Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), degree \(2\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} + \cdots + 80\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.1 | ||
Root | \(14.2764 - 24.7275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.6.e.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −14.7764 | − | 25.5935i | −0.947909 | − | 1.64183i | −0.749820 | − | 0.661642i | \(-0.769860\pi\) |
−0.198088 | − | 0.980184i | \(-0.563473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 35.6401 | + | 61.7304i | 0.637549 | + | 1.10427i | 0.985969 | + | 0.166929i | \(0.0533850\pi\) |
−0.348420 | + | 0.937339i | \(0.613282\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 252.315 | 1.94625 | 0.973125 | − | 0.230279i | \(-0.0739637\pi\) | ||||
0.973125 | + | 0.230279i | \(0.0739637\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −315.186 | + | 545.918i | −1.29706 | + | 2.24658i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 88.0323 | 0.219362 | 0.109681 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109681 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 307.862 | − | 533.232i | 0.505239 | − | 0.875100i | −0.494742 | − | 0.869040i | \(-0.664738\pi\) |
0.999982 | − | 0.00606030i | \(-0.00192907\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1053.27 | − | 1824.31i | 1.20868 | − | 2.09349i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 285.543 | + | 494.575i | 0.239634 | + | 0.415059i | 0.960609 | − | 0.277902i | \(-0.0896391\pi\) |
−0.720975 | + | 0.692961i | \(0.756306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 361.524 | − | 1531.47i | 0.229748 | − | 0.973250i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3728.32 | − | 6457.64i | −1.84487 | − | 3.19540i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1214.28 | + | 2103.20i | −0.478630 | + | 0.829011i | −0.999700 | − | 0.0245027i | \(-0.992200\pi\) |
0.521070 | + | 0.853514i | \(0.325533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −977.931 | + | 1693.83i | −0.312938 | + | 0.542024i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11447.9 | 3.02216 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1142.82 | − | 1979.43i | 0.252339 | − | 0.437064i | −0.711830 | − | 0.702351i | \(-0.752134\pi\) |
0.964169 | + | 0.265288i | \(0.0854669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3684.20 | 0.688555 | 0.344278 | − | 0.938868i | \(-0.388124\pi\) | ||||
0.344278 | + | 0.938868i | \(0.388124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1300.80 | − | 2253.06i | −0.207935 | − | 0.360153i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8992.54 | + | 15575.5i | 1.24083 | + | 2.14918i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3064.28 | 0.367980 | 0.183990 | − | 0.982928i | \(-0.441099\pi\) | ||||
0.183990 | + | 0.982928i | \(0.441099\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18196.4 | −1.91568 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1246.89 | − | 2159.67i | −0.115842 | − | 0.200645i | 0.802274 | − | 0.596956i | \(-0.203623\pi\) |
−0.918116 | + | 0.396311i | \(0.870290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2450.11 | − | 4243.71i | −0.202075 | − | 0.350005i | 0.747122 | − | 0.664687i | \(-0.231435\pi\) |
−0.949197 | + | 0.314682i | \(0.898102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −44933.0 | −3.30776 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8786.51 | − | 15218.7i | 0.580192 | − | 1.00492i | −0.415264 | − | 0.909701i | \(-0.636311\pi\) |
0.995456 | − | 0.0952210i | \(-0.0303558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46856.0 | 2.78789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8438.61 | − | 14616.1i | 0.454303 | − | 0.786876i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12713.9 | + | 22021.1i | −0.621712 | + | 1.07684i | 0.367455 | + | 0.930041i | \(0.380229\pi\) |
−0.989167 | + | 0.146795i | \(0.953104\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3137.48 | + | 5434.27i | 0.139854 | + | 0.242234i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −44537.7 | + | 13377.0i | −1.81569 | + | 0.545345i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11756.9 | − | 20363.5i | −0.439706 | − | 0.761592i | 0.557961 | − | 0.829867i | \(-0.311584\pi\) |
−0.997667 | + | 0.0682748i | \(0.978251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9886.00 | − | 17123.1i | 0.340170 | − | 0.589192i | −0.644294 | − | 0.764778i | \(-0.722849\pi\) |
0.984464 | + | 0.175586i | \(0.0561820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −79526.2 | + | 137743.i | −2.52440 | + | 4.37240i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 43888.8 | 1.28846 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13694.3 | + | 23719.2i | −0.372694 | + | 0.645525i | −0.989979 | − | 0.141214i | \(-0.954899\pi\) |
0.617285 | + | 0.786740i | \(0.288233\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 71771.0 | 1.81479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16750.0 | − | 29011.9i | −0.394339 | − | 0.683014i | 0.598678 | − | 0.800990i | \(-0.295693\pi\) |
−0.993017 | + | 0.117975i | \(0.962360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8986.08 | − | 15564.3i | −0.197362 | − | 0.341841i | 0.750310 | − | 0.661086i | \(-0.229904\pi\) |
−0.947672 | + | 0.319245i | \(0.896571\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 57801.3 | 1.18655 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22211.9 | 0.426932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41242.9 | + | 71434.8i | 0.743501 | + | 1.28778i | 0.950892 | + | 0.309523i | \(0.100169\pi\) |
−0.207391 | + | 0.978258i | \(0.566497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −92569.6 | − | 160335.i | −1.56767 | − | 2.71529i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 40274.4 | 0.641702 | 0.320851 | − | 0.947130i | \(-0.396031\pi\) | ||||
0.320851 | + | 0.947130i | \(0.396031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20353.5 | + | 35253.4i | −0.305557 | + | 0.529241i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −67547.4 | −0.956777 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −27641.5 | + | 47876.5i | −0.369902 | + | 0.640689i | −0.989550 | − | 0.144191i | \(-0.953942\pi\) |
0.619648 | + | 0.784880i | \(0.287275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 77678.2 | − | 134543.i | 0.983322 | − | 1.70316i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −54439.3 | − | 94291.7i | −0.652688 | − | 1.13049i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107423. | − | 32264.7i | 1.22120 | − | 0.366791i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13348.8 | + | 23120.7i | 0.144049 | + | 0.249501i | 0.929018 | − | 0.370035i | \(-0.120654\pi\) |
−0.784968 | + | 0.619536i | \(0.787321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −27746.6 | + | 48058.4i | −0.284525 | + | 0.492812i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60668.2 | + | 105080.i | −0.591777 | + | 1.02499i | 0.402216 | + | 0.915545i | \(0.368240\pi\) |
−0.993993 | + | 0.109443i | \(0.965093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −123258. | −1.14478 | −0.572392 | − | 0.819980i | \(-0.693985\pi\) | ||||
−0.572392 | + | 0.819980i | \(0.693985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 265755. | − | 460302.i | 2.35239 | − | 4.07445i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 225615. | 1.90506 | 0.952529 | − | 0.304449i | \(-0.0984722\pi\) | ||||
0.952529 | + | 0.304449i | \(0.0984722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −25583.8 | − | 44312.5i | −0.206253 | − | 0.357240i | 0.744279 | − | 0.667869i | \(-0.232793\pi\) |
−0.950531 | + | 0.310629i | \(0.899460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −45279.2 | − | 78425.8i | −0.348812 | − | 0.604160i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −113870. | −0.838909 | −0.419454 | − | 0.907776i | \(-0.637779\pi\) | ||||
−0.419454 | + | 0.907776i | \(0.637779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −173108. | −1.22060 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 194067. | + | 336134.i | 1.31065 | + | 2.27012i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 72046.9 | + | 124789.i | 0.466388 | + | 0.807808i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153301. | −0.951881 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −36849.1 | + | 63824.5i | −0.219616 | + | 0.380386i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 83336.4 | 0.477045 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −23234.7 | + | 40243.6i | −0.127828 | + | 0.221405i | −0.922835 | − | 0.385196i | \(-0.874134\pi\) |
0.795007 | + | 0.606601i | \(0.207467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −72407.6 | + | 125414.i | −0.383098 | + | 0.663546i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 142237. | + | 246361.i | 0.724157 | + | 1.25428i | 0.959320 | + | 0.282321i | \(0.0911044\pi\) |
−0.235163 | + | 0.971956i | \(0.575562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91217.9 | − | 386413.i | 0.447148 | − | 1.89419i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 408006. | + | 706687.i | 1.92678 | + | 3.33728i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −143955. | + | 249337.i | −0.655277 | + | 1.13497i | 0.326547 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189792i | \(0.939219\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88821.1 | − | 153843.i | 0.389923 | − | 0.675367i | −0.602515 | − | 0.798107i | \(-0.705835\pi\) |
0.992439 | + | 0.122740i | \(0.0391681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −519333. | −2.19988 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27101.8 | − | 46941.6i | 0.110830 | − | 0.191963i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 162921. | 0.643514 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −692365. | − | 1.19921e6i | −2.64266 | − | 4.57723i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −81129.1 | − | 140520.i | −0.299372 | − | 0.518527i | 0.676621 | − | 0.736332i | \(-0.263444\pi\) |
−0.975992 | + | 0.217805i | \(0.930110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −449650. | −1.60484 | −0.802420 | − | 0.596760i | \(-0.796455\pi\) | ||||
−0.802420 | + | 0.596760i | \(0.796455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −359996. | −1.24328 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 131305. | + | 227427.i | 0.438988 | + | 0.760349i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −27389.5 | − | 47440.1i | −0.0886820 | − | 0.153602i | 0.818272 | − | 0.574831i | \(-0.194932\pi\) |
−0.906954 | + | 0.421229i | \(0.861599\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 751464. | 2.35730 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −306382. | + | 530669.i | −0.931533 | + | 1.61346i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 207755. | 0.612467 | 0.306233 | − | 0.951956i | \(-0.400931\pi\) | ||||
0.306233 | + | 0.951956i | \(0.400931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 92721.5 | − | 160598.i | 0.265137 | − | 0.459231i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −136696. | + | 236765.i | −0.379284 | + | 0.656940i | −0.990958 | − | 0.134170i | \(-0.957163\pi\) |
0.611674 | + | 0.791110i | \(0.290496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3910.94 | − | 6773.94i | −0.0105333 | − | 0.0182442i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 722110. | + | 680060.i | 1.88848 | + | 1.77851i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −262508. | − | 454677.i | −0.666848 | − | 1.15501i | −0.978781 | − | 0.204910i | \(-0.934310\pi\) |
0.311933 | − | 0.950104i | \(-0.399024\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −246747. | + | 427378.i | −0.609055 | + | 1.05491i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −347449. | + | 601800.i | −0.833601 | + | 1.44384i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13590.9 | −0.0317041 | −0.0158520 | − | 0.999874i | \(-0.505046\pi\) | ||||
−0.0158520 | + | 0.999874i | \(0.505046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −36970.5 | + | 64034.9i | −0.0838802 | + | 0.145285i | −0.904913 | − | 0.425596i | \(-0.860065\pi\) |
0.821033 | + | 0.570880i | \(0.193398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −584319. | −1.28980 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 109211. | + | 189160.i | 0.234606 | + | 0.406349i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25137.0 | + | 43538.6i | 0.0525666 | + | 0.0910480i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.88849e6 | 5.88189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −522570. | −1.03648 | −0.518240 | − | 0.855235i | \(-0.673413\pi\) | ||||
−0.518240 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12411.0 | + | 21496.6i | 0.0239836 | + | 0.0415409i | 0.877768 | − | 0.479086i | \(-0.159032\pi\) |
−0.853784 | + | 0.520627i | \(0.825698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −648520. | − | 1.12327e6i | −1.22134 | − | 2.11543i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −363318. | −0.666993 | −0.333496 | − | 0.942751i | \(-0.608228\pi\) | ||||
−0.333496 | + | 0.942751i | \(0.608228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 40673.4 | − | 70448.5i | 0.0728078 | − | 0.126107i | −0.827323 | − | 0.561726i | \(-0.810137\pi\) |
0.900131 | + | 0.435620i | \(0.143471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 809411. | 1.41312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 288352. | − | 499440.i | 0.491114 | − | 0.850635i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 88878.3 | − | 153942.i | 0.147710 | − | 0.255842i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −765449. | − | 1.32580e6i | −1.24162 | − | 2.15056i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31825.8 | − | 134819.i | 0.0503980 | − | 0.213494i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −235569. | − | 408017.i | −0.364260 | − | 0.630917i | 0.624397 | − | 0.781107i | \(-0.285345\pi\) |
−0.988657 | + | 0.150190i | \(0.952011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −495011. | + | 857384.i | −0.747594 | + | 1.29487i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 174644. | − | 302492.i | 0.257666 | − | 0.446291i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 929580. | 1.34010 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −265564. | + | 459971.i | −0.374162 | + | 0.648068i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 351631. | 0.484291 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −650115. | − | 1.12603e6i | −0.875443 | − | 1.51631i | −0.856290 | − | 0.516495i | \(-0.827236\pi\) |
−0.0191530 | − | 0.999817i | \(-0.506097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −616460. | − | 1.06774e6i | −0.811799 | − | 1.40608i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −73342.4 | −0.0944692 | −0.0472346 | − | 0.998884i | \(-0.515041\pi\) | ||||
−0.0472346 | + | 0.998884i | \(0.515041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.25234e6 | −1.57809 | −0.789046 | − | 0.614335i | \(-0.789424\pi\) | ||||
−0.789046 | + | 0.614335i | \(0.789424\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −328213. | − | 568481.i | −0.404693 | − | 0.700949i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 544644. | + | 943351.i | 0.657238 | + | 1.13837i | 0.981328 | + | 0.192344i | \(0.0616089\pi\) |
−0.324089 | + | 0.946027i | \(0.605058\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.25261e6 | 1.47960 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.21885e6 | − | 2.11110e6i | 1.40954 | − | 2.44140i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 928359. | 1.05129 | 0.525644 | − | 0.850705i | \(-0.323825\pi\) | ||||
0.525644 | + | 0.850705i | \(0.323825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −49744.9 | + | 86160.6i | −0.0551703 | + | 0.0955578i | −0.892292 | − | 0.451460i | \(-0.850904\pi\) |
0.837121 | + | 0.547017i | \(0.184237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.34477e6 | + | 2.32921e6i | −1.46094 | + | 2.53043i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.66995e6 | + | 2.89244e6i | 1.77742 | + | 3.07857i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −705329. | − | 664256.i | −0.735613 | − | 0.692777i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −595112. | − | 1.03076e6i | −0.608275 | − | 1.05356i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −190030. | + | 329141.i | −0.190387 | + | 0.329760i | −0.945379 | − | 0.325975i | \(-0.894308\pi\) |
0.754992 | + | 0.655735i | \(0.227641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −106896. | + | 185149.i | −0.104993 | + | 0.181853i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.20301e6 | 1.15856 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −552645. | + | 957209.i | −0.521931 | + | 0.904012i | 0.477743 | + | 0.878500i | \(0.341455\pi\) |
−0.999675 | + | 0.0255121i | \(0.991878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 773166. | 0.716182 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 720404. | + | 1.24778e6i | 0.654598 | + | 1.13380i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −276003. | − | 478051.i | −0.246050 | − | 0.426172i | 0.716376 | − | 0.697714i | \(-0.245800\pi\) |
−0.962426 | + | 0.271543i | \(0.912466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81250e6 | −1.58549 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.63377e6 | 1.40253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 859906. | + | 1.48940e6i | 0.724553 | + | 1.25496i | 0.959158 | + | 0.282872i | \(0.0912872\pi\) |
−0.234604 | + | 0.972091i | \(0.575379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 451795. | + | 782532.i | 0.373696 | + | 0.647260i | 0.990131 | − | 0.140146i | \(-0.0447571\pi\) |
−0.616435 | + | 0.787406i | \(0.711424\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.59123e6 | −3.72840 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −86089.5 | + | 149111.i | −0.0686465 | + | 0.118899i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.04518e6 | −0.818447 | −0.409223 | − | 0.912434i | \(-0.634200\pi\) | ||||
−0.409223 | + | 0.912434i | \(0.634200\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.16121e6 | + | 2.01127e6i | −0.893099 | + | 1.54689i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −213159. | + | 369202.i | −0.161041 | + | 0.278932i | −0.935242 | − | 0.354008i | \(-0.884819\pi\) |
0.774201 | + | 0.632940i | \(0.218152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29882.7 | − | 51758.4i | −0.0221796 | − | 0.0384162i | 0.854723 | − | 0.519085i | \(-0.173727\pi\) |
−0.876902 | + | 0.480669i | \(0.840394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.41310e6 | − | 2.27258e6i | −1.75980 | − | 1.65732i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −314609. | − | 544918.i | −0.225458 | − | 0.390505i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 546859. | − | 947188.i | 0.385151 | − | 0.667101i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 394494. | − | 683284.i | 0.273092 | − | 0.473008i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.17326e6 | 0.798410 | 0.399205 | − | 0.916862i | \(-0.369286\pi\) | ||||
0.399205 | + | 0.916862i | \(0.369286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 838032. | − | 1.45151e6i | 0.560668 | − | 0.971105i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00779e6 | 0.662947 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 747661. | + | 1.29499e6i | 0.483645 | + | 0.837698i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −618199. | − | 1.07075e6i | −0.393289 | − | 0.681197i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.58584e6 | 2.24380 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.40935e6 | 0.867501 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −252040. | − | 436545.i | −0.152624 | − | 0.264353i | 0.779567 | − | 0.626318i | \(-0.215439\pi\) |
−0.932191 | + | 0.361966i | \(0.882106\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.82132e6 | + | 3.15462e6i | 1.08515 | + | 1.87954i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.39525e6 | 1.40426 | 0.702132 | − | 0.712046i | \(-0.252231\pi\) | ||||
0.702132 | + | 0.712046i | \(0.252231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.06455e6 | + | 1.84385e6i | −0.614193 | + | 1.06381i | 0.376332 | + | 0.926485i | \(0.377185\pi\) |
−0.990525 | + | 0.137329i | \(0.956148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.13373e7 | −6.43773 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −399285. | + | 691581.i | −0.223169 | + | 0.386541i | −0.955769 | − | 0.294120i | \(-0.904974\pi\) |
0.732599 | + | 0.680660i | \(0.238307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 100605. | − | 174254.i | 0.0553535 | − | 0.0958750i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.33378e6 | − | 5.77428e6i | −1.80582 | − | 3.12777i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 860657. | − | 258500.i | 0.459012 | − | 0.137865i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 602135. | + | 1.04293e6i | 0.316217 | + | 0.547704i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −756075. | + | 1.30956e6i | −0.391017 | + | 0.677261i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.21697e6 | − | 3.83991e6i | 1.12920 | − | 1.95583i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −224790. | −0.112773 | −0.0563867 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563867 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −965819. | + | 1.67285e6i | −0.477293 | + | 0.826696i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.95226e6 | −0.950444 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02795e6 | + | 1.78046e6i | 0.493056 | + | 0.853998i | 0.999968 | − | 0.00799964i | \(-0.00254639\pi\) |
−0.506912 | + | 0.861998i | \(0.669213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.68260e6 | + | 2.91435e6i | 0.795209 | + | 1.37734i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 324329. | 0.151043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.58183e6 | 3.47967 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.55792e6 | + | 4.43046e6i | 1.15702 | + | 2.00401i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.48248e6 | − | 2.56773e6i | −0.660946 | − | 1.14479i | −0.980368 | − | 0.197179i | \(-0.936822\pi\) |
0.319422 | − | 0.947613i | \(-0.396511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.25013e6 | 0.988883 | 0.494441 | − | 0.869211i | \(-0.335373\pi\) | ||||
0.494441 | + | 0.869211i | \(0.335373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.52438e6 | − | 6.10441e6i | 1.52692 | − | 2.64470i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.72711e6 | −0.737706 | −0.368853 | − | 0.929488i | \(-0.620249\pi\) | ||||
−0.368853 | + | 0.929488i | \(0.620249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.19394e6 | − | 2.06797e6i | 0.502820 | − | 0.870910i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12919e6 | − | 3.68787e6i | 0.884187 | − | 1.53146i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −526967. | − | 912734.i | −0.215798 | − | 0.373773i | 0.737721 | − | 0.675106i | \(-0.235902\pi\) |
−0.953519 | + | 0.301332i | \(0.902569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.21470e6 | − | 1.10732e6i | −0.894431 | − | 0.447205i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.26525e6 | + | 3.92352e6i | 0.902296 | + | 1.56282i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 640529. | − | 1.10943e6i | 0.251656 | − | 0.435881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.90021e6 | + | 3.29126e6i | −0.736438 | + | 1.27555i | 0.217651 | + | 0.976027i | \(0.430160\pi\) |
−0.954089 | + | 0.299522i | \(0.903173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.57200e6 | 0.601018 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.20791e6 | + | 5.55627e6i | −1.21001 | + | 2.09579i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.16264e6 | −0.432685 | −0.216342 | − | 0.976318i | \(-0.569413\pi\) | ||||
−0.216342 | + | 0.976318i | \(0.569413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.23141e6 | − | 2.13287e6i | −0.452195 | − | 0.783225i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −703663. | − | 1.21878e6i | −0.254983 | − | 0.441643i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.49509e6 | −0.534648 | −0.267324 | − | 0.963607i | \(-0.586139\pi\) | ||||
−0.267324 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37330e6 | 0.484678 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.52086e6 | − | 4.36626e6i | −0.878115 | − | 1.52094i | −0.853407 | − | 0.521246i | \(-0.825467\pi\) |
−0.0247088 | − | 0.999695i | \(-0.507866\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 791634. | + | 1.37115e6i | 0.272190 | + | 0.471448i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.08895e6 | 1.04842 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 612495. | − | 1.06087e6i | 0.205224 | − | 0.355459i | −0.744980 | − | 0.667087i | \(-0.767541\pi\) |
0.950204 | + | 0.311628i | \(0.100874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.38692e6 | −0.458785 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.20350e6 | − | 7.28067e6i | 1.37287 | − | 2.37788i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.93980e6 | + | 5.09188e6i | −0.948036 | + | 1.64205i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −639677. | − | 1.10795e6i | −0.203697 | − | 0.352813i | 0.746020 | − | 0.665924i | \(-0.231962\pi\) |
−0.949717 | + | 0.313110i | \(0.898629\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.12376e7 | + | 3.37522e6i | −3.53378 | + | 1.06138i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −473386. | − | 819928.i | −0.147013 | − | 0.254633i | 0.783109 | − | 0.621884i | \(-0.213632\pi\) |
−0.930122 | + | 0.367251i | \(0.880299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13422e6 | − | 1.96453e6i | 0.347885 | − | 0.602555i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.59838e6 | − | 1.14287e7i | 1.99894 | − | 3.46226i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 269756. | 0.0807208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.78713e6 | + | 3.09540e6i | −0.528260 | + | 0.914974i | 0.471197 | + | 0.882028i | \(0.343822\pi\) |
−0.999457 | + | 0.0329456i | \(0.989511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.50856e6 | 2.48457 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.96644e6 | − | 5.13803e6i | −0.855777 | − | 1.48225i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.43538e6 | + | 2.48616e6i | 0.409117 | + | 0.708611i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.24984e6 | −1.47845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.64582e6 | −1.29279 | −0.646395 | − | 0.763003i | \(-0.723724\pi\) | ||||
−0.646395 | + | 0.763003i | \(0.723724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59986e6 | + | 2.77104e6i | 0.439923 | + | 0.761970i | 0.997683 | − | 0.0680329i | \(-0.0216723\pi\) |
−0.557760 | + | 0.830002i | \(0.688339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.53877e6 | + | 9.59342e6i | 1.50509 | + | 2.60689i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.11697e6 | −0.299963 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.49439e6 | − | 4.32041e6i | 0.662056 | − | 1.14671i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.60187e6 | −0.420227 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.46054e6 | − | 4.26178e6i | 0.638025 | − | 1.10509i | −0.347841 | − | 0.937553i | \(-0.613085\pi\) |
0.985866 | − | 0.167537i | \(-0.0535815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.48931e6 | − | 2.57956e6i | 0.381738 | − | 0.661189i | −0.609573 | − | 0.792730i | \(-0.708659\pi\) |
0.991311 | + | 0.131541i | \(0.0419924\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.40740e6 | − | 4.16973e6i | −0.609992 | − | 1.05654i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.78199e6 | + | 2.61999e6i | 0.696871 | + | 0.656291i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.08758e6 | + | 1.88374e6i | 0.269339 | + | 0.466509i | 0.968691 | − | 0.248268i | \(-0.0798614\pi\) |
−0.699352 | + | 0.714777i | \(0.746528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47684e7 | + | 2.55795e7i | −3.61606 | + | 6.26320i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −189407. | + | 328062.i | −0.0458549 | + | 0.0794231i | −0.888042 | − | 0.459763i | \(-0.847935\pi\) |
0.842187 | + | 0.539186i | \(0.181268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.94058e6 | −0.943323 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.39760e6 | + | 4.15276e6i | −0.567554 | + | 0.983032i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.64067e6 | −1.32043 | −0.660214 | − | 0.751077i | \(-0.729534\pi\) | ||||
−0.660214 | + | 0.751077i | \(0.729534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −109766. | − | 190121.i | −0.0254114 | − | 0.0440138i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.64422e6 | + | 1.15081e7i | 1.52124 | + | 2.63487i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10738e7 | 2.50766 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −317551. | −0.0711252 | −0.0355626 | − | 0.999367i | \(-0.511322\pi\) | ||||
−0.0355626 | + | 0.999367i | \(0.511322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.26888e6 | + | 5.66187e6i | 0.724215 | + | 1.25438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.63141e6 | + | 2.82569e6i | 0.357529 | + | 0.619259i | 0.987547 | − | 0.157322i | \(-0.0502859\pi\) |
−0.630018 | + | 0.776580i | \(0.716953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.65368e6 | −1.65927 | −0.829636 | − | 0.558305i | \(-0.811452\pi\) | ||||
−0.829636 | + | 0.558305i | \(0.811452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.88044e6 | − | 6.72113e6i | 0.832241 | − | 1.44148i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 885237. | 0.187831 | 0.0939155 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939155 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.45528e6 | + | 5.98472e6i | −0.725356 | + | 1.25635i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −809439. | + | 1.40199e6i | −0.168125 | + | 0.291201i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −215689. | − | 373583.i | −0.0443276 | − | 0.0767777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.24050e6 | + | 2.11003e6i | 0.455628 | + | 0.429096i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.01448e6 | − | 1.38815e7i | −1.61280 | − | 2.79345i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.58332e6 | − | 4.47445e6i | 0.514447 | − | 0.891047i | −0.485413 | − | 0.874285i | \(-0.661331\pi\) |
0.999859 | − | 0.0167625i | \(-0.00533592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 943375. | − | 1.63397e6i | 0.185918 | − | 0.322020i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.81089e7 | 3.53203 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −951502. | + | 1.64805e6i | −0.183677 | + | 0.318138i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.53740e6 | −0.866931 | −0.433465 | − | 0.901170i | \(-0.642709\pi\) | ||||
−0.433465 | + | 0.901170i | \(0.642709\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.06988e6 | − | 5.31719e6i | −0.580563 | − | 1.00556i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.58323e6 | − | 7.93839e6i | −0.857963 | − | 1.48603i | −0.873869 | − | 0.486161i | \(-0.838397\pi\) |
0.0159066 | − | 0.999873i | \(-0.494937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30530e6 | 0.241876 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.95556e6 | −0.725596 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.22628e6 | − | 7.32014e6i | −0.767481 | − | 1.32932i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.86531e6 | − | 8.42697e6i | −0.874700 | − | 1.51503i | −0.857081 | − | 0.515181i | \(-0.827725\pi\) |
−0.0176190 | − | 0.999845i | \(-0.505609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.07952e6 | 1.43811 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.37084e6 | + | 9.30257e6i | −0.946503 | + | 1.63939i | −0.193791 | + | 0.981043i | \(0.562078\pi\) |
−0.752713 | + | 0.658349i | \(0.771255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.64888e6 | −1.50915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −115579. | + | 200189.i | −0.0199692 | + | 0.0345876i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.77946e6 | + | 4.81416e6i | −0.475516 | + | 0.823618i | −0.999607 | − | 0.0280444i | \(-0.991072\pi\) |
0.524090 | + | 0.851663i | \(0.324405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.26733e6 | − | 3.92712e6i | −0.384115 | − | 0.665307i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.13870e6 | − | 1.75322e7i | 0.694338 | − | 2.94132i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.39294e6 | − | 7.60880e6i | −0.729856 | − | 1.26415i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 773497. | − | 1.33974e6i | 0.127272 | − | 0.220441i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.75785e6 | + | 1.34370e7i | −1.26422 | + | 2.18970i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.44377e6 | −0.394427 | −0.197213 | − | 0.980361i | \(-0.563189\pi\) | ||||
−0.197213 | + | 0.980361i | \(0.563189\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.06842e6 | − | 3.58260e6i | 0.330662 | − | 0.572723i | −0.651980 | − | 0.758236i | \(-0.726061\pi\) |
0.982642 | + | 0.185513i | \(0.0593948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.45842e7 | 2.30931 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.05200e6 | + | 1.82211e6i | 0.165002 | + | 0.285791i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 269211. | + | 466288.i | 0.0418268 | + | 0.0724461i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.48224e7 | 2.28130 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.53547e6 | −0.234112 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.04093e6 | + | 1.39273e7i | 1.21457 | + | 2.10369i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 200825. | + | 347839.i | 0.0300526 | + | 0.0520526i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.12485e6 | 0.611555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 332076. | − | 575172.i | 0.0487803 | − | 0.0844899i | −0.840604 | − | 0.541650i | \(-0.817800\pi\) |
0.889385 | + | 0.457160i | \(0.151133\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.18517e6 | 0.318043 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.82362e6 | − | 3.15860e6i | 0.262992 | − | 0.455516i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.27290e6 | + | 3.93678e6i | −0.324797 | + | 0.562565i | −0.981471 | − | 0.191609i | \(-0.938629\pi\) |
0.656674 | + | 0.754174i | \(0.271963\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.23186e6 | + | 1.07939e7i | 0.882443 | + | 1.52844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.61828e6 | − | 2.46581e6i | −0.367398 | − | 0.346004i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.04062e7 | + | 1.80241e7i | 1.44704 | + | 2.50634i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.22751e6 | − | 5.59021e6i | 0.444769 | − | 0.770363i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.10469e6 | − | 7.10954e6i | 0.560586 | − | 0.970964i | −0.436859 | − | 0.899530i | \(-0.643909\pi\) |
0.997445 | − | 0.0714342i | \(-0.0227576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.01717e6 | −0.408386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 742871. | − | 1.28669e6i | 0.0996566 | − | 0.172610i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.32458e7 | −1.76119 | −0.880597 | − | 0.473866i | \(-0.842858\pi\) | ||||
−0.880597 | + | 0.473866i | \(0.842858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.05835e6 | − | 7.02927e6i | −0.534846 | − | 0.926380i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.33567e7 | − | 4.04550e7i | −3.05109 | − | 5.28464i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.11112e7 | 1.43873 | 0.719365 | − | 0.694632i | \(-0.244433\pi\) | ||||
0.719365 | + | 0.694632i | \(0.244433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.44176e7 | 1.85055 | 0.925277 | − | 0.379291i | \(-0.123832\pi\) | ||||
0.925277 | + | 0.379291i | \(0.123832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.72172e6 | + | 1.33744e7i | 0.982489 | + | 1.70172i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.37497e6 | − | 4.11356e6i | −0.299563 | − | 0.518858i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.63470e6 | −0.579538 | −0.289769 | − | 0.957097i | \(-0.593578\pi\) | ||||
−0.289769 | + | 0.957097i | \(0.593578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 366782. | − | 635285.i | 0.0454686 | − | 0.0787539i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.01618e7 | 1.24891 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.11923e6 | + | 1.93857e6i | −0.136380 | + | 0.236217i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.38331e7 | + | 2.39597e7i | −1.67121 | + | 2.89462i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −87378.3 | − | 151344.i | −0.0104667 | − | 0.0181288i | 0.860745 | − | 0.509037i | \(-0.169998\pi\) |
−0.871211 | + | 0.490908i | \(0.836665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.33193e6 | − | 5.64224e6i | 0.158195 | − | 0.670137i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.36854e6 | + | 9.29858e6i | 0.632248 | + | 1.09509i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 63610.1 | − | 110176.i | 0.00742830 | − | 0.0128662i | −0.862287 | − | 0.506419i | \(-0.830969\pi\) |
0.869716 | + | 0.493553i | \(0.164302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.13551e6 | + | 8.89497e6i | −0.594691 | + | 1.03003i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.40403e6 | −0.276061 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00216e6 | − | 1.38601e7i | 0.911255 | − | 1.57834i | 0.0989618 | − | 0.995091i | \(-0.468448\pi\) |
0.812293 | − | 0.583249i | \(-0.198219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.52423e7 | 1.72134 | 0.860668 | − | 0.509166i | \(-0.170046\pi\) | ||||
0.860668 | + | 0.509166i | \(0.170046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.63250e6 | − | 1.49519e7i | −0.966815 | − | 1.67457i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.46367e6 | − | 9.46336e6i | −0.606871 | − | 1.05113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.49576e7 | 1.64774 | 0.823870 | − | 0.566778i | \(-0.191810\pi\) | ||||
0.823870 | + | 0.566778i | \(0.191810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.70432e7 | −1.86213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.41005e6 | − | 9.37049e6i | −0.586271 | − | 1.01545i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 889245. | + | 1.54022e6i | 0.0955807 | + | 0.165551i | 0.909851 | − | 0.414936i | \(-0.136196\pi\) |
−0.814270 | + | 0.580486i | \(0.802863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.25322e6 | −0.560064 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.97293e6 | − | 1.38095e7i | 0.843150 | − | 1.46038i | −0.0440683 | − | 0.999029i | \(-0.514032\pi\) |
0.887218 | − | 0.461350i | \(-0.152635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.53524e7 | −1.61046 | −0.805231 | − | 0.592962i | \(-0.797959\pi\) | ||||
−0.805231 | + | 0.592962i | \(0.797959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.39010e7 | + | 2.40773e7i | −1.44650 | + | 2.50541i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.97438e6 | + | 1.20800e7i | −0.719922 | + | 1.24694i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.02615e6 | + | 1.04376e7i | 0.617078 | + | 1.06881i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.92076e6 | + | 1.17761e6i | −0.398292 | + | 0.119628i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 874985. | + | 1.51552e6i | 0.0881807 | + | 0.152734i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.84277e6 | − | 3.19177e6i | 0.184246 | − | 0.319123i | −0.759076 | − | 0.651002i | \(-0.774349\pi\) |
0.943322 | + | 0.331879i | \(0.107682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.96173e6 | + | 1.20581e7i | −0.690570 | + | 1.19610i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.31234e6 | −0.325988 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44252e7 | − | 2.49851e7i | 1.40855 | − | 2.43968i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.11175e7 | 2.04592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.60486e6 | + | 4.51176e6i | 0.250403 | + | 0.433711i | 0.963637 | − | 0.267215i | \(-0.0861035\pi\) |
−0.713234 | + | 0.700926i | \(0.752770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.62947e6 | + | 6.28642e6i | 0.346191 | + | 0.599620i | 0.985569 | − | 0.169272i | \(-0.0541417\pi\) |
−0.639379 | + | 0.768892i | \(0.720808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.03225e7 | −0.976976 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.49406e6 | −0.797728 | −0.398864 | − | 0.917010i | \(-0.630595\pi\) | ||||
−0.398864 | + | 0.917010i | \(0.630595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.03499e6 | − | 1.79265e6i | −0.0964545 | − | 0.167064i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.37359e7 | − | 2.37912e7i | −1.27029 | − | 2.20021i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.16393e7 | −1.06818 | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||||
−0.534089 | + | 0.845428i | \(0.679345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.01386e7 | + | 1.75606e7i | −0.923372 | + | 1.59933i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.13291e7 | 1.02396 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.86735e6 | + | 1.70907e7i | −0.885089 | + | 1.53302i | −0.0394769 | + | 0.999220i | \(0.512569\pi\) |
−0.845612 | + | 0.533798i | \(0.820764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.97821e6 | − | 1.38187e7i | 0.710235 | − | 1.23016i | −0.254534 | − | 0.967064i | \(-0.581922\pi\) |
0.964769 | − | 0.263099i | \(-0.0847446\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.19585e6 | − | 8.99947e6i | −0.459063 | − | 0.795121i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.71045e7 | − | 8.14088e6i | 2.37677 | − | 0.713867i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.77542e6 | + | 4.80717e6i | 0.241554 | + | 0.418384i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.92128e7 | + | 3.32775e7i | −1.65968 | + | 2.87465i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 870288. | − | 1.50738e6i | 0.0746202 | − | 0.129246i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.18685e7 | 1.01008 | 0.505041 | − | 0.863096i | \(-0.331477\pi\) | ||||
0.505041 | + | 0.863096i | \(0.331477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.11953e7 | + | 1.93908e7i | −0.945750 | + | 1.63809i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.13643e7 | −0.952952 | −0.476476 | − | 0.879188i | \(-0.658086\pi\) | ||||
−0.476476 | + | 0.879188i | \(0.658086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.36810e6 | + | 5.83372e6i | 0.280356 | + | 0.485591i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.08374e6 | + | 1.87709e6i | 0.0895482 | + | 0.155102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.33134e7 | 1.09204 | 0.546018 | − | 0.837774i | \(-0.316143\pi\) | ||||
0.546018 | + | 0.837774i | \(0.316143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.05223e7 | −1.67109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.85051e7 | + | 3.20517e7i | 1.49589 | + | 2.59095i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.82824e6 | + | 1.35589e7i | 0.628226 | + | 1.08812i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77578e7 | 1.41480 | 0.707400 | − | 0.706813i | \(-0.249868\pi\) | ||||
0.707400 | + | 0.706813i | \(0.249868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.00088e6 | + | 1.21259e7i | −0.553757 | + | 0.959136i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.26624e7 | 0.994381 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 712079. | − | 1.23336e6i | 0.0555196 | − | 0.0961628i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.60958e7 | − | 2.78787e7i | 1.24600 | − | 2.15814i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.58452e6 | + | 4.47652e6i | 0.198648 | + | 0.344069i | 0.948090 | − | 0.318001i | \(-0.103012\pi\) |
−0.749442 | + | 0.662070i | \(0.769678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10781e6 | − | 4.69286e6i | 0.0845429 | − | 0.358137i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.85091e7 | − | 3.20586e7i | −1.40253 | − | 2.42925i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.53075e7 | + | 2.65134e7i | −1.15175 | + | 1.99488i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.35081e6 | − | 1.09999e7i | 0.474476 | − | 0.821816i | −0.525097 | − | 0.851042i | \(-0.675971\pi\) |
0.999573 | + | 0.0292265i | \(0.00930441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.19967e7 | −3.85746 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.47366e6 | + | 7.74860e6i | −0.329563 | + | 0.570820i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.86364e6 | 0.282638 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.37178e7 | − | 2.37600e7i | −0.996524 | − | 1.72603i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.17643e7 | + | 2.03763e7i | 0.848678 | + | 1.46995i | 0.882388 | + | 0.470522i | \(0.155934\pi\) |
−0.0337101 | + | 0.999432i | \(0.510732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.11000e7 | −2.22804 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.94021e6 | 0.209186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23520e6 | + | 3.87149e6i | 0.157933 | + | 0.273548i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.08765e7 | + | 1.88387e7i | 0.763229 | + | 1.32195i | 0.941178 | + | 0.337911i | \(0.109720\pi\) |
−0.177949 | + | 0.984040i | \(0.556946\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.44949e7 | 2.40401 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.39922e6 | − | 2.42352e6i | 0.0968485 | − | 0.167746i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.80139e6 | −0.673795 | −0.336897 | − | 0.941541i | \(-0.609378\pi\) | ||||
−0.336897 | + | 0.941541i | \(0.609378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.93519e7 | − | 8.54800e7i | 3.36965 | − | 5.83641i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.20554e6 | + | 2.08806e6i | −0.0817548 | + | 0.141603i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.08883e6 | − | 1.22782e7i | −0.477489 | − | 0.827035i | 0.522178 | − | 0.852837i | \(-0.325120\pi\) |
−0.999667 | + | 0.0258011i | \(0.991786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.57842e6 | + | 2.78672e7i | −0.440125 | + | 1.86444i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.04168e6 | − | 5.26834e6i | −0.202135 | − | 0.350108i | 0.747081 | − | 0.664733i | \(-0.231455\pi\) |
−0.949216 | + | 0.314625i | \(0.898121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.78289e6 | − | 1.00163e7i | 0.381728 | − | 0.661173i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.26939e7 | + | 2.19865e7i | −0.832327 | + | 1.44163i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.69261e7 | 3.70772 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.05235e6 | − | 1.04830e7i | 0.391584 | − | 0.678243i | −0.601075 | − | 0.799193i | \(-0.705261\pi\) |
0.992659 | + | 0.120950i | \(0.0385941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.12318e7 | 0.721878 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.60255e7 | − | 2.77571e7i | −1.02316 | − | 1.77217i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −837126. | − | 1.44994e6i | −0.0530947 | − | 0.0919627i | 0.838257 | − | 0.545276i | \(-0.183575\pi\) |
−0.891351 | + | 0.453313i | \(0.850242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.31817e6 | 0.398095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.71108e7 | −1.07105 | −0.535525 | − | 0.844520i | \(-0.679886\pi\) | ||||
−0.535525 | + | 0.844520i | \(0.679886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.45519e6 | − | 1.11807e7i | −0.401419 | − | 0.695278i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.28303e7 | − | 2.22227e7i | −0.792653 | − | 1.37292i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.44780e7 | −0.888626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.88795e6 | + | 8.46617e6i | −0.298065 | + | 0.516263i | −0.975693 | − | 0.219141i | \(-0.929674\pi\) |
0.677628 | + | 0.735404i | \(0.263008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.26645e7 | 1.97897 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.30084e6 | + | 1.09134e7i | −0.379271 | + | 0.656916i | −0.990956 | − | 0.134185i | \(-0.957158\pi\) |
0.611686 | + | 0.791101i | \(0.290492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.60289e6 | + | 6.24039e6i | −0.215475 | + | 0.373214i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.14246e7 | − | 1.97880e7i | −0.678875 | − | 1.17585i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.75825e6 | + | 1.12880e6i | −0.221892 | + | 0.0666457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.47454e6 | − | 2.55398e6i | −0.0865027 | − | 0.149827i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.30830e7 | − | 2.26604e7i | 0.762610 | − | 1.32088i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.95233e6 | − | 3.38154e6i | 0.113078 | − | 0.195857i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.91406e7 | −1.10159 | −0.550795 | − | 0.834641i | \(-0.685675\pi\) | ||||
−0.550795 | + | 0.834641i | \(0.685675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.15667e6 | + | 1.41278e7i | −0.466466 | + | 0.807944i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.87312e7 | −1.63273 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.08704e6 | − | 1.05431e7i | −0.343735 | − | 0.595366i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.67823e7 | + | 4.63882e7i | 1.50290 | + | 2.60309i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.28733e6 | −0.0717865 | −0.0358932 | − | 0.999356i | \(-0.511428\pi\) | ||||
−0.0358932 | + | 0.999356i | \(0.511428\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.00357e7 | 0.556136 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.74244e7 | − | 3.01800e7i | −0.959572 | − | 1.66203i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −791066. | − | 1.37017e6i | −0.0432936 | − | 0.0749867i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.36779e7 | −2.37559 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.54127e7 | − | 4.40161e7i | 1.37362 | − | 2.37918i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.73676e7 | 1.47016 | 0.735082 | − | 0.677978i | \(-0.237144\pi\) | ||||
0.735082 | + | 0.677978i | \(0.237144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.68597e6 | + | 6.38429e6i | −0.196789 | + | 0.340848i | −0.947485 | − | 0.319799i | \(-0.896385\pi\) |
0.750697 | + | 0.660647i | \(0.229718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.33518e7 | − | 2.31260e7i | 0.708459 | − | 1.22709i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.40441e6 | + | 1.28248e7i | 0.390478 | + | 0.676327i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.38488e6 | + | 2.21806e6i | −0.387069 | + | 0.116257i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.89661e7 | + | 8.48118e7i | 2.55086 | + | 4.41821i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.13053e7 | − | 1.95813e7i | 0.585360 | − | 1.01387i | −0.409471 | − | 0.912323i | \(-0.634287\pi\) |
0.994830 | − | 0.101550i | \(-0.0323800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.42337e7 | − | 2.46536e7i | 0.732520 | − | 1.26876i | −0.223283 | − | 0.974754i | \(-0.571677\pi\) |
0.955803 | − | 0.294008i | \(-0.0949893\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.08839e6 | 0.260283 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.08685e6 | + | 8.81069e6i | −0.258634 | + | 0.447967i | −0.965876 | − | 0.259004i | \(-0.916606\pi\) |
0.707242 | + | 0.706971i | \(0.249939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.96805e6 | 0.251073 | 0.125536 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125536 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.54440e7 | + | 2.67498e7i | 0.775813 | + | 1.34375i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.33794e7 | + | 2.31738e7i | 0.668074 | + | 1.15714i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.94874e7 | −0.967250 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.21765e7 | 2.08093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.19839e6 | − | 9.00387e6i | −0.254955 | − | 0.441595i | 0.709928 | − | 0.704274i | \(-0.248727\pi\) |
−0.964883 | + | 0.262679i | \(0.915394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.64348e6 | + | 1.32389e7i | 0.372650 | + | 0.645449i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.25989e7 | 0.610610 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 278772. | − | 482847.i | 0.0134310 | − | 0.0232631i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.86803e7 | −1.85260 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −883119. | + | 1.52961e6i | −0.0420485 | + | 0.0728301i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.72090e6 | + | 6.44479e6i | −0.176126 | + | 0.305060i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.62456e6 | + | 2.81382e6i | 0.0764475 | + | 0.132411i | 0.901715 | − | 0.432331i | \(-0.142309\pi\) |
−0.825267 | + | 0.564742i | \(0.808976\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.62443e7 | + | 6.88135e7i | −0.759953 | + | 3.21928i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.16911e7 | − | 2.02495e7i | −0.543754 | − | 0.941810i | −0.998684 | − | 0.0512826i | \(-0.983669\pi\) |
0.454930 | − | 0.890527i | \(-0.349664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 469598. | − | 813368.i | 0.0217142 | − | 0.0376101i | −0.854964 | − | 0.518687i | \(-0.826421\pi\) |
0.876678 | + | 0.481077i | \(0.159754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.29758e6 | + | 1.61039e7i | −0.427427 | + | 0.740326i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.88566e7 | −1.77598 | −0.887989 | − | 0.459864i | \(-0.847898\pi\) | ||||
−0.887989 | + | 0.459864i | \(0.847898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.87116e7 | − | 3.24094e7i | 0.850296 | − | 1.47276i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.23225e7 | −1.46035 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.63071e6 | + | 6.28857e6i | 0.163095 | + | 0.282490i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.43189e6 | + | 1.46045e7i | 0.376599 | + | 0.652289i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.68294e7 | −0.747364 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.10270e7 | 0.928449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.05008e6 | + | 1.04790e7i | 0.265621 | + | 0.460069i | 0.967726 | − | 0.252004i | \(-0.0810897\pi\) |
−0.702105 | + | 0.712073i | \(0.747756\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.73366e7 | − | 3.00279e7i | −0.756819 | − | 1.31085i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.25012e7 | 0.542642 | 0.271321 | − | 0.962489i | \(-0.412539\pi\) | ||||
0.271321 | + | 0.962489i | \(0.412539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.22509e7 | + | 2.12191e7i | −0.528767 | + | 0.915852i | 0.470670 | + | 0.882309i | \(0.344012\pi\) |
−0.999437 | + | 0.0335424i | \(0.989321\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.95325e7 | −2.12585 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.48831e6 | − | 6.04194e6i | 0.148870 | − | 0.257850i | −0.781940 | − | 0.623353i | \(-0.785770\pi\) |
0.930810 | + | 0.365503i | \(0.119103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.86246e6 | + | 1.01541e7i | −0.248786 | + | 0.430910i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.14912e6 | − | 1.41147e7i | −0.343888 | − | 0.595631i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.01304e7 | − | 1.89582e7i | −0.844742 | − | 0.795551i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −484380. | − | 838971.i | −0.0202129 | − | 0.0350098i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.20955e7 | − | 3.82706e7i | 0.916903 | − | 1.58812i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.21039e6 | − | 7.29261e6i | 0.173749 | − | 0.300943i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.45215e7 | −0.595934 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.82696e7 | + | 3.16438e7i | −0.745605 | + | 1.29143i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.27053e6 | −0.213911 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.41679e7 | + | 2.45394e7i | 0.571855 | + | 0.990482i | 0.996376 | + | 0.0850637i | \(0.0271094\pi\) |
−0.424520 | + | 0.905418i | \(0.639557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.82435e7 | − | 6.62398e7i | −1.53514 | − | 2.65894i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.34867e6 | −0.293368 | −0.146684 | − | 0.989183i | \(-0.546860\pi\) | ||||
−0.146684 | + | 0.989183i | \(0.546860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.54545e6 | 0.140765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.08252e7 | − | 3.60703e7i | −0.822311 | − | 1.42428i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.58885e7 | + | 6.21606e7i | 1.40939 | + | 2.44114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.01362e7 | −0.395899 | −0.197949 | − | 0.980212i | \(-0.563428\pi\) | ||||
−0.197949 | + | 0.980212i | \(0.563428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.44849e6 | + | 1.29012e7i | −0.289347 | + | 0.501164i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.06267e7 | −0.796941 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.99666e6 | + | 5.19036e6i | −0.115155 | + | 0.199454i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.88493e7 | − | 6.72890e7i | 1.48486 | − | 2.57185i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.13628e7 | + | 1.96809e7i | 0.431961 | + | 0.748179i | 0.997042 | − | 0.0768569i | \(-0.0244885\pi\) |
−0.565081 | + | 0.825035i | \(0.691155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.69396e7 | − | 7.17586e7i | 0.640513 | − | 2.71331i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.53932e7 | − | 6.13028e7i | −1.33111 | − | 2.30556i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.79177e6 | + | 3.10344e6i | −0.0670275 | + | 0.116095i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.38676e6 | + | 2.40195e6i | −0.0516005 | + | 0.0893747i | −0.890672 | − | 0.454647i | \(-0.849766\pi\) |
0.839071 | + | 0.544021i | \(0.183099\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.29210e7 | 2.32880 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.59541e7 | + | 2.76333e7i | −0.587351 | + | 1.01732i | 0.407227 | + | 0.913327i | \(0.366496\pi\) |
−0.994578 | + | 0.103994i | \(0.966838\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.05629e6 | 0.221782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.02946e8 | + | 1.78308e8i | 3.74999 | + | 6.49518i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.89457e6 | + | 1.36738e7i | 0.286058 | + | 0.495466i | 0.972865 | − | 0.231373i | \(-0.0743218\pi\) |
−0.686808 | + | 0.726839i | \(0.740988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.10659e7 | −0.398860 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.36000e7 | 0.846176 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.02282e6 | + | 1.38959e7i | 0.286151 | + | 0.495628i | 0.972888 | − | 0.231278i | \(-0.0742909\pi\) |
−0.686737 | + | 0.726906i | \(0.740958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.86244e7 | − | 3.22585e7i | −0.660808 | − | 1.14455i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.94636e6 | −0.209880 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.63220e7 | + | 6.29116e7i | −1.27533 | + | 2.20894i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.50558e7 | −0.525891 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.11106e7 | + | 1.23167e8i | −2.47098 | + | 4.27986i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −884662. | + | 1.53228e6i | −0.0305815 | + | 0.0529687i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.12207e6 | + | 5.40759e6i | 0.107368 | + | 0.185968i | 0.914703 | − | 0.404126i | \(-0.132424\pi\) |
−0.807335 | + | 0.590093i | \(0.799091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.93334e7 | − | 1.82075e7i | −0.661451 | − | 0.622934i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.44348e7 | − | 2.50019e7i | −0.491319 | − | 0.850990i | 0.508631 | − | 0.860985i | \(-0.330152\pi\) |
−0.999950 | + | 0.00999502i | \(0.996818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.24109e7 | − | 3.88169e7i | 0.758888 | − | 1.31443i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.77948e7 | − | 3.08215e7i | 0.599490 | − | 1.03835i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.53409e6 | 0.0514179 | 0.0257089 | − | 0.999669i | \(-0.491816\pi\) | ||||
0.0257089 | + | 0.999669i | \(0.491816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.43335e6 | + | 4.21468e6i | −0.0811423 | + | 0.140543i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.22546e7 | 1.07009 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.37733e7 | + | 2.38561e7i | 0.454627 | + | 0.787437i | 0.998667 | − | 0.0516223i | \(-0.0164392\pi\) |
−0.544040 | + | 0.839060i | \(0.683106\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.29487e7 | − | 2.24278e7i | −0.425241 | − | 0.736538i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.31036e8 | −4.28151 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.19005e7 | 0.386878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.81799e7 | + | 3.14885e7i | 0.588040 | + | 1.01851i | 0.994489 | + | 0.104841i | \(0.0334334\pi\) |
−0.406449 | + | 0.913673i | \(0.633233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.32159e6 | + | 5.75316e6i | 0.106899 | + | 0.185154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.79842e6 | 0.185674 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15365e7 | − | 1.99819e7i | 0.367568 | − | 0.636646i | −0.621617 | − | 0.783322i | \(-0.713524\pi\) |
0.989185 | + | 0.146675i | \(0.0468572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.50798e7 | 1.11210 |
(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 | 76.6.e.a.45.1 | ✓ | 18 | |
3.2 | odd | 2 | 684.6.k.f.577.2 | 18 | |||
4.3 | odd | 2 | 304.6.i.d.273.9 | 18 | |||
19.11 | even | 3 | inner | 76.6.e.a.49.1 | yes | 18 | |
57.11 | odd | 6 | 684.6.k.f.505.2 | 18 | |||
76.11 | odd | 6 | 304.6.i.d.49.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
76.6.e.a.49.1 | yes | 18 | 19.11 | even | 3 | inner | |
304.6.i.d.49.9 | 18 | 76.11 | odd | 6 | |||
304.6.i.d.273.9 | 18 | 4.3 | odd | 2 | |||
684.6.k.f.505.2 | 18 | 57.11 | odd | 6 | |||
684.6.k.f.577.2 | 18 | 3.2 | odd | 2 |