Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,44,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 44, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 44);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 44 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(23.4220790691\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 24394519512 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-156187.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09715e6 | −0.707107 | ||||||||
\(3\) | 1.06542e8 | 0.00588052 | 0.00294026 | − | 0.999996i | \(-0.499064\pi\) | ||||
0.00294026 | + | 0.999996i | \(0.499064\pi\) | |||||||
\(4\) | 4.39805e12 | 0.500000 | ||||||||
\(5\) | −2.06968e15 | −1.94110 | −0.970552 | − | 0.240894i | \(-0.922560\pi\) | ||||
−0.970552 | + | 0.240894i | \(0.922560\pi\) | |||||||
\(6\) | −2.23436e14 | −0.00415815 | ||||||||
\(7\) | 1.84575e18 | 1.24901 | 0.624505 | − | 0.781021i | \(-0.285301\pi\) | ||||
0.624505 | + | 0.781021i | \(0.285301\pi\) | |||||||
\(8\) | −9.22337e18 | −0.353553 | ||||||||
\(9\) | −3.28246e20 | −0.999965 | ||||||||
\(10\) | 4.34044e21 | 1.37257 | ||||||||
\(11\) | −3.48878e22 | −1.42145 | −0.710723 | − | 0.703472i | \(-0.751632\pi\) | ||||
−0.710723 | + | 0.703472i | \(0.751632\pi\) | |||||||
\(12\) | 4.68578e20 | 0.00294026 | ||||||||
\(13\) | −4.35696e23 | −0.489104 | −0.244552 | − | 0.969636i | \(-0.578641\pi\) | ||||
−0.244552 | + | 0.969636i | \(0.578641\pi\) | |||||||
\(14\) | −3.87082e24 | −0.883183 | ||||||||
\(15\) | −2.20509e23 | −0.0114147 | ||||||||
\(16\) | 1.93428e25 | 0.250000 | ||||||||
\(17\) | −5.00873e24 | −0.0175823 | −0.00879115 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879115 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(18\) | 6.88381e26 | 0.707082 | ||||||||
\(19\) | 2.39806e27 | 0.770295 | 0.385147 | − | 0.922855i | \(-0.374151\pi\) | ||||
0.385147 | + | 0.922855i | \(0.374151\pi\) | |||||||
\(20\) | −9.10256e27 | −0.970552 | ||||||||
\(21\) | 1.96651e26 | 0.00734482 | ||||||||
\(22\) | 7.31649e28 | 1.00511 | ||||||||
\(23\) | 3.90831e27 | 0.0206462 | 0.0103231 | − | 0.999947i | \(-0.496714\pi\) | ||||
0.0103231 | + | 0.999947i | \(0.496714\pi\) | |||||||
\(24\) | −9.82680e26 | −0.00207908 | ||||||||
\(25\) | 3.14672e30 | 2.76788 | ||||||||
\(26\) | 9.13721e29 | 0.345849 | ||||||||
\(27\) | −6.99454e28 | −0.0117608 | ||||||||
\(28\) | 8.11771e30 | 0.624505 | ||||||||
\(29\) | 3.01099e31 | 1.08931 | 0.544657 | − | 0.838659i | \(-0.316660\pi\) | ||||
0.544657 | + | 0.838659i | \(0.316660\pi\) | |||||||
\(30\) | 4.62441e29 | 0.00807140 | ||||||||
\(31\) | 4.83774e31 | 0.417221 | 0.208610 | − | 0.977999i | \(-0.433106\pi\) | ||||
0.208610 | + | 0.977999i | \(0.433106\pi\) | |||||||
\(32\) | −4.05648e31 | −0.176777 | ||||||||
\(33\) | −3.71703e30 | −0.00835884 | ||||||||
\(34\) | 1.05041e31 | 0.0124326 | ||||||||
\(35\) | −3.82012e33 | −2.42446 | ||||||||
\(36\) | −1.44364e33 | −0.499983 | ||||||||
\(37\) | 3.30039e33 | 0.634203 | 0.317102 | − | 0.948392i | \(-0.397290\pi\) | ||||
0.317102 | + | 0.948392i | \(0.397290\pi\) | |||||||
\(38\) | −5.02909e33 | −0.544681 | ||||||||
\(39\) | −4.64201e31 | −0.00287619 | ||||||||
\(40\) | 1.90894e34 | 0.686284 | ||||||||
\(41\) | 4.18404e34 | 0.884591 | 0.442296 | − | 0.896869i | \(-0.354164\pi\) | ||||
0.442296 | + | 0.896869i | \(0.354164\pi\) | |||||||
\(42\) | −4.12407e32 | −0.00519357 | ||||||||
\(43\) | 3.60631e34 | 0.273836 | 0.136918 | − | 0.990582i | \(-0.456280\pi\) | ||||
0.136918 | + | 0.990582i | \(0.456280\pi\) | |||||||
\(44\) | −1.53438e35 | −0.710723 | ||||||||
\(45\) | 6.79364e35 | 1.94104 | ||||||||
\(46\) | −8.19632e33 | −0.0145991 | ||||||||
\(47\) | −1.27935e36 | −1.43511 | −0.717556 | − | 0.696501i | \(-0.754739\pi\) | ||||
−0.717556 | + | 0.696501i | \(0.754739\pi\) | |||||||
\(48\) | 2.06083e33 | 0.00147013 | ||||||||
\(49\) | 1.22299e36 | 0.560024 | ||||||||
\(50\) | −6.59914e36 | −1.95719 | ||||||||
\(51\) | −5.33642e32 | −0.000103393 0 | ||||||||
\(52\) | −1.91621e36 | −0.244552 | ||||||||
\(53\) | −1.39570e36 | −0.118266 | −0.0591330 | − | 0.998250i | \(-0.518834\pi\) | ||||
−0.0591330 | + | 0.998250i | \(0.518834\pi\) | |||||||
\(54\) | 1.46686e35 | 0.00831616 | ||||||||
\(55\) | 7.22066e37 | 2.75917 | ||||||||
\(56\) | −1.70241e37 | −0.441591 | ||||||||
\(57\) | 2.55495e35 | 0.00452973 | ||||||||
\(58\) | −6.31451e37 | −0.770261 | ||||||||
\(59\) | 1.27247e38 | 1.07480 | 0.537402 | − | 0.843326i | \(-0.319406\pi\) | ||||
0.537402 | + | 0.843326i | \(0.319406\pi\) | |||||||
\(60\) | −9.69808e35 | −0.00570734 | ||||||||
\(61\) | −1.47259e38 | −0.607422 | −0.303711 | − | 0.952764i | \(-0.598226\pi\) | ||||
−0.303711 | + | 0.952764i | \(0.598226\pi\) | |||||||
\(62\) | −1.01455e38 | −0.295020 | ||||||||
\(63\) | −6.05860e38 | −1.24897 | ||||||||
\(64\) | 8.50706e37 | 0.125000 | ||||||||
\(65\) | 9.01752e38 | 0.949402 | ||||||||
\(66\) | 7.79517e36 | 0.00591059 | ||||||||
\(67\) | −2.49457e39 | −1.36895 | −0.684474 | − | 0.729037i | \(-0.739968\pi\) | ||||
−0.684474 | + | 0.729037i | \(0.739968\pi\) | |||||||
\(68\) | −2.20286e37 | −0.00879115 | ||||||||
\(69\) | 4.16400e35 | 0.000121410 0 | ||||||||
\(70\) | 8.01138e39 | 1.71435 | ||||||||
\(71\) | 2.98574e39 | 0.470974 | 0.235487 | − | 0.971877i | \(-0.424331\pi\) | ||||
0.235487 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(72\) | 3.02753e39 | 0.353541 | ||||||||
\(73\) | 3.76985e38 | 0.0327252 | 0.0163626 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163626 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(74\) | −6.92142e39 | −0.448449 | ||||||||
\(75\) | 3.35259e38 | 0.0162766 | ||||||||
\(76\) | 1.05468e40 | 0.385147 | ||||||||
\(77\) | −6.43942e40 | −1.77540 | ||||||||
\(78\) | 9.73500e37 | 0.00203377 | ||||||||
\(79\) | −3.92521e40 | −0.623563 | −0.311781 | − | 0.950154i | \(-0.600926\pi\) | ||||
−0.311781 | + | 0.950154i | \(0.600926\pi\) | |||||||
\(80\) | −4.00335e40 | −0.485276 | ||||||||
\(81\) | 1.07741e41 | 0.999896 | ||||||||
\(82\) | −8.77456e40 | −0.625500 | ||||||||
\(83\) | 3.07544e41 | 1.68939 | 0.844693 | − | 0.535252i | \(-0.179783\pi\) | ||||
0.844693 | + | 0.535252i | \(0.179783\pi\) | |||||||
\(84\) | 8.64880e38 | 0.00367241 | ||||||||
\(85\) | 1.03665e40 | 0.0341291 | ||||||||
\(86\) | −7.56297e40 | −0.193631 | ||||||||
\(87\) | 3.20798e39 | 0.00640572 | ||||||||
\(88\) | 3.21783e41 | 0.502557 | ||||||||
\(89\) | 8.59629e41 | 1.05299 | 0.526497 | − | 0.850177i | \(-0.323505\pi\) | ||||
0.526497 | + | 0.850177i | \(0.323505\pi\) | |||||||
\(90\) | −1.42473e42 | −1.37252 | ||||||||
\(91\) | −8.04187e41 | −0.610896 | ||||||||
\(92\) | 1.71889e40 | 0.0103231 | ||||||||
\(93\) | 5.15424e39 | 0.00245347 | ||||||||
\(94\) | 2.68299e42 | 1.01478 | ||||||||
\(95\) | −4.96321e42 | −1.49522 | ||||||||
\(96\) | −4.32187e39 | −0.00103954 | ||||||||
\(97\) | −5.70573e42 | −1.09830 | −0.549148 | − | 0.835725i | \(-0.685047\pi\) | ||||
−0.549148 | + | 0.835725i | \(0.685047\pi\) | |||||||
\(98\) | −2.56479e42 | −0.395997 | ||||||||
\(99\) | 1.14518e43 | 1.42140 | ||||||||
\(100\) | 1.38394e43 | 1.38394 | ||||||||
\(101\) | −1.05999e42 | −0.0855842 | −0.0427921 | − | 0.999084i | \(-0.513625\pi\) | ||||
−0.0427921 | + | 0.999084i | \(0.513625\pi\) | |||||||
\(102\) | 1.11913e39 | 7.31099e−5 0 | ||||||||
\(103\) | 6.46081e42 | 0.342205 | 0.171103 | − | 0.985253i | \(-0.445267\pi\) | ||||
0.171103 | + | 0.985253i | \(0.445267\pi\) | |||||||
\(104\) | 4.01859e42 | 0.172925 | ||||||||
\(105\) | −4.07005e41 | −0.0142571 | ||||||||
\(106\) | 2.92699e42 | 0.0836267 | ||||||||
\(107\) | −2.23888e43 | −0.522733 | −0.261366 | − | 0.965240i | \(-0.584173\pi\) | ||||
−0.261366 | + | 0.965240i | \(0.584173\pi\) | |||||||
\(108\) | −3.07623e41 | −0.00588041 | ||||||||
\(109\) | −3.44429e43 | −0.540045 | −0.270022 | − | 0.962854i | \(-0.587031\pi\) | ||||
−0.270022 | + | 0.962854i | \(0.587031\pi\) | |||||||
\(110\) | −1.51428e44 | −1.95103 | ||||||||
\(111\) | 3.51632e41 | 0.00372944 | ||||||||
\(112\) | 3.57020e43 | 0.312252 | ||||||||
\(113\) | 1.79557e44 | 1.29723 | 0.648613 | − | 0.761118i | \(-0.275349\pi\) | ||||
0.648613 | + | 0.761118i | \(0.275349\pi\) | |||||||
\(114\) | −5.35811e41 | −0.00320300 | ||||||||
\(115\) | −8.08896e42 | −0.0400764 | ||||||||
\(116\) | 1.32425e44 | 0.544657 | ||||||||
\(117\) | 1.43015e44 | 0.489087 | ||||||||
\(118\) | −2.66856e44 | −0.760001 | ||||||||
\(119\) | −9.24487e42 | −0.0219605 | ||||||||
\(120\) | 2.03384e42 | 0.00403570 | ||||||||
\(121\) | 6.14755e44 | 1.02051 | ||||||||
\(122\) | 3.08825e44 | 0.429512 | ||||||||
\(123\) | 4.45777e42 | 0.00520185 | ||||||||
\(124\) | 2.12766e44 | 0.208610 | ||||||||
\(125\) | −4.15975e45 | −3.43164 | ||||||||
\(126\) | 1.27058e45 | 0.883152 | ||||||||
\(127\) | 2.00065e45 | 1.17325 | 0.586626 | − | 0.809858i | \(-0.300456\pi\) | ||||
0.586626 | + | 0.809858i | \(0.300456\pi\) | |||||||
\(128\) | −1.78406e44 | −0.0883883 | ||||||||
\(129\) | 3.84224e42 | 0.00161030 | ||||||||
\(130\) | −1.89111e45 | −0.671329 | ||||||||
\(131\) | −4.83548e45 | −1.45582 | −0.727909 | − | 0.685674i | \(-0.759508\pi\) | ||||
−0.727909 | + | 0.685674i | \(0.759508\pi\) | |||||||
\(132\) | −1.63477e43 | −0.00417942 | ||||||||
\(133\) | 4.42622e45 | 0.962105 | ||||||||
\(134\) | 5.23149e45 | 0.967993 | ||||||||
\(135\) | 1.44765e44 | 0.0228290 | ||||||||
\(136\) | 4.61974e43 | 0.00621628 | ||||||||
\(137\) | 1.55654e46 | 1.78924 | 0.894618 | − | 0.446832i | \(-0.147448\pi\) | ||||
0.894618 | + | 0.446832i | \(0.147448\pi\) | |||||||
\(138\) | −8.73255e41 | −8.58501e−5 0 | ||||||||
\(139\) | −5.96200e44 | −0.0501850 | −0.0250925 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250925 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(140\) | −1.68011e46 | −1.21223 | ||||||||
\(141\) | −1.36305e44 | −0.00843920 | ||||||||
\(142\) | −6.26154e45 | −0.333029 | ||||||||
\(143\) | 1.52005e46 | 0.695235 | ||||||||
\(144\) | −6.34919e45 | −0.249991 | ||||||||
\(145\) | −6.23180e46 | −2.11447 | ||||||||
\(146\) | −7.90594e44 | −0.0231402 | ||||||||
\(147\) | 1.30300e44 | 0.00329323 | ||||||||
\(148\) | 1.45153e46 | 0.317102 | ||||||||
\(149\) | 2.53943e46 | 0.479989 | 0.239995 | − | 0.970774i | \(-0.422854\pi\) | ||||
0.239995 | + | 0.970774i | \(0.422854\pi\) | |||||||
\(150\) | −7.03088e44 | −0.0115093 | ||||||||
\(151\) | 6.65104e46 | 0.943812 | 0.471906 | − | 0.881649i | \(-0.343566\pi\) | ||||
0.471906 | + | 0.881649i | \(0.343566\pi\) | |||||||
\(152\) | −2.21182e46 | −0.272340 | ||||||||
\(153\) | 1.64409e45 | 0.0175817 | ||||||||
\(154\) | 1.35044e47 | 1.25540 | ||||||||
\(155\) | −1.00126e47 | −0.809869 | ||||||||
\(156\) | −2.04158e44 | −0.00143809 | ||||||||
\(157\) | −2.40178e46 | −0.147465 | −0.0737327 | − | 0.997278i | \(-0.523491\pi\) | ||||
−0.0737327 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(158\) | 8.23176e46 | 0.440925 | ||||||||
\(159\) | −1.48701e44 | −0.000695466 0 | ||||||||
\(160\) | 8.39563e46 | 0.343142 | ||||||||
\(161\) | 7.21377e45 | 0.0257873 | ||||||||
\(162\) | −2.25950e47 | −0.707033 | ||||||||
\(163\) | −4.09519e47 | −1.12264 | −0.561320 | − | 0.827599i | \(-0.689706\pi\) | ||||
−0.561320 | + | 0.827599i | \(0.689706\pi\) | |||||||
\(164\) | 1.84016e47 | 0.442296 | ||||||||
\(165\) | 7.69306e45 | 0.0162254 | ||||||||
\(166\) | −6.44967e47 | −1.19458 | ||||||||
\(167\) | 8.96692e47 | 1.45962 | 0.729809 | − | 0.683652i | \(-0.239609\pi\) | ||||
0.729809 | + | 0.683652i | \(0.239609\pi\) | |||||||
\(168\) | −1.81378e45 | −0.00259679 | ||||||||
\(169\) | −6.03700e47 | −0.760777 | ||||||||
\(170\) | −2.17401e46 | −0.0241329 | ||||||||
\(171\) | −7.87151e47 | −0.770268 | ||||||||
\(172\) | 1.58607e47 | 0.136918 | ||||||||
\(173\) | 8.13600e47 | 0.620040 | 0.310020 | − | 0.950730i | \(-0.399664\pi\) | ||||
0.310020 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(174\) | −6.72763e45 | −0.00452953 | ||||||||
\(175\) | 5.80806e48 | 3.45711 | ||||||||
\(176\) | −6.74827e47 | −0.355361 | ||||||||
\(177\) | 1.35572e46 | 0.00632040 | ||||||||
\(178\) | −1.80277e48 | −0.744579 | ||||||||
\(179\) | −4.40713e48 | −1.61367 | −0.806836 | − | 0.590775i | \(-0.798822\pi\) | ||||
−0.806836 | + | 0.590775i | \(0.798822\pi\) | |||||||
\(180\) | 2.98788e48 | 0.970518 | ||||||||
\(181\) | −4.00198e48 | −1.15395 | −0.576973 | − | 0.816763i | \(-0.695766\pi\) | ||||
−0.576973 | + | 0.816763i | \(0.695766\pi\) | |||||||
\(182\) | 1.68650e48 | 0.431969 | ||||||||
\(183\) | −1.56893e46 | −0.00357195 | ||||||||
\(184\) | −3.60478e46 | −0.00729954 | ||||||||
\(185\) | −6.83076e48 | −1.23105 | ||||||||
\(186\) | −1.08092e46 | −0.00173487 | ||||||||
\(187\) | 1.74743e47 | 0.0249923 | ||||||||
\(188\) | −5.62665e48 | −0.717556 | ||||||||
\(189\) | −1.29102e47 | −0.0146894 | ||||||||
\(190\) | 1.04086e49 | 1.05728 | ||||||||
\(191\) | 5.52608e48 | 0.501418 | 0.250709 | − | 0.968063i | \(-0.419336\pi\) | ||||
0.250709 | + | 0.968063i | \(0.419336\pi\) | |||||||
\(192\) | 9.06362e45 | 0.000735065 0 | ||||||||
\(193\) | 1.07272e49 | 0.778043 | 0.389022 | − | 0.921229i | \(-0.372813\pi\) | ||||
0.389022 | + | 0.921229i | \(0.372813\pi\) | |||||||
\(194\) | 1.19658e49 | 0.776612 | ||||||||
\(195\) | 9.60749e46 | 0.00558297 | ||||||||
\(196\) | 5.37876e48 | 0.280012 | ||||||||
\(197\) | −2.18374e49 | −1.01901 | −0.509504 | − | 0.860468i | \(-0.670171\pi\) | ||||
−0.509504 | + | 0.860468i | \(0.670171\pi\) | |||||||
\(198\) | −2.40161e49 | −1.00508 | ||||||||
\(199\) | 3.52049e49 | 1.32209 | 0.661047 | − | 0.750344i | \(-0.270112\pi\) | ||||
0.661047 | + | 0.750344i | \(0.270112\pi\) | |||||||
\(200\) | −2.90233e49 | −0.978594 | ||||||||
\(201\) | −2.65777e47 | −0.00805012 | ||||||||
\(202\) | 2.22297e48 | 0.0605172 | ||||||||
\(203\) | 5.55755e49 | 1.36056 | ||||||||
\(204\) | −2.34698e45 | −5.16965e−5 0 | ||||||||
\(205\) | −8.65963e49 | −1.71708 | ||||||||
\(206\) | −1.35493e49 | −0.241976 | ||||||||
\(207\) | −1.28288e48 | −0.0206455 | ||||||||
\(208\) | −8.42759e48 | −0.122276 | ||||||||
\(209\) | −8.36628e49 | −1.09493 | ||||||||
\(210\) | 8.53551e47 | 0.0100813 | ||||||||
\(211\) | 1.53515e50 | 1.63711 | 0.818554 | − | 0.574430i | \(-0.194776\pi\) | ||||
0.818554 | + | 0.574430i | \(0.194776\pi\) | |||||||
\(212\) | −6.13834e48 | −0.0591330 | ||||||||
\(213\) | 3.18108e47 | 0.00276957 | ||||||||
\(214\) | 4.69527e49 | 0.369628 | ||||||||
\(215\) | −7.46391e49 | −0.531544 | ||||||||
\(216\) | 6.45132e47 | 0.00415808 | ||||||||
\(217\) | 8.92927e49 | 0.521113 | ||||||||
\(218\) | 7.22319e49 | 0.381869 | ||||||||
\(219\) | 4.01648e46 | 0.000192441 0 | ||||||||
\(220\) | 3.17568e50 | 1.37959 | ||||||||
\(221\) | 2.18228e48 | 0.00859958 | ||||||||
\(222\) | −7.37425e47 | −0.00263711 | ||||||||
\(223\) | 6.20052e49 | 0.201314 | 0.100657 | − | 0.994921i | \(-0.467906\pi\) | ||||
0.100657 | + | 0.994921i | \(0.467906\pi\) | |||||||
\(224\) | −7.48726e49 | −0.220796 | ||||||||
\(225\) | −1.03290e51 | −2.76779 | ||||||||
\(226\) | −3.76558e50 | −0.917278 | ||||||||
\(227\) | 4.13480e50 | 0.916006 | 0.458003 | − | 0.888951i | \(-0.348565\pi\) | ||||
0.458003 | + | 0.888951i | \(0.348565\pi\) | |||||||
\(228\) | 1.12368e48 | 0.00226487 | ||||||||
\(229\) | 1.11692e50 | 0.204909 | 0.102455 | − | 0.994738i | \(-0.467330\pi\) | ||||
0.102455 | + | 0.994738i | \(0.467330\pi\) | |||||||
\(230\) | 1.69638e49 | 0.0283383 | ||||||||
\(231\) | −6.86071e48 | −0.0104403 | ||||||||
\(232\) | −2.77715e50 | −0.385130 | ||||||||
\(233\) | −8.69051e50 | −1.09874 | −0.549368 | − | 0.835581i | \(-0.685131\pi\) | ||||
−0.549368 | + | 0.835581i | \(0.685131\pi\) | |||||||
\(234\) | −2.99925e50 | −0.345837 | ||||||||
\(235\) | 2.64785e51 | 2.78570 | ||||||||
\(236\) | 5.59638e50 | 0.537402 | ||||||||
\(237\) | −4.18201e48 | −0.00366687 | ||||||||
\(238\) | 1.93879e49 | 0.0155284 | ||||||||
\(239\) | −3.18038e50 | −0.232769 | −0.116384 | − | 0.993204i | \(-0.537130\pi\) | ||||
−0.116384 | + | 0.993204i | \(0.537130\pi\) | |||||||
\(240\) | −4.26526e48 | −0.00285367 | ||||||||
\(241\) | 2.26900e51 | 1.38825 | 0.694127 | − | 0.719853i | \(-0.255791\pi\) | ||||
0.694127 | + | 0.719853i | \(0.255791\pi\) | |||||||
\(242\) | −1.28923e51 | −0.721609 | ||||||||
\(243\) | 3.44391e49 | 0.0176407 | ||||||||
\(244\) | −6.47652e50 | −0.303711 | ||||||||
\(245\) | −2.53120e51 | −1.08706 | ||||||||
\(246\) | −9.34863e48 | −0.00367827 | ||||||||
\(247\) | −1.04482e51 | −0.376755 | ||||||||
\(248\) | −4.46203e50 | −0.147510 | ||||||||
\(249\) | 3.27665e49 | 0.00993446 | ||||||||
\(250\) | 8.72362e51 | 2.42654 | ||||||||
\(251\) | −6.50684e51 | −1.66106 | −0.830529 | − | 0.556975i | \(-0.811962\pi\) | ||||
−0.830529 | + | 0.556975i | \(0.811962\pi\) | |||||||
\(252\) | −2.66460e51 | −0.624483 | ||||||||
\(253\) | −1.36352e50 | −0.0293475 | ||||||||
\(254\) | −4.19567e51 | −0.829615 | ||||||||
\(255\) | 1.10447e48 | 0.000200696 0 | ||||||||
\(256\) | 3.74144e50 | 0.0625000 | ||||||||
\(257\) | 2.78532e51 | 0.427871 | 0.213935 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213935 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(258\) | −8.05777e48 | −0.00113865 | ||||||||
\(259\) | 6.09171e51 | 0.792126 | ||||||||
\(260\) | 3.96595e51 | 0.474701 | ||||||||
\(261\) | −9.88345e51 | −1.08928 | ||||||||
\(262\) | 1.01407e52 | 1.02942 | ||||||||
\(263\) | 6.39160e51 | 0.597807 | 0.298903 | − | 0.954283i | \(-0.403379\pi\) | ||||
0.298903 | + | 0.954283i | \(0.403379\pi\) | |||||||
\(264\) | 3.42835e49 | 0.00295529 | ||||||||
\(265\) | 2.88865e51 | 0.229567 | ||||||||
\(266\) | −9.28245e51 | −0.680311 | ||||||||
\(267\) | 9.15869e49 | 0.00619215 | ||||||||
\(268\) | −1.09712e52 | −0.684474 | ||||||||
\(269\) | 2.28281e52 | 1.31461 | 0.657303 | − | 0.753626i | \(-0.271697\pi\) | ||||
0.657303 | + | 0.753626i | \(0.271697\pi\) | |||||||
\(270\) | −3.03594e50 | −0.0161425 | ||||||||
\(271\) | 1.88294e52 | 0.924693 | 0.462347 | − | 0.886699i | \(-0.347008\pi\) | ||||
0.462347 | + | 0.886699i | \(0.347008\pi\) | |||||||
\(272\) | −9.68829e49 | −0.00439558 | ||||||||
\(273\) | −8.56800e49 | −0.00359238 | ||||||||
\(274\) | −3.26430e52 | −1.26518 | ||||||||
\(275\) | −1.09782e53 | −3.93439 | ||||||||
\(276\) | 1.83135e48 | 6.07052e−5 0 | ||||||||
\(277\) | 4.61782e52 | 1.41619 | 0.708095 | − | 0.706117i | \(-0.249555\pi\) | ||||
0.708095 | + | 0.706117i | \(0.249555\pi\) | |||||||
\(278\) | 1.25032e51 | 0.0354862 | ||||||||
\(279\) | −1.58797e52 | −0.417207 | ||||||||
\(280\) | 3.52344e52 | 0.857174 | ||||||||
\(281\) | 5.52503e52 | 1.24494 | 0.622471 | − | 0.782643i | \(-0.286129\pi\) | ||||
0.622471 | + | 0.782643i | \(0.286129\pi\) | |||||||
\(282\) | 2.85853e50 | 0.00596742 | ||||||||
\(283\) | 4.51872e51 | 0.0874193 | 0.0437097 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437097 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(284\) | 1.31314e52 | 0.235487 | ||||||||
\(285\) | −5.28793e50 | −0.00879267 | ||||||||
\(286\) | −3.18777e52 | −0.491606 | ||||||||
\(287\) | 7.72270e52 | 1.10486 | ||||||||
\(288\) | 1.33152e52 | 0.176771 | ||||||||
\(289\) | −8.11277e52 | −0.999691 | ||||||||
\(290\) | 1.30690e53 | 1.49516 | ||||||||
\(291\) | −6.07902e50 | −0.00645854 | ||||||||
\(292\) | 1.65800e51 | 0.0163626 | ||||||||
\(293\) | 2.13481e52 | 0.195752 | 0.0978758 | − | 0.995199i | \(-0.468795\pi\) | ||||
0.0978758 | + | 0.995199i | \(0.468795\pi\) | |||||||
\(294\) | −2.73259e50 | −0.00232867 | ||||||||
\(295\) | −2.63361e53 | −2.08631 | ||||||||
\(296\) | −3.04407e52 | −0.224225 | ||||||||
\(297\) | 2.44024e51 | 0.0167174 | ||||||||
\(298\) | −5.32557e52 | −0.339404 | ||||||||
\(299\) | −1.70283e51 | −0.0100982 | ||||||||
\(300\) | 1.47448e51 | 0.00813829 | ||||||||
\(301\) | 6.65635e52 | 0.342024 | ||||||||
\(302\) | −1.39482e53 | −0.667376 | ||||||||
\(303\) | −1.12934e50 | −0.000503280 0 | ||||||||
\(304\) | 4.63852e52 | 0.192574 | ||||||||
\(305\) | 3.04779e53 | 1.17907 | ||||||||
\(306\) | −3.44791e51 | −0.0124321 | ||||||||
\(307\) | 3.27926e52 | 0.110230 | 0.0551152 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551152 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(308\) | −2.83209e53 | −0.887700 | ||||||||
\(309\) | 6.88351e50 | 0.00201234 | ||||||||
\(310\) | 2.09979e53 | 0.572664 | ||||||||
\(311\) | −1.84457e53 | −0.469405 | −0.234702 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234702 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(312\) | 4.28150e50 | 0.00101689 | ||||||||
\(313\) | −3.25940e52 | −0.0722661 | −0.0361330 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361330 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(314\) | 5.03689e52 | 0.104274 | ||||||||
\(315\) | 1.25394e54 | 2.42437 | ||||||||
\(316\) | −1.72632e53 | −0.311781 | ||||||||
\(317\) | 2.60991e53 | 0.440404 | 0.220202 | − | 0.975454i | \(-0.429328\pi\) | ||||
0.220202 | + | 0.975454i | \(0.429328\pi\) | |||||||
\(318\) | 3.11849e50 | 0.000491768 0 | ||||||||
\(319\) | −1.05047e54 | −1.54840 | ||||||||
\(320\) | −1.76069e53 | −0.242638 | ||||||||
\(321\) | −2.38536e51 | −0.00307394 | ||||||||
\(322\) | −1.51284e52 | −0.0182344 | ||||||||
\(323\) | −1.20112e52 | −0.0135436 | ||||||||
\(324\) | 4.73852e53 | 0.499948 | ||||||||
\(325\) | −1.37101e54 | −1.35378 | ||||||||
\(326\) | 8.58823e53 | 0.793826 | ||||||||
\(327\) | −3.66963e51 | −0.00317574 | ||||||||
\(328\) | −3.85909e53 | −0.312750 | ||||||||
\(329\) | −2.36137e54 | −1.79247 | ||||||||
\(330\) | −1.61335e52 | −0.0114731 | ||||||||
\(331\) | −1.93099e53 | −0.128670 | −0.0643350 | − | 0.997928i | \(-0.520493\pi\) | ||||
−0.0643350 | + | 0.997928i | \(0.520493\pi\) | |||||||
\(332\) | 1.35259e54 | 0.844693 | ||||||||
\(333\) | −1.08334e54 | −0.634181 | ||||||||
\(334\) | −1.88050e54 | −1.03211 | ||||||||
\(335\) | 5.16296e54 | 2.65727 | ||||||||
\(336\) | 3.80378e51 | 0.00183620 | ||||||||
\(337\) | 2.65509e54 | 1.20237 | 0.601183 | − | 0.799111i | \(-0.294696\pi\) | ||||
0.601183 | + | 0.799111i | \(0.294696\pi\) | |||||||
\(338\) | 1.26605e54 | 0.537951 | ||||||||
\(339\) | 1.91304e52 | 0.00762836 | ||||||||
\(340\) | 4.55923e52 | 0.0170645 | ||||||||
\(341\) | −1.68778e54 | −0.593057 | ||||||||
\(342\) | 1.65078e54 | 0.544662 | ||||||||
\(343\) | −1.77345e54 | −0.549534 | ||||||||
\(344\) | −3.32623e53 | −0.0968157 | ||||||||
\(345\) | −8.61817e50 | −0.000235670 0 | ||||||||
\(346\) | −1.70624e54 | −0.438435 | ||||||||
\(347\) | 3.27098e54 | 0.789941 | 0.394970 | − | 0.918694i | \(-0.370755\pi\) | ||||
0.394970 | + | 0.918694i | \(0.370755\pi\) | |||||||
\(348\) | 1.41089e52 | 0.00320286 | ||||||||
\(349\) | 2.42552e54 | 0.517676 | 0.258838 | − | 0.965921i | \(-0.416660\pi\) | ||||
0.258838 | + | 0.965921i | \(0.416660\pi\) | |||||||
\(350\) | −1.21804e55 | −2.44455 | ||||||||
\(351\) | 3.04749e52 | 0.00575227 | ||||||||
\(352\) | 1.41522e54 | 0.251279 | ||||||||
\(353\) | −5.87621e54 | −0.981615 | −0.490807 | − | 0.871268i | \(-0.663298\pi\) | ||||
−0.490807 | + | 0.871268i | \(0.663298\pi\) | |||||||
\(354\) | −2.84315e52 | −0.00446920 | ||||||||
\(355\) | −6.17953e54 | −0.914209 | ||||||||
\(356\) | 3.78069e54 | 0.526497 | ||||||||
\(357\) | −9.84971e50 | −0.000129139 0 | ||||||||
\(358\) | 9.24241e54 | 1.14104 | ||||||||
\(359\) | 1.22420e55 | 1.42338 | 0.711690 | − | 0.702494i | \(-0.247930\pi\) | ||||
0.711690 | + | 0.702494i | \(0.247930\pi\) | |||||||
\(360\) | −6.26603e54 | −0.686260 | ||||||||
\(361\) | −3.94114e54 | −0.406646 | ||||||||
\(362\) | 8.39276e54 | 0.815963 | ||||||||
\(363\) | 6.54975e52 | 0.00600112 | ||||||||
\(364\) | −3.53685e54 | −0.305448 | ||||||||
\(365\) | −7.80238e53 | −0.0635230 | ||||||||
\(366\) | 3.29029e52 | 0.00252575 | ||||||||
\(367\) | 6.65116e54 | 0.481479 | 0.240739 | − | 0.970590i | \(-0.422610\pi\) | ||||
0.240739 | + | 0.970590i | \(0.422610\pi\) | |||||||
\(368\) | 7.55977e52 | 0.00516155 | ||||||||
\(369\) | −1.37339e55 | −0.884561 | ||||||||
\(370\) | 1.43251e55 | 0.870486 | ||||||||
\(371\) | −2.57611e54 | −0.147715 | ||||||||
\(372\) | 2.26686e52 | 0.00122674 | ||||||||
\(373\) | 1.69267e55 | 0.864632 | 0.432316 | − | 0.901722i | \(-0.357697\pi\) | ||||
0.432316 | + | 0.901722i | \(0.357697\pi\) | |||||||
\(374\) | −3.66463e53 | −0.0176722 | ||||||||
\(375\) | −4.43189e53 | −0.0201798 | ||||||||
\(376\) | 1.17999e55 | 0.507389 | ||||||||
\(377\) | −1.31188e55 | −0.532788 | ||||||||
\(378\) | 2.70746e53 | 0.0103870 | ||||||||
\(379\) | −4.11600e55 | −1.49188 | −0.745938 | − | 0.666016i | \(-0.767998\pi\) | ||||
−0.745938 | + | 0.666016i | \(0.767998\pi\) | |||||||
\(380\) | −2.18284e55 | −0.747611 | ||||||||
\(381\) | 2.13154e53 | 0.00689933 | ||||||||
\(382\) | −1.15890e55 | −0.354556 | ||||||||
\(383\) | −4.06771e55 | −1.17646 | −0.588229 | − | 0.808694i | \(-0.700175\pi\) | ||||
−0.588229 | + | 0.808694i | \(0.700175\pi\) | |||||||
\(384\) | −1.90078e52 | −0.000519769 0 | ||||||||
\(385\) | 1.33275e56 | 3.44623 | ||||||||
\(386\) | −2.24965e55 | −0.550160 | ||||||||
\(387\) | −1.18375e55 | −0.273827 | ||||||||
\(388\) | −2.50941e55 | −0.549148 | ||||||||
\(389\) | −3.95636e55 | −0.819180 | −0.409590 | − | 0.912270i | \(-0.634328\pi\) | ||||
−0.409590 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(390\) | −2.01484e53 | −0.00394776 | ||||||||
\(391\) | −1.95757e52 | −0.000363008 0 | ||||||||
\(392\) | −1.12801e55 | −0.197998 | ||||||||
\(393\) | −5.15184e53 | −0.00856096 | ||||||||
\(394\) | 4.57964e55 | 0.720547 | ||||||||
\(395\) | 8.12393e55 | 1.21040 | ||||||||
\(396\) | 5.03653e55 | 0.710698 | ||||||||
\(397\) | 1.01362e56 | 1.35481 | 0.677404 | − | 0.735611i | \(-0.263105\pi\) | ||||
0.677404 | + | 0.735611i | \(0.263105\pi\) | |||||||
\(398\) | −7.38301e55 | −0.934862 | ||||||||
\(399\) | 4.71580e53 | 0.00565768 | ||||||||
\(400\) | 6.08663e55 | 0.691970 | ||||||||
\(401\) | −6.40929e54 | −0.0690567 | −0.0345284 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345284 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(402\) | 5.57375e53 | 0.00569230 | ||||||||
\(403\) | −2.10778e55 | −0.204065 | ||||||||
\(404\) | −4.66190e54 | −0.0427921 | ||||||||
\(405\) | −2.22991e56 | −1.94090 | ||||||||
\(406\) | −1.16550e56 | −0.962063 | ||||||||
\(407\) | −1.15143e56 | −0.901486 | ||||||||
\(408\) | 4.92198e51 | 3.65550e−5 0 | ||||||||
\(409\) | −1.48591e55 | −0.104699 | −0.0523495 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523495 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(410\) | 1.81606e56 | 1.21416 | ||||||||
\(411\) | 1.65837e54 | 0.0105216 | ||||||||
\(412\) | 2.84150e55 | 0.171103 | ||||||||
\(413\) | 2.34866e56 | 1.34244 | ||||||||
\(414\) | 2.69040e54 | 0.0145986 | ||||||||
\(415\) | −6.36519e56 | −3.27927 | ||||||||
\(416\) | 1.76739e55 | 0.0864623 | ||||||||
\(417\) | −6.35206e52 | −0.000295114 0 | ||||||||
\(418\) | 1.75454e56 | 0.774234 | ||||||||
\(419\) | 3.48862e56 | 1.46235 | 0.731177 | − | 0.682187i | \(-0.238971\pi\) | ||||
0.731177 | + | 0.682187i | \(0.238971\pi\) | |||||||
\(420\) | −1.79003e54 | −0.00712853 | ||||||||
\(421\) | 3.31748e56 | 1.25529 | 0.627645 | − | 0.778500i | \(-0.284019\pi\) | ||||
0.627645 | + | 0.778500i | \(0.284019\pi\) | |||||||
\(422\) | −3.21944e56 | −1.15761 | ||||||||
\(423\) | 4.19942e56 | 1.43506 | ||||||||
\(424\) | 1.28730e55 | 0.0418134 | ||||||||
\(425\) | −1.57611e55 | −0.0486657 | ||||||||
\(426\) | −6.67120e53 | −0.00195838 | ||||||||
\(427\) | −2.71804e56 | −0.758676 | ||||||||
\(428\) | −9.84670e55 | −0.261366 | ||||||||
\(429\) | 1.61949e54 | 0.00408834 | ||||||||
\(430\) | 1.56529e56 | 0.375859 | ||||||||
\(431\) | 3.50172e56 | 0.799872 | 0.399936 | − | 0.916543i | \(-0.369032\pi\) | ||||
0.399936 | + | 0.916543i | \(0.369032\pi\) | |||||||
\(432\) | −1.35294e54 | −0.00294021 | ||||||||
\(433\) | −6.19424e56 | −1.28085 | −0.640425 | − | 0.768020i | \(-0.721242\pi\) | ||||
−0.640425 | + | 0.768020i | \(0.721242\pi\) | |||||||
\(434\) | −1.87260e56 | −0.368482 | ||||||||
\(435\) | −6.63951e54 | −0.0124342 | ||||||||
\(436\) | −1.51481e56 | −0.270022 | ||||||||
\(437\) | 9.37234e54 | 0.0159037 | ||||||||
\(438\) | −8.42318e52 | −0.000136076 0 | ||||||||
\(439\) | 9.86613e56 | 1.51761 | 0.758804 | − | 0.651319i | \(-0.225784\pi\) | ||||
0.758804 | + | 0.651319i | \(0.225784\pi\) | |||||||
\(440\) | −6.65988e56 | −0.975515 | ||||||||
\(441\) | −4.01441e56 | −0.560005 | ||||||||
\(442\) | −4.57658e54 | −0.00608082 | ||||||||
\(443\) | 4.08147e56 | 0.516579 | 0.258290 | − | 0.966068i | \(-0.416841\pi\) | ||||
0.258290 | + | 0.966068i | \(0.416841\pi\) | |||||||
\(444\) | 1.54649e54 | 0.00186472 | ||||||||
\(445\) | −1.77916e57 | −2.04397 | ||||||||
\(446\) | −1.30034e56 | −0.142350 | ||||||||
\(447\) | 2.70557e54 | 0.00282258 | ||||||||
\(448\) | 1.57019e56 | 0.156126 | ||||||||
\(449\) | 7.25652e56 | 0.687753 | 0.343876 | − | 0.939015i | \(-0.388260\pi\) | ||||
0.343876 | + | 0.939015i | \(0.388260\pi\) | |||||||
\(450\) | 2.16614e57 | 1.95712 | ||||||||
\(451\) | −1.45972e57 | −1.25740 | ||||||||
\(452\) | 7.89700e56 | 0.648613 | ||||||||
\(453\) | 7.08618e54 | 0.00555010 | ||||||||
\(454\) | −8.67130e56 | −0.647714 | ||||||||
\(455\) | 1.66441e57 | 1.18581 | ||||||||
\(456\) | −2.35652e54 | −0.00160150 | ||||||||
\(457\) | 5.03696e56 | 0.326565 | 0.163283 | − | 0.986579i | \(-0.447792\pi\) | ||||
0.163283 | + | 0.986579i | \(0.447792\pi\) | |||||||
\(458\) | −2.34236e56 | −0.144893 | ||||||||
\(459\) | 3.50337e53 | 0.000206782 0 | ||||||||
\(460\) | −3.55756e55 | −0.0200382 | ||||||||
\(461\) | 7.57000e56 | 0.406936 | 0.203468 | − | 0.979082i | \(-0.434779\pi\) | ||||
0.203468 | + | 0.979082i | \(0.434779\pi\) | |||||||
\(462\) | 1.43880e55 | 0.00738238 | ||||||||
\(463\) | 6.94436e56 | 0.340127 | 0.170063 | − | 0.985433i | \(-0.445603\pi\) | ||||
0.170063 | + | 0.985433i | \(0.445603\pi\) | |||||||
\(464\) | 5.82411e56 | 0.272328 | ||||||||
\(465\) | −1.06676e55 | −0.00476245 | ||||||||
\(466\) | 1.82253e57 | 0.776923 | ||||||||
\(467\) | −3.37517e57 | −1.37399 | −0.686994 | − | 0.726663i | \(-0.741070\pi\) | ||||
−0.686994 | + | 0.726663i | \(0.741070\pi\) | |||||||
\(468\) | 6.28988e56 | 0.244544 | ||||||||
\(469\) | −4.60436e57 | −1.70983 | ||||||||
\(470\) | −5.55295e57 | −1.96979 | ||||||||
\(471\) | −2.55891e54 | −0.000867173 0 | ||||||||
\(472\) | −1.17365e57 | −0.380001 | ||||||||
\(473\) | −1.25816e57 | −0.389243 | ||||||||
\(474\) | 8.77031e54 | 0.00259287 | ||||||||
\(475\) | 7.54600e57 | 2.13208 | ||||||||
\(476\) | −4.06594e55 | −0.0109802 | ||||||||
\(477\) | 4.58132e56 | 0.118262 | ||||||||
\(478\) | 6.66975e56 | 0.164592 | ||||||||
\(479\) | 2.97595e57 | 0.702121 | 0.351060 | − | 0.936353i | \(-0.385821\pi\) | ||||
0.351060 | + | 0.936353i | \(0.385821\pi\) | |||||||
\(480\) | 8.94490e54 | 0.00201785 | ||||||||
\(481\) | −1.43797e57 | −0.310192 | ||||||||
\(482\) | −4.75845e57 | −0.981644 | ||||||||
\(483\) | 7.68572e53 | 0.000151643 0 | ||||||||
\(484\) | 2.70372e57 | 0.510254 | ||||||||
\(485\) | 1.18091e58 | 2.13190 | ||||||||
\(486\) | −7.22240e55 | −0.0124739 | ||||||||
\(487\) | −6.28542e57 | −1.03863 | −0.519316 | − | 0.854582i | \(-0.673813\pi\) | ||||
−0.519316 | + | 0.854582i | \(0.673813\pi\) | |||||||
\(488\) | 1.35822e57 | 0.214756 | ||||||||
\(489\) | −4.36311e55 | −0.00660170 | ||||||||
\(490\) | 5.30831e57 | 0.768671 | ||||||||
\(491\) | 5.70226e57 | 0.790305 | 0.395153 | − | 0.918615i | \(-0.370692\pi\) | ||||
0.395153 | + | 0.918615i | \(0.370692\pi\) | |||||||
\(492\) | 1.96055e55 | 0.00260093 | ||||||||
\(493\) | −1.50812e56 | −0.0191526 | ||||||||
\(494\) | 2.19115e57 | 0.266406 | ||||||||
\(495\) | −2.37015e58 | −2.75908 | ||||||||
\(496\) | 9.35755e56 | 0.104305 | ||||||||
\(497\) | 5.51093e57 | 0.588251 | ||||||||
\(498\) | −6.87163e55 | −0.00702472 | ||||||||
\(499\) | −7.55319e57 | −0.739552 | −0.369776 | − | 0.929121i | \(-0.620566\pi\) | ||||
−0.369776 | + | 0.929121i | \(0.620566\pi\) | |||||||
\(500\) | −1.82948e58 | −1.71582 | ||||||||
\(501\) | 9.55357e55 | 0.00858330 | ||||||||
\(502\) | 1.36458e58 | 1.17455 | ||||||||
\(503\) | 1.01823e57 | 0.0839718 | 0.0419859 | − | 0.999118i | \(-0.486632\pi\) | ||||
0.0419859 | + | 0.999118i | \(0.486632\pi\) | |||||||
\(504\) | 5.58807e57 | 0.441576 | ||||||||
\(505\) | 2.19385e57 | 0.166128 | ||||||||
\(506\) | 2.85951e56 | 0.0207518 | ||||||||
\(507\) | −6.43197e55 | −0.00447376 | ||||||||
\(508\) | 8.79896e57 | 0.586626 | ||||||||
\(509\) | −1.61549e58 | −1.03246 | −0.516229 | − | 0.856451i | \(-0.672665\pi\) | ||||
−0.516229 | + | 0.856451i | \(0.672665\pi\) | |||||||
\(510\) | −2.31624e54 | −0.000141914 0 | ||||||||
\(511\) | 6.95820e56 | 0.0408741 | ||||||||
\(512\) | −7.84638e56 | −0.0441942 | ||||||||
\(513\) | −1.67733e56 | −0.00905930 | ||||||||
\(514\) | −5.84123e57 | −0.302550 | ||||||||
\(515\) | −1.33718e58 | −0.664256 | ||||||||
\(516\) | 1.68984e55 | 0.000805149 0 | ||||||||
\(517\) | 4.46337e58 | 2.03993 | ||||||||
\(518\) | −1.27752e58 | −0.560117 | ||||||||
\(519\) | 8.66829e55 | 0.00364616 | ||||||||
\(520\) | −8.31720e57 | −0.335664 | ||||||||
\(521\) | 2.87022e58 | 1.11148 | 0.555742 | − | 0.831355i | \(-0.312434\pi\) | ||||
0.555742 | + | 0.831355i | \(0.312434\pi\) | |||||||
\(522\) | 2.07271e58 | 0.770234 | ||||||||
\(523\) | 3.54622e58 | 1.26468 | 0.632339 | − | 0.774692i | \(-0.282095\pi\) | ||||
0.632339 | + | 0.774692i | \(0.282095\pi\) | |||||||
\(524\) | −2.12667e58 | −0.727909 | ||||||||
\(525\) | 6.18805e56 | 0.0203296 | ||||||||
\(526\) | −1.34042e58 | −0.422713 | ||||||||
\(527\) | −2.42309e56 | −0.00733571 | ||||||||
\(528\) | −7.18977e55 | −0.00208971 | ||||||||
\(529\) | −3.58189e58 | −0.999574 | ||||||||
\(530\) | −6.05794e57 | −0.162328 | ||||||||
\(531\) | −4.17683e58 | −1.07477 | ||||||||
\(532\) | 1.94667e58 | 0.481053 | ||||||||
\(533\) | −1.82297e58 | −0.432657 | ||||||||
\(534\) | −1.92072e56 | −0.00437851 | ||||||||
\(535\) | 4.63377e58 | 1.01468 | ||||||||
\(536\) | 2.30083e58 | 0.483996 | ||||||||
\(537\) | −4.69546e56 | −0.00948923 | ||||||||
\(538\) | −4.78740e58 | −0.929567 | ||||||||
\(539\) | −4.26673e58 | −0.796044 | ||||||||
\(540\) | 6.36682e56 | 0.0114145 | ||||||||
\(541\) | −6.62227e58 | −1.14095 | −0.570473 | − | 0.821316i | \(-0.693240\pi\) | ||||
−0.570473 | + | 0.821316i | \(0.693240\pi\) | |||||||
\(542\) | −3.94882e58 | −0.653857 | ||||||||
\(543\) | −4.26381e56 | −0.00678580 | ||||||||
\(544\) | 2.03178e56 | 0.00310814 | ||||||||
\(545\) | 7.12858e58 | 1.04828 | ||||||||
\(546\) | 1.79684e56 | 0.00254020 | ||||||||
\(547\) | −4.90873e58 | −0.667178 | −0.333589 | − | 0.942719i | \(-0.608260\pi\) | ||||
−0.333589 | + | 0.942719i | \(0.608260\pi\) | |||||||
\(548\) | 6.84573e58 | 0.894618 | ||||||||
\(549\) | 4.83371e58 | 0.607401 | ||||||||
\(550\) | 2.30229e59 | 2.78204 | ||||||||
\(551\) | 7.22053e58 | 0.839092 | ||||||||
\(552\) | −3.84062e54 | −4.29250e−5 0 | ||||||||
\(553\) | −7.24496e58 | −0.778836 | ||||||||
\(554\) | −9.68427e58 | −1.00140 | ||||||||
\(555\) | −7.27766e56 | −0.00723923 | ||||||||
\(556\) | −2.62212e57 | −0.0250925 | ||||||||
\(557\) | 2.53254e58 | 0.233168 | 0.116584 | − | 0.993181i | \(-0.462806\pi\) | ||||
0.116584 | + | 0.993181i | \(0.462806\pi\) | |||||||
\(558\) | 3.33021e58 | 0.295010 | ||||||||
\(559\) | −1.57125e58 | −0.133934 | ||||||||
\(560\) | −7.38919e58 | −0.606114 | ||||||||
\(561\) | 1.86176e55 | 0.000146968 0 | ||||||||
\(562\) | −1.15868e59 | −0.880307 | ||||||||
\(563\) | 2.25761e59 | 1.65089 | 0.825445 | − | 0.564483i | \(-0.190924\pi\) | ||||
0.825445 | + | 0.564483i | \(0.190924\pi\) | |||||||
\(564\) | −5.99476e56 | −0.00421960 | ||||||||
\(565\) | −3.71626e59 | −2.51805 | ||||||||
\(566\) | −9.47645e57 | −0.0618148 | ||||||||
\(567\) | 1.98864e59 | 1.24888 | ||||||||
\(568\) | −2.75386e58 | −0.166514 | ||||||||
\(569\) | −2.32353e59 | −1.35280 | −0.676402 | − | 0.736533i | \(-0.736462\pi\) | ||||
−0.676402 | + | 0.736533i | \(0.736462\pi\) | |||||||
\(570\) | 1.10896e57 | 0.00621736 | ||||||||
\(571\) | −7.96462e57 | −0.0430020 | −0.0215010 | − | 0.999769i | \(-0.506845\pi\) | ||||
−0.0215010 | + | 0.999769i | \(0.506845\pi\) | |||||||
\(572\) | 6.68523e58 | 0.347618 | ||||||||
\(573\) | 5.88762e56 | 0.00294860 | ||||||||
\(574\) | −1.61957e59 | −0.781256 | ||||||||
\(575\) | 1.22983e58 | 0.0571463 | ||||||||
\(576\) | −2.79240e58 | −0.124996 | ||||||||
\(577\) | 2.06427e59 | 0.890199 | 0.445099 | − | 0.895481i | \(-0.353168\pi\) | ||||
0.445099 | + | 0.895481i | \(0.353168\pi\) | |||||||
\(578\) | 1.70137e59 | 0.706888 | ||||||||
\(579\) | 1.14290e57 | 0.00457530 | ||||||||
\(580\) | −2.74077e59 | −1.05723 | ||||||||
\(581\) | 5.67651e59 | 2.11006 | ||||||||
\(582\) | 1.27486e57 | 0.00456688 | ||||||||
\(583\) | 4.86928e58 | 0.168109 | ||||||||
\(584\) | −3.47707e57 | −0.0115701 | ||||||||
\(585\) | −2.95996e59 | −0.949369 | ||||||||
\(586\) | −4.47702e58 | −0.138417 | ||||||||
\(587\) | −2.18486e59 | −0.651185 | −0.325593 | − | 0.945510i | \(-0.605564\pi\) | ||||
−0.325593 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(588\) | 5.73066e56 | 0.00164662 | ||||||||
\(589\) | 1.16012e59 | 0.321383 | ||||||||
\(590\) | 5.52308e59 | 1.47524 | ||||||||
\(591\) | −2.32661e57 | −0.00599229 | ||||||||
\(592\) | 6.38389e58 | 0.158551 | ||||||||
\(593\) | 1.66747e56 | 0.000399375 0 | 0.000199688 | − | 1.00000i | \(-0.499936\pi\) | ||||
0.000199688 | 1.00000i | \(0.499936\pi\) | ||||||||
\(594\) | −5.11755e57 | −0.0118210 | ||||||||
\(595\) | 1.91340e58 | 0.0426275 | ||||||||
\(596\) | 1.11685e59 | 0.239995 | ||||||||
\(597\) | 3.75082e57 | 0.00777460 | ||||||||
\(598\) | 3.57110e57 | 0.00714047 | ||||||||
\(599\) | −8.31418e59 | −1.60377 | −0.801887 | − | 0.597476i | \(-0.796170\pi\) | ||||
−0.801887 | + | 0.597476i | \(0.796170\pi\) | |||||||
\(600\) | −3.09222e57 | −0.00575464 | ||||||||
\(601\) | 3.62301e58 | 0.0650531 | 0.0325265 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325265 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(602\) | −1.39594e59 | −0.241847 | ||||||||
\(603\) | 8.18831e59 | 1.36890 | ||||||||
\(604\) | 2.92516e59 | 0.471906 | ||||||||
\(605\) | −1.27235e60 | −1.98091 | ||||||||
\(606\) | 2.36840e56 | 0.000355872 0 | ||||||||
\(607\) | −8.13623e59 | −1.17996 | −0.589979 | − | 0.807419i | \(-0.700864\pi\) | ||||
−0.589979 | + | 0.807419i | \(0.700864\pi\) | |||||||
\(608\) | −9.72767e58 | −0.136170 | ||||||||
\(609\) | 5.92114e57 | 0.00800081 | ||||||||
\(610\) | −6.39169e59 | −0.833727 | ||||||||
\(611\) | 5.57408e59 | 0.701920 | ||||||||
\(612\) | 7.23080e57 | 0.00879085 | ||||||||
\(613\) | 1.45687e60 | 1.71010 | 0.855050 | − | 0.518545i | \(-0.173526\pi\) | ||||
0.855050 | + | 0.518545i | \(0.173526\pi\) | |||||||
\(614\) | −6.87711e58 | −0.0779446 | ||||||||
\(615\) | −9.22618e57 | −0.0100973 | ||||||||
\(616\) | 5.93931e59 | 0.627698 | ||||||||
\(617\) | −8.99399e59 | −0.917955 | −0.458978 | − | 0.888448i | \(-0.651784\pi\) | ||||
−0.458978 | + | 0.888448i | \(0.651784\pi\) | |||||||
\(618\) | −1.44358e57 | −0.00142294 | ||||||||
\(619\) | −1.01581e60 | −0.967078 | −0.483539 | − | 0.875323i | \(-0.660649\pi\) | ||||
−0.483539 | + | 0.875323i | \(0.660649\pi\) | |||||||
\(620\) | −4.40358e59 | −0.404934 | ||||||||
\(621\) | −2.73368e56 | −0.000242817 0 | ||||||||
\(622\) | 3.86835e59 | 0.331919 | ||||||||
\(623\) | 1.58666e60 | 1.31520 | ||||||||
\(624\) | −8.97895e56 | −0.000719047 0 | ||||||||
\(625\) | 5.03195e60 | 3.89328 | ||||||||
\(626\) | 6.83546e58 | 0.0510998 | ||||||||
\(627\) | −8.91364e57 | −0.00643877 | ||||||||
\(628\) | −1.05631e59 | −0.0737327 | ||||||||
\(629\) | −1.65308e58 | −0.0111508 | ||||||||
\(630\) | −2.62970e60 | −1.71429 | ||||||||
\(631\) | −1.44520e60 | −0.910534 | −0.455267 | − | 0.890355i | \(-0.650456\pi\) | ||||
−0.455267 | + | 0.890355i | \(0.650456\pi\) | |||||||
\(632\) | 3.62037e59 | 0.220463 | ||||||||
\(633\) | 1.63558e58 | 0.00962704 | ||||||||
\(634\) | −5.47338e59 | −0.311413 | ||||||||
\(635\) | −4.14071e60 | −2.27740 | ||||||||
\(636\) | −6.53994e56 | −0.000347733 0 | ||||||||
\(637\) | −5.32851e59 | −0.273910 | ||||||||
\(638\) | 2.20299e60 | 1.09488 | ||||||||
\(639\) | −9.80055e59 | −0.470958 | ||||||||
\(640\) | 3.69244e59 | 0.171571 | ||||||||
\(641\) | −1.14193e59 | −0.0513089 | −0.0256545 | − | 0.999671i | \(-0.508167\pi\) | ||||
−0.0256545 | + | 0.999671i | \(0.508167\pi\) | |||||||
\(642\) | 5.00246e57 | 0.00217360 | ||||||||
\(643\) | −1.22490e59 | −0.0514712 | −0.0257356 | − | 0.999669i | \(-0.508193\pi\) | ||||
−0.0257356 | + | 0.999669i | \(0.508193\pi\) | |||||||
\(644\) | 3.17265e58 | 0.0128937 | ||||||||
\(645\) | −7.95223e57 | −0.00312575 | ||||||||
\(646\) | 2.51893e58 | 0.00957674 | ||||||||
\(647\) | 2.04374e60 | 0.751594 | 0.375797 | − | 0.926702i | \(-0.377369\pi\) | ||||
0.375797 | + | 0.926702i | \(0.377369\pi\) | |||||||
\(648\) | −9.93740e59 | −0.353517 | ||||||||
\(649\) | −4.43936e60 | −1.52778 | ||||||||
\(650\) | 2.87522e60 | 0.957269 | ||||||||
\(651\) | 9.51346e57 | 0.00306441 | ||||||||
\(652\) | −1.80108e60 | −0.561320 | ||||||||
\(653\) | −6.31762e59 | −0.190511 | −0.0952555 | − | 0.995453i | \(-0.530367\pi\) | ||||
−0.0952555 | + | 0.995453i | \(0.530367\pi\) | |||||||
\(654\) | 7.69576e57 | 0.00224559 | ||||||||
\(655\) | 1.00079e61 | 2.82589 | ||||||||
\(656\) | 8.09311e59 | 0.221148 | ||||||||
\(657\) | −1.23744e59 | −0.0327241 | ||||||||
\(658\) | 4.95214e60 | 1.26747 | ||||||||
\(659\) | −6.26841e60 | −1.55282 | −0.776409 | − | 0.630229i | \(-0.782961\pi\) | ||||
−0.776409 | + | 0.630229i | \(0.782961\pi\) | |||||||
\(660\) | 3.38344e58 | 0.00811268 | ||||||||
\(661\) | 4.90303e60 | 1.13798 | 0.568989 | − | 0.822345i | \(-0.307335\pi\) | ||||
0.568989 | + | 0.822345i | \(0.307335\pi\) | |||||||
\(662\) | 4.04957e59 | 0.0909834 | ||||||||
\(663\) | 2.32506e56 | 5.05700e−5 0 | ||||||||
\(664\) | −2.83660e60 | −0.597288 | ||||||||
\(665\) | −9.16087e60 | −1.86755 | ||||||||
\(666\) | 2.27193e60 | 0.448434 | ||||||||
\(667\) | 1.17679e59 | 0.0224902 | ||||||||
\(668\) | 3.94369e60 | 0.729809 | ||||||||
\(669\) | 6.60618e57 | 0.00118383 | ||||||||
\(670\) | −1.08275e61 | −1.87897 | ||||||||
\(671\) | 5.13754e60 | 0.863417 | ||||||||
\(672\) | −7.97711e57 | −0.00129839 | ||||||||
\(673\) | 6.30665e60 | 0.994203 | 0.497102 | − | 0.867692i | \(-0.334398\pi\) | ||||
0.497102 | + | 0.867692i | \(0.334398\pi\) | |||||||
\(674\) | −5.56813e60 | −0.850201 | ||||||||
\(675\) | −2.20098e59 | −0.0325526 | ||||||||
\(676\) | −2.65510e60 | −0.380388 | ||||||||
\(677\) | 9.09208e60 | 1.26185 | 0.630924 | − | 0.775845i | \(-0.282676\pi\) | ||||
0.630924 | + | 0.775845i | \(0.282676\pi\) | |||||||
\(678\) | −4.01194e58 | −0.00539407 | ||||||||
\(679\) | −1.05314e61 | −1.37178 | ||||||||
\(680\) | −9.56139e58 | −0.0120664 | ||||||||
\(681\) | 4.40531e58 | 0.00538659 | ||||||||
\(682\) | 3.53953e60 | 0.419355 | ||||||||
\(683\) | 9.34804e60 | 1.07319 | 0.536593 | − | 0.843841i | \(-0.319711\pi\) | ||||
0.536593 | + | 0.843841i | \(0.319711\pi\) | |||||||
\(684\) | −3.46193e60 | −0.385134 | ||||||||
\(685\) | −3.22154e61 | −3.47309 | ||||||||
\(686\) | 3.71919e60 | 0.388579 | ||||||||
\(687\) | 1.19000e58 | 0.00120497 | ||||||||
\(688\) | 6.97561e59 | 0.0684590 | ||||||||
\(689\) | 6.08100e59 | 0.0578445 | ||||||||
\(690\) | 1.80736e57 | 0.000166644 0 | ||||||||
\(691\) | 1.90200e61 | 1.69993 | 0.849967 | − | 0.526836i | \(-0.176622\pi\) | ||||
0.849967 | + | 0.526836i | \(0.176622\pi\) | |||||||
\(692\) | 3.57825e60 | 0.310020 | ||||||||
\(693\) | 2.11371e61 | 1.77534 | ||||||||
\(694\) | −6.85975e60 | −0.558572 | ||||||||
\(695\) | 1.23395e60 | 0.0974143 | ||||||||
\(696\) | −2.95884e58 | −0.00226477 | ||||||||
\(697\) | −2.09567e59 | −0.0155532 | ||||||||
\(698\) | −5.08668e60 | −0.366052 | ||||||||
\(699\) | −9.25908e58 | −0.00646113 | ||||||||
\(700\) | 2.55441e61 | 1.72855 | ||||||||
\(701\) | −2.19436e61 | −1.44002 | −0.720012 | − | 0.693962i | \(-0.755864\pi\) | ||||
−0.720012 | + | 0.693962i | \(0.755864\pi\) | |||||||
\(702\) | −6.39105e58 | −0.00406747 | ||||||||
\(703\) | 7.91452e60 | 0.488523 | ||||||||
\(704\) | −2.96792e60 | −0.177681 | ||||||||
\(705\) | 2.82108e59 | 0.0163814 | ||||||||
\(706\) | 1.23233e61 | 0.694106 | ||||||||
\(707\) | −1.95649e60 | −0.106896 | ||||||||
\(708\) | 5.96252e58 | 0.00316020 | ||||||||
\(709\) | −3.13056e61 | −1.60964 | −0.804818 | − | 0.593522i | \(-0.797737\pi\) | ||||
−0.804818 | + | 0.593522i | \(0.797737\pi\) | |||||||
\(710\) | 1.29594e61 | 0.646444 | ||||||||
\(711\) | 1.28843e61 | 0.623541 | ||||||||
\(712\) | −7.92868e60 | −0.372289 | ||||||||
\(713\) | 1.89074e59 | 0.00861403 | ||||||||
\(714\) | 2.06563e57 | 9.13149e−5 0 | ||||||||
\(715\) | −3.14601e61 | −1.34952 | ||||||||
\(716\) | −1.93827e61 | −0.806836 | ||||||||
\(717\) | −3.38846e58 | −0.00136880 | ||||||||
\(718\) | −2.56733e61 | −1.00648 | ||||||||
\(719\) | −4.08353e61 | −1.55369 | −0.776845 | − | 0.629691i | \(-0.783181\pi\) | ||||
−0.776845 | + | 0.629691i | \(0.783181\pi\) | |||||||
\(720\) | 1.31408e61 | 0.485259 | ||||||||
\(721\) | 1.19251e61 | 0.427418 | ||||||||
\(722\) | 8.26516e60 | 0.287542 | ||||||||
\(723\) | 2.41745e59 | 0.00816365 | ||||||||
\(724\) | −1.76009e61 | −0.576973 | ||||||||
\(725\) | 9.47474e61 | 3.01509 | ||||||||
\(726\) | −1.37358e59 | −0.00424343 | ||||||||
\(727\) | 3.27882e61 | 0.983395 | 0.491698 | − | 0.870766i | \(-0.336377\pi\) | ||||
0.491698 | + | 0.870766i | \(0.336377\pi\) | |||||||
\(728\) | 7.41732e60 | 0.215984 | ||||||||
\(729\) | −3.53632e61 | −0.999793 | ||||||||
\(730\) | 1.63628e60 | 0.0449175 | ||||||||
\(731\) | −1.80630e59 | −0.00481467 | ||||||||
\(732\) | −6.90024e58 | −0.00178598 | ||||||||
\(733\) | 8.88787e60 | 0.223389 | 0.111695 | − | 0.993743i | \(-0.464372\pi\) | ||||
0.111695 | + | 0.993743i | \(0.464372\pi\) | |||||||
\(734\) | −1.39485e61 | −0.340457 | ||||||||
\(735\) | −2.69680e59 | −0.00639250 | ||||||||
\(736\) | −1.58540e59 | −0.00364977 | ||||||||
\(737\) | 8.70299e61 | 1.94589 | ||||||||
\(738\) | 2.88021e61 | 0.625479 | ||||||||
\(739\) | −4.67983e61 | −0.987131 | −0.493565 | − | 0.869709i | \(-0.664307\pi\) | ||||
−0.493565 | + | 0.869709i | \(0.664307\pi\) | |||||||
\(740\) | −3.00420e61 | −0.615527 | ||||||||
\(741\) | −1.11318e59 | −0.00221551 | ||||||||
\(742\) | 5.40250e60 | 0.104451 | ||||||||
\(743\) | 7.75880e61 | 1.45725 | 0.728627 | − | 0.684911i | \(-0.240159\pi\) | ||||
0.728627 | + | 0.684911i | \(0.240159\pi\) | |||||||
\(744\) | −4.75395e58 | −0.000867434 0 | ||||||||
\(745\) | −5.25581e61 | −0.931709 | ||||||||
\(746\) | −3.54978e61 | −0.611387 | ||||||||
\(747\) | −1.00950e62 | −1.68933 | ||||||||
\(748\) | 7.68529e59 | 0.0124961 | ||||||||
\(749\) | −4.13242e61 | −0.652898 | ||||||||
\(750\) | 9.29436e59 | 0.0142693 | ||||||||
\(751\) | 8.12743e61 | 1.21254 | 0.606268 | − | 0.795260i | \(-0.292666\pi\) | ||||
0.606268 | + | 0.795260i | \(0.292666\pi\) | |||||||
\(752\) | −2.47463e61 | −0.358778 | ||||||||
\(753\) | −6.93254e59 | −0.00976788 | ||||||||
\(754\) | 2.75121e61 | 0.376738 | ||||||||
\(755\) | −1.37655e62 | −1.83204 | ||||||||
\(756\) | −5.67796e59 | −0.00734469 | ||||||||
\(757\) | 5.81763e61 | 0.731450 | 0.365725 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365725 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(758\) | 8.63188e61 | 1.05492 | ||||||||
\(759\) | −1.45273e58 | −0.000172578 0 | ||||||||
\(760\) | 4.57776e61 | 0.528641 | ||||||||
\(761\) | −8.00450e61 | −0.898595 | −0.449298 | − | 0.893382i | \(-0.648326\pi\) | ||||
−0.449298 | + | 0.893382i | \(0.648326\pi\) | |||||||
\(762\) | −4.47017e59 | −0.00487856 | ||||||||
\(763\) | −6.35730e61 | −0.674521 | ||||||||
\(764\) | 2.43040e61 | 0.250709 | ||||||||
\(765\) | −3.40275e60 | −0.0341279 | ||||||||
\(766\) | 8.53061e61 | 0.831882 | ||||||||
\(767\) | −5.54410e61 | −0.525691 | ||||||||
\(768\) | 3.98622e58 | 0.000367532 0 | ||||||||
\(769\) | 1.59678e62 | 1.43162 | 0.715810 | − | 0.698296i | \(-0.246058\pi\) | ||||
0.715810 | + | 0.698296i | \(0.246058\pi\) | |||||||
\(770\) | −2.79499e62 | −2.43685 | ||||||||
\(771\) | 2.96754e59 | 0.00251610 | ||||||||
\(772\) | 4.71787e61 | 0.389022 | ||||||||
\(773\) | 5.71876e61 | 0.458609 | 0.229304 | − | 0.973355i | \(-0.426355\pi\) | ||||
0.229304 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(774\) | 2.48251e61 | 0.193625 | ||||||||
\(775\) | 1.52230e62 | 1.15482 | ||||||||
\(776\) | 5.26261e61 | 0.388306 | ||||||||
\(777\) | 6.49025e59 | 0.00465811 | ||||||||
\(778\) | 8.29708e61 | 0.579247 | ||||||||
\(779\) | 1.00336e62 | 0.681396 | ||||||||
\(780\) | 4.22542e59 | 0.00279149 | ||||||||
\(781\) | −1.04166e62 | −0.669464 | ||||||||
\(782\) | 4.10531e58 | 0.000256685 0 | ||||||||
\(783\) | −2.10605e60 | −0.0128112 | ||||||||
\(784\) | 2.36560e61 | 0.140006 | ||||||||
\(785\) | 4.97091e61 | 0.286246 | ||||||||
\(786\) | 1.08042e60 | 0.00605351 | ||||||||
\(787\) | −2.96283e62 | −1.61529 | −0.807643 | − | 0.589671i | \(-0.799257\pi\) | ||||
−0.807643 | + | 0.589671i | \(0.799257\pi\) | |||||||
\(788\) | −9.60420e61 | −0.509504 | ||||||||
\(789\) | 6.80976e59 | 0.00351541 | ||||||||
\(790\) | −1.70371e62 | −0.855882 | ||||||||
\(791\) | 3.31418e62 | 1.62025 | ||||||||
\(792\) | −1.05624e62 | −0.502540 | ||||||||
\(793\) | 6.41602e61 | 0.297093 | ||||||||
\(794\) | −2.12571e62 | −0.957994 | ||||||||
\(795\) | 3.07764e59 | 0.00134997 | ||||||||
\(796\) | 1.54833e62 | 0.661047 | ||||||||
\(797\) | −1.51741e62 | −0.630594 | −0.315297 | − | 0.948993i | \(-0.602104\pi\) | ||||
−0.315297 | + | 0.948993i | \(0.602104\pi\) | |||||||
\(798\) | −9.88975e59 | −0.00400058 | ||||||||
\(799\) | 6.40793e60 | 0.0252326 | ||||||||
\(800\) | −1.27646e62 | −0.489297 | ||||||||
\(801\) | −2.82169e62 | −1.05296 | ||||||||
\(802\) | 1.34413e61 | 0.0488305 | ||||||||
\(803\) | −1.31521e61 | −0.0465171 | ||||||||
\(804\) | −1.16890e60 | −0.00402506 | ||||||||
\(805\) | −1.49302e61 | −0.0500558 | ||||||||
\(806\) | 4.42034e61 | 0.144295 | ||||||||
\(807\) | 2.43216e60 | 0.00773057 | ||||||||
\(808\) | 9.77672e60 | 0.0302586 | ||||||||
\(809\) | −2.93763e62 | −0.885327 | −0.442663 | − | 0.896688i | \(-0.645966\pi\) | ||||
−0.442663 | + | 0.896688i | \(0.645966\pi\) | |||||||
\(810\) | 4.67645e62 | 1.37242 | ||||||||
\(811\) | 3.67101e62 | 1.04915 | 0.524575 | − | 0.851364i | \(-0.324224\pi\) | ||||
0.524575 | + | 0.851364i | \(0.324224\pi\) | |||||||
\(812\) | 2.44424e62 | 0.680281 | ||||||||
\(813\) | 2.00613e60 | 0.00543767 | ||||||||
\(814\) | 2.41473e62 | 0.637447 | ||||||||
\(815\) | 8.47574e62 | 2.17916 | ||||||||
\(816\) | −1.03221e58 | −2.58483e−5 0 | ||||||||
\(817\) | 8.64812e61 | 0.210935 | ||||||||
\(818\) | 3.11619e61 | 0.0740334 | ||||||||
\(819\) | 2.63971e62 | 0.610875 | ||||||||
\(820\) | −3.80854e62 | −0.858541 | ||||||||
\(821\) | −7.97990e62 | −1.75235 | −0.876173 | − | 0.481997i | \(-0.839912\pi\) | ||||
−0.876173 | + | 0.481997i | \(0.839912\pi\) | |||||||
\(822\) | −3.47786e60 | −0.00743992 | ||||||||
\(823\) | −6.36565e62 | −1.32662 | −0.663309 | − | 0.748345i | \(-0.730849\pi\) | ||||
−0.663309 | + | 0.748345i | \(0.730849\pi\) | |||||||
\(824\) | −5.95905e61 | −0.120988 | ||||||||
\(825\) | −1.16964e61 | −0.0231363 | ||||||||
\(826\) | −4.92551e62 | −0.949248 | ||||||||
\(827\) | −3.36234e62 | −0.631355 | −0.315677 | − | 0.948867i | \(-0.602232\pi\) | ||||
−0.315677 | + | 0.948867i | \(0.602232\pi\) | |||||||
\(828\) | −5.64219e60 | −0.0103227 | ||||||||
\(829\) | 5.67452e62 | 1.01159 | 0.505797 | − | 0.862652i | \(-0.331198\pi\) | ||||
0.505797 | + | 0.862652i | \(0.331198\pi\) | |||||||
\(830\) | 1.33488e63 | 2.31879 | ||||||||
\(831\) | 4.91993e60 | 0.00832793 | ||||||||
\(832\) | −3.70649e61 | −0.0611380 | ||||||||
\(833\) | −6.12562e60 | −0.00984651 | ||||||||
\(834\) | 1.33212e59 | 0.000208677 0 | ||||||||
\(835\) | −1.85587e63 | −2.83327 | ||||||||
\(836\) | −3.67953e62 | −0.547466 | ||||||||
\(837\) | −3.38377e60 | −0.00490687 | ||||||||
\(838\) | −7.31618e62 | −1.03404 | ||||||||
\(839\) | 8.37436e62 | 1.15364 | 0.576819 | − | 0.816872i | \(-0.304294\pi\) | ||||
0.576819 | + | 0.816872i | \(0.304294\pi\) | |||||||
\(840\) | 3.75396e60 | 0.00504063 | ||||||||
\(841\) | 1.42571e62 | 0.186603 | ||||||||
\(842\) | −6.95727e62 | −0.887624 | ||||||||
\(843\) | 5.88650e60 | 0.00732090 | ||||||||
\(844\) | 6.75165e62 | 0.818554 | ||||||||
\(845\) | 1.24947e63 | 1.47675 | ||||||||
\(846\) | −8.80681e62 | −1.01474 | ||||||||
\(847\) | 1.13469e63 | 1.27462 | ||||||||
\(848\) | −2.69967e61 | −0.0295665 | ||||||||
\(849\) | 4.81436e59 | 0.000514071 0 | ||||||||
\(850\) | 3.30533e61 | 0.0344119 | ||||||||
\(851\) | 1.28989e61 | 0.0130939 | ||||||||
\(852\) | 1.39905e60 | 0.00138479 | ||||||||
\(853\) | −1.18819e63 | −1.14678 | −0.573392 | − | 0.819281i | \(-0.694373\pi\) | ||||
−0.573392 | + | 0.819281i | \(0.694373\pi\) | |||||||
\(854\) | 5.70014e62 | 0.536465 | ||||||||
\(855\) | 1.62915e63 | 1.49517 | ||||||||
\(856\) | 2.06500e62 | 0.184814 | ||||||||
\(857\) | 2.67982e62 | 0.233894 | 0.116947 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116947 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(858\) | −3.39632e60 | −0.00289090 | ||||||||
\(859\) | −3.65813e62 | −0.303673 | −0.151837 | − | 0.988406i | \(-0.548519\pi\) | ||||
−0.151837 | + | 0.988406i | \(0.548519\pi\) | |||||||
\(860\) | −3.28266e62 | −0.265772 | ||||||||
\(861\) | 8.22795e60 | 0.00649716 | ||||||||
\(862\) | −7.34365e62 | −0.565595 | ||||||||
\(863\) | −9.90631e61 | −0.0744183 | −0.0372091 | − | 0.999307i | \(-0.511847\pi\) | ||||
−0.0372091 | + | 0.999307i | \(0.511847\pi\) | |||||||
\(864\) | 2.83732e60 | 0.00207904 | ||||||||
\(865\) | −1.68389e63 | −1.20356 | ||||||||
\(866\) | 1.29903e63 | 0.905698 | ||||||||
\(867\) | −8.64354e60 | −0.00587870 | ||||||||
\(868\) | 3.92714e62 | 0.260556 | ||||||||
\(869\) | 1.36942e63 | 0.886361 | ||||||||
\(870\) | 1.39241e61 | 0.00879229 | ||||||||
\(871\) | 1.08687e63 | 0.669559 | ||||||||
\(872\) | 3.17679e62 | 0.190935 | ||||||||
\(873\) | 1.87288e63 | 1.09826 | ||||||||
\(874\) | −1.96552e61 | −0.0112456 | ||||||||
\(875\) | −7.67786e63 | −4.28615 | ||||||||
\(876\) | 1.76647e59 | 9.62205e−5 0 | ||||||||
\(877\) | 1.85432e63 | 0.985585 | 0.492793 | − | 0.870147i | \(-0.335976\pi\) | ||||
0.492793 | + | 0.870147i | \(0.335976\pi\) | |||||||
\(878\) | −2.06908e63 | −1.07311 | ||||||||
\(879\) | 2.27448e60 | 0.00115112 | ||||||||
\(880\) | 1.39668e63 | 0.689793 | ||||||||
\(881\) | −8.58814e62 | −0.413920 | −0.206960 | − | 0.978349i | \(-0.566357\pi\) | ||||
−0.206960 | + | 0.978349i | \(0.566357\pi\) | |||||||
\(882\) | 8.41882e62 | 0.395983 | ||||||||
\(883\) | −2.94353e63 | −1.35118 | −0.675589 | − | 0.737278i | \(-0.736111\pi\) | ||||
−0.675589 | + | 0.737278i | \(0.736111\pi\) | |||||||
\(884\) | 9.59778e60 | 0.00429979 | ||||||||
\(885\) | −2.80591e61 | −0.0122686 | ||||||||
\(886\) | −8.55947e62 | −0.365277 | ||||||||
\(887\) | −2.64455e62 | −0.110152 | −0.0550762 | − | 0.998482i | \(-0.517540\pi\) | ||||
−0.0550762 | + | 0.998482i | \(0.517540\pi\) | |||||||
\(888\) | −3.24323e60 | −0.00131856 | ||||||||
\(889\) | 3.69271e63 | 1.46540 | ||||||||
\(890\) | 3.73117e63 | 1.44530 | ||||||||
\(891\) | −3.75886e63 | −1.42130 | ||||||||
\(892\) | 2.72702e62 | 0.100657 | ||||||||
\(893\) | −3.06796e63 | −1.10546 | ||||||||
\(894\) | −5.67399e60 | −0.00199587 | ||||||||
\(895\) | 9.12135e63 | 3.13230 | ||||||||
\(896\) | −3.29293e62 | −0.110398 | ||||||||
\(897\) | −1.81424e59 | −5.93823e−5 0 | ||||||||
\(898\) | −1.52180e63 | −0.486315 | ||||||||
\(899\) | 1.45664e63 | 0.454484 | ||||||||
\(900\) | −4.54272e63 | −1.38389 | ||||||||
\(901\) | 6.99067e60 | 0.00207939 | ||||||||
\(902\) | 3.06125e63 | 0.889115 | ||||||||
\(903\) | 7.09183e60 | 0.00201128 | ||||||||
\(904\) | −1.65612e63 | −0.458639 | ||||||||
\(905\) | 8.28283e63 | 2.23993 | ||||||||
\(906\) | −1.48608e61 | −0.00392451 | ||||||||
\(907\) | 3.70525e63 | 0.955566 | 0.477783 | − | 0.878478i | \(-0.341441\pi\) | ||||
0.477783 | + | 0.878478i | \(0.341441\pi\) | |||||||
\(908\) | 1.81850e63 | 0.458003 | ||||||||
\(909\) | 3.47938e62 | 0.0855813 | ||||||||
\(910\) | −3.49052e63 | −0.838496 | ||||||||
\(911\) | −3.20223e63 | −0.751289 | −0.375644 | − | 0.926764i | \(-0.622579\pi\) | ||||
−0.375644 | + | 0.926764i | \(0.622579\pi\) | |||||||
\(912\) | 4.94198e60 | 0.00113243 | ||||||||
\(913\) | −1.07295e64 | −2.40137 | ||||||||
\(914\) | −1.05633e63 | −0.230916 | ||||||||
\(915\) | 3.24719e61 | 0.00693353 | ||||||||
\(916\) | 4.91229e62 | 0.102455 | ||||||||
\(917\) | −8.92510e63 | −1.81833 | ||||||||
\(918\) | −7.34711e59 | −0.000146217 0 | ||||||||
\(919\) | 2.79540e63 | 0.543452 | 0.271726 | − | 0.962375i | \(-0.412406\pi\) | ||||
0.271726 | + | 0.962375i | \(0.412406\pi\) | |||||||
\(920\) | 7.46074e61 | 0.0141692 | ||||||||
\(921\) | 3.49380e60 | 0.000648211 0 | ||||||||
\(922\) | −1.58754e63 | −0.287747 | ||||||||
\(923\) | −1.30087e63 | −0.230356 | ||||||||
\(924\) | −3.01737e61 | −0.00522013 | ||||||||
\(925\) | 1.03854e64 | 1.75540 | ||||||||
\(926\) | −1.45634e63 | −0.240506 | ||||||||
\(927\) | −2.12073e63 | −0.342194 | ||||||||
\(928\) | −1.22140e63 | −0.192565 | ||||||||
\(929\) | −4.76577e62 | −0.0734168 | −0.0367084 | − | 0.999326i | \(-0.511687\pi\) | ||||
−0.0367084 | + | 0.999326i | \(0.511687\pi\) | |||||||
\(930\) | 2.23717e61 | 0.00336756 | ||||||||
\(931\) | 2.93279e63 | 0.431384 | ||||||||
\(932\) | −3.82213e63 | −0.549368 | ||||||||
\(933\) | −1.96525e61 | −0.00276034 | ||||||||
\(934\) | 7.07824e63 | 0.971556 | ||||||||
\(935\) | −3.61663e62 | −0.0485126 | ||||||||
\(936\) | −1.31908e63 | −0.172919 | ||||||||
\(937\) | −8.61288e63 | −1.10344 | −0.551718 | − | 0.834031i | \(-0.686028\pi\) | ||||
−0.551718 | + | 0.834031i | \(0.686028\pi\) | |||||||
\(938\) | 9.65603e63 | 1.20903 | ||||||||
\(939\) | −3.47264e60 | −0.000424962 0 | ||||||||
\(940\) | 1.16454e64 | 1.39285 | ||||||||
\(941\) | 3.45409e63 | 0.403791 | 0.201895 | − | 0.979407i | \(-0.435290\pi\) | ||||
0.201895 | + | 0.979407i | \(0.435290\pi\) | |||||||
\(942\) | 5.36642e60 | 0.000613184 0 | ||||||||
\(943\) | 1.63525e62 | 0.0182635 | ||||||||
\(944\) | 2.46131e63 | 0.268701 | ||||||||
\(945\) | 2.67200e62 | 0.0285136 | ||||||||
\(946\) | 2.63855e63 | 0.275237 | ||||||||
\(947\) | 3.46532e63 | 0.353361 | 0.176680 | − | 0.984268i | \(-0.443464\pi\) | ||||
0.176680 | + | 0.984268i | \(0.443464\pi\) | |||||||
\(948\) | −1.83927e61 | −0.00183344 | ||||||||
\(949\) | −1.64251e62 | −0.0160060 | ||||||||
\(950\) | −1.58251e64 | −1.50761 | ||||||||
\(951\) | 2.78066e61 | 0.00258981 | ||||||||
\(952\) | 8.52689e61 | 0.00776419 | ||||||||
\(953\) | −7.53482e63 | −0.670773 | −0.335387 | − | 0.942081i | \(-0.608867\pi\) | ||||
−0.335387 | + | 0.942081i | \(0.608867\pi\) | |||||||
\(954\) | −9.60772e62 | −0.0836239 | ||||||||
\(955\) | −1.14372e64 | −0.973303 | ||||||||
\(956\) | −1.39875e63 | −0.116384 | ||||||||
\(957\) | −1.11919e62 | −0.00910539 | ||||||||
\(958\) | −6.24101e63 | −0.496474 | ||||||||
\(959\) | 2.87298e64 | 2.23477 | ||||||||
\(960\) | −1.87588e61 | −0.00142684 | ||||||||
\(961\) | −1.11044e64 | −0.825927 | ||||||||
\(962\) | 3.01564e63 | 0.219339 | ||||||||
\(963\) | 7.34903e63 | 0.522715 | ||||||||
\(964\) | 9.97919e63 | 0.694127 | ||||||||
\(965\) | −2.22019e64 | −1.51026 | ||||||||
\(966\) | −1.61181e60 | −0.000107228 0 | ||||||||
\(967\) | 9.70611e63 | 0.631504 | 0.315752 | − | 0.948842i | \(-0.397743\pi\) | ||||
0.315752 | + | 0.948842i | \(0.397743\pi\) | |||||||
\(968\) | −5.67011e63 | −0.360804 | ||||||||
\(969\) | −1.27970e60 | −7.96431e−5 0 | ||||||||
\(970\) | −2.47654e64 | −1.50748 | ||||||||
\(971\) | −6.64214e63 | −0.395453 | −0.197726 | − | 0.980257i | \(-0.563356\pi\) | ||||
−0.197726 | + | 0.980257i | \(0.563356\pi\) | |||||||
\(972\) | 1.51465e62 | 0.00882037 | ||||||||
\(973\) | −1.10044e63 | −0.0626815 | ||||||||
\(974\) | 1.31815e64 | 0.734423 | ||||||||
\(975\) | −1.46071e62 | −0.00796094 | ||||||||
\(976\) | −2.84840e63 | −0.151855 | ||||||||
\(977\) | 1.54974e64 | 0.808213 | 0.404107 | − | 0.914712i | \(-0.367582\pi\) | ||||
0.404107 | + | 0.914712i | \(0.367582\pi\) | |||||||
\(978\) | 9.15011e61 | 0.00466811 | ||||||||
\(979\) | −2.99905e64 | −1.49677 | ||||||||
\(980\) | −1.11323e64 | −0.543532 | ||||||||
\(981\) | 1.13057e64 | 0.540026 | ||||||||
\(982\) | −1.19585e64 | −0.558830 | ||||||||
\(983\) | 3.96381e64 | 1.81222 | 0.906112 | − | 0.423037i | \(-0.139036\pi\) | ||||
0.906112 | + | 0.423037i | \(0.139036\pi\) | |||||||
\(984\) | −4.11157e61 | −0.00183913 | ||||||||
\(985\) | 4.51965e64 | 1.97800 | ||||||||
\(986\) | 3.16277e62 | 0.0135430 | ||||||||
\(987\) | −2.51586e62 | −0.0105406 | ||||||||
\(988\) | −4.59518e63 | −0.188377 | ||||||||
\(989\) | 1.40946e62 | 0.00565368 | ||||||||
\(990\) | 4.97056e64 | 1.95096 | ||||||||
\(991\) | −2.80505e63 | −0.107735 | −0.0538676 | − | 0.998548i | \(-0.517155\pi\) | ||||
−0.0538676 | + | 0.998548i | \(0.517155\pi\) | |||||||
\(992\) | −1.96242e63 | −0.0737549 | ||||||||
\(993\) | −2.05732e61 | −0.000756646 0 | ||||||||
\(994\) | −1.15573e64 | −0.415956 | ||||||||
\(995\) | −7.28631e64 | −2.56632 | ||||||||
\(996\) | 1.44109e62 | 0.00496723 | ||||||||
\(997\) | −1.59618e64 | −0.538437 | −0.269219 | − | 0.963079i | \(-0.586765\pi\) | ||||
−0.269219 | + | 0.963079i | \(0.586765\pi\) | |||||||
\(998\) | 1.58402e64 | 0.522942 | ||||||||
\(999\) | −2.30847e62 | −0.00745876 |
(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 | 2.44.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 18.44.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 16.44.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.44.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.44.a.a.1.1 | 2 | 4.3 | odd | 2 | |||
18.44.a.e.1.2 | 2 | 3.2 | odd | 2 |