Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,18,Mod(1,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(12.8255461141\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 2290x^{2} - 4009x + 1104138 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(23.8876\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −181.857 | −0.502312 | −0.251156 | − | 0.967947i | \(-0.580811\pi\) | ||||
−0.251156 | + | 0.967947i | \(0.580811\pi\) | |||||||
\(3\) | 16535.0 | 1.45504 | 0.727520 | − | 0.686087i | \(-0.240673\pi\) | ||||
0.727520 | + | 0.686087i | \(0.240673\pi\) | |||||||
\(4\) | −98000.2 | −0.747682 | ||||||||
\(5\) | −359290. | −0.411340 | −0.205670 | − | 0.978621i | \(-0.565937\pi\) | ||||
−0.205670 | + | 0.978621i | \(0.565937\pi\) | |||||||
\(6\) | −3.00701e6 | −0.730884 | ||||||||
\(7\) | −5.76480e6 | −0.377964 | ||||||||
\(8\) | 4.16583e7 | 0.877883 | ||||||||
\(9\) | 1.44267e8 | 1.11714 | ||||||||
\(10\) | 6.53393e7 | 0.206621 | ||||||||
\(11\) | −5.17615e8 | −0.728063 | −0.364032 | − | 0.931387i | \(-0.618600\pi\) | ||||
−0.364032 | + | 0.931387i | \(0.618600\pi\) | |||||||
\(12\) | −1.62044e9 | −1.08791 | ||||||||
\(13\) | −4.13704e9 | −1.40660 | −0.703301 | − | 0.710892i | \(-0.748292\pi\) | ||||
−0.703301 | + | 0.710892i | \(0.748292\pi\) | |||||||
\(14\) | 1.04837e9 | 0.189856 | ||||||||
\(15\) | −5.94088e9 | −0.598515 | ||||||||
\(16\) | 5.26925e9 | 0.306711 | ||||||||
\(17\) | −2.18253e10 | −0.758831 | −0.379415 | − | 0.925226i | \(-0.623875\pi\) | ||||
−0.379415 | + | 0.925226i | \(0.623875\pi\) | |||||||
\(18\) | −2.62360e10 | −0.561153 | ||||||||
\(19\) | −9.10855e10 | −1.23039 | −0.615196 | − | 0.788374i | \(-0.710923\pi\) | ||||
−0.615196 | + | 0.788374i | \(0.710923\pi\) | |||||||
\(20\) | 3.52105e10 | 0.307551 | ||||||||
\(21\) | −9.53212e10 | −0.549953 | ||||||||
\(22\) | 9.41317e10 | 0.365715 | ||||||||
\(23\) | 3.15846e10 | 0.0840986 | 0.0420493 | − | 0.999116i | \(-0.486611\pi\) | ||||
0.0420493 | + | 0.999116i | \(0.486611\pi\) | |||||||
\(24\) | 6.88821e11 | 1.27735 | ||||||||
\(25\) | −6.33850e11 | −0.830800 | ||||||||
\(26\) | 7.52348e11 | 0.706554 | ||||||||
\(27\) | 2.50131e11 | 0.170441 | ||||||||
\(28\) | 5.64952e11 | 0.282597 | ||||||||
\(29\) | 1.03888e12 | 0.385641 | 0.192821 | − | 0.981234i | \(-0.438236\pi\) | ||||
0.192821 | + | 0.981234i | \(0.438236\pi\) | |||||||
\(30\) | 1.08039e12 | 0.300642 | ||||||||
\(31\) | 7.26717e12 | 1.53035 | 0.765175 | − | 0.643822i | \(-0.222652\pi\) | ||||
0.765175 | + | 0.643822i | \(0.222652\pi\) | |||||||
\(32\) | −6.41848e12 | −1.03195 | ||||||||
\(33\) | −8.55879e12 | −1.05936 | ||||||||
\(34\) | 3.96908e12 | 0.381170 | ||||||||
\(35\) | 2.07124e12 | 0.155472 | ||||||||
\(36\) | −1.41382e13 | −0.835265 | ||||||||
\(37\) | −2.70095e13 | −1.26416 | −0.632080 | − | 0.774903i | \(-0.717798\pi\) | ||||
−0.632080 | + | 0.774903i | \(0.717798\pi\) | |||||||
\(38\) | 1.65645e13 | 0.618041 | ||||||||
\(39\) | −6.84062e13 | −2.04666 | ||||||||
\(40\) | −1.49674e13 | −0.361108 | ||||||||
\(41\) | 9.47502e13 | 1.85318 | 0.926589 | − | 0.376075i | \(-0.122727\pi\) | ||||
0.926589 | + | 0.376075i | \(0.122727\pi\) | |||||||
\(42\) | 1.73348e13 | 0.276248 | ||||||||
\(43\) | 9.10093e13 | 1.18742 | 0.593709 | − | 0.804680i | \(-0.297663\pi\) | ||||
0.593709 | + | 0.804680i | \(0.297663\pi\) | |||||||
\(44\) | 5.07264e13 | 0.544360 | ||||||||
\(45\) | −5.18339e13 | −0.459524 | ||||||||
\(46\) | −5.74387e12 | −0.0422438 | ||||||||
\(47\) | −1.35606e14 | −0.830707 | −0.415353 | − | 0.909660i | \(-0.636342\pi\) | ||||
−0.415353 | + | 0.909660i | \(0.636342\pi\) | |||||||
\(48\) | 8.71273e13 | 0.446276 | ||||||||
\(49\) | 3.32329e13 | 0.142857 | ||||||||
\(50\) | 1.15270e14 | 0.417321 | ||||||||
\(51\) | −3.60883e14 | −1.10413 | ||||||||
\(52\) | 4.05431e14 | 1.05169 | ||||||||
\(53\) | 5.33679e14 | 1.17743 | 0.588715 | − | 0.808341i | \(-0.299634\pi\) | ||||
0.588715 | + | 0.808341i | \(0.299634\pi\) | |||||||
\(54\) | −4.54879e13 | −0.0856148 | ||||||||
\(55\) | 1.85974e14 | 0.299481 | ||||||||
\(56\) | −2.40152e14 | −0.331808 | ||||||||
\(57\) | −1.50610e15 | −1.79027 | ||||||||
\(58\) | −1.88928e14 | −0.193713 | ||||||||
\(59\) | −1.36156e15 | −1.20724 | −0.603619 | − | 0.797273i | \(-0.706275\pi\) | ||||
−0.603619 | + | 0.797273i | \(0.706275\pi\) | |||||||
\(60\) | 5.82208e14 | 0.447499 | ||||||||
\(61\) | 3.58851e14 | 0.239668 | 0.119834 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119834 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(62\) | −1.32158e15 | −0.768714 | ||||||||
\(63\) | −8.31673e14 | −0.422239 | ||||||||
\(64\) | 4.76592e14 | 0.211649 | ||||||||
\(65\) | 1.48640e15 | 0.578592 | ||||||||
\(66\) | 1.55647e15 | 0.532130 | ||||||||
\(67\) | 3.62448e15 | 1.09046 | 0.545231 | − | 0.838286i | \(-0.316442\pi\) | ||||
0.545231 | + | 0.838286i | \(0.316442\pi\) | |||||||
\(68\) | 2.13889e15 | 0.567364 | ||||||||
\(69\) | 5.22253e14 | 0.122367 | ||||||||
\(70\) | −3.76668e14 | −0.0780954 | ||||||||
\(71\) | −8.21132e15 | −1.50910 | −0.754548 | − | 0.656245i | \(-0.772144\pi\) | ||||
−0.754548 | + | 0.656245i | \(0.772144\pi\) | |||||||
\(72\) | 6.00993e15 | 0.980717 | ||||||||
\(73\) | 1.69268e15 | 0.245658 | 0.122829 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122829 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(74\) | 4.91185e15 | 0.635003 | ||||||||
\(75\) | −1.04807e16 | −1.20885 | ||||||||
\(76\) | 8.92639e15 | 0.919942 | ||||||||
\(77\) | 2.98395e15 | 0.275182 | ||||||||
\(78\) | 1.24401e16 | 1.02806 | ||||||||
\(79\) | −1.40597e16 | −1.04267 | −0.521335 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521335 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(80\) | −1.89319e15 | −0.126162 | ||||||||
\(81\) | −1.44948e16 | −0.869140 | ||||||||
\(82\) | −1.72309e16 | −0.930875 | ||||||||
\(83\) | −2.12860e16 | −1.03736 | −0.518682 | − | 0.854968i | \(-0.673577\pi\) | ||||
−0.518682 | + | 0.854968i | \(0.673577\pi\) | |||||||
\(84\) | 9.34150e15 | 0.411190 | ||||||||
\(85\) | 7.84163e15 | 0.312137 | ||||||||
\(86\) | −1.65506e16 | −0.596455 | ||||||||
\(87\) | 1.71780e16 | 0.561123 | ||||||||
\(88\) | −2.15630e16 | −0.639154 | ||||||||
\(89\) | −9.39599e15 | −0.253004 | −0.126502 | − | 0.991966i | \(-0.540375\pi\) | ||||
−0.126502 | + | 0.991966i | \(0.540375\pi\) | |||||||
\(90\) | 9.42634e15 | 0.230824 | ||||||||
\(91\) | 2.38492e16 | 0.531646 | ||||||||
\(92\) | −3.09530e15 | −0.0628790 | ||||||||
\(93\) | 1.20163e17 | 2.22672 | ||||||||
\(94\) | 2.46609e16 | 0.417274 | ||||||||
\(95\) | 3.27261e16 | 0.506109 | ||||||||
\(96\) | −1.06130e17 | −1.50152 | ||||||||
\(97\) | 1.65321e16 | 0.214175 | 0.107088 | − | 0.994250i | \(-0.465847\pi\) | ||||
0.107088 | + | 0.994250i | \(0.465847\pi\) | |||||||
\(98\) | −6.04363e15 | −0.0717589 | ||||||||
\(99\) | −7.46750e16 | −0.813347 | ||||||||
\(100\) | 6.21174e16 | 0.621174 | ||||||||
\(101\) | 5.36191e16 | 0.492706 | 0.246353 | − | 0.969180i | \(-0.420768\pi\) | ||||
0.246353 | + | 0.969180i | \(0.420768\pi\) | |||||||
\(102\) | 6.56289e16 | 0.554618 | ||||||||
\(103\) | −2.06651e16 | −0.160739 | −0.0803695 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803695 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(104\) | −1.72342e17 | −1.23483 | ||||||||
\(105\) | 3.42480e16 | 0.226218 | ||||||||
\(106\) | −9.70530e16 | −0.591438 | ||||||||
\(107\) | 4.13751e16 | 0.232797 | 0.116398 | − | 0.993203i | \(-0.462865\pi\) | ||||
0.116398 | + | 0.993203i | \(0.462865\pi\) | |||||||
\(108\) | −2.45128e16 | −0.127436 | ||||||||
\(109\) | 4.14022e17 | 1.99021 | 0.995103 | − | 0.0988449i | \(-0.0315148\pi\) | ||||
0.995103 | + | 0.0988449i | \(0.0315148\pi\) | |||||||
\(110\) | −3.38206e16 | −0.150433 | ||||||||
\(111\) | −4.46603e17 | −1.83940 | ||||||||
\(112\) | −3.03762e16 | −0.115926 | ||||||||
\(113\) | −2.51260e17 | −0.889113 | −0.444556 | − | 0.895751i | \(-0.646639\pi\) | ||||
−0.444556 | + | 0.895751i | \(0.646639\pi\) | |||||||
\(114\) | 2.73895e17 | 0.899274 | ||||||||
\(115\) | −1.13480e16 | −0.0345931 | ||||||||
\(116\) | −1.01811e17 | −0.288337 | ||||||||
\(117\) | −5.96841e17 | −1.57137 | ||||||||
\(118\) | 2.47608e17 | 0.606411 | ||||||||
\(119\) | 1.25819e17 | 0.286811 | ||||||||
\(120\) | −2.47487e17 | −0.525426 | ||||||||
\(121\) | −2.37522e17 | −0.469924 | ||||||||
\(122\) | −6.52595e16 | −0.120388 | ||||||||
\(123\) | 1.56670e18 | 2.69645 | ||||||||
\(124\) | −7.12184e17 | −1.14422 | ||||||||
\(125\) | 5.01853e17 | 0.753081 | ||||||||
\(126\) | 1.51245e17 | 0.212096 | ||||||||
\(127\) | 3.58876e17 | 0.470558 | 0.235279 | − | 0.971928i | \(-0.424400\pi\) | ||||
0.235279 | + | 0.971928i | \(0.424400\pi\) | |||||||
\(128\) | 7.54612e17 | 0.925633 | ||||||||
\(129\) | 1.50484e18 | 1.72774 | ||||||||
\(130\) | −2.70312e17 | −0.290634 | ||||||||
\(131\) | −1.68323e18 | −1.69565 | −0.847825 | − | 0.530276i | \(-0.822088\pi\) | ||||
−0.847825 | + | 0.530276i | \(0.822088\pi\) | |||||||
\(132\) | 8.38763e17 | 0.792065 | ||||||||
\(133\) | 5.25090e17 | 0.465044 | ||||||||
\(134\) | −6.59136e17 | −0.547752 | ||||||||
\(135\) | −8.98695e16 | −0.0701093 | ||||||||
\(136\) | −9.09206e17 | −0.666164 | ||||||||
\(137\) | −2.82456e18 | −1.94458 | −0.972290 | − | 0.233778i | \(-0.924891\pi\) | ||||
−0.972290 | + | 0.233778i | \(0.924891\pi\) | |||||||
\(138\) | −9.49751e16 | −0.0614664 | ||||||||
\(139\) | −4.10036e17 | −0.249572 | −0.124786 | − | 0.992184i | \(-0.539824\pi\) | ||||
−0.124786 | + | 0.992184i | \(0.539824\pi\) | |||||||
\(140\) | −2.02982e17 | −0.116243 | ||||||||
\(141\) | −2.24225e18 | −1.20871 | ||||||||
\(142\) | 1.49328e18 | 0.758038 | ||||||||
\(143\) | 2.14140e18 | 1.02410 | ||||||||
\(144\) | 7.60181e17 | 0.342638 | ||||||||
\(145\) | −3.73261e17 | −0.158630 | ||||||||
\(146\) | −3.07826e17 | −0.123397 | ||||||||
\(147\) | 5.49508e17 | 0.207863 | ||||||||
\(148\) | 2.64694e18 | 0.945189 | ||||||||
\(149\) | −5.35731e18 | −1.80661 | −0.903304 | − | 0.429001i | \(-0.858866\pi\) | ||||
−0.903304 | + | 0.429001i | \(0.858866\pi\) | |||||||
\(150\) | 1.90599e18 | 0.607218 | ||||||||
\(151\) | 2.59085e18 | 0.780077 | 0.390039 | − | 0.920798i | \(-0.372462\pi\) | ||||
0.390039 | + | 0.920798i | \(0.372462\pi\) | |||||||
\(152\) | −3.79446e18 | −1.08014 | ||||||||
\(153\) | −3.14869e18 | −0.847719 | ||||||||
\(154\) | −5.42650e17 | −0.138227 | ||||||||
\(155\) | −2.61102e18 | −0.629494 | ||||||||
\(156\) | 6.70382e18 | 1.53025 | ||||||||
\(157\) | −1.02610e18 | −0.221842 | −0.110921 | − | 0.993829i | \(-0.535380\pi\) | ||||
−0.110921 | + | 0.993829i | \(0.535380\pi\) | |||||||
\(158\) | 2.55686e18 | 0.523746 | ||||||||
\(159\) | 8.82441e18 | 1.71321 | ||||||||
\(160\) | 2.30610e18 | 0.424481 | ||||||||
\(161\) | −1.82079e17 | −0.0317863 | ||||||||
\(162\) | 2.63598e18 | 0.436580 | ||||||||
\(163\) | 4.62746e18 | 0.727358 | 0.363679 | − | 0.931524i | \(-0.381521\pi\) | ||||
0.363679 | + | 0.931524i | \(0.381521\pi\) | |||||||
\(164\) | −9.28554e18 | −1.38559 | ||||||||
\(165\) | 3.07509e18 | 0.435757 | ||||||||
\(166\) | 3.87100e18 | 0.521080 | ||||||||
\(167\) | −8.36584e18 | −1.07009 | −0.535044 | − | 0.844824i | \(-0.679705\pi\) | ||||
−0.535044 | + | 0.844824i | \(0.679705\pi\) | |||||||
\(168\) | −3.97092e18 | −0.482794 | ||||||||
\(169\) | 8.46471e18 | 0.978532 | ||||||||
\(170\) | −1.42605e18 | −0.156790 | ||||||||
\(171\) | −1.31407e19 | −1.37452 | ||||||||
\(172\) | −8.91893e18 | −0.887812 | ||||||||
\(173\) | 1.05223e19 | 0.997058 | 0.498529 | − | 0.866873i | \(-0.333874\pi\) | ||||
0.498529 | + | 0.866873i | \(0.333874\pi\) | |||||||
\(174\) | −3.12393e18 | −0.281859 | ||||||||
\(175\) | 3.65402e18 | 0.314013 | ||||||||
\(176\) | −2.72744e18 | −0.223305 | ||||||||
\(177\) | −2.25134e19 | −1.75658 | ||||||||
\(178\) | 1.70872e18 | 0.127087 | ||||||||
\(179\) | −2.28203e18 | −0.161835 | −0.0809173 | − | 0.996721i | \(-0.525785\pi\) | ||||
−0.0809173 | + | 0.996721i | \(0.525785\pi\) | |||||||
\(180\) | 5.07973e18 | 0.343578 | ||||||||
\(181\) | 1.33314e19 | 0.860220 | 0.430110 | − | 0.902777i | \(-0.358475\pi\) | ||||
0.430110 | + | 0.902777i | \(0.358475\pi\) | |||||||
\(182\) | −4.33714e18 | −0.267052 | ||||||||
\(183\) | 5.93362e18 | 0.348727 | ||||||||
\(184\) | 1.31576e18 | 0.0738287 | ||||||||
\(185\) | 9.70425e18 | 0.519999 | ||||||||
\(186\) | −2.18524e19 | −1.11851 | ||||||||
\(187\) | 1.12971e19 | 0.552477 | ||||||||
\(188\) | 1.32894e19 | 0.621105 | ||||||||
\(189\) | −1.44195e18 | −0.0644208 | ||||||||
\(190\) | −5.95146e18 | −0.254225 | ||||||||
\(191\) | −1.82726e19 | −0.746478 | −0.373239 | − | 0.927735i | \(-0.621753\pi\) | ||||
−0.373239 | + | 0.927735i | \(0.621753\pi\) | |||||||
\(192\) | 7.88046e18 | 0.307958 | ||||||||
\(193\) | −2.95687e19 | −1.10559 | −0.552796 | − | 0.833317i | \(-0.686439\pi\) | ||||
−0.552796 | + | 0.833317i | \(0.686439\pi\) | |||||||
\(194\) | −3.00648e18 | −0.107583 | ||||||||
\(195\) | 2.45777e19 | 0.841874 | ||||||||
\(196\) | −3.25683e18 | −0.106812 | ||||||||
\(197\) | 3.08412e19 | 0.968653 | 0.484326 | − | 0.874887i | \(-0.339065\pi\) | ||||
0.484326 | + | 0.874887i | \(0.339065\pi\) | |||||||
\(198\) | 1.35801e19 | 0.408555 | ||||||||
\(199\) | 3.29269e19 | 0.949074 | 0.474537 | − | 0.880235i | \(-0.342615\pi\) | ||||
0.474537 | + | 0.880235i | \(0.342615\pi\) | |||||||
\(200\) | −2.64051e19 | −0.729345 | ||||||||
\(201\) | 5.99310e19 | 1.58666 | ||||||||
\(202\) | −9.75098e18 | −0.247492 | ||||||||
\(203\) | −5.98895e18 | −0.145759 | ||||||||
\(204\) | 3.53666e19 | 0.825537 | ||||||||
\(205\) | −3.40428e19 | −0.762286 | ||||||||
\(206\) | 3.75809e18 | 0.0807412 | ||||||||
\(207\) | 4.55663e18 | 0.0939498 | ||||||||
\(208\) | −2.17991e19 | −0.431420 | ||||||||
\(209\) | 4.71472e19 | 0.895803 | ||||||||
\(210\) | −6.22822e18 | −0.113632 | ||||||||
\(211\) | −4.31546e18 | −0.0756181 | −0.0378091 | − | 0.999285i | \(-0.512038\pi\) | ||||
−0.0378091 | + | 0.999285i | \(0.512038\pi\) | |||||||
\(212\) | −5.23006e19 | −0.880344 | ||||||||
\(213\) | −1.35774e20 | −2.19579 | ||||||||
\(214\) | −7.52433e18 | −0.116937 | ||||||||
\(215\) | −3.26988e19 | −0.488432 | ||||||||
\(216\) | 1.04200e19 | 0.149627 | ||||||||
\(217\) | −4.18938e19 | −0.578418 | ||||||||
\(218\) | −7.52926e19 | −0.999705 | ||||||||
\(219\) | 2.79886e19 | 0.357443 | ||||||||
\(220\) | −1.82255e19 | −0.223917 | ||||||||
\(221\) | 9.02923e19 | 1.06737 | ||||||||
\(222\) | 8.12177e19 | 0.923954 | ||||||||
\(223\) | −8.31952e19 | −0.910976 | −0.455488 | − | 0.890242i | \(-0.650535\pi\) | ||||
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(224\) | 3.70013e19 | 0.390039 | ||||||||
\(225\) | −9.14439e19 | −0.928118 | ||||||||
\(226\) | 4.56933e19 | 0.446612 | ||||||||
\(227\) | 3.19266e19 | 0.300561 | 0.150281 | − | 0.988643i | \(-0.451982\pi\) | ||||
0.150281 | + | 0.988643i | \(0.451982\pi\) | |||||||
\(228\) | 1.47598e20 | 1.33855 | ||||||||
\(229\) | −5.56717e19 | −0.486444 | −0.243222 | − | 0.969971i | \(-0.578204\pi\) | ||||
−0.243222 | + | 0.969971i | \(0.578204\pi\) | |||||||
\(230\) | 2.06372e18 | 0.0173765 | ||||||||
\(231\) | 4.93397e19 | 0.400401 | ||||||||
\(232\) | 4.32781e19 | 0.338548 | ||||||||
\(233\) | 5.46463e19 | 0.412131 | 0.206065 | − | 0.978538i | \(-0.433934\pi\) | ||||
0.206065 | + | 0.978538i | \(0.433934\pi\) | |||||||
\(234\) | 1.08539e20 | 0.789319 | ||||||||
\(235\) | 4.87220e19 | 0.341703 | ||||||||
\(236\) | 1.33433e20 | 0.902631 | ||||||||
\(237\) | −2.32478e20 | −1.51713 | ||||||||
\(238\) | −2.28810e19 | −0.144069 | ||||||||
\(239\) | 2.48148e20 | 1.50775 | 0.753875 | − | 0.657018i | \(-0.228182\pi\) | ||||
0.753875 | + | 0.657018i | \(0.228182\pi\) | |||||||
\(240\) | −3.13040e19 | −0.183571 | ||||||||
\(241\) | −1.79431e20 | −1.01567 | −0.507834 | − | 0.861455i | \(-0.669554\pi\) | ||||
−0.507834 | + | 0.861455i | \(0.669554\pi\) | |||||||
\(242\) | 4.31949e19 | 0.236049 | ||||||||
\(243\) | −2.71974e20 | −1.43507 | ||||||||
\(244\) | −3.51675e19 | −0.179196 | ||||||||
\(245\) | −1.19403e19 | −0.0587628 | ||||||||
\(246\) | −2.84914e20 | −1.35446 | ||||||||
\(247\) | 3.76825e20 | 1.73067 | ||||||||
\(248\) | 3.02738e20 | 1.34347 | ||||||||
\(249\) | −3.51965e20 | −1.50940 | ||||||||
\(250\) | −9.12653e19 | −0.378282 | ||||||||
\(251\) | 3.77682e20 | 1.51321 | 0.756606 | − | 0.653871i | \(-0.226856\pi\) | ||||
0.756606 | + | 0.653871i | \(0.226856\pi\) | |||||||
\(252\) | 8.15041e19 | 0.315700 | ||||||||
\(253\) | −1.63487e19 | −0.0612291 | ||||||||
\(254\) | −6.52640e19 | −0.236367 | ||||||||
\(255\) | 1.29662e20 | 0.454172 | ||||||||
\(256\) | −1.99699e20 | −0.676606 | ||||||||
\(257\) | −5.38973e20 | −1.76659 | −0.883294 | − | 0.468819i | \(-0.844680\pi\) | ||||
−0.883294 | + | 0.468819i | \(0.844680\pi\) | |||||||
\(258\) | −2.73665e20 | −0.867865 | ||||||||
\(259\) | 1.55704e20 | 0.477807 | ||||||||
\(260\) | −1.45668e20 | −0.432603 | ||||||||
\(261\) | 1.49877e20 | 0.430815 | ||||||||
\(262\) | 3.06106e20 | 0.851746 | ||||||||
\(263\) | 3.86743e20 | 1.04183 | 0.520917 | − | 0.853607i | \(-0.325590\pi\) | ||||
0.520917 | + | 0.853607i | \(0.325590\pi\) | |||||||
\(264\) | −3.56544e20 | −0.929994 | ||||||||
\(265\) | −1.91746e20 | −0.484324 | ||||||||
\(266\) | −9.54910e19 | −0.233598 | ||||||||
\(267\) | −1.55363e20 | −0.368131 | ||||||||
\(268\) | −3.55200e20 | −0.815319 | ||||||||
\(269\) | −6.51556e19 | −0.144896 | −0.0724481 | − | 0.997372i | \(-0.523081\pi\) | ||||
−0.0724481 | + | 0.997372i | \(0.523081\pi\) | |||||||
\(270\) | 1.63434e19 | 0.0352168 | ||||||||
\(271\) | −1.10328e20 | −0.230381 | −0.115191 | − | 0.993343i | \(-0.536748\pi\) | ||||
−0.115191 | + | 0.993343i | \(0.536748\pi\) | |||||||
\(272\) | −1.15003e20 | −0.232742 | ||||||||
\(273\) | 3.94348e20 | 0.773566 | ||||||||
\(274\) | 5.13665e20 | 0.976787 | ||||||||
\(275\) | 3.28090e20 | 0.604875 | ||||||||
\(276\) | −5.11809e19 | −0.0914915 | ||||||||
\(277\) | 2.03040e20 | 0.351969 | 0.175984 | − | 0.984393i | \(-0.443689\pi\) | ||||
0.175984 | + | 0.984393i | \(0.443689\pi\) | |||||||
\(278\) | 7.45676e19 | 0.125363 | ||||||||
\(279\) | 1.04842e21 | 1.70961 | ||||||||
\(280\) | 8.62842e19 | 0.136486 | ||||||||
\(281\) | −2.83182e20 | −0.434572 | −0.217286 | − | 0.976108i | \(-0.569720\pi\) | ||||
−0.217286 | + | 0.976108i | \(0.569720\pi\) | |||||||
\(282\) | 4.07769e20 | 0.607151 | ||||||||
\(283\) | −4.43477e20 | −0.640746 | −0.320373 | − | 0.947291i | \(-0.603808\pi\) | ||||
−0.320373 | + | 0.947291i | \(0.603808\pi\) | |||||||
\(284\) | 8.04711e20 | 1.12832 | ||||||||
\(285\) | 5.41128e20 | 0.736409 | ||||||||
\(286\) | −3.89427e20 | −0.514416 | ||||||||
\(287\) | −5.46216e20 | −0.700436 | ||||||||
\(288\) | −9.25978e20 | −1.15283 | ||||||||
\(289\) | −3.50895e20 | −0.424176 | ||||||||
\(290\) | 6.78799e19 | 0.0796817 | ||||||||
\(291\) | 2.73360e20 | 0.311633 | ||||||||
\(292\) | −1.65883e20 | −0.183674 | ||||||||
\(293\) | −6.05067e20 | −0.650772 | −0.325386 | − | 0.945581i | \(-0.605494\pi\) | ||||
−0.325386 | + | 0.945581i | \(0.605494\pi\) | |||||||
\(294\) | −9.99316e19 | −0.104412 | ||||||||
\(295\) | 4.89194e20 | 0.496585 | ||||||||
\(296\) | −1.12517e21 | −1.10978 | ||||||||
\(297\) | −1.29471e20 | −0.124092 | ||||||||
\(298\) | 9.74263e20 | 0.907482 | ||||||||
\(299\) | −1.30667e20 | −0.118293 | ||||||||
\(300\) | 1.02711e21 | 0.903833 | ||||||||
\(301\) | −5.24650e20 | −0.448802 | ||||||||
\(302\) | −4.71162e20 | −0.391843 | ||||||||
\(303\) | 8.86594e20 | 0.716906 | ||||||||
\(304\) | −4.79952e20 | −0.377374 | ||||||||
\(305\) | −1.28932e20 | −0.0985852 | ||||||||
\(306\) | 5.72609e20 | 0.425820 | ||||||||
\(307\) | −1.90711e21 | −1.37943 | −0.689713 | − | 0.724083i | \(-0.742263\pi\) | ||||
−0.689713 | + | 0.724083i | \(0.742263\pi\) | |||||||
\(308\) | −2.92427e20 | −0.205749 | ||||||||
\(309\) | −3.41698e20 | −0.233882 | ||||||||
\(310\) | 4.74832e20 | 0.316203 | ||||||||
\(311\) | 3.83279e20 | 0.248343 | 0.124171 | − | 0.992261i | \(-0.460373\pi\) | ||||
0.124171 | + | 0.992261i | \(0.460373\pi\) | |||||||
\(312\) | −2.84968e21 | −1.79673 | ||||||||
\(313\) | 3.72919e20 | 0.228817 | 0.114408 | − | 0.993434i | \(-0.463503\pi\) | ||||
0.114408 | + | 0.993434i | \(0.463503\pi\) | |||||||
\(314\) | 1.86603e20 | 0.111434 | ||||||||
\(315\) | 2.98812e20 | 0.173684 | ||||||||
\(316\) | 1.37786e21 | 0.779586 | ||||||||
\(317\) | −1.31935e21 | −0.726700 | −0.363350 | − | 0.931653i | \(-0.618367\pi\) | ||||
−0.363350 | + | 0.931653i | \(0.618367\pi\) | |||||||
\(318\) | −1.60478e21 | −0.860565 | ||||||||
\(319\) | −5.37742e20 | −0.280771 | ||||||||
\(320\) | −1.71235e20 | −0.0870597 | ||||||||
\(321\) | 6.84138e20 | 0.338728 | ||||||||
\(322\) | 3.31123e19 | 0.0159667 | ||||||||
\(323\) | 1.98797e21 | 0.933659 | ||||||||
\(324\) | 1.42049e21 | 0.649840 | ||||||||
\(325\) | 2.62226e21 | 1.16861 | ||||||||
\(326\) | −8.41534e20 | −0.365361 | ||||||||
\(327\) | 6.84587e21 | 2.89583 | ||||||||
\(328\) | 3.94713e21 | 1.62687 | ||||||||
\(329\) | 7.81743e20 | 0.313978 | ||||||||
\(330\) | −5.59225e20 | −0.218886 | ||||||||
\(331\) | −4.78390e21 | −1.82492 | −0.912460 | − | 0.409165i | \(-0.865820\pi\) | ||||
−0.912460 | + | 0.409165i | \(0.865820\pi\) | |||||||
\(332\) | 2.08603e21 | 0.775618 | ||||||||
\(333\) | −3.89659e21 | −1.41224 | ||||||||
\(334\) | 1.52138e21 | 0.537519 | ||||||||
\(335\) | −1.30224e21 | −0.448550 | ||||||||
\(336\) | −5.02271e20 | −0.168677 | ||||||||
\(337\) | 2.40928e21 | 0.788919 | 0.394459 | − | 0.918913i | \(-0.370932\pi\) | ||||
0.394459 | + | 0.918913i | \(0.370932\pi\) | |||||||
\(338\) | −1.53936e21 | −0.491529 | ||||||||
\(339\) | −4.15460e21 | −1.29369 | ||||||||
\(340\) | −7.68482e20 | −0.233379 | ||||||||
\(341\) | −3.76160e21 | −1.11419 | ||||||||
\(342\) | 2.38972e21 | 0.690438 | ||||||||
\(343\) | −1.91581e20 | −0.0539949 | ||||||||
\(344\) | 3.79129e21 | 1.04241 | ||||||||
\(345\) | −1.87640e20 | −0.0503343 | ||||||||
\(346\) | −1.91356e21 | −0.500835 | ||||||||
\(347\) | −4.59537e21 | −1.17360 | −0.586800 | − | 0.809732i | \(-0.699612\pi\) | ||||
−0.586800 | + | 0.809732i | \(0.699612\pi\) | |||||||
\(348\) | −1.68345e21 | −0.419542 | ||||||||
\(349\) | −3.89744e21 | −0.947901 | −0.473950 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473950 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(350\) | −6.64507e20 | −0.157733 | ||||||||
\(351\) | −1.03480e21 | −0.239743 | ||||||||
\(352\) | 3.32230e21 | 0.751323 | ||||||||
\(353\) | −4.92306e21 | −1.08680 | −0.543401 | − | 0.839473i | \(-0.682864\pi\) | ||||
−0.543401 | + | 0.839473i | \(0.682864\pi\) | |||||||
\(354\) | 4.09420e21 | 0.882352 | ||||||||
\(355\) | 2.95025e21 | 0.620751 | ||||||||
\(356\) | 9.20809e20 | 0.189167 | ||||||||
\(357\) | 2.08042e21 | 0.417321 | ||||||||
\(358\) | 4.15003e20 | 0.0812915 | ||||||||
\(359\) | 2.24060e21 | 0.428609 | 0.214305 | − | 0.976767i | \(-0.431251\pi\) | ||||
0.214305 | + | 0.976767i | \(0.431251\pi\) | |||||||
\(360\) | −2.15931e21 | −0.403408 | ||||||||
\(361\) | 2.81618e21 | 0.513865 | ||||||||
\(362\) | −2.42441e21 | −0.432099 | ||||||||
\(363\) | −3.92743e21 | −0.683758 | ||||||||
\(364\) | −2.33723e21 | −0.397502 | ||||||||
\(365\) | −6.08165e20 | −0.101049 | ||||||||
\(366\) | −1.07907e21 | −0.175170 | ||||||||
\(367\) | 9.77120e21 | 1.54984 | 0.774919 | − | 0.632061i | \(-0.217791\pi\) | ||||
0.774919 | + | 0.632061i | \(0.217791\pi\) | |||||||
\(368\) | 1.66427e20 | 0.0257940 | ||||||||
\(369\) | 1.36694e22 | 2.07026 | ||||||||
\(370\) | −1.76478e21 | −0.261202 | ||||||||
\(371\) | −3.07655e21 | −0.445027 | ||||||||
\(372\) | −1.17760e22 | −1.66488 | ||||||||
\(373\) | −2.05508e21 | −0.283991 | −0.141995 | − | 0.989867i | \(-0.545352\pi\) | ||||
−0.141995 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(374\) | −2.05446e21 | −0.277516 | ||||||||
\(375\) | 8.29816e21 | 1.09576 | ||||||||
\(376\) | −5.64912e21 | −0.729263 | ||||||||
\(377\) | −4.29790e21 | −0.542444 | ||||||||
\(378\) | 2.62229e20 | 0.0323593 | ||||||||
\(379\) | 5.45735e21 | 0.658489 | 0.329245 | − | 0.944245i | \(-0.393206\pi\) | ||||
0.329245 | + | 0.944245i | \(0.393206\pi\) | |||||||
\(380\) | −3.20717e21 | −0.378409 | ||||||||
\(381\) | 5.93404e21 | 0.684681 | ||||||||
\(382\) | 3.32299e21 | 0.374965 | ||||||||
\(383\) | −5.20172e21 | −0.574060 | −0.287030 | − | 0.957922i | \(-0.592668\pi\) | ||||
−0.287030 | + | 0.957922i | \(0.592668\pi\) | |||||||
\(384\) | 1.24775e22 | 1.34683 | ||||||||
\(385\) | −1.07210e21 | −0.113193 | ||||||||
\(386\) | 5.37725e21 | 0.555352 | ||||||||
\(387\) | 1.31297e22 | 1.32651 | ||||||||
\(388\) | −1.62015e21 | −0.160135 | ||||||||
\(389\) | 1.16024e22 | 1.12196 | 0.560981 | − | 0.827829i | \(-0.310424\pi\) | ||||
0.560981 | + | 0.827829i | \(0.310424\pi\) | |||||||
\(390\) | −4.46961e21 | −0.422884 | ||||||||
\(391\) | −6.89344e20 | −0.0638166 | ||||||||
\(392\) | 1.38443e21 | 0.125412 | ||||||||
\(393\) | −2.78322e22 | −2.46724 | ||||||||
\(394\) | −5.60867e21 | −0.486566 | ||||||||
\(395\) | 5.05153e21 | 0.428892 | ||||||||
\(396\) | 7.31817e21 | 0.608125 | ||||||||
\(397\) | −8.51122e21 | −0.692265 | −0.346133 | − | 0.938186i | \(-0.612505\pi\) | ||||
−0.346133 | + | 0.938186i | \(0.612505\pi\) | |||||||
\(398\) | −5.98798e21 | −0.476732 | ||||||||
\(399\) | 8.68238e21 | 0.676658 | ||||||||
\(400\) | −3.33991e21 | −0.254815 | ||||||||
\(401\) | 1.27994e22 | 0.956014 | 0.478007 | − | 0.878356i | \(-0.341359\pi\) | ||||
0.478007 | + | 0.878356i | \(0.341359\pi\) | |||||||
\(402\) | −1.08988e22 | −0.797001 | ||||||||
\(403\) | −3.00646e22 | −2.15260 | ||||||||
\(404\) | −5.25468e21 | −0.368387 | ||||||||
\(405\) | 5.20785e21 | 0.357512 | ||||||||
\(406\) | 1.08913e21 | 0.0732165 | ||||||||
\(407\) | 1.39805e22 | 0.920388 | ||||||||
\(408\) | −1.50338e22 | −0.969295 | ||||||||
\(409\) | 8.57747e21 | 0.541641 | 0.270820 | − | 0.962630i | \(-0.412705\pi\) | ||||
0.270820 | + | 0.962630i | \(0.412705\pi\) | |||||||
\(410\) | 6.19091e21 | 0.382906 | ||||||||
\(411\) | −4.67042e22 | −2.82944 | ||||||||
\(412\) | 2.02518e21 | 0.120182 | ||||||||
\(413\) | 7.84909e21 | 0.456293 | ||||||||
\(414\) | −8.28653e20 | −0.0471922 | ||||||||
\(415\) | 7.64787e21 | 0.426709 | ||||||||
\(416\) | 2.65535e22 | 1.45154 | ||||||||
\(417\) | −6.77996e21 | −0.363137 | ||||||||
\(418\) | −8.57403e21 | −0.449973 | ||||||||
\(419\) | −1.00651e22 | −0.517606 | −0.258803 | − | 0.965930i | \(-0.583328\pi\) | ||||
−0.258803 | + | 0.965930i | \(0.583328\pi\) | |||||||
\(420\) | −3.35631e21 | −0.169139 | ||||||||
\(421\) | 2.06716e22 | 1.02088 | 0.510441 | − | 0.859913i | \(-0.329482\pi\) | ||||
0.510441 | + | 0.859913i | \(0.329482\pi\) | |||||||
\(422\) | 7.84794e20 | 0.0379839 | ||||||||
\(423\) | −1.95636e22 | −0.928015 | ||||||||
\(424\) | 2.22321e22 | 1.03365 | ||||||||
\(425\) | 1.38340e22 | 0.630436 | ||||||||
\(426\) | 2.46915e22 | 1.10297 | ||||||||
\(427\) | −2.06871e21 | −0.0905862 | ||||||||
\(428\) | −4.05476e21 | −0.174058 | ||||||||
\(429\) | 3.54081e22 | 1.49010 | ||||||||
\(430\) | 5.94648e21 | 0.245346 | ||||||||
\(431\) | 5.85800e20 | 0.0236969 | 0.0118485 | − | 0.999930i | \(-0.496228\pi\) | ||||
0.0118485 | + | 0.999930i | \(0.496228\pi\) | |||||||
\(432\) | 1.31800e21 | 0.0522762 | ||||||||
\(433\) | −2.65233e21 | −0.103153 | −0.0515763 | − | 0.998669i | \(-0.516425\pi\) | ||||
−0.0515763 | + | 0.998669i | \(0.516425\pi\) | |||||||
\(434\) | 7.61866e21 | 0.290547 | ||||||||
\(435\) | −6.17188e21 | −0.230812 | ||||||||
\(436\) | −4.05742e22 | −1.48804 | ||||||||
\(437\) | −2.87690e21 | −0.103474 | ||||||||
\(438\) | −5.08991e21 | −0.179548 | ||||||||
\(439\) | 6.42495e21 | 0.222291 | 0.111145 | − | 0.993804i | \(-0.464548\pi\) | ||||
0.111145 | + | 0.993804i | \(0.464548\pi\) | |||||||
\(440\) | 7.74736e21 | 0.262909 | ||||||||
\(441\) | 4.79443e21 | 0.159591 | ||||||||
\(442\) | −1.64203e22 | −0.536155 | ||||||||
\(443\) | 1.53379e22 | 0.491285 | 0.245643 | − | 0.969360i | \(-0.421001\pi\) | ||||
0.245643 | + | 0.969360i | \(0.421001\pi\) | |||||||
\(444\) | 4.37672e22 | 1.37529 | ||||||||
\(445\) | 3.37589e21 | 0.104071 | ||||||||
\(446\) | 1.51296e22 | 0.457595 | ||||||||
\(447\) | −8.85834e22 | −2.62868 | ||||||||
\(448\) | −2.74746e21 | −0.0799959 | ||||||||
\(449\) | 2.38064e22 | 0.680142 | 0.340071 | − | 0.940400i | \(-0.389549\pi\) | ||||
0.340071 | + | 0.940400i | \(0.389549\pi\) | |||||||
\(450\) | 1.66297e22 | 0.466205 | ||||||||
\(451\) | −4.90441e22 | −1.34923 | ||||||||
\(452\) | 2.46235e22 | 0.664774 | ||||||||
\(453\) | 4.28398e22 | 1.13504 | ||||||||
\(454\) | −5.80606e21 | −0.150976 | ||||||||
\(455\) | −8.56880e21 | −0.218687 | ||||||||
\(456\) | −6.27416e22 | −1.57165 | ||||||||
\(457\) | 2.08677e22 | 0.513082 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(458\) | 1.01243e22 | 0.244347 | ||||||||
\(459\) | −5.45918e21 | −0.129336 | ||||||||
\(460\) | 1.11211e21 | 0.0258646 | ||||||||
\(461\) | −5.38735e22 | −1.23003 | −0.615017 | − | 0.788513i | \(-0.710851\pi\) | ||||
−0.615017 | + | 0.788513i | \(0.710851\pi\) | |||||||
\(462\) | −8.97275e21 | −0.201126 | ||||||||
\(463\) | 9.60815e21 | 0.211447 | 0.105723 | − | 0.994396i | \(-0.466284\pi\) | ||||
0.105723 | + | 0.994396i | \(0.466284\pi\) | |||||||
\(464\) | 5.47414e21 | 0.118280 | ||||||||
\(465\) | −4.31734e22 | −0.915938 | ||||||||
\(466\) | −9.93778e21 | −0.207018 | ||||||||
\(467\) | −4.38850e22 | −0.897683 | −0.448841 | − | 0.893611i | \(-0.648163\pi\) | ||||
−0.448841 | + | 0.893611i | \(0.648163\pi\) | |||||||
\(468\) | 5.84905e22 | 1.17489 | ||||||||
\(469\) | −2.08944e22 | −0.412156 | ||||||||
\(470\) | −8.86042e21 | −0.171642 | ||||||||
\(471\) | −1.69666e22 | −0.322788 | ||||||||
\(472\) | −5.67200e22 | −1.05981 | ||||||||
\(473\) | −4.71078e22 | −0.864516 | ||||||||
\(474\) | 4.22777e22 | 0.762071 | ||||||||
\(475\) | 5.77345e22 | 1.02221 | ||||||||
\(476\) | −1.23303e22 | −0.214444 | ||||||||
\(477\) | 7.69925e22 | 1.31535 | ||||||||
\(478\) | −4.51274e22 | −0.757362 | ||||||||
\(479\) | 2.82508e21 | 0.0465778 | 0.0232889 | − | 0.999729i | \(-0.492586\pi\) | ||||
0.0232889 | + | 0.999729i | \(0.492586\pi\) | |||||||
\(480\) | 3.81315e22 | 0.617636 | ||||||||
\(481\) | 1.11739e23 | 1.77817 | ||||||||
\(482\) | 3.26307e22 | 0.510183 | ||||||||
\(483\) | −3.01068e21 | −0.0462503 | ||||||||
\(484\) | 2.32772e22 | 0.351354 | ||||||||
\(485\) | −5.93984e21 | −0.0880988 | ||||||||
\(486\) | 4.94603e22 | 0.720855 | ||||||||
\(487\) | 2.34513e22 | 0.335870 | 0.167935 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167935 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(488\) | 1.49491e22 | 0.210401 | ||||||||
\(489\) | 7.65153e22 | 1.05833 | ||||||||
\(490\) | 2.17142e21 | 0.0295173 | ||||||||
\(491\) | 3.75824e22 | 0.502103 | 0.251051 | − | 0.967974i | \(-0.419224\pi\) | ||||
0.251051 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(492\) | −1.53537e23 | −2.01609 | ||||||||
\(493\) | −2.26740e22 | −0.292637 | ||||||||
\(494\) | −6.85280e22 | −0.869339 | ||||||||
\(495\) | 2.68300e22 | 0.334562 | ||||||||
\(496\) | 3.82925e22 | 0.469375 | ||||||||
\(497\) | 4.73366e22 | 0.570385 | ||||||||
\(498\) | 6.40072e22 | 0.758192 | ||||||||
\(499\) | 2.82679e21 | 0.0329184 | 0.0164592 | − | 0.999865i | \(-0.494761\pi\) | ||||
0.0164592 | + | 0.999865i | \(0.494761\pi\) | |||||||
\(500\) | −4.91817e22 | −0.563065 | ||||||||
\(501\) | −1.38330e23 | −1.55702 | ||||||||
\(502\) | −6.86840e22 | −0.760105 | ||||||||
\(503\) | −4.74984e22 | −0.516834 | −0.258417 | − | 0.966033i | \(-0.583201\pi\) | ||||
−0.258417 | + | 0.966033i | \(0.583201\pi\) | |||||||
\(504\) | −3.46461e22 | −0.370676 | ||||||||
\(505\) | −1.92648e22 | −0.202669 | ||||||||
\(506\) | 2.97311e21 | 0.0307561 | ||||||||
\(507\) | 1.39964e23 | 1.42380 | ||||||||
\(508\) | −3.51700e22 | −0.351828 | ||||||||
\(509\) | 3.19613e22 | 0.314430 | 0.157215 | − | 0.987564i | \(-0.449748\pi\) | ||||
0.157215 | + | 0.987564i | \(0.449748\pi\) | |||||||
\(510\) | −2.35798e22 | −0.228136 | ||||||||
\(511\) | −9.75799e21 | −0.0928501 | ||||||||
\(512\) | −6.25919e22 | −0.585765 | ||||||||
\(513\) | −2.27833e22 | −0.209710 | ||||||||
\(514\) | 9.80158e22 | 0.887380 | ||||||||
\(515\) | 7.42478e21 | 0.0661183 | ||||||||
\(516\) | −1.47475e23 | −1.29180 | ||||||||
\(517\) | 7.01918e22 | 0.604807 | ||||||||
\(518\) | −2.83159e22 | −0.240009 | ||||||||
\(519\) | 1.73987e23 | 1.45076 | ||||||||
\(520\) | 6.19209e22 | 0.507936 | ||||||||
\(521\) | −1.75671e23 | −1.41768 | −0.708841 | − | 0.705369i | \(-0.750782\pi\) | ||||
−0.708841 | + | 0.705369i | \(0.750782\pi\) | |||||||
\(522\) | −2.72561e22 | −0.216404 | ||||||||
\(523\) | 2.05125e23 | 1.60234 | 0.801168 | − | 0.598439i | \(-0.204212\pi\) | ||||
0.801168 | + | 0.598439i | \(0.204212\pi\) | |||||||
\(524\) | 1.64956e23 | 1.26781 | ||||||||
\(525\) | 6.04193e22 | 0.456901 | ||||||||
\(526\) | −7.03318e22 | −0.523326 | ||||||||
\(527\) | −1.58608e23 | −1.16128 | ||||||||
\(528\) | −4.50984e22 | −0.324917 | ||||||||
\(529\) | −1.40052e23 | −0.992927 | ||||||||
\(530\) | 3.48702e22 | 0.243282 | ||||||||
\(531\) | −1.96428e23 | −1.34865 | ||||||||
\(532\) | −5.14589e22 | −0.347705 | ||||||||
\(533\) | −3.91986e23 | −2.60669 | ||||||||
\(534\) | 2.82538e22 | 0.184917 | ||||||||
\(535\) | −1.48657e22 | −0.0957585 | ||||||||
\(536\) | 1.50990e23 | 0.957297 | ||||||||
\(537\) | −3.77335e22 | −0.235476 | ||||||||
\(538\) | 1.18490e22 | 0.0727832 | ||||||||
\(539\) | −1.72019e22 | −0.104009 | ||||||||
\(540\) | 8.80723e21 | 0.0524195 | ||||||||
\(541\) | 1.41206e23 | 0.827325 | 0.413663 | − | 0.910430i | \(-0.364249\pi\) | ||||
0.413663 | + | 0.910430i | \(0.364249\pi\) | |||||||
\(542\) | 2.00639e22 | 0.115723 | ||||||||
\(543\) | 2.20436e23 | 1.25165 | ||||||||
\(544\) | 1.40085e23 | 0.783073 | ||||||||
\(545\) | −1.48754e23 | −0.818651 | ||||||||
\(546\) | −7.17148e22 | −0.388572 | ||||||||
\(547\) | 3.33679e23 | 1.78007 | 0.890033 | − | 0.455896i | \(-0.150681\pi\) | ||||
0.890033 | + | 0.455896i | \(0.150681\pi\) | |||||||
\(548\) | 2.76807e23 | 1.45393 | ||||||||
\(549\) | 5.17706e22 | 0.267743 | ||||||||
\(550\) | −5.96654e22 | −0.303836 | ||||||||
\(551\) | −9.46272e22 | −0.474490 | ||||||||
\(552\) | 2.17562e22 | 0.107424 | ||||||||
\(553\) | 8.10516e22 | 0.394092 | ||||||||
\(554\) | −3.69242e22 | −0.176798 | ||||||||
\(555\) | 1.60460e23 | 0.756619 | ||||||||
\(556\) | 4.01836e22 | 0.186600 | ||||||||
\(557\) | 2.77830e23 | 1.27061 | 0.635303 | − | 0.772263i | \(-0.280875\pi\) | ||||
0.635303 | + | 0.772263i | \(0.280875\pi\) | |||||||
\(558\) | −1.90661e23 | −0.858760 | ||||||||
\(559\) | −3.76509e23 | −1.67023 | ||||||||
\(560\) | 1.09139e22 | 0.0476849 | ||||||||
\(561\) | 1.86798e23 | 0.803875 | ||||||||
\(562\) | 5.14985e22 | 0.218291 | ||||||||
\(563\) | −2.71407e22 | −0.113318 | −0.0566590 | − | 0.998394i | \(-0.518045\pi\) | ||||
−0.0566590 | + | 0.998394i | \(0.518045\pi\) | |||||||
\(564\) | 2.19741e23 | 0.903731 | ||||||||
\(565\) | 9.02754e22 | 0.365727 | ||||||||
\(566\) | 8.06491e22 | 0.321855 | ||||||||
\(567\) | 8.35597e22 | 0.328504 | ||||||||
\(568\) | −3.42069e23 | −1.32481 | ||||||||
\(569\) | −1.86156e23 | −0.710270 | −0.355135 | − | 0.934815i | \(-0.615565\pi\) | ||||
−0.355135 | + | 0.934815i | \(0.615565\pi\) | |||||||
\(570\) | −9.84077e22 | −0.369907 | ||||||||
\(571\) | −5.54352e22 | −0.205295 | −0.102648 | − | 0.994718i | \(-0.532731\pi\) | ||||
−0.102648 | + | 0.994718i | \(0.532731\pi\) | |||||||
\(572\) | −2.09857e23 | −0.765698 | ||||||||
\(573\) | −3.02138e23 | −1.08615 | ||||||||
\(574\) | 9.93329e22 | 0.351838 | ||||||||
\(575\) | −2.00199e22 | −0.0698691 | ||||||||
\(576\) | 6.87567e22 | 0.236442 | ||||||||
\(577\) | −1.70022e23 | −0.576117 | −0.288059 | − | 0.957613i | \(-0.593010\pi\) | ||||
−0.288059 | + | 0.957613i | \(0.593010\pi\) | |||||||
\(578\) | 6.38126e22 | 0.213069 | ||||||||
\(579\) | −4.88919e23 | −1.60868 | ||||||||
\(580\) | 3.65796e22 | 0.118605 | ||||||||
\(581\) | 1.22710e23 | 0.392086 | ||||||||
\(582\) | −4.97122e22 | −0.156537 | ||||||||
\(583\) | −2.76240e23 | −0.857244 | ||||||||
\(584\) | 7.05143e22 | 0.215659 | ||||||||
\(585\) | 2.14439e23 | 0.646367 | ||||||||
\(586\) | 1.10035e23 | 0.326891 | ||||||||
\(587\) | 3.25116e23 | 0.951951 | 0.475975 | − | 0.879459i | \(-0.342095\pi\) | ||||
0.475975 | + | 0.879459i | \(0.342095\pi\) | |||||||
\(588\) | −5.38519e22 | −0.155415 | ||||||||
\(589\) | −6.61934e23 | −1.88293 | ||||||||
\(590\) | −8.89631e22 | −0.249441 | ||||||||
\(591\) | 5.09960e23 | 1.40943 | ||||||||
\(592\) | −1.42320e23 | −0.387731 | ||||||||
\(593\) | −3.66434e23 | −0.984081 | −0.492041 | − | 0.870572i | \(-0.663749\pi\) | ||||
−0.492041 | + | 0.870572i | \(0.663749\pi\) | |||||||
\(594\) | 2.35452e22 | 0.0623330 | ||||||||
\(595\) | −4.52055e22 | −0.117977 | ||||||||
\(596\) | 5.25018e23 | 1.35077 | ||||||||
\(597\) | 5.44448e23 | 1.38094 | ||||||||
\(598\) | 2.37626e22 | 0.0594202 | ||||||||
\(599\) | −6.01696e23 | −1.48337 | −0.741684 | − | 0.670750i | \(-0.765973\pi\) | ||||
−0.741684 | + | 0.670750i | \(0.765973\pi\) | |||||||
\(600\) | −4.36609e23 | −1.06122 | ||||||||
\(601\) | 3.50996e23 | 0.841142 | 0.420571 | − | 0.907260i | \(-0.361830\pi\) | ||||
0.420571 | + | 0.907260i | \(0.361830\pi\) | |||||||
\(602\) | 9.54111e22 | 0.225439 | ||||||||
\(603\) | 5.22895e23 | 1.21820 | ||||||||
\(604\) | −2.53904e23 | −0.583250 | ||||||||
\(605\) | 8.53393e22 | 0.193298 | ||||||||
\(606\) | −1.61233e23 | −0.360111 | ||||||||
\(607\) | −2.25258e21 | −0.00496107 | −0.00248054 | − | 0.999997i | \(-0.500790\pi\) | ||||
−0.00248054 | + | 0.999997i | \(0.500790\pi\) | |||||||
\(608\) | 5.84630e23 | 1.26970 | ||||||||
\(609\) | −9.90276e22 | −0.212085 | ||||||||
\(610\) | 2.34471e22 | 0.0495206 | ||||||||
\(611\) | 5.61009e23 | 1.16847 | ||||||||
\(612\) | 3.08572e23 | 0.633825 | ||||||||
\(613\) | −2.91522e23 | −0.590550 | −0.295275 | − | 0.955412i | \(-0.595411\pi\) | ||||
−0.295275 | + | 0.955412i | \(0.595411\pi\) | |||||||
\(614\) | 3.46820e23 | 0.692903 | ||||||||
\(615\) | −5.62900e23 | −1.10916 | ||||||||
\(616\) | 1.24306e23 | 0.241577 | ||||||||
\(617\) | −9.48194e23 | −1.81750 | −0.908748 | − | 0.417346i | \(-0.862960\pi\) | ||||
−0.908748 | + | 0.417346i | \(0.862960\pi\) | |||||||
\(618\) | 6.21401e22 | 0.117482 | ||||||||
\(619\) | 3.06667e23 | 0.571870 | 0.285935 | − | 0.958249i | \(-0.407696\pi\) | ||||
0.285935 | + | 0.958249i | \(0.407696\pi\) | |||||||
\(620\) | 2.55881e23 | 0.470661 | ||||||||
\(621\) | 7.90028e21 | 0.0143339 | ||||||||
\(622\) | −6.97018e22 | −0.124746 | ||||||||
\(623\) | 5.41660e22 | 0.0956265 | ||||||||
\(624\) | −3.60449e23 | −0.627733 | ||||||||
\(625\) | 3.03278e23 | 0.521028 | ||||||||
\(626\) | −6.78178e22 | −0.114937 | ||||||||
\(627\) | 7.79581e23 | 1.30343 | ||||||||
\(628\) | 1.00558e23 | 0.165867 | ||||||||
\(629\) | 5.89491e23 | 0.959283 | ||||||||
\(630\) | −5.43410e22 | −0.0872434 | ||||||||
\(631\) | 7.21382e23 | 1.14266 | 0.571329 | − | 0.820721i | \(-0.306428\pi\) | ||||
0.571329 | + | 0.820721i | \(0.306428\pi\) | |||||||
\(632\) | −5.85705e23 | −0.915342 | ||||||||
\(633\) | −7.13563e22 | −0.110027 | ||||||||
\(634\) | 2.39932e23 | 0.365031 | ||||||||
\(635\) | −1.28941e23 | −0.193559 | ||||||||
\(636\) | −8.64793e23 | −1.28093 | ||||||||
\(637\) | −1.37486e23 | −0.200943 | ||||||||
\(638\) | 9.77918e22 | 0.141035 | ||||||||
\(639\) | −1.18463e24 | −1.68587 | ||||||||
\(640\) | −2.71125e23 | −0.380750 | ||||||||
\(641\) | 6.65756e22 | 0.0922618 | 0.0461309 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461309 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(642\) | −1.24415e23 | −0.170147 | ||||||||
\(643\) | 5.21871e23 | 0.704320 | 0.352160 | − | 0.935940i | \(-0.385447\pi\) | ||||
0.352160 | + | 0.935940i | \(0.385447\pi\) | |||||||
\(644\) | 1.78438e22 | 0.0237660 | ||||||||
\(645\) | −5.40675e23 | −0.710688 | ||||||||
\(646\) | −3.61525e23 | −0.468989 | ||||||||
\(647\) | 3.24456e22 | 0.0415403 | 0.0207702 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207702 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(648\) | −6.03829e23 | −0.763003 | ||||||||
\(649\) | 7.04761e23 | 0.878946 | ||||||||
\(650\) | −4.76876e23 | −0.587005 | ||||||||
\(651\) | −6.92715e23 | −0.841621 | ||||||||
\(652\) | −4.53492e23 | −0.543832 | ||||||||
\(653\) | 6.71134e23 | 0.794414 | 0.397207 | − | 0.917729i | \(-0.369979\pi\) | ||||
0.397207 | + | 0.917729i | \(0.369979\pi\) | |||||||
\(654\) | −1.24497e24 | −1.45461 | ||||||||
\(655\) | 6.04767e23 | 0.697488 | ||||||||
\(656\) | 4.99262e23 | 0.568390 | ||||||||
\(657\) | 2.44199e23 | 0.274434 | ||||||||
\(658\) | −1.42165e23 | −0.157715 | ||||||||
\(659\) | 1.18160e24 | 1.29403 | 0.647013 | − | 0.762479i | \(-0.276018\pi\) | ||||
0.647013 | + | 0.762479i | \(0.276018\pi\) | |||||||
\(660\) | −3.01359e23 | −0.325808 | ||||||||
\(661\) | −1.60861e24 | −1.71687 | −0.858435 | − | 0.512923i | \(-0.828563\pi\) | ||||
−0.858435 | + | 0.512923i | \(0.828563\pi\) | |||||||
\(662\) | 8.69983e23 | 0.916681 | ||||||||
\(663\) | 1.49299e24 | 1.55307 | ||||||||
\(664\) | −8.86739e23 | −0.910683 | ||||||||
\(665\) | −1.88660e23 | −0.191291 | ||||||||
\(666\) | 7.08621e23 | 0.709386 | ||||||||
\(667\) | 3.28127e22 | 0.0324319 | ||||||||
\(668\) | 8.19854e23 | 0.800086 | ||||||||
\(669\) | −1.37564e24 | −1.32551 | ||||||||
\(670\) | 2.36821e23 | 0.225312 | ||||||||
\(671\) | −1.85747e23 | −0.174494 | ||||||||
\(672\) | 6.11818e23 | 0.567523 | ||||||||
\(673\) | 6.49909e23 | 0.595284 | 0.297642 | − | 0.954678i | \(-0.403800\pi\) | ||||
0.297642 | + | 0.954678i | \(0.403800\pi\) | |||||||
\(674\) | −4.38143e23 | −0.396284 | ||||||||
\(675\) | −1.58545e23 | −0.141603 | ||||||||
\(676\) | −8.29543e23 | −0.731631 | ||||||||
\(677\) | 8.20394e23 | 0.714527 | 0.357264 | − | 0.934004i | \(-0.383710\pi\) | ||||
0.357264 | + | 0.934004i | \(0.383710\pi\) | |||||||
\(678\) | 7.55541e23 | 0.649839 | ||||||||
\(679\) | −9.53045e22 | −0.0809506 | ||||||||
\(680\) | 3.26669e23 | 0.274020 | ||||||||
\(681\) | 5.27908e23 | 0.437328 | ||||||||
\(682\) | 6.84071e23 | 0.559672 | ||||||||
\(683\) | −1.13385e23 | −0.0916180 | −0.0458090 | − | 0.998950i | \(-0.514587\pi\) | ||||
−0.0458090 | + | 0.998950i | \(0.514587\pi\) | |||||||
\(684\) | 1.28779e24 | 1.02770 | ||||||||
\(685\) | 1.01484e24 | 0.799883 | ||||||||
\(686\) | 3.48403e22 | 0.0271223 | ||||||||
\(687\) | −9.20534e23 | −0.707795 | ||||||||
\(688\) | 4.79551e23 | 0.364194 | ||||||||
\(689\) | −2.20785e24 | −1.65618 | ||||||||
\(690\) | 3.41236e22 | 0.0252836 | ||||||||
\(691\) | −1.72294e24 | −1.26097 | −0.630486 | − | 0.776201i | \(-0.717144\pi\) | ||||
−0.630486 | + | 0.776201i | \(0.717144\pi\) | |||||||
\(692\) | −1.03119e24 | −0.745483 | ||||||||
\(693\) | 4.30487e23 | 0.307416 | ||||||||
\(694\) | 8.35698e23 | 0.589513 | ||||||||
\(695\) | 1.47322e23 | 0.102659 | ||||||||
\(696\) | 7.15605e23 | 0.492600 | ||||||||
\(697\) | −2.06795e24 | −1.40625 | ||||||||
\(698\) | 7.08774e23 | 0.476142 | ||||||||
\(699\) | 9.03578e23 | 0.599666 | ||||||||
\(700\) | −3.58094e23 | −0.234782 | ||||||||
\(701\) | −3.05383e23 | −0.197807 | −0.0989034 | − | 0.995097i | \(-0.531533\pi\) | ||||
−0.0989034 | + | 0.995097i | \(0.531533\pi\) | |||||||
\(702\) | 1.88185e23 | 0.120426 | ||||||||
\(703\) | 2.46017e24 | 1.55541 | ||||||||
\(704\) | −2.46691e23 | −0.154094 | ||||||||
\(705\) | 8.05621e23 | 0.497191 | ||||||||
\(706\) | 8.95291e23 | 0.545914 | ||||||||
\(707\) | −3.09103e23 | −0.186225 | ||||||||
\(708\) | 2.20631e24 | 1.31336 | ||||||||
\(709\) | −1.59973e24 | −0.940925 | −0.470462 | − | 0.882420i | \(-0.655913\pi\) | ||||
−0.470462 | + | 0.882420i | \(0.655913\pi\) | |||||||
\(710\) | −5.36522e23 | −0.311811 | ||||||||
\(711\) | −2.02836e24 | −1.16481 | ||||||||
\(712\) | −3.91421e23 | −0.222108 | ||||||||
\(713\) | 2.29531e23 | 0.128700 | ||||||||
\(714\) | −3.78338e23 | −0.209626 | ||||||||
\(715\) | −7.69383e23 | −0.421251 | ||||||||
\(716\) | 2.23640e23 | 0.121001 | ||||||||
\(717\) | 4.10314e24 | 2.19384 | ||||||||
\(718\) | −4.07468e23 | −0.215296 | ||||||||
\(719\) | −2.58321e24 | −1.34885 | −0.674425 | − | 0.738343i | \(-0.735609\pi\) | ||||
−0.674425 | + | 0.738343i | \(0.735609\pi\) | |||||||
\(720\) | −2.73126e23 | −0.140941 | ||||||||
\(721\) | 1.19130e23 | 0.0607536 | ||||||||
\(722\) | −5.12140e23 | −0.258121 | ||||||||
\(723\) | −2.96690e24 | −1.47784 | ||||||||
\(724\) | −1.30648e24 | −0.643171 | ||||||||
\(725\) | −6.58496e23 | −0.320391 | ||||||||
\(726\) | 7.14229e23 | 0.343460 | ||||||||
\(727\) | −2.76273e24 | −1.31309 | −0.656547 | − | 0.754285i | \(-0.727984\pi\) | ||||
−0.656547 | + | 0.754285i | \(0.727984\pi\) | |||||||
\(728\) | 9.93518e23 | 0.466723 | ||||||||
\(729\) | −2.62524e24 | −1.21895 | ||||||||
\(730\) | 1.10599e23 | 0.0507582 | ||||||||
\(731\) | −1.98631e24 | −0.901050 | ||||||||
\(732\) | −5.81496e23 | −0.260737 | ||||||||
\(733\) | 2.01898e24 | 0.894845 | 0.447423 | − | 0.894323i | \(-0.352342\pi\) | ||||
0.447423 | + | 0.894323i | \(0.352342\pi\) | |||||||
\(734\) | −1.77696e24 | −0.778503 | ||||||||
\(735\) | −1.97433e23 | −0.0855022 | ||||||||
\(736\) | −2.02725e23 | −0.0867853 | ||||||||
\(737\) | −1.87609e24 | −0.793925 | ||||||||
\(738\) | −2.48586e24 | −1.03992 | ||||||||
\(739\) | 4.01532e24 | 1.66051 | 0.830256 | − | 0.557382i | \(-0.188194\pi\) | ||||
0.830256 | + | 0.557382i | \(0.188194\pi\) | |||||||
\(740\) | −9.51019e23 | −0.388794 | ||||||||
\(741\) | 6.23081e24 | 2.51820 | ||||||||
\(742\) | 5.59491e23 | 0.223543 | ||||||||
\(743\) | 3.85515e24 | 1.52278 | 0.761388 | − | 0.648296i | \(-0.224518\pi\) | ||||
0.761388 | + | 0.648296i | \(0.224518\pi\) | |||||||
\(744\) | 5.00578e24 | 1.95480 | ||||||||
\(745\) | 1.92483e24 | 0.743130 | ||||||||
\(746\) | 3.73730e23 | 0.142652 | ||||||||
\(747\) | −3.07088e24 | −1.15888 | ||||||||
\(748\) | −1.10712e24 | −0.413077 | ||||||||
\(749\) | −2.38519e23 | −0.0879888 | ||||||||
\(750\) | −1.50908e24 | −0.550415 | ||||||||
\(751\) | 4.15814e24 | 1.49954 | 0.749772 | − | 0.661696i | \(-0.230163\pi\) | ||||
0.749772 | + | 0.661696i | \(0.230163\pi\) | |||||||
\(752\) | −7.14543e23 | −0.254787 | ||||||||
\(753\) | 6.24499e24 | 2.20178 | ||||||||
\(754\) | 7.81602e23 | 0.272477 | ||||||||
\(755\) | −9.30867e23 | −0.320877 | ||||||||
\(756\) | 1.41312e23 | 0.0481662 | ||||||||
\(757\) | −9.26353e23 | −0.312221 | −0.156110 | − | 0.987740i | \(-0.549896\pi\) | ||||
−0.156110 | + | 0.987740i | \(0.549896\pi\) | |||||||
\(758\) | −9.92455e23 | −0.330767 | ||||||||
\(759\) | −2.70326e23 | −0.0890907 | ||||||||
\(760\) | 1.36331e24 | 0.444304 | ||||||||
\(761\) | −1.38871e24 | −0.447551 | −0.223776 | − | 0.974641i | \(-0.571838\pi\) | ||||
−0.223776 | + | 0.974641i | \(0.571838\pi\) | |||||||
\(762\) | −1.07914e24 | −0.343924 | ||||||||
\(763\) | −2.38675e24 | −0.752227 | ||||||||
\(764\) | 1.79072e24 | 0.558128 | ||||||||
\(765\) | 1.13129e24 | 0.348701 | ||||||||
\(766\) | 9.45967e23 | 0.288358 | ||||||||
\(767\) | 5.63281e24 | 1.69811 | ||||||||
\(768\) | −3.30203e24 | −0.984489 | ||||||||
\(769\) | −2.57456e23 | −0.0759151 | −0.0379576 | − | 0.999279i | \(-0.512085\pi\) | ||||
−0.0379576 | + | 0.999279i | \(0.512085\pi\) | |||||||
\(770\) | 1.94969e23 | 0.0568584 | ||||||||
\(771\) | −8.91194e24 | −2.57046 | ||||||||
\(772\) | 2.89773e24 | 0.826631 | ||||||||
\(773\) | −8.82985e23 | −0.249131 | −0.124565 | − | 0.992211i | \(-0.539754\pi\) | ||||
−0.124565 | + | 0.992211i | \(0.539754\pi\) | |||||||
\(774\) | −2.38772e24 | −0.666323 | ||||||||
\(775\) | −4.60629e24 | −1.27141 | ||||||||
\(776\) | 6.88700e23 | 0.188021 | ||||||||
\(777\) | 2.57458e24 | 0.695228 | ||||||||
\(778\) | −2.10998e24 | −0.563575 | ||||||||
\(779\) | −8.63036e24 | −2.28014 | ||||||||
\(780\) | −2.40862e24 | −0.629454 | ||||||||
\(781\) | 4.25030e24 | 1.09872 | ||||||||
\(782\) | 1.25362e23 | 0.0320559 | ||||||||
\(783\) | 2.59856e23 | 0.0657292 | ||||||||
\(784\) | 1.75113e23 | 0.0438158 | ||||||||
\(785\) | 3.68668e23 | 0.0912523 | ||||||||
\(786\) | 5.06147e24 | 1.23932 | ||||||||
\(787\) | 5.12110e24 | 1.24045 | 0.620223 | − | 0.784426i | \(-0.287042\pi\) | ||||
0.620223 | + | 0.784426i | \(0.287042\pi\) | |||||||
\(788\) | −3.02244e24 | −0.724244 | ||||||||
\(789\) | 6.39481e24 | 1.51591 | ||||||||
\(790\) | −9.18654e23 | −0.215438 | ||||||||
\(791\) | 1.44846e24 | 0.336053 | ||||||||
\(792\) | −3.11083e24 | −0.714024 | ||||||||
\(793\) | −1.48458e24 | −0.337118 | ||||||||
\(794\) | 1.54782e24 | 0.347734 | ||||||||
\(795\) | −3.17052e24 | −0.704710 | ||||||||
\(796\) | −3.22685e24 | −0.709606 | ||||||||
\(797\) | −3.84853e24 | −0.837335 | −0.418667 | − | 0.908140i | \(-0.637503\pi\) | ||||
−0.418667 | + | 0.908140i | \(0.637503\pi\) | |||||||
\(798\) | −1.57895e24 | −0.339894 | ||||||||
\(799\) | 2.95965e24 | 0.630366 | ||||||||
\(800\) | 4.06835e24 | 0.857341 | ||||||||
\(801\) | −1.35554e24 | −0.282641 | ||||||||
\(802\) | −2.32766e24 | −0.480218 | ||||||||
\(803\) | −8.76159e23 | −0.178855 | ||||||||
\(804\) | −5.87325e24 | −1.18632 | ||||||||
\(805\) | 6.54192e22 | 0.0130750 | ||||||||
\(806\) | 5.46744e24 | 1.08128 | ||||||||
\(807\) | −1.07735e24 | −0.210830 | ||||||||
\(808\) | 2.23368e24 | 0.432538 | ||||||||
\(809\) | −6.88172e23 | −0.131867 | −0.0659333 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659333 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(810\) | −9.47081e23 | −0.179583 | ||||||||
\(811\) | 4.38304e24 | 0.822429 | 0.411215 | − | 0.911539i | \(-0.365105\pi\) | ||||
0.411215 | + | 0.911539i | \(0.365105\pi\) | |||||||
\(812\) | 5.86919e23 | 0.108981 | ||||||||
\(813\) | −1.82428e24 | −0.335214 | ||||||||
\(814\) | −2.54245e24 | −0.462322 | ||||||||
\(815\) | −1.66260e24 | −0.299191 | ||||||||
\(816\) | −1.90158e24 | −0.338648 | ||||||||
\(817\) | −8.28962e24 | −1.46099 | ||||||||
\(818\) | −1.55987e24 | −0.272073 | ||||||||
\(819\) | 3.44067e24 | 0.593922 | ||||||||
\(820\) | 3.33620e24 | 0.569948 | ||||||||
\(821\) | 6.99923e24 | 1.18341 | 0.591703 | − | 0.806156i | \(-0.298456\pi\) | ||||
0.591703 | + | 0.806156i | \(0.298456\pi\) | |||||||
\(822\) | 8.49347e24 | 1.42126 | ||||||||
\(823\) | −4.65710e24 | −0.771288 | −0.385644 | − | 0.922648i | \(-0.626021\pi\) | ||||
−0.385644 | + | 0.922648i | \(0.626021\pi\) | |||||||
\(824\) | −8.60873e23 | −0.141110 | ||||||||
\(825\) | 5.42499e24 | 0.880116 | ||||||||
\(826\) | −1.42741e24 | −0.229202 | ||||||||
\(827\) | 3.76035e24 | 0.597629 | 0.298815 | − | 0.954311i | \(-0.403409\pi\) | ||||
0.298815 | + | 0.954311i | \(0.403409\pi\) | |||||||
\(828\) | −4.46551e23 | −0.0702446 | ||||||||
\(829\) | 8.04278e24 | 1.25225 | 0.626127 | − | 0.779721i | \(-0.284639\pi\) | ||||
0.626127 | + | 0.779721i | \(0.284639\pi\) | |||||||
\(830\) | −1.39081e24 | −0.214341 | ||||||||
\(831\) | 3.35728e24 | 0.512128 | ||||||||
\(832\) | −1.97168e24 | −0.297706 | ||||||||
\(833\) | −7.25320e23 | −0.108404 | ||||||||
\(834\) | 1.23298e24 | 0.182408 | ||||||||
\(835\) | 3.00577e24 | 0.440170 | ||||||||
\(836\) | −4.62044e24 | −0.669776 | ||||||||
\(837\) | 1.81774e24 | 0.260835 | ||||||||
\(838\) | 1.83041e24 | 0.260000 | ||||||||
\(839\) | 9.27061e24 | 1.30356 | 0.651781 | − | 0.758407i | \(-0.274022\pi\) | ||||
0.651781 | + | 0.758407i | \(0.274022\pi\) | |||||||
\(840\) | 1.42671e24 | 0.198592 | ||||||||
\(841\) | −6.17787e24 | −0.851281 | ||||||||
\(842\) | −3.75926e24 | −0.512802 | ||||||||
\(843\) | −4.68243e24 | −0.632319 | ||||||||
\(844\) | 4.22916e23 | 0.0565383 | ||||||||
\(845\) | −3.04129e24 | −0.402509 | ||||||||
\(846\) | 3.55776e24 | 0.466153 | ||||||||
\(847\) | 1.36927e24 | 0.177615 | ||||||||
\(848\) | 2.81209e24 | 0.361131 | ||||||||
\(849\) | −7.33290e24 | −0.932311 | ||||||||
\(850\) | −2.51580e24 | −0.316676 | ||||||||
\(851\) | −8.53084e23 | −0.106314 | ||||||||
\(852\) | 1.33059e25 | 1.64176 | ||||||||
\(853\) | −1.02012e25 | −1.24619 | −0.623094 | − | 0.782147i | \(-0.714124\pi\) | ||||
−0.623094 | + | 0.782147i | \(0.714124\pi\) | |||||||
\(854\) | 3.76208e23 | 0.0455026 | ||||||||
\(855\) | 4.72132e24 | 0.565394 | ||||||||
\(856\) | 1.72361e24 | 0.204368 | ||||||||
\(857\) | −1.52446e25 | −1.78970 | −0.894848 | − | 0.446370i | \(-0.852716\pi\) | ||||
−0.894848 | + | 0.446370i | \(0.852716\pi\) | |||||||
\(858\) | −6.43919e24 | −0.748496 | ||||||||
\(859\) | 7.61607e24 | 0.876575 | 0.438287 | − | 0.898835i | \(-0.355585\pi\) | ||||
0.438287 | + | 0.898835i | \(0.355585\pi\) | |||||||
\(860\) | 3.20449e24 | 0.365192 | ||||||||
\(861\) | −9.03170e24 | −1.01916 | ||||||||
\(862\) | −1.06532e23 | −0.0119033 | ||||||||
\(863\) | −1.50221e24 | −0.166203 | −0.0831016 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831016 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(864\) | −1.60546e24 | −0.175886 | ||||||||
\(865\) | −3.78058e24 | −0.410130 | ||||||||
\(866\) | 4.82344e23 | 0.0518149 | ||||||||
\(867\) | −5.80207e24 | −0.617192 | ||||||||
\(868\) | 4.10560e24 | 0.432473 | ||||||||
\(869\) | 7.27753e24 | 0.759130 | ||||||||
\(870\) | 1.12240e24 | 0.115940 | ||||||||
\(871\) | −1.49946e25 | −1.53385 | ||||||||
\(872\) | 1.72474e25 | 1.74717 | ||||||||
\(873\) | 2.38505e24 | 0.239263 | ||||||||
\(874\) | 5.23183e23 | 0.0519764 | ||||||||
\(875\) | −2.89308e24 | −0.284638 | ||||||||
\(876\) | −2.74289e24 | −0.267253 | ||||||||
\(877\) | −1.14810e25 | −1.10786 | −0.553928 | − | 0.832564i | \(-0.686872\pi\) | ||||
−0.553928 | + | 0.832564i | \(0.686872\pi\) | |||||||
\(878\) | −1.16842e24 | −0.111659 | ||||||||
\(879\) | −1.00048e25 | −0.946899 | ||||||||
\(880\) | 9.79944e23 | 0.0918541 | ||||||||
\(881\) | 7.47390e24 | 0.693828 | 0.346914 | − | 0.937897i | \(-0.387230\pi\) | ||||
0.346914 | + | 0.937897i | \(0.387230\pi\) | |||||||
\(882\) | −8.71899e23 | −0.0801647 | ||||||||
\(883\) | −6.25058e24 | −0.569186 | −0.284593 | − | 0.958648i | \(-0.591858\pi\) | ||||
−0.284593 | + | 0.958648i | \(0.591858\pi\) | |||||||
\(884\) | −8.84867e24 | −0.798056 | ||||||||
\(885\) | 8.08884e24 | 0.722551 | ||||||||
\(886\) | −2.78929e24 | −0.246779 | ||||||||
\(887\) | 1.91184e25 | 1.67533 | 0.837664 | − | 0.546186i | \(-0.183921\pi\) | ||||
0.837664 | + | 0.546186i | \(0.183921\pi\) | |||||||
\(888\) | −1.86047e25 | −1.61478 | ||||||||
\(889\) | −2.06885e24 | −0.177854 | ||||||||
\(890\) | −6.13928e23 | −0.0522760 | ||||||||
\(891\) | 7.50273e24 | 0.632789 | ||||||||
\(892\) | 8.15315e24 | 0.681121 | ||||||||
\(893\) | 1.23518e25 | 1.02210 | ||||||||
\(894\) | 1.61095e25 | 1.32042 | ||||||||
\(895\) | 8.19913e23 | 0.0665690 | ||||||||
\(896\) | −4.35019e24 | −0.349856 | ||||||||
\(897\) | −2.16058e24 | −0.172121 | ||||||||
\(898\) | −4.32935e24 | −0.341644 | ||||||||
\(899\) | 7.54974e24 | 0.590167 | ||||||||
\(900\) | 8.96152e24 | 0.693938 | ||||||||
\(901\) | −1.16477e25 | −0.893471 | ||||||||
\(902\) | 8.91899e24 | 0.677736 | ||||||||
\(903\) | −8.67512e24 | −0.653024 | ||||||||
\(904\) | −1.04671e25 | −0.780537 | ||||||||
\(905\) | −4.78986e24 | −0.353842 | ||||||||
\(906\) | −7.79069e24 | −0.570146 | ||||||||
\(907\) | 2.92316e24 | 0.211929 | 0.105964 | − | 0.994370i | \(-0.466207\pi\) | ||||
0.105964 | + | 0.994370i | \(0.466207\pi\) | |||||||
\(908\) | −3.12881e24 | −0.224724 | ||||||||
\(909\) | 7.73549e24 | 0.550421 | ||||||||
\(910\) | 1.55829e24 | 0.109849 | ||||||||
\(911\) | 1.06255e25 | 0.742068 | 0.371034 | − | 0.928619i | \(-0.379003\pi\) | ||||
0.371034 | + | 0.928619i | \(0.379003\pi\) | |||||||
\(912\) | −7.93603e24 | −0.549095 | ||||||||
\(913\) | 1.10180e25 | 0.755266 | ||||||||
\(914\) | −3.79493e24 | −0.257727 | ||||||||
\(915\) | −2.13189e24 | −0.143445 | ||||||||
\(916\) | 5.45584e24 | 0.363706 | ||||||||
\(917\) | 9.70346e24 | 0.640896 | ||||||||
\(918\) | 9.92788e23 | 0.0649671 | ||||||||
\(919\) | 2.50761e25 | 1.62584 | 0.812920 | − | 0.582376i | \(-0.197877\pi\) | ||||
0.812920 | + | 0.582376i | \(0.197877\pi\) | |||||||
\(920\) | −4.72740e23 | −0.0303687 | ||||||||
\(921\) | −3.15341e25 | −2.00712 | ||||||||
\(922\) | 9.79725e24 | 0.617862 | ||||||||
\(923\) | 3.39706e25 | 2.12270 | ||||||||
\(924\) | −4.83530e24 | −0.299372 | ||||||||
\(925\) | 1.71200e25 | 1.05026 | ||||||||
\(926\) | −1.74731e24 | −0.106212 | ||||||||
\(927\) | −2.98130e24 | −0.179568 | ||||||||
\(928\) | −6.66805e24 | −0.397962 | ||||||||
\(929\) | −2.11336e24 | −0.124980 | −0.0624898 | − | 0.998046i | \(-0.519904\pi\) | ||||
−0.0624898 | + | 0.998046i | \(0.519904\pi\) | |||||||
\(930\) | 7.85137e24 | 0.460087 | ||||||||
\(931\) | −3.02704e24 | −0.175770 | ||||||||
\(932\) | −5.35534e24 | −0.308143 | ||||||||
\(933\) | 6.33753e24 | 0.361349 | ||||||||
\(934\) | 7.98078e24 | 0.450917 | ||||||||
\(935\) | −4.05895e24 | −0.227256 | ||||||||
\(936\) | −2.48634e25 | −1.37948 | ||||||||
\(937\) | −2.92602e25 | −1.60876 | −0.804379 | − | 0.594117i | \(-0.797502\pi\) | ||||
−0.804379 | + | 0.594117i | \(0.797502\pi\) | |||||||
\(938\) | 3.79979e24 | 0.207031 | ||||||||
\(939\) | 6.16623e24 | 0.332937 | ||||||||
\(940\) | −4.77477e24 | −0.255485 | ||||||||
\(941\) | −2.89238e25 | −1.53371 | −0.766856 | − | 0.641819i | \(-0.778180\pi\) | ||||
−0.766856 | + | 0.641819i | \(0.778180\pi\) | |||||||
\(942\) | 3.08549e24 | 0.162141 | ||||||||
\(943\) | 2.99265e24 | 0.155850 | ||||||||
\(944\) | −7.17438e24 | −0.370273 | ||||||||
\(945\) | 5.18080e23 | 0.0264988 | ||||||||
\(946\) | 8.56686e24 | 0.434257 | ||||||||
\(947\) | −3.39090e25 | −1.70349 | −0.851746 | − | 0.523954i | \(-0.824456\pi\) | ||||
−0.851746 | + | 0.523954i | \(0.824456\pi\) | |||||||
\(948\) | 2.27829e25 | 1.13433 | ||||||||
\(949\) | −7.00271e24 | −0.345544 | ||||||||
\(950\) | −1.04994e25 | −0.513468 | ||||||||
\(951\) | −2.18155e25 | −1.05738 | ||||||||
\(952\) | 5.24139e24 | 0.251786 | ||||||||
\(953\) | −2.63092e24 | −0.125262 | −0.0626308 | − | 0.998037i | \(-0.519949\pi\) | ||||
−0.0626308 | + | 0.998037i | \(0.519949\pi\) | |||||||
\(954\) | −1.40016e25 | −0.660718 | ||||||||
\(955\) | 6.56517e24 | 0.307056 | ||||||||
\(956\) | −2.43186e25 | −1.12732 | ||||||||
\(957\) | −8.89158e24 | −0.408533 | ||||||||
\(958\) | −5.13760e23 | −0.0233966 | ||||||||
\(959\) | 1.62830e25 | 0.734982 | ||||||||
\(960\) | −2.83138e24 | −0.126675 | ||||||||
\(961\) | 3.02616e25 | 1.34197 | ||||||||
\(962\) | −2.03205e25 | −0.893197 | ||||||||
\(963\) | 5.96908e24 | 0.260066 | ||||||||
\(964\) | 1.75843e25 | 0.759397 | ||||||||
\(965\) | 1.06237e25 | 0.454774 | ||||||||
\(966\) | 5.47513e23 | 0.0232321 | ||||||||
\(967\) | −4.60012e25 | −1.93484 | −0.967419 | − | 0.253181i | \(-0.918523\pi\) | ||||
−0.967419 | + | 0.253181i | \(0.918523\pi\) | |||||||
\(968\) | −9.89475e24 | −0.412538 | ||||||||
\(969\) | 3.28712e25 | 1.35851 | ||||||||
\(970\) | 1.08020e24 | 0.0442531 | ||||||||
\(971\) | −7.14898e24 | −0.290322 | −0.145161 | − | 0.989408i | \(-0.546370\pi\) | ||||
−0.145161 | + | 0.989408i | \(0.546370\pi\) | |||||||
\(972\) | 2.66535e25 | 1.07298 | ||||||||
\(973\) | 2.36377e24 | 0.0943293 | ||||||||
\(974\) | −4.26477e24 | −0.168712 | ||||||||
\(975\) | 4.33592e25 | 1.70037 | ||||||||
\(976\) | 1.89088e24 | 0.0735089 | ||||||||
\(977\) | 3.25867e25 | 1.25585 | 0.627923 | − | 0.778276i | \(-0.283905\pi\) | ||||
0.627923 | + | 0.778276i | \(0.283905\pi\) | |||||||
\(978\) | −1.39148e25 | −0.531614 | ||||||||
\(979\) | 4.86350e24 | 0.184203 | ||||||||
\(980\) | 1.17015e24 | 0.0439359 | ||||||||
\(981\) | 5.97299e25 | 2.22334 | ||||||||
\(982\) | −6.83461e24 | −0.252212 | ||||||||
\(983\) | −3.29176e25 | −1.20427 | −0.602135 | − | 0.798395i | \(-0.705683\pi\) | ||||
−0.602135 | + | 0.798395i | \(0.705683\pi\) | |||||||
\(984\) | 6.52659e25 | 2.36716 | ||||||||
\(985\) | −1.10809e25 | −0.398445 | ||||||||
\(986\) | 4.12341e24 | 0.146995 | ||||||||
\(987\) | 1.29261e25 | 0.456850 | ||||||||
\(988\) | −3.69289e25 | −1.29399 | ||||||||
\(989\) | 2.87449e24 | 0.0998603 | ||||||||
\(990\) | −4.87921e24 | −0.168055 | ||||||||
\(991\) | 1.54947e25 | 0.529124 | 0.264562 | − | 0.964369i | \(-0.414773\pi\) | ||||
0.264562 | + | 0.964369i | \(0.414773\pi\) | |||||||
\(992\) | −4.66442e25 | −1.57924 | ||||||||
\(993\) | −7.91020e25 | −2.65533 | ||||||||
\(994\) | −8.60847e24 | −0.286511 | ||||||||
\(995\) | −1.18303e25 | −0.390392 | ||||||||
\(996\) | 3.44927e25 | 1.12855 | ||||||||
\(997\) | 4.99514e25 | 1.62046 | 0.810231 | − | 0.586110i | \(-0.199342\pi\) | ||||
0.810231 | + | 0.586110i | \(0.199342\pi\) | |||||||
\(998\) | −5.14069e23 | −0.0165353 | ||||||||
\(999\) | −6.75590e24 | −0.215465 |
(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 | 7.18.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 63.18.a.b.1.3 | 4 | |||
4.3 | odd | 2 | 112.18.a.f.1.1 | 4 | |||
7.6 | odd | 2 | 49.18.a.c.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.18.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
49.18.a.c.1.2 | 4 | 7.6 | odd | 2 | |||
63.18.a.b.1.3 | 4 | 3.2 | odd | 2 | |||
112.18.a.f.1.1 | 4 | 4.3 | odd | 2 |