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 | 49.7 | ||
Root | \(-8.45017 - 14.6361i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.49 |
Dual form | 76.6.e.a.45.7 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 7.95017 | − | 13.7701i | 0.510004 | − | 0.883352i | −0.489929 | − | 0.871762i | \(-0.662977\pi\) |
0.999933 | − | 0.0115902i | \(-0.00368935\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.4645 | + | 26.7852i | −0.276637 | + | 0.479149i | −0.970547 | − | 0.240913i | \(-0.922553\pi\) |
0.693910 | + | 0.720062i | \(0.255887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 132.225 | 1.01993 | 0.509964 | − | 0.860196i | \(-0.329659\pi\) | ||||
0.509964 | + | 0.860196i | \(0.329659\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.91049 | − | 8.50521i | −0.0202078 | − | 0.0350009i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 670.612 | 1.67105 | 0.835525 | − | 0.549452i | \(-0.185163\pi\) | ||||
0.835525 | + | 0.549452i | \(0.185163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −411.330 | − | 712.445i | −0.675044 | − | 1.16921i | −0.976456 | − | 0.215717i | \(-0.930791\pi\) |
0.301412 | − | 0.953494i | \(-0.402542\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 245.890 | + | 425.895i | 0.282172 | + | 0.488736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 731.251 | − | 1266.56i | 0.613683 | − | 1.06293i | −0.376931 | − | 0.926241i | \(-0.623021\pi\) |
0.990614 | − | 0.136689i | \(-0.0436461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1573.26 | − | 30.7850i | −0.999809 | − | 0.0195639i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1051.21 | − | 1820.76i | 0.520167 | − | 0.900956i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1145.60 | − | 1984.23i | −0.451556 | − | 0.782118i | 0.546927 | − | 0.837180i | \(-0.315798\pi\) |
−0.998483 | + | 0.0550625i | \(0.982464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1084.20 | + | 1877.89i | 0.346944 | + | 0.600925i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3707.63 | 0.978783 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1381.18 | − | 2392.27i | −0.304968 | − | 0.528221i | 0.672286 | − | 0.740292i | \(-0.265313\pi\) |
−0.977254 | + | 0.212071i | \(0.931979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10591.8 | 1.97955 | 0.989776 | − | 0.142628i | \(-0.0455552\pi\) | ||||
0.989776 | + | 0.142628i | \(0.0455552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5331.48 | − | 9234.40i | 0.852242 | − | 1.47613i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2044.79 | + | 3541.69i | −0.282150 | + | 0.488698i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4815.22 | 0.578245 | 0.289122 | − | 0.957292i | \(-0.406637\pi\) | ||||
0.289122 | + | 0.957292i | \(0.406637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13080.6 | −1.37710 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7285.18 | + | 12618.3i | −0.676832 | + | 1.17231i | 0.299098 | + | 0.954222i | \(0.403314\pi\) |
−0.975930 | + | 0.218085i | \(0.930019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5150.23 | + | 8920.46i | −0.424772 | + | 0.735726i | −0.996399 | − | 0.0847874i | \(-0.972979\pi\) |
0.571628 | + | 0.820513i | \(0.306312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 303.752 | 0.0223608 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2555.09 | − | 4425.55i | −0.168718 | − | 0.292228i | 0.769251 | − | 0.638946i | \(-0.220629\pi\) |
−0.937969 | + | 0.346718i | \(0.887296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 676.549 | 0.0402540 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11627.1 | − | 20138.8i | −0.625961 | − | 1.08420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3724.23 | − | 6450.55i | −0.182115 | − | 0.315433i | 0.760485 | − | 0.649355i | \(-0.224961\pi\) |
−0.942601 | + | 0.333922i | \(0.891628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10370.7 | + | 17962.5i | −0.462274 | + | 0.800682i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12931.6 | + | 21419.2i | −0.527188 | + | 0.873206i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −17150.1 | + | 29704.9i | −0.641412 | + | 1.11096i | 0.343705 | + | 0.939077i | \(0.388318\pi\) |
−0.985118 | + | 0.171881i | \(0.945016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 20608.6 | + | 35695.1i | 0.709126 | + | 1.22824i | 0.965182 | + | 0.261580i | \(0.0842434\pi\) |
−0.256056 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −649.291 | − | 1124.60i | −0.0206105 | − | 0.0356984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25444.0 | 0.746968 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19625.6 | − | 33992.5i | −0.534116 | − | 0.925116i | −0.999206 | − | 0.0398521i | \(-0.987311\pi\) |
0.465090 | − | 0.885263i | \(-0.346022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −36430.7 | −0.921181 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5848.69 | − | 10130.2i | 0.137693 | − | 0.238492i | −0.788930 | − | 0.614483i | \(-0.789365\pi\) |
0.926623 | + | 0.375992i | \(0.122698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13696.8 | + | 23723.6i | −0.300824 | + | 0.521043i | −0.976323 | − | 0.216318i | \(-0.930595\pi\) |
0.675498 | + | 0.737361i | \(0.263928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 34478.3 | 0.707771 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 88671.9 | 1.70435 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2583.48 | + | 4474.71i | −0.0465733 | + | 0.0806673i | −0.888372 | − | 0.459124i | \(-0.848163\pi\) |
0.841799 | + | 0.539791i | \(0.181497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30669.5 | − | 53121.2i | 0.519391 | − | 0.899612i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −86152.6 | −1.37269 | −0.686346 | − | 0.727275i | \(-0.740786\pi\) | ||||
−0.686346 | + | 0.727275i | \(0.740786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22616.8 | + | 39173.5i | 0.339535 | + | 0.588091i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −43922.4 | −0.622140 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 25384.0 | + | 43966.4i | 0.339692 | + | 0.588364i | 0.984375 | − | 0.176087i | \(-0.0563438\pi\) |
−0.644683 | + | 0.764450i | \(0.723011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −54388.3 | − | 94203.3i | −0.688497 | − | 1.19251i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 84206.9 | − | 145851.i | 1.00958 | − | 1.74864i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25154.2 | − | 41664.1i | 0.285958 | − | 0.473645i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13304.7 | + | 23044.5i | −0.143574 | + | 0.248678i | −0.928840 | − | 0.370481i | \(-0.879193\pi\) |
0.785266 | + | 0.619159i | \(0.212526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3293.03 | − | 5703.70i | −0.0337682 | − | 0.0584882i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 32085.7 | + | 55574.0i | 0.312974 | + | 0.542086i | 0.979005 | − | 0.203838i | \(-0.0653416\pi\) |
−0.666031 | + | 0.745924i | \(0.732008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 66441.0 | 0.617082 | 0.308541 | − | 0.951211i | \(-0.400159\pi\) | ||||
0.308541 | + | 0.951211i | \(0.400159\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 32512.9 | + | 56314.1i | 0.287795 | + | 0.498475i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −187958. | −1.58709 | −0.793546 | − | 0.608510i | \(-0.791768\pi\) | ||||
−0.793546 | + | 0.608510i | \(0.791768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 89626.3 | − | 155237.i | 0.722552 | − | 1.25150i | −0.237422 | − | 0.971407i | \(-0.576302\pi\) |
0.959974 | − | 0.280090i | \(-0.0903643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 38281.8 | − | 66306.0i | 0.294907 | − | 0.510794i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −59332.4 | −0.437115 | −0.218557 | − | 0.975824i | \(-0.570135\pi\) | ||||
−0.218557 | + | 0.975824i | \(0.570135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 70864.1 | 0.499668 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4039.66 | + | 6996.90i | −0.0272823 | + | 0.0472542i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 96689.9 | − | 167472.i | 0.625913 | − | 1.08411i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 288669. | 1.79241 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 115837. | + | 200635.i | 0.690374 | + | 1.19576i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −163719. | −0.937184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −33405.1 | − | 57859.3i | −0.183782 | − | 0.318320i | 0.759383 | − | 0.650643i | \(-0.225501\pi\) |
−0.943165 | + | 0.332324i | \(0.892167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 81890.4 | + | 141838.i | 0.433270 | + | 0.750446i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −175425. | + | 303846.i | −0.893129 | + | 1.54695i | −0.0570264 | + | 0.998373i | \(0.518162\pi\) |
−0.836103 | + | 0.548573i | \(0.815171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −208025. | − | 4070.56i | −1.01973 | − | 0.0199538i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −57336.5 | + | 99309.7i | −0.270767 | + | 0.468983i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −124390. | − | 215450.i | −0.566219 | − | 0.980719i | −0.996935 | − | 0.0782321i | \(-0.975072\pi\) |
0.430717 | − | 0.902487i | \(-0.358261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 221518. | + | 383680.i | 0.972459 | + | 1.68435i | 0.688078 | + | 0.725637i | \(0.258455\pi\) |
0.284381 | + | 0.958711i | \(0.408212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −81253.7 | −0.344188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −275843. | − | 477774.i | −1.12803 | − | 1.95381i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 85436.8 | 0.337462 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5378.68 | − | 9316.15i | 0.0205297 | − | 0.0355585i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −120138. | + | 208085.i | −0.443317 | + | 0.767847i | −0.997933 | − | 0.0642591i | \(-0.979532\pi\) |
0.554617 | + | 0.832106i | \(0.312865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −166073. | −0.592730 | −0.296365 | − | 0.955075i | \(-0.595774\pi\) | ||||
−0.296365 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14363.2 | −0.0496046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −163797. | + | 283705.i | −0.547617 | + | 0.948501i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −50926.7 | + | 88207.7i | −0.164891 | + | 0.285599i | −0.936617 | − | 0.350356i | \(-0.886061\pi\) |
0.771726 | + | 0.635956i | \(0.219394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −118433. | −0.371518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −151477. | − | 262365.i | −0.460555 | − | 0.797704i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −256024. | −0.754764 | −0.377382 | − | 0.926058i | \(-0.623176\pi\) | ||||
−0.377382 | + | 0.926058i | \(0.623176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 164897. | + | 285610.i | 0.471523 | + | 0.816702i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 53946.9 | + | 93438.8i | 0.149684 | + | 0.259260i | 0.931111 | − | 0.364737i | \(-0.118841\pi\) |
−0.781427 | + | 0.623997i | \(0.785508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152738. | + | 264551.i | −0.411369 | + | 0.712512i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7463.64 | + | 13532.1i | 0.0195191 | + | 0.0353895i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 197251. | − | 341649.i | 0.501077 | − | 0.867890i | −0.498922 | − | 0.866647i | \(-0.666271\pi\) |
0.999999 | − | 0.00124378i | \(-0.000395908\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 143359. | + | 248305.i | 0.353858 | + | 0.612900i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 272693. | + | 472318.i | 0.654245 | + | 1.13319i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −229285. | −0.534863 | −0.267432 | − | 0.963577i | \(-0.586175\pi\) | ||||
−0.267432 | + | 0.963577i | \(0.586175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −269882. | − | 467449.i | −0.612318 | − | 1.06057i | −0.990849 | − | 0.134977i | \(-0.956904\pi\) |
0.378531 | − | 0.925589i | \(-0.376429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 655367. | 1.44663 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −74464.8 | + | 128977.i | −0.159964 | + | 0.277065i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 490386. | − | 849373.i | 1.02550 | − | 1.77621i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 490242. | 0.998289 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 448848. | 0.890259 | 0.445129 | − | 0.895466i | \(-0.353158\pi\) | ||||
0.445129 | + | 0.895466i | \(0.353158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23904.7 | − | 41404.2i | 0.0461945 | − | 0.0800113i | −0.842004 | − | 0.539472i | \(-0.818624\pi\) |
0.888198 | + | 0.459461i | \(0.151957\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 202284. | − | 350366.i | 0.380957 | − | 0.659836i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 43802.6 | 0.0804145 | 0.0402072 | − | 0.999191i | \(-0.487198\pi\) | ||||
0.0402072 | + | 0.999191i | \(0.487198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 300067. | + | 519730.i | 0.537137 | + | 0.930348i | 0.999057 | + | 0.0434264i | \(0.0138274\pi\) |
−0.461920 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −624107. | −1.08960 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −182627. | − | 316319.i | −0.311046 | − | 0.538747i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −225323. | − | 390271.i | −0.374473 | − | 0.648607i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11250.9 | + | 19487.1i | −0.0182499 | + | 0.0316097i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.05505e6 | − | 20644.8i | −1.67073 | − | 0.0326923i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 239624. | − | 415040.i | 0.370530 | − | 0.641777i | −0.619117 | − | 0.785299i | \(-0.712509\pi\) |
0.989647 | + | 0.143522i | \(0.0458427\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −92996.2 | − | 161074.i | −0.140448 | − | 0.243263i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −159291. | − | 275900.i | −0.235015 | − | 0.407058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.40051e6 | 2.01900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 217784. | + | 377214.i | 0.306843 | + | 0.531468i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.20314e6 | −1.65705 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −93000.5 | + | 161082.i | −0.125234 | + | 0.216912i | −0.921824 | − | 0.387608i | \(-0.873302\pi\) |
0.796590 | + | 0.604520i | \(0.206635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10647.9 | − | 18442.7i | 0.0140219 | − | 0.0242867i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 131418. | 0.169274 | 0.0846371 | − | 0.996412i | \(-0.473027\pi\) | ||||
0.0846371 | + | 0.996412i | \(0.473027\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 105774. | 0.133288 | 0.0666440 | − | 0.997777i | \(-0.478771\pi\) | ||||
0.0666440 | + | 0.997777i | \(0.478771\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 704957. | − | 1.22102e6i | 0.869226 | − | 1.50554i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 504870. | − | 874460.i | 0.609241 | − | 1.05524i | −0.382124 | − | 0.924111i | \(-0.624807\pi\) |
0.991366 | − | 0.131126i | \(-0.0418593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 158053. | 0.186695 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 41078.2 | + | 71149.5i | 0.0475051 | + | 0.0822813i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −538983. | −0.610351 | −0.305176 | − | 0.952296i | \(-0.598715\pi\) | ||||
−0.305176 | + | 0.952296i | \(0.598715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 618134. | + | 1.07064e6i | 0.685551 | + | 1.18741i | 0.973263 | + | 0.229692i | \(0.0737720\pi\) |
−0.287712 | + | 0.957717i | \(0.592895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −37179.3 | − | 64396.4i | −0.0403911 | − | 0.0699594i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10462.5 | + | 18121.5i | −0.0111357 | + | 0.0192877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 625197. | + | 1.13352e6i | 0.652040 | + | 1.18219i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −684928. | + | 1.18633e6i | −0.700078 | + | 1.21257i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −665047. | − | 1.15190e6i | −0.666298 | − | 1.15406i | −0.978932 | − | 0.204188i | \(-0.934545\pi\) |
0.312634 | − | 0.949874i | \(-0.398789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −768250. | − | 1.33065e6i | −0.754573 | − | 1.30696i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 719230. | 0.692656 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 471458. | + | 816590.i | 0.445257 | + | 0.771207i | 0.998070 | − | 0.0620979i | \(-0.0197791\pi\) |
−0.552813 | + | 0.833305i | \(0.686446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 636694. | 0.589768 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13564.5 | + | 23494.4i | −0.0123255 | + | 0.0213483i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −848058. | + | 1.46888e6i | −0.756025 | + | 1.30947i | 0.188838 | + | 0.982008i | \(0.439528\pi\) |
−0.944863 | + | 0.327465i | \(0.893806\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 230373. | 0.201519 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 807229. | 0.692977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 403755. | − | 699325.i | 0.340203 | − | 0.589248i | −0.644268 | − | 0.764800i | \(-0.722838\pi\) |
0.984470 | + | 0.175552i | \(0.0561710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.02987e6 | + | 1.78379e6i | −0.851845 | + | 1.47544i | 0.0276959 | + | 0.999616i | \(0.491183\pi\) |
−0.879541 | + | 0.475823i | \(0.842150\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.72958e6 | −1.40454 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 727078. | + | 1.25934e6i | 0.579761 | + | 1.00418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.06729e6 | −0.835761 | −0.417881 | − | 0.908502i | \(-0.637227\pi\) | ||||
−0.417881 | + | 0.908502i | \(0.637227\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −52011.1 | − | 90085.8i | −0.0400023 | − | 0.0692861i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −352862. | − | 611176.i | −0.266587 | − | 0.461743i | 0.701391 | − | 0.712777i | \(-0.252563\pi\) |
−0.967978 | + | 0.251034i | \(0.919229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 190924. | − | 330690.i | 0.141708 | − | 0.245446i | −0.786432 | − | 0.617677i | \(-0.788074\pi\) |
0.928140 | + | 0.372231i | \(0.121407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −373739. | − | 677613.i | −0.272556 | − | 0.494162i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −963286. | + | 1.66846e6i | −0.690320 | + | 1.19567i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −359527. | − | 622720.i | −0.253214 | − | 0.438579i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 211550. | + | 366415.i | 0.146447 | + | 0.253653i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.08651e6 | −1.41988 | −0.709941 | − | 0.704261i | \(-0.751278\pi\) | ||||
−0.709941 | + | 0.704261i | \(0.751278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −530435. | − | 918740.i | −0.354876 | − | 0.614664i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.48638e6 | 1.63560 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −942435. | + | 1.63235e6i | −0.609640 | + | 1.05593i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −680991. | + | 1.17951e6i | −0.433237 | + | 0.750388i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.02035e6 | 0.638471 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.27480e6 | −0.784681 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 805874. | − | 1.39582e6i | 0.488002 | − | 0.845244i | −0.511903 | − | 0.859043i | \(-0.671059\pi\) |
0.999905 | + | 0.0137995i | \(0.00439266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 528217. | − | 914899.i | 0.314714 | − | 0.545101i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 785721. | 0.460646 | 0.230323 | − | 0.973114i | \(-0.426022\pi\) | ||||
0.230323 | + | 0.973114i | \(0.426022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.34106e6 | + | 2.32278e6i | 0.773724 | + | 1.34013i | 0.935509 | + | 0.353303i | \(0.114942\pi\) |
−0.161785 | + | 0.986826i | \(0.551725\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40163.7 | 0.0228065 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.30544e6 | − | 2.26109e6i | −0.729642 | − | 1.26378i | −0.957034 | − | 0.289974i | \(-0.906353\pi\) |
0.227392 | − | 0.973803i | \(-0.426980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −926235. | − | 1.60429e6i | −0.509618 | − | 0.882684i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.49430e6 | + | 2.58821e6i | −0.809423 | + | 1.40196i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.18944e6 | + | 1.97012e6i | −0.634361 | + | 1.05072i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 891929. | − | 1.54487e6i | 0.468405 | − | 0.811302i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.42509e6 | − | 2.46833e6i | −0.737008 | − | 1.27654i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −337848. | − | 585170.i | −0.172080 | − | 0.298052i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.09316e6 | 1.05010 | 0.525052 | − | 0.851070i | \(-0.324046\pi\) | ||||
0.525052 | + | 0.851070i | \(0.324046\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23645.1 | − | 40954.4i | −0.0116850 | − | 0.0202391i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.21400e6 | 0.591024 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.63109e6 | + | 2.82513e6i | −0.782353 | + | 1.35508i | 0.148214 | + | 0.988955i | \(0.452647\pi\) |
−0.930568 | + | 0.366120i | \(0.880686\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −471703. | + | 817013.i | −0.222930 | + | 0.386127i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.10301e6 | 3.30793 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.13285e6 | −0.978872 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 563382. | − | 975805.i | 0.254833 | − | 0.441383i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 602372. | − | 1.04334e6i | 0.268560 | − | 0.465159i | −0.699930 | − | 0.714211i | \(-0.746786\pi\) |
0.968490 | + | 0.249052i | \(0.0801189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.97327e6 | 1.30668 | 0.653342 | − | 0.757063i | \(-0.273366\pi\) | ||||
0.653342 | + | 0.757063i | \(0.273366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.52506e6 | − | 2.64148e6i | −0.660722 | − | 1.14440i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.66290e6 | 1.13741 | 0.568706 | − | 0.822541i | \(-0.307444\pi\) | ||||
0.568706 | + | 0.822541i | \(0.307444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 180894. | + | 313317.i | 0.0761820 | + | 0.131951i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.53740e6 | − | 2.66286e6i | −0.638436 | − | 1.10580i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 415704. | − | 720020.i | 0.170235 | − | 0.294855i | −0.768267 | − | 0.640129i | \(-0.778881\pi\) |
0.938502 | + | 0.345274i | \(0.112214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.47420e6 | + | 96865.8i | 0.999235 | + | 0.0391203i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.29497e6 | − | 3.97501e6i | 0.914136 | − | 1.58333i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −423629. | − | 733746.i | −0.166438 | − | 0.288279i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 543635. | + | 941604.i | 0.210689 | + | 0.364925i | 0.951930 | − | 0.306314i | \(-0.0990958\pi\) |
−0.741241 | + | 0.671239i | \(0.765763\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 143095. | 0.0547090 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −492438. | − | 852927.i | −0.185745 | − | 0.321719i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00979e6 | 1.12012 | 0.560059 | − | 0.828452i | \(-0.310778\pi\) | ||||
0.560059 | + | 0.828452i | \(0.310778\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30160e6 | + | 2.25443e6i | −0.477967 | + | 0.827863i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.13624e6 | + | 1.96803e6i | −0.411734 | + | 0.713145i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.58924e6 | −0.568317 | −0.284158 | − | 0.958777i | \(-0.591714\pi\) | ||||
−0.284158 | + | 0.958777i | \(0.591714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06230e6 | −0.374918 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.14784e6 | − | 1.98811e6i | 0.399837 | − | 0.692538i | −0.593869 | − | 0.804562i | \(-0.702400\pi\) |
0.993705 | + | 0.112024i | \(0.0357335\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37126e6 | + | 2.37510e6i | −0.471486 | + | 0.816638i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 101160. | 0.0343347 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.12902e6 | − | 3.68757e6i | −0.713355 | − | 1.23557i | −0.963590 | − | 0.267383i | \(-0.913841\pi\) |
0.250235 | − | 0.968185i | \(-0.419492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.35087e6 | −1.10845 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.78933e6 | + | 4.83125e6i | 0.910999 | + | 1.57790i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −79904.2 | − | 138398.i | −0.0257678 | − | 0.0446311i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −173073. | + | 299772.i | −0.0551130 | + | 0.0954585i | −0.892266 | − | 0.451511i | \(-0.850885\pi\) |
0.837153 | + | 0.546969i | \(0.184219\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.70989e6 | + | 2.83216e6i | −0.537694 | + | 0.890607i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 777399. | − | 1.34649e6i | 0.241425 | − | 0.418161i | −0.719695 | − | 0.694290i | \(-0.755718\pi\) |
0.961121 | + | 0.276129i | \(0.0890517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.35674e6 | − | 7.54610e6i | −1.33629 | − | 2.31451i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 948576. | + | 1.64298e6i | 0.287365 | + | 0.497731i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.22914e6 | 0.966276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −796042. | − | 1.37878e6i | −0.235303 | − | 0.407557i | 0.724058 | − | 0.689739i | \(-0.242275\pi\) |
−0.959361 | + | 0.282183i | \(0.908942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.95569e6 | −1.15509 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.26768e6 | + | 3.92774e6i | −0.654195 | + | 1.13310i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.33230e6 | − | 2.30762e6i | 0.379737 | − | 0.657724i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.04441e6 | 1.98383 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.11283e6 | −1.14447 | −0.572236 | − | 0.820089i | \(-0.693924\pi\) | ||||
−0.572236 | + | 0.820089i | \(0.693924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.57964e6 | − | 2.73602e6i | 0.434364 | − | 0.752341i | −0.562879 | − | 0.826539i | \(-0.690306\pi\) |
0.997244 | + | 0.0741981i | \(0.0236397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25093.5 | + | 43463.2i | −0.00681883 | + | 0.0118106i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.17129e6 | 0.851655 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.72498e6 | + | 4.71980e6i | 0.723257 | + | 1.25272i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.77199e6 | −2.30120 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 508299. | + | 880400.i | 0.131803 | + | 0.228290i | 0.924372 | − | 0.381493i | \(-0.124590\pi\) |
−0.792568 | + | 0.609783i | \(0.791257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.49339e6 | − | 2.58663e6i | −0.382784 | − | 0.663001i | 0.608675 | − | 0.793419i | \(-0.291701\pi\) |
−0.991459 | + | 0.130419i | \(0.958368\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 679237. | − | 1.17647e6i | 0.172107 | − | 0.298098i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.74124e6 | + | 3.15698e6i | 0.436168 | + | 0.790802i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.05381e6 | + | 5.28936e6i | −0.756277 | + | 1.30991i | 0.188459 | + | 0.982081i | \(0.439651\pi\) |
−0.944737 | + | 0.327830i | \(0.893683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3322.18 | − | 5754.19i | −0.000813443 | − | 0.00140892i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.29170e6 | + | 3.96935e6i | 0.554816 | + | 0.960970i | 0.997918 | + | 0.0644983i | \(0.0205447\pi\) |
−0.443102 | + | 0.896471i | \(0.646122\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.57020e6 | −0.375885 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.91023e6 | + | 3.30862e6i | 0.452186 | + | 0.783210i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.65968e6 | −0.622607 | −0.311304 | − | 0.950310i | \(-0.600766\pi\) | ||||
−0.311304 | + | 0.950310i | \(0.600766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.88553e6 | + | 8.46199e6i | −1.13102 | + | 1.95899i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.32031e6 | + | 2.28684e6i | −0.302294 | + | 0.523589i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.36434e6 | 0.761854 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.09945e6 | 1.14217 | 0.571087 | − | 0.820889i | \(-0.306522\pi\) | ||||
0.571087 | + | 0.820889i | \(0.306522\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.71121e6 | − | 4.69595e6i | 0.600663 | − | 1.04038i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.18373e6 | − | 5.51438e6i | 0.697725 | − | 1.20849i | −0.271529 | − | 0.962430i | \(-0.587529\pi\) |
0.969254 | − | 0.246064i | \(-0.0791374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.07803e6 | −1.10089 | −0.550443 | − | 0.834873i | \(-0.685541\pi\) | ||||
−0.550443 | + | 0.834873i | \(0.685541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.60443e6 | + | 4.51101e6i | 0.558574 | + | 0.967478i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.58423e6 | 0.760507 | 0.380254 | − | 0.924882i | \(-0.375837\pi\) | ||||
0.380254 | + | 0.924882i | \(0.375837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.59500e6 | − | 4.49467e6i | −0.544760 | − | 0.943552i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 809753. | + | 1.40253e6i | 0.168190 | + | 0.291314i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.45381e6 | + | 5.98217e6i | −0.709815 | + | 1.22944i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.64792e6 | − | 2.98779e6i | −0.335121 | − | 0.607598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −36575.5 | + | 63350.7i | −0.00736029 | + | 0.0127484i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.65416e6 | − | 6.32919e6i | −0.727694 | − | 1.26040i | −0.957855 | − | 0.287251i | \(-0.907259\pi\) |
0.230161 | − | 0.973153i | \(-0.426075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.98064e6 | − | 3.43058e6i | −0.390341 | − | 0.676090i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.81706e6 | −0.939539 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −411501. | − | 712740.i | −0.0794358 | − | 0.137587i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.63917e6 | 1.07744 | 0.538719 | − | 0.842485i | \(-0.318908\pi\) | ||||
0.538719 | + | 0.842485i | \(0.318908\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.03543e6 | + | 3.52547e6i | −0.384932 | + | 0.666723i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.98866e6 | + | 6.90857e6i | −0.746661 | + | 1.29325i | 0.202754 | + | 0.979230i | \(0.435011\pi\) |
−0.949415 | + | 0.314025i | \(0.898322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.03995e6 | −0.748616 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 203700. | 0.0373661 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 773345. | − | 1.33947e6i | 0.140437 | − | 0.243244i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.71915e6 | − | 4.70971e6i | 0.488858 | − | 0.846727i | −0.511060 | − | 0.859545i | \(-0.670747\pi\) |
0.999918 | + | 0.0128184i | \(0.00408034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.71555e6 | 0.305358 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.08679e6 | + | 7.07853e6i | 0.720216 | + | 1.24745i | 0.960913 | + | 0.276850i | \(0.0892906\pi\) |
−0.240697 | + | 0.970600i | \(0.577376\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98475e6 | −0.346320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.42859e6 | + | 4.20645e6i | 0.419599 | + | 0.726767i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.63560e6 | − | 9.76115e6i | −0.964153 | − | 1.66996i | −0.711873 | − | 0.702308i | \(-0.752153\pi\) |
−0.252280 | − | 0.967654i | \(-0.581180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.81107e6 | + | 3.13686e6i | −0.306819 | + | 0.531427i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.83307e6 | − | 114139.i | −0.978596 | − | 0.0191488i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.02747e6 | + | 1.77964e6i | −0.170708 | + | 0.295674i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.71348e6 | − | 2.96783e6i | −0.281937 | − | 0.488329i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.13636e6 | − | 5.43234e6i | −0.511102 | − | 0.885255i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.41682e6 | 1.03568 | 0.517840 | − | 0.855477i | \(-0.326736\pi\) | ||||
0.517840 | + | 0.855477i | \(0.326736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.77525e6 | − | 3.07483e6i | −0.283796 | − | 0.491549i | 0.688520 | − | 0.725217i | \(-0.258261\pi\) |
−0.972317 | + | 0.233668i | \(0.924927\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.55891e6 | 0.721876 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.74529e6 | − | 1.34152e7i | 1.21482 | − | 2.10413i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 593395. | − | 1.02779e6i | 0.0921945 | − | 0.159686i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 336862. | 0.0518460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19865e7 | 1.82757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.90668e6 | − | 5.03451e6i | 0.439048 | − | 0.760454i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.82285e6 | + | 3.15727e6i | −0.272782 | + | 0.472473i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 453702. | 0.0672665 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.87812e6 | + | 4.98505e6i | 0.422781 | + | 0.732279i | 0.996210 | − | 0.0869765i | \(-0.0277205\pi\) |
−0.573429 | + | 0.819255i | \(0.694387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.58242e6 | −1.24914 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.77204e6 | + | 4.80132e6i | 0.399769 | + | 0.692420i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 561663. | + | 972828.i | 0.0802615 | + | 0.139017i | 0.903362 | − | 0.428878i | \(-0.141091\pi\) |
−0.823101 | + | 0.567895i | \(0.807758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 202396. | − | 350560.i | 0.0286597 | − | 0.0496400i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09931e6 | + | 3.80619e6i | 0.294576 | + | 0.534086i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −341601. | + | 591671.i | −0.0475014 | + | 0.0822749i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.18402e6 | + | 2.05077e6i | 0.163164 | + | 0.282609i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.85326e6 | + | 4.94199e6i | 0.389676 | + | 0.674938i | 0.992406 | − | 0.123007i | \(-0.0392537\pi\) |
−0.602730 | + | 0.797945i | \(0.705920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.47378e6 | 1.14696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.79730e6 | − | 1.35053e7i | −1.04601 | − | 1.81175i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.30560e7 | 1.73596 | 0.867980 | − | 0.496599i | \(-0.165418\pi\) | ||||
0.867980 | + | 0.496599i | \(0.165418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 917543. | − | 1.58923e6i | 0.120922 | − | 0.209443i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.05529e6 | − | 7.02397e6i | 0.529742 | − | 0.917540i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.04953e6 | 1.04229 | 0.521147 | − | 0.853467i | \(-0.325504\pi\) | ||||
0.521147 | + | 0.853467i | \(0.325504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −604331. | −0.0775683 | −0.0387842 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387842 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.56842e6 | − | 6.18069e6i | 0.454035 | − | 0.786412i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.48411e6 | − | 4.30260e6i | 0.313329 | − | 0.542702i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.91150e6 | 0.489107 | 0.244554 | − | 0.969636i | \(-0.421359\pi\) | ||||
0.244554 | + | 0.969636i | \(0.421359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −380093. | − | 658341.i | −0.0471188 | − | 0.0816121i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.13916e7 | −1.40005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.49751e6 | − | 4.32582e6i | −0.304324 | − | 0.527105i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −124942. | − | 216407.i | −0.0150945 | − | 0.0261445i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −720645. | + | 1.24819e6i | −0.0863229 | + | 0.149516i | −0.905954 | − | 0.423376i | \(-0.860845\pi\) |
0.819631 | + | 0.572891i | \(0.194178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.66637e7 | − | 326070.i | −1.97917 | − | 0.0387278i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 348238. | − | 603166.i | 0.0410117 | − | 0.0710343i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.01304e6 | − | 1.75464e6i | −0.118302 | − | 0.204904i | 0.800793 | − | 0.598941i | \(-0.204412\pi\) |
−0.919095 | + | 0.394037i | \(0.871078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.99052e6 | + | 5.17973e6i | 0.346301 | + | 0.599811i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.54232e6 | 1.09577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 697546. | + | 1.20819e6i | 0.0794339 | + | 0.137584i | 0.903006 | − | 0.429628i | \(-0.141355\pi\) |
−0.823572 | + | 0.567212i | \(0.808022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.12873e7 | −1.27469 | −0.637346 | − | 0.770578i | \(-0.719968\pi\) | ||||
−0.637346 | + | 0.770578i | \(0.719968\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −192742. | + | 333839.i | −0.0215866 | + | 0.0373890i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.46412e6 | + | 7.73208e6i | −0.495847 | + | 0.858832i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.45297e7 | 1.60061 | 0.800306 | − | 0.599591i | \(-0.204670\pi\) | ||||
0.800306 | + | 0.599591i | \(0.204670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.80766e6 | −0.634538 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.10197e6 | + | 3.64072e6i | −0.227784 | + | 0.394534i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.68601e6 | + | 1.33126e7i | −0.826133 | + | 1.43090i | 0.0749172 | + | 0.997190i | \(0.476131\pi\) |
−0.901050 | + | 0.433715i | \(0.857203\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.16543e6 | −0.763931 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.39641e6 | + | 2.41866e6i | 0.147673 | + | 0.255777i | 0.930367 | − | 0.366630i | \(-0.119488\pi\) |
−0.782694 | + | 0.622407i | \(0.786155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.26283e6 | −0.866766 | −0.433383 | − | 0.901210i | \(-0.642680\pi\) | ||||
−0.433383 | + | 0.901210i | \(0.642680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.24744e6 | − | 7.35678e6i | −0.441975 | − | 0.765524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.35641e6 | + | 5.81347e6i | 0.346461 | + | 0.600089i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −856296. | + | 1.48315e6i | −0.0876848 | + | 0.151874i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.67209e6 | + | 1.43640e7i | −0.880958 | + | 1.45917i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.52113e6 | − | 6.09878e6i | 0.354859 | − | 0.614634i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −329136. | − | 570081.i | −0.0329081 | − | 0.0569985i | 0.849102 | − | 0.528228i | \(-0.177144\pi\) |
−0.882010 | + | 0.471230i | \(0.843810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.81010e6 | − | 6.59929e6i | −0.377944 | − | 0.654618i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.06637e6 | 0.203364 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −278285. | − | 482004.i | −0.0271732 | − | 0.0470654i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −114880. | −0.0111299 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −626336. | + | 1.08485e6i | −0.0602091 | + | 0.104285i | −0.894559 | − | 0.446950i | \(-0.852510\pi\) |
0.834350 | + | 0.551236i | \(0.185843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.69468e6 | − | 1.33276e7i | 0.733945 | − | 1.27123i | −0.221240 | − | 0.975219i | \(-0.571010\pi\) |
0.955185 | − | 0.296010i | \(-0.0956562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.06557e6 | −0.479434 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.31905e6 | 0.123880 | 0.0619398 | − | 0.998080i | \(-0.480271\pi\) | ||||
0.0619398 | + | 0.998080i | \(0.480271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.15011e7 | + | 1.99205e7i | −1.07183 | + | 1.85647i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.11343e7 | − | 1.92852e7i | 1.02970 | − | 1.78349i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.35430e6 | −0.216062 | −0.108031 | − | 0.994148i | \(-0.534455\pi\) | ||||
−0.108031 | + | 0.994148i | \(0.534455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.42572e6 | − | 9.39762e6i | −0.494145 | − | 0.855884i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 269032. | 0.0243160 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.16918e6 | + | 2.02508e6i | 0.104874 | + | 0.181647i | 0.913687 | − | 0.406419i | \(-0.133223\pi\) |
−0.808813 | + | 0.588066i | \(0.799889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.27183e6 | + | 7.39902e6i | 0.380286 | + | 0.658674i | 0.991103 | − | 0.133098i | \(-0.0424924\pi\) |
−0.610817 | + | 0.791772i | \(0.709159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.56519e6 | + | 1.65674e7i | −0.845103 | + | 1.46376i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.32603e6 | − | 5.50905e6i | 0.291657 | − | 0.483084i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.16454e6 | + | 5.48115e6i | −0.275421 | + | 0.477042i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.47874e6 | + | 2.56125e6i | 0.127740 | + | 0.221252i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.38204e7 | + | 2.39376e7i | 1.18498 | + | 2.05245i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.81154e6 | 0.664813 | 0.332406 | − | 0.943136i | \(-0.392139\pi\) | ||||
0.332406 | + | 0.943136i | \(0.392139\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.01981e6 | + | 6.96252e6i | 0.339583 | + | 0.588175i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.38338e6 | −0.786842 | −0.393421 | − | 0.919358i | \(-0.628709\pi\) | ||||
−0.393421 | + | 0.919358i | \(0.628709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75922e6 | + | 3.04706e6i | −0.146435 | + | 0.253634i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.04480e6 | − | 1.80964e6i | 0.0863305 | − | 0.149529i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.64103e7 | −1.34606 | −0.673031 | − | 0.739614i | \(-0.735008\pi\) | ||||
−0.673031 | + | 0.739614i | \(0.735008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.69450e6 | 0.626547 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 840923. | − | 1.45652e6i | 0.0679774 | − | 0.117740i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.06377e6 | + | 5.30661e6i | −0.245872 | + | 0.425862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44148e7 | −1.14846 | −0.574228 | − | 0.818695i | \(-0.694698\pi\) | ||||
−0.574228 | + | 0.818695i | \(0.694698\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −435422. | − | 754173.i | −0.0344411 | − | 0.0596538i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.37026e7 | −1.07607 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.06546e7 | + | 1.84543e7i | 0.830721 | + | 1.43885i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.02760e6 | − | 1.39042e7i | −0.621431 | − | 1.07635i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.22639e6 | − | 1.59806e7i | 0.709148 | − | 1.22828i | −0.256025 | − | 0.966670i | \(-0.582413\pi\) |
0.965174 | − | 0.261610i | \(-0.0842536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.57559e6 | − | 148237.i | −0.578134 | − | 0.0113127i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.25654e6 | − | 2.17640e6i | 0.0952150 | − | 0.164917i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.24254e6 | + | 7.34829e6i | 0.319211 | + | 0.552889i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.36759e6 | + | 4.10078e6i | 0.176885 | + | 0.306373i | 0.940812 | − | 0.338929i | \(-0.110065\pi\) |
−0.763927 | + | 0.645302i | \(0.776731\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50744.5 | 0.00376457 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.21340e7 | − | 2.10166e7i | −0.893879 | − | 1.54824i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.70631e7 | 1.24822 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.28500e6 | + | 7.42185e6i | −0.311282 | + | 0.539155i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.63001e6 | + | 2.82326e6i | −0.117589 | + | 0.203671i | −0.918812 | − | 0.394696i | \(-0.870850\pi\) |
0.801222 | + | 0.598367i | \(0.204183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.78518e6 | 0.629379 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.96571e7 | 1.39853 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.99495e6 | − | 5.18740e6i | 0.211614 | − | 0.366526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.20435e7 | − | 2.08600e7i | 0.845117 | − | 1.46379i | −0.0404018 | − | 0.999184i | \(-0.512864\pi\) |
0.885519 | − | 0.464603i | \(-0.153803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.37231e7 | 0.956384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.53222e6 | + | 1.30462e7i | 0.521350 | + | 0.903005i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.14935e6 | 0.560225 | 0.280113 | − | 0.959967i | \(-0.409628\pi\) | ||||
0.280113 | + | 0.959967i | \(0.409628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 166357. | + | 288138.i | 0.0113585 | + | 0.0196736i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.31611e7 | − | 2.27958e7i | −0.892535 | − | 1.54592i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.07531e6 | + | 5.32659e6i | −0.207146 | + | 0.358788i | −0.950814 | − | 0.309761i | \(-0.899751\pi\) |
0.743668 | + | 0.668549i | \(0.233084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.05792e7 | + | 402686.i | 1.37684 | + | 0.0269415i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.28020e6 | + | 1.08776e7i | −0.417351 | + | 0.722873i | −0.995672 | − | 0.0929364i | \(-0.970375\pi\) |
0.578321 | + | 0.815809i | \(0.303708\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.71573e6 | − | 6.43584e6i | −0.245275 | − | 0.424829i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 423051. | + | 732746.i | 0.0277390 | + | 0.0480454i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.48529e7 | −1.61872 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.87642e6 | − | 1.19103e7i | −0.444900 | − | 0.770590i | 0.553145 | − | 0.833085i | \(-0.313428\pi\) |
−0.998045 | + | 0.0624953i | \(0.980094\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.11490e7 | −1.35926 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.56823e6 | − | 4.44831e6i | 0.163971 | − | 0.284006i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.85263e6 | + | 6.67296e6i | −0.244353 | + | 0.423232i | −0.961950 | − | 0.273227i | \(-0.911909\pi\) |
0.717596 | + | 0.696459i | \(0.245242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.44309e7 | −1.53934 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.30446e7 | −1.44247 | −0.721236 | − | 0.692689i | \(-0.756426\pi\) | ||||
−0.721236 | + | 0.692689i | \(0.756426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.18509e7 | − | 2.05263e7i | 0.736951 | − | 1.27644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 222119. | − | 384721.i | 0.0137225 | − | 0.0237680i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.82174e7 | 1.73193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.54029e6 | + | 1.47922e7i | 0.520783 | + | 0.902023i | 0.999708 | + | 0.0241667i | \(0.00769325\pi\) |
−0.478925 | + | 0.877856i | \(0.658973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.49927e7 | 0.908330 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.20473e6 | − | 1.24790e7i | −0.433680 | − | 0.751155i | 0.563507 | − | 0.826111i | \(-0.309452\pi\) |
−0.997187 | + | 0.0749561i | \(0.976118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.14837e7 | + | 1.98903e7i | 0.686794 | + | 1.18956i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.06183e6 | − | 8.76734e6i | 0.300784 | − | 0.520973i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.18500e7 | − | 1.96276e7i | 0.699637 | − | 1.15884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.92220e6 | − | 6.79345e6i | 0.230092 | − | 0.398532i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.12090e6 | − | 8.86965e6i | −0.298498 | − | 0.517014i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.57511e6 | − | 2.72817e6i | −0.0912298 | − | 0.158015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.96282e7 | −1.70518 | −0.852588 | − | 0.522584i | \(-0.824968\pi\) | ||||
−0.852588 | + | 0.522584i | \(0.824968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.34844e7 | + | 2.33557e7i | 0.771151 | + | 1.33567i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.84525e6 | −0.445826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.69538e7 | − | 2.93649e7i | 0.957382 | − | 1.65823i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.83150e6 | − | 3.17226e6i | 0.102776 | − | 0.178013i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.29223e7 | 1.27824 | 0.639121 | − | 0.769107i | \(-0.279298\pi\) | ||||
0.639121 | + | 0.769107i | \(0.279298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.47365e6 | −0.414158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 249296. | − | 431793.i | 0.0137288 | − | 0.0237790i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.18526e6 | + | 1.59093e7i | −0.502693 | + | 0.870690i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.37003e6 | 0.509625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.41985e6 | − | 1.11195e7i | −0.347009 | − | 0.601038i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.65984e6 | 0.250322 | 0.125161 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125161 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 848246. | + | 1.46921e6i | 0.0452866 | + | 0.0784387i | 0.887780 | − | 0.460268i | \(-0.152247\pi\) |
−0.842494 | + | 0.538706i | \(0.818913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.63753e7 | + | 2.83629e7i | 0.868889 | + | 1.50496i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.95927e6 | − | 6.85766e6i | 0.208795 | − | 0.361644i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.37727e6 | − | 1.38757e7i | 0.439084 | − | 0.727275i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −534146. | + | 925167.i | −0.0278259 | + | 0.0481959i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 469873. | + | 813845.i | 0.0243289 | + | 0.0421389i | 0.877934 | − | 0.478783i | \(-0.158922\pi\) |
−0.853605 | + | 0.520921i | \(0.825588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.57070e7 | − | 2.72053e7i | −0.808338 | − | 1.40008i | −0.914014 | − | 0.405682i | \(-0.867034\pi\) |
0.105676 | − | 0.994401i | \(-0.466299\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.31216e7 | 1.18272 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.21728e6 | + | 7.30454e6i | 0.214421 | + | 0.371389i | 0.953093 | − | 0.302676i | \(-0.0978801\pi\) |
−0.738672 | + | 0.674065i | \(0.764547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.81671e6 | −0.496112 | −0.248056 | − | 0.968746i | \(-0.579792\pi\) | ||||
−0.248056 | + | 0.968746i | \(0.579792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.48513e6 | + | 1.46967e7i | −0.426242 | + | 0.738272i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 494727. | − | 856892.i | 0.0247032 | − | 0.0427872i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.33704e6 | −0.165632 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.92706e7 | 1.93755 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.20733e7 | + | 2.09116e7i | −0.592135 | + | 1.02561i | 0.401809 | + | 0.915723i | \(0.368382\pi\) |
−0.993944 | + | 0.109885i | \(0.964952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.44027e6 | − | 1.11549e7i | 0.313989 | − | 0.543844i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.12213e7 | −0.543842 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.72403e6 | − | 8.18227e6i | −0.227599 | − | 0.394214i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.81694e7 | 1.82813 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.03576e6 | − | 5.25809e6i | −0.144543 | − | 0.250356i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.51629e6 | − | 9.55449e6i | −0.261110 | − | 0.452255i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.09389e7 | + | 1.89467e7i | −0.514754 | + | 0.891580i | 0.485099 | + | 0.874459i | \(0.338783\pi\) |
−0.999853 | + | 0.0171210i | \(0.994550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −477881. | − | 9351.02i | −0.0223566 | − | 0.000437465i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 664571. | − | 1.15107e6i | 0.0309093 | − | 0.0535365i | −0.850157 | − | 0.526529i | \(-0.823493\pi\) |
0.881066 | + | 0.472993i | \(0.156826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.07444e6 | − | 1.39853e7i | −0.373362 | − | 0.646681i | 0.616719 | − | 0.787184i | \(-0.288462\pi\) |
−0.990080 | + | 0.140502i | \(0.955128\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.53166e7 | + | 2.65291e7i | 0.704132 | + | 1.21959i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.37431e7 | −0.628141 | −0.314071 | − | 0.949400i | \(-0.601693\pi\) | ||||
−0.314071 | + | 0.949400i | \(0.601693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.10077e6 | + | 1.05668e7i | 0.277233 | + | 0.480181i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.14332e7 | −0.516560 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.73251e6 | + | 3.00080e6i | −0.0778263 | + | 0.134799i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.61452e7 | + | 2.79643e7i | −0.721103 | + | 1.24899i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 261331. | 0.0116053 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.16478e7 | −0.955860 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.51904e7 | + | 2.63106e7i | −0.666916 | + | 1.15513i | 0.311846 | + | 0.950133i | \(0.399053\pi\) |
−0.978762 | + | 0.205000i | \(0.934281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.65881e7 | + | 2.87315e7i | −0.724145 | + | 1.25426i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.96130e7 | −0.851341 | −0.425671 | − | 0.904878i | \(-0.639962\pi\) | ||||
−0.425671 | + | 0.904878i | \(0.639962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.76660e6 | − | 1.69162e7i | −0.421543 | − | 0.730133i | 0.574548 | − | 0.818471i | \(-0.305178\pi\) |
−0.996091 | + | 0.0883376i | \(0.971845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.68682e7 | −0.723953 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00975e6 | − | 6.94508e6i | −0.171123 | − | 0.296393i | 0.767690 | − | 0.640822i | \(-0.221406\pi\) |
−0.938813 | + | 0.344428i | \(0.888073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.41700e6 | − | 7.65047e6i | −0.187445 | − | 0.324663i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.05674e7 | − | 3.56237e7i | 0.867929 | − | 1.50330i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.88359e6 | + | 7.04120e6i | 0.162969 | + | 0.295473i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.54577e6 | − | 6.14145e6i | 0.147963 | − | 0.256279i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.49850e7 | + | 2.59549e7i | 0.621838 | + | 1.07705i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.46292e7 | − | 2.53386e7i | −0.603701 | − | 1.04564i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.08934e7 | −0.447045 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.08280e7 | + | 1.87546e7i | 0.441905 | + | 0.765401i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.66943e7 | 0.677558 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.11897e6 | + | 1.93811e6i | −0.0451647 | + | 0.0782276i | −0.887724 | − | 0.460376i | \(-0.847715\pi\) |
0.842559 | + | 0.538604i | \(0.181048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 315112. | − | 545791.i | 0.0126490 | − | 0.0219087i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.98221e7 | −1.58975 | −0.794874 | − | 0.606774i | \(-0.792463\pi\) | ||||
−0.794874 | + | 0.606774i | \(0.792463\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.77750e7 | −2.29384 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.01349e7 | + | 1.75542e7i | −0.400190 | + | 0.693150i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.31957e7 | + | 4.01761e7i | −0.910928 | + | 1.57777i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.32391e6 | 0.325116 | 0.162558 | − | 0.986699i | \(-0.448025\pi\) | ||||
0.162558 | + | 0.986699i | \(0.448025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.28137e7 | − | 2.21939e7i | −0.497765 | − | 0.862155i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.62297e6 | −0.371796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.22066e6 | + | 9.04245e6i | 0.200619 | + | 0.347482i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −326257. | − | 565094.i | −0.0124698 | − | 0.0215984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.49343e6 | − | 7.78285e6i | 0.170820 | − | 0.295869i | −0.767887 | − | 0.640586i | \(-0.778692\pi\) |
0.938707 | + | 0.344717i | \(0.112025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06439e6 | − | 20827.6i | −0.0402463 | − | 0.000787526i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.24662e6 | − | 1.08195e7i | 0.234931 | − | 0.406913i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.51671e7 | + | 2.62702e7i | 0.567380 | + | 0.982730i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −623801. | − | 1.08045e6i | −0.0232112 | − | 0.0402029i | 0.854187 | − | 0.519967i | \(-0.174056\pi\) |
−0.877398 | + | 0.479764i | \(0.840722\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.26465e7 | 1.57841 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.30000e6 | − | 2.25167e6i | −0.0478596 | − | 0.0828953i | 0.841103 | − | 0.540875i | \(-0.181907\pi\) |
−0.888963 | + | 0.457979i | \(0.848573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.33835e7 | 1.22251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.58134e6 | + | 1.31313e7i | −0.276163 | + | 0.478329i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.03456e7 | − | 1.79192e7i | 0.374871 | − | 0.649296i | −0.615437 | − | 0.788186i | \(-0.711020\pi\) |
0.990308 | + | 0.138891i | \(0.0443537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.25357e7 | 0.812279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.15140e7 | −1.48848 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.50162e7 | − | 2.60089e7i | 0.535586 | − | 0.927662i | −0.463549 | − | 0.886071i | \(-0.653424\pi\) |
0.999135 | − | 0.0415907i | \(-0.0132426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.94120e6 | + | 1.20225e7i | −0.246278 | + | 0.426567i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.94549e7 | −1.03963 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.64475e7 | − | 2.84879e7i | −0.577502 | − | 1.00026i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.35579e7 | 2.91863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 922967. | + | 1.59863e6i | 0.0320716 | + | 0.0555496i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 739348. | + | 1.28059e6i | 0.0255582 | + | 0.0442681i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.38839e6 | − | 1.27971e7i | 0.254088 | − | 0.440093i | −0.710560 | − | 0.703637i | \(-0.751558\pi\) |
0.964647 | + | 0.263544i | \(0.0848915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.76726e7 | + | 3.20415e7i | 0.604630 | + | 1.09624i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.30678e6 | + | 9.19161e6i | −0.180627 | + | 0.312855i | −0.942094 | − | 0.335348i | \(-0.891146\pi\) |
0.761467 | + | 0.648203i | \(0.224479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.92903e7 | + | 5.07322e7i | 0.991839 | + | 1.71791i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.41820e7 | − | 2.45639e7i | −0.477777 | − | 0.827534i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.66481e7 | −1.22833 | −0.614165 | − | 0.789177i | \(-0.710507\pi\) | ||||
−0.614165 | + | 0.789177i | \(0.710507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.70228e7 | + | 2.94844e7i | 0.567642 | + | 0.983186i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.76043e6 | −0.0584046 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.80511e6 | + | 1.17868e7i | −0.224621 | + | 0.389056i | −0.956206 | − | 0.292695i | \(-0.905448\pi\) |
0.731584 | + | 0.681751i | \(0.238781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −677384. | + | 1.17326e6i | −0.0222456 | + | 0.0385305i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.07438e7 | −0.351047 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.36003e7 | 0.767232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.59467e6 | − | 2.76205e6i | 0.0515806 | − | 0.0893402i | −0.839082 | − | 0.544005i | \(-0.816907\pi\) |
0.890663 | + | 0.454664i | \(0.150241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.66410e7 | − | 2.88230e7i | 0.535557 | − | 0.927612i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.85615e7 | −0.594367 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.71729e7 | − | 2.97444e7i | −0.547150 | − | 0.947692i | −0.998468 | − | 0.0553288i | \(-0.982379\pi\) |
0.451318 | − | 0.892363i | \(-0.350954\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.78530e7 | 0.565976 |
(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.49.7 | yes | 18 | |
3.2 | odd | 2 | 684.6.k.f.505.5 | 18 | |||
4.3 | odd | 2 | 304.6.i.d.49.3 | 18 | |||
19.7 | even | 3 | inner | 76.6.e.a.45.7 | ✓ | 18 | |
57.26 | odd | 6 | 684.6.k.f.577.5 | 18 | |||
76.7 | odd | 6 | 304.6.i.d.273.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.7 | ✓ | 18 | 19.7 | even | 3 | inner | |
76.6.e.a.49.7 | yes | 18 | 1.1 | even | 1 | trivial | |
304.6.i.d.49.3 | 18 | 4.3 | odd | 2 | |||
304.6.i.d.273.3 | 18 | 76.7 | odd | 6 | |||
684.6.k.f.505.5 | 18 | 3.2 | odd | 2 | |||
684.6.k.f.577.5 | 18 | 57.26 | odd | 6 |