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 | 49.8 | ||
Root | \(-10.9539 - 18.9727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.49 |
Dual form | 76.6.e.a.45.8 |
$q$-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 | ||||||||
\(3\) | 10.4539 | − | 18.1067i | 0.670619 | − | 1.16155i | −0.307110 | − | 0.951674i | \(-0.599362\pi\) |
0.977729 | − | 0.209872i | \(-0.0673048\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 50.5928 | − | 87.6293i | 0.905031 | − | 1.56756i | 0.0841554 | − | 0.996453i | \(-0.473181\pi\) |
0.820876 | − | 0.571107i | \(-0.193486\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 95.5451 | 0.736993 | 0.368497 | − | 0.929629i | \(-0.379873\pi\) | ||||
0.368497 | + | 0.929629i | \(0.379873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −97.0688 | − | 168.128i | −0.399460 | − | 0.691885i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −119.504 | −0.297784 | −0.148892 | − | 0.988853i | \(-0.547571\pi\) | ||||
−0.148892 | + | 0.988853i | \(0.547571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 297.428 | + | 515.161i | 0.488117 | + | 0.845443i | 0.999907 | − | 0.0136677i | \(-0.00435069\pi\) |
−0.511790 | + | 0.859111i | \(0.671017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1057.79 | − | 1832.14i | −1.21386 | − | 2.10247i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −459.911 | + | 796.589i | −0.385968 | + | 0.668517i | −0.991903 | − | 0.126998i | \(-0.959466\pi\) |
0.605935 | + | 0.795514i | \(0.292799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −806.703 | − | 1351.05i | −0.512660 | − | 0.858592i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 998.821 | − | 1730.01i | 0.494242 | − | 0.856052i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2124.58 | + | 3679.89i | 0.837441 | + | 1.45049i | 0.892027 | + | 0.451981i | \(0.149283\pi\) |
−0.0545863 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3556.76 | − | 6160.48i | −1.13816 | − | 1.97135i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1021.61 | 0.269696 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2214.69 | − | 3835.95i | −0.489009 | − | 0.846989i | 0.510911 | − | 0.859634i | \(-0.329308\pi\) |
−0.999920 | + | 0.0126447i | \(0.995975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4955.30 | −0.926116 | −0.463058 | − | 0.886328i | \(-0.653248\pi\) | ||||
−0.463058 | + | 0.886328i | \(0.653248\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1249.29 | + | 2163.83i | −0.199700 | + | 0.345890i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4833.89 | − | 8372.55i | 0.667002 | − | 1.15528i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7651.95 | 0.918900 | 0.459450 | − | 0.888204i | \(-0.348047\pi\) | ||||
0.459450 | + | 0.888204i | \(0.348047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12437.2 | 1.30936 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2006.97 | − | 3476.18i | 0.186458 | − | 0.322955i | −0.757609 | − | 0.652709i | \(-0.773632\pi\) |
0.944067 | + | 0.329754i | \(0.106966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5228.80 | + | 9056.55i | −0.431252 | + | 0.746950i | −0.996981 | − | 0.0776405i | \(-0.975261\pi\) |
0.565729 | + | 0.824591i | \(0.308595\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19643.9 | −1.44610 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4318.48 | + | 7479.83i | 0.285159 | + | 0.493909i | 0.972648 | − | 0.232286i | \(-0.0746204\pi\) |
−0.687489 | + | 0.726195i | \(0.741287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7678.13 | −0.456841 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9615.75 | + | 16655.0i | 0.517675 | + | 0.896640i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18534.0 | + | 32101.9i | 0.906318 | + | 1.56979i | 0.819139 | + | 0.573596i | \(0.194452\pi\) |
0.0871791 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6046.06 | + | 10472.1i | −0.269504 | + | 0.466795i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −32896.2 | + | 482.998i | −1.34109 | + | 0.0196906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20727.5 | + | 35901.1i | −0.775207 | + | 1.34270i | 0.159472 | + | 0.987203i | \(0.449021\pi\) |
−0.934678 | + | 0.355495i | \(0.884312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2244.12 | − | 3886.93i | −0.0772186 | − | 0.133747i | 0.824830 | − | 0.565380i | \(-0.191271\pi\) |
−0.902049 | + | 0.431634i | \(0.857937\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9274.45 | − | 16063.8i | −0.294399 | − | 0.509915i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 60190.9 | 1.76704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 18484.7 | + | 32016.5i | 0.503067 | + | 0.871338i | 0.999994 | + | 0.00354526i | \(0.00112849\pi\) |
−0.496927 | + | 0.867793i | \(0.665538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 88840.9 | 2.24642 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23408.1 | − | 40543.9i | 0.551086 | − | 0.954509i | −0.447110 | − | 0.894479i | \(-0.647547\pi\) |
0.998197 | − | 0.0600303i | \(-0.0191197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40666.6 | − | 70436.6i | 0.893163 | − | 1.54700i | 0.0571012 | − | 0.998368i | \(-0.481814\pi\) |
0.836062 | − | 0.548635i | \(-0.184852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −148728. | −3.05309 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11418.1 | −0.219465 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6656.35 | − | 11529.1i | 0.119996 | − | 0.207840i | −0.799770 | − | 0.600307i | \(-0.795045\pi\) |
0.919766 | + | 0.392467i | \(0.128378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34267.5 | − | 59353.1i | 0.580323 | − | 1.00515i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18380.7 | −0.292864 | −0.146432 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146432 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46536.4 | + | 80603.3i | 0.698627 | + | 1.21006i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −92608.6 | −1.31176 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7307.86 | − | 12657.6i | −0.0977946 | − | 0.169385i | 0.812977 | − | 0.582296i | \(-0.197846\pi\) |
−0.910772 | + | 0.412911i | \(0.864512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28417.8 | + | 49221.1i | 0.359739 | + | 0.623086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −51802.3 | + | 89724.2i | −0.621071 | + | 1.07573i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −159205. | + | 2337.52i | −1.80987 | + | 0.0265733i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61844.5 | − | 107118.i | 0.667378 | − | 1.15593i | −0.311257 | − | 0.950326i | \(-0.600750\pi\) |
0.978635 | − | 0.205606i | \(-0.0659166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11600.1 | + | 20092.0i | 0.118953 | + | 0.206033i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −24891.8 | − | 43113.9i | −0.242803 | − | 0.420546i | 0.718709 | − | 0.695311i | \(-0.244733\pi\) |
−0.961511 | + | 0.274765i | \(0.911400\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −102447. | −0.951496 | −0.475748 | − | 0.879582i | \(-0.657823\pi\) | ||||
−0.475748 | + | 0.879582i | \(0.657823\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −101066. | − | 175052.i | −0.894608 | − | 1.54951i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 45310.9 | 0.382598 | 0.191299 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191299 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75259.9 | − | 130354.i | 0.606733 | − | 1.05089i | −0.385042 | − | 0.922899i | \(-0.625813\pi\) |
0.991775 | − | 0.127993i | \(-0.0408535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 79992.9 | − | 138552.i | 0.616232 | − | 1.06734i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 71068.5 | 0.523577 | 0.261789 | − | 0.965125i | \(-0.415688\pi\) | ||||
0.261789 | + | 0.965125i | \(0.415688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 429954. | 3.03164 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 57742.0 | − | 100012.i | 0.389966 | − | 0.675442i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −43942.3 | + | 76110.2i | −0.284456 | + | 0.492692i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −146770. | −0.911324 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −41961.5 | − | 72679.4i | −0.250085 | − | 0.433160i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −403580. | −2.31023 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 65658.5 | + | 113724.i | 0.361228 | + | 0.625666i | 0.988163 | − | 0.153406i | \(-0.0490242\pi\) |
−0.626935 | + | 0.779071i | \(0.715691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 109323. | + | 189353.i | 0.578412 | + | 1.00184i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −100412. | + | 173920.i | −0.511222 | + | 0.885462i | 0.488694 | + | 0.872456i | \(0.337474\pi\) |
−0.999915 | + | 0.0130067i | \(0.995860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −77076.5 | − | 129086.i | −0.377827 | − | 0.632776i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 51685.9 | − | 89522.6i | 0.244083 | − | 0.422764i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 181520. | + | 314402.i | 0.826272 | + | 1.43114i | 0.900944 | + | 0.433936i | \(0.142876\pi\) |
−0.0746720 | + | 0.997208i | \(0.523791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 190140. | + | 329331.i | 0.834710 | + | 1.44576i | 0.894266 | + | 0.447535i | \(0.147698\pi\) |
−0.0595567 | + | 0.998225i | \(0.518969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180580. | 0.764931 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35544.0 | − | 61563.9i | −0.145354 | − | 0.251760i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −448188. | −1.77027 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −80266.5 | + | 139026.i | −0.306366 | + | 0.530642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21911.4 | + | 37951.7i | −0.0808546 | + | 0.140044i | −0.903617 | − | 0.428341i | \(-0.859098\pi\) |
0.822763 | + | 0.568385i | \(0.192432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −131110. | −0.467942 | −0.233971 | − | 0.972244i | \(-0.575172\pi\) | ||||
−0.233971 | + | 0.972244i | \(0.575172\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 178572. | 0.616716 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −250702. | + | 434229.i | −0.838164 | + | 1.45174i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 239102. | − | 414137.i | 0.774166 | − | 1.34089i | −0.161096 | − | 0.986939i | \(-0.551503\pi\) |
0.935262 | − | 0.353956i | \(-0.115164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 775013. | 2.43118 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 202994. | + | 351595.i | 0.617188 | + | 1.06900i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −389081. | −1.14702 | −0.573509 | − | 0.819199i | \(-0.694418\pi\) | ||||
−0.573509 | + | 0.819199i | \(0.694418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 126410. | + | 218948.i | 0.361469 | + | 0.626083i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −261490. | − | 452914.i | −0.725544 | − | 1.25668i | −0.958750 | − | 0.284252i | \(-0.908255\pi\) |
0.233206 | − | 0.972427i | \(-0.425078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8719.47 | − | 15102.6i | 0.0234841 | − | 0.0406756i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −148843. | + | 266774.i | −0.389260 | + | 0.697675i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −228433. | + | 395658.i | −0.580289 | + | 1.00509i | 0.415156 | + | 0.909750i | \(0.363727\pi\) |
−0.995445 | + | 0.0953400i | \(0.969606\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −339831. | − | 588604.i | −0.838818 | − | 1.45288i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 433368. | + | 750615.i | 1.03974 | + | 1.80088i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 380329. | 0.887211 | 0.443606 | − | 0.896222i | \(-0.353699\pi\) | ||||
0.443606 | + | 0.896222i | \(0.353699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −172037. | − | 297977.i | −0.390325 | − | 0.676062i | 0.602168 | − | 0.798370i | \(-0.294304\pi\) |
−0.992492 | + | 0.122308i | \(0.960971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −93839.5 | −0.207137 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 387134. | − | 670535.i | 0.831633 | − | 1.44043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 54961.4 | − | 95195.9i | 0.114935 | − | 0.199074i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 97609.5 | 0.198764 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −699156. | −1.38673 | −0.693363 | − | 0.720588i | \(-0.743872\pi\) | ||||
−0.693363 | + | 0.720588i | \(0.743872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27621.7 | − | 47842.2i | 0.0533774 | − | 0.0924524i | −0.838102 | − | 0.545513i | \(-0.816335\pi\) |
0.891480 | + | 0.453061i | \(0.149668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 629230. | − | 1.08986e6i | 1.18501 | − | 2.05250i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00021e6 | −1.83623 | −0.918113 | − | 0.396318i | \(-0.870288\pi\) | ||||
−0.918113 | + | 0.396318i | \(0.870288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 246676. | + | 427255.i | 0.441564 | + | 0.764811i | 0.997806 | − | 0.0662094i | \(-0.0210905\pi\) |
−0.556242 | + | 0.831020i | \(0.687757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 772951. | 1.34947 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −211602. | − | 366506.i | −0.360397 | − | 0.624225i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −203077. | − | 351739.i | −0.337501 | − | 0.584569i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 412462. | − | 714405.i | 0.669049 | − | 1.15883i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 96404.5 | + | 161456.i | 0.152662 | + | 0.255675i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −309293. | + | 535711.i | −0.478259 | + | 0.828369i | −0.999689 | − | 0.0249246i | \(-0.992065\pi\) |
0.521430 | + | 0.853294i | \(0.325399\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −489412. | − | 847686.i | −0.739138 | − | 1.28022i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 529079. | + | 916392.i | 0.780593 | + | 1.35203i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −473455. | −0.682541 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −850251. | − | 1.47268e6i | −1.19794 | − | 2.07490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −547162. | −0.753590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −75025.2 | + | 129947.i | −0.101029 | + | 0.174987i | −0.912109 | − | 0.409948i | \(-0.865547\pi\) |
0.811080 | + | 0.584935i | \(0.198880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −690500. | + | 1.19598e6i | −0.909301 | + | 1.57496i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.05214e6 | 1.35522 | 0.677610 | − | 0.735421i | \(-0.263016\pi\) | ||||
0.677610 | + | 0.735421i | \(0.263016\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 766814. | 0.966276 | 0.483138 | − | 0.875544i | \(-0.339497\pi\) | ||||
0.483138 | + | 0.875544i | \(0.339497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −119363. | + | 206744.i | −0.147177 | + | 0.254919i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −722964. | + | 1.25221e6i | −0.872423 | + | 1.51108i | −0.0129403 | + | 0.999916i | \(0.504119\pi\) |
−0.859483 | + | 0.511165i | \(0.829214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 873936. | 1.03231 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −139170. | − | 241049.i | −0.160944 | − | 0.278763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −749353. | −0.848578 | −0.424289 | − | 0.905527i | \(-0.639476\pi\) | ||||
−0.424289 | + | 0.905527i | \(0.639476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −459395. | − | 795696.i | −0.509499 | − | 0.882479i | −0.999939 | − | 0.0110040i | \(-0.996497\pi\) |
0.490440 | − | 0.871475i | \(-0.336836\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −592334. | − | 1.02595e6i | −0.643504 | − | 1.11458i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −388458. | + | 672829.i | −0.413455 | + | 0.716126i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 456071. | − | 817421.i | 0.475652 | − | 0.852518i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −192150. | + | 332814.i | −0.196400 | + | 0.340176i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 158549. | + | 274616.i | 0.158848 | + | 0.275132i | 0.934453 | − | 0.356086i | \(-0.115889\pi\) |
−0.775606 | + | 0.631218i | \(0.782556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −253897. | − | 439762.i | −0.249377 | − | 0.431933i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.94595e6 | 1.87405 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −293395. | − | 508174.i | −0.277089 | − | 0.479932i | 0.693571 | − | 0.720388i | \(-0.256036\pi\) |
−0.970660 | + | 0.240456i | \(0.922703\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 731107. | 0.677223 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −429954. | + | 744702.i | −0.390680 | + | 0.676677i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −602410. | + | 1.04341e6i | −0.537036 | + | 0.930173i | 0.462026 | + | 0.886866i | \(0.347123\pi\) |
−0.999062 | + | 0.0433068i | \(0.986211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.75075e6 | 3.28098 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −305583. | −0.262332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 154072. | − | 266860.i | 0.129820 | − | 0.224855i | −0.793787 | − | 0.608196i | \(-0.791893\pi\) |
0.923607 | + | 0.383341i | \(0.125227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 476222. | − | 824840.i | 0.393900 | − | 0.682255i | −0.599060 | − | 0.800704i | \(-0.704459\pi\) |
0.992960 | + | 0.118449i | \(0.0377923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.18831e6 | 0.964991 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 425048. | + | 736205.i | 0.338927 | + | 0.587039i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −575120. | −0.450359 | −0.225179 | − | 0.974317i | \(-0.572297\pi\) | ||||
−0.225179 | + | 0.974317i | \(0.572297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 481005. | + | 833125.i | 0.369947 | + | 0.640766i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −917605. | − | 1.58934e6i | −0.693250 | − | 1.20074i | −0.970767 | − | 0.240023i | \(-0.922845\pi\) |
0.277517 | − | 0.960721i | \(-0.410488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −615501. | + | 1.06608e6i | −0.456838 | + | 0.791267i | −0.998792 | − | 0.0491413i | \(-0.984352\pi\) |
0.541954 | + | 0.840408i | \(0.317685\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.62199e6 | + | 2.90711e6i | −1.18287 | + | 2.12007i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 191757. | − | 332132.i | 0.137419 | − | 0.238016i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 286892. | + | 496912.i | 0.202057 | + | 0.349973i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.29303e6 | − | 2.23960e6i | −0.895113 | − | 1.55038i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −923293. | −0.628305 | −0.314153 | − | 0.949373i | \(-0.601720\pi\) | ||||
−0.314153 | + | 0.949373i | \(0.601720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09733e6 | + | 3.63268e6i | 1.40317 | + | 2.43037i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −122086. | −0.0803112 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.26382e6 | + | 2.18900e6i | −0.817538 | + | 1.41602i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −499587. | + | 865310.i | −0.317830 | + | 0.550497i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.04087e6 | −0.651312 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −454145. | −0.279541 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 843091. | − | 1.46028e6i | 0.510539 | − | 0.884279i | −0.489387 | − | 0.872067i | \(-0.662779\pi\) |
0.999925 | − | 0.0122119i | \(-0.00388726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.07097e6 | + | 1.85498e6i | −0.638091 | + | 1.10521i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.06080e6 | −0.621915 | −0.310957 | − | 0.950424i | \(-0.600650\pi\) | ||||
−0.310957 | + | 0.950424i | \(0.600650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8090.23 | + | 14012.7i | 0.00466767 | + | 0.00808464i | 0.868350 | − | 0.495952i | \(-0.165181\pi\) |
−0.863682 | + | 0.504037i | \(0.831848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.87688e6 | −1.06576 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.27571e6 | + | 2.20960e6i | 0.713024 | + | 1.23499i | 0.963717 | + | 0.266927i | \(0.0860082\pi\) |
−0.250693 | + | 0.968067i | \(0.580658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 264665. | + | 458413.i | 0.145619 | + | 0.252220i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 473676. | − | 820431.i | 0.256578 | − | 0.444406i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.44724e6 | − | 21249.1i | 0.771853 | − | 0.0113327i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.11576e6 | − | 3.66460e6i | 1.11111 | − | 1.92450i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.57352e6 | − | 2.72542e6i | −0.813773 | − | 1.40950i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 412610. | + | 714661.i | 0.210160 | + | 0.364008i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14830e6 | 0.576082 | 0.288041 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288041 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −742766. | − | 1.28651e6i | −0.367064 | − | 0.635773i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.74077e6 | 1.82117 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −742181. | + | 1.28549e6i | −0.355988 | + | 0.616589i | −0.987286 | − | 0.158951i | \(-0.949189\pi\) |
0.631299 | + | 0.775540i | \(0.282522\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 742944. | − | 1.28682e6i | 0.351121 | − | 0.608160i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 592180. | 0.275783 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.33943e6 | −1.07368 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.49471e6 | − | 7.78506e6i | 2.03308 | − | 3.52139i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.09955e6 | − | 1.90448e6i | 0.490222 | − | 0.849089i | −0.509715 | − | 0.860343i | \(-0.670249\pi\) |
0.999937 | + | 0.0112544i | \(0.00358245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.81500e6 | −1.67660 | −0.838302 | − | 0.545206i | \(-0.816451\pi\) | ||||
−0.838302 | + | 0.545206i | \(0.816451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 303855. | + | 526292.i | 0.131643 | + | 0.228012i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 550982. | 0.235342 | 0.117671 | − | 0.993053i | \(-0.462457\pi\) | ||||
0.117671 | + | 0.993053i | \(0.462457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.36856e6 | − | 4.10246e6i | −0.997500 | − | 1.72772i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 918738. | + | 1.59130e6i | 0.381523 | + | 0.660818i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −110651. | + | 191653.i | −0.0453126 | + | 0.0784838i | −0.887792 | − | 0.460245i | \(-0.847762\pi\) |
0.842480 | + | 0.538728i | \(0.181095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.17456e6 | + | 2.17979e6i | −0.474359 | + | 0.880331i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.53432e6 | + | 2.65752e6i | −0.611152 | + | 1.05855i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.11487e6 | − | 7.12717e6i | −1.61668 | − | 2.80017i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −680360. | − | 1.17842e6i | −0.263678 | − | 0.456704i | 0.703538 | − | 0.710657i | \(-0.251602\pi\) |
−0.967216 | + | 0.253954i | \(0.918269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −779258. | −0.297931 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.77084e6 | + | 3.06718e6i | 0.667950 | + | 1.15692i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.37071e6 | 1.62660 | 0.813298 | − | 0.581848i | \(-0.197670\pi\) | ||||
0.813298 | + | 0.581848i | \(0.197670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.21899e6 | + | 7.30751e6i | −1.54928 | + | 2.68344i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.31742e6 | − | 2.28184e6i | 0.477387 | − | 0.826859i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.26062e6 | −1.16601 | −0.583005 | − | 0.812469i | \(-0.698123\pi\) | ||||
−0.583005 | + | 0.812469i | \(0.698123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.74555e6 | 0.968986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.11542e6 | − | 1.93197e6i | 0.388546 | − | 0.672981i | −0.603708 | − | 0.797205i | \(-0.706311\pi\) |
0.992254 | + | 0.124224i | \(0.0396441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −577671. | + | 1.00056e6i | −0.198623 | + | 0.344025i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.03021e6 | 0.689072 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 520809. | + | 902068.i | 0.174504 | + | 0.302249i | 0.939989 | − | 0.341204i | \(-0.110835\pi\) |
−0.765486 | + | 0.643453i | \(0.777501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.90848e6 | −1.29290 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.09941e6 | + | 3.63628e6i | 0.685670 | + | 1.18762i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −673527. | − | 1.16658e6i | −0.217201 | − | 0.376203i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.19687e6 | + | 3.80509e6i | −0.699565 | + | 1.21168i | 0.269053 | + | 0.963125i | \(0.413289\pi\) |
−0.968618 | + | 0.248556i | \(0.920044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.14308e6 | + | 46148.1i | −0.988377 | + | 0.0145118i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 393217. | − | 681071.i | 0.122116 | − | 0.211510i | −0.798486 | − | 0.602013i | \(-0.794365\pi\) |
0.920602 | + | 0.390503i | \(0.127699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.47385e6 | − | 2.55277e6i | −0.452053 | − | 0.782979i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.46738e6 | − | 6.00567e6i | −1.05042 | − | 1.81938i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −914442. | −0.273634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −584641. | − | 1.01263e6i | −0.172815 | − | 0.299324i | 0.766588 | − | 0.642139i | \(-0.221953\pi\) |
−0.939403 | + | 0.342815i | \(0.888620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.59038e6 | 2.21645 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98041e6 | + | 3.43018e6i | −0.571322 | + | 0.989559i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −929930. | + | 1.61069e6i | −0.265051 | + | 0.459082i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.95081e6 | 2.23909 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.14739e6 | −1.15409 | −0.577045 | − | 0.816712i | \(-0.695794\pi\) | ||||
−0.577045 | + | 0.816712i | \(0.695794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59962e6 | − | 2.77063e6i | 0.439858 | − | 0.761857i | −0.557820 | − | 0.829962i | \(-0.688362\pi\) |
0.997678 | + | 0.0681052i | \(0.0216954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 838380. | − | 1.45212e6i | 0.227819 | − | 0.394594i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.54317e6 | 1.75718 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −214415. | − | 371378.i | −0.0569096 | − | 0.0985703i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.48629e6 | −0.389908 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.91306e6 | + | 5.04557e6i | 0.755364 | + | 1.30833i | 0.945193 | + | 0.326511i | \(0.105873\pi\) |
−0.189830 | + | 0.981817i | \(0.560794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.29561e6 | + | 2.24407e6i | 0.332090 | + | 0.575196i | 0.982921 | − | 0.184026i | \(-0.0589130\pi\) |
−0.650832 | + | 0.759222i | \(0.725580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.68533e6 | + | 8.11522e6i | −1.18718 | + | 2.05626i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.25779e6 | − | 5.83899e6i | 0.816056 | − | 1.46263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 986761. | − | 1.70912e6i | 0.244372 | − | 0.423264i | −0.717583 | − | 0.696473i | \(-0.754752\pi\) |
0.961955 | + | 0.273209i | \(0.0880850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 745307. | + | 1.29091e6i | 0.182490 | + | 0.316082i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 73870.7 | + | 127948.i | 0.0178839 | + | 0.0309759i | 0.874829 | − | 0.484432i | \(-0.160974\pi\) |
−0.856945 | + | 0.515408i | \(0.827640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.47890e6 | −0.354029 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 458120. | + | 793487.i | 0.108445 | + | 0.187833i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.33075e6 | −1.48197 | −0.740985 | − | 0.671522i | \(-0.765641\pi\) | ||||
−0.740985 | + | 0.671522i | \(0.765641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −239842. | + | 415419.i | −0.0555244 | + | 0.0961711i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.37061e6 | + | 2.37396e6i | −0.313811 | + | 0.543536i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.75094e6 | 1.30230 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −175313. | −0.0392667 | −0.0196334 | − | 0.999807i | \(-0.506250\pi\) | ||||
−0.0196334 | + | 0.999807i | \(0.506250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −469848. | + | 813801.i | −0.104094 | + | 0.180296i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.20957e6 | + | 5.55914e6i | −0.703388 | + | 1.21830i | 0.263882 | + | 0.964555i | \(0.414997\pi\) |
−0.967270 | + | 0.253749i | \(0.918336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.17798e6 | 0.472174 | 0.236087 | − | 0.971732i | \(-0.424135\pi\) | ||||
0.236087 | + | 0.971732i | \(0.424135\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.24164e6 | + | 9.07879e6i | 1.12418 | + | 1.94713i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 742392. | 0.157522 | 0.0787610 | − | 0.996894i | \(-0.474904\pi\) | ||||
0.0787610 | + | 0.996894i | \(0.474904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.76613e6 | + | 3.05902e6i | 0.370757 | + | 0.642170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.99910e6 | − | 8.65870e6i | −1.03834 | − | 1.79846i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 624865. | − | 1.08230e6i | 0.128420 | − | 0.222430i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.45386e6 | + | 9.77503e6i | −1.10910 | + | 1.98785i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.59815e6 | − | 6.23219e6i | 0.724076 | − | 1.25414i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.42943e6 | − | 4.20789e6i | −0.483799 | − | 0.837965i | 0.516028 | − | 0.856572i | \(-0.327410\pi\) |
−0.999827 | + | 0.0186069i | \(0.994077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.27591e6 | + | 3.94199e6i | 0.448530 | + | 0.776877i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.48832e6 | 1.65559 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.25777e6 | − | 1.08388e7i | −1.20800 | − | 2.09231i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.50290e6 | 0.669275 | 0.334638 | − | 0.942347i | \(-0.391386\pi\) | ||||
0.334638 | + | 0.942347i | \(0.391386\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.06742e6 | + | 7.04497e6i | −0.769213 | + | 1.33232i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 368324. | − | 637956.i | 0.0689488 | − | 0.119423i | −0.829490 | − | 0.558521i | \(-0.811369\pi\) |
0.898439 | + | 0.439099i | \(0.144702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.07424e6 | 0.754968 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.34753e6 | 0.430625 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.23653e6 | − | 3.87378e6i | 0.406147 | − | 0.703467i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9216.83 | − | 15964.0i | 0.00165703 | − | 0.00287006i | −0.865196 | − | 0.501434i | \(-0.832806\pi\) |
0.866853 | + | 0.498564i | \(0.166139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.09344e7 | −1.94625 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 249975. | + | 432970.i | 0.0440532 | + | 0.0763024i | 0.887211 | − | 0.461363i | \(-0.152640\pi\) |
−0.843158 | + | 0.537666i | \(0.819306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.03738e6 | −0.878975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −182305. | − | 315762.i | −0.0314977 | − | 0.0545557i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.32529e6 | − | 4.02752e6i | −0.397816 | − | 0.689038i | 0.595640 | − | 0.803252i | \(-0.296899\pi\) |
−0.993456 | + | 0.114213i | \(0.963565\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.88550e6 | − | 6.72988e6i | 0.658255 | − | 1.14013i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −824133. | − | 1.38024e6i | −0.138262 | − | 0.231559i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.18309e6 | + | 8.97737e6i | −0.861133 | + | 1.49153i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −516077. | − | 893872.i | −0.0849158 | − | 0.147078i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.77605e6 | + | 8.27236e6i | 0.778306 | + | 1.34807i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.64507e6 | 1.23392 | 0.616960 | − | 0.786994i | \(-0.288364\pi\) | ||||
0.616960 | + | 0.786994i | \(0.288364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 794941. | + | 1.37688e6i | 0.127081 | + | 0.220111i | 0.922544 | − | 0.385891i | \(-0.126106\pi\) |
−0.795463 | + | 0.606002i | \(0.792773\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.42103e7 | −2.25011 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.27900e6 | − | 3.94734e6i | 0.357451 | − | 0.619124i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.80954e6 | + | 1.00624e7i | −0.902615 | + | 1.56338i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.04799e6 | 1.23866 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.38772e6 | 0.364054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.29240e6 | − | 3.97056e6i | 0.346263 | − | 0.599746i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.97593e6 | − | 6.88651e6i | 0.594981 | − | 1.03054i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 917570. | 0.136040 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.63644e6 | − | 4.56645e6i | −0.387280 | − | 0.670789i | 0.604803 | − | 0.796375i | \(-0.293252\pi\) |
−0.992083 | + | 0.125587i | \(0.959919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.19385e6 | −1.04704 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.61521e6 | − | 1.31899e7i | −1.09822 | − | 1.90218i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.94792e6 | − | 3.37389e6i | −0.278357 | − | 0.482128i | 0.692620 | − | 0.721303i | \(-0.256456\pi\) |
−0.970977 | + | 0.239175i | \(0.923123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −435669. | + | 754600.i | −0.0616915 | + | 0.106853i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39596e6 | + | 6.08662e6i | −0.476522 | + | 0.854077i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 635982. | − | 1.10155e6i | 0.0884366 | − | 0.153177i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.09413e6 | − | 1.40194e7i | −1.11542 | − | 1.93196i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.90618e6 | + | 6.76570e6i | 0.533475 | + | 0.924006i | 0.999235 | + | 0.0390950i | \(0.0124475\pi\) |
−0.465761 | + | 0.884911i | \(0.654219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.22077e6 | −0.842005 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14912e6 | − | 1.99034e6i | −0.154156 | − | 0.267005i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.01256e6 | 0.932407 | 0.466204 | − | 0.884677i | \(-0.345621\pi\) | ||||
0.466204 | + | 0.884677i | \(0.345621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.59555e6 | − | 6.22768e6i | 0.473854 | − | 0.820739i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.27409e6 | − | 5.67090e6i | 0.427694 | − | 0.740788i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.70622e6 | 0.868355 | 0.434177 | − | 0.900827i | \(-0.357039\pi\) | ||||
0.434177 | + | 0.900827i | \(0.357039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.59306e6 | 0.717893 | 0.358946 | − | 0.933358i | \(-0.383136\pi\) | ||||
0.358946 | + | 0.933358i | \(0.383136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.30892e6 | + | 1.26594e7i | −0.929965 | + | 1.61075i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.51133e7 | − | 2.61769e7i | 1.90629 | − | 3.30179i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.19869e7 | 1.49888 | 0.749442 | − | 0.662070i | \(-0.230322\pi\) | ||||
0.749442 | + | 0.662070i | \(0.230322\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −577510. | − | 1.00028e6i | −0.0715918 | − | 0.124001i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.75619e6 | −0.215839 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.21490e6 | − | 3.83632e6i | −0.269887 | − | 0.467458i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.84266e6 | − | 1.01198e7i | −0.705863 | − | 1.22259i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.13321e6 | − | 1.23551e7i | 0.854456 | − | 1.47996i | −0.0226925 | − | 0.999742i | \(-0.507224\pi\) |
0.877149 | − | 0.480219i | \(-0.159443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.99745e6 | + | 6.69484e6i | 0.474783 | + | 0.795156i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.04561e7 | + | 1.81105e7i | −1.23141 | + | 2.13286i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.81201e6 | + | 6.60260e6i | 0.445161 | + | 0.771042i | 0.998063 | − | 0.0622043i | \(-0.0198130\pi\) |
−0.552902 | + | 0.833246i | \(0.686480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.44632e6 | + | 7.70126e6i | 0.514883 | + | 0.891803i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.03149e7 | 1.18448 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.20469e6 | − | 9.01479e6i | −0.592691 | − | 1.02657i | −0.993868 | − | 0.110570i | \(-0.964732\pi\) |
0.401178 | − | 0.916000i | \(-0.368601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.96843e6 | 0.222297 | 0.111149 | − | 0.993804i | \(-0.464547\pi\) | ||||
0.111149 | + | 0.993804i | \(0.464547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.58858e6 | − | 6.21560e6i | 0.401911 | − | 0.696129i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.42549e6 | + | 1.28613e7i | −0.824777 | + | 1.42856i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.79114e7 | −1.97314 | −0.986569 | − | 0.163347i | \(-0.947771\pi\) | ||||
−0.986569 | + | 0.163347i | \(0.947771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.84830e6 | −0.966755 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.56888e6 | + | 4.44942e6i | −0.278381 | + | 0.482171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −206107. | + | 356988.i | −0.0221535 | + | 0.0383709i | −0.876890 | − | 0.480692i | \(-0.840386\pi\) |
0.854736 | + | 0.519063i | \(0.173719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.49179e6 | −0.905339 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.97181e6 | + | 1.20755e7i | 0.737281 | + | 1.27701i | 0.953715 | + | 0.300711i | \(0.0972238\pi\) |
−0.216435 | + | 0.976297i | \(0.569443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.59596e7 | −1.67415 | −0.837075 | − | 0.547088i | \(-0.815736\pi\) | ||||
−0.837075 | + | 0.547088i | \(0.815736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.17049e6 | + | 3.75940e6i | 0.225854 | + | 0.391191i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −698230. | − | 1.20937e6i | −0.0720740 | − | 0.124836i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.30336e6 | + | 1.61139e7i | −0.952664 | + | 1.65006i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.93124e6 | − | 57720.4i | 0.399357 | − | 0.00586354i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.51922e6 | + | 6.09547e6i | −0.354666 | + | 0.614300i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.10790e6 | + | 5.38304e6i | 0.310737 | + | 0.538213i | 0.978522 | − | 0.206141i | \(-0.0660907\pi\) |
−0.667785 | + | 0.744354i | \(0.732757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.46664e6 | + | 1.12005e7i | 0.641460 | + | 1.11104i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.32874e7 | 1.30769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.28369e6 | − | 3.95547e6i | −0.222992 | − | 0.386233i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.08877e6 | −0.880548 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.32033e6 | − | 7.48302e6i | 0.415309 | − | 0.719337i | −0.580152 | − | 0.814508i | \(-0.697007\pi\) |
0.995461 | + | 0.0951719i | \(0.0303401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.07254e6 | + | 1.39820e7i | −0.769985 | + | 1.33365i | 0.167585 | + | 0.985858i | \(0.446403\pi\) |
−0.937570 | + | 0.347796i | \(0.886930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.21238e7 | 2.09392 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.16344e6 | 0.766677 | 0.383338 | − | 0.923608i | \(-0.374774\pi\) | ||||
0.383338 | + | 0.923608i | \(0.374774\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.47703e6 | − | 4.29034e6i | 0.230844 | − | 0.399834i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.94946e6 | + | 8.57271e6i | −0.457725 | + | 0.792803i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.08567e7 | 0.996359 | 0.498179 | − | 0.867074i | \(-0.334002\pi\) | ||||
0.498179 | + | 0.867074i | \(0.334002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.01603e7 | + | 1.75981e7i | 0.925343 | + | 1.60274i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.57898e7 | −1.42713 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.49623e6 | + | 4.32359e6i | 0.223908 | + | 0.387821i | 0.955991 | − | 0.293395i | \(-0.0947850\pi\) |
−0.732083 | + | 0.681215i | \(0.761452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.54002e6 | − | 1.30597e7i | −0.671226 | − | 1.16260i | −0.977557 | − | 0.210673i | \(-0.932435\pi\) |
0.306330 | − | 0.951925i | \(-0.400899\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.71999e6 | + | 9.90731e6i | −0.505372 | + | 0.875330i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.52112e7 | + | 223338.i | −1.33386 | + | 0.0195844i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.41057e6 | − | 1.62996e7i | 0.819033 | − | 1.41861i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.56862e6 | + | 2.71692e6i | 0.135504 | + | 0.234699i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 268182. | + | 464505.i | 0.0229945 | + | 0.0398276i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.89452e7 | −1.61236 | −0.806180 | − | 0.591671i | \(-0.798469\pi\) | ||||
−0.806180 | + | 0.591671i | \(0.798469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.63361e6 | − | 6.29359e6i | −0.306958 | − | 0.531666i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.05825e6 | −0.340304 | −0.170152 | − | 0.985418i | \(-0.554426\pi\) | ||||
−0.170152 | + | 0.985418i | \(0.554426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.90894e6 | − | 1.02346e7i | 0.491853 | − | 0.851914i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.09990e7 | − | 1.90508e7i | 0.908836 | − | 1.57415i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.85503e6 | 0.234185 | 0.117092 | − | 0.993121i | \(-0.462643\pi\) | ||||
0.117092 | + | 0.993121i | \(0.462643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.67344e7 | 2.99121 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.01621e6 | − | 1.38845e7i | 0.648003 | − | 1.12237i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.10251e7 | + | 1.90960e7i | −0.884778 | + | 1.53248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.38220e6 | 0.349138 | 0.174569 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174569 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.10834e6 | + | 1.91970e6i | 0.0876675 | + | 0.151845i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.84788e7 | 3.02175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84606e6 | + | 3.19747e6i | 0.143934 | + | 0.249301i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.51156e7 | + | 2.61810e7i | 1.17013 | + | 2.02672i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.33852e6 | + | 4.05044e6i | −0.179741 | + | 0.311320i | −0.941792 | − | 0.336197i | \(-0.890859\pi\) |
0.762051 | + | 0.647517i | \(0.224193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.17285e6 | − | 1.03382e7i | −0.471083 | − | 0.788959i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.13605e6 | − | 1.58241e7i | 0.692287 | − | 1.19908i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.37829e6 | − | 4.11932e6i | −0.178944 | − | 0.309940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −177992. | − | 308291.i | −0.0132980 | − | 0.0230328i | 0.859300 | − | 0.511472i | \(-0.170900\pi\) |
−0.872598 | + | 0.488439i | \(0.837566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.58450e6 | −0.191735 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.05279e7 | − | 1.82349e7i | −0.775568 | − | 1.34332i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.19307e6 | −0.526198 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.83368e6 | + | 1.35683e7i | −0.569073 | + | 0.985663i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −705747. | + | 1.22239e6i | −0.0509128 | + | 0.0881835i | −0.890359 | − | 0.455260i | \(-0.849546\pi\) |
0.839446 | + | 0.543443i | \(0.182880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.78833e6 | −0.701246 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.92099e7 | −1.36672 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.57542e7 | + | 2.72871e7i | −1.11314 | + | 1.92802i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.82049e6 | − | 1.18134e7i | 0.478608 | − | 0.828973i | −0.521091 | − | 0.853501i | \(-0.674475\pi\) |
0.999699 | + | 0.0245278i | \(0.00780822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.11485e6 | −0.565538 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.80957e6 | − | 8.33042e6i | −0.332899 | − | 0.576598i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.66079e7 | −1.82915 | −0.914577 | − | 0.404412i | \(-0.867476\pi\) | ||||
−0.914577 | + | 0.404412i | \(0.867476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.12181e6 | + | 1.40674e7i | 0.554542 | + | 0.960495i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.20900e6 | − | 3.82611e6i | −0.149806 | − | 0.259471i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.22169e6 | − | 7.31218e6i | 0.284364 | − | 0.492533i | −0.688091 | − | 0.725625i | \(-0.741551\pi\) |
0.972455 | + | 0.233091i | \(0.0748842\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00331e7 | − | 1.68032e7i | −0.671258 | − | 1.12421i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.70095e6 | + | 4.67819e6i | −0.179492 | + | 0.310889i | −0.941707 | − | 0.336435i | \(-0.890779\pi\) |
0.762215 | + | 0.647324i | \(0.224112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.21712e6 | + | 3.84016e6i | 0.146352 | + | 0.253489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.78419e6 | + | 3.09031e6i | 0.116988 | + | 0.202629i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.32923e6 | 0.281972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.66101e6 | + | 1.15372e7i | 0.430963 | + | 0.746450i | 0.996956 | − | 0.0779599i | \(-0.0248406\pi\) |
−0.565994 | + | 0.824410i | \(0.691507\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.62985e6 | 0.426105 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.63319e6 | + | 1.14890e7i | −0.423502 | + | 0.733527i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.61706e6 | − | 2.80083e6i | 0.102562 | − | 0.177642i | −0.810178 | − | 0.586185i | \(-0.800629\pi\) |
0.912739 | + | 0.408542i | \(0.133963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.06169e7 | −0.668948 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 602035. | 0.0376843 | 0.0188421 | − | 0.999822i | \(-0.494002\pi\) | ||||
0.0188421 | + | 0.999822i | \(0.494002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.19072e6 | − | 1.24547e7i | 0.447158 | − | 0.774500i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.03446e6 | − | 1.56481e7i | 0.558147 | − | 0.966739i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.46598e7 | −1.51357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.81675e6 | − | 1.70031e7i | −0.598621 | − | 1.03684i | −0.993025 | − | 0.117904i | \(-0.962382\pi\) |
0.394404 | − | 0.918937i | \(-0.370951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.22685e7 | −0.743285 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.03679e6 | + | 3.52782e6i | 0.122602 | + | 0.212353i | 0.920793 | − | 0.390052i | \(-0.127543\pi\) |
−0.798191 | + | 0.602404i | \(0.794210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.76248e7 | + | 3.05270e7i | 1.05407 | + | 1.82570i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.64293e6 | − | 1.32379e7i | 0.454159 | − | 0.786626i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.31552e6 | + | 92727.4i | −0.372877 | + | 0.00547475i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.79736e6 | + | 4.84518e6i | −0.164105 | + | 0.284238i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.26254e6 | − | 3.91883e6i | −0.131884 | − | 0.228429i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.41937e7 | − | 4.19047e7i | −1.40129 | − | 2.42710i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.13033e6 | 0.237710 | 0.118855 | − | 0.992912i | \(-0.462078\pi\) | ||||
0.118855 | + | 0.992912i | \(0.462078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.25951e7 | + | 2.18154e7i | 0.720293 | + | 1.24758i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.79025e6 | 0.385873 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.33493e6 | − | 2.31217e6i | 0.0753834 | − | 0.130568i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.92101e7 | − | 6.79138e7i | 2.20029 | − | 3.81101i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.62791e6 | −0.202307 | −0.101154 | − | 0.994871i | \(-0.532253\pi\) | ||||
−0.101154 | + | 0.994871i | \(0.532253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.94447e6 | −0.440249 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.41873e6 | + | 2.45731e6i | −0.0781301 | + | 0.135325i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.85983e6 | + | 8.41748e6i | −0.265970 | + | 0.460674i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.10800e7 | 2.23430 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.22131e6 | − | 5.57947e6i | −0.174120 | − | 0.301585i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.98904e6 | 0.321726 | 0.160863 | − | 0.986977i | \(-0.448572\pi\) | ||||
0.160863 | + | 0.986977i | \(0.448572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.65166e6 | − | 1.49851e7i | −0.461899 | − | 0.800033i | 0.537156 | − | 0.843483i | \(-0.319499\pi\) |
−0.999056 | + | 0.0434495i | \(0.986165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.95677e6 | − | 1.72456e7i | −0.528314 | − | 0.915066i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.96847e7 | + | 3.40948e7i | −1.03809 | + | 1.79802i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.64539e7 | − | 241584.i | 0.862411 | − | 0.0126623i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.51697e6 | − | 9.55567e6i | 0.287403 | − | 0.497796i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.04373e6 | − | 1.22001e7i | −0.364708 | − | 0.631692i | 0.624022 | − | 0.781407i | \(-0.285498\pi\) |
−0.988729 | + | 0.149715i | \(0.952164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.76700e6 | + | 3.06053e6i | 0.0909361 | + | 0.157506i | 0.907905 | − | 0.419175i | \(-0.137681\pi\) |
−0.816969 | + | 0.576681i | \(0.804347\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.77737e7 | 0.909164 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.25927e6 | − | 9.10933e6i | −0.267400 | − | 0.463151i | 0.700789 | − | 0.713368i | \(-0.252831\pi\) |
−0.968190 | + | 0.250217i | \(0.919498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.82603e7 | 1.93358 | 0.966790 | − | 0.255571i | \(-0.0822636\pi\) | ||||
0.966790 | + | 0.255571i | \(0.0822636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.01225e6 | + | 1.04135e7i | −0.302019 | + | 0.523113i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.53126e6 | − | 6.11632e6i | 0.176326 | − | 0.305406i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.29180e7 | −2.62656 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.06236e6 | −0.249770 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.04200e7 | − | 1.80480e7i | 0.511050 | − | 0.885164i | −0.488868 | − | 0.872358i | \(-0.662590\pi\) |
0.999918 | − | 0.0128063i | \(-0.00407650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 445904. | − | 772328.i | 0.0217396 | − | 0.0376541i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.83703e7 | −1.85963 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −882284. | − | 1.52816e6i | −0.0425076 | − | 0.0736253i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40231e7 | −0.671640 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.28688e7 | + | 2.22894e7i | 0.612729 | + | 1.06128i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62572e7 | + | 2.81583e7i | 0.769524 | + | 1.33286i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.06809e7 | − | 1.84999e7i | 0.502617 | − | 0.870558i | −0.497379 | − | 0.867534i | \(-0.665704\pi\) |
0.999995 | − | 0.00302417i | \(-0.000962625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.58468e7 | + | 2.65399e7i | 0.741355 | + | 1.24161i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.36791e7 | + | 2.36929e7i | −0.636216 | + | 1.10196i | 0.350040 | + | 0.936735i | \(0.386168\pi\) |
−0.986256 | + | 0.165224i | \(0.947165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.27009e6 | + | 5.66397e6i | 0.151209 | + | 0.261901i | 0.931672 | − | 0.363300i | \(-0.118350\pi\) |
−0.780463 | + | 0.625202i | \(0.785017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00921e6 | − | 6.94416e6i | −0.184311 | − | 0.319236i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.18151e7 | −1.45414 | −0.727069 | − | 0.686564i | \(-0.759118\pi\) | ||||
−0.727069 | + | 0.686564i | \(0.759118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.31142e7 | + | 4.00349e7i | 1.05036 | + | 1.81928i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.19966e7 | 0.542013 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −795463. | + | 1.37778e6i | −0.0357331 | + | 0.0618915i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.09958e7 | + | 1.90452e7i | −0.491111 | + | 0.850629i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.40127e7 | −1.06636 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.85601e7 | −1.70262 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.41774e7 | − | 2.45560e7i | 0.622442 | − | 1.07810i | −0.366588 | − | 0.930383i | \(-0.619474\pi\) |
0.989030 | − | 0.147717i | \(-0.0471925\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.65203e6 | + | 1.67178e7i | −0.421353 | + | 0.729806i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.86162e6 | 0.211029 | 0.105514 | − | 0.994418i | \(-0.466351\pi\) | ||||
0.105514 | + | 0.994418i | \(0.466351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −412959. | − | 715267.i | −0.0178240 | − | 0.0308721i | 0.856976 | − | 0.515357i | \(-0.172341\pi\) |
−0.874800 | + | 0.484485i | \(0.839007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.77011e7 | 3.76398 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.55015e6 | + | 1.13452e7i | 0.279539 | + | 0.484176i | 0.971270 | − | 0.237979i | \(-0.0764850\pi\) |
−0.691731 | + | 0.722155i | \(0.743152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.27335e6 | + | 1.08658e7i | 0.266223 | + | 0.461111i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.09512e6 | + | 7.09295e6i | −0.172811 | + | 0.299318i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.62188e6 | − | 1.18685e7i | 0.277877 | − | 0.498042i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.92419e7 | − | 3.33280e7i | 0.802954 | − | 1.39076i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.64238e7 | + | 4.57673e7i | 1.09651 | + | 1.89922i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.09744e7 | + | 1.90083e7i | 0.452880 | + | 0.784410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.40960e7 | −1.39924 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.04453e7 | + | 1.80918e7i | 0.426286 | + | 0.738348i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.48154e7 | −1.41302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.54799e6 | − | 7.87734e6i | 0.183570 | − | 0.317952i | −0.759524 | − | 0.650479i | \(-0.774568\pi\) |
0.943094 | + | 0.332527i | \(0.107901\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.83244e6 | + | 8.37003e6i | −0.193980 | + | 0.335983i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.66286e6 | 0.186147 | 0.0930737 | − | 0.995659i | \(-0.470331\pi\) | ||||
0.0930737 | + | 0.995659i | \(0.470331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.19657e6 | 0.0872105 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.74760e6 | + | 8.22308e6i | −0.187466 | + | 0.324700i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.59392e6 | + | 1.66172e7i | −0.376767 | + | 0.652580i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.34522e7 | −1.30658 | −0.653291 | − | 0.757107i | \(-0.726612\pi\) | ||||
−0.653291 | + | 0.757107i | \(0.726612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.76272e7 | − | 3.05312e7i | −0.684754 | − | 1.18603i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.78489e7 | 1.07598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72161e7 | − | 4.71397e7i | −1.04586 | − | 1.81148i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.94443e6 | + | 1.72243e7i | 0.380085 | + | 0.658326i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.29234e6 | + | 7.43456e6i | −0.163176 | + | 0.282628i | −0.936006 | − | 0.351984i | \(-0.885507\pi\) |
0.772830 | + | 0.634613i | \(0.218840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.19397e6 | + | 1.03735e7i | 0.234204 | + | 0.392240i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.10895e7 | + | 1.92075e7i | −0.417068 | + | 0.722383i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.56130e6 | − | 9.63245e6i | −0.208040 | − | 0.360336i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.35809e7 | − | 4.08434e7i | −0.877429 | − | 1.51975i | −0.854153 | − | 0.520022i | \(-0.825924\pi\) |
−0.0232757 | − | 0.999729i | \(-0.507410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 338298. | 0.0125209 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.05661e7 | + | 1.83010e7i | 0.388992 | + | 0.673754i | 0.992314 | − | 0.123744i | \(-0.0394900\pi\) |
−0.603322 | + | 0.797498i | \(0.706157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.70559e7 | 0.624592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.93834e6 | − | 8.55345e6i | 0.179888 | − | 0.311574i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.04875e7 | + | 1.81649e7i | −0.380012 | + | 0.658199i | −0.991063 | − | 0.133391i | \(-0.957413\pi\) |
0.611052 | + | 0.791591i | \(0.290747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83816e7 | 1.74387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.33447e7 | 1.91267 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.41521e7 | + | 4.18327e7i | −0.861435 | + | 1.49205i | 0.00910824 | + | 0.999959i | \(0.497101\pi\) |
−0.870544 | + | 0.492091i | \(0.836233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.53723e7 | + | 6.12665e7i | −1.25503 | + | 2.17378i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.10671e7 | 0.390621 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.73433e7 | + | 3.00396e7i | 0.608957 | + | 1.05474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.07418e6 | −0.142309 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.39827e6 | − | 7.61803e6i | −0.152833 | − | 0.264714i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.79492e6 | − | 4.84094e6i | −0.0966164 | − | 0.167345i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.71370e7 | − | 4.70027e7i | 0.933247 | − | 1.61643i | 0.155516 | − | 0.987833i | \(-0.450296\pi\) |
0.777731 | − | 0.628597i | \(-0.216371\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.47446e7 | − | 2.64269e7i | 0.504456 | − | 0.904143i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.62480e7 | − | 2.81423e7i | 0.553033 | − | 0.957882i | −0.445021 | − | 0.895520i | \(-0.646804\pi\) |
0.998054 | − | 0.0623611i | \(-0.0198631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.81669e7 | + | 3.14660e7i | 0.615175 | + | 1.06552i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.42360e7 | − | 7.66189e7i | −1.49027 | − | 2.58122i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.98320e6 | −0.234055 | −0.117028 | − | 0.993129i | \(-0.537337\pi\) | ||||
−0.117028 | + | 0.993129i | \(0.537337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 873321. | + | 1.51264e6i | 0.0291217 | + | 0.0504403i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.92216e7 | −0.969462 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.88200e6 | + | 4.99177e6i | −0.0951285 | + | 0.164767i | −0.909662 | − | 0.415349i | \(-0.863660\pi\) |
0.814534 | + | 0.580116i | \(0.196993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.06035e7 | + | 8.76478e7i | −1.66184 | + | 2.87839i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.72536e7 | 0.563749 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.44361e7 | −1.44459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.74277e6 | − | 6.48266e6i | 0.121062 | − | 0.209686i | −0.799125 | − | 0.601165i | \(-0.794703\pi\) |
0.920187 | + | 0.391480i | \(0.128037\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.20042e7 | − | 2.07919e7i | 0.386331 | − | 0.669146i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.99200e7 | 1.59852 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00119e7 | − | 1.73412e7i | −0.318992 | − | 0.552510i | 0.661286 | − | 0.750134i | \(-0.270011\pi\) |
−0.980278 | + | 0.197624i | \(0.936678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.81729e6 | 0.247823 |
(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.49.8 | yes | 18 | |
3.2 | odd | 2 | 684.6.k.f.505.1 | 18 | |||
4.3 | odd | 2 | 304.6.i.d.49.2 | 18 | |||
19.7 | even | 3 | inner | 76.6.e.a.45.8 | ✓ | 18 | |
57.26 | odd | 6 | 684.6.k.f.577.1 | 18 | |||
76.7 | odd | 6 | 304.6.i.d.273.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.8 | ✓ | 18 | 19.7 | even | 3 | inner | |
76.6.e.a.49.8 | yes | 18 | 1.1 | even | 1 | trivial | |
304.6.i.d.49.2 | 18 | 4.3 | odd | 2 | |||
304.6.i.d.273.2 | 18 | 76.7 | odd | 6 | |||
684.6.k.f.505.1 | 18 | 3.2 | odd | 2 | |||
684.6.k.f.577.1 | 18 | 57.26 | odd | 6 |