Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,40,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 40, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 40);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(9.63395513897\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 175630027x - 142249227846 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{5}\cdot 5\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-12827.3\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10652e6 | 1.49236 | 0.746181 | − | 0.665743i | \(-0.231885\pi\) | ||||
0.746181 | + | 0.665743i | \(0.231885\pi\) | |||||||
\(3\) | 2.98790e9 | 1.48423 | 0.742116 | − | 0.670271i | \(-0.233822\pi\) | ||||
0.742116 | + | 0.670271i | \(0.233822\pi\) | |||||||
\(4\) | 6.74631e11 | 1.22715 | ||||||||
\(5\) | 2.54496e13 | 0.596713 | 0.298356 | − | 0.954455i | \(-0.403562\pi\) | ||||
0.298356 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(6\) | 3.30617e15 | 2.21501 | ||||||||
\(7\) | −5.05826e16 | −1.67722 | −0.838609 | − | 0.544734i | \(-0.816631\pi\) | ||||
−0.838609 | + | 0.544734i | \(0.816631\pi\) | |||||||
\(8\) | 1.38177e17 | 0.338984 | ||||||||
\(9\) | 4.87501e18 | 1.20295 | ||||||||
\(10\) | 2.81604e19 | 0.890511 | ||||||||
\(11\) | 7.53597e19 | 0.371520 | 0.185760 | − | 0.982595i | \(-0.440525\pi\) | ||||
0.185760 | + | 0.982595i | \(0.440525\pi\) | |||||||
\(12\) | 2.01573e21 | 1.82137 | ||||||||
\(13\) | 3.07373e21 | 0.583136 | 0.291568 | − | 0.956550i | \(-0.405823\pi\) | ||||
0.291568 | + | 0.956550i | \(0.405823\pi\) | |||||||
\(14\) | −5.59707e22 | −2.50302 | ||||||||
\(15\) | 7.60408e22 | 0.885660 | ||||||||
\(16\) | −2.17987e23 | −0.721258 | ||||||||
\(17\) | −4.56106e23 | −0.462713 | −0.231357 | − | 0.972869i | \(-0.574316\pi\) | ||||
−0.231357 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(18\) | 5.39430e24 | 1.79523 | ||||||||
\(19\) | −1.63031e24 | −0.189050 | −0.0945248 | − | 0.995523i | \(-0.530133\pi\) | ||||
−0.0945248 | + | 0.995523i | \(0.530133\pi\) | |||||||
\(20\) | 1.71691e25 | 0.732253 | ||||||||
\(21\) | −1.51136e26 | −2.48938 | ||||||||
\(22\) | 8.33870e25 | 0.554442 | ||||||||
\(23\) | 2.17009e26 | 0.606436 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(24\) | 4.12858e26 | 0.503132 | ||||||||
\(25\) | −1.17131e27 | −0.643934 | ||||||||
\(26\) | 3.40114e27 | 0.870250 | ||||||||
\(27\) | 2.45742e27 | 0.301222 | ||||||||
\(28\) | −3.41246e28 | −2.05819 | ||||||||
\(29\) | −6.88782e27 | −0.209566 | −0.104783 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104783 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(30\) | 8.41407e28 | 1.32173 | ||||||||
\(31\) | 1.62636e29 | 1.34792 | 0.673959 | − | 0.738769i | \(-0.264593\pi\) | ||||
0.673959 | + | 0.738769i | \(0.264593\pi\) | |||||||
\(32\) | −3.17170e29 | −1.41536 | ||||||||
\(33\) | 2.25168e29 | 0.551422 | ||||||||
\(34\) | −5.04690e29 | −0.690536 | ||||||||
\(35\) | −1.28730e30 | −1.00082 | ||||||||
\(36\) | 3.28883e30 | 1.47619 | ||||||||
\(37\) | −1.23773e30 | −0.325606 | −0.162803 | − | 0.986659i | \(-0.552054\pi\) | ||||
−0.162803 | + | 0.986659i | \(0.552054\pi\) | |||||||
\(38\) | −1.80397e30 | −0.282130 | ||||||||
\(39\) | 9.18399e30 | 0.865509 | ||||||||
\(40\) | 3.51653e30 | 0.202276 | ||||||||
\(41\) | 1.60595e31 | 0.570751 | 0.285375 | − | 0.958416i | \(-0.407882\pi\) | ||||
0.285375 | + | 0.958416i | \(0.407882\pi\) | |||||||
\(42\) | −1.67235e32 | −3.71506 | ||||||||
\(43\) | 1.28211e32 | 1.80007 | 0.900036 | − | 0.435815i | \(-0.143540\pi\) | ||||
0.900036 | + | 0.435815i | \(0.143540\pi\) | |||||||
\(44\) | 5.08400e31 | 0.455909 | ||||||||
\(45\) | 1.24067e32 | 0.717814 | ||||||||
\(46\) | 2.40125e32 | 0.905022 | ||||||||
\(47\) | −6.09258e32 | −1.50971 | −0.754854 | − | 0.655893i | \(-0.772292\pi\) | ||||
−0.754854 | + | 0.655893i | \(0.772292\pi\) | |||||||
\(48\) | −6.51324e32 | −1.07052 | ||||||||
\(49\) | 1.64906e33 | 1.81306 | ||||||||
\(50\) | −1.29608e33 | −0.960983 | ||||||||
\(51\) | −1.36280e33 | −0.686774 | ||||||||
\(52\) | 2.07363e33 | 0.715593 | ||||||||
\(53\) | 1.51248e33 | 0.360006 | 0.180003 | − | 0.983666i | \(-0.442389\pi\) | ||||
0.180003 | + | 0.983666i | \(0.442389\pi\) | |||||||
\(54\) | 2.71918e33 | 0.449532 | ||||||||
\(55\) | 1.91787e33 | 0.221690 | ||||||||
\(56\) | −6.98933e33 | −0.568551 | ||||||||
\(57\) | −4.87122e33 | −0.280594 | ||||||||
\(58\) | −7.62152e33 | −0.312749 | ||||||||
\(59\) | −4.73479e34 | −1.39215 | −0.696076 | − | 0.717969i | \(-0.745072\pi\) | ||||
−0.696076 | + | 0.717969i | \(0.745072\pi\) | |||||||
\(60\) | 5.12995e34 | 1.08683 | ||||||||
\(61\) | 7.02166e34 | 1.07772 | 0.538862 | − | 0.842394i | \(-0.318854\pi\) | ||||
0.538862 | + | 0.842394i | \(0.318854\pi\) | |||||||
\(62\) | 1.79960e35 | 2.01158 | ||||||||
\(63\) | −2.46591e35 | −2.01760 | ||||||||
\(64\) | −2.31116e35 | −1.39098 | ||||||||
\(65\) | 7.82250e34 | 0.347964 | ||||||||
\(66\) | 2.49152e35 | 0.822921 | ||||||||
\(67\) | −9.34963e34 | −0.230322 | −0.115161 | − | 0.993347i | \(-0.536738\pi\) | ||||
−0.115161 | + | 0.993347i | \(0.536738\pi\) | |||||||
\(68\) | −3.07703e35 | −0.567817 | ||||||||
\(69\) | 6.48402e35 | 0.900092 | ||||||||
\(70\) | −1.42443e36 | −1.49358 | ||||||||
\(71\) | 2.40247e36 | 1.91038 | 0.955190 | − | 0.295994i | \(-0.0956509\pi\) | ||||
0.955190 | + | 0.295994i | \(0.0956509\pi\) | |||||||
\(72\) | 6.73613e35 | 0.407781 | ||||||||
\(73\) | −7.72964e35 | −0.357572 | −0.178786 | − | 0.983888i | \(-0.557217\pi\) | ||||
−0.178786 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(74\) | −1.36958e36 | −0.485923 | ||||||||
\(75\) | −3.49976e36 | −0.955748 | ||||||||
\(76\) | −1.09986e36 | −0.231991 | ||||||||
\(77\) | −3.81189e36 | −0.623119 | ||||||||
\(78\) | 1.01623e37 | 1.29165 | ||||||||
\(79\) | 1.44777e37 | 1.43540 | 0.717699 | − | 0.696353i | \(-0.245195\pi\) | ||||
0.717699 | + | 0.696353i | \(0.245195\pi\) | |||||||
\(80\) | −5.54767e36 | −0.430384 | ||||||||
\(81\) | −1.24137e37 | −0.755865 | ||||||||
\(82\) | 1.77702e37 | 0.851767 | ||||||||
\(83\) | 1.12684e37 | 0.426423 | 0.213212 | − | 0.977006i | \(-0.431608\pi\) | ||||
0.213212 | + | 0.977006i | \(0.431608\pi\) | |||||||
\(84\) | −1.01961e38 | −3.05483 | ||||||||
\(85\) | −1.16077e37 | −0.276107 | ||||||||
\(86\) | 1.41868e38 | 2.68636 | ||||||||
\(87\) | −2.05802e37 | −0.311045 | ||||||||
\(88\) | 1.04129e37 | 0.125939 | ||||||||
\(89\) | −1.09111e38 | −1.05868 | −0.529338 | − | 0.848411i | \(-0.677560\pi\) | ||||
−0.529338 | + | 0.848411i | \(0.677560\pi\) | |||||||
\(90\) | 1.37282e38 | 1.07124 | ||||||||
\(91\) | −1.55477e38 | −0.978045 | ||||||||
\(92\) | 1.46401e38 | 0.744185 | ||||||||
\(93\) | 4.85940e38 | 2.00062 | ||||||||
\(94\) | −6.74156e38 | −2.25303 | ||||||||
\(95\) | −4.14907e37 | −0.112808 | ||||||||
\(96\) | −9.47674e38 | −2.10073 | ||||||||
\(97\) | 7.84026e37 | 0.141998 | 0.0709989 | − | 0.997476i | \(-0.477381\pi\) | ||||
0.0709989 | + | 0.997476i | \(0.477381\pi\) | |||||||
\(98\) | 1.82471e39 | 2.70574 | ||||||||
\(99\) | 3.67379e38 | 0.446919 | ||||||||
\(100\) | −7.90201e38 | −0.790201 | ||||||||
\(101\) | 1.53402e39 | 1.26347 | 0.631734 | − | 0.775185i | \(-0.282344\pi\) | ||||
0.631734 | + | 0.775185i | \(0.282344\pi\) | |||||||
\(102\) | −1.50797e39 | −1.02492 | ||||||||
\(103\) | −1.10618e39 | −0.621586 | −0.310793 | − | 0.950478i | \(-0.600595\pi\) | ||||
−0.310793 | + | 0.950478i | \(0.600595\pi\) | |||||||
\(104\) | 4.24717e38 | 0.197674 | ||||||||
\(105\) | −3.84634e39 | −1.48545 | ||||||||
\(106\) | 1.67359e39 | 0.537260 | ||||||||
\(107\) | 2.25314e39 | 0.602288 | 0.301144 | − | 0.953579i | \(-0.402631\pi\) | ||||
0.301144 | + | 0.953579i | \(0.402631\pi\) | |||||||
\(108\) | 1.65785e39 | 0.369643 | ||||||||
\(109\) | −3.29726e38 | −0.0614239 | −0.0307119 | − | 0.999528i | \(-0.509777\pi\) | ||||
−0.0307119 | + | 0.999528i | \(0.509777\pi\) | |||||||
\(110\) | 2.12216e39 | 0.330843 | ||||||||
\(111\) | −3.69822e39 | −0.483276 | ||||||||
\(112\) | 1.10263e40 | 1.20971 | ||||||||
\(113\) | −9.62984e39 | −0.888361 | −0.444181 | − | 0.895937i | \(-0.646505\pi\) | ||||
−0.444181 | + | 0.895937i | \(0.646505\pi\) | |||||||
\(114\) | −5.39010e39 | −0.418747 | ||||||||
\(115\) | 5.52278e39 | 0.361868 | ||||||||
\(116\) | −4.64674e39 | −0.257168 | ||||||||
\(117\) | 1.49844e40 | 0.701482 | ||||||||
\(118\) | −5.23914e40 | −2.07759 | ||||||||
\(119\) | 2.30710e40 | 0.776070 | ||||||||
\(120\) | 1.05071e40 | 0.300225 | ||||||||
\(121\) | −3.54657e40 | −0.861973 | ||||||||
\(122\) | 7.76961e40 | 1.60836 | ||||||||
\(123\) | 4.79842e40 | 0.847127 | ||||||||
\(124\) | 1.09719e41 | 1.65409 | ||||||||
\(125\) | −7.61018e40 | −0.980956 | ||||||||
\(126\) | −2.72858e41 | −3.01100 | ||||||||
\(127\) | −7.59694e40 | −0.718565 | −0.359282 | − | 0.933229i | \(-0.616978\pi\) | ||||
−0.359282 | + | 0.933229i | \(0.616978\pi\) | |||||||
\(128\) | −8.13679e40 | −0.660479 | ||||||||
\(129\) | 3.83082e41 | 2.67173 | ||||||||
\(130\) | 8.65575e40 | 0.519289 | ||||||||
\(131\) | −2.08014e41 | −1.07474 | −0.537368 | − | 0.843348i | \(-0.680581\pi\) | ||||
−0.537368 | + | 0.843348i | \(0.680581\pi\) | |||||||
\(132\) | 1.51905e41 | 0.676675 | ||||||||
\(133\) | 8.24654e40 | 0.317077 | ||||||||
\(134\) | −1.03456e41 | −0.343724 | ||||||||
\(135\) | 6.25403e40 | 0.179743 | ||||||||
\(136\) | −6.30232e40 | −0.156853 | ||||||||
\(137\) | −3.53926e41 | −0.763592 | −0.381796 | − | 0.924247i | \(-0.624694\pi\) | ||||
−0.381796 | + | 0.924247i | \(0.624694\pi\) | |||||||
\(138\) | 7.17470e41 | 1.34326 | ||||||||
\(139\) | −5.01395e39 | −0.00815438 | −0.00407719 | − | 0.999992i | \(-0.501298\pi\) | ||||
−0.00407719 | + | 0.999992i | \(0.501298\pi\) | |||||||
\(140\) | −8.68455e41 | −1.22815 | ||||||||
\(141\) | −1.82040e42 | −2.24076 | ||||||||
\(142\) | 2.65838e42 | 2.85098 | ||||||||
\(143\) | 2.31635e41 | 0.216646 | ||||||||
\(144\) | −1.06269e42 | −0.867636 | ||||||||
\(145\) | −1.75292e41 | −0.125051 | ||||||||
\(146\) | −8.55300e41 | −0.533627 | ||||||||
\(147\) | 4.92722e42 | 2.69100 | ||||||||
\(148\) | −8.35012e41 | −0.399567 | ||||||||
\(149\) | 1.36965e42 | 0.574749 | 0.287374 | − | 0.957818i | \(-0.407218\pi\) | ||||
0.287374 | + | 0.957818i | \(0.407218\pi\) | |||||||
\(150\) | −3.87255e42 | −1.42632 | ||||||||
\(151\) | −2.28466e42 | −0.739214 | −0.369607 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369607 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(152\) | −2.25271e41 | −0.0640848 | ||||||||
\(153\) | −2.22352e42 | −0.556620 | ||||||||
\(154\) | −4.21793e42 | −0.929920 | ||||||||
\(155\) | 4.13901e42 | 0.804319 | ||||||||
\(156\) | 6.19580e42 | 1.06211 | ||||||||
\(157\) | −3.22622e42 | −0.488260 | −0.244130 | − | 0.969743i | \(-0.578502\pi\) | ||||
−0.244130 | + | 0.969743i | \(0.578502\pi\) | |||||||
\(158\) | 1.60199e43 | 2.14213 | ||||||||
\(159\) | 4.51914e42 | 0.534333 | ||||||||
\(160\) | −8.07185e42 | −0.844565 | ||||||||
\(161\) | −1.09769e43 | −1.01712 | ||||||||
\(162\) | −1.37360e43 | −1.12802 | ||||||||
\(163\) | −4.44788e42 | −0.323963 | −0.161981 | − | 0.986794i | \(-0.551788\pi\) | ||||
−0.161981 | + | 0.986794i | \(0.551788\pi\) | |||||||
\(164\) | 1.08342e43 | 0.700395 | ||||||||
\(165\) | 5.73041e42 | 0.329040 | ||||||||
\(166\) | 1.24688e43 | 0.636378 | ||||||||
\(167\) | 4.33425e42 | 0.196762 | 0.0983812 | − | 0.995149i | \(-0.468634\pi\) | ||||
0.0983812 | + | 0.995149i | \(0.468634\pi\) | |||||||
\(168\) | −2.08834e43 | −0.843862 | ||||||||
\(169\) | −1.83360e43 | −0.659953 | ||||||||
\(170\) | −1.28441e43 | −0.412051 | ||||||||
\(171\) | −7.94779e42 | −0.227417 | ||||||||
\(172\) | 8.64950e43 | 2.20895 | ||||||||
\(173\) | 2.21391e43 | 0.504965 | 0.252482 | − | 0.967601i | \(-0.418753\pi\) | ||||
0.252482 | + | 0.967601i | \(0.418753\pi\) | |||||||
\(174\) | −2.27724e43 | −0.464192 | ||||||||
\(175\) | 5.92479e43 | 1.08002 | ||||||||
\(176\) | −1.64274e43 | −0.267962 | ||||||||
\(177\) | −1.41471e44 | −2.06628 | ||||||||
\(178\) | −1.20733e44 | −1.57993 | ||||||||
\(179\) | 1.32994e44 | 1.56026 | 0.780130 | − | 0.625618i | \(-0.215153\pi\) | ||||
0.780130 | + | 0.625618i | \(0.215153\pi\) | |||||||
\(180\) | 8.36993e43 | 0.880863 | ||||||||
\(181\) | −1.07254e44 | −1.01317 | −0.506584 | − | 0.862191i | \(-0.669092\pi\) | ||||
−0.506584 | + | 0.862191i | \(0.669092\pi\) | |||||||
\(182\) | −1.72038e44 | −1.45960 | ||||||||
\(183\) | 2.09800e44 | 1.59959 | ||||||||
\(184\) | 2.99856e43 | 0.205572 | ||||||||
\(185\) | −3.14997e43 | −0.194293 | ||||||||
\(186\) | 5.37703e44 | 2.98566 | ||||||||
\(187\) | −3.43720e43 | −0.171907 | ||||||||
\(188\) | −4.11024e44 | −1.85263 | ||||||||
\(189\) | −1.24303e44 | −0.505214 | ||||||||
\(190\) | −4.59103e43 | −0.168351 | ||||||||
\(191\) | 2.71109e44 | 0.897414 | 0.448707 | − | 0.893679i | \(-0.351885\pi\) | ||||
0.448707 | + | 0.893679i | \(0.351885\pi\) | |||||||
\(192\) | −6.90551e44 | −2.06453 | ||||||||
\(193\) | −8.26925e43 | −0.223408 | −0.111704 | − | 0.993742i | \(-0.535631\pi\) | ||||
−0.111704 | + | 0.993742i | \(0.535631\pi\) | |||||||
\(194\) | 8.67541e43 | 0.211912 | ||||||||
\(195\) | 2.33729e44 | 0.516460 | ||||||||
\(196\) | 1.11250e45 | 2.22489 | ||||||||
\(197\) | −5.36056e44 | −0.970776 | −0.485388 | − | 0.874299i | \(-0.661322\pi\) | ||||
−0.485388 | + | 0.874299i | \(0.661322\pi\) | |||||||
\(198\) | 4.06513e44 | 0.666965 | ||||||||
\(199\) | −1.00046e45 | −1.48787 | −0.743935 | − | 0.668252i | \(-0.767043\pi\) | ||||
−0.743935 | + | 0.668252i | \(0.767043\pi\) | |||||||
\(200\) | −1.61848e44 | −0.218284 | ||||||||
\(201\) | −2.79358e44 | −0.341852 | ||||||||
\(202\) | 1.69742e45 | 1.88555 | ||||||||
\(203\) | 3.48404e44 | 0.351488 | ||||||||
\(204\) | −9.19387e44 | −0.842772 | ||||||||
\(205\) | 4.08707e44 | 0.340574 | ||||||||
\(206\) | −1.22401e45 | −0.927631 | ||||||||
\(207\) | 1.05792e45 | 0.729511 | ||||||||
\(208\) | −6.70032e44 | −0.420592 | ||||||||
\(209\) | −1.22860e44 | −0.0702356 | ||||||||
\(210\) | −4.25605e45 | −2.21682 | ||||||||
\(211\) | −1.34673e45 | −0.639402 | −0.319701 | − | 0.947518i | \(-0.603582\pi\) | ||||
−0.319701 | + | 0.947518i | \(0.603582\pi\) | |||||||
\(212\) | 1.02037e45 | 0.441780 | ||||||||
\(213\) | 7.17834e45 | 2.83545 | ||||||||
\(214\) | 2.49314e45 | 0.898832 | ||||||||
\(215\) | 3.26291e45 | 1.07413 | ||||||||
\(216\) | 3.39558e44 | 0.102109 | ||||||||
\(217\) | −8.22655e45 | −2.26075 | ||||||||
\(218\) | −3.64849e44 | −0.0916667 | ||||||||
\(219\) | −2.30954e45 | −0.530720 | ||||||||
\(220\) | 1.29385e45 | 0.272047 | ||||||||
\(221\) | −1.40194e45 | −0.269825 | ||||||||
\(222\) | −4.09216e45 | −0.721223 | ||||||||
\(223\) | −4.53007e45 | −0.731409 | −0.365705 | − | 0.930731i | \(-0.619172\pi\) | ||||
−0.365705 | + | 0.930731i | \(0.619172\pi\) | |||||||
\(224\) | 1.60433e46 | 2.37387 | ||||||||
\(225\) | −5.71015e45 | −0.774619 | ||||||||
\(226\) | −1.06556e46 | −1.32576 | ||||||||
\(227\) | 1.08195e46 | 1.23510 | 0.617550 | − | 0.786532i | \(-0.288125\pi\) | ||||
0.617550 | + | 0.786532i | \(0.288125\pi\) | |||||||
\(228\) | −3.28627e45 | −0.344329 | ||||||||
\(229\) | 1.83988e46 | 1.77010 | 0.885051 | − | 0.465494i | \(-0.154123\pi\) | ||||
0.885051 | + | 0.465494i | \(0.154123\pi\) | |||||||
\(230\) | 6.11107e45 | 0.540038 | ||||||||
\(231\) | −1.13896e46 | −0.924854 | ||||||||
\(232\) | −9.51736e44 | −0.0710397 | ||||||||
\(233\) | −1.58389e46 | −1.08714 | −0.543570 | − | 0.839364i | \(-0.682928\pi\) | ||||
−0.543570 | + | 0.839364i | \(0.682928\pi\) | |||||||
\(234\) | 1.65806e46 | 1.04687 | ||||||||
\(235\) | −1.55053e46 | −0.900861 | ||||||||
\(236\) | −3.19423e46 | −1.70837 | ||||||||
\(237\) | 4.32581e46 | 2.13047 | ||||||||
\(238\) | 2.55285e46 | 1.15818 | ||||||||
\(239\) | −2.86406e46 | −1.19736 | −0.598678 | − | 0.800990i | \(-0.704307\pi\) | ||||
−0.598678 | + | 0.800990i | \(0.704307\pi\) | |||||||
\(240\) | −1.65759e46 | −0.638790 | ||||||||
\(241\) | 1.94777e46 | 0.692159 | 0.346080 | − | 0.938205i | \(-0.387513\pi\) | ||||
0.346080 | + | 0.938205i | \(0.387513\pi\) | |||||||
\(242\) | −3.92435e46 | −1.28638 | ||||||||
\(243\) | −4.70498e46 | −1.42310 | ||||||||
\(244\) | 4.73703e46 | 1.32253 | ||||||||
\(245\) | 4.19677e46 | 1.08187 | ||||||||
\(246\) | 5.30955e46 | 1.26422 | ||||||||
\(247\) | −5.01113e45 | −0.110242 | ||||||||
\(248\) | 2.24725e46 | 0.456923 | ||||||||
\(249\) | 3.36690e46 | 0.632911 | ||||||||
\(250\) | −8.42081e46 | −1.46394 | ||||||||
\(251\) | 6.63788e46 | 1.06756 | 0.533779 | − | 0.845624i | \(-0.320771\pi\) | ||||
0.533779 | + | 0.845624i | \(0.320771\pi\) | |||||||
\(252\) | −1.66358e47 | −2.47590 | ||||||||
\(253\) | 1.63537e46 | 0.225303 | ||||||||
\(254\) | −8.40616e46 | −1.07236 | ||||||||
\(255\) | −3.46827e46 | −0.409807 | ||||||||
\(256\) | 3.70220e46 | 0.405303 | ||||||||
\(257\) | −1.60889e47 | −1.63241 | −0.816206 | − | 0.577761i | \(-0.803927\pi\) | ||||
−0.816206 | + | 0.577761i | \(0.803927\pi\) | |||||||
\(258\) | 4.23888e47 | 3.98719 | ||||||||
\(259\) | 6.26077e46 | 0.546113 | ||||||||
\(260\) | 5.27730e46 | 0.427003 | ||||||||
\(261\) | −3.35782e46 | −0.252097 | ||||||||
\(262\) | −2.30171e47 | −1.60390 | ||||||||
\(263\) | 3.82398e46 | 0.247388 | 0.123694 | − | 0.992320i | \(-0.460526\pi\) | ||||
0.123694 | + | 0.992320i | \(0.460526\pi\) | |||||||
\(264\) | 3.11129e46 | 0.186923 | ||||||||
\(265\) | 3.84919e46 | 0.214820 | ||||||||
\(266\) | 9.12497e46 | 0.473194 | ||||||||
\(267\) | −3.26013e47 | −1.57132 | ||||||||
\(268\) | −6.30755e46 | −0.282639 | ||||||||
\(269\) | 7.76998e46 | 0.323780 | 0.161890 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161890 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(270\) | 6.92020e46 | 0.268241 | ||||||||
\(271\) | 2.35011e47 | 0.847591 | 0.423796 | − | 0.905758i | \(-0.360697\pi\) | ||||
0.423796 | + | 0.905758i | \(0.360697\pi\) | |||||||
\(272\) | 9.94252e46 | 0.333736 | ||||||||
\(273\) | −4.64550e47 | −1.45165 | ||||||||
\(274\) | −3.91626e47 | −1.13956 | ||||||||
\(275\) | −8.82695e46 | −0.239234 | ||||||||
\(276\) | 4.37432e47 | 1.10454 | ||||||||
\(277\) | 4.19090e47 | 0.986170 | 0.493085 | − | 0.869981i | \(-0.335869\pi\) | ||||
0.493085 | + | 0.869981i | \(0.335869\pi\) | |||||||
\(278\) | −5.54803e45 | −0.0121693 | ||||||||
\(279\) | 7.92852e47 | 1.62147 | ||||||||
\(280\) | −1.77875e47 | −0.339261 | ||||||||
\(281\) | 2.30674e46 | 0.0410417 | 0.0205209 | − | 0.999789i | \(-0.493468\pi\) | ||||
0.0205209 | + | 0.999789i | \(0.493468\pi\) | |||||||
\(282\) | −2.01431e48 | −3.34402 | ||||||||
\(283\) | 6.25956e47 | 0.969858 | 0.484929 | − | 0.874554i | \(-0.338846\pi\) | ||||
0.484929 | + | 0.874554i | \(0.338846\pi\) | |||||||
\(284\) | 1.62078e48 | 2.34431 | ||||||||
\(285\) | −1.23970e47 | −0.167434 | ||||||||
\(286\) | 2.56309e47 | 0.323315 | ||||||||
\(287\) | −8.12331e47 | −0.957273 | ||||||||
\(288\) | −1.54621e48 | −1.70261 | ||||||||
\(289\) | −7.63613e47 | −0.785897 | ||||||||
\(290\) | −1.93964e47 | −0.186621 | ||||||||
\(291\) | 2.34259e47 | 0.210758 | ||||||||
\(292\) | −5.21465e47 | −0.438793 | ||||||||
\(293\) | 4.49093e47 | 0.353523 | 0.176762 | − | 0.984254i | \(-0.443438\pi\) | ||||
0.176762 | + | 0.984254i | \(0.443438\pi\) | |||||||
\(294\) | 5.45207e48 | 4.01595 | ||||||||
\(295\) | −1.20498e48 | −0.830714 | ||||||||
\(296\) | −1.71026e47 | −0.110376 | ||||||||
\(297\) | 1.85190e47 | 0.111910 | ||||||||
\(298\) | 1.51555e48 | 0.857733 | ||||||||
\(299\) | 6.67026e47 | 0.353634 | ||||||||
\(300\) | −2.36105e48 | −1.17284 | ||||||||
\(301\) | −6.48524e48 | −3.01911 | ||||||||
\(302\) | −2.52802e48 | −1.10318 | ||||||||
\(303\) | 4.58350e48 | 1.87528 | ||||||||
\(304\) | 3.55387e47 | 0.136354 | ||||||||
\(305\) | 1.78698e48 | 0.643092 | ||||||||
\(306\) | −2.46037e48 | −0.830678 | ||||||||
\(307\) | 5.77022e48 | 1.82808 | 0.914038 | − | 0.405628i | \(-0.132947\pi\) | ||||
0.914038 | + | 0.405628i | \(0.132947\pi\) | |||||||
\(308\) | −2.57162e48 | −0.764659 | ||||||||
\(309\) | −3.30517e48 | −0.922578 | ||||||||
\(310\) | 4.57990e48 | 1.20034 | ||||||||
\(311\) | −3.50073e48 | −0.861651 | −0.430826 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430826 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(312\) | 1.26901e48 | 0.293394 | ||||||||
\(313\) | 4.32088e48 | 0.938551 | 0.469276 | − | 0.883052i | \(-0.344515\pi\) | ||||
0.469276 | + | 0.883052i | \(0.344515\pi\) | |||||||
\(314\) | −3.56988e48 | −0.728661 | ||||||||
\(315\) | −6.27563e48 | −1.20393 | ||||||||
\(316\) | 9.76713e48 | 1.76144 | ||||||||
\(317\) | −3.38834e47 | −0.0574554 | −0.0287277 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287277 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(318\) | 5.00052e48 | 0.797419 | ||||||||
\(319\) | −5.19065e47 | −0.0778580 | ||||||||
\(320\) | −5.88179e48 | −0.830014 | ||||||||
\(321\) | 6.73216e48 | 0.893936 | ||||||||
\(322\) | −1.21461e49 | −1.51792 | ||||||||
\(323\) | 7.43595e47 | 0.0874757 | ||||||||
\(324\) | −8.37468e48 | −0.927556 | ||||||||
\(325\) | −3.60028e48 | −0.375501 | ||||||||
\(326\) | −4.92167e48 | −0.483470 | ||||||||
\(327\) | −9.85191e47 | −0.0911673 | ||||||||
\(328\) | 2.21905e48 | 0.193476 | ||||||||
\(329\) | 3.08178e49 | 2.53211 | ||||||||
\(330\) | 6.34082e48 | 0.491047 | ||||||||
\(331\) | −1.23716e49 | −0.903189 | −0.451595 | − | 0.892223i | \(-0.649145\pi\) | ||||
−0.451595 | + | 0.892223i | \(0.649145\pi\) | |||||||
\(332\) | 7.60203e48 | 0.523284 | ||||||||
\(333\) | −6.03396e48 | −0.391688 | ||||||||
\(334\) | 4.79593e48 | 0.293641 | ||||||||
\(335\) | −2.37944e48 | −0.137436 | ||||||||
\(336\) | 3.29457e49 | 1.79549 | ||||||||
\(337\) | −1.65140e49 | −0.849316 | −0.424658 | − | 0.905354i | \(-0.639606\pi\) | ||||
−0.424658 | + | 0.905354i | \(0.639606\pi\) | |||||||
\(338\) | −2.02891e49 | −0.984889 | ||||||||
\(339\) | −2.87730e49 | −1.31853 | ||||||||
\(340\) | −7.83091e48 | −0.338823 | ||||||||
\(341\) | 1.22562e49 | 0.500778 | ||||||||
\(342\) | −8.79439e48 | −0.339388 | ||||||||
\(343\) | −3.74064e49 | −1.36368 | ||||||||
\(344\) | 1.77157e49 | 0.610197 | ||||||||
\(345\) | 1.65015e49 | 0.537096 | ||||||||
\(346\) | 2.44974e49 | 0.753591 | ||||||||
\(347\) | 3.18063e49 | 0.924885 | 0.462443 | − | 0.886649i | \(-0.346973\pi\) | ||||
0.462443 | + | 0.886649i | \(0.346973\pi\) | |||||||
\(348\) | −1.38840e49 | −0.381698 | ||||||||
\(349\) | 1.04623e49 | 0.271976 | 0.135988 | − | 0.990711i | \(-0.456579\pi\) | ||||
0.135988 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(350\) | 6.55590e49 | 1.61178 | ||||||||
\(351\) | 7.55343e48 | 0.175653 | ||||||||
\(352\) | −2.39019e49 | −0.525835 | ||||||||
\(353\) | −3.28850e49 | −0.684527 | −0.342263 | − | 0.939604i | \(-0.611194\pi\) | ||||
−0.342263 | + | 0.939604i | \(0.611194\pi\) | |||||||
\(354\) | −1.56540e50 | −3.08363 | ||||||||
\(355\) | 6.11417e49 | 1.13995 | ||||||||
\(356\) | −7.36096e49 | −1.29915 | ||||||||
\(357\) | 6.89340e49 | 1.15187 | ||||||||
\(358\) | 1.47160e50 | 2.32847 | ||||||||
\(359\) | 4.88065e49 | 0.731367 | 0.365684 | − | 0.930739i | \(-0.380835\pi\) | ||||
0.365684 | + | 0.930739i | \(0.380835\pi\) | |||||||
\(360\) | 1.71431e49 | 0.243328 | ||||||||
\(361\) | −7.17108e49 | −0.964260 | ||||||||
\(362\) | −1.18679e50 | −1.51201 | ||||||||
\(363\) | −1.05968e50 | −1.27937 | ||||||||
\(364\) | −1.04890e50 | −1.20020 | ||||||||
\(365\) | −1.96716e49 | −0.213368 | ||||||||
\(366\) | 2.32148e50 | 2.38718 | ||||||||
\(367\) | 7.14273e49 | 0.696428 | 0.348214 | − | 0.937415i | \(-0.386788\pi\) | ||||
0.348214 | + | 0.937415i | \(0.386788\pi\) | |||||||
\(368\) | −4.73051e49 | −0.437397 | ||||||||
\(369\) | 7.82902e49 | 0.686583 | ||||||||
\(370\) | −3.48551e49 | −0.289956 | ||||||||
\(371\) | −7.65051e49 | −0.603809 | ||||||||
\(372\) | 3.27830e50 | 2.45506 | ||||||||
\(373\) | 1.05915e50 | 0.752724 | 0.376362 | − | 0.926473i | \(-0.377175\pi\) | ||||
0.376362 | + | 0.926473i | \(0.377175\pi\) | |||||||
\(374\) | −3.80333e49 | −0.256548 | ||||||||
\(375\) | −2.27385e50 | −1.45597 | ||||||||
\(376\) | −8.41852e49 | −0.511767 | ||||||||
\(377\) | −2.11713e49 | −0.122206 | ||||||||
\(378\) | −1.37543e50 | −0.753962 | ||||||||
\(379\) | −1.87195e50 | −0.974605 | −0.487302 | − | 0.873233i | \(-0.662019\pi\) | ||||
−0.487302 | + | 0.873233i | \(0.662019\pi\) | |||||||
\(380\) | −2.79909e49 | −0.138432 | ||||||||
\(381\) | −2.26989e50 | −1.06652 | ||||||||
\(382\) | 2.99987e50 | 1.33927 | ||||||||
\(383\) | 3.66531e50 | 1.55502 | 0.777508 | − | 0.628873i | \(-0.216484\pi\) | ||||
0.777508 | + | 0.628873i | \(0.216484\pi\) | |||||||
\(384\) | −2.43120e50 | −0.980305 | ||||||||
\(385\) | −9.70109e49 | −0.371823 | ||||||||
\(386\) | −9.15009e49 | −0.333406 | ||||||||
\(387\) | 6.25030e50 | 2.16539 | ||||||||
\(388\) | 5.28928e49 | 0.174252 | ||||||||
\(389\) | −4.12272e49 | −0.129171 | −0.0645857 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645857 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(390\) | 2.58625e50 | 0.770746 | ||||||||
\(391\) | −9.89791e49 | −0.280606 | ||||||||
\(392\) | 2.27861e50 | 0.614598 | ||||||||
\(393\) | −6.21525e50 | −1.59516 | ||||||||
\(394\) | −5.93157e50 | −1.44875 | ||||||||
\(395\) | 3.68452e50 | 0.856520 | ||||||||
\(396\) | 2.47845e50 | 0.548435 | ||||||||
\(397\) | 4.25670e50 | 0.896723 | 0.448361 | − | 0.893852i | \(-0.352008\pi\) | ||||
0.448361 | + | 0.893852i | \(0.352008\pi\) | |||||||
\(398\) | −1.10703e51 | −2.22044 | ||||||||
\(399\) | 2.46399e50 | 0.470616 | ||||||||
\(400\) | 2.55330e50 | 0.464443 | ||||||||
\(401\) | −6.90511e50 | −1.19634 | −0.598171 | − | 0.801368i | \(-0.704106\pi\) | ||||
−0.598171 | + | 0.801368i | \(0.704106\pi\) | |||||||
\(402\) | −3.09115e50 | −0.510167 | ||||||||
\(403\) | 4.99898e50 | 0.786019 | ||||||||
\(404\) | 1.03490e51 | 1.55046 | ||||||||
\(405\) | −3.15924e50 | −0.451034 | ||||||||
\(406\) | 3.85516e50 | 0.524548 | ||||||||
\(407\) | −9.32751e49 | −0.120969 | ||||||||
\(408\) | −1.88307e50 | −0.232806 | ||||||||
\(409\) | −5.24800e50 | −0.618571 | −0.309286 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309286 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(410\) | 4.52243e50 | 0.508260 | ||||||||
\(411\) | −1.05750e51 | −1.13335 | ||||||||
\(412\) | −7.46265e50 | −0.762776 | ||||||||
\(413\) | 2.39498e51 | 2.33494 | ||||||||
\(414\) | 1.17061e51 | 1.08869 | ||||||||
\(415\) | 2.86777e50 | 0.254452 | ||||||||
\(416\) | −9.74895e50 | −0.825349 | ||||||||
\(417\) | −1.49812e49 | −0.0121030 | ||||||||
\(418\) | −1.35947e50 | −0.104817 | ||||||||
\(419\) | 1.54729e51 | 1.13867 | 0.569334 | − | 0.822106i | \(-0.307201\pi\) | ||||
0.569334 | + | 0.822106i | \(0.307201\pi\) | |||||||
\(420\) | −2.59486e51 | −1.82286 | ||||||||
\(421\) | −1.69195e51 | −1.13472 | −0.567359 | − | 0.823471i | \(-0.692035\pi\) | ||||
−0.567359 | + | 0.823471i | \(0.692035\pi\) | |||||||
\(422\) | −1.49019e51 | −0.954220 | ||||||||
\(423\) | −2.97014e51 | −1.81610 | ||||||||
\(424\) | 2.08989e50 | 0.122037 | ||||||||
\(425\) | 5.34241e50 | 0.297957 | ||||||||
\(426\) | 7.94298e51 | 4.23152 | ||||||||
\(427\) | −3.55174e51 | −1.80758 | ||||||||
\(428\) | 1.52004e51 | 0.739096 | ||||||||
\(429\) | 6.92103e50 | 0.321554 | ||||||||
\(430\) | 3.61048e51 | 1.60299 | ||||||||
\(431\) | 2.11949e51 | 0.899341 | 0.449670 | − | 0.893195i | \(-0.351541\pi\) | ||||
0.449670 | + | 0.893195i | \(0.351541\pi\) | |||||||
\(432\) | −5.35686e50 | −0.217259 | ||||||||
\(433\) | 1.57391e51 | 0.610193 | 0.305097 | − | 0.952321i | \(-0.401311\pi\) | ||||
0.305097 | + | 0.952321i | \(0.401311\pi\) | |||||||
\(434\) | −9.10284e51 | −3.37386 | ||||||||
\(435\) | −5.23756e50 | −0.185604 | ||||||||
\(436\) | −2.22444e50 | −0.0753761 | ||||||||
\(437\) | −3.53792e50 | −0.114646 | ||||||||
\(438\) | −2.55555e51 | −0.792027 | ||||||||
\(439\) | 7.36309e50 | 0.218274 | 0.109137 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109137 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(440\) | 2.65005e50 | 0.0751496 | ||||||||
\(441\) | 8.03916e51 | 2.18101 | ||||||||
\(442\) | −1.55128e51 | −0.402676 | ||||||||
\(443\) | −3.79349e51 | −0.942251 | −0.471125 | − | 0.882066i | \(-0.656152\pi\) | ||||
−0.471125 | + | 0.882066i | \(0.656152\pi\) | |||||||
\(444\) | −2.49494e51 | −0.593050 | ||||||||
\(445\) | −2.77683e51 | −0.631726 | ||||||||
\(446\) | −5.01262e51 | −1.09153 | ||||||||
\(447\) | 4.09239e51 | 0.853061 | ||||||||
\(448\) | 1.16904e52 | 2.33297 | ||||||||
\(449\) | 7.69430e51 | 1.47016 | 0.735081 | − | 0.677979i | \(-0.237144\pi\) | ||||
0.735081 | + | 0.677979i | \(0.237144\pi\) | |||||||
\(450\) | −6.31839e51 | −1.15601 | ||||||||
\(451\) | 1.21024e51 | 0.212045 | ||||||||
\(452\) | −6.49659e51 | −1.09015 | ||||||||
\(453\) | −6.82633e51 | −1.09717 | ||||||||
\(454\) | 1.19720e52 | 1.84322 | ||||||||
\(455\) | −3.95682e51 | −0.583612 | ||||||||
\(456\) | −6.73088e50 | −0.0951168 | ||||||||
\(457\) | −9.48171e51 | −1.28387 | −0.641935 | − | 0.766759i | \(-0.721868\pi\) | ||||
−0.641935 | + | 0.766759i | \(0.721868\pi\) | |||||||
\(458\) | 2.03587e52 | 2.64163 | ||||||||
\(459\) | −1.12084e51 | −0.139379 | ||||||||
\(460\) | 3.72584e51 | 0.444065 | ||||||||
\(461\) | −1.00315e52 | −1.14604 | −0.573018 | − | 0.819543i | \(-0.694227\pi\) | ||||
−0.573018 | + | 0.819543i | \(0.694227\pi\) | |||||||
\(462\) | −1.26028e52 | −1.38022 | ||||||||
\(463\) | −6.38266e51 | −0.670151 | −0.335075 | − | 0.942191i | \(-0.608762\pi\) | ||||
−0.335075 | + | 0.942191i | \(0.608762\pi\) | |||||||
\(464\) | 1.50146e51 | 0.151151 | ||||||||
\(465\) | 1.23670e52 | 1.19380 | ||||||||
\(466\) | −1.75261e52 | −1.62241 | ||||||||
\(467\) | 8.44728e51 | 0.749960 | 0.374980 | − | 0.927033i | \(-0.377650\pi\) | ||||
0.374980 | + | 0.927033i | \(0.377650\pi\) | |||||||
\(468\) | 1.01090e52 | 0.860821 | ||||||||
\(469\) | 4.72929e51 | 0.386300 | ||||||||
\(470\) | −1.71570e52 | −1.34441 | ||||||||
\(471\) | −9.63964e51 | −0.724692 | ||||||||
\(472\) | −6.54237e51 | −0.471918 | ||||||||
\(473\) | 9.66194e51 | 0.668762 | ||||||||
\(474\) | 4.78659e52 | 3.17943 | ||||||||
\(475\) | 1.90960e51 | 0.121735 | ||||||||
\(476\) | 1.55644e52 | 0.952352 | ||||||||
\(477\) | 7.37335e51 | 0.433069 | ||||||||
\(478\) | −3.16914e52 | −1.78689 | ||||||||
\(479\) | 3.34415e51 | 0.181027 | 0.0905134 | − | 0.995895i | \(-0.471149\pi\) | ||||
0.0905134 | + | 0.995895i | \(0.471149\pi\) | |||||||
\(480\) | −2.41179e52 | −1.25353 | ||||||||
\(481\) | −3.80445e51 | −0.189873 | ||||||||
\(482\) | 2.15525e52 | 1.03295 | ||||||||
\(483\) | −3.27978e52 | −1.50965 | ||||||||
\(484\) | −2.39262e52 | −1.05777 | ||||||||
\(485\) | 1.99531e51 | 0.0847319 | ||||||||
\(486\) | −5.20616e52 | −2.12378 | ||||||||
\(487\) | 3.02586e52 | 1.18586 | 0.592931 | − | 0.805254i | \(-0.297971\pi\) | ||||
0.592931 | + | 0.805254i | \(0.297971\pi\) | |||||||
\(488\) | 9.70229e51 | 0.365332 | ||||||||
\(489\) | −1.32898e52 | −0.480836 | ||||||||
\(490\) | 4.64381e52 | 1.61455 | ||||||||
\(491\) | 5.39058e52 | 1.80114 | 0.900568 | − | 0.434715i | \(-0.143151\pi\) | ||||
0.900568 | + | 0.434715i | \(0.143151\pi\) | |||||||
\(492\) | 3.23716e52 | 1.03955 | ||||||||
\(493\) | 3.14158e51 | 0.0969690 | ||||||||
\(494\) | −5.54492e51 | −0.164520 | ||||||||
\(495\) | 9.34964e51 | 0.266682 | ||||||||
\(496\) | −3.54525e52 | −0.972197 | ||||||||
\(497\) | −1.21523e53 | −3.20412 | ||||||||
\(498\) | 3.72554e52 | 0.944533 | ||||||||
\(499\) | 4.77343e52 | 1.16378 | 0.581888 | − | 0.813269i | \(-0.302314\pi\) | ||||
0.581888 | + | 0.813269i | \(0.302314\pi\) | |||||||
\(500\) | −5.13406e52 | −1.20378 | ||||||||
\(501\) | 1.29503e52 | 0.292041 | ||||||||
\(502\) | 7.34494e52 | 1.59318 | ||||||||
\(503\) | 4.55769e51 | 0.0950974 | 0.0475487 | − | 0.998869i | \(-0.484859\pi\) | ||||
0.0475487 | + | 0.998869i | \(0.484859\pi\) | |||||||
\(504\) | −3.40731e52 | −0.683937 | ||||||||
\(505\) | 3.90401e52 | 0.753927 | ||||||||
\(506\) | 1.80957e52 | 0.336234 | ||||||||
\(507\) | −5.47861e52 | −0.979524 | ||||||||
\(508\) | −5.12513e52 | −0.881784 | ||||||||
\(509\) | −4.13304e52 | −0.684341 | −0.342170 | − | 0.939638i | \(-0.611162\pi\) | ||||
−0.342170 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(510\) | −3.83771e52 | −0.611580 | ||||||||
\(511\) | 3.90985e52 | 0.599726 | ||||||||
\(512\) | 8.56980e52 | 1.26534 | ||||||||
\(513\) | −4.00636e51 | −0.0569458 | ||||||||
\(514\) | −1.78027e53 | −2.43615 | ||||||||
\(515\) | −2.81519e52 | −0.370908 | ||||||||
\(516\) | 2.58439e53 | 3.27860 | ||||||||
\(517\) | −4.59135e52 | −0.560886 | ||||||||
\(518\) | 6.92767e52 | 0.814998 | ||||||||
\(519\) | 6.61495e52 | 0.749486 | ||||||||
\(520\) | 1.08089e52 | 0.117955 | ||||||||
\(521\) | −4.81863e52 | −0.506510 | −0.253255 | − | 0.967400i | \(-0.581501\pi\) | ||||
−0.253255 | + | 0.967400i | \(0.581501\pi\) | |||||||
\(522\) | −3.71550e52 | −0.376220 | ||||||||
\(523\) | 1.41580e52 | 0.138108 | 0.0690541 | − | 0.997613i | \(-0.478002\pi\) | ||||
0.0690541 | + | 0.997613i | \(0.478002\pi\) | |||||||
\(524\) | −1.40333e53 | −1.31886 | ||||||||
\(525\) | 1.77027e53 | 1.60300 | ||||||||
\(526\) | 4.23131e52 | 0.369193 | ||||||||
\(527\) | −7.41792e52 | −0.623699 | ||||||||
\(528\) | −4.90836e52 | −0.397718 | ||||||||
\(529\) | −8.09589e52 | −0.632236 | ||||||||
\(530\) | 4.25921e52 | 0.320590 | ||||||||
\(531\) | −2.30821e53 | −1.67468 | ||||||||
\(532\) | 5.56337e52 | 0.389100 | ||||||||
\(533\) | 4.93625e52 | 0.332825 | ||||||||
\(534\) | −3.60740e53 | −2.34498 | ||||||||
\(535\) | 5.73414e52 | 0.359393 | ||||||||
\(536\) | −1.29190e52 | −0.0780756 | ||||||||
\(537\) | 3.97372e53 | 2.31579 | ||||||||
\(538\) | 8.59763e52 | 0.483197 | ||||||||
\(539\) | 1.24272e53 | 0.673587 | ||||||||
\(540\) | 4.21916e52 | 0.220570 | ||||||||
\(541\) | 1.61080e53 | 0.812258 | 0.406129 | − | 0.913816i | \(-0.366878\pi\) | ||||
0.406129 | + | 0.913816i | \(0.366878\pi\) | |||||||
\(542\) | 2.60044e53 | 1.26491 | ||||||||
\(543\) | −3.20465e53 | −1.50378 | ||||||||
\(544\) | 1.44663e53 | 0.654907 | ||||||||
\(545\) | −8.39139e51 | −0.0366524 | ||||||||
\(546\) | −5.14034e53 | −2.16638 | ||||||||
\(547\) | −2.03359e52 | −0.0827010 | −0.0413505 | − | 0.999145i | \(-0.513166\pi\) | ||||
−0.0413505 | + | 0.999145i | \(0.513166\pi\) | |||||||
\(548\) | −2.38769e53 | −0.937039 | ||||||||
\(549\) | 3.42307e53 | 1.29645 | ||||||||
\(550\) | −9.76720e52 | −0.357024 | ||||||||
\(551\) | 1.12293e52 | 0.0396184 | ||||||||
\(552\) | 8.95940e52 | 0.305117 | ||||||||
\(553\) | −7.32322e53 | −2.40747 | ||||||||
\(554\) | 4.63731e53 | 1.47172 | ||||||||
\(555\) | −9.41182e52 | −0.288377 | ||||||||
\(556\) | −3.38256e51 | −0.0100066 | ||||||||
\(557\) | −4.33061e53 | −1.23701 | −0.618505 | − | 0.785781i | \(-0.712261\pi\) | ||||
−0.618505 | + | 0.785781i | \(0.712261\pi\) | |||||||
\(558\) | 8.77306e53 | 2.41983 | ||||||||
\(559\) | 3.94085e53 | 1.04969 | ||||||||
\(560\) | 2.80616e53 | 0.721847 | ||||||||
\(561\) | −1.02700e53 | −0.255150 | ||||||||
\(562\) | 2.55246e52 | 0.0612491 | ||||||||
\(563\) | −6.67730e53 | −1.54770 | −0.773851 | − | 0.633368i | \(-0.781672\pi\) | ||||
−0.773851 | + | 0.633368i | \(0.781672\pi\) | |||||||
\(564\) | −1.22810e54 | −2.74974 | ||||||||
\(565\) | −2.45075e53 | −0.530096 | ||||||||
\(566\) | 6.92632e53 | 1.44738 | ||||||||
\(567\) | 6.27918e53 | 1.26775 | ||||||||
\(568\) | 3.31965e53 | 0.647589 | ||||||||
\(569\) | 9.32793e53 | 1.75831 | 0.879156 | − | 0.476534i | \(-0.158107\pi\) | ||||
0.879156 | + | 0.476534i | \(0.158107\pi\) | |||||||
\(570\) | −1.37176e53 | −0.249872 | ||||||||
\(571\) | −2.47736e53 | −0.436099 | −0.218049 | − | 0.975938i | \(-0.569969\pi\) | ||||
−0.218049 | + | 0.975938i | \(0.569969\pi\) | |||||||
\(572\) | 1.56268e53 | 0.265857 | ||||||||
\(573\) | 8.10046e53 | 1.33197 | ||||||||
\(574\) | −8.98860e53 | −1.42860 | ||||||||
\(575\) | −2.54185e53 | −0.390505 | ||||||||
\(576\) | −1.12669e54 | −1.67327 | ||||||||
\(577\) | 4.60066e53 | 0.660528 | 0.330264 | − | 0.943889i | \(-0.392862\pi\) | ||||
0.330264 | + | 0.943889i | \(0.392862\pi\) | |||||||
\(578\) | −8.44953e53 | −1.17284 | ||||||||
\(579\) | −2.47077e53 | −0.331590 | ||||||||
\(580\) | −1.18257e53 | −0.153456 | ||||||||
\(581\) | −5.69987e53 | −0.715204 | ||||||||
\(582\) | 2.59213e53 | 0.314527 | ||||||||
\(583\) | 1.13980e53 | 0.133749 | ||||||||
\(584\) | −1.06806e53 | −0.121211 | ||||||||
\(585\) | 3.81348e53 | 0.418583 | ||||||||
\(586\) | 4.96930e53 | 0.527585 | ||||||||
\(587\) | 1.03979e54 | 1.06783 | 0.533916 | − | 0.845537i | \(-0.320720\pi\) | ||||
0.533916 | + | 0.845537i | \(0.320720\pi\) | |||||||
\(588\) | 3.32405e54 | 3.30225 | ||||||||
\(589\) | −2.65147e53 | −0.254823 | ||||||||
\(590\) | −1.33334e54 | −1.23973 | ||||||||
\(591\) | −1.60168e54 | −1.44086 | ||||||||
\(592\) | 2.69809e53 | 0.234846 | ||||||||
\(593\) | −4.68001e53 | −0.394167 | −0.197084 | − | 0.980387i | \(-0.563147\pi\) | ||||
−0.197084 | + | 0.980387i | \(0.563147\pi\) | |||||||
\(594\) | 2.04917e53 | 0.167010 | ||||||||
\(595\) | 5.87147e53 | 0.463091 | ||||||||
\(596\) | 9.24009e53 | 0.705301 | ||||||||
\(597\) | −2.98928e54 | −2.20835 | ||||||||
\(598\) | 7.38078e53 | 0.527751 | ||||||||
\(599\) | 1.95085e54 | 1.35021 | 0.675106 | − | 0.737721i | \(-0.264098\pi\) | ||||
0.675106 | + | 0.737721i | \(0.264098\pi\) | |||||||
\(600\) | −4.83585e53 | −0.323984 | ||||||||
\(601\) | 2.02439e54 | 1.31293 | 0.656467 | − | 0.754355i | \(-0.272050\pi\) | ||||
0.656467 | + | 0.754355i | \(0.272050\pi\) | |||||||
\(602\) | −7.17605e54 | −4.50561 | ||||||||
\(603\) | −4.55796e53 | −0.277066 | ||||||||
\(604\) | −1.54130e54 | −0.907124 | ||||||||
\(605\) | −9.02586e53 | −0.514350 | ||||||||
\(606\) | 5.07174e54 | 2.79860 | ||||||||
\(607\) | 2.12357e54 | 1.13472 | 0.567359 | − | 0.823471i | \(-0.307965\pi\) | ||||
0.567359 | + | 0.823471i | \(0.307965\pi\) | |||||||
\(608\) | 5.17087e53 | 0.267574 | ||||||||
\(609\) | 1.04100e54 | 0.521690 | ||||||||
\(610\) | 1.97733e54 | 0.959726 | ||||||||
\(611\) | −1.87269e54 | −0.880364 | ||||||||
\(612\) | −1.50006e54 | −0.683054 | ||||||||
\(613\) | −3.14022e54 | −1.38510 | −0.692549 | − | 0.721371i | \(-0.743512\pi\) | ||||
−0.692549 | + | 0.721371i | \(0.743512\pi\) | |||||||
\(614\) | 6.38487e54 | 2.72815 | ||||||||
\(615\) | 1.22118e54 | 0.505492 | ||||||||
\(616\) | −5.26714e53 | −0.211228 | ||||||||
\(617\) | −2.88947e54 | −1.12268 | −0.561341 | − | 0.827585i | \(-0.689714\pi\) | ||||
−0.561341 | + | 0.827585i | \(0.689714\pi\) | |||||||
\(618\) | −3.65723e54 | −1.37682 | ||||||||
\(619\) | −8.69334e53 | −0.317116 | −0.158558 | − | 0.987350i | \(-0.550685\pi\) | ||||
−0.158558 | + | 0.987350i | \(0.550685\pi\) | |||||||
\(620\) | 2.79230e54 | 0.987017 | ||||||||
\(621\) | 5.33282e53 | 0.182672 | ||||||||
\(622\) | −3.87363e54 | −1.28590 | ||||||||
\(623\) | 5.51912e54 | 1.77563 | ||||||||
\(624\) | −2.00199e54 | −0.624256 | ||||||||
\(625\) | 1.93843e53 | 0.0585853 | ||||||||
\(626\) | 4.78114e54 | 1.40066 | ||||||||
\(627\) | −3.67093e53 | −0.104246 | ||||||||
\(628\) | −2.17651e54 | −0.599166 | ||||||||
\(629\) | 5.64537e53 | 0.150662 | ||||||||
\(630\) | −6.94411e54 | −1.79670 | ||||||||
\(631\) | −2.40764e54 | −0.603976 | −0.301988 | − | 0.953312i | \(-0.597650\pi\) | ||||
−0.301988 | + | 0.953312i | \(0.597650\pi\) | |||||||
\(632\) | 2.00048e54 | 0.486578 | ||||||||
\(633\) | −4.02391e54 | −0.949022 | ||||||||
\(634\) | −3.74926e53 | −0.0857443 | ||||||||
\(635\) | −1.93339e54 | −0.428777 | ||||||||
\(636\) | 3.04875e54 | 0.655705 | ||||||||
\(637\) | 5.06874e54 | 1.05726 | ||||||||
\(638\) | −5.74355e53 | −0.116192 | ||||||||
\(639\) | 1.17121e55 | 2.29809 | ||||||||
\(640\) | −2.07078e54 | −0.394116 | ||||||||
\(641\) | −2.69211e53 | −0.0497005 | −0.0248503 | − | 0.999691i | \(-0.507911\pi\) | ||||
−0.0248503 | + | 0.999691i | \(0.507911\pi\) | |||||||
\(642\) | 7.44927e54 | 1.33408 | ||||||||
\(643\) | −3.09318e54 | −0.537393 | −0.268696 | − | 0.963225i | \(-0.586593\pi\) | ||||
−0.268696 | + | 0.963225i | \(0.586593\pi\) | |||||||
\(644\) | −7.40534e54 | −1.24816 | ||||||||
\(645\) | 9.74926e54 | 1.59425 | ||||||||
\(646\) | 8.22803e53 | 0.130545 | ||||||||
\(647\) | −1.66944e54 | −0.257003 | −0.128501 | − | 0.991709i | \(-0.541017\pi\) | ||||
−0.128501 | + | 0.991709i | \(0.541017\pi\) | |||||||
\(648\) | −1.71529e54 | −0.256226 | ||||||||
\(649\) | −3.56812e54 | −0.517212 | ||||||||
\(650\) | −3.98379e54 | −0.560384 | ||||||||
\(651\) | −2.45801e55 | −3.35548 | ||||||||
\(652\) | −3.00068e54 | −0.397549 | ||||||||
\(653\) | 1.05739e55 | 1.35965 | 0.679824 | − | 0.733375i | \(-0.262056\pi\) | ||||
0.679824 | + | 0.733375i | \(0.262056\pi\) | |||||||
\(654\) | −1.09013e54 | −0.136055 | ||||||||
\(655\) | −5.29386e54 | −0.641309 | ||||||||
\(656\) | −3.50076e54 | −0.411659 | ||||||||
\(657\) | −3.76821e54 | −0.430140 | ||||||||
\(658\) | 3.41006e55 | 3.77882 | ||||||||
\(659\) | 3.28150e54 | 0.353026 | 0.176513 | − | 0.984298i | \(-0.443518\pi\) | ||||
0.176513 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(660\) | 3.86591e54 | 0.403781 | ||||||||
\(661\) | 1.10445e55 | 1.12000 | 0.560001 | − | 0.828492i | \(-0.310801\pi\) | ||||
0.560001 | + | 0.828492i | \(0.310801\pi\) | |||||||
\(662\) | −1.36894e55 | −1.34789 | ||||||||
\(663\) | −4.18887e54 | −0.400482 | ||||||||
\(664\) | 1.55703e54 | 0.144551 | ||||||||
\(665\) | 2.09871e54 | 0.189204 | ||||||||
\(666\) | −6.67670e54 | −0.584540 | ||||||||
\(667\) | −1.49472e54 | −0.127088 | ||||||||
\(668\) | 2.92402e54 | 0.241456 | ||||||||
\(669\) | −1.35354e55 | −1.08558 | ||||||||
\(670\) | −2.63290e54 | −0.205105 | ||||||||
\(671\) | 5.29150e54 | 0.400396 | ||||||||
\(672\) | 4.79358e55 | 3.52338 | ||||||||
\(673\) | −1.32277e55 | −0.944478 | −0.472239 | − | 0.881471i | \(-0.656554\pi\) | ||||
−0.472239 | + | 0.881471i | \(0.656554\pi\) | |||||||
\(674\) | −1.82731e55 | −1.26749 | ||||||||
\(675\) | −2.87840e54 | −0.193967 | ||||||||
\(676\) | −1.23700e55 | −0.809858 | ||||||||
\(677\) | 1.10632e54 | 0.0703723 | 0.0351861 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351861 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(678\) | −3.18379e55 | −1.96773 | ||||||||
\(679\) | −3.96581e54 | −0.238161 | ||||||||
\(680\) | −1.60391e54 | −0.0935959 | ||||||||
\(681\) | 3.23276e55 | 1.83318 | ||||||||
\(682\) | 1.35617e55 | 0.747342 | ||||||||
\(683\) | 1.00248e55 | 0.536873 | 0.268437 | − | 0.963297i | \(-0.413493\pi\) | ||||
0.268437 | + | 0.963297i | \(0.413493\pi\) | |||||||
\(684\) | −5.36182e54 | −0.279073 | ||||||||
\(685\) | −9.00726e54 | −0.455645 | ||||||||
\(686\) | −4.13910e55 | −2.03510 | ||||||||
\(687\) | 5.49739e55 | 2.62724 | ||||||||
\(688\) | −2.79483e55 | −1.29832 | ||||||||
\(689\) | 4.64895e54 | 0.209933 | ||||||||
\(690\) | 1.82593e55 | 0.801542 | ||||||||
\(691\) | −1.51432e55 | −0.646242 | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323121 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(692\) | 1.49357e55 | 0.619666 | ||||||||
\(693\) | −1.85830e55 | −0.749580 | ||||||||
\(694\) | 3.51943e55 | 1.38026 | ||||||||
\(695\) | −1.27603e53 | −0.00486582 | ||||||||
\(696\) | −2.84370e54 | −0.105439 | ||||||||
\(697\) | −7.32483e54 | −0.264094 | ||||||||
\(698\) | 1.15767e55 | 0.405886 | ||||||||
\(699\) | −4.73252e55 | −1.61357 | ||||||||
\(700\) | 3.99704e55 | 1.32534 | ||||||||
\(701\) | 4.82172e55 | 1.55489 | 0.777447 | − | 0.628948i | \(-0.216514\pi\) | ||||
0.777447 | + | 0.628948i | \(0.216514\pi\) | |||||||
\(702\) | 8.35803e54 | 0.262138 | ||||||||
\(703\) | 2.01789e54 | 0.0615557 | ||||||||
\(704\) | −1.74168e55 | −0.516775 | ||||||||
\(705\) | −4.63285e55 | −1.33709 | ||||||||
\(706\) | −3.63879e55 | −1.02156 | ||||||||
\(707\) | −7.75947e55 | −2.11911 | ||||||||
\(708\) | −9.54406e55 | −2.53562 | ||||||||
\(709\) | 6.05445e53 | 0.0156485 | 0.00782426 | − | 0.999969i | \(-0.497509\pi\) | ||||
0.00782426 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(710\) | 6.76545e55 | 1.70121 | ||||||||
\(711\) | 7.05791e55 | 1.72671 | ||||||||
\(712\) | −1.50766e55 | −0.358875 | ||||||||
\(713\) | 3.52934e55 | 0.817425 | ||||||||
\(714\) | 7.62768e55 | 1.71901 | ||||||||
\(715\) | 5.89501e54 | 0.129276 | ||||||||
\(716\) | 8.97216e55 | 1.91467 | ||||||||
\(717\) | −8.55754e55 | −1.77716 | ||||||||
\(718\) | 5.40053e55 | 1.09147 | ||||||||
\(719\) | −7.05056e54 | −0.138679 | −0.0693394 | − | 0.997593i | \(-0.522089\pi\) | ||||
−0.0693394 | + | 0.997593i | \(0.522089\pi\) | |||||||
\(720\) | −2.70450e55 | −0.517729 | ||||||||
\(721\) | 5.59536e55 | 1.04253 | ||||||||
\(722\) | −7.93495e55 | −1.43903 | ||||||||
\(723\) | 5.81976e55 | 1.02733 | ||||||||
\(724\) | −7.23568e55 | −1.24330 | ||||||||
\(725\) | 8.06777e54 | 0.134947 | ||||||||
\(726\) | −1.17256e56 | −1.90928 | ||||||||
\(727\) | 7.92077e55 | 1.25559 | 0.627793 | − | 0.778380i | \(-0.283958\pi\) | ||||
0.627793 | + | 0.778380i | \(0.283958\pi\) | |||||||
\(728\) | −2.14833e55 | −0.331542 | ||||||||
\(729\) | −9.02730e55 | −1.35635 | ||||||||
\(730\) | −2.17670e55 | −0.318422 | ||||||||
\(731\) | −5.84777e55 | −0.832917 | ||||||||
\(732\) | 1.41538e56 | 1.96294 | ||||||||
\(733\) | −6.30225e55 | −0.851076 | −0.425538 | − | 0.904941i | \(-0.639915\pi\) | ||||
−0.425538 | + | 0.904941i | \(0.639915\pi\) | |||||||
\(734\) | 7.90358e55 | 1.03932 | ||||||||
\(735\) | 1.25396e56 | 1.60575 | ||||||||
\(736\) | −6.88288e55 | −0.858327 | ||||||||
\(737\) | −7.04586e54 | −0.0855692 | ||||||||
\(738\) | 8.66297e55 | 1.02463 | ||||||||
\(739\) | −1.14548e56 | −1.31954 | −0.659768 | − | 0.751469i | \(-0.729345\pi\) | ||||
−0.659768 | + | 0.751469i | \(0.729345\pi\) | |||||||
\(740\) | −2.12507e55 | −0.238426 | ||||||||
\(741\) | −1.49728e55 | −0.163624 | ||||||||
\(742\) | −8.46545e55 | −0.901101 | ||||||||
\(743\) | 3.14628e55 | 0.326224 | 0.163112 | − | 0.986608i | \(-0.447847\pi\) | ||||
0.163112 | + | 0.986608i | \(0.447847\pi\) | |||||||
\(744\) | 6.71456e55 | 0.678180 | ||||||||
\(745\) | 3.48570e55 | 0.342960 | ||||||||
\(746\) | 1.17197e56 | 1.12334 | ||||||||
\(747\) | 5.49338e55 | 0.512965 | ||||||||
\(748\) | −2.31884e55 | −0.210955 | ||||||||
\(749\) | −1.13970e56 | −1.01017 | ||||||||
\(750\) | −2.51606e56 | −2.17283 | ||||||||
\(751\) | 1.74710e56 | 1.47007 | 0.735036 | − | 0.678028i | \(-0.237165\pi\) | ||||
0.735036 | + | 0.678028i | \(0.237165\pi\) | |||||||
\(752\) | 1.32810e56 | 1.08889 | ||||||||
\(753\) | 1.98333e56 | 1.58451 | ||||||||
\(754\) | −2.34264e55 | −0.182375 | ||||||||
\(755\) | −5.81435e55 | −0.441098 | ||||||||
\(756\) | −8.38584e55 | −0.619971 | ||||||||
\(757\) | 2.77438e55 | 0.199893 | 0.0999463 | − | 0.994993i | \(-0.468133\pi\) | ||||
0.0999463 | + | 0.994993i | \(0.468133\pi\) | |||||||
\(758\) | −2.07134e56 | −1.45446 | ||||||||
\(759\) | 4.88634e55 | 0.334402 | ||||||||
\(760\) | −5.73305e54 | −0.0382402 | ||||||||
\(761\) | −2.40584e56 | −1.56411 | −0.782053 | − | 0.623212i | \(-0.785827\pi\) | ||||
−0.782053 | + | 0.623212i | \(0.785827\pi\) | |||||||
\(762\) | −2.51168e56 | −1.59163 | ||||||||
\(763\) | 1.66784e55 | 0.103021 | ||||||||
\(764\) | 1.82898e56 | 1.10126 | ||||||||
\(765\) | −5.65876e55 | −0.332142 | ||||||||
\(766\) | 4.05574e56 | 2.32065 | ||||||||
\(767\) | −1.45534e56 | −0.811813 | ||||||||
\(768\) | 1.10618e56 | 0.601565 | ||||||||
\(769\) | 3.04973e56 | 1.61695 | 0.808477 | − | 0.588528i | \(-0.200292\pi\) | ||||
0.808477 | + | 0.588528i | \(0.200292\pi\) | |||||||
\(770\) | −1.07345e56 | −0.554895 | ||||||||
\(771\) | −4.80720e56 | −2.42288 | ||||||||
\(772\) | −5.57869e55 | −0.274154 | ||||||||
\(773\) | 4.36657e55 | 0.209238 | 0.104619 | − | 0.994512i | \(-0.466638\pi\) | ||||
0.104619 | + | 0.994512i | \(0.466638\pi\) | |||||||
\(774\) | 6.91608e56 | 3.23155 | ||||||||
\(775\) | −1.90497e56 | −0.867970 | ||||||||
\(776\) | 1.08334e55 | 0.0481351 | ||||||||
\(777\) | 1.87066e56 | 0.810559 | ||||||||
\(778\) | −4.56187e55 | −0.192771 | ||||||||
\(779\) | −2.61820e55 | −0.107900 | ||||||||
\(780\) | 1.57680e56 | 0.633772 | ||||||||
\(781\) | 1.81049e56 | 0.709744 | ||||||||
\(782\) | −1.09522e56 | −0.418766 | ||||||||
\(783\) | −1.69263e55 | −0.0631258 | ||||||||
\(784\) | −3.59473e56 | −1.30768 | ||||||||
\(785\) | −8.21060e55 | −0.291351 | ||||||||
\(786\) | −6.87730e56 | −2.38056 | ||||||||
\(787\) | −4.86747e56 | −1.64360 | −0.821800 | − | 0.569777i | \(-0.807030\pi\) | ||||
−0.821800 | + | 0.569777i | \(0.807030\pi\) | |||||||
\(788\) | −3.61640e56 | −1.19128 | ||||||||
\(789\) | 1.14257e56 | 0.367182 | ||||||||
\(790\) | 4.07700e56 | 1.27824 | ||||||||
\(791\) | 4.87102e56 | 1.48997 | ||||||||
\(792\) | 5.07632e55 | 0.151499 | ||||||||
\(793\) | 2.15827e56 | 0.628460 | ||||||||
\(794\) | 4.71012e56 | 1.33824 | ||||||||
\(795\) | 1.15010e56 | 0.318843 | ||||||||
\(796\) | −6.74942e56 | −1.82583 | ||||||||
\(797\) | 5.82796e56 | 1.53844 | 0.769218 | − | 0.638986i | \(-0.220646\pi\) | ||||
0.769218 | + | 0.638986i | \(0.220646\pi\) | |||||||
\(798\) | 2.72645e56 | 0.702330 | ||||||||
\(799\) | 2.77886e56 | 0.698561 | ||||||||
\(800\) | 3.71505e56 | 0.911401 | ||||||||
\(801\) | −5.31917e56 | −1.27353 | ||||||||
\(802\) | −7.64064e56 | −1.78538 | ||||||||
\(803\) | −5.82503e55 | −0.132845 | ||||||||
\(804\) | −1.88463e56 | −0.419502 | ||||||||
\(805\) | −2.79357e56 | −0.606931 | ||||||||
\(806\) | 5.53147e56 | 1.17303 | ||||||||
\(807\) | 2.32159e56 | 0.480565 | ||||||||
\(808\) | 2.11966e56 | 0.428296 | ||||||||
\(809\) | −7.85718e56 | −1.54978 | −0.774891 | − | 0.632095i | \(-0.782195\pi\) | ||||
−0.774891 | + | 0.632095i | \(0.782195\pi\) | |||||||
\(810\) | −3.49576e56 | −0.673106 | ||||||||
\(811\) | 4.57812e56 | 0.860558 | 0.430279 | − | 0.902696i | \(-0.358415\pi\) | ||||
0.430279 | + | 0.902696i | \(0.358415\pi\) | |||||||
\(812\) | 2.35044e56 | 0.431327 | ||||||||
\(813\) | 7.02189e56 | 1.25802 | ||||||||
\(814\) | −1.03211e56 | −0.180530 | ||||||||
\(815\) | −1.13197e56 | −0.193312 | ||||||||
\(816\) | 2.97073e56 | 0.495342 | ||||||||
\(817\) | −2.09024e56 | −0.340303 | ||||||||
\(818\) | −5.80702e56 | −0.923132 | ||||||||
\(819\) | −7.57952e56 | −1.17654 | ||||||||
\(820\) | 2.75726e56 | 0.417934 | ||||||||
\(821\) | 5.79486e56 | 0.857731 | 0.428866 | − | 0.903368i | \(-0.358913\pi\) | ||||
0.428866 | + | 0.903368i | \(0.358913\pi\) | |||||||
\(822\) | −1.17014e57 | −1.69137 | ||||||||
\(823\) | −1.26890e57 | −1.79114 | −0.895572 | − | 0.444916i | \(-0.853233\pi\) | ||||
−0.895572 | + | 0.444916i | \(0.853233\pi\) | |||||||
\(824\) | −1.52849e56 | −0.210708 | ||||||||
\(825\) | −2.63741e56 | −0.355079 | ||||||||
\(826\) | 2.65009e57 | 3.48458 | ||||||||
\(827\) | 3.04410e56 | 0.390932 | 0.195466 | − | 0.980710i | \(-0.437378\pi\) | ||||
0.195466 | + | 0.980710i | \(0.437378\pi\) | |||||||
\(828\) | 7.13706e56 | 0.895216 | ||||||||
\(829\) | −4.36698e56 | −0.535017 | −0.267509 | − | 0.963555i | \(-0.586200\pi\) | ||||
−0.267509 | + | 0.963555i | \(0.586200\pi\) | |||||||
\(830\) | 3.17324e56 | 0.379735 | ||||||||
\(831\) | 1.25220e57 | 1.46371 | ||||||||
\(832\) | −7.10386e56 | −0.811129 | ||||||||
\(833\) | −7.52144e56 | −0.838926 | ||||||||
\(834\) | −1.65770e55 | −0.0180621 | ||||||||
\(835\) | 1.10305e56 | 0.117411 | ||||||||
\(836\) | −8.28850e55 | −0.0861894 | ||||||||
\(837\) | 3.99665e56 | 0.406022 | ||||||||
\(838\) | 1.71210e57 | 1.69931 | ||||||||
\(839\) | 1.05819e56 | 0.102614 | 0.0513070 | − | 0.998683i | \(-0.483661\pi\) | ||||
0.0513070 | + | 0.998683i | \(0.483661\pi\) | |||||||
\(840\) | −5.31475e56 | −0.503543 | ||||||||
\(841\) | −1.03280e57 | −0.956082 | ||||||||
\(842\) | −1.87218e57 | −1.69341 | ||||||||
\(843\) | 6.89232e55 | 0.0609155 | ||||||||
\(844\) | −9.08549e56 | −0.784640 | ||||||||
\(845\) | −4.66642e56 | −0.393802 | ||||||||
\(846\) | −3.28652e57 | −2.71028 | ||||||||
\(847\) | 1.79395e57 | 1.44572 | ||||||||
\(848\) | −3.29701e56 | −0.259658 | ||||||||
\(849\) | 1.87029e57 | 1.43949 | ||||||||
\(850\) | 5.91149e56 | 0.444660 | ||||||||
\(851\) | −2.68599e56 | −0.197459 | ||||||||
\(852\) | 4.84273e57 | 3.47951 | ||||||||
\(853\) | −1.08758e57 | −0.763756 | −0.381878 | − | 0.924213i | \(-0.624723\pi\) | ||||
−0.381878 | + | 0.924213i | \(0.624723\pi\) | |||||||
\(854\) | −3.93007e57 | −2.69756 | ||||||||
\(855\) | −2.02268e56 | −0.135702 | ||||||||
\(856\) | 3.11331e56 | 0.204166 | ||||||||
\(857\) | 1.97964e57 | 1.26900 | 0.634498 | − | 0.772925i | \(-0.281207\pi\) | ||||
0.634498 | + | 0.772925i | \(0.281207\pi\) | |||||||
\(858\) | 7.65826e56 | 0.479875 | ||||||||
\(859\) | 5.66557e56 | 0.347038 | 0.173519 | − | 0.984831i | \(-0.444486\pi\) | ||||
0.173519 | + | 0.984831i | \(0.444486\pi\) | |||||||
\(860\) | 2.20126e57 | 1.31811 | ||||||||
\(861\) | −2.42717e57 | −1.42082 | ||||||||
\(862\) | 2.34526e57 | 1.34214 | ||||||||
\(863\) | −5.59601e56 | −0.313089 | −0.156545 | − | 0.987671i | \(-0.550036\pi\) | ||||
−0.156545 | + | 0.987671i | \(0.550036\pi\) | |||||||
\(864\) | −7.79421e56 | −0.426338 | ||||||||
\(865\) | 5.63431e56 | 0.301319 | ||||||||
\(866\) | 1.74157e57 | 0.910629 | ||||||||
\(867\) | −2.28160e57 | −1.16645 | ||||||||
\(868\) | −5.54988e57 | −2.77427 | ||||||||
\(869\) | 1.09104e57 | 0.533279 | ||||||||
\(870\) | −5.79546e56 | −0.276989 | ||||||||
\(871\) | −2.87382e56 | −0.134309 | ||||||||
\(872\) | −4.55605e55 | −0.0208217 | ||||||||
\(873\) | 3.82214e56 | 0.170816 | ||||||||
\(874\) | −3.91478e56 | −0.171094 | ||||||||
\(875\) | 3.84943e57 | 1.64528 | ||||||||
\(876\) | −1.55809e57 | −0.651271 | ||||||||
\(877\) | −3.51912e57 | −1.43861 | −0.719304 | − | 0.694695i | \(-0.755539\pi\) | ||||
−0.719304 | + | 0.694695i | \(0.755539\pi\) | |||||||
\(878\) | 8.14740e56 | 0.325744 | ||||||||
\(879\) | 1.34185e57 | 0.524711 | ||||||||
\(880\) | −4.18071e56 | −0.159896 | ||||||||
\(881\) | −2.67197e57 | −0.999542 | −0.499771 | − | 0.866158i | \(-0.666583\pi\) | ||||
−0.499771 | + | 0.866158i | \(0.666583\pi\) | |||||||
\(882\) | 8.89550e57 | 3.25486 | ||||||||
\(883\) | 3.97981e57 | 1.42439 | 0.712194 | − | 0.701982i | \(-0.247701\pi\) | ||||
0.712194 | + | 0.701982i | \(0.247701\pi\) | |||||||
\(884\) | −9.45795e56 | −0.331114 | ||||||||
\(885\) | −3.60037e57 | −1.23297 | ||||||||
\(886\) | −4.19757e57 | −1.40618 | ||||||||
\(887\) | −2.01262e57 | −0.659555 | −0.329778 | − | 0.944059i | \(-0.606974\pi\) | ||||
−0.329778 | + | 0.944059i | \(0.606974\pi\) | |||||||
\(888\) | −5.11008e56 | −0.163823 | ||||||||
\(889\) | 3.84273e57 | 1.20519 | ||||||||
\(890\) | −3.07261e57 | −0.942764 | ||||||||
\(891\) | −9.35494e56 | −0.280819 | ||||||||
\(892\) | −3.05613e57 | −0.897546 | ||||||||
\(893\) | 9.93280e56 | 0.285409 | ||||||||
\(894\) | 4.52831e57 | 1.27308 | ||||||||
\(895\) | 3.38463e57 | 0.931026 | ||||||||
\(896\) | 4.11580e57 | 1.10777 | ||||||||
\(897\) | 1.99301e57 | 0.524876 | ||||||||
\(898\) | 8.51389e57 | 2.19401 | ||||||||
\(899\) | −1.12021e57 | −0.282478 | ||||||||
\(900\) | −3.85224e57 | −0.950571 | ||||||||
\(901\) | −6.89851e56 | −0.166580 | ||||||||
\(902\) | 1.33915e57 | 0.316448 | ||||||||
\(903\) | −1.93773e58 | −4.48107 | ||||||||
\(904\) | −1.33062e57 | −0.301141 | ||||||||
\(905\) | −2.72957e57 | −0.604570 | ||||||||
\(906\) | −7.55347e57 | −1.63737 | ||||||||
\(907\) | −1.92035e57 | −0.407416 | −0.203708 | − | 0.979032i | \(-0.565299\pi\) | ||||
−0.203708 | + | 0.979032i | \(0.565299\pi\) | |||||||
\(908\) | 7.29915e57 | 1.51565 | ||||||||
\(909\) | 7.47836e57 | 1.51989 | ||||||||
\(910\) | −4.37830e57 | −0.870961 | ||||||||
\(911\) | 5.42803e57 | 1.05690 | 0.528450 | − | 0.848964i | \(-0.322773\pi\) | ||||
0.528450 | + | 0.848964i | \(0.322773\pi\) | |||||||
\(912\) | 1.06186e57 | 0.202380 | ||||||||
\(913\) | 8.49186e56 | 0.158425 | ||||||||
\(914\) | −1.04917e58 | −1.91600 | ||||||||
\(915\) | 5.33933e57 | 0.954498 | ||||||||
\(916\) | 1.24124e58 | 2.17217 | ||||||||
\(917\) | 1.05219e58 | 1.80257 | ||||||||
\(918\) | −1.24024e57 | −0.208004 | ||||||||
\(919\) | −1.06801e58 | −1.75357 | −0.876785 | − | 0.480883i | \(-0.840316\pi\) | ||||
−0.876785 | + | 0.480883i | \(0.840316\pi\) | |||||||
\(920\) | 7.63119e56 | 0.122668 | ||||||||
\(921\) | 1.72409e58 | 2.71329 | ||||||||
\(922\) | −1.11001e58 | −1.71030 | ||||||||
\(923\) | 7.38452e57 | 1.11401 | ||||||||
\(924\) | −7.68375e57 | −1.13493 | ||||||||
\(925\) | 1.44977e57 | 0.209669 | ||||||||
\(926\) | −7.06255e57 | −1.00011 | ||||||||
\(927\) | −5.39265e57 | −0.747735 | ||||||||
\(928\) | 2.18461e57 | 0.296612 | ||||||||
\(929\) | −9.61260e57 | −1.27801 | −0.639005 | − | 0.769202i | \(-0.720654\pi\) | ||||
−0.639005 | + | 0.769202i | \(0.720654\pi\) | |||||||
\(930\) | 1.36843e58 | 1.78158 | ||||||||
\(931\) | −2.68848e57 | −0.342758 | ||||||||
\(932\) | −1.06854e58 | −1.33408 | ||||||||
\(933\) | −1.04599e58 | −1.27889 | ||||||||
\(934\) | 9.34709e57 | 1.11921 | ||||||||
\(935\) | −8.74753e56 | −0.102579 | ||||||||
\(936\) | 2.07050e57 | 0.237791 | ||||||||
\(937\) | −6.32461e57 | −0.711396 | −0.355698 | − | 0.934601i | \(-0.615757\pi\) | ||||
−0.355698 | + | 0.934601i | \(0.615757\pi\) | |||||||
\(938\) | 5.23305e57 | 0.576500 | ||||||||
\(939\) | 1.29104e58 | 1.39303 | ||||||||
\(940\) | −1.04604e58 | −1.10549 | ||||||||
\(941\) | 4.44546e57 | 0.460171 | 0.230085 | − | 0.973170i | \(-0.426099\pi\) | ||||
0.230085 | + | 0.973170i | \(0.426099\pi\) | |||||||
\(942\) | −1.06665e58 | −1.08150 | ||||||||
\(943\) | 3.48505e57 | 0.346124 | ||||||||
\(944\) | 1.03212e58 | 1.00410 | ||||||||
\(945\) | −3.16345e57 | −0.301467 | ||||||||
\(946\) | 1.06911e58 | 0.998036 | ||||||||
\(947\) | −2.02681e58 | −1.85348 | −0.926739 | − | 0.375705i | \(-0.877401\pi\) | ||||
−0.926739 | + | 0.375705i | \(0.877401\pi\) | |||||||
\(948\) | 2.91832e58 | 2.61439 | ||||||||
\(949\) | −2.37588e57 | −0.208513 | ||||||||
\(950\) | 2.11301e57 | 0.181673 | ||||||||
\(951\) | −1.01240e57 | −0.0852772 | ||||||||
\(952\) | 3.18788e57 | 0.263076 | ||||||||
\(953\) | −2.18717e58 | −1.76837 | −0.884183 | − | 0.467141i | \(-0.845284\pi\) | ||||
−0.884183 | + | 0.467141i | \(0.845284\pi\) | |||||||
\(954\) | 8.15876e57 | 0.646295 | ||||||||
\(955\) | 6.89959e57 | 0.535498 | ||||||||
\(956\) | −1.93218e58 | −1.46933 | ||||||||
\(957\) | −1.55091e57 | −0.115559 | ||||||||
\(958\) | 3.70037e57 | 0.270158 | ||||||||
\(959\) | 1.79025e58 | 1.28071 | ||||||||
\(960\) | −1.75742e58 | −1.23193 | ||||||||
\(961\) | 1.18923e58 | 0.816882 | ||||||||
\(962\) | −4.20970e57 | −0.283359 | ||||||||
\(963\) | 1.09841e58 | 0.724521 | ||||||||
\(964\) | 1.31403e58 | 0.849381 | ||||||||
\(965\) | −2.10449e57 | −0.133310 | ||||||||
\(966\) | −3.62915e58 | −2.25295 | ||||||||
\(967\) | −8.40382e57 | −0.511282 | −0.255641 | − | 0.966772i | \(-0.582287\pi\) | ||||
−0.255641 | + | 0.966772i | \(0.582287\pi\) | |||||||
\(968\) | −4.90053e57 | −0.292195 | ||||||||
\(969\) | 2.22179e57 | 0.129834 | ||||||||
\(970\) | 2.20785e57 | 0.126451 | ||||||||
\(971\) | 2.19465e58 | 1.23194 | 0.615972 | − | 0.787768i | \(-0.288763\pi\) | ||||
0.615972 | + | 0.787768i | \(0.288763\pi\) | |||||||
\(972\) | −3.17413e58 | −1.74635 | ||||||||
\(973\) | 2.53618e56 | 0.0136767 | ||||||||
\(974\) | 3.34817e58 | 1.76974 | ||||||||
\(975\) | −1.07573e58 | −0.557331 | ||||||||
\(976\) | −1.53063e58 | −0.777318 | ||||||||
\(977\) | 4.53213e57 | 0.225610 | 0.112805 | − | 0.993617i | \(-0.464016\pi\) | ||||
0.112805 | + | 0.993617i | \(0.464016\pi\) | |||||||
\(978\) | −1.47055e58 | −0.717581 | ||||||||
\(979\) | −8.22257e57 | −0.393319 | ||||||||
\(980\) | 2.83127e58 | 1.32762 | ||||||||
\(981\) | −1.60742e57 | −0.0738897 | ||||||||
\(982\) | 5.96479e58 | 2.68795 | ||||||||
\(983\) | −3.96363e58 | −1.75105 | −0.875527 | − | 0.483169i | \(-0.839486\pi\) | ||||
−0.875527 | + | 0.483169i | \(0.839486\pi\) | |||||||
\(984\) | 6.63030e57 | 0.287163 | ||||||||
\(985\) | −1.36424e58 | −0.579274 | ||||||||
\(986\) | 3.47622e57 | 0.144713 | ||||||||
\(987\) | 9.20807e58 | 3.75824 | ||||||||
\(988\) | −3.38066e57 | −0.135282 | ||||||||
\(989\) | 2.78229e58 | 1.09163 | ||||||||
\(990\) | 1.03456e58 | 0.397986 | ||||||||
\(991\) | −1.58403e58 | −0.597486 | −0.298743 | − | 0.954334i | \(-0.596567\pi\) | ||||
−0.298743 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(992\) | −5.15833e58 | −1.90779 | ||||||||
\(993\) | −3.69650e58 | −1.34054 | ||||||||
\(994\) | −1.34468e59 | −4.78171 | ||||||||
\(995\) | −2.54613e58 | −0.887831 | ||||||||
\(996\) | 2.27141e58 | 0.776675 | ||||||||
\(997\) | 6.66270e57 | 0.223406 | 0.111703 | − | 0.993742i | \(-0.464369\pi\) | ||||
0.111703 | + | 0.993742i | \(0.464369\pi\) | |||||||
\(998\) | 5.28189e58 | 1.73678 | ||||||||
\(999\) | −3.04163e57 | −0.0980797 |
(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 | 1.40.a.a.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 9.40.a.b.1.1 | 3 | |||
4.3 | odd | 2 | 16.40.a.c.1.1 | 3 | |||
5.2 | odd | 4 | 25.40.b.a.24.6 | 6 | |||
5.3 | odd | 4 | 25.40.b.a.24.1 | 6 | |||
5.4 | even | 2 | 25.40.a.a.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.40.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.40.a.b.1.1 | 3 | 3.2 | odd | 2 | |||
16.40.a.c.1.1 | 3 | 4.3 | odd | 2 | |||
25.40.a.a.1.1 | 3 | 5.4 | even | 2 | |||
25.40.b.a.24.1 | 6 | 5.3 | odd | 4 | |||
25.40.b.a.24.6 | 6 | 5.2 | odd | 4 |