Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [26,8,Mod(1,26)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(26, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("26.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.a (trivial) |
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: | yes |
Analytic conductor: | \(8.12201066259\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 26.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −87.0000 | −1.86035 | −0.930175 | − | 0.367115i | \(-0.880345\pi\) | ||||
−0.930175 | + | 0.367115i | \(0.880345\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 321.000 | 1.14844 | 0.574222 | − | 0.818699i | \(-0.305305\pi\) | ||||
0.574222 | + | 0.818699i | \(0.305305\pi\) | |||||||
\(6\) | −696.000 | −1.31547 | ||||||||
\(7\) | −181.000 | −0.199451 | −0.0997253 | − | 0.995015i | \(-0.531796\pi\) | ||||
−0.0997253 | + | 0.995015i | \(0.531796\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 5382.00 | 2.46091 | ||||||||
\(10\) | 2568.00 | 0.812073 | ||||||||
\(11\) | 7782.00 | 1.76286 | 0.881428 | − | 0.472318i | \(-0.156583\pi\) | ||||
0.881428 | + | 0.472318i | \(0.156583\pi\) | |||||||
\(12\) | −5568.00 | −0.930175 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | −1448.00 | −0.141033 | ||||||||
\(15\) | −27927.0 | −2.13651 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 9069.00 | 0.447701 | 0.223851 | − | 0.974623i | \(-0.428137\pi\) | ||||
0.223851 | + | 0.974623i | \(0.428137\pi\) | |||||||
\(18\) | 43056.0 | 1.74012 | ||||||||
\(19\) | −37150.0 | −1.24257 | −0.621286 | − | 0.783584i | \(-0.713389\pi\) | ||||
−0.621286 | + | 0.783584i | \(0.713389\pi\) | |||||||
\(20\) | 20544.0 | 0.574222 | ||||||||
\(21\) | 15747.0 | 0.371048 | ||||||||
\(22\) | 62256.0 | 1.24653 | ||||||||
\(23\) | 19008.0 | 0.325753 | 0.162877 | − | 0.986646i | \(-0.447923\pi\) | ||||
0.162877 | + | 0.986646i | \(0.447923\pi\) | |||||||
\(24\) | −44544.0 | −0.657733 | ||||||||
\(25\) | 24916.0 | 0.318925 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | −277965. | −2.71780 | ||||||||
\(28\) | −11584.0 | −0.0997253 | ||||||||
\(29\) | 174750. | 1.33053 | 0.665264 | − | 0.746608i | \(-0.268319\pi\) | ||||
0.665264 | + | 0.746608i | \(0.268319\pi\) | |||||||
\(30\) | −223416. | −1.51074 | ||||||||
\(31\) | 29012.0 | 0.174909 | 0.0874544 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874544 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −677034. | −3.27953 | ||||||||
\(34\) | 72552.0 | 0.316572 | ||||||||
\(35\) | −58101.0 | −0.229058 | ||||||||
\(36\) | 344448. | 1.23045 | ||||||||
\(37\) | 323669. | 1.05050 | 0.525249 | − | 0.850949i | \(-0.323972\pi\) | ||||
0.525249 | + | 0.850949i | \(0.323972\pi\) | |||||||
\(38\) | −297200. | −0.878630 | ||||||||
\(39\) | −191139. | −0.515968 | ||||||||
\(40\) | 164352. | 0.406036 | ||||||||
\(41\) | 795312. | 1.80216 | 0.901081 | − | 0.433650i | \(-0.142775\pi\) | ||||
0.901081 | + | 0.433650i | \(0.142775\pi\) | |||||||
\(42\) | 125976. | 0.262371 | ||||||||
\(43\) | −314137. | −0.602531 | −0.301266 | − | 0.953540i | \(-0.597409\pi\) | ||||
−0.301266 | + | 0.953540i | \(0.597409\pi\) | |||||||
\(44\) | 498048. | 0.881428 | ||||||||
\(45\) | 1.72762e6 | 2.82621 | ||||||||
\(46\) | 152064. | 0.230342 | ||||||||
\(47\) | −447441. | −0.628627 | −0.314314 | − | 0.949319i | \(-0.601774\pi\) | ||||
−0.314314 | + | 0.949319i | \(0.601774\pi\) | |||||||
\(48\) | −356352. | −0.465088 | ||||||||
\(49\) | −790782. | −0.960219 | ||||||||
\(50\) | 199328. | 0.225514 | ||||||||
\(51\) | −789003. | −0.832881 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | −1.46923e6 | −1.35558 | −0.677790 | − | 0.735256i | \(-0.737062\pi\) | ||||
−0.677790 | + | 0.735256i | \(0.737062\pi\) | |||||||
\(54\) | −2.22372e6 | −1.92177 | ||||||||
\(55\) | 2.49802e6 | 2.02454 | ||||||||
\(56\) | −92672.0 | −0.0705165 | ||||||||
\(57\) | 3.23205e6 | 2.31162 | ||||||||
\(58\) | 1.39800e6 | 0.940826 | ||||||||
\(59\) | 1.62777e6 | 1.03184 | 0.515918 | − | 0.856638i | \(-0.327451\pi\) | ||||
0.515918 | + | 0.856638i | \(0.327451\pi\) | |||||||
\(60\) | −1.78733e6 | −1.06825 | ||||||||
\(61\) | −2.39961e6 | −1.35359 | −0.676793 | − | 0.736173i | \(-0.736631\pi\) | ||||
−0.676793 | + | 0.736173i | \(0.736631\pi\) | |||||||
\(62\) | 232096. | 0.123679 | ||||||||
\(63\) | −974142. | −0.490829 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 705237. | 0.318521 | ||||||||
\(66\) | −5.41627e6 | −2.31898 | ||||||||
\(67\) | −64066.0 | −0.0260235 | −0.0130118 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130118 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(68\) | 580416. | 0.223851 | ||||||||
\(69\) | −1.65370e6 | −0.606016 | ||||||||
\(70\) | −464808. | −0.161968 | ||||||||
\(71\) | −322383. | −0.106898 | −0.0534488 | − | 0.998571i | \(-0.517021\pi\) | ||||
−0.0534488 | + | 0.998571i | \(0.517021\pi\) | |||||||
\(72\) | 2.75558e6 | 0.870061 | ||||||||
\(73\) | −4.45478e6 | −1.34028 | −0.670141 | − | 0.742233i | \(-0.733767\pi\) | ||||
−0.670141 | + | 0.742233i | \(0.733767\pi\) | |||||||
\(74\) | 2.58935e6 | 0.742814 | ||||||||
\(75\) | −2.16769e6 | −0.593312 | ||||||||
\(76\) | −2.37760e6 | −0.621286 | ||||||||
\(77\) | −1.40854e6 | −0.351603 | ||||||||
\(78\) | −1.52911e6 | −0.364845 | ||||||||
\(79\) | 753560. | 0.171958 | 0.0859791 | − | 0.996297i | \(-0.472598\pi\) | ||||
0.0859791 | + | 0.996297i | \(0.472598\pi\) | |||||||
\(80\) | 1.31482e6 | 0.287111 | ||||||||
\(81\) | 1.24125e7 | 2.59515 | ||||||||
\(82\) | 6.36250e6 | 1.27432 | ||||||||
\(83\) | −1.21909e6 | −0.234025 | −0.117013 | − | 0.993130i | \(-0.537332\pi\) | ||||
−0.117013 | + | 0.993130i | \(0.537332\pi\) | |||||||
\(84\) | 1.00781e6 | 0.185524 | ||||||||
\(85\) | 2.91115e6 | 0.514160 | ||||||||
\(86\) | −2.51310e6 | −0.426054 | ||||||||
\(87\) | −1.52032e7 | −2.47525 | ||||||||
\(88\) | 3.98438e6 | 0.623264 | ||||||||
\(89\) | 3.39033e6 | 0.509773 | 0.254887 | − | 0.966971i | \(-0.417962\pi\) | ||||
0.254887 | + | 0.966971i | \(0.417962\pi\) | |||||||
\(90\) | 1.38210e7 | 1.99843 | ||||||||
\(91\) | −397657. | −0.0553177 | ||||||||
\(92\) | 1.21651e6 | 0.162877 | ||||||||
\(93\) | −2.52404e6 | −0.325392 | ||||||||
\(94\) | −3.57953e6 | −0.444507 | ||||||||
\(95\) | −1.19252e7 | −1.42702 | ||||||||
\(96\) | −2.85082e6 | −0.328867 | ||||||||
\(97\) | 1.62877e6 | 0.181201 | 0.0906003 | − | 0.995887i | \(-0.471121\pi\) | ||||
0.0906003 | + | 0.995887i | \(0.471121\pi\) | |||||||
\(98\) | −6.32626e6 | −0.678978 | ||||||||
\(99\) | 4.18827e7 | 4.33822 | ||||||||
\(100\) | 1.59462e6 | 0.159462 | ||||||||
\(101\) | −1.53503e7 | −1.48249 | −0.741244 | − | 0.671236i | \(-0.765764\pi\) | ||||
−0.741244 | + | 0.671236i | \(0.765764\pi\) | |||||||
\(102\) | −6.31202e6 | −0.588936 | ||||||||
\(103\) | 6.87643e6 | 0.620058 | 0.310029 | − | 0.950727i | \(-0.399661\pi\) | ||||
0.310029 | + | 0.950727i | \(0.399661\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | 5.05479e6 | 0.426128 | ||||||||
\(106\) | −1.17539e7 | −0.958539 | ||||||||
\(107\) | −1.52027e7 | −1.19971 | −0.599857 | − | 0.800107i | \(-0.704776\pi\) | ||||
−0.599857 | + | 0.800107i | \(0.704776\pi\) | |||||||
\(108\) | −1.77898e7 | −1.35890 | ||||||||
\(109\) | 6.73260e6 | 0.497955 | 0.248978 | − | 0.968509i | \(-0.419905\pi\) | ||||
0.248978 | + | 0.968509i | \(0.419905\pi\) | |||||||
\(110\) | 1.99842e7 | 1.43157 | ||||||||
\(111\) | −2.81592e7 | −1.95429 | ||||||||
\(112\) | −741376. | −0.0498627 | ||||||||
\(113\) | −1.15292e7 | −0.751667 | −0.375833 | − | 0.926687i | \(-0.622644\pi\) | ||||
−0.375833 | + | 0.926687i | \(0.622644\pi\) | |||||||
\(114\) | 2.58564e7 | 1.63456 | ||||||||
\(115\) | 6.10157e6 | 0.374110 | ||||||||
\(116\) | 1.11840e7 | 0.665264 | ||||||||
\(117\) | 1.18243e7 | 0.682532 | ||||||||
\(118\) | 1.30222e7 | 0.729619 | ||||||||
\(119\) | −1.64149e6 | −0.0892943 | ||||||||
\(120\) | −1.42986e7 | −0.755370 | ||||||||
\(121\) | 4.10724e7 | 2.10766 | ||||||||
\(122\) | −1.91969e7 | −0.957130 | ||||||||
\(123\) | −6.91921e7 | −3.35266 | ||||||||
\(124\) | 1.85677e6 | 0.0874544 | ||||||||
\(125\) | −1.70801e7 | −0.782177 | ||||||||
\(126\) | −7.79314e6 | −0.347069 | ||||||||
\(127\) | 2.06699e7 | 0.895418 | 0.447709 | − | 0.894179i | \(-0.352240\pi\) | ||||
0.447709 | + | 0.894179i | \(0.352240\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 2.73299e7 | 1.12092 | ||||||||
\(130\) | 5.64190e6 | 0.225228 | ||||||||
\(131\) | −1.90949e7 | −0.742107 | −0.371054 | − | 0.928611i | \(-0.621003\pi\) | ||||
−0.371054 | + | 0.928611i | \(0.621003\pi\) | |||||||
\(132\) | −4.33302e7 | −1.63977 | ||||||||
\(133\) | 6.72415e6 | 0.247832 | ||||||||
\(134\) | −512528. | −0.0184014 | ||||||||
\(135\) | −8.92268e7 | −3.12124 | ||||||||
\(136\) | 4.64333e6 | 0.158286 | ||||||||
\(137\) | 2.96901e7 | 0.986482 | 0.493241 | − | 0.869893i | \(-0.335812\pi\) | ||||
0.493241 | + | 0.869893i | \(0.335812\pi\) | |||||||
\(138\) | −1.32296e7 | −0.428518 | ||||||||
\(139\) | 1.55652e7 | 0.491591 | 0.245795 | − | 0.969322i | \(-0.420951\pi\) | ||||
0.245795 | + | 0.969322i | \(0.420951\pi\) | |||||||
\(140\) | −3.71846e6 | −0.114529 | ||||||||
\(141\) | 3.89274e7 | 1.16947 | ||||||||
\(142\) | −2.57906e6 | −0.0755880 | ||||||||
\(143\) | 1.70971e7 | 0.488928 | ||||||||
\(144\) | 2.20447e7 | 0.615226 | ||||||||
\(145\) | 5.60948e7 | 1.52804 | ||||||||
\(146\) | −3.56383e7 | −0.947723 | ||||||||
\(147\) | 6.87980e7 | 1.78635 | ||||||||
\(148\) | 2.07148e7 | 0.525249 | ||||||||
\(149\) | −2.49675e6 | −0.0618334 | −0.0309167 | − | 0.999522i | \(-0.509843\pi\) | ||||
−0.0309167 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(150\) | −1.73415e7 | −0.419535 | ||||||||
\(151\) | 2.39802e7 | 0.566804 | 0.283402 | − | 0.959001i | \(-0.408537\pi\) | ||||
0.283402 | + | 0.959001i | \(0.408537\pi\) | |||||||
\(152\) | −1.90208e7 | −0.439315 | ||||||||
\(153\) | 4.88094e7 | 1.10175 | ||||||||
\(154\) | −1.12683e7 | −0.248621 | ||||||||
\(155\) | 9.31285e6 | 0.200873 | ||||||||
\(156\) | −1.22329e7 | −0.257984 | ||||||||
\(157\) | 1.70550e7 | 0.351725 | 0.175863 | − | 0.984415i | \(-0.443729\pi\) | ||||
0.175863 | + | 0.984415i | \(0.443729\pi\) | |||||||
\(158\) | 6.02848e6 | 0.121593 | ||||||||
\(159\) | 1.27823e8 | 2.52185 | ||||||||
\(160\) | 1.05185e7 | 0.203018 | ||||||||
\(161\) | −3.44045e6 | −0.0649717 | ||||||||
\(162\) | 9.93002e7 | 1.83505 | ||||||||
\(163\) | −7.34586e7 | −1.32857 | −0.664287 | − | 0.747477i | \(-0.731265\pi\) | ||||
−0.664287 | + | 0.747477i | \(0.731265\pi\) | |||||||
\(164\) | 5.09000e7 | 0.901081 | ||||||||
\(165\) | −2.17328e8 | −3.76636 | ||||||||
\(166\) | −9.75274e6 | −0.165481 | ||||||||
\(167\) | 4.66860e7 | 0.775674 | 0.387837 | − | 0.921728i | \(-0.373222\pi\) | ||||
0.387837 | + | 0.921728i | \(0.373222\pi\) | |||||||
\(168\) | 8.06246e6 | 0.131185 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 2.32892e7 | 0.363566 | ||||||||
\(171\) | −1.99941e8 | −3.05785 | ||||||||
\(172\) | −2.01048e7 | −0.301266 | ||||||||
\(173\) | −7.80931e7 | −1.14670 | −0.573352 | − | 0.819309i | \(-0.694357\pi\) | ||||
−0.573352 | + | 0.819309i | \(0.694357\pi\) | |||||||
\(174\) | −1.21626e8 | −1.75027 | ||||||||
\(175\) | −4.50980e6 | −0.0636098 | ||||||||
\(176\) | 3.18751e7 | 0.440714 | ||||||||
\(177\) | −1.41616e8 | −1.91958 | ||||||||
\(178\) | 2.71226e7 | 0.360464 | ||||||||
\(179\) | −5.56163e7 | −0.724797 | −0.362399 | − | 0.932023i | \(-0.618042\pi\) | ||||
−0.362399 | + | 0.932023i | \(0.618042\pi\) | |||||||
\(180\) | 1.10568e8 | 1.41311 | ||||||||
\(181\) | −1.19435e8 | −1.49711 | −0.748557 | − | 0.663070i | \(-0.769253\pi\) | ||||
−0.748557 | + | 0.663070i | \(0.769253\pi\) | |||||||
\(182\) | −3.18126e6 | −0.0391155 | ||||||||
\(183\) | 2.08766e8 | 2.51815 | ||||||||
\(184\) | 9.73210e6 | 0.115171 | ||||||||
\(185\) | 1.03898e8 | 1.20644 | ||||||||
\(186\) | −2.01924e7 | −0.230087 | ||||||||
\(187\) | 7.05750e7 | 0.789233 | ||||||||
\(188\) | −2.86362e7 | −0.314314 | ||||||||
\(189\) | 5.03117e7 | 0.542066 | ||||||||
\(190\) | −9.54012e7 | −1.00906 | ||||||||
\(191\) | 1.05485e8 | 1.09540 | 0.547700 | − | 0.836675i | \(-0.315504\pi\) | ||||
0.547700 | + | 0.836675i | \(0.315504\pi\) | |||||||
\(192\) | −2.28065e7 | −0.232544 | ||||||||
\(193\) | 2.12059e7 | 0.212327 | 0.106164 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106164 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(194\) | 1.30302e7 | 0.128128 | ||||||||
\(195\) | −6.13556e7 | −0.592561 | ||||||||
\(196\) | −5.06100e7 | −0.480110 | ||||||||
\(197\) | −1.66535e8 | −1.55194 | −0.775969 | − | 0.630771i | \(-0.782739\pi\) | ||||
−0.775969 | + | 0.630771i | \(0.782739\pi\) | |||||||
\(198\) | 3.35062e8 | 3.06759 | ||||||||
\(199\) | −1.26351e8 | −1.13656 | −0.568279 | − | 0.822836i | \(-0.692391\pi\) | ||||
−0.568279 | + | 0.822836i | \(0.692391\pi\) | |||||||
\(200\) | 1.27570e7 | 0.112757 | ||||||||
\(201\) | 5.57374e6 | 0.0484129 | ||||||||
\(202\) | −1.22802e8 | −1.04828 | ||||||||
\(203\) | −3.16298e7 | −0.265375 | ||||||||
\(204\) | −5.04962e7 | −0.416441 | ||||||||
\(205\) | 2.55295e8 | 2.06968 | ||||||||
\(206\) | 5.50114e7 | 0.438448 | ||||||||
\(207\) | 1.02301e8 | 0.801648 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | −2.89101e8 | −2.19047 | ||||||||
\(210\) | 4.04383e7 | 0.301318 | ||||||||
\(211\) | 1.08571e8 | 0.795655 | 0.397828 | − | 0.917460i | \(-0.369764\pi\) | ||||
0.397828 | + | 0.917460i | \(0.369764\pi\) | |||||||
\(212\) | −9.40308e7 | −0.677790 | ||||||||
\(213\) | 2.80473e7 | 0.198867 | ||||||||
\(214\) | −1.21622e8 | −0.848326 | ||||||||
\(215\) | −1.00838e8 | −0.691974 | ||||||||
\(216\) | −1.42318e8 | −0.960886 | ||||||||
\(217\) | −5.25117e6 | −0.0348857 | ||||||||
\(218\) | 5.38608e7 | 0.352108 | ||||||||
\(219\) | 3.87566e8 | 2.49340 | ||||||||
\(220\) | 1.59873e8 | 1.01227 | ||||||||
\(221\) | 1.99246e7 | 0.124170 | ||||||||
\(222\) | −2.25274e8 | −1.38189 | ||||||||
\(223\) | −1.25603e8 | −0.758459 | −0.379229 | − | 0.925303i | \(-0.623811\pi\) | ||||
−0.379229 | + | 0.925303i | \(0.623811\pi\) | |||||||
\(224\) | −5.93101e6 | −0.0352582 | ||||||||
\(225\) | 1.34098e8 | 0.784844 | ||||||||
\(226\) | −9.22338e7 | −0.531509 | ||||||||
\(227\) | 1.90774e8 | 1.08250 | 0.541252 | − | 0.840861i | \(-0.317951\pi\) | ||||
0.541252 | + | 0.840861i | \(0.317951\pi\) | |||||||
\(228\) | 2.06851e8 | 1.15581 | ||||||||
\(229\) | −5.28911e7 | −0.291044 | −0.145522 | − | 0.989355i | \(-0.546486\pi\) | ||||
−0.145522 | + | 0.989355i | \(0.546486\pi\) | |||||||
\(230\) | 4.88125e7 | 0.264536 | ||||||||
\(231\) | 1.22543e8 | 0.654104 | ||||||||
\(232\) | 8.94720e7 | 0.470413 | ||||||||
\(233\) | 1.51254e8 | 0.783359 | 0.391680 | − | 0.920102i | \(-0.371894\pi\) | ||||
0.391680 | + | 0.920102i | \(0.371894\pi\) | |||||||
\(234\) | 9.45940e7 | 0.482623 | ||||||||
\(235\) | −1.43629e8 | −0.721944 | ||||||||
\(236\) | 1.04177e8 | 0.515918 | ||||||||
\(237\) | −6.55597e7 | −0.319903 | ||||||||
\(238\) | −1.31319e7 | −0.0631406 | ||||||||
\(239\) | 2.61917e8 | 1.24100 | 0.620498 | − | 0.784208i | \(-0.286930\pi\) | ||||
0.620498 | + | 0.784208i | \(0.286930\pi\) | |||||||
\(240\) | −1.14389e8 | −0.534127 | ||||||||
\(241\) | −1.31752e8 | −0.606312 | −0.303156 | − | 0.952941i | \(-0.598040\pi\) | ||||
−0.303156 | + | 0.952941i | \(0.598040\pi\) | |||||||
\(242\) | 3.28579e8 | 1.49034 | ||||||||
\(243\) | −4.71980e8 | −2.11009 | ||||||||
\(244\) | −1.53575e8 | −0.676793 | ||||||||
\(245\) | −2.53841e8 | −1.10276 | ||||||||
\(246\) | −5.53537e8 | −2.37069 | ||||||||
\(247\) | −8.16186e7 | −0.344627 | ||||||||
\(248\) | 1.48541e7 | 0.0618396 | ||||||||
\(249\) | 1.06061e8 | 0.435370 | ||||||||
\(250\) | −1.36641e8 | −0.553083 | ||||||||
\(251\) | 2.47061e8 | 0.986159 | 0.493080 | − | 0.869984i | \(-0.335871\pi\) | ||||
0.493080 | + | 0.869984i | \(0.335871\pi\) | |||||||
\(252\) | −6.23451e7 | −0.245415 | ||||||||
\(253\) | 1.47920e8 | 0.574256 | ||||||||
\(254\) | 1.65359e8 | 0.633156 | ||||||||
\(255\) | −2.53270e8 | −0.956518 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 2.27286e8 | 0.835231 | 0.417616 | − | 0.908624i | \(-0.362866\pi\) | ||||
0.417616 | + | 0.908624i | \(0.362866\pi\) | |||||||
\(258\) | 2.18639e8 | 0.792610 | ||||||||
\(259\) | −5.85841e7 | −0.209522 | ||||||||
\(260\) | 4.51352e7 | 0.159261 | ||||||||
\(261\) | 9.40504e8 | 3.27430 | ||||||||
\(262\) | −1.52759e8 | −0.524749 | ||||||||
\(263\) | −4.25872e8 | −1.44356 | −0.721779 | − | 0.692124i | \(-0.756675\pi\) | ||||
−0.721779 | + | 0.692124i | \(0.756675\pi\) | |||||||
\(264\) | −3.46641e8 | −1.15949 | ||||||||
\(265\) | −4.71623e8 | −1.55681 | ||||||||
\(266\) | 5.37932e7 | 0.175243 | ||||||||
\(267\) | −2.94959e8 | −0.948357 | ||||||||
\(268\) | −4.10022e6 | −0.0130118 | ||||||||
\(269\) | −5.14154e8 | −1.61050 | −0.805250 | − | 0.592936i | \(-0.797969\pi\) | ||||
−0.805250 | + | 0.592936i | \(0.797969\pi\) | |||||||
\(270\) | −7.13814e8 | −2.20705 | ||||||||
\(271\) | 4.57096e7 | 0.139513 | 0.0697565 | − | 0.997564i | \(-0.477778\pi\) | ||||
0.0697565 | + | 0.997564i | \(0.477778\pi\) | |||||||
\(272\) | 3.71466e7 | 0.111925 | ||||||||
\(273\) | 3.45962e7 | 0.102910 | ||||||||
\(274\) | 2.37521e8 | 0.697548 | ||||||||
\(275\) | 1.93896e8 | 0.562218 | ||||||||
\(276\) | −1.05837e8 | −0.303008 | ||||||||
\(277\) | −2.73964e8 | −0.774487 | −0.387244 | − | 0.921977i | \(-0.626573\pi\) | ||||
−0.387244 | + | 0.921977i | \(0.626573\pi\) | |||||||
\(278\) | 1.24522e8 | 0.347607 | ||||||||
\(279\) | 1.56143e8 | 0.430434 | ||||||||
\(280\) | −2.97477e7 | −0.0809842 | ||||||||
\(281\) | 4.21707e8 | 1.13381 | 0.566903 | − | 0.823784i | \(-0.308141\pi\) | ||||
0.566903 | + | 0.823784i | \(0.308141\pi\) | |||||||
\(282\) | 3.11419e8 | 0.826938 | ||||||||
\(283\) | 3.81957e8 | 1.00176 | 0.500878 | − | 0.865518i | \(-0.333010\pi\) | ||||
0.500878 | + | 0.865518i | \(0.333010\pi\) | |||||||
\(284\) | −2.06325e7 | −0.0534488 | ||||||||
\(285\) | 1.03749e9 | 2.65477 | ||||||||
\(286\) | 1.36776e8 | 0.345724 | ||||||||
\(287\) | −1.43951e8 | −0.359443 | ||||||||
\(288\) | 1.76357e8 | 0.435031 | ||||||||
\(289\) | −3.28092e8 | −0.799564 | ||||||||
\(290\) | 4.48758e8 | 1.08049 | ||||||||
\(291\) | −1.41703e8 | −0.337097 | ||||||||
\(292\) | −2.85106e8 | −0.670141 | ||||||||
\(293\) | −4.04833e8 | −0.940240 | −0.470120 | − | 0.882602i | \(-0.655789\pi\) | ||||
−0.470120 | + | 0.882602i | \(0.655789\pi\) | |||||||
\(294\) | 5.50384e8 | 1.26314 | ||||||||
\(295\) | 5.22514e8 | 1.18501 | ||||||||
\(296\) | 1.65719e8 | 0.371407 | ||||||||
\(297\) | −2.16312e9 | −4.79108 | ||||||||
\(298\) | −1.99740e7 | −0.0437228 | ||||||||
\(299\) | 4.17606e7 | 0.0903477 | ||||||||
\(300\) | −1.38732e8 | −0.296656 | ||||||||
\(301\) | 5.68588e7 | 0.120175 | ||||||||
\(302\) | 1.91841e8 | 0.400791 | ||||||||
\(303\) | 1.33547e9 | 2.75795 | ||||||||
\(304\) | −1.52166e8 | −0.310643 | ||||||||
\(305\) | −7.70274e8 | −1.55452 | ||||||||
\(306\) | 3.90475e8 | 0.779055 | ||||||||
\(307\) | −4.75520e7 | −0.0937960 | −0.0468980 | − | 0.998900i | \(-0.514934\pi\) | ||||
−0.0468980 | + | 0.998900i | \(0.514934\pi\) | |||||||
\(308\) | −9.01467e7 | −0.175801 | ||||||||
\(309\) | −5.98249e8 | −1.15353 | ||||||||
\(310\) | 7.45028e7 | 0.142039 | ||||||||
\(311\) | −3.02841e8 | −0.570892 | −0.285446 | − | 0.958395i | \(-0.592142\pi\) | ||||
−0.285446 | + | 0.958395i | \(0.592142\pi\) | |||||||
\(312\) | −9.78632e7 | −0.182422 | ||||||||
\(313\) | −6.31685e8 | −1.16438 | −0.582191 | − | 0.813052i | \(-0.697804\pi\) | ||||
−0.582191 | + | 0.813052i | \(0.697804\pi\) | |||||||
\(314\) | 1.36440e8 | 0.248707 | ||||||||
\(315\) | −3.12700e8 | −0.563690 | ||||||||
\(316\) | 4.82278e7 | 0.0859791 | ||||||||
\(317\) | 7.93332e8 | 1.39877 | 0.699387 | − | 0.714743i | \(-0.253456\pi\) | ||||
0.699387 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(318\) | 1.02259e9 | 1.78322 | ||||||||
\(319\) | 1.35990e9 | 2.34553 | ||||||||
\(320\) | 8.41482e7 | 0.143556 | ||||||||
\(321\) | 1.32264e9 | 2.23189 | ||||||||
\(322\) | −2.75236e7 | −0.0459420 | ||||||||
\(323\) | −3.36913e8 | −0.556300 | ||||||||
\(324\) | 7.94401e8 | 1.29757 | ||||||||
\(325\) | 5.47405e7 | 0.0884538 | ||||||||
\(326\) | −5.87669e8 | −0.939444 | ||||||||
\(327\) | −5.85737e8 | −0.926372 | ||||||||
\(328\) | 4.07200e8 | 0.637161 | ||||||||
\(329\) | 8.09868e7 | 0.125380 | ||||||||
\(330\) | −1.73862e9 | −2.66322 | ||||||||
\(331\) | −1.21628e9 | −1.84346 | −0.921731 | − | 0.387829i | \(-0.873225\pi\) | ||||
−0.921731 | + | 0.387829i | \(0.873225\pi\) | |||||||
\(332\) | −7.80219e7 | −0.117013 | ||||||||
\(333\) | 1.74199e9 | 2.58518 | ||||||||
\(334\) | 3.73488e8 | 0.548484 | ||||||||
\(335\) | −2.05652e7 | −0.0298866 | ||||||||
\(336\) | 6.44997e7 | 0.0927620 | ||||||||
\(337\) | −1.51221e8 | −0.215232 | −0.107616 | − | 0.994193i | \(-0.534322\pi\) | ||||
−0.107616 | + | 0.994193i | \(0.534322\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 1.00304e9 | 1.39836 | ||||||||
\(340\) | 1.86314e8 | 0.257080 | ||||||||
\(341\) | 2.25771e8 | 0.308339 | ||||||||
\(342\) | −1.59953e9 | −2.16223 | ||||||||
\(343\) | 2.92193e8 | 0.390967 | ||||||||
\(344\) | −1.60838e8 | −0.213027 | ||||||||
\(345\) | −5.30836e8 | −0.695975 | ||||||||
\(346\) | −6.24745e8 | −0.810842 | ||||||||
\(347\) | −5.97234e8 | −0.767347 | −0.383673 | − | 0.923469i | \(-0.625341\pi\) | ||||
−0.383673 | + | 0.923469i | \(0.625341\pi\) | |||||||
\(348\) | −9.73008e8 | −1.23762 | ||||||||
\(349\) | 1.19600e8 | 0.150606 | 0.0753029 | − | 0.997161i | \(-0.476008\pi\) | ||||
0.0753029 | + | 0.997161i | \(0.476008\pi\) | |||||||
\(350\) | −3.60784e7 | −0.0449789 | ||||||||
\(351\) | −6.10689e8 | −0.753781 | ||||||||
\(352\) | 2.55001e8 | 0.311632 | ||||||||
\(353\) | −4.66414e8 | −0.564366 | −0.282183 | − | 0.959361i | \(-0.591058\pi\) | ||||
−0.282183 | + | 0.959361i | \(0.591058\pi\) | |||||||
\(354\) | −1.13293e9 | −1.35735 | ||||||||
\(355\) | −1.03485e8 | −0.122766 | ||||||||
\(356\) | 2.16981e8 | 0.254887 | ||||||||
\(357\) | 1.42810e8 | 0.166119 | ||||||||
\(358\) | −4.44931e8 | −0.512509 | ||||||||
\(359\) | −7.70102e8 | −0.878451 | −0.439225 | − | 0.898377i | \(-0.644747\pi\) | ||||
−0.439225 | + | 0.898377i | \(0.644747\pi\) | |||||||
\(360\) | 8.84542e8 | 0.999217 | ||||||||
\(361\) | 4.86251e8 | 0.543983 | ||||||||
\(362\) | −9.55477e8 | −1.05862 | ||||||||
\(363\) | −3.57329e9 | −3.92099 | ||||||||
\(364\) | −2.54500e7 | −0.0276588 | ||||||||
\(365\) | −1.42999e9 | −1.53924 | ||||||||
\(366\) | 1.67013e9 | 1.78060 | ||||||||
\(367\) | −8.55319e8 | −0.903227 | −0.451613 | − | 0.892214i | \(-0.649151\pi\) | ||||
−0.451613 | + | 0.892214i | \(0.649151\pi\) | |||||||
\(368\) | 7.78568e7 | 0.0814384 | ||||||||
\(369\) | 4.28037e9 | 4.43495 | ||||||||
\(370\) | 8.31182e8 | 0.853081 | ||||||||
\(371\) | 2.65931e8 | 0.270371 | ||||||||
\(372\) | −1.61539e8 | −0.162696 | ||||||||
\(373\) | −5.29609e8 | −0.528414 | −0.264207 | − | 0.964466i | \(-0.585110\pi\) | ||||
−0.264207 | + | 0.964466i | \(0.585110\pi\) | |||||||
\(374\) | 5.64600e8 | 0.558072 | ||||||||
\(375\) | 1.48597e9 | 1.45512 | ||||||||
\(376\) | −2.29090e8 | −0.222253 | ||||||||
\(377\) | 3.83926e8 | 0.369022 | ||||||||
\(378\) | 4.02493e8 | 0.383299 | ||||||||
\(379\) | 1.98358e9 | 1.87159 | 0.935797 | − | 0.352540i | \(-0.114682\pi\) | ||||
0.935797 | + | 0.352540i | \(0.114682\pi\) | |||||||
\(380\) | −7.63210e8 | −0.713512 | ||||||||
\(381\) | −1.79828e9 | −1.66579 | ||||||||
\(382\) | 8.43877e8 | 0.774564 | ||||||||
\(383\) | 8.98756e8 | 0.817422 | 0.408711 | − | 0.912664i | \(-0.365978\pi\) | ||||
0.408711 | + | 0.912664i | \(0.365978\pi\) | |||||||
\(384\) | −1.82452e8 | −0.164433 | ||||||||
\(385\) | −4.52142e8 | −0.403796 | ||||||||
\(386\) | 1.69647e8 | 0.150138 | ||||||||
\(387\) | −1.69069e9 | −1.48277 | ||||||||
\(388\) | 1.04242e8 | 0.0906003 | ||||||||
\(389\) | 1.82475e9 | 1.57174 | 0.785868 | − | 0.618395i | \(-0.212217\pi\) | ||||
0.785868 | + | 0.618395i | \(0.212217\pi\) | |||||||
\(390\) | −4.90845e8 | −0.419004 | ||||||||
\(391\) | 1.72384e8 | 0.145840 | ||||||||
\(392\) | −4.04880e8 | −0.339489 | ||||||||
\(393\) | 1.66125e9 | 1.38058 | ||||||||
\(394\) | −1.33228e9 | −1.09739 | ||||||||
\(395\) | 2.41893e8 | 0.197485 | ||||||||
\(396\) | 2.68049e9 | 2.16911 | ||||||||
\(397\) | 4.93083e8 | 0.395506 | 0.197753 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197753 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(398\) | −1.01081e9 | −0.803668 | ||||||||
\(399\) | −5.85001e8 | −0.461054 | ||||||||
\(400\) | 1.02056e8 | 0.0797312 | ||||||||
\(401\) | −5.68280e8 | −0.440105 | −0.220053 | − | 0.975488i | \(-0.570623\pi\) | ||||
−0.220053 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(402\) | 4.45899e7 | 0.0342331 | ||||||||
\(403\) | 6.37394e7 | 0.0485110 | ||||||||
\(404\) | −9.82417e8 | −0.741244 | ||||||||
\(405\) | 3.98442e9 | 2.98039 | ||||||||
\(406\) | −2.53038e8 | −0.187648 | ||||||||
\(407\) | 2.51879e9 | 1.85188 | ||||||||
\(408\) | −4.03970e8 | −0.294468 | ||||||||
\(409\) | −1.28472e9 | −0.928489 | −0.464245 | − | 0.885707i | \(-0.653674\pi\) | ||||
−0.464245 | + | 0.885707i | \(0.653674\pi\) | |||||||
\(410\) | 2.04236e9 | 1.46349 | ||||||||
\(411\) | −2.58304e9 | −1.83520 | ||||||||
\(412\) | 4.40091e8 | 0.310029 | ||||||||
\(413\) | −2.94626e8 | −0.205801 | ||||||||
\(414\) | 8.18408e8 | 0.566851 | ||||||||
\(415\) | −3.91329e8 | −0.268765 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | −1.35418e9 | −0.914532 | ||||||||
\(418\) | −2.31281e9 | −1.54890 | ||||||||
\(419\) | 2.74847e8 | 0.182533 | 0.0912667 | − | 0.995826i | \(-0.470908\pi\) | ||||
0.0912667 | + | 0.995826i | \(0.470908\pi\) | |||||||
\(420\) | 3.23506e8 | 0.213064 | ||||||||
\(421\) | 7.51368e8 | 0.490756 | 0.245378 | − | 0.969428i | \(-0.421088\pi\) | ||||
0.245378 | + | 0.969428i | \(0.421088\pi\) | |||||||
\(422\) | 8.68568e8 | 0.562613 | ||||||||
\(423\) | −2.40813e9 | −1.54699 | ||||||||
\(424\) | −7.52247e8 | −0.479270 | ||||||||
\(425\) | 2.25963e8 | 0.142783 | ||||||||
\(426\) | 2.24379e8 | 0.140620 | ||||||||
\(427\) | 4.34329e8 | 0.269974 | ||||||||
\(428\) | −9.72974e8 | −0.599857 | ||||||||
\(429\) | −1.48744e9 | −0.909578 | ||||||||
\(430\) | −8.06704e8 | −0.489299 | ||||||||
\(431\) | −1.30756e8 | −0.0786668 | −0.0393334 | − | 0.999226i | \(-0.512523\pi\) | ||||
−0.0393334 | + | 0.999226i | \(0.512523\pi\) | |||||||
\(432\) | −1.13854e9 | −0.679449 | ||||||||
\(433\) | 1.66736e9 | 0.987010 | 0.493505 | − | 0.869743i | \(-0.335716\pi\) | ||||
0.493505 | + | 0.869743i | \(0.335716\pi\) | |||||||
\(434\) | −4.20094e7 | −0.0246679 | ||||||||
\(435\) | −4.88024e9 | −2.84269 | ||||||||
\(436\) | 4.30887e8 | 0.248978 | ||||||||
\(437\) | −7.06147e8 | −0.404772 | ||||||||
\(438\) | 3.10053e9 | 1.76310 | ||||||||
\(439\) | 2.31478e9 | 1.30582 | 0.652910 | − | 0.757436i | \(-0.273548\pi\) | ||||
0.652910 | + | 0.757436i | \(0.273548\pi\) | |||||||
\(440\) | 1.27899e9 | 0.715784 | ||||||||
\(441\) | −4.25599e9 | −2.36301 | ||||||||
\(442\) | 1.59397e8 | 0.0878014 | ||||||||
\(443\) | −6.90047e8 | −0.377108 | −0.188554 | − | 0.982063i | \(-0.560380\pi\) | ||||
−0.188554 | + | 0.982063i | \(0.560380\pi\) | |||||||
\(444\) | −1.80219e9 | −0.977147 | ||||||||
\(445\) | 1.08830e9 | 0.585446 | ||||||||
\(446\) | −1.00482e9 | −0.536311 | ||||||||
\(447\) | 2.17217e8 | 0.115032 | ||||||||
\(448\) | −4.74481e7 | −0.0249313 | ||||||||
\(449\) | 2.63806e9 | 1.37538 | 0.687690 | − | 0.726004i | \(-0.258625\pi\) | ||||
0.687690 | + | 0.726004i | \(0.258625\pi\) | |||||||
\(450\) | 1.07278e9 | 0.554968 | ||||||||
\(451\) | 6.18912e9 | 3.17695 | ||||||||
\(452\) | −7.37870e8 | −0.375833 | ||||||||
\(453\) | −2.08627e9 | −1.05445 | ||||||||
\(454\) | 1.52619e9 | 0.765445 | ||||||||
\(455\) | −1.27648e8 | −0.0635293 | ||||||||
\(456\) | 1.65481e9 | 0.817280 | ||||||||
\(457\) | −6.16222e8 | −0.302016 | −0.151008 | − | 0.988533i | \(-0.548252\pi\) | ||||
−0.151008 | + | 0.988533i | \(0.548252\pi\) | |||||||
\(458\) | −4.23129e8 | −0.205799 | ||||||||
\(459\) | −2.52086e9 | −1.21676 | ||||||||
\(460\) | 3.90500e8 | 0.187055 | ||||||||
\(461\) | 1.23621e9 | 0.587679 | 0.293839 | − | 0.955855i | \(-0.405067\pi\) | ||||
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(462\) | 9.80345e8 | 0.462522 | ||||||||
\(463\) | 6.78469e7 | 0.0317685 | 0.0158843 | − | 0.999874i | \(-0.494944\pi\) | ||||
0.0158843 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(464\) | 7.15776e8 | 0.332632 | ||||||||
\(465\) | −8.10218e8 | −0.373694 | ||||||||
\(466\) | 1.21003e9 | 0.553919 | ||||||||
\(467\) | −1.17502e9 | −0.533869 | −0.266934 | − | 0.963715i | \(-0.586011\pi\) | ||||
−0.266934 | + | 0.963715i | \(0.586011\pi\) | |||||||
\(468\) | 7.56752e8 | 0.341266 | ||||||||
\(469\) | 1.15959e7 | 0.00519040 | ||||||||
\(470\) | −1.14903e9 | −0.510491 | ||||||||
\(471\) | −1.48379e9 | −0.654332 | ||||||||
\(472\) | 8.33418e8 | 0.364809 | ||||||||
\(473\) | −2.44461e9 | −1.06218 | ||||||||
\(474\) | −5.24478e8 | −0.226205 | ||||||||
\(475\) | −9.25629e8 | −0.396287 | ||||||||
\(476\) | −1.05055e8 | −0.0446471 | ||||||||
\(477\) | −7.90741e9 | −3.33595 | ||||||||
\(478\) | 2.09533e9 | 0.877517 | ||||||||
\(479\) | 3.96154e8 | 0.164699 | 0.0823494 | − | 0.996604i | \(-0.473758\pi\) | ||||
0.0823494 | + | 0.996604i | \(0.473758\pi\) | |||||||
\(480\) | −9.15112e8 | −0.377685 | ||||||||
\(481\) | 7.11101e8 | 0.291356 | ||||||||
\(482\) | −1.05401e9 | −0.428728 | ||||||||
\(483\) | 2.99319e8 | 0.120870 | ||||||||
\(484\) | 2.62863e9 | 1.05383 | ||||||||
\(485\) | 5.22836e8 | 0.208099 | ||||||||
\(486\) | −3.77584e9 | −1.49206 | ||||||||
\(487\) | −3.03665e9 | −1.19136 | −0.595680 | − | 0.803222i | \(-0.703117\pi\) | ||||
−0.595680 | + | 0.803222i | \(0.703117\pi\) | |||||||
\(488\) | −1.22860e9 | −0.478565 | ||||||||
\(489\) | 6.39090e9 | 2.47162 | ||||||||
\(490\) | −2.03073e9 | −0.779768 | ||||||||
\(491\) | −2.91974e9 | −1.11316 | −0.556582 | − | 0.830793i | \(-0.687887\pi\) | ||||
−0.556582 | + | 0.830793i | \(0.687887\pi\) | |||||||
\(492\) | −4.42830e9 | −1.67633 | ||||||||
\(493\) | 1.58481e9 | 0.595679 | ||||||||
\(494\) | −6.52948e8 | −0.243688 | ||||||||
\(495\) | 1.34444e10 | 4.98221 | ||||||||
\(496\) | 1.18833e8 | 0.0437272 | ||||||||
\(497\) | 5.83513e7 | 0.0213208 | ||||||||
\(498\) | 8.48488e8 | 0.307853 | ||||||||
\(499\) | −1.62343e9 | −0.584898 | −0.292449 | − | 0.956281i | \(-0.594470\pi\) | ||||
−0.292449 | + | 0.956281i | \(0.594470\pi\) | |||||||
\(500\) | −1.09313e9 | −0.391089 | ||||||||
\(501\) | −4.06168e9 | −1.44303 | ||||||||
\(502\) | 1.97649e9 | 0.697320 | ||||||||
\(503\) | 4.75888e9 | 1.66731 | 0.833655 | − | 0.552285i | \(-0.186244\pi\) | ||||
0.833655 | + | 0.552285i | \(0.186244\pi\) | |||||||
\(504\) | −4.98761e8 | −0.173534 | ||||||||
\(505\) | −4.92744e9 | −1.70256 | ||||||||
\(506\) | 1.18336e9 | 0.406061 | ||||||||
\(507\) | −4.19932e8 | −0.143104 | ||||||||
\(508\) | 1.32288e9 | 0.447709 | ||||||||
\(509\) | −9.19375e8 | −0.309016 | −0.154508 | − | 0.987992i | \(-0.549379\pi\) | ||||
−0.154508 | + | 0.987992i | \(0.549379\pi\) | |||||||
\(510\) | −2.02616e9 | −0.676360 | ||||||||
\(511\) | 8.06316e8 | 0.267320 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 1.03264e10 | 3.37706 | ||||||||
\(514\) | 1.81829e9 | 0.590598 | ||||||||
\(515\) | 2.20733e9 | 0.712103 | ||||||||
\(516\) | 1.74911e9 | 0.560460 | ||||||||
\(517\) | −3.48199e9 | −1.10818 | ||||||||
\(518\) | −4.68673e8 | −0.148155 | ||||||||
\(519\) | 6.79410e9 | 2.13327 | ||||||||
\(520\) | 3.61081e8 | 0.112614 | ||||||||
\(521\) | −1.46089e9 | −0.452569 | −0.226284 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226284 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(522\) | 7.52404e9 | 2.31528 | ||||||||
\(523\) | 2.12856e9 | 0.650624 | 0.325312 | − | 0.945607i | \(-0.394531\pi\) | ||||
0.325312 | + | 0.945607i | \(0.394531\pi\) | |||||||
\(524\) | −1.22207e9 | −0.371054 | ||||||||
\(525\) | 3.92352e8 | 0.118336 | ||||||||
\(526\) | −3.40698e9 | −1.02075 | ||||||||
\(527\) | 2.63110e8 | 0.0783069 | ||||||||
\(528\) | −2.77313e9 | −0.819883 | ||||||||
\(529\) | −3.04352e9 | −0.893885 | ||||||||
\(530\) | −3.77299e9 | −1.10083 | ||||||||
\(531\) | 8.76066e9 | 2.53925 | ||||||||
\(532\) | 4.30346e8 | 0.123916 | ||||||||
\(533\) | 1.74730e9 | 0.499830 | ||||||||
\(534\) | −2.35967e9 | −0.670590 | ||||||||
\(535\) | −4.88007e9 | −1.37781 | ||||||||
\(536\) | −3.28018e7 | −0.00920070 | ||||||||
\(537\) | 4.83862e9 | 1.34838 | ||||||||
\(538\) | −4.11323e9 | −1.13879 | ||||||||
\(539\) | −6.15387e9 | −1.69273 | ||||||||
\(540\) | −5.71051e9 | −1.56062 | ||||||||
\(541\) | −1.72479e7 | −0.00468324 | −0.00234162 | − | 0.999997i | \(-0.500745\pi\) | ||||
−0.00234162 | + | 0.999997i | \(0.500745\pi\) | |||||||
\(542\) | 3.65677e8 | 0.0986507 | ||||||||
\(543\) | 1.03908e10 | 2.78516 | ||||||||
\(544\) | 2.97173e8 | 0.0791431 | ||||||||
\(545\) | 2.16117e9 | 0.571874 | ||||||||
\(546\) | 2.76769e8 | 0.0727685 | ||||||||
\(547\) | 7.51154e8 | 0.196234 | 0.0981168 | − | 0.995175i | \(-0.468718\pi\) | ||||
0.0981168 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(548\) | 1.90016e9 | 0.493241 | ||||||||
\(549\) | −1.29147e10 | −3.33105 | ||||||||
\(550\) | 1.55117e9 | 0.397549 | ||||||||
\(551\) | −6.49196e9 | −1.65328 | ||||||||
\(552\) | −8.46692e8 | −0.214259 | ||||||||
\(553\) | −1.36394e8 | −0.0342972 | ||||||||
\(554\) | −2.19171e9 | −0.547645 | ||||||||
\(555\) | −9.03910e9 | −2.24440 | ||||||||
\(556\) | 9.96175e8 | 0.245795 | ||||||||
\(557\) | 3.00701e9 | 0.737295 | 0.368647 | − | 0.929569i | \(-0.379821\pi\) | ||||
0.368647 | + | 0.929569i | \(0.379821\pi\) | |||||||
\(558\) | 1.24914e9 | 0.304363 | ||||||||
\(559\) | −6.90159e8 | −0.167112 | ||||||||
\(560\) | −2.37982e8 | −0.0572645 | ||||||||
\(561\) | −6.14002e9 | −1.46825 | ||||||||
\(562\) | 3.37366e9 | 0.801722 | ||||||||
\(563\) | 2.82880e9 | 0.668070 | 0.334035 | − | 0.942561i | \(-0.391590\pi\) | ||||
0.334035 | + | 0.942561i | \(0.391590\pi\) | |||||||
\(564\) | 2.49135e9 | 0.584734 | ||||||||
\(565\) | −3.70088e9 | −0.863248 | ||||||||
\(566\) | 3.05566e9 | 0.708349 | ||||||||
\(567\) | −2.24667e9 | −0.517604 | ||||||||
\(568\) | −1.65060e8 | −0.0377940 | ||||||||
\(569\) | 7.67290e9 | 1.74609 | 0.873045 | − | 0.487639i | \(-0.162142\pi\) | ||||
0.873045 | + | 0.487639i | \(0.162142\pi\) | |||||||
\(570\) | 8.29990e9 | 1.87720 | ||||||||
\(571\) | −3.09363e9 | −0.695411 | −0.347706 | − | 0.937604i | \(-0.613039\pi\) | ||||
−0.347706 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(572\) | 1.09421e9 | 0.244464 | ||||||||
\(573\) | −9.17717e9 | −2.03783 | ||||||||
\(574\) | −1.15161e9 | −0.254164 | ||||||||
\(575\) | 4.73603e8 | 0.103891 | ||||||||
\(576\) | 1.41086e9 | 0.307613 | ||||||||
\(577\) | 3.71815e9 | 0.805770 | 0.402885 | − | 0.915251i | \(-0.368007\pi\) | ||||
0.402885 | + | 0.915251i | \(0.368007\pi\) | |||||||
\(578\) | −2.62474e9 | −0.565377 | ||||||||
\(579\) | −1.84491e9 | −0.395003 | ||||||||
\(580\) | 3.59006e9 | 0.764019 | ||||||||
\(581\) | 2.20656e8 | 0.0466765 | ||||||||
\(582\) | −1.13363e9 | −0.238363 | ||||||||
\(583\) | −1.14336e10 | −2.38969 | ||||||||
\(584\) | −2.28085e9 | −0.473862 | ||||||||
\(585\) | 3.79559e9 | 0.783851 | ||||||||
\(586\) | −3.23866e9 | −0.664850 | ||||||||
\(587\) | −2.74853e9 | −0.560876 | −0.280438 | − | 0.959872i | \(-0.590480\pi\) | ||||
−0.280438 | + | 0.959872i | \(0.590480\pi\) | |||||||
\(588\) | 4.40307e9 | 0.893173 | ||||||||
\(589\) | −1.07780e9 | −0.217337 | ||||||||
\(590\) | 4.18011e9 | 0.837927 | ||||||||
\(591\) | 1.44886e10 | 2.88715 | ||||||||
\(592\) | 1.32575e9 | 0.262624 | ||||||||
\(593\) | −9.11262e9 | −1.79453 | −0.897267 | − | 0.441488i | \(-0.854451\pi\) | ||||
−0.897267 | + | 0.441488i | \(0.854451\pi\) | |||||||
\(594\) | −1.73050e10 | −3.38781 | ||||||||
\(595\) | −5.26918e8 | −0.102550 | ||||||||
\(596\) | −1.59792e8 | −0.0309167 | ||||||||
\(597\) | 1.09925e10 | 2.11440 | ||||||||
\(598\) | 3.34085e8 | 0.0638855 | ||||||||
\(599\) | −5.52493e9 | −1.05035 | −0.525174 | − | 0.850995i | \(-0.676000\pi\) | ||||
−0.525174 | + | 0.850995i | \(0.676000\pi\) | |||||||
\(600\) | −1.10986e9 | −0.209767 | ||||||||
\(601\) | −1.78219e9 | −0.334883 | −0.167441 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167441 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(602\) | 4.54870e8 | 0.0849767 | ||||||||
\(603\) | −3.44803e8 | −0.0640414 | ||||||||
\(604\) | 1.53473e9 | 0.283402 | ||||||||
\(605\) | 1.31842e10 | 2.42053 | ||||||||
\(606\) | 1.06838e10 | 1.95016 | ||||||||
\(607\) | 9.53705e9 | 1.73083 | 0.865414 | − | 0.501058i | \(-0.167056\pi\) | ||||
0.865414 | + | 0.501058i | \(0.167056\pi\) | |||||||
\(608\) | −1.21733e9 | −0.219658 | ||||||||
\(609\) | 2.75179e9 | 0.493690 | ||||||||
\(610\) | −6.16219e9 | −1.09921 | ||||||||
\(611\) | −9.83028e8 | −0.174350 | ||||||||
\(612\) | 3.12380e9 | 0.550875 | ||||||||
\(613\) | −1.18627e9 | −0.208004 | −0.104002 | − | 0.994577i | \(-0.533165\pi\) | ||||
−0.104002 | + | 0.994577i | \(0.533165\pi\) | |||||||
\(614\) | −3.80416e8 | −0.0663238 | ||||||||
\(615\) | −2.22107e10 | −3.85034 | ||||||||
\(616\) | −7.21174e8 | −0.124310 | ||||||||
\(617\) | 1.32256e9 | 0.226682 | 0.113341 | − | 0.993556i | \(-0.463845\pi\) | ||||
0.113341 | + | 0.993556i | \(0.463845\pi\) | |||||||
\(618\) | −4.78599e9 | −0.815666 | ||||||||
\(619\) | −3.59450e9 | −0.609147 | −0.304573 | − | 0.952489i | \(-0.598514\pi\) | ||||
−0.304573 | + | 0.952489i | \(0.598514\pi\) | |||||||
\(620\) | 5.96023e8 | 0.100437 | ||||||||
\(621\) | −5.28356e9 | −0.885332 | ||||||||
\(622\) | −2.42273e9 | −0.403681 | ||||||||
\(623\) | −6.13650e8 | −0.101675 | ||||||||
\(624\) | −7.82905e8 | −0.128992 | ||||||||
\(625\) | −7.42927e9 | −1.21721 | ||||||||
\(626\) | −5.05348e9 | −0.823343 | ||||||||
\(627\) | 2.51518e10 | 4.07505 | ||||||||
\(628\) | 1.09152e9 | 0.175863 | ||||||||
\(629\) | 2.93535e9 | 0.470309 | ||||||||
\(630\) | −2.50160e9 | −0.398589 | ||||||||
\(631\) | 7.49102e6 | 0.00118697 | 0.000593483 | − | 1.00000i | \(-0.499811\pi\) | ||||
0.000593483 | 1.00000i | \(0.499811\pi\) | ||||||||
\(632\) | 3.85823e8 | 0.0607964 | ||||||||
\(633\) | −9.44567e9 | −1.48020 | ||||||||
\(634\) | 6.34666e9 | 0.989083 | ||||||||
\(635\) | 6.63505e9 | 1.02834 | ||||||||
\(636\) | 8.18068e9 | 1.26093 | ||||||||
\(637\) | −1.73735e9 | −0.266317 | ||||||||
\(638\) | 1.08792e10 | 1.65854 | ||||||||
\(639\) | −1.73507e9 | −0.263065 | ||||||||
\(640\) | 6.73186e8 | 0.101509 | ||||||||
\(641\) | 4.06396e9 | 0.609462 | 0.304731 | − | 0.952438i | \(-0.401433\pi\) | ||||
0.304731 | + | 0.952438i | \(0.401433\pi\) | |||||||
\(642\) | 1.05811e10 | 1.57818 | ||||||||
\(643\) | 1.56544e6 | 0.000232219 0 | 0.000116109 | − | 1.00000i | \(-0.499963\pi\) | ||||
0.000116109 | 1.00000i | \(0.499963\pi\) | ||||||||
\(644\) | −2.20189e8 | −0.0324859 | ||||||||
\(645\) | 8.77290e9 | 1.28731 | ||||||||
\(646\) | −2.69531e9 | −0.393364 | ||||||||
\(647\) | 1.31025e10 | 1.90191 | 0.950956 | − | 0.309325i | \(-0.100103\pi\) | ||||
0.950956 | + | 0.309325i | \(0.100103\pi\) | |||||||
\(648\) | 6.35521e9 | 0.917524 | ||||||||
\(649\) | 1.26673e10 | 1.81898 | ||||||||
\(650\) | 4.37924e8 | 0.0625463 | ||||||||
\(651\) | 4.56852e8 | 0.0648996 | ||||||||
\(652\) | −4.70135e9 | −0.664287 | ||||||||
\(653\) | 7.63326e9 | 1.07279 | 0.536394 | − | 0.843968i | \(-0.319786\pi\) | ||||
0.536394 | + | 0.843968i | \(0.319786\pi\) | |||||||
\(654\) | −4.68589e9 | −0.655044 | ||||||||
\(655\) | −6.12945e9 | −0.852269 | ||||||||
\(656\) | 3.25760e9 | 0.450541 | ||||||||
\(657\) | −2.39756e10 | −3.29831 | ||||||||
\(658\) | 6.47895e8 | 0.0886571 | ||||||||
\(659\) | −9.25900e9 | −1.26027 | −0.630137 | − | 0.776484i | \(-0.717001\pi\) | ||||
−0.630137 | + | 0.776484i | \(0.717001\pi\) | |||||||
\(660\) | −1.39090e10 | −1.88318 | ||||||||
\(661\) | 4.79962e9 | 0.646401 | 0.323201 | − | 0.946330i | \(-0.395241\pi\) | ||||
0.323201 | + | 0.946330i | \(0.395241\pi\) | |||||||
\(662\) | −9.73021e9 | −1.30352 | ||||||||
\(663\) | −1.73344e9 | −0.231000 | ||||||||
\(664\) | −6.24175e8 | −0.0827405 | ||||||||
\(665\) | 2.15845e9 | 0.284621 | ||||||||
\(666\) | 1.39359e10 | 1.82799 | ||||||||
\(667\) | 3.32165e9 | 0.433424 | ||||||||
\(668\) | 2.98791e9 | 0.387837 | ||||||||
\(669\) | 1.09274e10 | 1.41100 | ||||||||
\(670\) | −1.64521e8 | −0.0211330 | ||||||||
\(671\) | −1.86737e10 | −2.38618 | ||||||||
\(672\) | 5.15998e8 | 0.0655927 | ||||||||
\(673\) | −1.08997e10 | −1.37836 | −0.689182 | − | 0.724589i | \(-0.742030\pi\) | ||||
−0.689182 | + | 0.724589i | \(0.742030\pi\) | |||||||
\(674\) | −1.20977e9 | −0.152192 | ||||||||
\(675\) | −6.92578e9 | −0.866773 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 3.44099e9 | 0.426210 | 0.213105 | − | 0.977029i | \(-0.431642\pi\) | ||||
0.213105 | + | 0.977029i | \(0.431642\pi\) | |||||||
\(678\) | 8.02434e9 | 0.988793 | ||||||||
\(679\) | −2.94808e8 | −0.0361406 | ||||||||
\(680\) | 1.49051e9 | 0.181783 | ||||||||
\(681\) | −1.65974e10 | −2.01384 | ||||||||
\(682\) | 1.80617e9 | 0.218029 | ||||||||
\(683\) | 5.53553e9 | 0.664794 | 0.332397 | − | 0.943140i | \(-0.392143\pi\) | ||||
0.332397 | + | 0.943140i | \(0.392143\pi\) | |||||||
\(684\) | −1.27962e10 | −1.52892 | ||||||||
\(685\) | 9.53051e9 | 1.13292 | ||||||||
\(686\) | 2.33754e9 | 0.276455 | ||||||||
\(687\) | 4.60153e9 | 0.541444 | ||||||||
\(688\) | −1.28671e9 | −0.150633 | ||||||||
\(689\) | −3.22790e9 | −0.375970 | ||||||||
\(690\) | −4.24669e9 | −0.492129 | ||||||||
\(691\) | 4.21595e8 | 0.0486097 | 0.0243048 | − | 0.999705i | \(-0.492263\pi\) | ||||
0.0243048 | + | 0.999705i | \(0.492263\pi\) | |||||||
\(692\) | −4.99796e9 | −0.573352 | ||||||||
\(693\) | −7.58077e9 | −0.865261 | ||||||||
\(694\) | −4.77788e9 | −0.542596 | ||||||||
\(695\) | 4.99644e9 | 0.564565 | ||||||||
\(696\) | −7.78406e9 | −0.875133 | ||||||||
\(697\) | 7.21268e9 | 0.806830 | ||||||||
\(698\) | 9.56799e8 | 0.106494 | ||||||||
\(699\) | −1.31591e10 | −1.45732 | ||||||||
\(700\) | −2.88627e8 | −0.0318049 | ||||||||
\(701\) | −5.14995e9 | −0.564663 | −0.282332 | − | 0.959317i | \(-0.591108\pi\) | ||||
−0.282332 | + | 0.959317i | \(0.591108\pi\) | |||||||
\(702\) | −4.88551e9 | −0.533004 | ||||||||
\(703\) | −1.20243e10 | −1.30532 | ||||||||
\(704\) | 2.04000e9 | 0.220357 | ||||||||
\(705\) | 1.24957e10 | 1.34307 | ||||||||
\(706\) | −3.73132e9 | −0.399067 | ||||||||
\(707\) | 2.77840e9 | 0.295683 | ||||||||
\(708\) | −9.06342e9 | −0.959789 | ||||||||
\(709\) | 1.05683e10 | 1.11363 | 0.556817 | − | 0.830635i | \(-0.312022\pi\) | ||||
0.556817 | + | 0.830635i | \(0.312022\pi\) | |||||||
\(710\) | −8.27880e8 | −0.0868086 | ||||||||
\(711\) | 4.05566e9 | 0.423173 | ||||||||
\(712\) | 1.73585e9 | 0.180232 | ||||||||
\(713\) | 5.51460e8 | 0.0569772 | ||||||||
\(714\) | 1.14248e9 | 0.117464 | ||||||||
\(715\) | 5.48815e9 | 0.561507 | ||||||||
\(716\) | −3.55944e9 | −0.362399 | ||||||||
\(717\) | −2.27868e10 | −2.30869 | ||||||||
\(718\) | −6.16081e9 | −0.621159 | ||||||||
\(719\) | 1.53690e10 | 1.54204 | 0.771020 | − | 0.636811i | \(-0.219747\pi\) | ||||
0.771020 | + | 0.636811i | \(0.219747\pi\) | |||||||
\(720\) | 7.07634e9 | 0.706553 | ||||||||
\(721\) | −1.24463e9 | −0.123671 | ||||||||
\(722\) | 3.89001e9 | 0.384654 | ||||||||
\(723\) | 1.14624e10 | 1.12795 | ||||||||
\(724\) | −7.64381e9 | −0.748557 | ||||||||
\(725\) | 4.35407e9 | 0.424339 | ||||||||
\(726\) | −2.85864e10 | −2.77256 | ||||||||
\(727\) | 4.88599e9 | 0.471609 | 0.235804 | − | 0.971801i | \(-0.424228\pi\) | ||||
0.235804 | + | 0.971801i | \(0.424228\pi\) | |||||||
\(728\) | −2.03600e8 | −0.0195577 | ||||||||
\(729\) | 1.39161e10 | 1.33036 | ||||||||
\(730\) | −1.14399e10 | −1.08841 | ||||||||
\(731\) | −2.84891e9 | −0.269754 | ||||||||
\(732\) | 1.33610e10 | 1.25907 | ||||||||
\(733\) | 3.59889e9 | 0.337524 | 0.168762 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168762 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(734\) | −6.84255e9 | −0.638678 | ||||||||
\(735\) | 2.20842e10 | 2.05152 | ||||||||
\(736\) | 6.22854e8 | 0.0575856 | ||||||||
\(737\) | −4.98562e8 | −0.0458757 | ||||||||
\(738\) | 3.42430e10 | 3.13598 | ||||||||
\(739\) | 2.78886e9 | 0.254198 | 0.127099 | − | 0.991890i | \(-0.459433\pi\) | ||||
0.127099 | + | 0.991890i | \(0.459433\pi\) | |||||||
\(740\) | 6.64946e9 | 0.603219 | ||||||||
\(741\) | 7.10081e9 | 0.641127 | ||||||||
\(742\) | 2.12745e9 | 0.191181 | ||||||||
\(743\) | −3.08130e9 | −0.275597 | −0.137798 | − | 0.990460i | \(-0.544003\pi\) | ||||
−0.137798 | + | 0.990460i | \(0.544003\pi\) | |||||||
\(744\) | −1.29231e9 | −0.115043 | ||||||||
\(745\) | −8.01457e8 | −0.0710122 | ||||||||
\(746\) | −4.23687e9 | −0.373645 | ||||||||
\(747\) | −6.56115e9 | −0.575915 | ||||||||
\(748\) | 4.51680e9 | 0.394616 | ||||||||
\(749\) | 2.75169e9 | 0.239284 | ||||||||
\(750\) | 1.18877e10 | 1.02893 | ||||||||
\(751\) | −6.41281e8 | −0.0552470 | −0.0276235 | − | 0.999618i | \(-0.508794\pi\) | ||||
−0.0276235 | + | 0.999618i | \(0.508794\pi\) | |||||||
\(752\) | −1.83272e9 | −0.157157 | ||||||||
\(753\) | −2.14943e10 | −1.83460 | ||||||||
\(754\) | 3.07141e9 | 0.260938 | ||||||||
\(755\) | 7.69763e9 | 0.650943 | ||||||||
\(756\) | 3.21995e9 | 0.271033 | ||||||||
\(757\) | −1.60219e10 | −1.34239 | −0.671195 | − | 0.741280i | \(-0.734219\pi\) | ||||
−0.671195 | + | 0.741280i | \(0.734219\pi\) | |||||||
\(758\) | 1.58686e10 | 1.32342 | ||||||||
\(759\) | −1.28691e10 | −1.06832 | ||||||||
\(760\) | −6.10568e9 | −0.504529 | ||||||||
\(761\) | −5.73623e9 | −0.471824 | −0.235912 | − | 0.971774i | \(-0.575808\pi\) | ||||
−0.235912 | + | 0.971774i | \(0.575808\pi\) | |||||||
\(762\) | −1.43863e10 | −1.17789 | ||||||||
\(763\) | −1.21860e9 | −0.0993175 | ||||||||
\(764\) | 6.75102e9 | 0.547700 | ||||||||
\(765\) | 1.56678e10 | 1.26530 | ||||||||
\(766\) | 7.19005e9 | 0.578005 | ||||||||
\(767\) | 3.57621e9 | 0.286180 | ||||||||
\(768\) | −1.45962e9 | −0.116272 | ||||||||
\(769\) | 2.45874e10 | 1.94971 | 0.974857 | − | 0.222832i | \(-0.0715300\pi\) | ||||
0.974857 | + | 0.222832i | \(0.0715300\pi\) | |||||||
\(770\) | −3.61714e9 | −0.285527 | ||||||||
\(771\) | −1.97739e10 | −1.55382 | ||||||||
\(772\) | 1.35718e9 | 0.106164 | ||||||||
\(773\) | −1.31517e10 | −1.02413 | −0.512065 | − | 0.858947i | \(-0.671119\pi\) | ||||
−0.512065 | + | 0.858947i | \(0.671119\pi\) | |||||||
\(774\) | −1.35255e10 | −1.04848 | ||||||||
\(775\) | 7.22863e8 | 0.0557828 | ||||||||
\(776\) | 8.33932e8 | 0.0640641 | ||||||||
\(777\) | 5.09682e9 | 0.389785 | ||||||||
\(778\) | 1.45980e10 | 1.11138 | ||||||||
\(779\) | −2.95458e10 | −2.23932 | ||||||||
\(780\) | −3.92676e9 | −0.296281 | ||||||||
\(781\) | −2.50878e9 | −0.188445 | ||||||||
\(782\) | 1.37907e9 | 0.103125 | ||||||||
\(783\) | −4.85744e10 | −3.61611 | ||||||||
\(784\) | −3.23904e9 | −0.240055 | ||||||||
\(785\) | 5.47466e9 | 0.403937 | ||||||||
\(786\) | 1.32900e10 | 0.976218 | ||||||||
\(787\) | −7.38863e9 | −0.540322 | −0.270161 | − | 0.962815i | \(-0.587077\pi\) | ||||
−0.270161 | + | 0.962815i | \(0.587077\pi\) | |||||||
\(788\) | −1.06583e10 | −0.775969 | ||||||||
\(789\) | 3.70509e10 | 2.68552 | ||||||||
\(790\) | 1.93514e9 | 0.139643 | ||||||||
\(791\) | 2.08679e9 | 0.149920 | ||||||||
\(792\) | 2.14440e10 | 1.53379 | ||||||||
\(793\) | −5.27194e9 | −0.375417 | ||||||||
\(794\) | 3.94467e9 | 0.279665 | ||||||||
\(795\) | 4.10312e10 | 2.89621 | ||||||||
\(796\) | −8.08645e9 | −0.568279 | ||||||||
\(797\) | −5.22399e9 | −0.365509 | −0.182754 | − | 0.983159i | \(-0.558501\pi\) | ||||
−0.182754 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(798\) | −4.68001e9 | −0.326014 | ||||||||
\(799\) | −4.05784e9 | −0.281437 | ||||||||
\(800\) | 8.16447e8 | 0.0563785 | ||||||||
\(801\) | 1.82468e10 | 1.25450 | ||||||||
\(802\) | −4.54624e9 | −0.311202 | ||||||||
\(803\) | −3.46671e10 | −2.36273 | ||||||||
\(804\) | 3.56719e8 | 0.0242064 | ||||||||
\(805\) | −1.10438e9 | −0.0746164 | ||||||||
\(806\) | 5.09915e8 | 0.0343024 | ||||||||
\(807\) | 4.47314e10 | 2.99609 | ||||||||
\(808\) | −7.85934e9 | −0.524139 | ||||||||
\(809\) | −7.92102e9 | −0.525970 | −0.262985 | − | 0.964800i | \(-0.584707\pi\) | ||||
−0.262985 | + | 0.964800i | \(0.584707\pi\) | |||||||
\(810\) | 3.18754e10 | 2.10745 | ||||||||
\(811\) | −8.16607e9 | −0.537576 | −0.268788 | − | 0.963199i | \(-0.586623\pi\) | ||||
−0.268788 | + | 0.963199i | \(0.586623\pi\) | |||||||
\(812\) | −2.02430e9 | −0.132687 | ||||||||
\(813\) | −3.97674e9 | −0.259543 | ||||||||
\(814\) | 2.01503e10 | 1.30947 | ||||||||
\(815\) | −2.35802e10 | −1.52579 | ||||||||
\(816\) | −3.23176e9 | −0.208220 | ||||||||
\(817\) | 1.16702e10 | 0.748688 | ||||||||
\(818\) | −1.02778e10 | −0.656541 | ||||||||
\(819\) | −2.14019e9 | −0.136132 | ||||||||
\(820\) | 1.63389e10 | 1.03484 | ||||||||
\(821\) | 2.63749e10 | 1.66338 | 0.831688 | − | 0.555244i | \(-0.187375\pi\) | ||||
0.831688 | + | 0.555244i | \(0.187375\pi\) | |||||||
\(822\) | −2.06643e10 | −1.29768 | ||||||||
\(823\) | 2.04085e10 | 1.27618 | 0.638090 | − | 0.769962i | \(-0.279725\pi\) | ||||
0.638090 | + | 0.769962i | \(0.279725\pi\) | |||||||
\(824\) | 3.52073e9 | 0.219224 | ||||||||
\(825\) | −1.68690e10 | −1.04592 | ||||||||
\(826\) | −2.35701e9 | −0.145523 | ||||||||
\(827\) | −2.55307e10 | −1.56962 | −0.784809 | − | 0.619738i | \(-0.787239\pi\) | ||||
−0.784809 | + | 0.619738i | \(0.787239\pi\) | |||||||
\(828\) | 6.54727e9 | 0.400824 | ||||||||
\(829\) | 8.48208e9 | 0.517085 | 0.258542 | − | 0.966000i | \(-0.416758\pi\) | ||||
0.258542 | + | 0.966000i | \(0.416758\pi\) | |||||||
\(830\) | −3.13063e9 | −0.190046 | ||||||||
\(831\) | 2.38349e10 | 1.44082 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | −7.17160e9 | −0.429891 | ||||||||
\(834\) | −1.08334e10 | −0.646672 | ||||||||
\(835\) | 1.49862e10 | 0.890819 | ||||||||
\(836\) | −1.85025e10 | −1.09524 | ||||||||
\(837\) | −8.06432e9 | −0.475367 | ||||||||
\(838\) | 2.19878e9 | 0.129071 | ||||||||
\(839\) | −2.29323e10 | −1.34055 | −0.670273 | − | 0.742115i | \(-0.733823\pi\) | ||||
−0.670273 | + | 0.742115i | \(0.733823\pi\) | |||||||
\(840\) | 2.58805e9 | 0.150659 | ||||||||
\(841\) | 1.32877e10 | 0.770306 | ||||||||
\(842\) | 6.01094e9 | 0.347017 | ||||||||
\(843\) | −3.66885e10 | −2.10928 | ||||||||
\(844\) | 6.94854e9 | 0.397828 | ||||||||
\(845\) | 1.54941e9 | 0.0883419 | ||||||||
\(846\) | −1.92650e10 | −1.09389 | ||||||||
\(847\) | −7.43410e9 | −0.420374 | ||||||||
\(848\) | −6.01797e9 | −0.338895 | ||||||||
\(849\) | −3.32303e10 | −1.86362 | ||||||||
\(850\) | 1.80771e9 | 0.100963 | ||||||||
\(851\) | 6.15230e9 | 0.342203 | ||||||||
\(852\) | 1.79503e9 | 0.0994335 | ||||||||
\(853\) | 2.47175e10 | 1.36358 | 0.681792 | − | 0.731546i | \(-0.261201\pi\) | ||||
0.681792 | + | 0.731546i | \(0.261201\pi\) | |||||||
\(854\) | 3.47463e9 | 0.190900 | ||||||||
\(855\) | −6.41812e10 | −3.51177 | ||||||||
\(856\) | −7.78379e9 | −0.424163 | ||||||||
\(857\) | 1.19081e10 | 0.646265 | 0.323133 | − | 0.946354i | \(-0.395264\pi\) | ||||
0.323133 | + | 0.946354i | \(0.395264\pi\) | |||||||
\(858\) | −1.18995e10 | −0.643169 | ||||||||
\(859\) | −4.94214e9 | −0.266035 | −0.133018 | − | 0.991114i | \(-0.542467\pi\) | ||||
−0.133018 | + | 0.991114i | \(0.542467\pi\) | |||||||
\(860\) | −6.45363e9 | −0.345987 | ||||||||
\(861\) | 1.25238e10 | 0.668689 | ||||||||
\(862\) | −1.04605e9 | −0.0556259 | ||||||||
\(863\) | −2.05387e10 | −1.08776 | −0.543881 | − | 0.839162i | \(-0.683046\pi\) | ||||
−0.543881 | + | 0.839162i | \(0.683046\pi\) | |||||||
\(864\) | −9.10836e9 | −0.480443 | ||||||||
\(865\) | −2.50679e10 | −1.31693 | ||||||||
\(866\) | 1.33389e10 | 0.697921 | ||||||||
\(867\) | 2.85440e10 | 1.48747 | ||||||||
\(868\) | −3.36075e8 | −0.0174428 | ||||||||
\(869\) | 5.86420e9 | 0.303138 | ||||||||
\(870\) | −3.90419e10 | −2.01008 | ||||||||
\(871\) | −1.40753e8 | −0.00721762 | ||||||||
\(872\) | 3.44709e9 | 0.176054 | ||||||||
\(873\) | 8.76606e9 | 0.445918 | ||||||||
\(874\) | −5.64918e9 | −0.286217 | ||||||||
\(875\) | 3.09150e9 | 0.156006 | ||||||||
\(876\) | 2.48042e10 | 1.24670 | ||||||||
\(877\) | −1.42584e10 | −0.713791 | −0.356895 | − | 0.934144i | \(-0.616165\pi\) | ||||
−0.356895 | + | 0.934144i | \(0.616165\pi\) | |||||||
\(878\) | 1.85182e10 | 0.923354 | ||||||||
\(879\) | 3.52204e10 | 1.74918 | ||||||||
\(880\) | 1.02319e10 | 0.506136 | ||||||||
\(881\) | 1.78398e10 | 0.878971 | 0.439486 | − | 0.898250i | \(-0.355161\pi\) | ||||
0.439486 | + | 0.898250i | \(0.355161\pi\) | |||||||
\(882\) | −3.40479e10 | −1.67090 | ||||||||
\(883\) | 3.79954e10 | 1.85724 | 0.928622 | − | 0.371028i | \(-0.120995\pi\) | ||||
0.928622 | + | 0.371028i | \(0.120995\pi\) | |||||||
\(884\) | 1.27517e9 | 0.0620850 | ||||||||
\(885\) | −4.54587e10 | −2.20453 | ||||||||
\(886\) | −5.52038e9 | −0.266656 | ||||||||
\(887\) | 8.45195e7 | 0.00406653 | 0.00203327 | − | 0.999998i | \(-0.499353\pi\) | ||||
0.00203327 | + | 0.999998i | \(0.499353\pi\) | |||||||
\(888\) | −1.44175e10 | −0.690947 | ||||||||
\(889\) | −3.74126e9 | −0.178592 | ||||||||
\(890\) | 8.70637e9 | 0.413973 | ||||||||
\(891\) | 9.65942e10 | 4.57488 | ||||||||
\(892\) | −8.03857e9 | −0.379229 | ||||||||
\(893\) | 1.66224e10 | 0.781114 | ||||||||
\(894\) | 1.73774e9 | 0.0813398 | ||||||||
\(895\) | −1.78528e10 | −0.832390 | ||||||||
\(896\) | −3.79585e8 | −0.0176291 | ||||||||
\(897\) | −3.63317e9 | −0.168079 | ||||||||
\(898\) | 2.11045e10 | 0.972541 | ||||||||
\(899\) | 5.06985e9 | 0.232721 | ||||||||
\(900\) | 8.58227e9 | 0.392422 | ||||||||
\(901\) | −1.33245e10 | −0.606894 | ||||||||
\(902\) | 4.95129e10 | 2.24645 | ||||||||
\(903\) | −4.94672e9 | −0.223568 | ||||||||
\(904\) | −5.90296e9 | −0.265754 | ||||||||
\(905\) | −3.83385e10 | −1.71935 | ||||||||
\(906\) | −1.66902e10 | −0.745611 | ||||||||
\(907\) | 1.82024e10 | 0.810033 | 0.405017 | − | 0.914309i | \(-0.367266\pi\) | ||||
0.405017 | + | 0.914309i | \(0.367266\pi\) | |||||||
\(908\) | 1.22096e10 | 0.541252 | ||||||||
\(909\) | −8.26151e10 | −3.64826 | ||||||||
\(910\) | −1.02118e9 | −0.0449220 | ||||||||
\(911\) | −3.66963e10 | −1.60808 | −0.804040 | − | 0.594575i | \(-0.797320\pi\) | ||||
−0.804040 | + | 0.594575i | \(0.797320\pi\) | |||||||
\(912\) | 1.32385e10 | 0.577905 | ||||||||
\(913\) | −9.48697e9 | −0.412553 | ||||||||
\(914\) | −4.92978e9 | −0.213558 | ||||||||
\(915\) | 6.70139e10 | 2.89195 | ||||||||
\(916\) | −3.38503e9 | −0.145522 | ||||||||
\(917\) | 3.45617e9 | 0.148014 | ||||||||
\(918\) | −2.01669e10 | −0.860380 | ||||||||
\(919\) | 1.33474e10 | 0.567275 | 0.283638 | − | 0.958932i | \(-0.408459\pi\) | ||||
0.283638 | + | 0.958932i | \(0.408459\pi\) | |||||||
\(920\) | 3.12400e9 | 0.132268 | ||||||||
\(921\) | 4.13702e9 | 0.174493 | ||||||||
\(922\) | 9.88970e9 | 0.415552 | ||||||||
\(923\) | −7.08275e8 | −0.0296481 | ||||||||
\(924\) | 7.84276e9 | 0.327052 | ||||||||
\(925\) | 8.06454e9 | 0.335030 | ||||||||
\(926\) | 5.42775e8 | 0.0224637 | ||||||||
\(927\) | 3.70089e10 | 1.52591 | ||||||||
\(928\) | 5.72621e9 | 0.235206 | ||||||||
\(929\) | 2.71771e10 | 1.11211 | 0.556055 | − | 0.831146i | \(-0.312314\pi\) | ||||
0.556055 | + | 0.831146i | \(0.312314\pi\) | |||||||
\(930\) | −6.48174e9 | −0.264242 | ||||||||
\(931\) | 2.93776e10 | 1.19314 | ||||||||
\(932\) | 9.68025e9 | 0.391680 | ||||||||
\(933\) | 2.63472e10 | 1.06206 | ||||||||
\(934\) | −9.40012e9 | −0.377502 | ||||||||
\(935\) | 2.26546e10 | 0.906390 | ||||||||
\(936\) | 6.05402e9 | 0.241312 | ||||||||
\(937\) | 4.04333e10 | 1.60565 | 0.802825 | − | 0.596214i | \(-0.203329\pi\) | ||||
0.802825 | + | 0.596214i | \(0.203329\pi\) | |||||||
\(938\) | 9.27676e7 | 0.00367017 | ||||||||
\(939\) | 5.49566e10 | 2.16616 | ||||||||
\(940\) | −9.19223e9 | −0.360972 | ||||||||
\(941\) | −8.49843e9 | −0.332487 | −0.166244 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166244 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(942\) | −1.18703e10 | −0.462683 | ||||||||
\(943\) | 1.51173e10 | 0.587061 | ||||||||
\(944\) | 6.66735e9 | 0.257959 | ||||||||
\(945\) | 1.61500e10 | 0.622533 | ||||||||
\(946\) | −1.95569e10 | −0.751072 | ||||||||
\(947\) | −4.40082e9 | −0.168387 | −0.0841935 | − | 0.996449i | \(-0.526831\pi\) | ||||
−0.0841935 | + | 0.996449i | \(0.526831\pi\) | |||||||
\(948\) | −4.19582e9 | −0.159951 | ||||||||
\(949\) | −9.78716e9 | −0.371728 | ||||||||
\(950\) | −7.40504e9 | −0.280217 | ||||||||
\(951\) | −6.90199e10 | −2.60221 | ||||||||
\(952\) | −8.40442e8 | −0.0315703 | ||||||||
\(953\) | −1.73133e10 | −0.647970 | −0.323985 | − | 0.946062i | \(-0.605023\pi\) | ||||
−0.323985 | + | 0.946062i | \(0.605023\pi\) | |||||||
\(954\) | −6.32593e10 | −2.35887 | ||||||||
\(955\) | 3.38606e10 | 1.25801 | ||||||||
\(956\) | 1.67627e10 | 0.620498 | ||||||||
\(957\) | −1.18312e11 | −4.36351 | ||||||||
\(958\) | 3.16924e9 | 0.116460 | ||||||||
\(959\) | −5.37390e9 | −0.196754 | ||||||||
\(960\) | −7.32090e9 | −0.267064 | ||||||||
\(961\) | −2.66709e10 | −0.969407 | ||||||||
\(962\) | 5.68881e9 | 0.206020 | ||||||||
\(963\) | −8.18210e10 | −2.95238 | ||||||||
\(964\) | −8.43211e9 | −0.303156 | ||||||||
\(965\) | 6.80708e9 | 0.243846 | ||||||||
\(966\) | 2.39455e9 | 0.0854681 | ||||||||
\(967\) | 1.40918e10 | 0.501158 | 0.250579 | − | 0.968096i | \(-0.419379\pi\) | ||||
0.250579 | + | 0.968096i | \(0.419379\pi\) | |||||||
\(968\) | 2.10290e10 | 0.745171 | ||||||||
\(969\) | 2.93115e10 | 1.03491 | ||||||||
\(970\) | 4.18269e9 | 0.147148 | ||||||||
\(971\) | −7.27843e9 | −0.255135 | −0.127568 | − | 0.991830i | \(-0.540717\pi\) | ||||
−0.127568 | + | 0.991830i | \(0.540717\pi\) | |||||||
\(972\) | −3.02067e10 | −1.05505 | ||||||||
\(973\) | −2.81731e9 | −0.0980481 | ||||||||
\(974\) | −2.42932e10 | −0.842419 | ||||||||
\(975\) | −4.76242e9 | −0.164555 | ||||||||
\(976\) | −9.82879e9 | −0.338397 | ||||||||
\(977\) | 2.43791e10 | 0.836348 | 0.418174 | − | 0.908367i | \(-0.362670\pi\) | ||||
0.418174 | + | 0.908367i | \(0.362670\pi\) | |||||||
\(978\) | 5.11272e10 | 1.74770 | ||||||||
\(979\) | 2.63835e10 | 0.898657 | ||||||||
\(980\) | −1.62458e10 | −0.551379 | ||||||||
\(981\) | 3.62349e10 | 1.22542 | ||||||||
\(982\) | −2.33579e10 | −0.787126 | ||||||||
\(983\) | 4.06556e10 | 1.36516 | 0.682579 | − | 0.730811i | \(-0.260858\pi\) | ||||
0.682579 | + | 0.730811i | \(0.260858\pi\) | |||||||
\(984\) | −3.54264e10 | −1.18534 | ||||||||
\(985\) | −5.34578e10 | −1.78231 | ||||||||
\(986\) | 1.26785e10 | 0.421209 | ||||||||
\(987\) | −7.04585e9 | −0.233251 | ||||||||
\(988\) | −5.22359e9 | −0.172314 | ||||||||
\(989\) | −5.97112e9 | −0.196277 | ||||||||
\(990\) | 1.07555e11 | 3.52295 | ||||||||
\(991\) | −4.86636e10 | −1.58835 | −0.794175 | − | 0.607689i | \(-0.792097\pi\) | ||||
−0.794175 | + | 0.607689i | \(0.792097\pi\) | |||||||
\(992\) | 9.50665e8 | 0.0309198 | ||||||||
\(993\) | 1.05816e11 | 3.42949 | ||||||||
\(994\) | 4.66811e8 | 0.0150761 | ||||||||
\(995\) | −4.05586e10 | −1.30527 | ||||||||
\(996\) | 6.78790e9 | 0.217685 | ||||||||
\(997\) | −1.76682e10 | −0.564622 | −0.282311 | − | 0.959323i | \(-0.591101\pi\) | ||||
−0.282311 | + | 0.959323i | \(0.591101\pi\) | |||||||
\(998\) | −1.29874e10 | −0.413586 | ||||||||
\(999\) | −8.99687e10 | −2.85504 |
(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 | 26.8.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 234.8.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 208.8.a.e.1.1 | 1 | |||
13.5 | odd | 4 | 338.8.b.a.337.1 | 2 | |||
13.8 | odd | 4 | 338.8.b.a.337.2 | 2 | |||
13.12 | even | 2 | 338.8.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
26.8.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
208.8.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
234.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
338.8.a.a.1.1 | 1 | 13.12 | even | 2 | |||
338.8.b.a.337.1 | 2 | 13.5 | odd | 4 | |||
338.8.b.a.337.2 | 2 | 13.8 | odd | 4 |