Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,36,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(193.987826584\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 24844388x^{4} + 154310903773636x^{2} + 6999547445919666225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(213.765i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.36.b.a.24.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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.i | − 0.890730i | −0.895349 | − | 0.445365i | \(-0.853074\pi\) | ||||
0.895349 | − | 0.445365i | \(-0.146926\pi\) | |||||||
\(3\) | 3.45913e8i | 1.54648i | 0.634111 | + | 0.773242i | \(0.281366\pi\) | ||||
−0.634111 | + | 0.773242i | \(0.718634\pi\) | |||||||
\(4\) | 7.09870e9 | 0.206599 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.71135e13 | 1.37750 | ||||||||
\(7\) | − 1.25160e14i | − 0.203353i | −0.994818 | − | 0.101676i | \(-0.967579\pi\) | ||||
0.994818 | − | 0.101676i | \(-0.0324206\pi\) | |||||||
\(8\) | − 6.84517e15i | − 1.07475i | ||||||||
\(9\) | −6.96245e16 | −1.39161 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70842e18 | −1.01911 | −0.509557 | − | 0.860437i | \(-0.670191\pi\) | ||||
−0.509557 | + | 0.860437i | \(0.670191\pi\) | |||||||
\(12\) | 2.45554e18i | 0.319503i | ||||||||
\(13\) | 4.94986e19i | 1.58703i | 0.608552 | + | 0.793514i | \(0.291751\pi\) | ||||
−0.608552 | + | 0.793514i | \(0.708249\pi\) | |||||||
\(14\) | −2.06651e19 | −0.181132 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.86291e20 | −0.750717 | ||||||||
\(17\) | 1.32045e21i | 0.387137i | 0.981087 | + | 0.193569i | \(0.0620062\pi\) | ||||
−0.981087 | + | 0.193569i | \(0.937994\pi\) | |||||||
\(18\) | 1.14956e22i | 1.23955i | ||||||||
\(19\) | −3.94388e21 | −0.165096 | −0.0825479 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825479 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.32945e22 | 0.314482 | ||||||||
\(22\) | 2.82076e23i | 0.907756i | ||||||||
\(23\) | 3.48881e23i | 0.515750i | 0.966178 | + | 0.257875i | \(0.0830224\pi\) | ||||
−0.966178 | + | 0.257875i | \(0.916978\pi\) | |||||||
\(24\) | 2.36784e24 | 1.66209 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.17268e24 | 1.41361 | ||||||||
\(27\) | − 6.77748e24i | − 0.605623i | ||||||||
\(28\) | − 8.88473e23i | − 0.0420125i | ||||||||
\(29\) | −3.21628e25 | −0.822979 | −0.411489 | − | 0.911415i | \(-0.634991\pi\) | ||||
−0.411489 | + | 0.911415i | \(0.634991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.41044e25 | 0.271632 | 0.135816 | − | 0.990734i | \(-0.456634\pi\) | ||||
0.135816 | + | 0.990734i | \(0.456634\pi\) | |||||||
\(32\) | − 8.88635e25i | − 0.406068i | ||||||||
\(33\) | − 5.90965e26i | − 1.57604i | ||||||||
\(34\) | 2.18018e26 | 0.344835 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.94244e26 | −0.287506 | ||||||||
\(37\) | − 4.03624e27i | − 1.45361i | −0.686845 | − | 0.726804i | \(-0.741005\pi\) | ||||
0.686845 | − | 0.726804i | \(-0.258995\pi\) | |||||||
\(38\) | 6.51171e26i | 0.147056i | ||||||||
\(39\) | −1.71222e28 | −2.45431 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.65857e27 | 0.517283 | 0.258642 | − | 0.965973i | \(-0.416725\pi\) | ||||
0.258642 | + | 0.965973i | \(0.416725\pi\) | |||||||
\(42\) | − 7.14832e27i | − 0.280118i | ||||||||
\(43\) | − 9.89389e26i | − 0.0256844i | −0.999918 | − | 0.0128422i | \(-0.995912\pi\) | ||||
0.999918 | − | 0.0128422i | \(-0.00408791\pi\) | |||||||
\(44\) | −1.21276e28 | −0.210548 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.76034e28 | 0.459395 | ||||||||
\(47\) | 1.95852e29i | 1.07205i | 0.844202 | + | 0.536025i | \(0.180075\pi\) | ||||
−0.844202 | + | 0.536025i | \(0.819925\pi\) | |||||||
\(48\) | − 3.06580e29i | − 1.16097i | ||||||||
\(49\) | 3.63154e29 | 0.958648 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.56760e29 | −0.598702 | ||||||||
\(52\) | 3.51376e29i | 0.327879i | ||||||||
\(53\) | 9.96909e29i | 0.666543i | 0.942831 | + | 0.333271i | \(0.108153\pi\) | ||||
−0.942831 | + | 0.333271i | \(0.891847\pi\) | |||||||
\(54\) | −1.11902e30 | −0.539447 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.56741e29 | −0.218554 | ||||||||
\(57\) | − 1.36424e30i | − 0.255318i | ||||||||
\(58\) | 5.31037e30i | 0.733052i | ||||||||
\(59\) | −3.91953e30 | −0.401166 | −0.200583 | − | 0.979677i | \(-0.564284\pi\) | ||||
−0.200583 | + | 0.979677i | \(0.564284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.64909e29 | 0.0436855 | 0.0218428 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218428 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(62\) | − 5.63096e30i | − 0.241951i | ||||||||
\(63\) | 8.71420e30i | 0.282988i | ||||||||
\(64\) | −4.51249e31 | −1.11241 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.75738e31 | −1.40383 | ||||||||
\(67\) | − 1.64301e32i | − 1.81690i | −0.417992 | − | 0.908451i | \(-0.637266\pi\) | ||||
0.417992 | − | 0.908451i | \(-0.362734\pi\) | |||||||
\(68\) | 9.37346e30i | 0.0799823i | ||||||||
\(69\) | −1.20682e32 | −0.797600 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.65930e31 | 0.307021 | 0.153510 | − | 0.988147i | \(-0.450942\pi\) | ||||
0.153510 | + | 0.988147i | \(0.450942\pi\) | |||||||
\(72\) | 4.76592e32i | 1.49564i | ||||||||
\(73\) | 7.08063e32i | 1.74551i | 0.488160 | + | 0.872754i | \(0.337668\pi\) | ||||
−0.488160 | + | 0.872754i | \(0.662332\pi\) | |||||||
\(74\) | −6.66421e32 | −1.29477 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.79964e31 | −0.0341087 | ||||||||
\(77\) | 2.13826e32i | 0.207239i | ||||||||
\(78\) | 2.82704e33i | 2.18613i | ||||||||
\(79\) | −2.34599e33 | −1.45162 | −0.725809 | − | 0.687896i | \(-0.758534\pi\) | ||||
−0.725809 | + | 0.687896i | \(0.758534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.13900e33 | −0.455027 | ||||||||
\(82\) | − 1.42961e33i | − 0.460760i | ||||||||
\(83\) | − 5.18971e33i | − 1.35293i | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
0.736473 | − | 0.676467i | \(-0.236490\pi\) | |||||||
\(84\) | 3.07335e32 | 0.0649717 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.63357e32 | −0.0228779 | ||||||||
\(87\) | − 1.11255e34i | − 1.27272i | ||||||||
\(88\) | 1.16944e34i | 1.09530i | ||||||||
\(89\) | −1.44578e34 | −1.11116 | −0.555582 | − | 0.831461i | \(-0.687505\pi\) | ||||
−0.555582 | + | 0.831461i | \(0.687505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.19525e33 | 0.322726 | ||||||||
\(92\) | 2.47660e33i | 0.106554i | ||||||||
\(93\) | 1.17972e34i | 0.420075i | ||||||||
\(94\) | 3.23369e34 | 0.954907 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.07391e34 | 0.627978 | ||||||||
\(97\) | − 2.87399e34i | − 0.489756i | −0.969554 | − | 0.244878i | \(-0.921252\pi\) | ||||
0.969554 | − | 0.244878i | \(-0.0787479\pi\) | |||||||
\(98\) | − 5.99600e34i | − 0.853897i | ||||||||
\(99\) | 1.18948e35 | 1.41821 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13198e35 | 0.951079 | 0.475539 | − | 0.879694i | \(-0.342253\pi\) | ||||
0.475539 | + | 0.879694i | \(0.342253\pi\) | |||||||
\(102\) | 7.54153e34i | 0.533282i | ||||||||
\(103\) | − 2.53635e35i | − 1.51202i | −0.654559 | − | 0.756011i | \(-0.727145\pi\) | ||||
0.654559 | − | 0.756011i | \(-0.272855\pi\) | |||||||
\(104\) | 3.38826e35 | 1.70567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.64599e35 | 0.593710 | ||||||||
\(107\) | − 3.63939e35i | − 1.11381i | −0.830575 | − | 0.556907i | \(-0.811988\pi\) | ||||
0.830575 | − | 0.556907i | \(-0.188012\pi\) | |||||||
\(108\) | − 4.81113e34i | − 0.125121i | ||||||||
\(109\) | 4.65371e34 | 0.103000 | 0.0514998 | − | 0.998673i | \(-0.483600\pi\) | ||||
0.0514998 | + | 0.998673i | \(0.483600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.39619e36 | 2.24798 | ||||||||
\(112\) | 1.10928e35i | 0.152660i | ||||||||
\(113\) | 2.18346e35i | 0.257201i | 0.991696 | + | 0.128601i | \(0.0410485\pi\) | ||||
−0.991696 | + | 0.128601i | \(0.958951\pi\) | |||||||
\(114\) | −2.25249e35 | −0.227419 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.28314e35 | −0.170027 | ||||||||
\(117\) | − 3.44632e36i | − 2.20853i | ||||||||
\(118\) | 6.47150e35i | 0.357330i | ||||||||
\(119\) | 1.65267e35 | 0.0787254 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.08456e35 | 0.0385932 | ||||||||
\(122\) | − 1.26293e35i | − 0.0389120i | ||||||||
\(123\) | 2.99511e36i | 0.799970i | ||||||||
\(124\) | 2.42097e35 | 0.0561191 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.43880e36 | 0.252066 | ||||||||
\(127\) | 4.19558e36i | 0.640070i | 0.947406 | + | 0.320035i | \(0.103695\pi\) | ||||
−0.947406 | + | 0.320035i | \(0.896305\pi\) | |||||||
\(128\) | 4.39721e36i | 0.584793i | ||||||||
\(129\) | 3.42243e35 | 0.0397205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.40631e36 | 0.213355 | 0.106678 | − | 0.994294i | \(-0.465979\pi\) | ||||
0.106678 | + | 0.994294i | \(0.465979\pi\) | |||||||
\(132\) | − 4.19509e36i | − 0.325610i | ||||||||
\(133\) | 4.93616e35i | 0.0335727i | ||||||||
\(134\) | −2.71276e37 | −1.61837 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.03869e36 | 0.416078 | ||||||||
\(137\) | − 2.14718e37i | − 0.869477i | −0.900557 | − | 0.434739i | \(-0.856841\pi\) | ||||
0.900557 | − | 0.434739i | \(-0.143159\pi\) | |||||||
\(138\) | 1.99258e37i | 0.710446i | ||||||||
\(139\) | −2.63209e37 | −0.827068 | −0.413534 | − | 0.910489i | \(-0.635706\pi\) | ||||
−0.413534 | + | 0.910489i | \(0.635706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.77477e37 | −1.65791 | ||||||||
\(142\) | − 1.26462e37i | − 0.273473i | ||||||||
\(143\) | − 8.45645e37i | − 1.61736i | ||||||||
\(144\) | 6.17076e37 | 1.04471 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.16908e38 | 1.55478 | ||||||||
\(147\) | 1.25620e38i | 1.48253i | ||||||||
\(148\) | − 2.86521e37i | − 0.300314i | ||||||||
\(149\) | 1.74389e38 | 1.62465 | 0.812324 | − | 0.583206i | \(-0.198202\pi\) | ||||
0.812324 | + | 0.583206i | \(0.198202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.40947e38 | −1.03982 | −0.519912 | − | 0.854220i | \(-0.674035\pi\) | ||||
−0.519912 | + | 0.854220i | \(0.674035\pi\) | |||||||
\(152\) | 2.69965e37i | 0.177437i | ||||||||
\(153\) | − 9.19355e37i | − 0.538745i | ||||||||
\(154\) | 3.53046e37 | 0.184595 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.21546e38 | −0.507059 | ||||||||
\(157\) | 1.49924e38i | 0.559277i | 0.960105 | + | 0.279639i | \(0.0902147\pi\) | ||||
−0.960105 | + | 0.279639i | \(0.909785\pi\) | |||||||
\(158\) | 3.87345e38i | 1.29300i | ||||||||
\(159\) | −3.44844e38 | −1.03080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.36659e37 | 0.104879 | ||||||||
\(162\) | 1.88060e38i | 0.405306i | ||||||||
\(163\) | − 8.60787e38i | − 1.66576i | −0.553453 | − | 0.832880i | \(-0.686690\pi\) | ||||
0.553453 | − | 0.832880i | \(-0.313310\pi\) | |||||||
\(164\) | 6.14646e37 | 0.106870 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.56869e38 | −1.20510 | ||||||||
\(167\) | − 9.23344e38i | − 1.16903i | −0.811383 | − | 0.584515i | \(-0.801285\pi\) | ||||
0.811383 | − | 0.584515i | \(-0.198715\pi\) | |||||||
\(168\) | − 2.96358e38i | − 0.337991i | ||||||||
\(169\) | −1.47733e39 | −1.51866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.74591e38 | 0.229749 | ||||||||
\(172\) | − 7.02337e36i | − 0.00530638i | ||||||||
\(173\) | 1.33161e39i | 0.909012i | 0.890744 | + | 0.454506i | \(0.150184\pi\) | ||||
−0.890744 | + | 0.454506i | \(0.849816\pi\) | |||||||
\(174\) | −1.83693e39 | −1.13365 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.51416e39 | 0.765066 | ||||||||
\(177\) | − 1.35582e39i | − 0.620396i | ||||||||
\(178\) | 2.38712e39i | 0.989748i | ||||||||
\(179\) | −6.27202e38 | −0.235765 | −0.117883 | − | 0.993028i | \(-0.537611\pi\) | ||||
−0.117883 | + | 0.993028i | \(0.537611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.39965e39 | −0.742629 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(182\) | − 1.02289e39i | − 0.287462i | ||||||||
\(183\) | 2.64592e38i | 0.0675590i | ||||||||
\(184\) | 2.38815e39 | 0.554305 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.94782e39 | 0.374174 | ||||||||
\(187\) | − 2.25588e39i | − 0.394537i | ||||||||
\(188\) | 1.39029e39i | 0.221485i | ||||||||
\(189\) | −8.48269e38 | −0.123155 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.14518e39 | 0.983596 | 0.491798 | − | 0.870709i | \(-0.336340\pi\) | ||||
0.491798 | + | 0.870709i | \(0.336340\pi\) | |||||||
\(192\) | − 1.56093e40i | − 1.72033i | ||||||||
\(193\) | − 1.38549e40i | − 1.39428i | −0.716936 | − | 0.697139i | \(-0.754456\pi\) | ||||
0.716936 | − | 0.697139i | \(-0.245544\pi\) | |||||||
\(194\) | −4.74522e39 | −0.436240 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.57792e39 | 0.198056 | ||||||||
\(197\) | − 1.15539e40i | − 0.812026i | −0.913867 | − | 0.406013i | \(-0.866919\pi\) | ||||
0.913867 | − | 0.406013i | \(-0.133081\pi\) | |||||||
\(198\) | − 1.96394e40i | − 1.26324i | ||||||||
\(199\) | 4.76691e39 | 0.280742 | 0.140371 | − | 0.990099i | \(-0.455170\pi\) | ||||
0.140371 | + | 0.990099i | \(0.455170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.68340e40 | 2.80981 | ||||||||
\(202\) | − 1.86901e40i | − 0.847155i | ||||||||
\(203\) | 4.02549e39i | 0.167355i | ||||||||
\(204\) | −3.24241e39 | −0.123691 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.18775e40 | −1.34680 | ||||||||
\(207\) | − 2.42906e40i | − 0.717725i | ||||||||
\(208\) | − 4.38702e40i | − 1.19141i | ||||||||
\(209\) | 6.73781e39 | 0.168251 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.87354e40 | −0.396022 | −0.198011 | − | 0.980200i | \(-0.563448\pi\) | ||||
−0.198011 | + | 0.980200i | \(0.563448\pi\) | |||||||
\(212\) | 7.07676e39i | 0.137707i | ||||||||
\(213\) | 2.64945e40i | 0.474803i | ||||||||
\(214\) | −6.00896e40 | −0.992107 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.63930e40 | −0.650896 | ||||||||
\(217\) | − 4.26851e39i | − 0.0552371i | ||||||||
\(218\) | − 7.68370e39i | − 0.0917448i | ||||||||
\(219\) | −2.44929e41 | −2.69940 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.53603e40 | −0.614398 | ||||||||
\(222\) | − 2.30524e41i | − 2.00234i | ||||||||
\(223\) | 7.12100e40i | 0.571750i | 0.958267 | + | 0.285875i | \(0.0922841\pi\) | ||||
−0.958267 | + | 0.285875i | \(0.907716\pi\) | |||||||
\(224\) | −1.11222e40 | −0.0825750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.60510e40 | 0.229097 | ||||||||
\(227\) | − 1.04005e41i | − 0.611787i | −0.952066 | − | 0.305893i | \(-0.901045\pi\) | ||||
0.952066 | − | 0.305893i | \(-0.0989551\pi\) | |||||||
\(228\) | − 9.68434e39i | − 0.0527485i | ||||||||
\(229\) | −1.82859e41 | −0.922564 | −0.461282 | − | 0.887254i | \(-0.652610\pi\) | ||||
−0.461282 | + | 0.887254i | \(0.652610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.39652e40 | −0.320493 | ||||||||
\(232\) | 2.20160e41i | 0.884501i | ||||||||
\(233\) | − 1.57847e41i | − 0.588177i | −0.955778 | − | 0.294088i | \(-0.904984\pi\) | ||||
0.955778 | − | 0.294088i | \(-0.0950160\pi\) | |||||||
\(234\) | −5.69019e41 | −1.96720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.78236e40 | −0.0828806 | ||||||||
\(237\) | − 8.11510e41i | − 2.24490i | ||||||||
\(238\) | − 2.72871e40i | − 0.0701231i | ||||||||
\(239\) | −5.00984e41 | −1.19636 | −0.598178 | − | 0.801363i | \(-0.704108\pi\) | ||||
−0.598178 | + | 0.801363i | \(0.704108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.33164e41 | −0.687638 | −0.343819 | − | 0.939036i | \(-0.611721\pi\) | ||||
−0.343819 | + | 0.939036i | \(0.611721\pi\) | |||||||
\(242\) | − 1.79072e40i | − 0.0343762i | ||||||||
\(243\) | − 7.33084e41i | − 1.30931i | ||||||||
\(244\) | 5.42986e39 | 0.00902540 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94521e41 | 0.712558 | ||||||||
\(247\) | − 1.95217e41i | − 0.262011i | ||||||||
\(248\) | − 2.33451e41i | − 0.291938i | ||||||||
\(249\) | 1.79519e42 | 2.09229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.52760e42 | 1.54782 | 0.773909 | − | 0.633297i | \(-0.218299\pi\) | ||||
0.773909 | + | 0.633297i | \(0.218299\pi\) | |||||||
\(252\) | 6.18595e40i | 0.0584652i | ||||||||
\(253\) | − 5.96035e41i | − 0.525608i | ||||||||
\(254\) | 6.92730e41 | 0.570130 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.24460e41 | −0.591521 | ||||||||
\(257\) | − 2.72482e42i | − 1.82603i | −0.407925 | − | 0.913016i | \(-0.633747\pi\) | ||||
0.407925 | − | 0.913016i | \(-0.366253\pi\) | |||||||
\(258\) | − 5.65074e40i | − 0.0353802i | ||||||||
\(259\) | −5.05176e41 | −0.295595 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23932e42 | 1.14527 | ||||||||
\(262\) | − 3.97303e41i | − 0.190042i | ||||||||
\(263\) | − 4.22055e40i | − 0.0188861i | −0.999955 | − | 0.00944307i | \(-0.996994\pi\) | ||||
0.999955 | − | 0.00944307i | \(-0.00300587\pi\) | |||||||
\(264\) | −4.04526e42 | −1.69386 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.15005e40 | 0.0299042 | ||||||||
\(267\) | − 5.00116e42i | − 1.71840i | ||||||||
\(268\) | − 1.16632e42i | − 0.375371i | ||||||||
\(269\) | 1.30618e42 | 0.393858 | 0.196929 | − | 0.980418i | \(-0.436903\pi\) | ||||
0.196929 | + | 0.980418i | \(0.436903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.11918e41 | −0.109106 | −0.0545529 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545529 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(272\) | − 1.17030e42i | − 0.290631i | ||||||||
\(273\) | 2.14302e42i | 0.499091i | ||||||||
\(274\) | −3.54519e42 | −0.774470 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.56689e41 | −0.164784 | ||||||||
\(277\) | 7.38232e42i | 1.33290i | 0.745551 | + | 0.666449i | \(0.232187\pi\) | ||||
−0.745551 | + | 0.666449i | \(0.767813\pi\) | |||||||
\(278\) | 4.34582e42i | 0.736694i | ||||||||
\(279\) | −2.37451e42 | −0.378007 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.08223e42 | 0.573505 | 0.286752 | − | 0.958005i | \(-0.407424\pi\) | ||||
0.286752 | + | 0.958005i | \(0.407424\pi\) | |||||||
\(282\) | 1.11858e43i | 1.47675i | ||||||||
\(283\) | 1.06503e43i | 1.32159i | 0.750565 | + | 0.660796i | \(0.229781\pi\) | ||||
−0.750565 | + | 0.660796i | \(0.770219\pi\) | |||||||
\(284\) | 5.43711e41 | 0.0634303 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.39624e43 | −1.44063 | ||||||||
\(287\) | − 1.08371e42i | − 0.105191i | ||||||||
\(288\) | 6.18708e42i | 0.565089i | ||||||||
\(289\) | 9.88997e42 | 0.850125 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.94151e42 | 0.757399 | ||||||||
\(292\) | 5.02633e42i | 0.360621i | ||||||||
\(293\) | − 1.90474e43i | − 1.28722i | −0.765353 | − | 0.643610i | \(-0.777436\pi\) | ||||
0.765353 | − | 0.643610i | \(-0.222564\pi\) | |||||||
\(294\) | 2.07410e43 | 1.32054 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.76288e43 | −1.56227 | ||||||||
\(297\) | 1.15788e43i | 0.617199i | ||||||||
\(298\) | − 2.87932e43i | − 1.44712i | ||||||||
\(299\) | −1.72691e43 | −0.818510 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.23832e41 | −0.00522298 | ||||||||
\(302\) | 2.32717e43i | 0.926203i | ||||||||
\(303\) | 3.91569e43i | 1.47083i | ||||||||
\(304\) | 3.49543e42 | 0.123940 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.51794e43 | −0.479877 | ||||||||
\(307\) | − 1.39752e43i | − 0.417288i | −0.977992 | − | 0.208644i | \(-0.933095\pi\) | ||||
0.977992 | − | 0.208644i | \(-0.0669050\pi\) | |||||||
\(308\) | 1.51789e42i | 0.0428156i | ||||||||
\(309\) | 8.77359e43 | 2.33832 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22377e43 | 0.529399 | 0.264700 | − | 0.964331i | \(-0.414727\pi\) | ||||
0.264700 | + | 0.964331i | \(0.414727\pi\) | |||||||
\(312\) | 1.17205e44i | 2.63778i | ||||||||
\(313\) | − 3.63171e43i | − 0.772833i | −0.922324 | − | 0.386417i | \(-0.873713\pi\) | ||||
0.922324 | − | 0.386417i | \(-0.126287\pi\) | |||||||
\(314\) | 2.47538e43 | 0.498165 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.66535e43 | −0.299903 | ||||||||
\(317\) | 5.29385e43i | 0.902058i | 0.892509 | + | 0.451029i | \(0.148943\pi\) | ||||
−0.892509 | + | 0.451029i | \(0.851057\pi\) | |||||||
\(318\) | 5.69370e43i | 0.918163i | ||||||||
\(319\) | 5.49476e43 | 0.838709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.25891e44 | 1.72249 | ||||||||
\(322\) | − 7.20964e42i | − 0.0934191i | ||||||||
\(323\) | − 5.20769e42i | − 0.0639147i | ||||||||
\(324\) | −8.08544e42 | −0.0940083 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.42124e44 | −1.48374 | ||||||||
\(327\) | 1.60978e43i | 0.159287i | ||||||||
\(328\) | − 5.92693e43i | − 0.555953i | ||||||||
\(329\) | 2.45128e43 | 0.218004 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.25551e43 | 0.500349 | 0.250174 | − | 0.968201i | \(-0.419512\pi\) | ||||
0.250174 | + | 0.968201i | \(0.419512\pi\) | |||||||
\(332\) | − 3.68402e43i | − 0.279515i | ||||||||
\(333\) | 2.81022e44i | 2.02286i | ||||||||
\(334\) | −1.52453e44 | −1.04129 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.83715e43 | −0.236087 | ||||||||
\(337\) | − 1.04185e44i | − 0.608529i | −0.952588 | − | 0.304264i | \(-0.901589\pi\) | ||||
0.952588 | − | 0.304264i | \(-0.0984106\pi\) | |||||||
\(338\) | 2.43920e44i | 1.35271i | ||||||||
\(339\) | −7.55289e43 | −0.397757 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.82647e43 | −0.276824 | ||||||||
\(342\) | − 4.53375e43i | − 0.204645i | ||||||||
\(343\) | − 9.28652e43i | − 0.398296i | ||||||||
\(344\) | −6.77253e42 | −0.0276044 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.19861e44 | 0.809685 | ||||||||
\(347\) | − 3.07657e44i | − 1.07721i | −0.842557 | − | 0.538606i | \(-0.818951\pi\) | ||||
0.842557 | − | 0.538606i | \(-0.181049\pi\) | |||||||
\(348\) | − 7.89769e43i | − 0.262944i | ||||||||
\(349\) | 2.62767e44 | 0.832005 | 0.416003 | − | 0.909363i | \(-0.363431\pi\) | ||||
0.416003 | + | 0.909363i | \(0.363431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.35476e44 | 0.961140 | ||||||||
\(352\) | 1.51816e44i | 0.413830i | ||||||||
\(353\) | − 7.06671e44i | − 1.83299i | −0.400048 | − | 0.916494i | \(-0.631006\pi\) | ||||
0.400048 | − | 0.916494i | \(-0.368994\pi\) | |||||||
\(354\) | −2.23858e44 | −0.552606 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.02632e44 | −0.229566 | ||||||||
\(357\) | 5.71681e43i | 0.121748i | ||||||||
\(358\) | 1.03557e44i | 0.210003i | ||||||||
\(359\) | 5.35788e44 | 1.03476 | 0.517380 | − | 0.855756i | \(-0.326907\pi\) | ||||
0.517380 | + | 0.855756i | \(0.326907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.55104e44 | −0.972743 | ||||||||
\(362\) | 3.96204e44i | 0.661483i | ||||||||
\(363\) | 3.75165e43i | 0.0596838i | ||||||||
\(364\) | 4.39782e43 | 0.0666750 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.36866e43 | 0.0601768 | ||||||||
\(367\) | − 3.00056e44i | − 0.394045i | −0.980399 | − | 0.197022i | \(-0.936873\pi\) | ||||
0.980399 | − | 0.197022i | \(-0.0631272\pi\) | |||||||
\(368\) | − 3.09210e44i | − 0.387183i | ||||||||
\(369\) | −6.02849e44 | −0.719858 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.24773e44 | 0.135543 | ||||||||
\(372\) | 8.37447e43i | 0.0867872i | ||||||||
\(373\) | − 1.08201e45i | − 1.06986i | −0.844895 | − | 0.534932i | \(-0.820337\pi\) | ||||
0.844895 | − | 0.534932i | \(-0.179663\pi\) | |||||||
\(374\) | −3.72466e44 | −0.351426 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.34064e45 | 1.15219 | ||||||||
\(377\) | − 1.59201e45i | − 1.30609i | ||||||||
\(378\) | 1.40057e44i | 0.109698i | ||||||||
\(379\) | −1.21847e45 | −0.911229 | −0.455614 | − | 0.890177i | \(-0.650580\pi\) | ||||
−0.455614 | + | 0.890177i | \(0.650580\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45131e45 | −0.989858 | ||||||||
\(382\) | − 1.34484e45i | − 0.876119i | ||||||||
\(383\) | 9.53201e43i | 0.0593207i | 0.999560 | + | 0.0296603i | \(0.00944256\pi\) | ||||
−0.999560 | + | 0.0296603i | \(0.990557\pi\) | |||||||
\(384\) | −1.52105e45 | −0.904373 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.28757e45 | −1.24193 | ||||||||
\(387\) | 6.88857e43i | 0.0357427i | ||||||||
\(388\) | − 2.04016e44i | − 0.101183i | ||||||||
\(389\) | −1.90493e45 | −0.903152 | −0.451576 | − | 0.892233i | \(-0.649138\pi\) | ||||
−0.451576 | + | 0.892233i | \(0.649138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.60678e44 | −0.199666 | ||||||||
\(392\) | − 2.48585e45i | − 1.03031i | ||||||||
\(393\) | 8.32373e44i | 0.329950i | ||||||||
\(394\) | −1.90766e45 | −0.723296 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.44376e44 | 0.293002 | ||||||||
\(397\) | 3.96399e45i | 1.31613i | 0.752961 | + | 0.658065i | \(0.228625\pi\) | ||||
−0.752961 | + | 0.658065i | \(0.771375\pi\) | |||||||
\(398\) | − 7.87060e44i | − 0.250066i | ||||||||
\(399\) | −1.70748e44 | −0.0519196 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.53039e44 | −0.154074 | −0.0770369 | − | 0.997028i | \(-0.524546\pi\) | ||||
−0.0770369 | + | 0.997028i | \(0.524546\pi\) | |||||||
\(402\) | − 9.38381e45i | − 2.50278i | ||||||||
\(403\) | 1.68812e45i | 0.431088i | ||||||||
\(404\) | 8.03562e44 | 0.196492 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.64646e44 | 0.149068 | ||||||||
\(407\) | 6.89560e45i | 1.48139i | ||||||||
\(408\) | 3.12660e45i | 0.643457i | ||||||||
\(409\) | −3.35495e45 | −0.661498 | −0.330749 | − | 0.943719i | \(-0.607301\pi\) | ||||
−0.330749 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.42738e45 | 1.34463 | ||||||||
\(412\) | − 1.80048e45i | − 0.312383i | ||||||||
\(413\) | 4.90568e44i | 0.0815781i | ||||||||
\(414\) | −4.01061e45 | −0.639299 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.39862e45 | 0.644441 | ||||||||
\(417\) | − 9.10474e45i | − 1.27905i | ||||||||
\(418\) | − 1.11247e45i | − 0.149867i | ||||||||
\(419\) | 7.69138e45 | 0.993708 | 0.496854 | − | 0.867834i | \(-0.334488\pi\) | ||||
0.496854 | + | 0.867834i | \(0.334488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.77229e45 | −0.329535 | −0.164767 | − | 0.986332i | \(-0.552687\pi\) | ||||
−0.164767 | + | 0.986332i | \(0.552687\pi\) | |||||||
\(422\) | 3.09338e45i | 0.352749i | ||||||||
\(423\) | − 1.36361e46i | − 1.49188i | ||||||||
\(424\) | 6.82401e45 | 0.716370 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.37449e45 | 0.422921 | ||||||||
\(427\) | − 9.57360e43i | − 0.00888357i | ||||||||
\(428\) | − 2.58349e45i | − 0.230113i | ||||||||
\(429\) | 2.92520e46 | 2.50122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.18484e45 | 0.487502 | 0.243751 | − | 0.969838i | \(-0.421622\pi\) | ||||
0.243751 | + | 0.969838i | \(0.421622\pi\) | |||||||
\(432\) | 6.00681e45i | 0.454651i | ||||||||
\(433\) | − 2.21783e46i | − 1.61209i | −0.591852 | − | 0.806047i | \(-0.701603\pi\) | ||||
0.591852 | − | 0.806047i | \(-0.298397\pi\) | |||||||
\(434\) | −7.04770e44 | −0.0492014 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.30353e44 | 0.0212796 | ||||||||
\(437\) | − 1.37594e45i | − 0.0851482i | ||||||||
\(438\) | 4.04399e46i | 2.40444i | ||||||||
\(439\) | −1.91766e45 | −0.109557 | −0.0547787 | − | 0.998499i | \(-0.517445\pi\) | ||||
−0.0547787 | + | 0.998499i | \(0.517445\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.52844e46 | −1.33407 | ||||||||
\(442\) | 1.07916e46i | 0.547263i | ||||||||
\(443\) | 3.00864e46i | 1.46658i | 0.679916 | + | 0.733290i | \(0.262016\pi\) | ||||
−0.679916 | + | 0.733290i | \(0.737984\pi\) | |||||||
\(444\) | 9.91114e45 | 0.464431 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.17574e46 | 0.509275 | ||||||||
\(447\) | 6.03235e46i | 2.51249i | ||||||||
\(448\) | 5.64783e45i | 0.226212i | ||||||||
\(449\) | −5.68788e45 | −0.219099 | −0.109549 | − | 0.993981i | \(-0.534941\pi\) | ||||
−0.109549 | + | 0.993981i | \(0.534941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.47925e46 | −0.527171 | ||||||||
\(452\) | 1.54997e45i | 0.0531376i | ||||||||
\(453\) | − 4.87555e46i | − 1.60807i | ||||||||
\(454\) | −1.71721e46 | −0.544937 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.33846e45 | −0.274404 | ||||||||
\(457\) | 4.67626e46i | 1.32241i | 0.750206 | + | 0.661204i | \(0.229954\pi\) | ||||
−0.750206 | + | 0.661204i | \(0.770046\pi\) | |||||||
\(458\) | 3.01918e46i | 0.821755i | ||||||||
\(459\) | 8.94930e45 | 0.234459 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.72978e46 | −0.905560 | −0.452780 | − | 0.891622i | \(-0.649568\pi\) | ||||
−0.452780 | + | 0.891622i | \(0.649568\pi\) | |||||||
\(462\) | 1.22123e46i | 0.285472i | ||||||||
\(463\) | 3.67649e46i | 0.827497i | 0.910391 | + | 0.413748i | \(0.135781\pi\) | ||||
−0.910391 | + | 0.413748i | \(0.864219\pi\) | |||||||
\(464\) | 2.85056e46 | 0.617825 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.60620e46 | −0.523907 | ||||||||
\(467\) | − 2.37743e46i | − 0.460323i | −0.973152 | − | 0.230161i | \(-0.926075\pi\) | ||||
0.973152 | − | 0.230161i | \(-0.0739254\pi\) | |||||||
\(468\) | − 2.44644e46i | − 0.456280i | ||||||||
\(469\) | −2.05639e46 | −0.369472 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.18607e46 | −0.864914 | ||||||||
\(472\) | 2.68298e46i | 0.431155i | ||||||||
\(473\) | 1.69029e45i | 0.0261753i | ||||||||
\(474\) | −1.33988e47 | −1.99960 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.17318e45 | 0.0162646 | ||||||||
\(477\) | − 6.94094e46i | − 0.927569i | ||||||||
\(478\) | 8.27170e46i | 1.06563i | ||||||||
\(479\) | 8.80315e46 | 1.09337 | 0.546684 | − | 0.837339i | \(-0.315890\pi\) | ||||
0.546684 | + | 0.837339i | \(0.315890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.99788e47 | 2.30691 | ||||||||
\(482\) | 5.50084e46i | 0.612500i | ||||||||
\(483\) | 1.51046e46i | 0.162194i | ||||||||
\(484\) | 7.69900e44 | 0.00797334 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.21039e47 | −1.16625 | ||||||||
\(487\) | 7.13443e46i | 0.663136i | 0.943431 | + | 0.331568i | \(0.107578\pi\) | ||||
−0.943431 | + | 0.331568i | \(0.892422\pi\) | |||||||
\(488\) | − 5.23593e45i | − 0.0469512i | ||||||||
\(489\) | 2.97758e47 | 2.57607 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.49115e46 | 0.683975 | 0.341988 | − | 0.939704i | \(-0.388900\pi\) | ||||
0.341988 | + | 0.939704i | \(0.388900\pi\) | |||||||
\(492\) | 2.12614e46i | 0.165273i | ||||||||
\(493\) | − 4.24693e46i | − 0.318606i | ||||||||
\(494\) | −3.22321e46 | −0.233382 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.02265e46 | −0.203919 | ||||||||
\(497\) | − 9.58638e45i | − 0.0624335i | ||||||||
\(498\) | − 2.96402e47i | − 1.86367i | ||||||||
\(499\) | 1.75876e47 | 1.06770 | 0.533848 | − | 0.845581i | \(-0.320745\pi\) | ||||
0.533848 | + | 0.845581i | \(0.320745\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.19397e47 | 1.80789 | ||||||||
\(502\) | − 2.52221e47i | − 1.37869i | ||||||||
\(503\) | − 1.24051e47i | − 0.654880i | −0.944872 | − | 0.327440i | \(-0.893814\pi\) | ||||
0.944872 | − | 0.327440i | \(-0.106186\pi\) | |||||||
\(504\) | 5.96502e46 | 0.304143 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.84108e46 | −0.468175 | ||||||||
\(507\) | − 5.11027e47i | − 2.34858i | ||||||||
\(508\) | 2.97832e46i | 0.132238i | ||||||||
\(509\) | −3.71512e47 | −1.59372 | −0.796859 | − | 0.604166i | \(-0.793507\pi\) | ||||
−0.796859 | + | 0.604166i | \(0.793507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.86212e46 | 0.354954 | ||||||||
\(512\) | 2.87213e47i | 1.11168i | ||||||||
\(513\) | 2.67296e46i | 0.0999857i | ||||||||
\(514\) | −4.49893e47 | −1.62650 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.42948e45 | 0.00820623 | ||||||||
\(517\) | − 3.34597e47i | − 1.09254i | ||||||||
\(518\) | 8.34092e46i | 0.263295i | ||||||||
\(519\) | −4.60621e47 | −1.40577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.89659e45 | 0.0225309 | 0.0112655 | − | 0.999937i | \(-0.496414\pi\) | ||||
0.0112655 | + | 0.999937i | \(0.496414\pi\) | |||||||
\(522\) | − 3.69732e47i | − 1.02012i | ||||||||
\(523\) | − 1.18122e47i | − 0.315175i | −0.987505 | − | 0.157588i | \(-0.949628\pi\) | ||||
0.987505 | − | 0.157588i | \(-0.0503717\pi\) | |||||||
\(524\) | 1.70816e46 | 0.0440790 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.96851e45 | −0.0168225 | ||||||||
\(527\) | 4.50331e46i | 0.105159i | ||||||||
\(528\) | 5.23767e47i | 1.18316i | ||||||||
\(529\) | 3.35870e47 | 0.734001 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.72895e47 | 0.558267 | ||||||||
\(532\) | 3.50403e45i | 0.00693609i | ||||||||
\(533\) | 4.28587e47i | 0.820943i | ||||||||
\(534\) | −8.25738e47 | −1.53063 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.12467e48 | −1.95272 | ||||||||
\(537\) | − 2.16958e47i | − 0.364607i | ||||||||
\(538\) | − 2.15663e47i | − 0.350821i | ||||||||
\(539\) | −6.20419e47 | −0.976971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.62658e47 | −0.977997 | −0.488998 | − | 0.872285i | \(-0.662638\pi\) | ||||
−0.488998 | + | 0.872285i | \(0.662638\pi\) | |||||||
\(542\) | 6.80114e46i | 0.0971839i | ||||||||
\(543\) | − 8.30070e47i | − 1.14846i | ||||||||
\(544\) | 1.17340e47 | 0.157204 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.53832e47 | 0.444555 | ||||||||
\(547\) | − 1.12424e47i | − 0.136798i | −0.997658 | − | 0.0683990i | \(-0.978211\pi\) | ||||
0.997658 | − | 0.0683990i | \(-0.0217891\pi\) | |||||||
\(548\) | − 1.52422e47i | − 0.179633i | ||||||||
\(549\) | −5.32564e46 | −0.0607933 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26846e47 | 0.135870 | ||||||||
\(552\) | 8.26092e47i | 0.857224i | ||||||||
\(553\) | 2.93624e47i | 0.295190i | ||||||||
\(554\) | 1.21889e48 | 1.18725 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.86844e47 | −0.170872 | ||||||||
\(557\) | 6.68090e47i | 0.592064i | 0.955178 | + | 0.296032i | \(0.0956636\pi\) | ||||
−0.955178 | + | 0.296032i | \(0.904336\pi\) | |||||||
\(558\) | 3.92053e47i | 0.336702i | ||||||||
\(559\) | 4.89734e46 | 0.0407618 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.80339e47 | 0.610145 | ||||||||
\(562\) | − 6.74014e47i | − 0.510838i | ||||||||
\(563\) | − 2.47733e48i | − 1.82007i | −0.414536 | − | 0.910033i | \(-0.636056\pi\) | ||||
0.414536 | − | 0.910033i | \(-0.363944\pi\) | |||||||
\(564\) | −4.80921e47 | −0.342523 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.75846e48 | 1.17718 | ||||||||
\(567\) | 1.42558e47i | 0.0925309i | ||||||||
\(568\) | − 5.24292e47i | − 0.329972i | ||||||||
\(569\) | −8.59661e47 | −0.524641 | −0.262321 | − | 0.964981i | \(-0.584488\pi\) | ||||
−0.262321 | + | 0.964981i | \(0.584488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.39185e48 | −1.94673 | −0.973364 | − | 0.229266i | \(-0.926367\pi\) | ||||
−0.973364 | + | 0.229266i | \(0.926367\pi\) | |||||||
\(572\) | − 6.00298e47i | − 0.334146i | ||||||||
\(573\) | 2.81753e48i | 1.52112i | ||||||||
\(574\) | −1.78930e47 | −0.0936968 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.14180e48 | 1.54805 | ||||||||
\(577\) | 2.12534e48i | 1.01590i | 0.861386 | + | 0.507951i | \(0.169597\pi\) | ||||
−0.861386 | + | 0.507951i | \(0.830403\pi\) | |||||||
\(578\) | − 1.63292e48i | − 0.757232i | ||||||||
\(579\) | 4.79258e48 | 2.15623 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.49544e47 | −0.275123 | ||||||||
\(582\) | − 1.64143e48i | − 0.674639i | ||||||||
\(583\) | − 1.70314e48i | − 0.679283i | ||||||||
\(584\) | 4.84681e48 | 1.87599 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.14491e48 | −1.14657 | ||||||||
\(587\) | 1.06269e48i | 0.376044i | 0.982165 | + | 0.188022i | \(0.0602076\pi\) | ||||
−0.982165 | + | 0.188022i | \(0.939792\pi\) | |||||||
\(588\) | 8.91737e47i | 0.306290i | ||||||||
\(589\) | −1.34504e47 | −0.0448453 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.99665e48 | 1.25578 | ||||||||
\(592\) | 3.57728e48i | 1.09125i | ||||||||
\(593\) | 3.98260e48i | 1.17953i | 0.807574 | + | 0.589766i | \(0.200780\pi\) | ||||
−0.807574 | + | 0.589766i | \(0.799220\pi\) | |||||||
\(594\) | 1.91176e48 | 0.549758 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.23794e48 | 0.335651 | ||||||||
\(597\) | 1.64894e48i | 0.434163i | ||||||||
\(598\) | 2.85129e48i | 0.729072i | ||||||||
\(599\) | −5.14535e48 | −1.27775 | −0.638874 | − | 0.769311i | \(-0.720599\pi\) | ||||
−0.638874 | + | 0.769311i | \(0.720599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.83878e48 | −0.430751 | −0.215375 | − | 0.976531i | \(-0.569098\pi\) | ||||
−0.215375 | + | 0.976531i | \(0.569098\pi\) | |||||||
\(602\) | 2.04458e46i | 0.00465227i | ||||||||
\(603\) | 1.14394e49i | 2.52842i | ||||||||
\(604\) | −1.00054e48 | −0.214827 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.46516e48 | 1.31011 | ||||||||
\(607\) | 2.06846e48i | 0.407236i | 0.979050 | + | 0.203618i | \(0.0652700\pi\) | ||||
−0.979050 | + | 0.203618i | \(0.934730\pi\) | |||||||
\(608\) | 3.50467e47i | 0.0670401i | ||||||||
\(609\) | −1.39247e48 | −0.258812 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.69439e48 | −1.70137 | ||||||||
\(612\) | − 6.52623e47i | − 0.111304i | ||||||||
\(613\) | − 1.02050e48i | − 0.169143i | −0.996417 | − | 0.0845717i | \(-0.973048\pi\) | ||||
0.996417 | − | 0.0845717i | \(-0.0269522\pi\) | |||||||
\(614\) | −2.30743e48 | −0.371691 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.46367e48 | 0.222732 | ||||||||
\(617\) | − 3.46313e48i | − 0.512246i | −0.966644 | − | 0.256123i | \(-0.917555\pi\) | ||||
0.966644 | − | 0.256123i | \(-0.0824452\pi\) | |||||||
\(618\) | − 1.44860e49i | − 2.08281i | ||||||||
\(619\) | −6.56428e48 | −0.917488 | −0.458744 | − | 0.888568i | \(-0.651701\pi\) | ||||
−0.458744 | + | 0.888568i | \(0.651701\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.36453e48 | 0.312350 | ||||||||
\(622\) | − 3.67165e48i | − 0.471552i | ||||||||
\(623\) | 1.80954e48i | 0.225958i | ||||||||
\(624\) | 1.51753e49 | 1.84249 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.99629e48 | −0.688386 | ||||||||
\(627\) | 2.33070e48i | 0.260198i | ||||||||
\(628\) | 1.06427e48i | 0.115546i | ||||||||
\(629\) | 5.32965e48 | 0.562746 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.18692e48 | 0.518079 | 0.259039 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259039 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(632\) | 1.60587e49i | 1.56013i | ||||||||
\(633\) | − 6.48082e48i | − 0.612442i | ||||||||
\(634\) | 8.74063e48 | 0.803490 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.44795e48 | −0.212962 | ||||||||
\(637\) | 1.79756e49i | 1.52140i | ||||||||
\(638\) | − 9.07235e48i | − 0.747064i | ||||||||
\(639\) | −5.33275e48 | −0.427254 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.15569e48 | −0.466940 | −0.233470 | − | 0.972364i | \(-0.575008\pi\) | ||||
−0.233470 | + | 0.972364i | \(0.575008\pi\) | |||||||
\(642\) | − 2.07858e49i | − 1.53428i | ||||||||
\(643\) | 6.50853e48i | 0.467510i | 0.972296 | + | 0.233755i | \(0.0751013\pi\) | ||||
−0.972296 | + | 0.233755i | \(0.924899\pi\) | |||||||
\(644\) | 3.09971e47 | 0.0216680 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.59837e47 | −0.0569308 | ||||||||
\(647\) | 2.43533e49i | 1.56940i | 0.619878 | + | 0.784698i | \(0.287182\pi\) | ||||
−0.619878 | + | 0.784698i | \(0.712818\pi\) | |||||||
\(648\) | 7.79667e48i | 0.489042i | ||||||||
\(649\) | 6.69620e48 | 0.408833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.47654e48 | 0.0854233 | ||||||||
\(652\) | − 6.11047e48i | − 0.344145i | ||||||||
\(653\) | − 4.33343e48i | − 0.237602i | −0.992918 | − | 0.118801i | \(-0.962095\pi\) | ||||
0.992918 | − | 0.118801i | \(-0.0379051\pi\) | |||||||
\(654\) | 2.65789e48 | 0.141882 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.67401e48 | −0.388334 | ||||||||
\(657\) | − 4.92986e49i | − 2.42907i | ||||||||
\(658\) | − 4.04729e48i | − 0.194183i | ||||||||
\(659\) | −2.26798e49 | −1.05960 | −0.529802 | − | 0.848121i | \(-0.677734\pi\) | ||||
−0.529802 | + | 0.848121i | \(0.677734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.84364e49 | −1.25994 | −0.629969 | − | 0.776620i | \(-0.716932\pi\) | ||||
−0.629969 | + | 0.776620i | \(0.716932\pi\) | |||||||
\(662\) | − 1.03284e49i | − 0.445676i | ||||||||
\(663\) | − 2.26090e49i | − 0.950156i | ||||||||
\(664\) | −3.55245e49 | −1.45407 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.63992e49 | 1.80182 | ||||||||
\(667\) | − 1.12210e49i | − 0.424452i | ||||||||
\(668\) | − 6.55455e48i | − 0.241521i | ||||||||
\(669\) | −2.46325e49 | −0.884202 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.30679e48 | −0.0445205 | ||||||||
\(672\) | − 3.84730e48i | − 0.127701i | ||||||||
\(673\) | − 1.14434e49i | − 0.370077i | −0.982731 | − | 0.185039i | \(-0.940759\pi\) | ||||
0.982731 | − | 0.185039i | \(-0.0592410\pi\) | |||||||
\(674\) | −1.72019e49 | −0.542035 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.04871e49 | −0.313753 | ||||||||
\(677\) | − 3.00594e49i | − 0.876351i | −0.898890 | − | 0.438175i | \(-0.855625\pi\) | ||||
0.898890 | − | 0.438175i | \(-0.144375\pi\) | |||||||
\(678\) | 1.24705e49i | 0.354295i | ||||||||
\(679\) | −3.59708e48 | −0.0995931 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.59766e49 | 0.946119 | ||||||||
\(682\) | 9.62004e48i | 0.246576i | ||||||||
\(683\) | 7.78736e49i | 1.94549i | 0.231885 | + | 0.972743i | \(0.425511\pi\) | ||||
−0.231885 | + | 0.972743i | \(0.574489\pi\) | |||||||
\(684\) | 1.94924e48 | 0.0474661 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.53329e49 | −0.354774 | ||||||||
\(687\) | − 6.32535e49i | − 1.42673i | ||||||||
\(688\) | 8.76886e47i | 0.0192817i | ||||||||
\(689\) | −4.93456e49 | −1.05782 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.61614e49 | 1.95945 | 0.979726 | − | 0.200340i | \(-0.0642046\pi\) | ||||
0.979726 | + | 0.200340i | \(0.0642046\pi\) | |||||||
\(692\) | 9.45269e48i | 0.187801i | ||||||||
\(693\) | − 1.48875e49i | − 0.288397i | ||||||||
\(694\) | −5.07971e49 | −0.959506 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.61562e49 | −1.36787 | ||||||||
\(697\) | 1.14332e49i | 0.200260i | ||||||||
\(698\) | − 4.33853e49i | − 0.741093i | ||||||||
\(699\) | 5.46014e49 | 0.909606 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.19741e49 | 0.189748 | 0.0948742 | − | 0.995489i | \(-0.469755\pi\) | ||||
0.0948742 | + | 0.995489i | \(0.469755\pi\) | |||||||
\(702\) | − 5.53901e49i | − 0.856116i | ||||||||
\(703\) | 1.59185e49i | 0.239984i | ||||||||
\(704\) | 7.70923e49 | 1.13368 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.16678e50 | −1.63270 | ||||||||
\(707\) | − 1.41679e49i | − 0.193404i | ||||||||
\(708\) | − 9.62454e48i | − 0.128173i | ||||||||
\(709\) | 4.80032e49 | 0.623680 | 0.311840 | − | 0.950135i | \(-0.399055\pi\) | ||||
0.311840 | + | 0.950135i | \(0.399055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.63339e50 | 2.02009 | ||||||||
\(712\) | 9.89664e49i | 1.19423i | ||||||||
\(713\) | 1.18984e49i | 0.140094i | ||||||||
\(714\) | 9.43898e48 | 0.108444 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.45232e48 | −0.0487089 | ||||||||
\(717\) | − 1.73297e50i | − 1.85015i | ||||||||
\(718\) | − 8.84635e49i | − 0.921693i | ||||||||
\(719\) | 1.45387e49 | 0.147832 | 0.0739162 | − | 0.997264i | \(-0.476450\pi\) | ||||
0.0739162 | + | 0.997264i | \(0.476450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.17450e49 | −0.307474 | ||||||||
\(722\) | 9.16528e49i | 0.866452i | ||||||||
\(723\) | − 1.15246e50i | − 1.06342i | ||||||||
\(724\) | −1.70344e49 | −0.153427 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.19432e48 | 0.0531622 | ||||||||
\(727\) | 1.25503e50i | 1.05148i | 0.850644 | + | 0.525742i | \(0.176212\pi\) | ||||
−0.850644 | + | 0.525742i | \(0.823788\pi\) | |||||||
\(728\) | − 4.24075e49i | − 0.346851i | ||||||||
\(729\) | 1.96598e50 | 1.56981 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.30644e48 | 0.00994338 | ||||||||
\(732\) | 1.87826e48i | 0.0139576i | ||||||||
\(733\) | 1.40440e50i | 1.01899i | 0.860473 | + | 0.509495i | \(0.170168\pi\) | ||||
−0.860473 | + | 0.509495i | \(0.829832\pi\) | |||||||
\(734\) | −4.95419e49 | −0.350988 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.10027e49 | 0.209430 | ||||||||
\(737\) | 2.80695e50i | 1.85163i | ||||||||
\(738\) | 9.95358e49i | 0.641199i | ||||||||
\(739\) | −2.93572e49 | −0.184687 | −0.0923435 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923435 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.75281e49 | 0.405197 | ||||||||
\(742\) | − 2.06012e49i | − 0.120732i | ||||||||
\(743\) | − 1.10795e50i | − 0.634185i | −0.948395 | − | 0.317093i | \(-0.897293\pi\) | ||||
0.948395 | − | 0.317093i | \(-0.102707\pi\) | |||||||
\(744\) | 8.07537e49 | 0.451478 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.78650e50 | −0.952960 | ||||||||
\(747\) | 3.61331e50i | 1.88276i | ||||||||
\(748\) | − 1.60138e49i | − 0.0815111i | ||||||||
\(749\) | −4.55506e49 | −0.226497 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.13601e50 | −1.96283 | −0.981416 | − | 0.191892i | \(-0.938538\pi\) | ||||
−0.981416 | + | 0.191892i | \(0.938538\pi\) | |||||||
\(752\) | − 1.73582e50i | − 0.804806i | ||||||||
\(753\) | 5.28418e50i | 2.39368i | ||||||||
\(754\) | −2.62856e50 | −1.16337 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.02161e48 | −0.0254437 | ||||||||
\(757\) | 3.15399e50i | 1.30221i | 0.758987 | + | 0.651106i | \(0.225695\pi\) | ||||
−0.758987 | + | 0.651106i | \(0.774305\pi\) | |||||||
\(758\) | 2.01180e50i | 0.811659i | ||||||||
\(759\) | 2.06176e50 | 0.812845 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.65841e50 | −1.37740 | −0.688702 | − | 0.725045i | \(-0.741819\pi\) | ||||
−0.688702 | + | 0.725045i | \(0.741819\pi\) | |||||||
\(762\) | 2.39624e50i | 0.881696i | ||||||||
\(763\) | − 5.82458e48i | − 0.0209452i | ||||||||
\(764\) | 5.78202e49 | 0.203210 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.57382e49 | 0.0528387 | ||||||||
\(767\) | − 1.94011e50i | − 0.636661i | ||||||||
\(768\) | − 2.85192e50i | − 0.914778i | ||||||||
\(769\) | 2.07264e50 | 0.649849 | 0.324925 | − | 0.945740i | \(-0.394661\pi\) | ||||
0.324925 | + | 0.945740i | \(0.394661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.42552e50 | 2.82393 | ||||||||
\(772\) | − 9.83516e49i | − 0.288057i | ||||||||
\(773\) | − 2.04692e50i | − 0.586084i | −0.956100 | − | 0.293042i | \(-0.905332\pi\) | ||||
0.956100 | − | 0.293042i | \(-0.0946675\pi\) | |||||||
\(774\) | 1.13737e49 | 0.0318371 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.96729e50 | −0.526367 | ||||||||
\(777\) | − 1.74747e50i | − 0.457133i | ||||||||
\(778\) | 3.14521e50i | 0.804465i | ||||||||
\(779\) | −3.41484e49 | −0.0854013 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30853e50 | −0.312889 | ||||||||
\(782\) | 7.60622e49i | 0.177849i | ||||||||
\(783\) | 2.17983e50i | 0.498415i | ||||||||
\(784\) | −3.21860e50 | −0.719673 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.37432e50 | 0.293897 | ||||||||
\(787\) | − 2.74398e50i | − 0.573882i | −0.957948 | − | 0.286941i | \(-0.907362\pi\) | ||||
0.957948 | − | 0.286941i | \(-0.0926383\pi\) | |||||||
\(788\) | − 8.20177e49i | − 0.167764i | ||||||||
\(789\) | 1.45994e49 | 0.0292071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.73282e49 | 0.0523025 | ||||||||
\(792\) | − 8.14219e50i | − 1.52423i | ||||||||
\(793\) | 3.78619e49i | 0.0693301i | ||||||||
\(794\) | 6.54491e50 | 1.17232 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.38388e49 | 0.0580012 | ||||||||
\(797\) | 3.73868e50i | 0.626899i | 0.949605 | + | 0.313450i | \(0.101485\pi\) | ||||
−0.949605 | + | 0.313450i | \(0.898515\pi\) | |||||||
\(798\) | 2.81921e49i | 0.0462463i | ||||||||
\(799\) | −2.58612e50 | −0.415030 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00662e51 | 1.54631 | ||||||||
\(802\) | 9.13117e49i | 0.137238i | ||||||||
\(803\) | − 1.20967e51i | − 1.77887i | ||||||||
\(804\) | 4.03447e50 | 0.580505 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.78725e50 | 0.383983 | ||||||||
\(807\) | 4.51827e50i | 0.609095i | ||||||||
\(808\) | − 7.74862e50i | − 1.02218i | ||||||||
\(809\) | 3.87407e50 | 0.500114 | 0.250057 | − | 0.968231i | \(-0.419551\pi\) | ||||
0.250057 | + | 0.968231i | \(0.419551\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.21816e50 | −1.13967 | −0.569835 | − | 0.821759i | \(-0.692993\pi\) | ||||
−0.569835 | + | 0.821759i | \(0.692993\pi\) | |||||||
\(812\) | 2.85758e49i | 0.0345754i | ||||||||
\(813\) | − 1.42488e50i | − 0.168730i | ||||||||
\(814\) | 1.13853e51 | 1.31952 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.04823e50 | 0.449456 | ||||||||
\(817\) | 3.90203e48i | 0.00424038i | ||||||||
\(818\) | 5.53933e50i | 0.589216i | ||||||||
\(819\) | −4.31341e50 | −0.449110 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.64737e51 | 1.64357 | 0.821783 | − | 0.569801i | \(-0.192980\pi\) | ||||
0.821783 | + | 0.569801i | \(0.192980\pi\) | |||||||
\(822\) | − 1.22633e51i | − 1.19771i | ||||||||
\(823\) | 6.02163e50i | 0.575727i | 0.957671 | + | 0.287864i | \(0.0929449\pi\) | ||||
−0.957671 | + | 0.287864i | \(0.907055\pi\) | |||||||
\(824\) | −1.73618e51 | −1.62505 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.09973e49 | 0.0726641 | ||||||||
\(827\) | − 4.30476e50i | − 0.378097i | −0.981968 | − | 0.189048i | \(-0.939460\pi\) | ||||
0.981968 | − | 0.189048i | \(-0.0605403\pi\) | |||||||
\(828\) | − 1.72432e50i | − 0.148282i | ||||||||
\(829\) | −8.88751e50 | −0.748300 | −0.374150 | − | 0.927368i | \(-0.622065\pi\) | ||||
−0.374150 | + | 0.927368i | \(0.622065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.55364e51 | −2.06131 | ||||||||
\(832\) | − 2.23362e51i | − 1.76543i | ||||||||
\(833\) | 4.79525e50i | 0.371128i | ||||||||
\(834\) | −1.50328e51 | −1.13929 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.78297e49 | 0.0347606 | ||||||||
\(837\) | − 2.31142e50i | − 0.164507i | ||||||||
\(838\) | − 1.26992e51i | − 0.885126i | ||||||||
\(839\) | −3.76912e50 | −0.257280 | −0.128640 | − | 0.991691i | \(-0.541061\pi\) | ||||
−0.128640 | + | 0.991691i | \(0.541061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.92875e50 | −0.322706 | ||||||||
\(842\) | 4.57730e50i | 0.293527i | ||||||||
\(843\) | 1.41210e51i | 0.886916i | ||||||||
\(844\) | −1.32997e50 | −0.0818179 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.25144e51 | −1.32886 | ||||||||
\(847\) | − 1.35744e49i | − 0.00784804i | ||||||||
\(848\) | − 8.83551e50i | − 0.500385i | ||||||||
\(849\) | −3.68407e51 | −2.04382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.40817e51 | 0.749699 | ||||||||
\(852\) | 1.88077e50i | 0.0980940i | ||||||||
\(853\) | 3.00248e51i | 1.53417i | 0.641547 | + | 0.767083i | \(0.278293\pi\) | ||||
−0.641547 | + | 0.767083i | \(0.721707\pi\) | |||||||
\(854\) | −1.58069e49 | −0.00791286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.49122e51 | −1.19708 | ||||||||
\(857\) | − 2.46088e50i | − 0.115858i | −0.998321 | − | 0.0579291i | \(-0.981550\pi\) | ||||
0.998321 | − | 0.0579291i | \(-0.0184497\pi\) | |||||||
\(858\) | − 4.82977e51i | − 2.22792i | ||||||||
\(859\) | −2.64506e51 | −1.19551 | −0.597757 | − | 0.801677i | \(-0.703941\pi\) | ||||
−0.597757 | + | 0.801677i | \(0.703941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.74868e50 | 0.162676 | ||||||||
\(862\) | − 1.02117e51i | − 0.434233i | ||||||||
\(863\) | 9.93861e50i | 0.414130i | 0.978327 | + | 0.207065i | \(0.0663911\pi\) | ||||
−0.978327 | + | 0.207065i | \(0.933609\pi\) | |||||||
\(864\) | −6.02270e50 | −0.245924 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.66184e51 | −1.43594 | ||||||||
\(867\) | 3.42107e51i | 1.31470i | ||||||||
\(868\) | − 3.03009e49i | − 0.0114120i | ||||||||
\(869\) | 4.00794e51 | 1.47936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.13268e51 | 2.88347 | ||||||||
\(872\) | − 3.18554e50i | − 0.110699i | ||||||||
\(873\) | 2.00100e51i | 0.681550i | ||||||||
\(874\) | −2.27181e50 | −0.0758441 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.73867e51 | −0.557695 | ||||||||
\(877\) | − 2.79832e50i | − 0.0879842i | −0.999032 | − | 0.0439921i | \(-0.985992\pi\) | ||||
0.999032 | − | 0.0439921i | \(-0.0140076\pi\) | |||||||
\(878\) | 3.16623e50i | 0.0975861i | ||||||||
\(879\) | 6.58876e51 | 1.99067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.95050e50 | −0.172773 | −0.0863863 | − | 0.996262i | \(-0.527532\pi\) | ||||
−0.0863863 | + | 0.996262i | \(0.527532\pi\) | |||||||
\(882\) | 4.17469e51i | 1.18829i | ||||||||
\(883\) | 3.85350e51i | 1.07533i | 0.843157 | + | 0.537667i | \(0.180694\pi\) | ||||
−0.843157 | + | 0.537667i | \(0.819306\pi\) | |||||||
\(884\) | −4.63973e50 | −0.126934 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.96755e51 | 1.30633 | ||||||||
\(887\) | − 4.56338e50i | − 0.117658i | −0.998268 | − | 0.0588292i | \(-0.981263\pi\) | ||||
0.998268 | − | 0.0588292i | \(-0.0187367\pi\) | |||||||
\(888\) | − 9.55716e51i | − 2.41603i | ||||||||
\(889\) | 5.25119e50 | 0.130160 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.94590e51 | 0.463724 | ||||||||
\(892\) | 5.05498e50i | 0.118123i | ||||||||
\(893\) | − 7.72416e50i | − 0.176991i | ||||||||
\(894\) | 9.95996e51 | 2.23795 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.50354e50 | 0.118919 | ||||||||
\(897\) | − 5.97362e51i | − 1.26581i | ||||||||
\(898\) | 9.39122e50i | 0.195158i | ||||||||
\(899\) | −1.09689e51 | −0.223548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.31637e51 | −0.258044 | ||||||||
\(902\) | 2.44237e51i | 0.469567i | ||||||||
\(903\) | − 4.28351e49i | − 0.00807726i | ||||||||
\(904\) | 1.49462e51 | 0.276428 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.04998e51 | −1.43236 | ||||||||
\(907\) | − 4.12286e51i | − 0.719566i | −0.933036 | − | 0.359783i | \(-0.882851\pi\) | ||||
0.933036 | − | 0.359783i | \(-0.117149\pi\) | |||||||
\(908\) | − 7.38298e50i | − 0.126395i | ||||||||
\(909\) | −7.88139e51 | −1.32353 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.95561e51 | 1.12399 | 0.561996 | − | 0.827140i | \(-0.310034\pi\) | ||||
0.561996 | + | 0.827140i | \(0.310034\pi\) | |||||||
\(912\) | 1.20911e51i | 0.191672i | ||||||||
\(913\) | 8.86621e51i | 1.37879i | ||||||||
\(914\) | 7.72094e51 | 1.17791 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.29806e51 | −0.190601 | ||||||||
\(917\) | − 3.01173e50i | − 0.0433863i | ||||||||
\(918\) | − 1.47761e51i | − 0.208840i | ||||||||
\(919\) | −1.23335e51 | −0.171027 | −0.0855136 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855136 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.83420e51 | 0.645329 | ||||||||
\(922\) | 6.15821e51i | 0.806610i | ||||||||
\(923\) | 3.79125e51i | 0.487251i | ||||||||
\(924\) | −5.25057e50 | −0.0662136 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.07023e51 | 0.737076 | ||||||||
\(927\) | 1.76592e52i | 2.10415i | ||||||||
\(928\) | 2.85810e51i | 0.334185i | ||||||||
\(929\) | 9.97208e51 | 1.14422 | 0.572112 | − | 0.820176i | \(-0.306124\pi\) | ||||
0.572112 | + | 0.820176i | \(0.306124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.43224e51 | −0.158269 | ||||||||
\(932\) | − 1.12051e51i | − 0.121517i | ||||||||
\(933\) | 7.69232e51i | 0.818707i | ||||||||
\(934\) | −3.92536e51 | −0.410024 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.35906e52 | −2.37363 | ||||||||
\(937\) | 6.01334e51i | 0.593844i | 0.954902 | + | 0.296922i | \(0.0959602\pi\) | ||||
−0.954902 | + | 0.296922i | \(0.904040\pi\) | |||||||
\(938\) | 3.39529e51i | 0.329100i | ||||||||
\(939\) | 1.25626e52 | 1.19517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.38035e52 | 1.26523 | 0.632617 | − | 0.774465i | \(-0.281981\pi\) | ||||
0.632617 | + | 0.774465i | \(0.281981\pi\) | |||||||
\(942\) | 8.56268e51i | 0.770405i | ||||||||
\(943\) | 3.02081e51i | 0.266789i | ||||||||
\(944\) | 3.47384e51 | 0.301162 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.79083e50 | 0.0233151 | ||||||||
\(947\) | − 9.01648e51i | − 0.739456i | −0.929140 | − | 0.369728i | \(-0.879451\pi\) | ||||
0.929140 | − | 0.369728i | \(-0.120549\pi\) | |||||||
\(948\) | − 5.76067e51i | − 0.463796i | ||||||||
\(949\) | −3.50482e52 | −2.77017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.83121e52 | −1.39502 | ||||||||
\(952\) | − 1.13128e51i | − 0.0846105i | ||||||||
\(953\) | − 4.32450e51i | − 0.317549i | −0.987315 | − | 0.158774i | \(-0.949246\pi\) | ||||
0.987315 | − | 0.158774i | \(-0.0507542\pi\) | |||||||
\(954\) | −1.14601e52 | −0.826214 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.55633e51 | −0.247166 | ||||||||
\(957\) | 1.90071e52i | 1.29705i | ||||||||
\(958\) | − 1.45348e52i | − 0.973897i | ||||||||
\(959\) | −2.68741e51 | −0.176810 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.46006e52 | −0.926216 | ||||||||
\(962\) | − 3.29869e52i | − 2.05484i | ||||||||
\(963\) | 2.53391e52i | 1.55000i | ||||||||
\(964\) | −2.36503e51 | −0.142066 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.49391e51 | 0.144471 | ||||||||
\(967\) | − 1.91085e51i | − 0.108709i | −0.998522 | − | 0.0543543i | \(-0.982690\pi\) | ||||
0.998522 | − | 0.0543543i | \(-0.0173101\pi\) | |||||||
\(968\) | − 7.42403e50i | − 0.0414783i | ||||||||
\(969\) | 1.80141e51 | 0.0988431 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.54698e52 | 1.34800 | 0.674000 | − | 0.738732i | \(-0.264575\pi\) | ||||
0.674000 | + | 0.738732i | \(0.264575\pi\) | |||||||
\(972\) | − 5.20394e51i | − 0.270504i | ||||||||
\(973\) | 3.29432e51i | 0.168186i | ||||||||
\(974\) | 1.17796e52 | 0.590675 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.77932e50 | −0.0327955 | ||||||||
\(977\) | 2.34465e52i | 1.11410i | 0.830480 | + | 0.557048i | \(0.188066\pi\) | ||||
−0.830480 | + | 0.557048i | \(0.811934\pi\) | |||||||
\(978\) | − 4.91625e52i | − 2.29459i | ||||||||
\(979\) | 2.47001e52 | 1.13240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.24012e51 | −0.143335 | ||||||||
\(982\) | − 1.40197e52i | − 0.609238i | ||||||||
\(983\) | − 1.06892e52i | − 0.456308i | −0.973625 | − | 0.228154i | \(-0.926731\pi\) | ||||
0.973625 | − | 0.228154i | \(-0.0732690\pi\) | |||||||
\(984\) | 2.05021e52 | 0.859772 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.01207e51 | −0.283792 | ||||||||
\(987\) | 8.47931e51i | 0.337140i | ||||||||
\(988\) | − 1.38579e51i | − 0.0541314i | ||||||||
\(989\) | 3.45178e50 | 0.0132467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.97227e52 | 0.730597 | 0.365298 | − | 0.930891i | \(-0.380967\pi\) | ||||
0.365298 | + | 0.930891i | \(0.380967\pi\) | |||||||
\(992\) | − 3.03064e51i | − 0.110301i | ||||||||
\(993\) | 2.16387e52i | 0.773782i | ||||||||
\(994\) | −1.58280e51 | −0.0556114 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.27435e52 | 0.432266 | ||||||||
\(997\) | − 1.44359e52i | − 0.481149i | −0.970631 | − | 0.240575i | \(-0.922664\pi\) | ||||
0.970631 | − | 0.240575i | \(-0.0773358\pi\) | |||||||
\(998\) | − 2.90388e52i | − 0.951029i | ||||||||
\(999\) | −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 | 25.36.b.a.24.2 | 6 | ||
5.2 | odd | 4 | 25.36.a.a.1.3 | 3 | |||
5.3 | odd | 4 | 1.36.a.a.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 25.36.b.a.24.5 | 6 | ||
15.8 | even | 4 | 9.36.a.b.1.3 | 3 | |||
20.3 | even | 4 | 16.36.a.d.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.36.a.a.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
9.36.a.b.1.3 | 3 | 15.8 | even | 4 | |||
16.36.a.d.1.3 | 3 | 20.3 | even | 4 | |||
25.36.a.a.1.3 | 3 | 5.2 | odd | 4 | |||
25.36.b.a.24.2 | 6 | 1.1 | even | 1 | trivial | ||
25.36.b.a.24.5 | 6 | 5.4 | even | 2 | inner |