470822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 534237. | − | 925326.i | 0.0352650 | − | 0.0610807i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.75817e6 | − | 4.77729e6i | −0.180851 | − | 0.313242i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.35567e7 | − | 2.11328e7i | −0.882976 | − | 1.37642i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.45604e6 | + | 1.11822e7i | 0.417702 | + | 0.723481i | 0.995708 | − | 0.0925517i | \(-0.0295024\pi\) |
−0.578006 | + | 0.816032i | \(0.696169\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04533e6 | − | 3.54261e6i | 0.131454 | − | 0.227686i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 319517. | 0.0203998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.64315e7 | −1.67642 | −0.838209 | − | 0.545349i | \(-0.816397\pi\) | ||||
−0.838209 | + | 0.545349i | \(0.816397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.95107e6 | − | 6.84346e6i | 0.248949 | − | 0.431192i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.11069e6 | − | 1.05840e7i | −0.382498 | − | 0.662506i | 0.608921 | − | 0.793231i | \(-0.291603\pi\) |
−0.991419 | + | 0.130725i | \(0.958269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22040e7 | − | 2.36249e7i | 0.758914 | − | 1.46912i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −844668. | − | 1.46301e6i | −0.0521834 | − | 0.0903843i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.25710e6 | − | 2.17736e6i | 0.0771582 | − | 0.133642i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.10654e6 | 0.372374 | 0.186187 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186187 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.90364e6 | 0.478841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.51110e6 | − | 2.61730e6i | 0.0909588 | − | 0.157545i | −0.816956 | − | 0.576700i | \(-0.804340\pi\) |
0.907915 | + | 0.419155i | \(0.137674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.26718e6 | − | 7.39098e6i | −0.255204 | − | 0.442026i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.32028e7 | − | 618051.i | 0.784536 | − | 0.0367259i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.38219e6 | + | 2.39403e6i | 0.0816065 | + | 0.141347i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.14785e6 | − | 8.91634e6i | 0.301994 | − | 0.523069i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.76199e6 | 0.102707 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.34150e6 | −0.367297 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.04143e7 | + | 1.80380e7i | −0.599365 | + | 1.03813i | 0.393550 | + | 0.919303i | \(0.371247\pi\) |
−0.992915 | + | 0.118828i | \(0.962086\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.82420e6 | + | 1.52840e7i | 0.504642 | + | 0.874065i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.04299e6 | + | 282885.i | −0.343408 | + | 0.0160757i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.33556e6 | + | 4.04532e6i | 0.131889 | + | 0.228439i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.46970e6 | − | 2.54560e6i | 0.0824731 | − | 0.142848i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.32328e7 | 1.29556 | 0.647778 | − | 0.761829i | \(-0.275698\pi\) | ||||
0.647778 | + | 0.761829i | \(0.275698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00094e7 | −2.21715 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.65434e6 | − | 8.06156e6i | 0.256317 | − | 0.443954i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.68948e6 | + | 8.12241e6i | 0.256647 | + | 0.444525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.13629e6 | − | 4.13547e6i | 0.116190 | − | 0.224924i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.74208e6 | + | 8.21352e6i | 0.256321 | + | 0.443962i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.43338e6 | + | 9.41090e6i | −0.291876 | + | 0.505545i | −0.974253 | − | 0.225456i | \(-0.927613\pi\) |
0.682377 | + | 0.731000i | \(0.260946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.22632e7 | 1.18860 | 0.594299 | − | 0.804244i | \(-0.297430\pi\) | ||||
0.594299 | + | 0.804244i | \(0.297430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 945531. | 0.0501706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.45878e6 | + | 2.52667e6i | −0.0769298 | + | 0.133246i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −647308. | − | 1.12117e6i | −0.0339278 | − | 0.0587647i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.74636e6 | − | 2.72231e6i | −0.0909754 | − | 0.141817i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.19405e6 | + | 1.07284e7i | 0.320713 | + | 0.555491i | 0.980635 | − | 0.195843i | \(-0.0627442\pi\) |
−0.659922 | + | 0.751334i | \(0.729411\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 847404. | − | 1.46775e6i | 0.0436105 | − | 0.0755356i | −0.843396 | − | 0.537292i | \(-0.819447\pi\) |
0.887007 | + | 0.461757i | \(0.152781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.27268e6 | 0.372014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 378495. | 0.0192440 | 0.00962202 | − | 0.999954i | \(-0.496937\pi\) | ||||
0.00962202 | + | 0.999954i | \(0.496937\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.21437e6 | − | 9.03156e6i | 0.263521 | − | 0.456432i | −0.703654 | − | 0.710543i | \(-0.748449\pi\) |
0.967175 | + | 0.254111i | \(0.0817827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.92416e6 | + | 3.33275e6i | 0.0966584 | + | 0.167417i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.32853e7 | + | 2.89646e7i | −0.663373 | + | 1.44629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00084e6 | − | 3.46557e6i | −0.0993110 | − | 0.172012i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.03554e6 | − | 1.79362e6i | 0.0510923 | − | 0.0884944i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.04082e7 | −1.49137 | −0.745686 | − | 0.666297i | \(-0.767878\pi\) | ||||
−0.745686 | + | 0.666297i | \(0.767878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46693e7 | −0.715185 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.87495e6 | + | 4.97956e6i | −0.139335 | + | 0.241336i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.52036e6 | + | 2.63334e6i | 0.0732495 | + | 0.126872i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.20830e6 | − | 9.67778e6i | −0.297347 | − | 0.463519i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.10314e7 | − | 1.91069e7i | −0.525244 | − | 0.909750i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.84873e7 | − | 3.20209e7i | 0.875083 | − | 1.51569i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.80315e7 | 1.31909 | 0.659544 | − | 0.751666i | \(-0.270750\pi\) | ||||
0.659544 | + | 0.751666i | \(0.270750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 146124. | 0.00683607 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.40148e6 | + | 1.62838e7i | −0.437264 | + | 0.757364i | −0.997477 | − | 0.0709844i | \(-0.977386\pi\) |
0.560213 | + | 0.828349i | \(0.310719\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.93162e6 | + | 6.80976e6i | 0.181798 | + | 0.314883i | 0.942493 | − | 0.334227i | \(-0.108475\pi\) |
−0.760695 | + | 0.649109i | \(0.775142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.02639e6 | + | 1.74735e7i | −0.414960 | + | 0.803288i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.64288e6 | − | 9.77376e6i | −0.257913 | − | 0.446719i | 0.707769 | − | 0.706444i | \(-0.249702\pi\) |
−0.965683 | + | 0.259724i | \(0.916368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 906653. | − | 1.57037e6i | 0.0412003 | − | 0.0713611i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.95746e7 | 0.884394 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.63930e6 | 0.163481 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.94001e6 | − | 8.55635e6i | 0.220639 | − | 0.382158i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.27584e6 | − | 1.08701e7i | −0.278700 | − | 0.482722i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.73076e6 | − | 408706.i | 0.385507 | − | 0.0180464i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.70750e6 | − | 1.16177e7i | −0.294484 | − | 0.510062i | 0.680381 | − | 0.732859i | \(-0.261814\pi\) |
−0.974865 | + | 0.222797i | \(0.928481\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.72276e6 | + | 1.33762e7i | −0.337132 | + | 0.583930i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.18547e7 | 1.38272 | 0.691359 | − | 0.722511i | \(-0.257012\pi\) | ||||
0.691359 | + | 0.722511i | \(0.257012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.05922e7 | 1.32041 | 0.660205 | − | 0.751086i | \(-0.270470\pi\) | ||||
0.660205 | + | 0.751086i | \(0.270470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −404068. | + | 699867.i | −0.0173419 | + | 0.0300371i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.31886e6 | − | 4.01638e6i | −0.0989613 | − | 0.171406i | 0.812294 | − | 0.583249i | \(-0.198219\pi\) |
−0.911255 | + | 0.411843i | \(0.864885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.94153e7 | + | 1.84511e6i | −1.67267 | + | 0.0783013i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 882454. | + | 1.52846e6i | 0.0372390 | + | 0.0644998i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.73036e6 | − | 2.99708e6i | 0.0726121 | − | 0.125768i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −336908. | −0.0140590 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.04781e6 | −0.375459 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.43335e6 | − | 5.94673e6i | 0.141683 | − | 0.245403i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.81471e7 | + | 4.87522e7i | 1.15510 | + | 2.00070i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.22724e6 | − | 8.18318e6i | 0.172519 | − | 0.333966i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.58266e6 | + | 6.20534e6i | 0.145406 | + | 0.251851i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 302188. | − | 523405.i | 0.0121972 | − | 0.0211261i | −0.859862 | − | 0.510526i | \(-0.829451\pi\) |
0.872060 | + | 0.489400i | \(0.162784\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.71317e6 | −0.349757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.44059e7 | 0.974315 | 0.487157 | − | 0.873314i | \(-0.338034\pi\) | ||||
0.487157 | + | 0.873314i | \(0.338034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.15985e6 | − | 1.58653e7i | 0.363673 | − | 0.629901i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −750717. | − | 1.30028e6i | −0.0296431 | − | 0.0513433i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 931210. | + | 1.45161e6i | 0.0365699 | + | 0.0570069i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.83547e7 | + | 3.17914e7i | 0.716902 | + | 1.24171i | 0.962221 | + | 0.272268i | \(0.0877737\pi\) |
−0.245320 | + | 0.969442i | \(0.578893\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.14036e6 | − | 1.40995e7i | 0.316224 | − | 0.547715i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.17884e7 | −0.455460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.40293e7 | 1.30767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 361908. | − | 626843.i | 0.0138324 | − | 0.0239585i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.14544e7 | + | 1.98396e7i | 0.435446 | + | 0.754214i | 0.997332 | − | 0.0730004i | \(-0.0232574\pi\) |
−0.561886 | + | 0.827215i | \(0.689924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.59515e6 | − | 2.24788e6i | −0.0603151 | − | 0.0849961i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.84655e6 | + | 1.18586e7i | 0.257494 | + | 0.445993i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.80513e6 | − | 4.85863e6i | 0.104936 | − | 0.181754i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.99611e6 | −0.223111 | −0.111555 | − | 0.993758i | \(-0.535583\pi\) | ||||
−0.111555 | + | 0.993758i | \(0.535583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.21356e7 | −0.449156 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.82579e6 | − | 1.00906e7i | 0.214477 | − | 0.371485i | −0.738634 | − | 0.674107i | \(-0.764529\pi\) |
0.953111 | + | 0.302622i | \(0.0978619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.75090e7 | + | 4.76470e7i | 1.00738 | + | 1.74484i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 561330. | + | 875027.i | 0.0204474 | + | 0.0318744i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −554632. | − | 960651.i | −0.0200969 | − | 0.0348089i | 0.855802 | − | 0.517303i | \(-0.173064\pi\) |
−0.875899 | + | 0.482495i | \(0.839731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.36936e6 | − | 9.30001e6i | 0.193534 | − | 0.335211i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −447255. | −0.0160363 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05743e7 | 0.377155 | 0.188578 | − | 0.982058i | \(-0.439612\pi\) | ||||
0.188578 | + | 0.982058i | \(0.439612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.16548e6 | + | 7.21482e6i | −0.147794 | + | 0.255987i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.92578e6 | + | 5.06760e6i | 0.103267 | + | 0.178864i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.36966e7 | + | 4.58724e7i | −0.832031 | + | 1.61066i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.02789e7 | + | 1.78036e7i | 0.359037 | + | 0.621871i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.84351e6 | − | 1.35854e7i | 0.272549 | − | 0.472069i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.76373e6 | −0.0609696 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.32666e6 | −0.217575 | −0.108787 | − | 0.994065i | \(-0.534697\pi\) | ||||
−0.108787 | + | 0.994065i | \(0.534697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.39925e6 | + | 2.42357e6i | −0.0478724 | + | 0.0829174i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.96197e7 | + | 3.39824e7i | 0.667798 | + | 1.15666i | 0.978519 | + | 0.206158i | \(0.0660962\pi\) |
−0.310721 | + | 0.950501i | \(0.600570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.98220e7 | − | 1.39603e6i | 1.00985 | − | 0.0472731i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.16354e6 | − | 7.21147e6i | −0.140266 | − | 0.242947i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 775371. | − | 1.34298e6i | 0.0259880 | − | 0.0450126i | −0.852739 | − | 0.522337i | \(-0.825060\pi\) |
0.878727 | + | 0.477325i | \(0.158393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.09140e7 | 1.03086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66139e7 | 0.551187 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.43742e7 | + | 4.22174e7i | −0.804538 | + | 1.39350i | 0.112064 | + | 0.993701i | \(0.464254\pi\) |
−0.916602 | + | 0.399801i | \(0.869079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 339559. | + | 588133.i | 0.0111513 | + | 0.0193146i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.45944e7 | − | 1.15132e6i | 0.803606 | − | 0.0376185i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.28830e7 | − | 2.23140e7i | −0.418819 | − | 0.725416i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −962758. | + | 1.66754e6i | −0.0311410 | + | 0.0539378i | −0.881176 | − | 0.472789i | \(-0.843247\pi\) |
0.850035 | + | 0.526726i | \(0.176581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.42905e7 | −0.459912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.07999e6 | −0.130648 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.71282e7 | + | 4.69874e7i | −0.864337 | + | 1.49708i | 0.00336739 | + | 0.999994i | \(0.498928\pi\) |
−0.867704 | + | 0.497081i | \(0.834405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.12906e6 | + | 7.15173e6i | 0.130899 | + | 0.226724i |
(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.b.193.1 | 2 | ||
4.3 | odd | 2 | 21.6.e.a.4.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 336.6.q.b.289.1 | 2 | ||
12.11 | even | 2 | 63.6.e.a.46.1 | 2 | |||
28.3 | even | 6 | 147.6.a.d.1.1 | 1 | |||
28.11 | odd | 6 | 147.6.a.c.1.1 | 1 | |||
28.19 | even | 6 | 147.6.e.g.79.1 | 2 | |||
28.23 | odd | 6 | 21.6.e.a.16.1 | yes | 2 | ||
28.27 | even | 2 | 147.6.e.g.67.1 | 2 | |||
84.11 | even | 6 | 441.6.a.g.1.1 | 1 | |||
84.23 | even | 6 | 63.6.e.a.37.1 | 2 | |||
84.59 | odd | 6 | 441.6.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.a.4.1 | ✓ | 2 | 4.3 | odd | 2 | ||
21.6.e.a.16.1 | yes | 2 | 28.23 | odd | 6 | ||
63.6.e.a.37.1 | 2 | 84.23 | even | 6 | |||
63.6.e.a.46.1 | 2 | 12.11 | even | 2 | |||
147.6.a.c.1.1 | 1 | 28.11 | odd | 6 | |||
147.6.a.d.1.1 | 1 | 28.3 | even | 6 | |||
147.6.e.g.67.1 | 2 | 28.27 | even | 2 | |||
147.6.e.g.79.1 | 2 | 28.19 | even | 6 | |||
336.6.q.b.193.1 | 2 | 1.1 | even | 1 | trivial | ||
336.6.q.b.289.1 | 2 | 7.2 | even | 3 | inner | ||
441.6.a.g.1.1 | 1 | 84.11 | even | 6 | |||
441.6.a.h.1.1 | 1 | 84.59 | odd | 6 |