Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,36,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, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
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: | \(7.75951306336\) |
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: | \( x^{3} - 12422194x - 2645665785 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-213.765\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −165109. | −0.890730 | −0.445365 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445365 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(3\) | −3.45913e8 | −1.54648 | −0.773242 | − | 0.634111i | \(-0.781366\pi\) | ||||
−0.773242 | + | 0.634111i | \(0.781366\pi\) | |||||||
\(4\) | −7.09870e9 | −0.206599 | ||||||||
\(5\) | −2.05014e12 | −1.20173 | −0.600866 | − | 0.799350i | \(-0.705177\pi\) | ||||
−0.600866 | + | 0.799350i | \(0.705177\pi\) | |||||||
\(6\) | 5.71135e13 | 1.37750 | ||||||||
\(7\) | −1.25160e14 | −0.203353 | −0.101676 | − | 0.994818i | \(-0.532421\pi\) | ||||
−0.101676 | + | 0.994818i | \(0.532421\pi\) | |||||||
\(8\) | 6.84517e15 | 1.07475 | ||||||||
\(9\) | 6.96245e16 | 1.39161 | ||||||||
\(10\) | 3.38496e17 | 1.07042 | ||||||||
\(11\) | −1.70842e18 | −1.01911 | −0.509557 | − | 0.860437i | \(-0.670191\pi\) | ||||
−0.509557 | + | 0.860437i | \(0.670191\pi\) | |||||||
\(12\) | 2.45554e18 | 0.319503 | ||||||||
\(13\) | −4.94986e19 | −1.58703 | −0.793514 | − | 0.608552i | \(-0.791751\pi\) | ||||
−0.793514 | + | 0.608552i | \(0.791751\pi\) | |||||||
\(14\) | 2.06651e19 | 0.181132 | ||||||||
\(15\) | 7.09169e20 | 1.85846 | ||||||||
\(16\) | −8.86291e20 | −0.750717 | ||||||||
\(17\) | 1.32045e21 | 0.387137 | 0.193569 | − | 0.981087i | \(-0.437994\pi\) | ||||
0.193569 | + | 0.981087i | \(0.437994\pi\) | |||||||
\(18\) | −1.14956e22 | −1.23955 | ||||||||
\(19\) | 3.94388e21 | 0.165096 | 0.0825479 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825479 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(20\) | 1.45533e22 | 0.248277 | ||||||||
\(21\) | 4.32945e22 | 0.314482 | ||||||||
\(22\) | 2.82076e23 | 0.907756 | ||||||||
\(23\) | −3.48881e23 | −0.515750 | −0.257875 | − | 0.966178i | \(-0.583022\pi\) | ||||
−0.257875 | + | 0.966178i | \(0.583022\pi\) | |||||||
\(24\) | −2.36784e24 | −1.66209 | ||||||||
\(25\) | 1.29267e24 | 0.444159 | ||||||||
\(26\) | 8.17268e24 | 1.41361 | ||||||||
\(27\) | −6.77748e24 | −0.605623 | ||||||||
\(28\) | 8.88473e23 | 0.0420125 | ||||||||
\(29\) | 3.21628e25 | 0.822979 | 0.411489 | − | 0.911415i | \(-0.365009\pi\) | ||||
0.411489 | + | 0.911415i | \(0.365009\pi\) | |||||||
\(30\) | −1.17090e26 | −1.65539 | ||||||||
\(31\) | 3.41044e25 | 0.271632 | 0.135816 | − | 0.990734i | \(-0.456634\pi\) | ||||
0.135816 | + | 0.990734i | \(0.456634\pi\) | |||||||
\(32\) | −8.88635e25 | −0.406068 | ||||||||
\(33\) | 5.90965e26 | 1.57604 | ||||||||
\(34\) | −2.18018e26 | −0.344835 | ||||||||
\(35\) | 2.56595e26 | 0.244375 | ||||||||
\(36\) | −4.94244e26 | −0.287506 | ||||||||
\(37\) | −4.03624e27 | −1.45361 | −0.726804 | − | 0.686845i | \(-0.758995\pi\) | ||||
−0.726804 | + | 0.686845i | \(0.758995\pi\) | |||||||
\(38\) | −6.51171e26 | −0.147056 | ||||||||
\(39\) | 1.71222e28 | 2.45431 | ||||||||
\(40\) | −1.40335e28 | −1.29157 | ||||||||
\(41\) | 8.65857e27 | 0.517283 | 0.258642 | − | 0.965973i | \(-0.416725\pi\) | ||||
0.258642 | + | 0.965973i | \(0.416725\pi\) | |||||||
\(42\) | −7.14832e27 | −0.280118 | ||||||||
\(43\) | 9.89389e26 | 0.0256844 | 0.0128422 | − | 0.999918i | \(-0.495912\pi\) | ||||
0.0128422 | + | 0.999918i | \(0.495912\pi\) | |||||||
\(44\) | 1.21276e28 | 0.210548 | ||||||||
\(45\) | −1.42740e29 | −1.67234 | ||||||||
\(46\) | 5.76034e28 | 0.459395 | ||||||||
\(47\) | 1.95852e29 | 1.07205 | 0.536025 | − | 0.844202i | \(-0.319925\pi\) | ||||
0.536025 | + | 0.844202i | \(0.319925\pi\) | |||||||
\(48\) | 3.06580e29 | 1.16097 | ||||||||
\(49\) | −3.63154e29 | −0.958648 | ||||||||
\(50\) | −2.13432e29 | −0.395626 | ||||||||
\(51\) | −4.56760e29 | −0.598702 | ||||||||
\(52\) | 3.51376e29 | 0.327879 | ||||||||
\(53\) | −9.96909e29 | −0.666543 | −0.333271 | − | 0.942831i | \(-0.608153\pi\) | ||||
−0.333271 | + | 0.942831i | \(0.608153\pi\) | |||||||
\(54\) | 1.11902e30 | 0.539447 | ||||||||
\(55\) | 3.50249e30 | 1.22470 | ||||||||
\(56\) | −8.56741e29 | −0.218554 | ||||||||
\(57\) | −1.36424e30 | −0.255318 | ||||||||
\(58\) | −5.31037e30 | −0.733052 | ||||||||
\(59\) | 3.91953e30 | 0.401166 | 0.200583 | − | 0.979677i | \(-0.435716\pi\) | ||||
0.200583 | + | 0.979677i | \(0.435716\pi\) | |||||||
\(60\) | −5.03418e30 | −0.383956 | ||||||||
\(61\) | 7.64909e29 | 0.0436855 | 0.0218428 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218428 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(62\) | −5.63096e30 | −0.241951 | ||||||||
\(63\) | −8.71420e30 | −0.282988 | ||||||||
\(64\) | 4.51249e31 | 1.11241 | ||||||||
\(65\) | 1.01479e32 | 1.90718 | ||||||||
\(66\) | −9.75738e31 | −1.40383 | ||||||||
\(67\) | −1.64301e32 | −1.81690 | −0.908451 | − | 0.417992i | \(-0.862734\pi\) | ||||
−0.908451 | + | 0.417992i | \(0.862734\pi\) | |||||||
\(68\) | −9.37346e30 | −0.0799823 | ||||||||
\(69\) | 1.20682e32 | 0.797600 | ||||||||
\(70\) | −4.23662e31 | −0.217672 | ||||||||
\(71\) | 7.65930e31 | 0.307021 | 0.153510 | − | 0.988147i | \(-0.450942\pi\) | ||||
0.153510 | + | 0.988147i | \(0.450942\pi\) | |||||||
\(72\) | 4.76592e32 | 1.49564 | ||||||||
\(73\) | −7.08063e32 | −1.74551 | −0.872754 | − | 0.488160i | \(-0.837668\pi\) | ||||
−0.872754 | + | 0.488160i | \(0.837668\pi\) | |||||||
\(74\) | 6.66421e32 | 1.29477 | ||||||||
\(75\) | −4.47152e32 | −0.686884 | ||||||||
\(76\) | −2.79964e31 | −0.0341087 | ||||||||
\(77\) | 2.13826e32 | 0.207239 | ||||||||
\(78\) | −2.82704e33 | −2.18613 | ||||||||
\(79\) | 2.34599e33 | 1.45162 | 0.725809 | − | 0.687896i | \(-0.241466\pi\) | ||||
0.725809 | + | 0.687896i | \(0.241466\pi\) | |||||||
\(80\) | 1.81702e33 | 0.902161 | ||||||||
\(81\) | −1.13900e33 | −0.455027 | ||||||||
\(82\) | −1.42961e33 | −0.460760 | ||||||||
\(83\) | 5.18971e33 | 1.35293 | 0.676467 | − | 0.736473i | \(-0.263510\pi\) | ||||
0.676467 | + | 0.736473i | \(0.263510\pi\) | |||||||
\(84\) | −3.07335e32 | −0.0649717 | ||||||||
\(85\) | −2.70710e33 | −0.465235 | ||||||||
\(86\) | −1.63357e32 | −0.0228779 | ||||||||
\(87\) | −1.11255e34 | −1.27272 | ||||||||
\(88\) | −1.16944e34 | −1.09530 | ||||||||
\(89\) | 1.44578e34 | 1.11116 | 0.555582 | − | 0.831461i | \(-0.312495\pi\) | ||||
0.555582 | + | 0.831461i | \(0.312495\pi\) | |||||||
\(90\) | 2.35676e34 | 1.48961 | ||||||||
\(91\) | 6.19525e33 | 0.322726 | ||||||||
\(92\) | 2.47660e33 | 0.106554 | ||||||||
\(93\) | −1.17972e34 | −0.420075 | ||||||||
\(94\) | −3.23369e34 | −0.954907 | ||||||||
\(95\) | −8.08549e33 | −0.198401 | ||||||||
\(96\) | 3.07391e34 | 0.627978 | ||||||||
\(97\) | −2.87399e34 | −0.489756 | −0.244878 | − | 0.969554i | \(-0.578748\pi\) | ||||
−0.244878 | + | 0.969554i | \(0.578748\pi\) | |||||||
\(98\) | 5.99600e34 | 0.853897 | ||||||||
\(99\) | −1.18948e35 | −1.41821 | ||||||||
\(100\) | −9.17629e33 | −0.0917629 | ||||||||
\(101\) | 1.13198e35 | 0.951079 | 0.475539 | − | 0.879694i | \(-0.342253\pi\) | ||||
0.475539 | + | 0.879694i | \(0.342253\pi\) | |||||||
\(102\) | 7.54153e34 | 0.533282 | ||||||||
\(103\) | 2.53635e35 | 1.51202 | 0.756011 | − | 0.654559i | \(-0.227145\pi\) | ||||
0.756011 | + | 0.654559i | \(0.227145\pi\) | |||||||
\(104\) | −3.38826e35 | −1.70567 | ||||||||
\(105\) | −8.87596e34 | −0.377922 | ||||||||
\(106\) | 1.64599e35 | 0.593710 | ||||||||
\(107\) | −3.63939e35 | −1.11381 | −0.556907 | − | 0.830575i | \(-0.688012\pi\) | ||||
−0.556907 | + | 0.830575i | \(0.688012\pi\) | |||||||
\(108\) | 4.81113e34 | 0.125121 | ||||||||
\(109\) | −4.65371e34 | −0.103000 | −0.0514998 | − | 0.998673i | \(-0.516400\pi\) | ||||
−0.0514998 | + | 0.998673i | \(0.516400\pi\) | |||||||
\(110\) | −5.78294e35 | −1.09088 | ||||||||
\(111\) | 1.39619e36 | 2.24798 | ||||||||
\(112\) | 1.10928e35 | 0.152660 | ||||||||
\(113\) | −2.18346e35 | −0.257201 | −0.128601 | − | 0.991696i | \(-0.541049\pi\) | ||||
−0.128601 | + | 0.991696i | \(0.541049\pi\) | |||||||
\(114\) | 2.25249e35 | 0.227419 | ||||||||
\(115\) | 7.15252e35 | 0.619794 | ||||||||
\(116\) | −2.28314e35 | −0.170027 | ||||||||
\(117\) | −3.44632e36 | −2.20853 | ||||||||
\(118\) | −6.47150e35 | −0.357330 | ||||||||
\(119\) | −1.65267e35 | −0.0787254 | ||||||||
\(120\) | 4.85438e36 | 1.99739 | ||||||||
\(121\) | 1.08456e35 | 0.0385932 | ||||||||
\(122\) | −1.26293e35 | −0.0389120 | ||||||||
\(123\) | −2.99511e36 | −0.799970 | ||||||||
\(124\) | −2.42097e35 | −0.0561191 | ||||||||
\(125\) | 3.31653e36 | 0.667972 | ||||||||
\(126\) | 1.43880e36 | 0.252066 | ||||||||
\(127\) | 4.19558e36 | 0.640070 | 0.320035 | − | 0.947406i | \(-0.396305\pi\) | ||||
0.320035 | + | 0.947406i | \(0.396305\pi\) | |||||||
\(128\) | −4.39721e36 | −0.584793 | ||||||||
\(129\) | −3.42243e35 | −0.0397205 | ||||||||
\(130\) | −1.67551e37 | −1.69878 | ||||||||
\(131\) | 2.40631e36 | 0.213355 | 0.106678 | − | 0.994294i | \(-0.465979\pi\) | ||||
0.106678 | + | 0.994294i | \(0.465979\pi\) | |||||||
\(132\) | −4.19509e36 | −0.325610 | ||||||||
\(133\) | −4.93616e35 | −0.0335727 | ||||||||
\(134\) | 2.71276e37 | 1.61837 | ||||||||
\(135\) | 1.38947e37 | 0.727796 | ||||||||
\(136\) | 9.03869e36 | 0.416078 | ||||||||
\(137\) | −2.14718e37 | −0.869477 | −0.434739 | − | 0.900557i | \(-0.643159\pi\) | ||||
−0.434739 | + | 0.900557i | \(0.643159\pi\) | |||||||
\(138\) | −1.99258e37 | −0.710446 | ||||||||
\(139\) | 2.63209e37 | 0.827068 | 0.413534 | − | 0.910489i | \(-0.364294\pi\) | ||||
0.413534 | + | 0.910489i | \(0.364294\pi\) | |||||||
\(140\) | −1.82149e36 | −0.0504878 | ||||||||
\(141\) | −6.77477e37 | −1.65791 | ||||||||
\(142\) | −1.26462e37 | −0.273473 | ||||||||
\(143\) | 8.45645e37 | 1.61736 | ||||||||
\(144\) | −6.17076e37 | −1.04471 | ||||||||
\(145\) | −6.59381e37 | −0.989000 | ||||||||
\(146\) | 1.16908e38 | 1.55478 | ||||||||
\(147\) | 1.25620e38 | 1.48253 | ||||||||
\(148\) | 2.86521e37 | 0.300314 | ||||||||
\(149\) | −1.74389e38 | −1.62465 | −0.812324 | − | 0.583206i | \(-0.801798\pi\) | ||||
−0.812324 | + | 0.583206i | \(0.801798\pi\) | |||||||
\(150\) | 7.38290e37 | 0.611829 | ||||||||
\(151\) | −1.40947e38 | −1.03982 | −0.519912 | − | 0.854220i | \(-0.674035\pi\) | ||||
−0.519912 | + | 0.854220i | \(0.674035\pi\) | |||||||
\(152\) | 2.69965e37 | 0.177437 | ||||||||
\(153\) | 9.19355e37 | 0.538745 | ||||||||
\(154\) | −3.53046e37 | −0.184595 | ||||||||
\(155\) | −6.99187e37 | −0.326429 | ||||||||
\(156\) | −1.21546e38 | −0.507059 | ||||||||
\(157\) | 1.49924e38 | 0.559277 | 0.279639 | − | 0.960105i | \(-0.409785\pi\) | ||||
0.279639 | + | 0.960105i | \(0.409785\pi\) | |||||||
\(158\) | −3.87345e38 | −1.29300 | ||||||||
\(159\) | 3.44844e38 | 1.03080 | ||||||||
\(160\) | 1.82182e38 | 0.487985 | ||||||||
\(161\) | 4.36659e37 | 0.104879 | ||||||||
\(162\) | 1.88060e38 | 0.405306 | ||||||||
\(163\) | 8.60787e38 | 1.66576 | 0.832880 | − | 0.553453i | \(-0.186690\pi\) | ||||
0.832880 | + | 0.553453i | \(0.186690\pi\) | |||||||
\(164\) | −6.14646e37 | −0.106870 | ||||||||
\(165\) | −1.21156e39 | −1.89398 | ||||||||
\(166\) | −8.56869e38 | −1.20510 | ||||||||
\(167\) | −9.23344e38 | −1.16903 | −0.584515 | − | 0.811383i | \(-0.698715\pi\) | ||||
−0.584515 | + | 0.811383i | \(0.698715\pi\) | |||||||
\(168\) | 2.96358e38 | 0.337991 | ||||||||
\(169\) | 1.47733e39 | 1.51866 | ||||||||
\(170\) | 4.46966e38 | 0.414399 | ||||||||
\(171\) | 2.74591e38 | 0.229749 | ||||||||
\(172\) | −7.02337e36 | −0.00530638 | ||||||||
\(173\) | −1.33161e39 | −0.909012 | −0.454506 | − | 0.890744i | \(-0.650184\pi\) | ||||
−0.454506 | + | 0.890744i | \(0.650184\pi\) | |||||||
\(174\) | 1.83693e39 | 1.13365 | ||||||||
\(175\) | −1.61791e38 | −0.0903208 | ||||||||
\(176\) | 1.51416e39 | 0.765066 | ||||||||
\(177\) | −1.35582e39 | −0.620396 | ||||||||
\(178\) | −2.38712e39 | −0.989748 | ||||||||
\(179\) | 6.27202e38 | 0.235765 | 0.117883 | − | 0.993028i | \(-0.462389\pi\) | ||||
0.117883 | + | 0.993028i | \(0.462389\pi\) | |||||||
\(180\) | 1.01327e39 | 0.345505 | ||||||||
\(181\) | −2.39965e39 | −0.742629 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(182\) | −1.02289e39 | −0.287462 | ||||||||
\(183\) | −2.64592e38 | −0.0675590 | ||||||||
\(184\) | −2.38815e39 | −0.554305 | ||||||||
\(185\) | 8.27484e39 | 1.74685 | ||||||||
\(186\) | 1.94782e39 | 0.374174 | ||||||||
\(187\) | −2.25588e39 | −0.394537 | ||||||||
\(188\) | −1.39029e39 | −0.221485 | ||||||||
\(189\) | 8.48269e38 | 0.123155 | ||||||||
\(190\) | 1.33499e39 | 0.176722 | ||||||||
\(191\) | 8.14518e39 | 0.983596 | 0.491798 | − | 0.870709i | \(-0.336340\pi\) | ||||
0.491798 | + | 0.870709i | \(0.336340\pi\) | |||||||
\(192\) | −1.56093e40 | −1.72033 | ||||||||
\(193\) | 1.38549e40 | 1.39428 | 0.697139 | − | 0.716936i | \(-0.254456\pi\) | ||||
0.697139 | + | 0.716936i | \(0.254456\pi\) | |||||||
\(194\) | 4.74522e39 | 0.436240 | ||||||||
\(195\) | −3.51029e40 | −2.94942 | ||||||||
\(196\) | 2.57792e39 | 0.198056 | ||||||||
\(197\) | −1.15539e40 | −0.812026 | −0.406013 | − | 0.913867i | \(-0.633081\pi\) | ||||
−0.406013 | + | 0.913867i | \(0.633081\pi\) | |||||||
\(198\) | 1.96394e40 | 1.26324 | ||||||||
\(199\) | −4.76691e39 | −0.280742 | −0.140371 | − | 0.990099i | \(-0.544830\pi\) | ||||
−0.140371 | + | 0.990099i | \(0.544830\pi\) | |||||||
\(200\) | 8.84856e39 | 0.477362 | ||||||||
\(201\) | 5.68340e40 | 2.80981 | ||||||||
\(202\) | −1.86901e40 | −0.847155 | ||||||||
\(203\) | −4.02549e39 | −0.167355 | ||||||||
\(204\) | 3.24241e39 | 0.123691 | ||||||||
\(205\) | −1.77512e40 | −0.621636 | ||||||||
\(206\) | −4.18775e40 | −1.34680 | ||||||||
\(207\) | −2.42906e40 | −0.717725 | ||||||||
\(208\) | 4.38702e40 | 1.19141 | ||||||||
\(209\) | −6.73781e39 | −0.168251 | ||||||||
\(210\) | 1.46550e40 | 0.336627 | ||||||||
\(211\) | −1.87354e40 | −0.396022 | −0.198011 | − | 0.980200i | \(-0.563448\pi\) | ||||
−0.198011 | + | 0.980200i | \(0.563448\pi\) | |||||||
\(212\) | 7.07676e39 | 0.137707 | ||||||||
\(213\) | −2.64945e40 | −0.474803 | ||||||||
\(214\) | 6.00896e40 | 0.992107 | ||||||||
\(215\) | −2.02838e39 | −0.0308657 | ||||||||
\(216\) | −4.63930e40 | −0.650896 | ||||||||
\(217\) | −4.26851e39 | −0.0552371 | ||||||||
\(218\) | 7.68370e39 | 0.0917448 | ||||||||
\(219\) | 2.44929e41 | 2.69940 | ||||||||
\(220\) | −2.48631e40 | −0.253023 | ||||||||
\(221\) | −6.53603e40 | −0.614398 | ||||||||
\(222\) | −2.30524e41 | −2.00234 | ||||||||
\(223\) | −7.12100e40 | −0.571750 | −0.285875 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285875 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(224\) | 1.11222e40 | 0.0825750 | ||||||||
\(225\) | 9.00017e40 | 0.618097 | ||||||||
\(226\) | 3.60510e40 | 0.229097 | ||||||||
\(227\) | −1.04005e41 | −0.611787 | −0.305893 | − | 0.952066i | \(-0.598955\pi\) | ||||
−0.305893 | + | 0.952066i | \(0.598955\pi\) | |||||||
\(228\) | 9.68434e39 | 0.0527485 | ||||||||
\(229\) | 1.82859e41 | 0.922564 | 0.461282 | − | 0.887254i | \(-0.347390\pi\) | ||||
0.461282 | + | 0.887254i | \(0.347390\pi\) | |||||||
\(230\) | −1.18095e41 | −0.552069 | ||||||||
\(231\) | −7.39652e40 | −0.320493 | ||||||||
\(232\) | 2.20160e41 | 0.884501 | ||||||||
\(233\) | 1.57847e41 | 0.588177 | 0.294088 | − | 0.955778i | \(-0.404984\pi\) | ||||
0.294088 | + | 0.955778i | \(0.404984\pi\) | |||||||
\(234\) | 5.69019e41 | 1.96720 | ||||||||
\(235\) | −4.01523e41 | −1.28832 | ||||||||
\(236\) | −2.78236e40 | −0.0828806 | ||||||||
\(237\) | −8.11510e41 | −2.24490 | ||||||||
\(238\) | 2.72871e40 | 0.0701231 | ||||||||
\(239\) | 5.00984e41 | 1.19636 | 0.598178 | − | 0.801363i | \(-0.295892\pi\) | ||||
0.598178 | + | 0.801363i | \(0.295892\pi\) | |||||||
\(240\) | −6.28530e41 | −1.39518 | ||||||||
\(241\) | −3.33164e41 | −0.687638 | −0.343819 | − | 0.939036i | \(-0.611721\pi\) | ||||
−0.343819 | + | 0.939036i | \(0.611721\pi\) | |||||||
\(242\) | −1.79072e40 | −0.0343762 | ||||||||
\(243\) | 7.33084e41 | 1.30931 | ||||||||
\(244\) | −5.42986e39 | −0.00902540 | ||||||||
\(245\) | 7.44514e41 | 1.15204 | ||||||||
\(246\) | 4.94521e41 | 0.712558 | ||||||||
\(247\) | −1.95217e41 | −0.262011 | ||||||||
\(248\) | 2.33451e41 | 0.291938 | ||||||||
\(249\) | −1.79519e42 | −2.09229 | ||||||||
\(250\) | −5.47589e41 | −0.594983 | ||||||||
\(251\) | 1.52760e42 | 1.54782 | 0.773909 | − | 0.633297i | \(-0.218299\pi\) | ||||
0.773909 | + | 0.633297i | \(0.218299\pi\) | |||||||
\(252\) | 6.18595e40 | 0.0584652 | ||||||||
\(253\) | 5.96035e41 | 0.525608 | ||||||||
\(254\) | −6.92730e41 | −0.570130 | ||||||||
\(255\) | 9.36421e41 | 0.719479 | ||||||||
\(256\) | −8.24460e41 | −0.591521 | ||||||||
\(257\) | −2.72482e42 | −1.82603 | −0.913016 | − | 0.407925i | \(-0.866253\pi\) | ||||
−0.913016 | + | 0.407925i | \(0.866253\pi\) | |||||||
\(258\) | 5.65074e40 | 0.0353802 | ||||||||
\(259\) | 5.05176e41 | 0.295595 | ||||||||
\(260\) | −7.20368e41 | −0.394022 | ||||||||
\(261\) | 2.23932e42 | 1.14527 | ||||||||
\(262\) | −3.97303e41 | −0.190042 | ||||||||
\(263\) | 4.22055e40 | 0.0188861 | 0.00944307 | − | 0.999955i | \(-0.496994\pi\) | ||||
0.00944307 | + | 0.999955i | \(0.496994\pi\) | |||||||
\(264\) | 4.04526e42 | 1.69386 | ||||||||
\(265\) | 2.04380e42 | 0.801005 | ||||||||
\(266\) | 8.15005e40 | 0.0299042 | ||||||||
\(267\) | −5.00116e42 | −1.71840 | ||||||||
\(268\) | 1.16632e42 | 0.375371 | ||||||||
\(269\) | −1.30618e42 | −0.393858 | −0.196929 | − | 0.980418i | \(-0.563097\pi\) | ||||
−0.196929 | + | 0.980418i | \(0.563097\pi\) | |||||||
\(270\) | −2.29415e42 | −0.648270 | ||||||||
\(271\) | −4.11918e41 | −0.109106 | −0.0545529 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545529 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(272\) | −1.17030e42 | −0.290631 | ||||||||
\(273\) | −2.14302e42 | −0.499091 | ||||||||
\(274\) | 3.54519e42 | 0.774470 | ||||||||
\(275\) | −2.20843e42 | −0.452648 | ||||||||
\(276\) | −8.56689e41 | −0.164784 | ||||||||
\(277\) | 7.38232e42 | 1.33290 | 0.666449 | − | 0.745551i | \(-0.267813\pi\) | ||||
0.666449 | + | 0.745551i | \(0.267813\pi\) | |||||||
\(278\) | −4.34582e42 | −0.736694 | ||||||||
\(279\) | 2.37451e42 | 0.378007 | ||||||||
\(280\) | 1.75644e42 | 0.262643 | ||||||||
\(281\) | 4.08223e42 | 0.573505 | 0.286752 | − | 0.958005i | \(-0.407424\pi\) | ||||
0.286752 | + | 0.958005i | \(0.407424\pi\) | |||||||
\(282\) | 1.11858e43 | 1.47675 | ||||||||
\(283\) | −1.06503e43 | −1.32159 | −0.660796 | − | 0.750565i | \(-0.729781\pi\) | ||||
−0.660796 | + | 0.750565i | \(0.729781\pi\) | |||||||
\(284\) | −5.43711e41 | −0.0634303 | ||||||||
\(285\) | 2.79688e42 | 0.306824 | ||||||||
\(286\) | −1.39624e43 | −1.44063 | ||||||||
\(287\) | −1.08371e42 | −0.105191 | ||||||||
\(288\) | −6.18708e42 | −0.565089 | ||||||||
\(289\) | −9.88997e42 | −0.850125 | ||||||||
\(290\) | 1.08870e43 | 0.880932 | ||||||||
\(291\) | 9.94151e42 | 0.757399 | ||||||||
\(292\) | 5.02633e42 | 0.360621 | ||||||||
\(293\) | 1.90474e43 | 1.28722 | 0.643610 | − | 0.765353i | \(-0.277436\pi\) | ||||
0.643610 | + | 0.765353i | \(0.277436\pi\) | |||||||
\(294\) | −2.07410e43 | −1.32054 | ||||||||
\(295\) | −8.03556e42 | −0.482093 | ||||||||
\(296\) | −2.76288e43 | −1.56227 | ||||||||
\(297\) | 1.15788e43 | 0.617199 | ||||||||
\(298\) | 2.87932e43 | 1.44712 | ||||||||
\(299\) | 1.72691e43 | 0.818510 | ||||||||
\(300\) | 3.17420e42 | 0.141910 | ||||||||
\(301\) | −1.23832e41 | −0.00522298 | ||||||||
\(302\) | 2.32717e43 | 0.926203 | ||||||||
\(303\) | −3.91569e43 | −1.47083 | ||||||||
\(304\) | −3.49543e42 | −0.123940 | ||||||||
\(305\) | −1.56817e42 | −0.0524983 | ||||||||
\(306\) | −1.51794e43 | −0.479877 | ||||||||
\(307\) | −1.39752e43 | −0.417288 | −0.208644 | − | 0.977992i | \(-0.566905\pi\) | ||||
−0.208644 | + | 0.977992i | \(0.566905\pi\) | |||||||
\(308\) | −1.51789e42 | −0.0428156 | ||||||||
\(309\) | −8.77359e43 | −2.33832 | ||||||||
\(310\) | 1.15442e43 | 0.290760 | ||||||||
\(311\) | 2.22377e43 | 0.529399 | 0.264700 | − | 0.964331i | \(-0.414727\pi\) | ||||
0.264700 | + | 0.964331i | \(0.414727\pi\) | |||||||
\(312\) | 1.17205e44 | 2.63778 | ||||||||
\(313\) | 3.63171e43 | 0.772833 | 0.386417 | − | 0.922324i | \(-0.373713\pi\) | ||||
0.386417 | + | 0.922324i | \(0.373713\pi\) | |||||||
\(314\) | −2.47538e43 | −0.498165 | ||||||||
\(315\) | 1.78653e43 | 0.340076 | ||||||||
\(316\) | −1.66535e43 | −0.299903 | ||||||||
\(317\) | 5.29385e43 | 0.902058 | 0.451029 | − | 0.892509i | \(-0.351057\pi\) | ||||
0.451029 | + | 0.892509i | \(0.351057\pi\) | |||||||
\(318\) | −5.69370e43 | −0.918163 | ||||||||
\(319\) | −5.49476e43 | −0.838709 | ||||||||
\(320\) | −9.25121e43 | −1.33682 | ||||||||
\(321\) | 1.25891e44 | 1.72249 | ||||||||
\(322\) | −7.20964e42 | −0.0934191 | ||||||||
\(323\) | 5.20769e42 | 0.0639147 | ||||||||
\(324\) | 8.08544e42 | 0.0940083 | ||||||||
\(325\) | −6.39855e43 | −0.704892 | ||||||||
\(326\) | −1.42124e44 | −1.48374 | ||||||||
\(327\) | 1.60978e43 | 0.159287 | ||||||||
\(328\) | 5.92693e43 | 0.555953 | ||||||||
\(329\) | −2.45128e43 | −0.218004 | ||||||||
\(330\) | 2.00040e44 | 1.68703 | ||||||||
\(331\) | 6.25551e43 | 0.500349 | 0.250174 | − | 0.968201i | \(-0.419512\pi\) | ||||
0.250174 | + | 0.968201i | \(0.419512\pi\) | |||||||
\(332\) | −3.68402e43 | −0.279515 | ||||||||
\(333\) | −2.81022e44 | −2.02286 | ||||||||
\(334\) | 1.52453e44 | 1.04129 | ||||||||
\(335\) | 3.36840e44 | 2.18343 | ||||||||
\(336\) | −3.83715e43 | −0.236087 | ||||||||
\(337\) | −1.04185e44 | −0.608529 | −0.304264 | − | 0.952588i | \(-0.598411\pi\) | ||||
−0.304264 | + | 0.952588i | \(0.598411\pi\) | |||||||
\(338\) | −2.43920e44 | −1.35271 | ||||||||
\(339\) | 7.55289e43 | 0.397757 | ||||||||
\(340\) | 1.92169e43 | 0.0961173 | ||||||||
\(341\) | −5.82647e43 | −0.276824 | ||||||||
\(342\) | −4.53375e43 | −0.204645 | ||||||||
\(343\) | 9.28652e43 | 0.398296 | ||||||||
\(344\) | 6.77253e42 | 0.0276044 | ||||||||
\(345\) | −2.47415e44 | −0.958501 | ||||||||
\(346\) | 2.19861e44 | 0.809685 | ||||||||
\(347\) | −3.07657e44 | −1.07721 | −0.538606 | − | 0.842557i | \(-0.681049\pi\) | ||||
−0.538606 | + | 0.842557i | \(0.681049\pi\) | |||||||
\(348\) | 7.89769e43 | 0.262944 | ||||||||
\(349\) | −2.62767e44 | −0.832005 | −0.416003 | − | 0.909363i | \(-0.636569\pi\) | ||||
−0.416003 | + | 0.909363i | \(0.636569\pi\) | |||||||
\(350\) | 2.67131e43 | 0.0804515 | ||||||||
\(351\) | 3.35476e44 | 0.961140 | ||||||||
\(352\) | 1.51816e44 | 0.413830 | ||||||||
\(353\) | 7.06671e44 | 1.83299 | 0.916494 | − | 0.400048i | \(-0.131006\pi\) | ||||
0.916494 | + | 0.400048i | \(0.131006\pi\) | |||||||
\(354\) | 2.23858e44 | 0.552606 | ||||||||
\(355\) | −1.57026e44 | −0.368957 | ||||||||
\(356\) | −1.02632e44 | −0.229566 | ||||||||
\(357\) | 5.71681e43 | 0.121748 | ||||||||
\(358\) | −1.03557e44 | −0.210003 | ||||||||
\(359\) | −5.35788e44 | −1.03476 | −0.517380 | − | 0.855756i | \(-0.673093\pi\) | ||||
−0.517380 | + | 0.855756i | \(0.673093\pi\) | |||||||
\(360\) | −9.77077e44 | −1.79736 | ||||||||
\(361\) | −5.55104e44 | −0.972743 | ||||||||
\(362\) | 3.96204e44 | 0.661483 | ||||||||
\(363\) | −3.75165e43 | −0.0596838 | ||||||||
\(364\) | −4.39782e43 | −0.0666750 | ||||||||
\(365\) | 1.45163e45 | 2.09763 | ||||||||
\(366\) | 4.36866e43 | 0.0601768 | ||||||||
\(367\) | −3.00056e44 | −0.394045 | −0.197022 | − | 0.980399i | \(-0.563127\pi\) | ||||
−0.197022 | + | 0.980399i | \(0.563127\pi\) | |||||||
\(368\) | 3.09210e44 | 0.387183 | ||||||||
\(369\) | 6.02849e44 | 0.719858 | ||||||||
\(370\) | −1.36625e45 | −1.55597 | ||||||||
\(371\) | 1.24773e44 | 0.135543 | ||||||||
\(372\) | 8.37447e43 | 0.0867872 | ||||||||
\(373\) | 1.08201e45 | 1.06986 | 0.534932 | − | 0.844895i | \(-0.320337\pi\) | ||||
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(374\) | 3.72466e44 | 0.351426 | ||||||||
\(375\) | −1.14723e45 | −1.03301 | ||||||||
\(376\) | 1.34064e45 | 1.15219 | ||||||||
\(377\) | −1.59201e45 | −1.30609 | ||||||||
\(378\) | −1.40057e44 | −0.109698 | ||||||||
\(379\) | 1.21847e45 | 0.911229 | 0.455614 | − | 0.890177i | \(-0.349420\pi\) | ||||
0.455614 | + | 0.890177i | \(0.349420\pi\) | |||||||
\(380\) | 5.73965e43 | 0.0409895 | ||||||||
\(381\) | −1.45131e45 | −0.989858 | ||||||||
\(382\) | −1.34484e45 | −0.876119 | ||||||||
\(383\) | −9.53201e43 | −0.0593207 | −0.0296603 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296603 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(384\) | 1.52105e45 | 0.904373 | ||||||||
\(385\) | −4.38372e44 | −0.249046 | ||||||||
\(386\) | −2.28757e45 | −1.24193 | ||||||||
\(387\) | 6.88857e43 | 0.0357427 | ||||||||
\(388\) | 2.04016e44 | 0.101183 | ||||||||
\(389\) | 1.90493e45 | 0.903152 | 0.451576 | − | 0.892233i | \(-0.350862\pi\) | ||||
0.451576 | + | 0.892233i | \(0.350862\pi\) | |||||||
\(390\) | 5.79581e45 | 2.62714 | ||||||||
\(391\) | −4.60678e44 | −0.199666 | ||||||||
\(392\) | −2.48585e45 | −1.03031 | ||||||||
\(393\) | −8.32373e44 | −0.329950 | ||||||||
\(394\) | 1.90766e45 | 0.723296 | ||||||||
\(395\) | −4.80960e45 | −1.74446 | ||||||||
\(396\) | 8.44376e44 | 0.293002 | ||||||||
\(397\) | 3.96399e45 | 1.31613 | 0.658065 | − | 0.752961i | \(-0.271375\pi\) | ||||
0.658065 | + | 0.752961i | \(0.271375\pi\) | |||||||
\(398\) | 7.87060e44 | 0.250066 | ||||||||
\(399\) | 1.70748e44 | 0.0519196 | ||||||||
\(400\) | −1.14568e45 | −0.333438 | ||||||||
\(401\) | −5.53039e44 | −0.154074 | −0.0770369 | − | 0.997028i | \(-0.524546\pi\) | ||||
−0.0770369 | + | 0.997028i | \(0.524546\pi\) | |||||||
\(402\) | −9.38381e45 | −2.50278 | ||||||||
\(403\) | −1.68812e45 | −0.431088 | ||||||||
\(404\) | −8.03562e44 | −0.196492 | ||||||||
\(405\) | 2.33511e45 | 0.546820 | ||||||||
\(406\) | 6.64646e44 | 0.149068 | ||||||||
\(407\) | 6.89560e45 | 1.48139 | ||||||||
\(408\) | −3.12660e45 | −0.643457 | ||||||||
\(409\) | 3.35495e45 | 0.661498 | 0.330749 | − | 0.943719i | \(-0.392699\pi\) | ||||
0.330749 | + | 0.943719i | \(0.392699\pi\) | |||||||
\(410\) | 2.93089e45 | 0.553710 | ||||||||
\(411\) | 7.42738e45 | 1.34463 | ||||||||
\(412\) | −1.80048e45 | −0.312383 | ||||||||
\(413\) | −4.90568e44 | −0.0815781 | ||||||||
\(414\) | 4.01061e45 | 0.639299 | ||||||||
\(415\) | −1.06396e46 | −1.62586 | ||||||||
\(416\) | 4.39862e45 | 0.644441 | ||||||||
\(417\) | −9.10474e45 | −1.27905 | ||||||||
\(418\) | 1.11247e45 | 0.149867 | ||||||||
\(419\) | −7.69138e45 | −0.993708 | −0.496854 | − | 0.867834i | \(-0.665512\pi\) | ||||
−0.496854 | + | 0.867834i | \(0.665512\pi\) | |||||||
\(420\) | 6.30078e44 | 0.0780785 | ||||||||
\(421\) | −2.77229e45 | −0.329535 | −0.164767 | − | 0.986332i | \(-0.552687\pi\) | ||||
−0.164767 | + | 0.986332i | \(0.552687\pi\) | |||||||
\(422\) | 3.09338e45 | 0.352749 | ||||||||
\(423\) | 1.36361e46 | 1.49188 | ||||||||
\(424\) | −6.82401e45 | −0.716370 | ||||||||
\(425\) | 1.70691e45 | 0.171950 | ||||||||
\(426\) | 4.37449e45 | 0.422921 | ||||||||
\(427\) | −9.57360e43 | −0.00888357 | ||||||||
\(428\) | 2.58349e45 | 0.230113 | ||||||||
\(429\) | −2.92520e46 | −2.50122 | ||||||||
\(430\) | 3.34904e44 | 0.0274930 | ||||||||
\(431\) | 6.18484e45 | 0.487502 | 0.243751 | − | 0.969838i | \(-0.421622\pi\) | ||||
0.243751 | + | 0.969838i | \(0.421622\pi\) | |||||||
\(432\) | 6.00681e45 | 0.454651 | ||||||||
\(433\) | 2.21783e46 | 1.61209 | 0.806047 | − | 0.591852i | \(-0.201603\pi\) | ||||
0.806047 | + | 0.591852i | \(0.201603\pi\) | |||||||
\(434\) | 7.04770e44 | 0.0492014 | ||||||||
\(435\) | 2.28089e46 | 1.52947 | ||||||||
\(436\) | 3.30353e44 | 0.0212796 | ||||||||
\(437\) | −1.37594e45 | −0.0851482 | ||||||||
\(438\) | −4.04399e46 | −2.40444 | ||||||||
\(439\) | 1.91766e45 | 0.109557 | 0.0547787 | − | 0.998499i | \(-0.482555\pi\) | ||||
0.0547787 | + | 0.998499i | \(0.482555\pi\) | |||||||
\(440\) | 2.39752e46 | 1.31625 | ||||||||
\(441\) | −2.52844e46 | −1.33407 | ||||||||
\(442\) | 1.07916e46 | 0.547263 | ||||||||
\(443\) | −3.00864e46 | −1.46658 | −0.733290 | − | 0.679916i | \(-0.762016\pi\) | ||||
−0.733290 | + | 0.679916i | \(0.762016\pi\) | |||||||
\(444\) | −9.91114e45 | −0.464431 | ||||||||
\(445\) | −2.96405e46 | −1.33532 | ||||||||
\(446\) | 1.17574e46 | 0.509275 | ||||||||
\(447\) | 6.03235e46 | 2.51249 | ||||||||
\(448\) | −5.64783e45 | −0.226212 | ||||||||
\(449\) | 5.68788e45 | 0.219099 | 0.109549 | − | 0.993981i | \(-0.465059\pi\) | ||||
0.109549 | + | 0.993981i | \(0.465059\pi\) | |||||||
\(450\) | −1.48601e46 | −0.550558 | ||||||||
\(451\) | −1.47925e46 | −0.527171 | ||||||||
\(452\) | 1.54997e45 | 0.0531376 | ||||||||
\(453\) | 4.87555e46 | 1.60807 | ||||||||
\(454\) | 1.71721e46 | 0.544937 | ||||||||
\(455\) | −1.27011e46 | −0.387830 | ||||||||
\(456\) | −9.33846e45 | −0.274404 | ||||||||
\(457\) | 4.67626e46 | 1.32241 | 0.661204 | − | 0.750206i | \(-0.270046\pi\) | ||||
0.661204 | + | 0.750206i | \(0.270046\pi\) | |||||||
\(458\) | −3.01918e46 | −0.821755 | ||||||||
\(459\) | −8.94930e45 | −0.234459 | ||||||||
\(460\) | −5.07736e45 | −0.128049 | ||||||||
\(461\) | −3.72978e46 | −0.905560 | −0.452780 | − | 0.891622i | \(-0.649568\pi\) | ||||
−0.452780 | + | 0.891622i | \(0.649568\pi\) | |||||||
\(462\) | 1.22123e46 | 0.285472 | ||||||||
\(463\) | −3.67649e46 | −0.827497 | −0.413748 | − | 0.910391i | \(-0.635781\pi\) | ||||
−0.413748 | + | 0.910391i | \(0.635781\pi\) | |||||||
\(464\) | −2.85056e46 | −0.617825 | ||||||||
\(465\) | 2.41858e46 | 0.504817 | ||||||||
\(466\) | −2.60620e46 | −0.523907 | ||||||||
\(467\) | −2.37743e46 | −0.460323 | −0.230161 | − | 0.973152i | \(-0.573925\pi\) | ||||
−0.230161 | + | 0.973152i | \(0.573925\pi\) | |||||||
\(468\) | 2.44644e46 | 0.456280 | ||||||||
\(469\) | 2.05639e46 | 0.369472 | ||||||||
\(470\) | 6.62951e46 | 1.14754 | ||||||||
\(471\) | −5.18607e46 | −0.864914 | ||||||||
\(472\) | 2.68298e46 | 0.431155 | ||||||||
\(473\) | −1.69029e45 | −0.0261753 | ||||||||
\(474\) | 1.33988e47 | 1.99960 | ||||||||
\(475\) | 5.09814e45 | 0.0733287 | ||||||||
\(476\) | 1.17318e45 | 0.0162646 | ||||||||
\(477\) | −6.94094e46 | −0.927569 | ||||||||
\(478\) | −8.27170e46 | −1.06563 | ||||||||
\(479\) | −8.80315e46 | −1.09337 | −0.546684 | − | 0.837339i | \(-0.684110\pi\) | ||||
−0.546684 | + | 0.837339i | \(0.684110\pi\) | |||||||
\(480\) | −6.30193e46 | −0.754661 | ||||||||
\(481\) | 1.99788e47 | 2.30691 | ||||||||
\(482\) | 5.50084e46 | 0.612500 | ||||||||
\(483\) | −1.51046e46 | −0.162194 | ||||||||
\(484\) | −7.69900e44 | −0.00797334 | ||||||||
\(485\) | 5.89206e46 | 0.588555 | ||||||||
\(486\) | −1.21039e47 | −1.16625 | ||||||||
\(487\) | 7.13443e46 | 0.663136 | 0.331568 | − | 0.943431i | \(-0.392422\pi\) | ||||
0.331568 | + | 0.943431i | \(0.392422\pi\) | |||||||
\(488\) | 5.23593e45 | 0.0469512 | ||||||||
\(489\) | −2.97758e47 | −2.57607 | ||||||||
\(490\) | −1.22926e47 | −1.02615 | ||||||||
\(491\) | 8.49115e46 | 0.683975 | 0.341988 | − | 0.939704i | \(-0.388900\pi\) | ||||
0.341988 | + | 0.939704i | \(0.388900\pi\) | |||||||
\(492\) | 2.12614e46 | 0.165273 | ||||||||
\(493\) | 4.24693e46 | 0.318606 | ||||||||
\(494\) | 3.22321e46 | 0.233382 | ||||||||
\(495\) | 2.43859e47 | 1.70431 | ||||||||
\(496\) | −3.02265e46 | −0.203919 | ||||||||
\(497\) | −9.58638e45 | −0.0624335 | ||||||||
\(498\) | 2.96402e47 | 1.86367 | ||||||||
\(499\) | −1.75876e47 | −1.06770 | −0.533848 | − | 0.845581i | \(-0.679255\pi\) | ||||
−0.533848 | + | 0.845581i | \(0.679255\pi\) | |||||||
\(500\) | −2.35430e46 | −0.138003 | ||||||||
\(501\) | 3.19397e47 | 1.80789 | ||||||||
\(502\) | −2.52221e47 | −1.37869 | ||||||||
\(503\) | 1.24051e47 | 0.654880 | 0.327440 | − | 0.944872i | \(-0.393814\pi\) | ||||
0.327440 | + | 0.944872i | \(0.393814\pi\) | |||||||
\(504\) | −5.96502e46 | −0.304143 | ||||||||
\(505\) | −2.32072e47 | −1.14294 | ||||||||
\(506\) | −9.84108e46 | −0.468175 | ||||||||
\(507\) | −5.11027e47 | −2.34858 | ||||||||
\(508\) | −2.97832e46 | −0.132238 | ||||||||
\(509\) | 3.71512e47 | 1.59372 | 0.796859 | − | 0.604166i | \(-0.206493\pi\) | ||||
0.796859 | + | 0.604166i | \(0.206493\pi\) | |||||||
\(510\) | −1.54612e47 | −0.640861 | ||||||||
\(511\) | 8.86212e46 | 0.354954 | ||||||||
\(512\) | 2.87213e47 | 1.11168 | ||||||||
\(513\) | −2.67296e46 | −0.0999857 | ||||||||
\(514\) | 4.49893e47 | 1.62650 | ||||||||
\(515\) | −5.19987e47 | −1.81705 | ||||||||
\(516\) | 2.42948e45 | 0.00820623 | ||||||||
\(517\) | −3.34597e47 | −1.09254 | ||||||||
\(518\) | −8.34092e46 | −0.263295 | ||||||||
\(519\) | 4.60621e47 | 1.40577 | ||||||||
\(520\) | 6.94640e47 | 2.04975 | ||||||||
\(521\) | 7.89659e45 | 0.0225309 | 0.0112655 | − | 0.999937i | \(-0.496414\pi\) | ||||
0.0112655 | + | 0.999937i | \(0.496414\pi\) | |||||||
\(522\) | −3.69732e47 | −1.02012 | ||||||||
\(523\) | 1.18122e47 | 0.315175 | 0.157588 | − | 0.987505i | \(-0.449628\pi\) | ||||
0.157588 | + | 0.987505i | \(0.449628\pi\) | |||||||
\(524\) | −1.70816e46 | −0.0440790 | ||||||||
\(525\) | 5.59656e46 | 0.139680 | ||||||||
\(526\) | −6.96851e45 | −0.0168225 | ||||||||
\(527\) | 4.50331e46 | 0.105159 | ||||||||
\(528\) | −5.23767e47 | −1.18316 | ||||||||
\(529\) | −3.35870e47 | −0.734001 | ||||||||
\(530\) | −3.37450e47 | −0.713480 | ||||||||
\(531\) | 2.72895e47 | 0.558267 | ||||||||
\(532\) | 3.50403e45 | 0.00693609 | ||||||||
\(533\) | −4.28587e47 | −0.820943 | ||||||||
\(534\) | 8.25738e47 | 1.53063 | ||||||||
\(535\) | 7.46124e47 | 1.33850 | ||||||||
\(536\) | −1.12467e48 | −1.95272 | ||||||||
\(537\) | −2.16958e47 | −0.364607 | ||||||||
\(538\) | 2.15663e47 | 0.350821 | ||||||||
\(539\) | 6.20419e47 | 0.976971 | ||||||||
\(540\) | −9.86346e46 | −0.150362 | ||||||||
\(541\) | −6.62658e47 | −0.977997 | −0.488998 | − | 0.872285i | \(-0.662638\pi\) | ||||
−0.488998 | + | 0.872285i | \(0.662638\pi\) | |||||||
\(542\) | 6.80114e46 | 0.0971839 | ||||||||
\(543\) | 8.30070e47 | 1.14846 | ||||||||
\(544\) | −1.17340e47 | −0.157204 | ||||||||
\(545\) | 9.54073e46 | 0.123778 | ||||||||
\(546\) | 3.53832e47 | 0.444555 | ||||||||
\(547\) | −1.12424e47 | −0.136798 | −0.0683990 | − | 0.997658i | \(-0.521789\pi\) | ||||
−0.0683990 | + | 0.997658i | \(0.521789\pi\) | |||||||
\(548\) | 1.52422e47 | 0.179633 | ||||||||
\(549\) | 5.32564e46 | 0.0607933 | ||||||||
\(550\) | 3.64631e47 | 0.403188 | ||||||||
\(551\) | 1.26846e47 | 0.135870 | ||||||||
\(552\) | 8.26092e47 | 0.857224 | ||||||||
\(553\) | −2.93624e47 | −0.295190 | ||||||||
\(554\) | −1.21889e48 | −1.18725 | ||||||||
\(555\) | −2.86238e48 | −2.70147 | ||||||||
\(556\) | −1.86844e47 | −0.170872 | ||||||||
\(557\) | 6.68090e47 | 0.592064 | 0.296032 | − | 0.955178i | \(-0.404336\pi\) | ||||
0.296032 | + | 0.955178i | \(0.404336\pi\) | |||||||
\(558\) | −3.92053e47 | −0.336702 | ||||||||
\(559\) | −4.89734e46 | −0.0407618 | ||||||||
\(560\) | −2.27418e47 | −0.183457 | ||||||||
\(561\) | 7.80339e47 | 0.610145 | ||||||||
\(562\) | −6.74014e47 | −0.510838 | ||||||||
\(563\) | 2.47733e48 | 1.82007 | 0.910033 | − | 0.414536i | \(-0.136056\pi\) | ||||
0.910033 | + | 0.414536i | \(0.136056\pi\) | |||||||
\(564\) | 4.80921e47 | 0.342523 | ||||||||
\(565\) | 4.47639e47 | 0.309087 | ||||||||
\(566\) | 1.75846e48 | 1.17718 | ||||||||
\(567\) | 1.42558e47 | 0.0925309 | ||||||||
\(568\) | 5.24292e47 | 0.329972 | ||||||||
\(569\) | 8.59661e47 | 0.524641 | 0.262321 | − | 0.964981i | \(-0.415512\pi\) | ||||
0.262321 | + | 0.964981i | \(0.415512\pi\) | |||||||
\(570\) | −4.61790e47 | −0.273297 | ||||||||
\(571\) | −3.39185e48 | −1.94673 | −0.973364 | − | 0.229266i | \(-0.926367\pi\) | ||||
−0.973364 | + | 0.229266i | \(0.926367\pi\) | |||||||
\(572\) | −6.00298e47 | −0.334146 | ||||||||
\(573\) | −2.81753e48 | −1.52112 | ||||||||
\(574\) | 1.78930e47 | 0.0936968 | ||||||||
\(575\) | −4.50988e47 | −0.229075 | ||||||||
\(576\) | 3.14180e48 | 1.54805 | ||||||||
\(577\) | 2.12534e48 | 1.01590 | 0.507951 | − | 0.861386i | \(-0.330403\pi\) | ||||
0.507951 | + | 0.861386i | \(0.330403\pi\) | |||||||
\(578\) | 1.63292e48 | 0.757232 | ||||||||
\(579\) | −4.79258e48 | −2.15623 | ||||||||
\(580\) | 4.68075e47 | 0.204327 | ||||||||
\(581\) | −6.49544e47 | −0.275123 | ||||||||
\(582\) | −1.64143e48 | −0.674639 | ||||||||
\(583\) | 1.70314e48 | 0.679283 | ||||||||
\(584\) | −4.84681e48 | −1.87599 | ||||||||
\(585\) | 7.06542e48 | 2.65406 | ||||||||
\(586\) | −3.14491e48 | −1.14657 | ||||||||
\(587\) | 1.06269e48 | 0.376044 | 0.188022 | − | 0.982165i | \(-0.439792\pi\) | ||||
0.188022 | + | 0.982165i | \(0.439792\pi\) | |||||||
\(588\) | −8.91737e47 | −0.306290 | ||||||||
\(589\) | 1.34504e47 | 0.0448453 | ||||||||
\(590\) | 1.32675e48 | 0.429415 | ||||||||
\(591\) | 3.99665e48 | 1.25578 | ||||||||
\(592\) | 3.57728e48 | 1.09125 | ||||||||
\(593\) | −3.98260e48 | −1.17953 | −0.589766 | − | 0.807574i | \(-0.700780\pi\) | ||||
−0.589766 | + | 0.807574i | \(0.700780\pi\) | |||||||
\(594\) | −1.91176e48 | −0.549758 | ||||||||
\(595\) | 3.38820e47 | 0.0946068 | ||||||||
\(596\) | 1.23794e48 | 0.335651 | ||||||||
\(597\) | 1.64894e48 | 0.434163 | ||||||||
\(598\) | −2.85129e48 | −0.729072 | ||||||||
\(599\) | 5.14535e48 | 1.27775 | 0.638874 | − | 0.769311i | \(-0.279401\pi\) | ||||
0.638874 | + | 0.769311i | \(0.279401\pi\) | |||||||
\(600\) | −3.06083e48 | −0.738232 | ||||||||
\(601\) | −1.83878e48 | −0.430751 | −0.215375 | − | 0.976531i | \(-0.569098\pi\) | ||||
−0.215375 | + | 0.976531i | \(0.569098\pi\) | |||||||
\(602\) | 2.04458e46 | 0.00465227 | ||||||||
\(603\) | −1.14394e49 | −2.52842 | ||||||||
\(604\) | 1.00054e48 | 0.214827 | ||||||||
\(605\) | −2.22350e47 | −0.0463787 | ||||||||
\(606\) | 6.46516e48 | 1.31011 | ||||||||
\(607\) | 2.06846e48 | 0.407236 | 0.203618 | − | 0.979050i | \(-0.434730\pi\) | ||||
0.203618 | + | 0.979050i | \(0.434730\pi\) | |||||||
\(608\) | −3.50467e47 | −0.0670401 | ||||||||
\(609\) | 1.39247e48 | 0.258812 | ||||||||
\(610\) | 2.58919e47 | 0.0467618 | ||||||||
\(611\) | −9.69439e48 | −1.70137 | ||||||||
\(612\) | −6.52623e47 | −0.111304 | ||||||||
\(613\) | 1.02050e48 | 0.169143 | 0.0845717 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845717 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(614\) | 2.30743e48 | 0.371691 | ||||||||
\(615\) | 6.14039e48 | 0.961350 | ||||||||
\(616\) | 1.46367e48 | 0.222732 | ||||||||
\(617\) | −3.46313e48 | −0.512246 | −0.256123 | − | 0.966644i | \(-0.582445\pi\) | ||||
−0.256123 | + | 0.966644i | \(0.582445\pi\) | |||||||
\(618\) | 1.44860e49 | 2.08281 | ||||||||
\(619\) | 6.56428e48 | 0.917488 | 0.458744 | − | 0.888568i | \(-0.348299\pi\) | ||||
0.458744 | + | 0.888568i | \(0.348299\pi\) | |||||||
\(620\) | 4.96332e47 | 0.0674400 | ||||||||
\(621\) | 2.36453e48 | 0.312350 | ||||||||
\(622\) | −3.67165e48 | −0.471552 | ||||||||
\(623\) | −1.80954e48 | −0.225958 | ||||||||
\(624\) | −1.51753e49 | −1.84249 | ||||||||
\(625\) | −1.05615e49 | −1.24688 | ||||||||
\(626\) | −5.99629e48 | −0.688386 | ||||||||
\(627\) | 2.33070e48 | 0.260198 | ||||||||
\(628\) | −1.06427e48 | −0.115546 | ||||||||
\(629\) | −5.32965e48 | −0.562746 | ||||||||
\(630\) | −2.94972e48 | −0.302916 | ||||||||
\(631\) | 5.18692e48 | 0.518079 | 0.259039 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259039 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(632\) | 1.60587e49 | 1.56013 | ||||||||
\(633\) | 6.48082e48 | 0.612442 | ||||||||
\(634\) | −8.74063e48 | −0.803490 | ||||||||
\(635\) | −8.60152e48 | −0.769192 | ||||||||
\(636\) | −2.44795e48 | −0.212962 | ||||||||
\(637\) | 1.79756e49 | 1.52140 | ||||||||
\(638\) | 9.07235e48 | 0.747064 | ||||||||
\(639\) | 5.33275e48 | 0.427254 | ||||||||
\(640\) | 9.01487e48 | 0.702765 | ||||||||
\(641\) | −6.15569e48 | −0.466940 | −0.233470 | − | 0.972364i | \(-0.575008\pi\) | ||||
−0.233470 | + | 0.972364i | \(0.575008\pi\) | |||||||
\(642\) | −2.07858e49 | −1.53428 | ||||||||
\(643\) | −6.50853e48 | −0.467510 | −0.233755 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233755 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(644\) | −3.09971e47 | −0.0216680 | ||||||||
\(645\) | 7.01644e47 | 0.0477333 | ||||||||
\(646\) | −8.59837e47 | −0.0569308 | ||||||||
\(647\) | 2.43533e49 | 1.56940 | 0.784698 | − | 0.619878i | \(-0.212818\pi\) | ||||
0.784698 | + | 0.619878i | \(0.212818\pi\) | |||||||
\(648\) | −7.79667e48 | −0.489042 | ||||||||
\(649\) | −6.69620e48 | −0.408833 | ||||||||
\(650\) | 1.05646e49 | 0.627869 | ||||||||
\(651\) | 1.47654e48 | 0.0854233 | ||||||||
\(652\) | −6.11047e48 | −0.344145 | ||||||||
\(653\) | 4.33343e48 | 0.237602 | 0.118801 | − | 0.992918i | \(-0.462095\pi\) | ||||
0.118801 | + | 0.992918i | \(0.462095\pi\) | |||||||
\(654\) | −2.65789e48 | −0.141882 | ||||||||
\(655\) | −4.93325e48 | −0.256396 | ||||||||
\(656\) | −7.67401e48 | −0.388334 | ||||||||
\(657\) | −4.92986e49 | −2.42907 | ||||||||
\(658\) | 4.04729e48 | 0.194183 | ||||||||
\(659\) | 2.26798e49 | 1.05960 | 0.529802 | − | 0.848121i | \(-0.322266\pi\) | ||||
0.529802 | + | 0.848121i | \(0.322266\pi\) | |||||||
\(660\) | 8.60050e48 | 0.391295 | ||||||||
\(661\) | −2.84364e49 | −1.25994 | −0.629969 | − | 0.776620i | \(-0.716932\pi\) | ||||
−0.629969 | + | 0.776620i | \(0.716932\pi\) | |||||||
\(662\) | −1.03284e49 | −0.445676 | ||||||||
\(663\) | 2.26090e49 | 0.950156 | ||||||||
\(664\) | 3.55245e49 | 1.45407 | ||||||||
\(665\) | 1.01198e48 | 0.0403453 | ||||||||
\(666\) | 4.63992e49 | 1.80182 | ||||||||
\(667\) | −1.12210e49 | −0.424452 | ||||||||
\(668\) | 6.55455e48 | 0.241521 | ||||||||
\(669\) | 2.46325e49 | 0.884202 | ||||||||
\(670\) | −5.56153e49 | −1.94485 | ||||||||
\(671\) | −1.30679e48 | −0.0445205 | ||||||||
\(672\) | −3.84730e48 | −0.127701 | ||||||||
\(673\) | 1.14434e49 | 0.370077 | 0.185039 | − | 0.982731i | \(-0.440759\pi\) | ||||
0.185039 | + | 0.982731i | \(0.440759\pi\) | |||||||
\(674\) | 1.72019e49 | 0.542035 | ||||||||
\(675\) | −8.76105e48 | −0.268993 | ||||||||
\(676\) | −1.04871e49 | −0.313753 | ||||||||
\(677\) | −3.00594e49 | −0.876351 | −0.438175 | − | 0.898890i | \(-0.644375\pi\) | ||||
−0.438175 | + | 0.898890i | \(0.644375\pi\) | |||||||
\(678\) | −1.24705e49 | −0.354295 | ||||||||
\(679\) | 3.59708e48 | 0.0995931 | ||||||||
\(680\) | −1.85305e49 | −0.500014 | ||||||||
\(681\) | 3.59766e49 | 0.946119 | ||||||||
\(682\) | 9.62004e48 | 0.246576 | ||||||||
\(683\) | −7.78736e49 | −1.94549 | −0.972743 | − | 0.231885i | \(-0.925511\pi\) | ||||
−0.972743 | + | 0.231885i | \(0.925511\pi\) | |||||||
\(684\) | −1.94924e48 | −0.0474661 | ||||||||
\(685\) | 4.40201e49 | 1.04488 | ||||||||
\(686\) | −1.53329e49 | −0.354774 | ||||||||
\(687\) | −6.32535e49 | −1.42673 | ||||||||
\(688\) | −8.76886e47 | −0.0192817 | ||||||||
\(689\) | 4.93456e49 | 1.05782 | ||||||||
\(690\) | 4.08505e49 | 0.853766 | ||||||||
\(691\) | 9.61614e49 | 1.95945 | 0.979726 | − | 0.200340i | \(-0.0642046\pi\) | ||||
0.979726 | + | 0.200340i | \(0.0642046\pi\) | |||||||
\(692\) | 9.45269e48 | 0.187801 | ||||||||
\(693\) | 1.48875e49 | 0.288397 | ||||||||
\(694\) | 5.07971e49 | 0.959506 | ||||||||
\(695\) | −5.39613e49 | −0.993913 | ||||||||
\(696\) | −7.61562e49 | −1.36787 | ||||||||
\(697\) | 1.14332e49 | 0.200260 | ||||||||
\(698\) | 4.33853e49 | 0.741093 | ||||||||
\(699\) | −5.46014e49 | −0.909606 | ||||||||
\(700\) | 1.14850e48 | 0.0186602 | ||||||||
\(701\) | 1.19741e49 | 0.189748 | 0.0948742 | − | 0.995489i | \(-0.469755\pi\) | ||||
0.0948742 | + | 0.995489i | \(0.469755\pi\) | |||||||
\(702\) | −5.53901e49 | −0.856116 | ||||||||
\(703\) | −1.59185e49 | −0.239984 | ||||||||
\(704\) | −7.70923e49 | −1.13368 | ||||||||
\(705\) | 1.38892e50 | 1.99236 | ||||||||
\(706\) | −1.16678e50 | −1.63270 | ||||||||
\(707\) | −1.41679e49 | −0.193404 | ||||||||
\(708\) | 9.62454e48 | 0.128173 | ||||||||
\(709\) | −4.80032e49 | −0.623680 | −0.311840 | − | 0.950135i | \(-0.600945\pi\) | ||||
−0.311840 | + | 0.950135i | \(0.600945\pi\) | |||||||
\(710\) | 2.59264e49 | 0.328641 | ||||||||
\(711\) | 1.63339e50 | 2.02009 | ||||||||
\(712\) | 9.89664e49 | 1.19423 | ||||||||
\(713\) | −1.18984e49 | −0.140094 | ||||||||
\(714\) | −9.43898e48 | −0.108444 | ||||||||
\(715\) | −1.73369e50 | −1.94363 | ||||||||
\(716\) | −4.45232e48 | −0.0487089 | ||||||||
\(717\) | −1.73297e50 | −1.85015 | ||||||||
\(718\) | 8.84635e49 | 0.921693 | ||||||||
\(719\) | −1.45387e49 | −0.147832 | −0.0739162 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739162 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(720\) | 1.26509e50 | 1.25546 | ||||||||
\(721\) | −3.17450e49 | −0.307474 | ||||||||
\(722\) | 9.16528e49 | 0.866452 | ||||||||
\(723\) | 1.15246e50 | 1.06342 | ||||||||
\(724\) | 1.70344e49 | 0.153427 | ||||||||
\(725\) | 4.15759e49 | 0.365533 | ||||||||
\(726\) | 6.19432e48 | 0.0531622 | ||||||||
\(727\) | 1.25503e50 | 1.05148 | 0.525742 | − | 0.850644i | \(-0.323788\pi\) | ||||
0.525742 | + | 0.850644i | \(0.323788\pi\) | |||||||
\(728\) | 4.24075e49 | 0.346851 | ||||||||
\(729\) | −1.96598e50 | −1.56981 | ||||||||
\(730\) | −2.39677e50 | −1.86843 | ||||||||
\(731\) | 1.30644e48 | 0.00994338 | ||||||||
\(732\) | 1.87826e48 | 0.0139576 | ||||||||
\(733\) | −1.40440e50 | −1.01899 | −0.509495 | − | 0.860473i | \(-0.670168\pi\) | ||||
−0.509495 | + | 0.860473i | \(0.670168\pi\) | |||||||
\(734\) | 4.95419e49 | 0.350988 | ||||||||
\(735\) | −2.57537e50 | −1.78161 | ||||||||
\(736\) | 3.10027e49 | 0.209430 | ||||||||
\(737\) | 2.80695e50 | 1.85163 | ||||||||
\(738\) | −9.95358e49 | −0.641199 | ||||||||
\(739\) | 2.93572e49 | 0.184687 | 0.0923435 | − | 0.995727i | \(-0.470564\pi\) | ||||
0.0923435 | + | 0.995727i | \(0.470564\pi\) | |||||||
\(740\) | −5.87406e49 | −0.360897 | ||||||||
\(741\) | 6.75281e49 | 0.405197 | ||||||||
\(742\) | −2.06012e49 | −0.120732 | ||||||||
\(743\) | 1.10795e50 | 0.634185 | 0.317093 | − | 0.948395i | \(-0.397293\pi\) | ||||
0.317093 | + | 0.948395i | \(0.397293\pi\) | |||||||
\(744\) | −8.07537e49 | −0.451478 | ||||||||
\(745\) | 3.57521e50 | 1.95239 | ||||||||
\(746\) | −1.78650e50 | −0.952960 | ||||||||
\(747\) | 3.61331e50 | 1.88276 | ||||||||
\(748\) | 1.60138e49 | 0.0815111 | ||||||||
\(749\) | 4.55506e49 | 0.226497 | ||||||||
\(750\) | 1.89418e50 | 0.920132 | ||||||||
\(751\) | −4.13601e50 | −1.96283 | −0.981416 | − | 0.191892i | \(-0.938538\pi\) | ||||
−0.981416 | + | 0.191892i | \(0.938538\pi\) | |||||||
\(752\) | −1.73582e50 | −0.804806 | ||||||||
\(753\) | −5.28418e50 | −2.39368 | ||||||||
\(754\) | 2.62856e50 | 1.16337 | ||||||||
\(755\) | 2.88961e50 | 1.24959 | ||||||||
\(756\) | −6.02161e48 | −0.0254437 | ||||||||
\(757\) | 3.15399e50 | 1.30221 | 0.651106 | − | 0.758987i | \(-0.274305\pi\) | ||||
0.651106 | + | 0.758987i | \(0.274305\pi\) | |||||||
\(758\) | −2.01180e50 | −0.811659 | ||||||||
\(759\) | −2.06176e50 | −0.812845 | ||||||||
\(760\) | −5.53465e49 | −0.213232 | ||||||||
\(761\) | −3.65841e50 | −1.37740 | −0.688702 | − | 0.725045i | \(-0.741819\pi\) | ||||
−0.688702 | + | 0.725045i | \(0.741819\pi\) | |||||||
\(762\) | 2.39624e50 | 0.881696 | ||||||||
\(763\) | 5.82458e48 | 0.0209452 | ||||||||
\(764\) | −5.78202e49 | −0.203210 | ||||||||
\(765\) | −1.88480e50 | −0.647427 | ||||||||
\(766\) | 1.57382e49 | 0.0528387 | ||||||||
\(767\) | −1.94011e50 | −0.636661 | ||||||||
\(768\) | 2.85192e50 | 0.914778 | ||||||||
\(769\) | −2.07264e50 | −0.649849 | −0.324925 | − | 0.945740i | \(-0.605339\pi\) | ||||
−0.324925 | + | 0.945740i | \(0.605339\pi\) | |||||||
\(770\) | 7.23792e49 | 0.221833 | ||||||||
\(771\) | 9.42552e50 | 2.82393 | ||||||||
\(772\) | −9.83516e49 | −0.288057 | ||||||||
\(773\) | 2.04692e50 | 0.586084 | 0.293042 | − | 0.956100i | \(-0.405332\pi\) | ||||
0.293042 | + | 0.956100i | \(0.405332\pi\) | |||||||
\(774\) | −1.13737e49 | −0.0318371 | ||||||||
\(775\) | 4.40859e49 | 0.120648 | ||||||||
\(776\) | −1.96729e50 | −0.526367 | ||||||||
\(777\) | −1.74747e50 | −0.457133 | ||||||||
\(778\) | −3.14521e50 | −0.804465 | ||||||||
\(779\) | 3.41484e49 | 0.0854013 | ||||||||
\(780\) | 2.49185e50 | 0.609349 | ||||||||
\(781\) | −1.30853e50 | −0.312889 | ||||||||
\(782\) | 7.60622e49 | 0.177849 | ||||||||
\(783\) | −2.17983e50 | −0.498415 | ||||||||
\(784\) | 3.21860e50 | 0.719673 | ||||||||
\(785\) | −3.07365e50 | −0.672101 | ||||||||
\(786\) | 1.37432e50 | 0.293897 | ||||||||
\(787\) | −2.74398e50 | −0.573882 | −0.286941 | − | 0.957948i | \(-0.592638\pi\) | ||||
−0.286941 | + | 0.957948i | \(0.592638\pi\) | |||||||
\(788\) | 8.20177e49 | 0.167764 | ||||||||
\(789\) | −1.45994e49 | −0.0292071 | ||||||||
\(790\) | 7.94109e50 | 1.55384 | ||||||||
\(791\) | 2.73282e49 | 0.0523025 | ||||||||
\(792\) | −8.14219e50 | −1.52423 | ||||||||
\(793\) | −3.78619e49 | −0.0693301 | ||||||||
\(794\) | −6.54491e50 | −1.17232 | ||||||||
\(795\) | −7.06978e50 | −1.23874 | ||||||||
\(796\) | 3.38388e49 | 0.0580012 | ||||||||
\(797\) | 3.73868e50 | 0.626899 | 0.313450 | − | 0.949605i | \(-0.398515\pi\) | ||||
0.313450 | + | 0.949605i | \(0.398515\pi\) | |||||||
\(798\) | −2.81921e49 | −0.0462463 | ||||||||
\(799\) | 2.58612e50 | 0.415030 | ||||||||
\(800\) | −1.14871e50 | −0.180359 | ||||||||
\(801\) | 1.00662e51 | 1.54631 | ||||||||
\(802\) | 9.13117e49 | 0.137238 | ||||||||
\(803\) | 1.20967e51 | 1.77887 | ||||||||
\(804\) | −4.03447e50 | −0.580505 | ||||||||
\(805\) | −8.95210e49 | −0.126037 | ||||||||
\(806\) | 2.78725e50 | 0.383983 | ||||||||
\(807\) | 4.51827e50 | 0.609095 | ||||||||
\(808\) | 7.74862e50 | 1.02218 | ||||||||
\(809\) | −3.87407e50 | −0.500114 | −0.250057 | − | 0.968231i | \(-0.580449\pi\) | ||||
−0.250057 | + | 0.968231i | \(0.580449\pi\) | |||||||
\(810\) | −3.85548e50 | −0.487069 | ||||||||
\(811\) | −9.21816e50 | −1.13967 | −0.569835 | − | 0.821759i | \(-0.692993\pi\) | ||||
−0.569835 | + | 0.821759i | \(0.692993\pi\) | |||||||
\(812\) | 2.85758e49 | 0.0345754 | ||||||||
\(813\) | 1.42488e50 | 0.168730 | ||||||||
\(814\) | −1.13853e51 | −1.31952 | ||||||||
\(815\) | −1.76473e51 | −2.00180 | ||||||||
\(816\) | 4.04823e50 | 0.449456 | ||||||||
\(817\) | 3.90203e48 | 0.00424038 | ||||||||
\(818\) | −5.53933e50 | −0.589216 | ||||||||
\(819\) | 4.31341e50 | 0.449110 | ||||||||
\(820\) | 1.26011e50 | 0.128430 | ||||||||
\(821\) | 1.64737e51 | 1.64357 | 0.821783 | − | 0.569801i | \(-0.192980\pi\) | ||||
0.821783 | + | 0.569801i | \(0.192980\pi\) | |||||||
\(822\) | −1.22633e51 | −1.19771 | ||||||||
\(823\) | −6.02163e50 | −0.575727 | −0.287864 | − | 0.957671i | \(-0.592945\pi\) | ||||
−0.287864 | + | 0.957671i | \(0.592945\pi\) | |||||||
\(824\) | 1.73618e51 | 1.62505 | ||||||||
\(825\) | 7.63924e50 | 0.700013 | ||||||||
\(826\) | 8.09973e49 | 0.0726641 | ||||||||
\(827\) | −4.30476e50 | −0.378097 | −0.189048 | − | 0.981968i | \(-0.560540\pi\) | ||||
−0.189048 | + | 0.981968i | \(0.560540\pi\) | |||||||
\(828\) | 1.72432e50 | 0.148282 | ||||||||
\(829\) | 8.88751e50 | 0.748300 | 0.374150 | − | 0.927368i | \(-0.377935\pi\) | ||||
0.374150 | + | 0.927368i | \(0.377935\pi\) | |||||||
\(830\) | 1.75670e51 | 1.44821 | ||||||||
\(831\) | −2.55364e51 | −2.06131 | ||||||||
\(832\) | −2.23362e51 | −1.76543 | ||||||||
\(833\) | −4.79525e50 | −0.371128 | ||||||||
\(834\) | 1.50328e51 | 1.13929 | ||||||||
\(835\) | 1.89298e51 | 1.40486 | ||||||||
\(836\) | 4.78297e49 | 0.0347606 | ||||||||
\(837\) | −2.31142e50 | −0.164507 | ||||||||
\(838\) | 1.26992e51 | 0.885126 | ||||||||
\(839\) | 3.76912e50 | 0.257280 | 0.128640 | − | 0.991691i | \(-0.458939\pi\) | ||||
0.128640 | + | 0.991691i | \(0.458939\pi\) | |||||||
\(840\) | −6.07574e50 | −0.406174 | ||||||||
\(841\) | −4.92875e50 | −0.322706 | ||||||||
\(842\) | 4.57730e50 | 0.293527 | ||||||||
\(843\) | −1.41210e51 | −0.886916 | ||||||||
\(844\) | 1.32997e50 | 0.0818179 | ||||||||
\(845\) | −3.02872e51 | −1.82502 | ||||||||
\(846\) | −2.25144e51 | −1.32886 | ||||||||
\(847\) | −1.35744e49 | −0.00784804 | ||||||||
\(848\) | 8.83551e50 | 0.500385 | ||||||||
\(849\) | 3.68407e51 | 2.04382 | ||||||||
\(850\) | −2.81826e50 | −0.153161 | ||||||||
\(851\) | 1.40817e51 | 0.749699 | ||||||||
\(852\) | 1.88077e50 | 0.0980940 | ||||||||
\(853\) | −3.00248e51 | −1.53417 | −0.767083 | − | 0.641547i | \(-0.778293\pi\) | ||||
−0.767083 | + | 0.641547i | \(0.778293\pi\) | |||||||
\(854\) | 1.58069e49 | 0.00791286 | ||||||||
\(855\) | −5.62949e50 | −0.276097 | ||||||||
\(856\) | −2.49122e51 | −1.19708 | ||||||||
\(857\) | −2.46088e50 | −0.115858 | −0.0579291 | − | 0.998321i | \(-0.518450\pi\) | ||||
−0.0579291 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(858\) | 4.82977e51 | 2.22792 | ||||||||
\(859\) | 2.64506e51 | 1.19551 | 0.597757 | − | 0.801677i | \(-0.296059\pi\) | ||||
0.597757 | + | 0.801677i | \(0.296059\pi\) | |||||||
\(860\) | 1.43989e49 | 0.00637684 | ||||||||
\(861\) | 3.74868e50 | 0.162676 | ||||||||
\(862\) | −1.02117e51 | −0.434233 | ||||||||
\(863\) | −9.93861e50 | −0.414130 | −0.207065 | − | 0.978327i | \(-0.566391\pi\) | ||||
−0.207065 | + | 0.978327i | \(0.566391\pi\) | |||||||
\(864\) | 6.02270e50 | 0.245924 | ||||||||
\(865\) | 2.72998e51 | 1.09239 | ||||||||
\(866\) | −3.66184e51 | −1.43594 | ||||||||
\(867\) | 3.42107e51 | 1.31470 | ||||||||
\(868\) | 3.03009e49 | 0.0114120 | ||||||||
\(869\) | −4.00794e51 | −1.47936 | ||||||||
\(870\) | −3.76595e51 | −1.36235 | ||||||||
\(871\) | 8.13268e51 | 2.88347 | ||||||||
\(872\) | −3.18554e50 | −0.110699 | ||||||||
\(873\) | −2.00100e51 | −0.681550 | ||||||||
\(874\) | 2.27181e50 | 0.0758441 | ||||||||
\(875\) | −4.15096e50 | −0.135834 | ||||||||
\(876\) | −1.73867e51 | −0.557695 | ||||||||
\(877\) | −2.79832e50 | −0.0879842 | −0.0439921 | − | 0.999032i | \(-0.514008\pi\) | ||||
−0.0439921 | + | 0.999032i | \(0.514008\pi\) | |||||||
\(878\) | −3.16623e50 | −0.0975861 | ||||||||
\(879\) | −6.58876e51 | −1.99067 | ||||||||
\(880\) | −3.10423e51 | −0.919404 | ||||||||
\(881\) | −5.95050e50 | −0.172773 | −0.0863863 | − | 0.996262i | \(-0.527532\pi\) | ||||
−0.0863863 | + | 0.996262i | \(0.527532\pi\) | |||||||
\(882\) | 4.17469e51 | 1.18829 | ||||||||
\(883\) | −3.85350e51 | −1.07533 | −0.537667 | − | 0.843157i | \(-0.680694\pi\) | ||||
−0.537667 | + | 0.843157i | \(0.680694\pi\) | |||||||
\(884\) | 4.63973e50 | 0.126934 | ||||||||
\(885\) | 2.77961e51 | 0.745550 | ||||||||
\(886\) | 4.96755e51 | 1.30633 | ||||||||
\(887\) | −4.56338e50 | −0.117658 | −0.0588292 | − | 0.998268i | \(-0.518737\pi\) | ||||
−0.0588292 | + | 0.998268i | \(0.518737\pi\) | |||||||
\(888\) | 9.55716e51 | 2.41603 | ||||||||
\(889\) | −5.25119e50 | −0.130160 | ||||||||
\(890\) | 4.89393e51 | 1.18941 | ||||||||
\(891\) | 1.94590e51 | 0.463724 | ||||||||
\(892\) | 5.05498e50 | 0.118123 | ||||||||
\(893\) | 7.72416e50 | 0.176991 | ||||||||
\(894\) | −9.95996e51 | −2.23795 | ||||||||
\(895\) | −1.28585e51 | −0.283326 | ||||||||
\(896\) | 5.50354e50 | 0.118919 | ||||||||
\(897\) | −5.97362e51 | −1.26581 | ||||||||
\(898\) | −9.39122e50 | −0.195158 | ||||||||
\(899\) | 1.09689e51 | 0.223548 | ||||||||
\(900\) | −6.38895e50 | −0.127698 | ||||||||
\(901\) | −1.31637e51 | −0.258044 | ||||||||
\(902\) | 2.44237e51 | 0.469567 | ||||||||
\(903\) | 4.28351e49 | 0.00807726 | ||||||||
\(904\) | −1.49462e51 | −0.276428 | ||||||||
\(905\) | 4.91960e51 | 0.892441 | ||||||||
\(906\) | −8.04998e51 | −1.43236 | ||||||||
\(907\) | −4.12286e51 | −0.719566 | −0.359783 | − | 0.933036i | \(-0.617149\pi\) | ||||
−0.359783 | + | 0.933036i | \(0.617149\pi\) | |||||||
\(908\) | 7.38298e50 | 0.126395 | ||||||||
\(909\) | 7.88139e51 | 1.32353 | ||||||||
\(910\) | 2.09707e51 | 0.345452 | ||||||||
\(911\) | 6.95561e51 | 1.12399 | 0.561996 | − | 0.827140i | \(-0.310034\pi\) | ||||
0.561996 | + | 0.827140i | \(0.310034\pi\) | |||||||
\(912\) | 1.20911e51 | 0.191672 | ||||||||
\(913\) | −8.86621e51 | −1.37879 | ||||||||
\(914\) | −7.72094e51 | −1.17791 | ||||||||
\(915\) | 5.42450e50 | 0.0811877 | ||||||||
\(916\) | −1.29806e51 | −0.190601 | ||||||||
\(917\) | −3.01173e50 | −0.0433863 | ||||||||
\(918\) | 1.47761e51 | 0.208840 | ||||||||
\(919\) | 1.23335e51 | 0.171027 | 0.0855136 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855136 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(920\) | 4.89602e51 | 0.666126 | ||||||||
\(921\) | 4.83420e51 | 0.645329 | ||||||||
\(922\) | 6.15821e51 | 0.806610 | ||||||||
\(923\) | −3.79125e51 | −0.487251 | ||||||||
\(924\) | 5.25057e50 | 0.0662136 | ||||||||
\(925\) | −5.21754e51 | −0.645632 | ||||||||
\(926\) | 6.07023e51 | 0.737076 | ||||||||
\(927\) | 1.76592e52 | 2.10415 | ||||||||
\(928\) | −2.85810e51 | −0.334185 | ||||||||
\(929\) | −9.97208e51 | −1.14422 | −0.572112 | − | 0.820176i | \(-0.693876\pi\) | ||||
−0.572112 | + | 0.820176i | \(0.693876\pi\) | |||||||
\(930\) | −3.99330e51 | −0.449656 | ||||||||
\(931\) | −1.43224e51 | −0.158269 | ||||||||
\(932\) | −1.12051e51 | −0.121517 | ||||||||
\(933\) | −7.69232e51 | −0.818707 | ||||||||
\(934\) | 3.92536e51 | 0.410024 | ||||||||
\(935\) | 4.62486e51 | 0.474128 | ||||||||
\(936\) | −2.35906e52 | −2.37363 | ||||||||
\(937\) | 6.01334e51 | 0.593844 | 0.296922 | − | 0.954902i | \(-0.404040\pi\) | ||||
0.296922 | + | 0.954902i | \(0.404040\pi\) | |||||||
\(938\) | −3.39529e51 | −0.329100 | ||||||||
\(939\) | −1.25626e52 | −1.19517 | ||||||||
\(940\) | 2.85029e51 | 0.266165 | ||||||||
\(941\) | 1.38035e52 | 1.26523 | 0.632617 | − | 0.774465i | \(-0.281981\pi\) | ||||
0.632617 | + | 0.774465i | \(0.281981\pi\) | |||||||
\(942\) | 8.56268e51 | 0.770405 | ||||||||
\(943\) | −3.02081e51 | −0.266789 | ||||||||
\(944\) | −3.47384e51 | −0.301162 | ||||||||
\(945\) | −1.73907e51 | −0.147999 | ||||||||
\(946\) | 2.79083e50 | 0.0233151 | ||||||||
\(947\) | −9.01648e51 | −0.739456 | −0.369728 | − | 0.929140i | \(-0.620549\pi\) | ||||
−0.369728 | + | 0.929140i | \(0.620549\pi\) | |||||||
\(948\) | 5.76067e51 | 0.463796 | ||||||||
\(949\) | 3.50482e52 | 2.77017 | ||||||||
\(950\) | −8.41750e50 | −0.0653161 | ||||||||
\(951\) | −1.83121e52 | −1.39502 | ||||||||
\(952\) | −1.13128e51 | −0.0846105 | ||||||||
\(953\) | 4.32450e51 | 0.317549 | 0.158774 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158774 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(954\) | 1.14601e52 | 0.826214 | ||||||||
\(955\) | −1.66987e52 | −1.18202 | ||||||||
\(956\) | −3.55633e51 | −0.247166 | ||||||||
\(957\) | 1.90071e52 | 1.29705 | ||||||||
\(958\) | 1.45348e52 | 0.973897 | ||||||||
\(959\) | 2.68741e51 | 0.176810 | ||||||||
\(960\) | 3.20012e52 | 2.06738 | ||||||||
\(961\) | −1.46006e52 | −0.926216 | ||||||||
\(962\) | −3.29869e52 | −2.05484 | ||||||||
\(963\) | −2.53391e52 | −1.55000 | ||||||||
\(964\) | 2.36503e51 | 0.142066 | ||||||||
\(965\) | −2.84044e52 | −1.67555 | ||||||||
\(966\) | 2.49391e51 | 0.144471 | ||||||||
\(967\) | −1.91085e51 | −0.108709 | −0.0543543 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543543 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(968\) | 7.42403e50 | 0.0414783 | ||||||||
\(969\) | −1.80141e51 | −0.0988431 | ||||||||
\(970\) | −9.72834e51 | −0.524244 | ||||||||
\(971\) | 2.54698e52 | 1.34800 | 0.674000 | − | 0.738732i | \(-0.264575\pi\) | ||||
0.674000 | + | 0.738732i | \(0.264575\pi\) | |||||||
\(972\) | −5.20394e51 | −0.270504 | ||||||||
\(973\) | −3.29432e51 | −0.168186 | ||||||||
\(974\) | −1.17796e52 | −0.590675 | ||||||||
\(975\) | 2.21334e52 | 1.09010 | ||||||||
\(976\) | −6.77932e50 | −0.0327955 | ||||||||
\(977\) | 2.34465e52 | 1.11410 | 0.557048 | − | 0.830480i | \(-0.311934\pi\) | ||||
0.557048 | + | 0.830480i | \(0.311934\pi\) | |||||||
\(978\) | 4.91625e52 | 2.29459 | ||||||||
\(979\) | −2.47001e52 | −1.13240 | ||||||||
\(980\) | −5.28508e51 | −0.238010 | ||||||||
\(981\) | −3.24012e51 | −0.143335 | ||||||||
\(982\) | −1.40197e52 | −0.609238 | ||||||||
\(983\) | 1.06892e52 | 0.456308 | 0.228154 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(984\) | −2.05021e52 | −0.859772 | ||||||||
\(985\) | 2.36871e52 | 0.975837 | ||||||||
\(986\) | −7.01207e51 | −0.283792 | ||||||||
\(987\) | 8.47931e51 | 0.337140 | ||||||||
\(988\) | 1.38579e51 | 0.0541314 | ||||||||
\(989\) | −3.45178e50 | −0.0132467 | ||||||||
\(990\) | −4.02634e52 | −1.51808 | ||||||||
\(991\) | 1.97227e52 | 0.730597 | 0.365298 | − | 0.930891i | \(-0.380967\pi\) | ||||
0.365298 | + | 0.930891i | \(0.380967\pi\) | |||||||
\(992\) | −3.03064e51 | −0.110301 | ||||||||
\(993\) | −2.16387e52 | −0.773782 | ||||||||
\(994\) | 1.58280e51 | 0.0556114 | ||||||||
\(995\) | 9.77280e51 | 0.337377 | ||||||||
\(996\) | 1.27435e52 | 0.432266 | ||||||||
\(997\) | −1.44359e52 | −0.481149 | −0.240575 | − | 0.970631i | \(-0.577336\pi\) | ||||
−0.240575 | + | 0.970631i | \(0.577336\pi\) | |||||||
\(998\) | 2.90388e52 | 0.951029 | ||||||||
\(999\) | 2.73555e52 | 0.880338 |
(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 | 1.36.a.a.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 9.36.a.b.1.3 | 3 | |||
4.3 | odd | 2 | 16.36.a.d.1.3 | 3 | |||
5.2 | odd | 4 | 25.36.b.a.24.2 | 6 | |||
5.3 | odd | 4 | 25.36.b.a.24.5 | 6 | |||
5.4 | even | 2 | 25.36.a.a.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.36.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.36.a.b.1.3 | 3 | 3.2 | odd | 2 | |||
16.36.a.d.1.3 | 3 | 4.3 | odd | 2 | |||
25.36.a.a.1.3 | 3 | 5.4 | even | 2 | |||
25.36.b.a.24.2 | 6 | 5.2 | odd | 4 | |||
25.36.b.a.24.5 | 6 | 5.3 | odd | 4 |