Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,6,Mod(49,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("304.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.i (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: | \(48.7566812231\) |
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: | \( x^{18} - 5 x^{17} - 3057 x^{16} + 14564 x^{15} + 3829838 x^{14} - 15907074 x^{13} - 2546775754 x^{12} + 7879525640 x^{11} + 976140188391 x^{10} + \cdots + 66\!\cdots\!83 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.6 | ||
Root | \(-6.49256 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.49 |
Dual form | 304.6.i.d.273.6 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.99628 | − | 6.92176i | 0.256361 | − | 0.444031i | −0.708903 | − | 0.705306i | \(-0.750810\pi\) |
0.965264 | + | 0.261275i | \(0.0841430\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 31.6056 | − | 54.7425i | 0.565378 | − | 0.979263i | −0.431637 | − | 0.902048i | \(-0.642064\pi\) |
0.997014 | − | 0.0772156i | \(-0.0246030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 80.2775 | 0.619225 | 0.309613 | − | 0.950863i | \(-0.399801\pi\) | ||||
0.309613 | + | 0.950863i | \(0.399801\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 89.5595 | + | 155.122i | 0.368558 | + | 0.638361i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 475.169 | 1.18404 | 0.592020 | − | 0.805923i | \(-0.298331\pi\) | ||||
0.592020 | + | 0.805923i | \(0.298331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −337.473 | − | 584.520i | −0.553835 | − | 0.959270i | −0.997993 | − | 0.0633218i | \(-0.979831\pi\) |
0.444158 | − | 0.895948i | \(-0.353503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −252.609 | − | 437.532i | −0.289882 | − | 0.502090i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 866.499 | − | 1500.82i | 0.727186 | − | 1.25952i | −0.230881 | − | 0.972982i | \(-0.574161\pi\) |
0.958068 | − | 0.286542i | \(-0.0925058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 574.366 | + | 1464.99i | 0.365010 | + | 0.931004i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 320.811 | − | 555.661i | 0.158745 | − | 0.274955i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2424.72 | + | 4199.73i | 0.955743 | + | 1.65540i | 0.732658 | + | 0.680597i | \(0.238279\pi\) |
0.223085 | + | 0.974799i | \(0.428387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −435.326 | − | 754.007i | −0.139304 | − | 0.241282i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3373.81 | 0.890658 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2394.08 | + | 4146.67i | 0.528620 | + | 0.915597i | 0.999443 | + | 0.0333693i | \(0.0106237\pi\) |
−0.470823 | + | 0.882228i | \(0.656043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.218 | 0.0237764 | 0.0118882 | − | 0.999929i | \(-0.496216\pi\) | ||||
0.0118882 | + | 0.999929i | \(0.496216\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1898.91 | − | 3289.01i | 0.303542 | − | 0.525751i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2537.22 | − | 4394.59i | 0.350096 | − | 0.606384i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13949.4 | −1.67514 | −0.837570 | − | 0.546331i | \(-0.816024\pi\) | ||||
−0.837570 | + | 0.546331i | \(0.816024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5394.54 | −0.567927 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7883.24 | − | 13654.2i | 0.732394 | − | 1.26854i | −0.223463 | − | 0.974712i | \(-0.571736\pi\) |
0.955857 | − | 0.293831i | \(-0.0949304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −964.112 | + | 1669.89i | −0.0795163 | + | 0.137726i | −0.903041 | − | 0.429554i | \(-0.858671\pi\) |
0.823525 | + | 0.567280i | \(0.192004\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11322.3 | 0.833498 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8099.51 | − | 14028.8i | −0.534828 | − | 0.926349i | −0.999172 | − | 0.0406941i | \(-0.987043\pi\) |
0.464344 | − | 0.885655i | \(-0.346290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10362.5 | −0.616560 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6925.54 | − | 11995.4i | −0.372845 | − | 0.645786i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8925.98 | + | 15460.3i | 0.436482 | + | 0.756009i | 0.997415 | − | 0.0718520i | \(-0.0228909\pi\) |
−0.560933 | + | 0.827861i | \(0.689558\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15018.0 | − | 26011.9i | 0.669430 | − | 1.15949i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12435.6 | + | 1878.90i | 0.506969 | + | 0.0765978i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8424.75 | + | 14592.1i | −0.315084 | + | 0.545742i | −0.979455 | − | 0.201661i | \(-0.935366\pi\) |
0.664371 | + | 0.747403i | \(0.268699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11641.7 | + | 20164.0i | 0.400583 | + | 0.693830i | 0.993796 | − | 0.111215i | \(-0.0354743\pi\) |
−0.593214 | + | 0.805045i | \(0.702141\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7189.61 | + | 12452.8i | 0.228220 | + | 0.395289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42664.1 | −1.25250 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13618.4 | − | 23587.8i | −0.370630 | − | 0.641950i | 0.619033 | − | 0.785365i | \(-0.287525\pi\) |
−0.989663 | + | 0.143415i | \(0.954192\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38759.3 | 0.980062 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37449.3 | − | 64864.1i | 0.881654 | − | 1.52707i | 0.0321524 | − | 0.999483i | \(-0.489764\pi\) |
0.849501 | − | 0.527586i | \(-0.176903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34900.9 | − | 60450.1i | 0.766530 | − | 1.32767i | −0.172903 | − | 0.984939i | \(-0.555315\pi\) |
0.939434 | − | 0.342731i | \(-0.111352\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6958.73 | −0.142849 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 38145.4 | 0.733188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11408.5 | + | 19760.1i | −0.205665 | + | 0.356222i | −0.950344 | − | 0.311200i | \(-0.899269\pi\) |
0.744680 | + | 0.667422i | \(0.232602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8280.29 | + | 14341.9i | −0.140227 | + | 0.242881i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58008.8 | 0.924270 | 0.462135 | − | 0.886810i | \(-0.347084\pi\) | ||||
0.462135 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54772.4 | − | 94868.6i | −0.822270 | − | 1.42421i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 38269.6 | 0.542071 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8203.84 | + | 14209.5i | 0.109785 | + | 0.190153i | 0.915683 | − | 0.401901i | \(-0.131651\pi\) |
−0.805898 | + | 0.592054i | \(0.798317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27091.5 | − | 46923.8i | −0.342948 | − | 0.594004i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 508.400 | − | 880.575i | 0.00609535 | − | 0.0105575i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 98350.5 | + | 14859.7i | 1.11807 | + | 0.168928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 65710.8 | − | 113814.i | 0.709100 | − | 1.22820i | −0.256092 | − | 0.966653i | \(-0.582435\pi\) |
0.965191 | − | 0.261544i | \(-0.0842318\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42555.9 | + | 73709.0i | 0.436387 | + | 0.755845i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −46068.0 | − | 79792.2i | −0.449362 | − | 0.778318i | 0.548983 | − | 0.835834i | \(-0.315015\pi\) |
−0.998345 | + | 0.0575159i | \(0.981682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −149801. | −1.39130 | −0.695651 | − | 0.718380i | \(-0.744884\pi\) | ||||
−0.695651 | + | 0.718380i | \(0.744884\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20278.8 | − | 35124.0i | −0.179502 | − | 0.310907i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −62370.7 | −0.526649 | −0.263324 | − | 0.964707i | \(-0.584819\pi\) | ||||
−0.263324 | + | 0.964707i | \(0.584819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27370.0 | + | 47406.1i | −0.220652 | + | 0.382180i | −0.955006 | − | 0.296586i | \(-0.904152\pi\) |
0.734354 | + | 0.678767i | \(0.237485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −55745.6 | + | 96554.3i | −0.429441 | + | 0.743813i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −84395.3 | −0.621759 | −0.310879 | − | 0.950449i | \(-0.600624\pi\) | ||||
−0.310879 | + | 0.950449i | \(0.600624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 306538. | 2.16142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 60447.8 | − | 104699.i | 0.408240 | − | 0.707093i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 69560.4 | − | 120482.i | 0.450292 | − | 0.779929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 64734.8 | 0.401952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −63007.2 | − | 109132.i | −0.375515 | − | 0.650411i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 142500. | 0.815717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −59200.7 | − | 102539.i | −0.325700 | − | 0.564128i | 0.655954 | − | 0.754801i | \(-0.272266\pi\) |
−0.981654 | + | 0.190672i | \(0.938933\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7705.72 | + | 13346.7i | 0.0407698 | + | 0.0706154i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 37228.3 | − | 64481.4i | 0.189538 | − | 0.328289i | −0.755559 | − | 0.655081i | \(-0.772634\pi\) |
0.945096 | + | 0.326792i | \(0.105968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 46108.6 | + | 117606.i | 0.226023 | + | 0.576501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 106631. | − | 184691.i | 0.503559 | − | 0.872189i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −70227.1 | − | 121637.i | −0.319671 | − | 0.553686i | 0.660748 | − | 0.750607i | \(-0.270239\pi\) |
−0.980419 | + | 0.196921i | \(0.936906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 112322. | + | 194548.i | 0.493093 | + | 0.854061i | 0.999968 | − | 0.00795774i | \(-0.00253305\pi\) |
−0.506876 | + | 0.862019i | \(0.669200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −129472. | −0.548437 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160357. | − | 277746.i | −0.655763 | − | 1.13581i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 302665. | 1.19548 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41411.5 | + | 71726.9i | −0.158062 | + | 0.273772i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −146994. | + | 254601.i | −0.542417 | + | 0.939494i | 0.456347 | + | 0.889802i | \(0.349157\pi\) |
−0.998765 | + | 0.0496923i | \(0.984176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −366703. | −1.30880 | −0.654398 | − | 0.756150i | \(-0.727078\pi\) | ||||
−0.654398 | + | 0.756150i | \(0.727078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 310413. | 1.07204 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4020.81 | − | 6964.26i | 0.0134426 | − | 0.0232833i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14338.2 | − | 24834.5i | 0.0464243 | − | 0.0804093i | −0.841880 | − | 0.539666i | \(-0.818551\pi\) |
0.888304 | + | 0.459256i | \(0.151884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 142683. | 0.447588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 194650. | + | 337144.i | 0.591820 | + | 1.02506i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12767.3 | −0.0376383 | −0.0188192 | − | 0.999823i | \(-0.505991\pi\) | ||||
−0.0188192 | + | 0.999823i | \(0.505991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −120032. | − | 207902.i | −0.343232 | − | 0.594495i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 121547. | + | 210526.i | 0.337252 | + | 0.584138i | 0.983915 | − | 0.178638i | \(-0.0571692\pi\) |
−0.646663 | + | 0.762776i | \(0.723836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42129.2 | + | 72969.8i | −0.113466 | + | 0.196529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −175812. | + | 220301.i | −0.459789 | + | 0.576137i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −213672. | + | 370091.i | −0.542792 | + | 0.940143i | 0.455951 | + | 0.890005i | \(0.349299\pi\) |
−0.998742 | + | 0.0501376i | \(0.984034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34946.9 | − | 60529.7i | −0.0862607 | − | 0.149408i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 67335.2 | + | 116628.i | 0.161551 | + | 0.279814i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −41174.1 | −0.0960488 | −0.0480244 | − | 0.998846i | \(-0.515293\pi\) | ||||
−0.0480244 | + | 0.998846i | \(0.515293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −241411. | − | 418136.i | −0.547723 | − | 0.948684i | −0.998430 | − | 0.0560122i | \(-0.982161\pi\) |
0.450707 | − | 0.892672i | \(-0.351172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 186094. | 0.410776 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −440879. | + | 763624.i | −0.947087 | + | 1.64040i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 411734. | − | 713144.i | 0.861018 | − | 1.49133i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 270841. | 0.551518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −218201. | −0.432786 | −0.216393 | − | 0.976306i | \(-0.569429\pi\) | ||||
−0.216393 | + | 0.976306i | \(0.569429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 357570. | − | 619329.i | 0.690983 | − | 1.19682i | −0.280533 | − | 0.959844i | \(-0.590511\pi\) |
0.971516 | − | 0.236973i | \(-0.0761554\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −170498. | + | 295310.i | −0.321094 | + | 0.556150i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17740.5 | 0.0325686 | 0.0162843 | − | 0.999867i | \(-0.494816\pi\) | ||||
0.0162843 | + | 0.999867i | \(0.494816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 290101. | + | 502469.i | 0.519297 | + | 0.899449i | 0.999748 | + | 0.0224275i | \(0.00713948\pi\) |
−0.480451 | + | 0.877021i | \(0.659527\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −217692. | −0.380061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 192191. | + | 332884.i | 0.327335 | + | 0.566961i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −498309. | − | 863096.i | −0.828159 | − | 1.43441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −434313. | + | 752252.i | −0.704493 | + | 1.22022i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 272921. | + | 696119.i | 0.432186 | + | 1.10235i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −418159. | + | 724272.i | −0.646599 | + | 1.11994i | 0.337330 | + | 0.941386i | \(0.390476\pi\) |
−0.983930 | + | 0.178556i | \(0.942857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −299316. | − | 518430.i | −0.452044 | − | 0.782963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 60942.6 | + | 105556.i | 0.0899135 | + | 0.155735i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10212.8 | 0.0147229 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −278947. | − | 483151.i | −0.393017 | − | 0.680726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.16968e6 | −1.61096 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −349535. | + | 605413.i | −0.470684 | + | 0.815248i | −0.999438 | − | 0.0335271i | \(-0.989326\pi\) |
0.528754 | + | 0.848775i | \(0.322659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 77975.2 | − | 135057.i | 0.102683 | − | 0.177853i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −813403. | −1.04771 | −0.523855 | − | 0.851808i | \(-0.675507\pi\) | ||||
−0.523855 | + | 0.851808i | \(0.675507\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.18902e6 | −1.49830 | −0.749151 | − | 0.662399i | \(-0.769538\pi\) | ||||
−0.749151 | + | 0.662399i | \(0.769538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 152440. | − | 264033.i | 0.187961 | − | 0.325558i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −106736. | + | 184872.i | −0.128801 | + | 0.223091i | −0.923212 | − | 0.384290i | \(-0.874446\pi\) |
0.794411 | + | 0.607381i | \(0.207780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.02396e6 | −1.20952 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 91182.9 | + | 157933.i | 0.105449 | + | 0.182643i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 965775. | 1.09366 | 0.546829 | − | 0.837245i | \(-0.315835\pi\) | ||||
0.546829 | + | 0.837245i | \(0.315835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 391235. | + | 677639.i | 0.433906 | + | 0.751547i | 0.997206 | − | 0.0747059i | \(-0.0238018\pi\) |
−0.563300 | + | 0.826252i | \(0.690468\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 476099. | + | 824627.i | 0.517227 | + | 0.895863i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −327514. | + | 567270.i | −0.348590 | + | 0.603775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 662485. | − | 830123.i | 0.690929 | − | 0.865765i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 231819. | − | 401523.i | 0.236947 | − | 0.410404i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 448780. | + | 777310.i | 0.449624 | + | 0.778771i | 0.998361 | − | 0.0572236i | \(-0.0182248\pi\) |
−0.548738 | + | 0.835995i | \(0.684891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15215e6 | + | 1.99558e6i | 1.13164 | + | 1.96006i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −875543. | −0.843193 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −552328. | − | 956660.i | −0.521632 | − | 0.903493i | −0.999683 | − | 0.0251612i | \(-0.991990\pi\) |
0.478051 | − | 0.878332i | \(-0.341343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.11982e6 | −1.03729 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −428825. | + | 742747.i | −0.389654 | + | 0.674901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 306009. | − | 530023.i | 0.272800 | − | 0.472504i | −0.696778 | − | 0.717287i | \(-0.745384\pi\) |
0.969578 | + | 0.244783i | \(0.0787169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12844e6 | 0.987109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 131139. | 0.112578 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −248820. | + | 430969.i | −0.209655 | + | 0.363133i | −0.951606 | − | 0.307321i | \(-0.900567\pi\) |
0.741951 | + | 0.670454i | \(0.233901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −724980. | + | 1.25570e6i | −0.599657 | + | 1.03864i | 0.393214 | + | 0.919447i | \(0.371363\pi\) |
−0.992871 | + | 0.119190i | \(0.961970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −433060. | −0.351675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −206853. | − | 358281.i | −0.164942 | − | 0.285688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −87028.2 | −0.0681492 | −0.0340746 | − | 0.999419i | \(-0.510848\pi\) | ||||
−0.0340746 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11393.6 | + | 19734.3i | 0.00876297 | + | 0.0151779i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 949563. | + | 1.64469e6i | 0.717394 | + | 1.24256i | 0.962029 | + | 0.272948i | \(0.0879987\pi\) |
−0.244635 | + | 0.969615i | \(0.578668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 727473. | − | 1.26002e6i | 0.539946 | − | 0.935214i | −0.458960 | − | 0.888457i | \(-0.651778\pi\) |
0.998906 | − | 0.0467574i | \(-0.0148888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 495891. | − | 621374.i | 0.361638 | − | 0.453149i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 632846. | − | 1.09612e6i | 0.453517 | − | 0.785514i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −791713. | − | 1.37129e6i | −0.557600 | − | 0.965792i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −525197. | − | 909668.i | −0.363572 | − | 0.629724i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 795288. | 0.541197 | 0.270598 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270598 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 532538. | + | 922383.i | 0.356283 | + | 0.617101i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.60313e6 | 1.05458 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63655e6 | − | 2.83459e6i | 1.05865 | − | 1.83363i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −77396.5 | + | 134055.i | −0.0492385 | + | 0.0852836i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −736403. | −0.460796 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.47177e6 | 0.905923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −964887. | + | 1.67123e6i | −0.584293 | + | 1.01202i | 0.410670 | + | 0.911784i | \(0.365295\pi\) |
−0.994963 | + | 0.100241i | \(0.968039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −598646. | + | 1.03689e6i | −0.356676 | + | 0.617781i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.42463e6 | −0.835220 | −0.417610 | − | 0.908626i | \(-0.637132\pi\) | ||||
−0.417610 | + | 0.908626i | \(0.637132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12004e6 | + | 1.93997e6i | 0.646209 | + | 1.11927i | 0.984021 | + | 0.178053i | \(0.0569800\pi\) |
−0.337812 | + | 0.941214i | \(0.609687\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 908928. | 0.516123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −278493. | − | 482363.i | −0.155656 | − | 0.269604i | 0.777642 | − | 0.628708i | \(-0.216416\pi\) |
−0.933298 | + | 0.359104i | \(0.883082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.13759e6 | + | 1.97037e6i | 0.625908 | + | 1.08410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −249251. | + | 431715.i | −0.135012 | + | 0.233848i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.69638e6 | + | 407395.i | 1.43805 | + | 0.217275i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −293821. | + | 508913.i | −0.154303 | + | 0.267261i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 218756. | + | 378896.i | 0.113133 | + | 0.195953i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −650208. | − | 1.12619e6i | −0.331179 | − | 0.573619i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.85079e6 | 0.928511 | 0.464256 | − | 0.885701i | \(-0.346322\pi\) | ||||
0.464256 | + | 0.885701i | \(0.346322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.24930e6 | − | 2.16385e6i | −0.617386 | − | 1.06934i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.72168e6 | −0.838184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.16626e6 | − | 2.02003e6i | 0.559399 | − | 0.968907i | −0.438148 | − | 0.898903i | \(-0.644365\pi\) |
0.997547 | − | 0.0700041i | \(-0.0223013\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −337267. | + | 584163.i | −0.159395 | + | 0.276080i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 60450.3 | 0.0281522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.18110e6 | −1.00101 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.22501e6 | − | 2.12178e6i | 0.554106 | − | 0.959739i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.33391e6 | + | 2.31041e6i | −0.594708 | + | 1.03006i | 0.398880 | + | 0.917003i | \(0.369399\pi\) |
−0.993588 | + | 0.113062i | \(0.963934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.33528e6 | −1.02630 | −0.513152 | − | 0.858298i | \(-0.671522\pi\) | ||||
−0.513152 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.13857e6 | − | 1.97206e6i | −0.493278 | − | 0.854382i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.57168e6 | −1.09845 | −0.549225 | − | 0.835675i | \(-0.685077\pi\) | ||||
−0.549225 | + | 0.835675i | \(0.685077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.36722e6 | − | 4.10014e6i | −0.996935 | − | 1.72674i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −555965. | − | 962960.i | −0.230875 | − | 0.399887i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.06014e6 | − | 3.56826e6i | 0.843645 | − | 1.46124i | −0.0431473 | − | 0.999069i | \(-0.513738\pi\) |
0.886793 | − | 0.462168i | \(-0.152928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.81631e6 | + | 1.68288e6i | −0.733536 | + | 0.679651i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 258698. | − | 448078.i | 0.103045 | − | 0.178479i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.20613e6 | − | 3.82112e6i | −0.866759 | − | 1.50127i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.76851e6 | + | 3.06315e6i | 0.685398 | + | 1.18714i | 0.973312 | + | 0.229487i | \(0.0737050\pi\) |
−0.287914 | + | 0.957656i | \(0.592962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.82408e6 | 1.07972 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 716555. | + | 1.24111e6i | 0.270281 | + | 0.468140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.14142e6 | −1.16910 | −0.584552 | − | 0.811356i | \(-0.698730\pi\) | ||||
−0.584552 | + | 0.811356i | \(0.698730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 569469. | − | 986350.i | 0.209118 | − | 0.362204i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.61587e6 | − | 2.79878e6i | 0.585537 | − | 1.01418i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.24166e6 | −0.444021 | −0.222011 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222011 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −946329. | −0.333987 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.41220e6 | + | 2.44600e6i | −0.491924 | + | 0.852038i | −0.999957 | − | 0.00929990i | \(-0.997040\pi\) |
0.508032 | + | 0.861338i | \(0.330373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.20561e6 | − | 2.08817e6i | 0.414528 | − | 0.717984i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −345382. | −0.117225 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.26664e6 | + | 3.92593e6i | 0.759465 | + | 1.31543i | 0.943124 | + | 0.332442i | \(0.107873\pi\) |
−0.183658 | + | 0.982990i | \(0.558794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.40405e6 | 2.78001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −297550. | − | 515371.i | −0.0971802 | − | 0.168321i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 721143. | + | 1.24906e6i | 0.232557 | + | 0.402800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 968813. | − | 1.67803e6i | 0.308506 | − | 0.534348i | −0.669530 | − | 0.742785i | \(-0.733504\pi\) |
0.978036 | + | 0.208437i | \(0.0668377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 998302. | + | 150833.i | 0.313928 | + | 0.0474313i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.21857e6 | − | 3.84268e6i | 0.688990 | − | 1.19336i | −0.283176 | − | 0.959068i | \(-0.591388\pi\) |
0.972165 | − | 0.234297i | \(-0.0752788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42932.8 | − | 74361.7i | −0.0131682 | − | 0.0228080i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 523407. | + | 906567.i | 0.158563 | + | 0.274639i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.62832e6 | −1.98343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.20721e6 | + | 5.55506e6i | 0.948025 | + | 1.64203i | 0.749579 | + | 0.661915i | \(0.230256\pi\) |
0.198446 | + | 0.980112i | \(0.436411\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.12259e6 | −0.327805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −676317. | + | 1.17142e6i | −0.195108 | + | 0.337937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.83340e6 | − | 3.17555e6i | 0.522562 | − | 0.905103i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.79548e6 | 0.505639 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.16492e6 | −0.602429 | −0.301215 | − | 0.953556i | \(-0.597392\pi\) | ||||
−0.301215 | + | 0.953556i | \(0.597392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.39931e6 | − | 5.88777e6i | 0.934727 | − | 1.61900i | 0.159608 | − | 0.987180i | \(-0.448977\pi\) |
0.775119 | − | 0.631815i | \(-0.217690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.45078e6 | − | 2.51282e6i | 0.394230 | − | 0.682826i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50884e6 | −0.405201 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 934567. | + | 1.61872e6i | 0.248051 | + | 0.429637i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.56332e6 | −0.672449 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −101699. | − | 176148.i | −0.0263708 | − | 0.0456756i | 0.852539 | − | 0.522664i | \(-0.175062\pi\) |
−0.878910 | + | 0.476988i | \(0.841728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 487850. | + | 844981.i | 0.125045 | + | 0.216584i | 0.921751 | − | 0.387783i | \(-0.126759\pi\) |
−0.796705 | + | 0.604368i | \(0.793426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.20953e6 | − | 2.09497e6i | 0.306475 | − | 0.530830i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.75990e6 | + | 5.96437e6i | −1.19232 | + | 1.49404i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.96789e6 | − | 3.40848e6i | 0.487348 | − | 0.844111i | −0.512546 | − | 0.858660i | \(-0.671298\pi\) |
0.999894 | + | 0.0145483i | \(0.00463102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −928063. | − | 1.60745e6i | −0.227238 | − | 0.393588i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.39091e6 | − | 2.40913e6i | −0.336737 | − | 0.583246i | 0.647080 | − | 0.762422i | \(-0.275990\pi\) |
−0.983817 | + | 0.179176i | \(0.942657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03715e6 | 0.248279 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.17486e6 | + | 2.03491e6i | 0.278110 | + | 0.481700i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.91764e6 | 1.61936 | 0.809678 | − | 0.586875i | \(-0.199642\pi\) | ||||
0.809678 | + | 0.586875i | \(0.199642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.74587e6 | − | 6.48804e6i | 0.867184 | − | 1.50201i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.46545e6 | + | 2.53823e6i | −0.335525 | + | 0.581146i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.42497e6 | −0.775582 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.44928e6 | 1.44451 | 0.722256 | − | 0.691626i | \(-0.243105\pi\) | ||||
0.722256 | + | 0.691626i | \(0.243105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.92340e6 | − | 5.06348e6i | 0.647675 | − | 1.12181i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 610341. | − | 1.05714e6i | 0.133758 | − | 0.231676i | −0.791364 | − | 0.611345i | \(-0.790629\pi\) |
0.925122 | + | 0.379669i | \(0.123962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −847245. | −0.183678 | −0.0918388 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918388 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32136.6 | − | 55662.2i | −0.00689235 | − | 0.0119379i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 76212.7 | 0.0161709 | 0.00808547 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808547 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.09325e6 | − | 1.89357e6i | −0.229503 | − | 0.397512i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −114599. | − | 198491.i | −0.0238028 | − | 0.0412276i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −458116. | + | 793481.i | −0.0941505 | + | 0.163074i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 854578. | − | 1.07082e6i | 0.173787 | − | 0.217763i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.59881e6 | + | 2.76923e6i | −0.321738 | + | 0.557266i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.33045e6 | + | 2.30441e6i | 0.264947 | + | 0.458902i | 0.967550 | − | 0.252680i | \(-0.0813121\pi\) |
−0.702602 | + | 0.711583i | \(0.747979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.70754e6 | + | 8.15370e6i | 0.927750 | + | 1.60691i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.11150e6 | 0.606879 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.15366e6 | − | 7.19434e6i | −0.801819 | − | 1.38879i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.81426e6 | −1.11089 | −0.555446 | − | 0.831552i | \(-0.687453\pi\) | ||||
−0.555446 | + | 0.831552i | \(0.687453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −51021.7 | + | 88372.2i | −0.00964901 | + | 0.0167126i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.27968e6 | + | 3.94853e6i | −0.426747 | + | 0.739148i | −0.996582 | − | 0.0826113i | \(-0.973674\pi\) |
0.569834 | + | 0.821760i | \(0.307007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.29787e6 | 1.53762 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.38002e6 | 0.986895 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00634e6 | − | 5.20713e6i | 0.545942 | − | 0.945600i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.38613e6 | + | 5.86495e6i | −0.608769 | + | 1.05442i | 0.382675 | + | 0.923883i | \(0.375003\pi\) |
−0.991444 | + | 0.130536i | \(0.958330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.94295e6 | 0.345833 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.62169e6 | − | 4.54089e6i | −0.462020 | − | 0.800242i | 0.537042 | − | 0.843556i | \(-0.319542\pi\) |
−0.999062 | + | 0.0433140i | \(0.986208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.82403e6 | −1.01624 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 336720. | + | 583215.i | 0.0581766 | + | 0.100765i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.68578e6 | − | 8.11601e6i | −0.801655 | − | 1.38851i | −0.918526 | − | 0.395360i | \(-0.870620\pi\) |
0.116872 | − | 0.993147i | \(-0.462713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.80175e6 | − | 4.85278e6i | 0.474655 | − | 0.822126i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.93780e6 | + | 4.94261e6i | 0.325099 | + | 0.829206i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.73455e6 | + | 8.20047e6i | −0.786611 | + | 1.36245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.84864e6 | − | 6.66604e6i | −0.633258 | − | 1.09683i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.70779e6 | + | 2.95798e6i | 0.278302 | + | 0.482032i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 244496. | 0.0394619 | 0.0197309 | − | 0.999805i | \(-0.493719\pi\) | ||||
0.0197309 | + | 0.999805i | \(0.493719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.04939e6 | + | 3.54964e6i | 0.327619 | + | 0.567453i | 0.982039 | − | 0.188678i | \(-0.0604204\pi\) |
−0.654420 | + | 0.756131i | \(0.727087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −558630. | −0.0884557 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 110235. | − | 190932.i | 0.0172899 | − | 0.0299469i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.54032e6 | + | 1.47923e7i | −1.32689 | + | 2.29824i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.01807e6 | −0.464507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.06415e7 | −1.62250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.97126e6 | + | 3.41433e6i | −0.297756 | + | 0.515728i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −164543. | + | 284997.i | −0.0246232 | + | 0.0426486i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.92395e6 | −0.730032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 227501. | + | 394043.i | 0.0334187 | + | 0.0578829i | 0.882251 | − | 0.470779i | \(-0.156027\pi\) |
−0.848832 | + | 0.528662i | \(0.822694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.85898e6 | −0.561660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.73009e6 | + | 2.99660e6i | 0.249503 | + | 0.432153i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.19066e6 | + | 7.25843e6i | 0.598844 | + | 1.03723i | 0.992992 | + | 0.118182i | \(0.0377065\pi\) |
−0.394148 | + | 0.919047i | \(0.628960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.08525e6 | + | 3.61176e6i | −0.295276 | + | 0.511433i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.69976e6 | + | 5.88901e6i | −0.659473 | + | 0.826349i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −915844. | + | 1.58629e6i | −0.127353 | + | 0.220582i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.52375e6 | + | 6.10331e6i | 0.485593 | + | 0.841071i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.14702e6 | − | 3.71874e6i | −0.293222 | − | 0.507876i | 0.681347 | − | 0.731960i | \(-0.261394\pi\) |
−0.974570 | + | 0.224084i | \(0.928061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.30145e6 | 0.176156 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.29080e6 | − | 5.69984e6i | −0.441464 | − | 0.764637i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.43360e6 | 0.722465 | 0.361232 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361232 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.66736e6 | + | 4.62001e6i | −0.351529 | + | 0.608866i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −664720. | + | 1.15133e6i | −0.0868323 | + | 0.150398i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.53732e6 | 0.587514 | 0.293757 | − | 0.955880i | \(-0.405094\pi\) | ||||
0.293757 | + | 0.955880i | \(0.405094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.75132e6 | 0.224789 | 0.112395 | − | 0.993664i | \(-0.464148\pi\) | ||||
0.112395 | + | 0.993664i | \(0.464148\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −871992. | + | 1.51033e6i | −0.110950 | + | 0.192170i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.11108e6 | − | 3.65650e6i | 0.266278 | − | 0.461208i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.69353e6 | 0.336808 | 0.168404 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168404 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.85790e6 | − | 4.95002e6i | −0.354283 | − | 0.613636i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.65680e6 | 0.572331 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.24135e6 | + | 7.34624e6i | 0.516812 | + | 0.895145i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.82098e6 | − | 6.61812e6i | −0.461620 | − | 0.799549i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.95802e6 | + | 3.39138e6i | −0.234542 | + | 0.406239i | −0.959140 | − | 0.282934i | \(-0.908692\pi\) |
0.724597 | + | 0.689172i | \(0.242026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 73069.9 | + | 186374.i | 0.00867862 | + | 0.0221359i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 70895.9 | − | 122795.i | 0.00834934 | − | 0.0144615i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.66866e6 | − | 9.81841e6i | −0.661978 | − | 1.14658i | −0.980095 | − | 0.198528i | \(-0.936384\pi\) |
0.318117 | − | 0.948051i | \(-0.396950\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.39699e6 | − | 7.61581e6i | −0.509170 | − | 0.881909i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.63729e6 | 0.532511 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.86543e6 | − | 6.69512e6i | −0.440180 | − | 0.762414i | 0.557522 | − | 0.830162i | \(-0.311752\pi\) |
−0.997702 | + | 0.0677475i | \(0.978419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.87953e6 | −0.776913 | −0.388457 | − | 0.921467i | \(-0.626992\pi\) | ||||
−0.388457 | + | 0.921467i | \(0.626992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.43932e6 | − | 4.22503e6i | 0.273197 | − | 0.473191i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.04598e6 | − | 3.54374e6i | 0.227255 | − | 0.393617i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.19598e7 | −1.31750 | −0.658750 | − | 0.752362i | \(-0.728915\pi\) | ||||
−0.658750 | + | 0.752362i | \(0.728915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.07219e6 | 0.335664 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.46673e6 | + | 9.46865e6i | −0.592413 | + | 1.02609i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49181e6 | − | 2.58389e6i | 0.160347 | − | 0.277730i | −0.774646 | − | 0.632395i | \(-0.782072\pi\) |
0.934993 | + | 0.354666i | \(0.115405\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.96552e6 | −0.849232 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.62649e6 | − | 4.54922e6i | −0.277756 | − | 0.481087i | 0.693071 | − | 0.720869i | \(-0.256257\pi\) |
−0.970827 | + | 0.239782i | \(0.922924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.09695e7 | 1.15069 | 0.575346 | − | 0.817910i | \(-0.304867\pi\) | ||||
0.575346 | + | 0.817910i | \(0.304867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.18053e6 | + | 1.41691e7i | 0.851241 | + | 1.47439i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 658583. | + | 1.14070e6i | 0.0679815 | + | 0.117747i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.86419e6 | − | 1.01571e7i | 0.600493 | − | 1.04008i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.90904e6 | + | 892794.i | 0.600272 | + | 0.0906949i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.20871e7 | + | 2.09355e7i | −1.21814 | + | 2.10988i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.73436e6 | + | 6.46811e6i | 0.373373 | + | 0.646701i | 0.990082 | − | 0.140490i | \(-0.0448678\pi\) |
−0.616709 | + | 0.787191i | \(0.711534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.34216e6 | + | 5.78879e6i | 0.331526 | + | 0.574220i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.48429e6 | −0.736573 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.49707e6 | + | 6.05710e6i | 0.341473 | + | 0.591448i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.34158e7 | 1.29976 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.26419e6 | + | 1.43140e7i | −0.794430 | + | 1.37599i | 0.128771 | + | 0.991674i | \(0.458897\pi\) |
−0.923201 | + | 0.384318i | \(0.874437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.29383e6 | − | 1.09012e7i | 0.600326 | − | 1.03980i | −0.392445 | − | 0.919775i | \(-0.628371\pi\) |
0.992771 | − | 0.120020i | \(-0.0382959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 974175. | 0.0922014 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.21912e7 | −1.14494 | −0.572472 | − | 0.819924i | \(-0.694015\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00318e6 | + | 6.93371e6i | −0.373073 | + | 0.646181i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 40813.1 | − | 70690.4i | 0.00377439 | − | 0.00653744i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.52249e6 | −0.690365 | −0.345182 | − | 0.938536i | \(-0.612183\pi\) | ||||
−0.345182 | + | 0.938536i | \(0.612183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.35325e6 | − | 4.07594e6i | −0.214321 | − | 0.371214i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.25028e7 | 1.13004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.02028e6 | − | 1.38915e7i | −0.719409 | − | 1.24605i | −0.961234 | − | 0.275733i | \(-0.911079\pi\) |
0.241825 | − | 0.970320i | \(-0.422254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.26368e6 | + | 1.08490e7i | 0.557604 | + | 0.965798i | 0.997696 | + | 0.0678454i | \(0.0216125\pi\) |
−0.440092 | + | 0.897953i | \(0.645054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.67436e6 | + | 8.09623e6i | −0.412989 | + | 0.715318i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.89533e6 | + | 1.19290e6i | 0.692335 | + | 0.104605i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.16099e7 | + | 2.01090e7i | −1.01045 | + | 1.75015i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.79368e6 | + | 4.83880e6i | 0.241330 | + | 0.417996i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.53178e6 | + | 9.58133e6i | 0.474306 | + | 0.821523i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.50054e6 | −0.638344 | −0.319172 | − | 0.947697i | \(-0.603405\pi\) | ||||
−0.319172 | + | 0.947697i | \(0.603405\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.46871e6 | − | 2.54388e6i | −0.124073 | − | 0.214900i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.19677e7 | 1.00355 | 0.501777 | − | 0.864997i | \(-0.332680\pi\) | ||||
0.501777 | + | 0.864997i | \(0.332680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.27510e6 | − | 9.13673e6i | 0.439092 | − | 0.760530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.25058e6 | + | 5.63017e6i | −0.268592 | + | 0.465215i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.11577e6 | −0.665699 | −0.332850 | − | 0.942980i | \(-0.608010\pi\) | ||||
−0.332850 | + | 0.942980i | \(0.608010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87827e6 | −0.722939 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.75164e6 | + | 8.23009e6i | −0.384107 | + | 0.665293i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.02455e6 | − | 1.04348e7i | 0.483478 | − | 0.837408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.23034e7 | 0.980235 | 0.490117 | − | 0.871657i | \(-0.336954\pi\) | ||||
0.490117 | + | 0.871657i | \(0.336954\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.41628e6 | + | 5.91717e6i | 0.270222 | + | 0.468038i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.42000e7 | 1.11513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36616e7 | − | 2.36626e7i | −1.06517 | − | 1.84494i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 853093. | + | 1.47760e6i | 0.0660394 | + | 0.114384i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.04732e6 | + | 1.22063e7i | −0.541663 | + | 0.938188i | 0.457146 | + | 0.889392i | \(0.348872\pi\) |
−0.998809 | + | 0.0487959i | \(0.984462\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.01205e6 | − | 2.04358e7i | −0.611442 | − | 1.55956i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.09202e6 | + | 7.08759e6i | −0.310074 | + | 0.537064i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.69823e6 | − | 6.40552e6i | −0.278256 | − | 0.481954i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.13108e6 | − | 3.69113e6i | −0.159215 | − | 0.275768i | 0.775371 | − | 0.631506i | \(-0.217563\pi\) |
−0.934586 | + | 0.355738i | \(0.884230\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.08695e6 | −0.303197 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 308469. | + | 534283.i | 0.0227241 | + | 0.0393593i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.02727e7 | −1.48302 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.85950e6 | − | 6.68486e6i | 0.280371 | − | 0.485617i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.85763e6 | + | 1.18778e7i | −0.494711 | + | 0.856865i | −0.999981 | − | 0.00609644i | \(-0.998059\pi\) |
0.505270 | + | 0.862961i | \(0.331393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.20256e7 | −0.861529 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.25394e6 | 0.444946 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.08441e6 | − | 3.61031e6i | 0.147278 | − | 0.255093i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.05919e7 | − | 1.83457e7i | 0.743256 | − | 1.28736i | −0.207749 | − | 0.978182i | \(-0.566614\pi\) |
0.951005 | − | 0.309175i | \(-0.100053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.58627e6 | 0.249933 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.67080e6 | + | 2.89392e6i | 0.115646 | + | 0.200305i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.01308e6 | 0.413368 | 0.206684 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206684 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.61767e6 | + | 4.53394e6i | 0.178730 | + | 0.309569i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.47107e6 | − | 1.12082e7i | −0.438841 | − | 0.760095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.41424e6 | − | 1.45739e7i | 0.566766 | − | 0.981667i | −0.430117 | − | 0.902773i | \(-0.641528\pi\) |
0.996883 | − | 0.0788942i | \(-0.0251389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.09844e6 | − | 7.90296e6i | −0.207299 | − | 0.528742i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.01935e6 | − | 3.49762e6i | 0.134196 | − | 0.232434i | −0.791094 | − | 0.611695i | \(-0.790488\pi\) |
0.925290 | + | 0.379260i | \(0.123821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.29165e6 | + | 1.60936e7i | 0.613341 | + | 1.06234i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.19524e6 | + | 8.99842e6i | 0.340647 | + | 0.590018i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.00696e6 | −0.326114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 351347. | + | 608550.i | 0.0227319 | + | 0.0393728i | 0.877168 | − | 0.480184i | \(-0.159430\pi\) |
−0.854436 | + | 0.519557i | \(0.826097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.17380e6 | 0.461064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.15899e7 | + | 2.00742e7i | −0.739964 | + | 1.28166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.19882e7 | − | 2.07642e7i | 0.760354 | − | 1.31697i | −0.182314 | − | 0.983240i | \(-0.558359\pi\) |
0.942668 | − | 0.333731i | \(-0.108308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.84172e7 | 1.16043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.29063e7 | −0.807869 | −0.403934 | − | 0.914788i | \(-0.632358\pi\) | ||||
−0.403934 | + | 0.914788i | \(0.632358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.19719e6 | + | 3.80565e6i | −0.136633 | + | 0.236656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.81078e6 | − | 1.69928e7i | 0.606108 | − | 1.04981i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.13725e7 | 0.698019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05367e7 | − | 1.82501e7i | −0.642524 | − | 1.11288i | −0.984867 | − | 0.173310i | \(-0.944554\pi\) |
0.342343 | − | 0.939575i | \(-0.388779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.82902e6 | −0.534905 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.35234e6 | + | 7.53848e6i | 0.261984 | + | 0.453769i | 0.966769 | − | 0.255652i | \(-0.0822900\pi\) |
−0.704785 | + | 0.709421i | \(0.748957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −55381.5 | − | 95923.6i | −0.00331215 | − | 0.00573682i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.47512e6 | + | 7.75113e6i | −0.265921 | + | 0.460588i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.45311e7 | + | 3.70640e6i | 1.44835 | + | 0.218831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.77948e7 | − | 3.08214e7i | 1.04391 | − | 1.80811i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.07717e6 | + | 1.39901e7i | 0.470820 | + | 0.815484i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −906334. | − | 1.56982e6i | −0.0524946 | − | 0.0909232i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.69329e6 | 0.155005 | 0.0775026 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.44579e6 | − | 4.23624e6i | −0.139871 | − | 0.242263i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.77504e6 | −0.385009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.85752e6 | − | 1.36096e7i | 0.443713 | − | 0.768534i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.50957e6 | − | 7.81081e6i | 0.253057 | − | 0.438307i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.67101e6 | −0.260474 | −0.130237 | − | 0.991483i | \(-0.541574\pi\) | ||||
−0.130237 | + | 0.991483i | \(0.541574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.80729e7 | −1.55568 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.46946e6 | + | 2.54519e6i | −0.0809240 | + | 0.140165i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.65838e7 | − | 2.87240e7i | 0.907603 | − | 1.57201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.46081e7 | 1.33841 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.98871e6 | + | 3.44455e6i | 0.107495 | + | 0.186186i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.82792e7 | −0.981941 | −0.490970 | − | 0.871176i | \(-0.663358\pi\) | ||||
−0.490970 | + | 0.871176i | \(0.663358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.38560e6 | + | 1.62563e7i | 0.501083 | + | 0.867902i | 0.999999 | + | 0.00125119i | \(0.000398266\pi\) |
−0.498916 | + | 0.866650i | \(0.666268\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.79445e6 | + | 1.00363e7i | 0.307458 | + | 0.532533i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −403518. | + | 698914.i | −0.0212799 | + | 0.0368578i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.00013e6 | − | 453289.i | −0.157248 | − | 0.0237585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.85260e6 | − | 8.40494e6i | 0.252793 | − | 0.437850i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.00143e6 | + | 8.66273e6i | 0.258962 | + | 0.448536i | 0.965964 | − | 0.258676i | \(-0.0832861\pi\) |
−0.707002 | + | 0.707212i | \(0.749953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.31371e6 | + | 9.20361e6i | 0.273463 | + | 0.473651i | 0.969746 | − | 0.244116i | \(-0.0784977\pi\) |
−0.696283 | + | 0.717767i | \(0.745164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.30658e6 | −0.169139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.74700e6 | + | 4.75795e6i | 0.139668 | + | 0.241911i | 0.927371 | − | 0.374144i | \(-0.122063\pi\) |
−0.787703 | + | 0.616055i | \(0.788730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.66282e6 | 0.336722 | 0.168361 | − | 0.985725i | \(-0.446153\pi\) | ||||
0.168361 | + | 0.985725i | \(0.446153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −347789. | + | 602388.i | −0.0174708 | + | 0.0302603i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.97912e6 | + | 1.55523e7i | −0.448354 | + | 0.776572i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53663e7 | 0.762699 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 429211. | 0.0211766 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.62638e6 | − | 6.28107e6i | 0.177856 | − | 0.308055i | −0.763290 | − | 0.646056i | \(-0.776417\pi\) |
0.941146 | + | 0.338001i | \(0.109751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20767e6 | + | 2.09174e6i | −0.0588786 | + | 0.101981i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.51789e7 | 0.735649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.66303e6 | + | 4.61251e6i | 0.128302 | + | 0.222226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.19674e6 | 0.248899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.81436e6 | − | 1.00708e7i | −0.276843 | − | 0.479506i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.38233e7 | − | 5.85837e7i | −1.60100 | − | 2.77302i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39644e7 | − | 2.41871e7i | 0.657130 | − | 1.13818i | −0.324225 | − | 0.945980i | \(-0.605104\pi\) |
0.981355 | − | 0.192202i | \(-0.0615630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.50315e6 | + | 1.65871e7i | 0.304235 | + | 0.775989i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.35275e6 | + | 2.34304e6i | −0.0629169 | + | 0.108975i | −0.895768 | − | 0.444522i | \(-0.853374\pi\) |
0.832851 | + | 0.553497i | \(0.186707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.45030e7 | − | 2.51199e7i | −0.670616 | − | 1.16154i | −0.977730 | − | 0.209868i | \(-0.932697\pi\) |
0.307114 | − | 0.951673i | \(-0.400637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.05806e6 | − | 8.76081e6i | −0.232528 | − | 0.402751i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.44738e6 | 0.386096 | 0.193048 | − | 0.981189i | \(-0.438163\pi\) | ||||
0.193048 | + | 0.981189i | \(0.438163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.35065e7 | + | 2.33939e7i | 0.613765 | + | 1.06307i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.26556e7 | −0.571789 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42096e6 | + | 9.38937e6i | −0.243515 | + | 0.421781i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.19171e6 | + | 1.59205e7i | −0.410536 | + | 0.711068i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.35401e7 | 1.04538 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14395e7 | 0.505113 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25597e7 | + | 2.17540e7i | −0.551416 | + | 0.955080i | 0.446757 | + | 0.894655i | \(0.352579\pi\) |
−0.998173 | + | 0.0604245i | \(0.980755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.17819e6 | − | 5.50479e6i | 0.138742 | − | 0.240308i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.95758e7 | −0.849728 | −0.424864 | − | 0.905257i | \(-0.639678\pi\) | ||||
−0.424864 | + | 0.905257i | \(0.639678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.40024e6 | + | 2.42528e6i | 0.0604366 | + | 0.104679i | 0.894661 | − | 0.446746i | \(-0.147417\pi\) |
−0.834224 | + | 0.551426i | \(0.814084\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.51268e6 | 0.365349 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.11985e7 | − | 3.67169e7i | −0.904682 | − | 1.56696i | −0.821343 | − | 0.570435i | \(-0.806775\pi\) |
−0.0833393 | − | 0.996521i | \(-0.526559\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.75248e6 | − | 8.23154e6i | −0.201681 | − | 0.349322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.93454e6 | + | 6.81482e6i | −0.166035 | + | 0.287581i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.59000e7 | − | 1.99234e7i | 0.667217 | − | 0.836053i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.30133e6 | + | 2.25397e6i | −0.0543039 | + | 0.0940571i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.30802e7 | − | 2.26556e7i | −0.542793 | − | 0.940145i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 304571. | + | 527533.i | 0.0125687 | + | 0.0217696i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.09374e7 | 1.26962 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 618595. | + | 1.07144e6i | 0.0252457 | + | 0.0437268i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.05198e7 | −1.23868 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.00865e7 | + | 1.74703e7i | −0.407118 | + | 0.705149i | −0.994565 | − | 0.104113i | \(-0.966800\pi\) |
0.587447 | + | 0.809262i | \(0.300133\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.25167e6 | − | 1.42923e7i | 0.331232 | − | 0.573710i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89915e7 | 1.55659 | 0.778294 | − | 0.627900i | \(-0.216085\pi\) | ||||
0.778294 | + | 0.627900i | \(0.216085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.75640e7 | 1.09437 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.88161e6 | − | 1.01873e7i | 0.232244 | − | 0.402258i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.98860e6 | − | 5.17640e6i | 0.117366 | − | 0.203285i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.96447e6 | −0.389193 | −0.194597 | − | 0.980883i | \(-0.562340\pi\) | ||||
−0.194597 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.71191e6 | + | 1.33574e7i | 0.299580 | + | 0.518888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.05525e7 | −1.95316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.07253e6 | + | 1.05179e7i | 0.233354 | + | 0.404181i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.34161e7 | − | 2.32374e7i | −0.512775 | − | 0.888153i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00913e6 | − | 1.04081e7i | 0.228440 | − | 0.395670i | −0.728906 | − | 0.684614i | \(-0.759971\pi\) |
0.957346 | + | 0.288944i | \(0.0933042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.95188e6 | − | 1.51810e7i | −0.225050 | − | 0.574020i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.69322e6 | + | 9.86094e6i | −0.214118 | + | 0.370864i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.60262e7 | − | 4.50786e7i | −0.973601 | − | 1.68633i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.90689e7 | + | 3.30284e7i | 0.709541 | + | 1.22896i | 0.965027 | + | 0.262149i | \(0.0844311\pi\) |
−0.255486 | + | 0.966813i | \(0.582236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.79040e7 | 0.662652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.78331e6 | + | 1.52131e7i | 0.323358 | + | 0.560073i | 0.981179 | − | 0.193102i | \(-0.0618548\pi\) |
−0.657820 | + | 0.753175i | \(0.728521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.64584e7 | 2.79992 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.56009e6 | − | 1.48265e7i | 0.311816 | − | 0.540081i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.41786e7 | + | 4.18786e7i | −0.876106 | + | 1.51746i | −0.0205267 | + | 0.999789i | \(0.506534\pi\) |
−0.855580 | + | 0.517671i | \(0.826799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.71124e7 | −1.69812 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.45174e6 | −0.159617 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.89643e7 | + | 3.28471e7i | −0.676402 | + | 1.17156i | 0.299656 | + | 0.954047i | \(0.403128\pi\) |
−0.976057 | + | 0.217514i | \(0.930205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.89637e6 | + | 1.19449e7i | −0.244688 | + | 0.423812i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.81846e7 | 0.641834 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.63765e6 | − | 9.76470e6i | −0.197948 | − | 0.342856i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86130e7 | −0.999435 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.58589e6 | − | 9.67504e6i | −0.194100 | − | 0.336192i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.26024e7 | − | 3.91485e7i | −0.781333 | − | 1.35331i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.31734e6 | − | 1.44061e7i | 0.286034 | − | 0.495426i | −0.686825 | − | 0.726823i | \(-0.740996\pi\) |
0.972859 | + | 0.231397i | \(0.0743295\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.35954e7 | − | 1.70356e7i | 0.465138 | − | 0.582838i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.41242e7 | − | 2.44638e7i | 0.480746 | − | 0.832677i | −0.519010 | − | 0.854768i | \(-0.673699\pi\) |
0.999756 | + | 0.0220914i | \(0.00703248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01694e6 | + | 1.56178e7i | 0.305335 | + | 0.528856i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.34838e6 | + | 4.06752e6i | 0.0791147 | + | 0.137031i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.01881e7 | −1.01181 | −0.505906 | − | 0.862589i | \(-0.668842\pi\) | ||||
−0.505906 | + | 0.862589i | \(0.668842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.89821e6 | + | 6.75190e6i | 0.129990 | + | 0.225149i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.80496e6 | −0.325292 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2321.02 | − | 4020.12i | 7.66117e−5 | − | 0.000132695i | −0.865987 | − | 0.500066i | \(-0.833309\pi\) |
0.866064 | + | 0.499934i | \(0.166642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 560698. | − | 971158.i | 0.0184136 | − | 0.0318933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.03936e7 | −0.339606 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.35079e6 | −0.303989 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.56708e7 | + | 2.71426e7i | −0.506882 | + | 0.877945i | 0.493087 | + | 0.869980i | \(0.335869\pi\) |
−0.999968 | + | 0.00796469i | \(0.997465\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.39627e6 | − | 1.28107e7i | 0.238034 | − | 0.412288i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.66752e7 | 1.17440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.11856e7 | − | 1.93740e7i | −0.356387 | − | 0.617280i | 0.630968 | − | 0.775809i | \(-0.282658\pi\) |
−0.987354 | + | 0.158529i | \(0.949325\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.70626e7 | −1.49198 |
(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 | 304.6.i.d.49.6 | 18 | ||
4.3 | odd | 2 | 76.6.e.a.49.4 | yes | 18 | ||
12.11 | even | 2 | 684.6.k.f.505.3 | 18 | |||
19.7 | even | 3 | inner | 304.6.i.d.273.6 | 18 | ||
76.7 | odd | 6 | 76.6.e.a.45.4 | ✓ | 18 | ||
228.83 | even | 6 | 684.6.k.f.577.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.4 | ✓ | 18 | 76.7 | odd | 6 | ||
76.6.e.a.49.4 | yes | 18 | 4.3 | odd | 2 | ||
304.6.i.d.49.6 | 18 | 1.1 | even | 1 | trivial | ||
304.6.i.d.273.6 | 18 | 19.7 | even | 3 | inner | ||
684.6.k.f.505.3 | 18 | 12.11 | even | 2 | |||
684.6.k.f.577.3 | 18 | 228.83 | even | 6 |