Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(197.998389976\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.26.b.b.49.2 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4096.00i | − 0.707107i | ||||||||
\(3\) | 162864.i | 0.176933i | 0.996079 | + | 0.0884666i | \(0.0281967\pi\) | ||||
−0.996079 | + | 0.0884666i | \(0.971803\pi\) | |||||||
\(4\) | −1.67772e7 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.67091e8 | 0.125111 | ||||||||
\(7\) | 1.76009e10i | 0.480628i | 0.970695 | + | 0.240314i | \(0.0772504\pi\) | ||||
−0.970695 | + | 0.240314i | \(0.922750\pi\) | |||||||
\(8\) | 6.87195e10i | 0.353553i | ||||||||
\(9\) | 8.20764e11 | 0.968695 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.12404e13 | −1.07987 | −0.539936 | − | 0.841706i | \(-0.681552\pi\) | ||||
−0.539936 | + | 0.841706i | \(0.681552\pi\) | |||||||
\(12\) | − 2.73240e12i | − 0.0884666i | ||||||||
\(13\) | 4.24221e12i | 0.0505010i | 0.999681 | + | 0.0252505i | \(0.00803834\pi\) | ||||
−0.999681 | + | 0.0252505i | \(0.991962\pi\) | |||||||
\(14\) | 7.20933e13 | 0.339855 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.13786e15i | 0.473670i | 0.971550 | + | 0.236835i | \(0.0761101\pi\) | ||||
−0.971550 | + | 0.236835i | \(0.923890\pi\) | |||||||
\(18\) | − 3.36185e15i | − 0.684971i | ||||||||
\(19\) | −2.98985e15 | −0.309905 | −0.154953 | − | 0.987922i | \(-0.549522\pi\) | ||||
−0.154953 | + | 0.987922i | \(0.549522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.86655e15 | −0.0850391 | ||||||||
\(22\) | 4.60406e16i | 0.763585i | ||||||||
\(23\) | − 1.22305e17i | − 1.16372i | −0.813290 | − | 0.581859i | \(-0.802325\pi\) | ||||
0.813290 | − | 0.581859i | \(-0.197675\pi\) | |||||||
\(24\) | −1.11919e16 | −0.0625553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.73761e16 | 0.0357096 | ||||||||
\(27\) | 2.71666e17i | 0.348328i | ||||||||
\(28\) | − 2.95294e17i | − 0.240314i | ||||||||
\(29\) | 2.12048e18 | 1.11291 | 0.556453 | − | 0.830879i | \(-0.312162\pi\) | ||||
0.556453 | + | 0.830879i | \(0.312162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.22586e18 | 0.963594 | 0.481797 | − | 0.876283i | \(-0.339984\pi\) | ||||
0.481797 | + | 0.876283i | \(0.339984\pi\) | |||||||
\(32\) | − 1.15292e18i | − 0.176777i | ||||||||
\(33\) | − 1.83065e18i | − 0.191065i | ||||||||
\(34\) | 4.66066e18 | 0.334935 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.37701e19 | −0.484347 | ||||||||
\(37\) | − 2.41679e19i | − 0.603555i | −0.953378 | − | 0.301778i | \(-0.902420\pi\) | ||||
0.953378 | − | 0.301778i | \(-0.0975800\pi\) | |||||||
\(38\) | 1.22464e19i | 0.219136i | ||||||||
\(39\) | −6.90903e17 | −0.00893531 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.61564e20 | −1.11827 | −0.559136 | − | 0.829076i | \(-0.688867\pi\) | ||||
−0.559136 | + | 0.829076i | \(0.688867\pi\) | |||||||
\(42\) | 1.17414e19i | 0.0601317i | ||||||||
\(43\) | − 3.11612e20i | − 1.18921i | −0.804018 | − | 0.594605i | \(-0.797308\pi\) | ||||
0.804018 | − | 0.594605i | \(-0.202692\pi\) | |||||||
\(44\) | 1.88582e20 | 0.539936 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00963e20 | −0.822873 | ||||||||
\(47\) | 1.22586e21i | 1.53892i | 0.638694 | + | 0.769461i | \(0.279475\pi\) | ||||
−0.638694 | + | 0.769461i | \(0.720525\pi\) | |||||||
\(48\) | 4.58421e19i | 0.0442333i | ||||||||
\(49\) | 1.03128e21 | 0.768997 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.85316e20 | −0.0838079 | ||||||||
\(52\) | − 7.11725e19i | − 0.0252505i | ||||||||
\(53\) | − 4.78915e20i | − 0.133909i | −0.997756 | − | 0.0669546i | \(-0.978672\pi\) | ||||
0.997756 | − | 0.0669546i | \(-0.0213283\pi\) | |||||||
\(54\) | 1.11274e21 | 0.246305 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.20952e21 | −0.169928 | ||||||||
\(57\) | − 4.86938e20i | − 0.0548325i | ||||||||
\(58\) | − 8.68547e21i | − 0.786943i | ||||||||
\(59\) | −1.21434e22 | −0.888566 | −0.444283 | − | 0.895887i | \(-0.646541\pi\) | ||||
−0.444283 | + | 0.895887i | \(0.646541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.03328e22 | −0.980786 | −0.490393 | − | 0.871501i | \(-0.663147\pi\) | ||||
−0.490393 | + | 0.871501i | \(0.663147\pi\) | |||||||
\(62\) | − 1.73091e22i | − 0.681364i | ||||||||
\(63\) | 1.44462e22i | 0.465582i | ||||||||
\(64\) | −4.72237e21 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.49835e21 | −0.135104 | ||||||||
\(67\) | − 6.15653e22i | − 0.919180i | −0.888131 | − | 0.459590i | \(-0.847996\pi\) | ||||
0.888131 | − | 0.459590i | \(-0.152004\pi\) | |||||||
\(68\) | − 1.90901e22i | − 0.236835i | ||||||||
\(69\) | 1.99192e22 | 0.205900 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.34077e23 | 0.969669 | 0.484835 | − | 0.874606i | \(-0.338880\pi\) | ||||
0.484835 | + | 0.874606i | \(0.338880\pi\) | |||||||
\(72\) | 5.64025e22i | 0.342485i | ||||||||
\(73\) | 2.23779e23i | 1.14362i | 0.820385 | + | 0.571811i | \(0.193759\pi\) | ||||
−0.820385 | + | 0.571811i | \(0.806241\pi\) | |||||||
\(74\) | −9.89916e22 | −0.426778 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.01613e22 | 0.154953 | ||||||||
\(77\) | − 1.97841e23i | − 0.519017i | ||||||||
\(78\) | 2.82994e21i | 0.00631822i | ||||||||
\(79\) | −3.82350e23 | −0.727985 | −0.363992 | − | 0.931402i | \(-0.618587\pi\) | ||||
−0.363992 | + | 0.931402i | \(0.618587\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.51179e23 | 0.907064 | ||||||||
\(82\) | 6.61767e23i | 0.790737i | ||||||||
\(83\) | − 7.71818e23i | − 0.792572i | −0.918127 | − | 0.396286i | \(-0.870299\pi\) | ||||
0.918127 | − | 0.396286i | \(-0.129701\pi\) | |||||||
\(84\) | 4.80928e22 | 0.0425195 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.27636e24 | −0.840899 | ||||||||
\(87\) | 3.45349e23i | 0.196910i | ||||||||
\(88\) | − 7.72433e23i | − 0.381792i | ||||||||
\(89\) | 8.40581e23 | 0.360748 | 0.180374 | − | 0.983598i | \(-0.442269\pi\) | ||||
0.180374 | + | 0.983598i | \(0.442269\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.46667e22 | −0.0242722 | ||||||||
\(92\) | 2.05195e24i | 0.581859i | ||||||||
\(93\) | 6.88241e23i | 0.170492i | ||||||||
\(94\) | 5.02111e24 | 1.08818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.87769e23 | 0.0312777 | ||||||||
\(97\) | 6.19164e24i | 0.906064i | 0.891494 | + | 0.453032i | \(0.149658\pi\) | ||||
−0.891494 | + | 0.453032i | \(0.850342\pi\) | |||||||
\(98\) | − 4.22411e24i | − 0.543763i | ||||||||
\(99\) | −9.22569e24 | −1.04607 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.64342e24 | 0.586644 | 0.293322 | − | 0.956014i | \(-0.405239\pi\) | ||||
0.293322 | + | 0.956014i | \(0.405239\pi\) | |||||||
\(102\) | 7.59053e23i | 0.0592612i | ||||||||
\(103\) | 1.36741e25i | 0.945004i | 0.881330 | + | 0.472502i | \(0.156649\pi\) | ||||
−0.881330 | + | 0.472502i | \(0.843351\pi\) | |||||||
\(104\) | −2.91522e23 | −0.0178548 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.96164e24 | −0.0946881 | ||||||||
\(107\) | − 1.97392e24i | − 0.0847290i | −0.999102 | − | 0.0423645i | \(-0.986511\pi\) | ||||
0.999102 | − | 0.0423645i | \(-0.0134891\pi\) | |||||||
\(108\) | − 4.55779e24i | − 0.174164i | ||||||||
\(109\) | −4.86252e25 | −1.65588 | −0.827942 | − | 0.560813i | \(-0.810489\pi\) | ||||
−0.827942 | + | 0.560813i | \(0.810489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.93608e24 | 0.106789 | ||||||||
\(112\) | 4.95421e24i | 0.120157i | ||||||||
\(113\) | 4.58410e25i | 0.994886i | 0.867497 | + | 0.497443i | \(0.165728\pi\) | ||||
−0.867497 | + | 0.497443i | \(0.834272\pi\) | |||||||
\(114\) | −1.99450e24 | −0.0387724 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.55757e25 | −0.556453 | ||||||||
\(117\) | 3.48185e24i | 0.0489201i | ||||||||
\(118\) | 4.97393e25i | 0.628311i | ||||||||
\(119\) | −2.00273e25 | −0.227659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.79989e25 | 0.166123 | ||||||||
\(122\) | 8.32832e25i | 0.693521i | ||||||||
\(123\) | − 2.63130e25i | − 0.197859i | ||||||||
\(124\) | −7.08982e25 | −0.481797 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.91715e25 | 0.329216 | ||||||||
\(127\) | 1.31721e26i | 0.663911i | 0.943295 | + | 0.331955i | \(0.107708\pi\) | ||||
−0.943295 | + | 0.331955i | \(0.892292\pi\) | |||||||
\(128\) | 1.93428e25i | 0.0883883i | ||||||||
\(129\) | 5.07504e25 | 0.210411 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.36281e25 | −0.251856 | −0.125928 | − | 0.992039i | \(-0.540191\pi\) | ||||
−0.125928 | + | 0.992039i | \(0.540191\pi\) | |||||||
\(132\) | 3.07132e25i | 0.0955326i | ||||||||
\(133\) | − 5.26240e25i | − 0.148949i | ||||||||
\(134\) | −2.52171e26 | −0.649959 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.81929e25 | −0.167468 | ||||||||
\(137\) | 9.58320e26i | 1.87285i | 0.350866 | + | 0.936426i | \(0.385887\pi\) | ||||
−0.350866 | + | 0.936426i | \(0.614113\pi\) | |||||||
\(138\) | − 8.15889e25i | − 0.145594i | ||||||||
\(139\) | 4.90566e26 | 0.799858 | 0.399929 | − | 0.916546i | \(-0.369035\pi\) | ||||
0.399929 | + | 0.916546i | \(0.369035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.99648e26 | −0.272286 | ||||||||
\(142\) | − 5.49178e26i | − 0.685660i | ||||||||
\(143\) | − 4.76840e25i | − 0.0545346i | ||||||||
\(144\) | 2.31025e26 | 0.242174 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.16597e26 | 0.808664 | ||||||||
\(147\) | 1.67958e26i | 0.136061i | ||||||||
\(148\) | 4.05470e26i | 0.301778i | ||||||||
\(149\) | −9.09615e26 | −0.622342 | −0.311171 | − | 0.950354i | \(-0.600721\pi\) | ||||
−0.311171 | + | 0.950354i | \(0.600721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.24560e26 | 0.477541 | 0.238770 | − | 0.971076i | \(-0.423256\pi\) | ||||
0.238770 | + | 0.971076i | \(0.423256\pi\) | |||||||
\(152\) | − 2.05461e26i | − 0.109568i | ||||||||
\(153\) | 9.33911e26i | 0.458841i | ||||||||
\(154\) | −8.10355e26 | −0.367000 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.15914e25 | 0.00446765 | ||||||||
\(157\) | − 9.72907e26i | − 0.346199i | −0.984904 | − | 0.173099i | \(-0.944622\pi\) | ||||
0.984904 | − | 0.173099i | \(-0.0553782\pi\) | |||||||
\(158\) | 1.56610e27i | 0.514763i | ||||||||
\(159\) | 7.79981e25 | 0.0236930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.15269e27 | 0.559316 | ||||||||
\(162\) | − 2.66723e27i | − 0.641391i | ||||||||
\(163\) | − 2.54973e27i | − 0.567740i | −0.958863 | − | 0.283870i | \(-0.908382\pi\) | ||||
0.958863 | − | 0.283870i | \(-0.0916184\pi\) | |||||||
\(164\) | 2.71060e27 | 0.559136 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.16137e27 | −0.560433 | ||||||||
\(167\) | − 8.09067e27i | − 1.33054i | −0.746602 | − | 0.665271i | \(-0.768316\pi\) | ||||
0.746602 | − | 0.665271i | \(-0.231684\pi\) | |||||||
\(168\) | − 1.96988e26i | − 0.0300659i | ||||||||
\(169\) | 7.03841e27 | 0.997450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.45396e27 | −0.300203 | ||||||||
\(172\) | 5.22799e27i | 0.594605i | ||||||||
\(173\) | 4.51555e27i | 0.477677i | 0.971059 | + | 0.238838i | \(0.0767667\pi\) | ||||
−0.971059 | + | 0.238838i | \(0.923233\pi\) | |||||||
\(174\) | 1.41455e27 | 0.139236 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.16388e27 | −0.269968 | ||||||||
\(177\) | − 1.97772e27i | − 0.157217i | ||||||||
\(178\) | − 3.44302e27i | − 0.255088i | ||||||||
\(179\) | 1.94694e28 | 1.34490 | 0.672450 | − | 0.740143i | \(-0.265242\pi\) | ||||
0.672450 | + | 0.740143i | \(0.265242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.21952e28 | −0.733176 | −0.366588 | − | 0.930383i | \(-0.619474\pi\) | ||||
−0.366588 | + | 0.930383i | \(0.619474\pi\) | |||||||
\(182\) | 3.05835e26i | 0.0171630i | ||||||||
\(183\) | − 3.31148e27i | − 0.173534i | ||||||||
\(184\) | 8.40477e27 | 0.411437 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.81903e27 | 0.120556 | ||||||||
\(187\) | − 1.27899e28i | − 0.511503i | ||||||||
\(188\) | − 2.05665e28i | − 0.769461i | ||||||||
\(189\) | −4.78156e27 | −0.167416 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.11119e28 | 1.87590 | 0.937948 | − | 0.346775i | \(-0.112723\pi\) | ||||
0.937948 | + | 0.346775i | \(0.112723\pi\) | |||||||
\(192\) | − 7.69103e26i | − 0.0221167i | ||||||||
\(193\) | 6.48935e28i | 1.74878i | 0.485226 | + | 0.874389i | \(0.338737\pi\) | ||||
−0.485226 | + | 0.874389i | \(0.661263\pi\) | |||||||
\(194\) | 2.53610e28 | 0.640684 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.73020e28 | −0.384498 | ||||||||
\(197\) | 3.17525e28i | 0.662140i | 0.943606 | + | 0.331070i | \(0.107410\pi\) | ||||
−0.943606 | + | 0.331070i | \(0.892590\pi\) | |||||||
\(198\) | 3.77884e28i | 0.739680i | ||||||||
\(199\) | 7.39236e28 | 1.35869 | 0.679344 | − | 0.733820i | \(-0.262265\pi\) | ||||
0.679344 | + | 0.733820i | \(0.262265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00268e28 | 0.162634 | ||||||||
\(202\) | − 2.72115e28i | − 0.414820i | ||||||||
\(203\) | 3.73223e28i | 0.534894i | ||||||||
\(204\) | 3.10908e27 | 0.0419040 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.60091e28 | 0.668218 | ||||||||
\(207\) | − 1.00384e29i | − 1.12729i | ||||||||
\(208\) | 1.19408e27i | 0.0126253i | ||||||||
\(209\) | 3.36070e28 | 0.334658 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.18016e28 | 0.104330 | 0.0521652 | − | 0.998638i | \(-0.483388\pi\) | ||||
0.0521652 | + | 0.998638i | \(0.483388\pi\) | |||||||
\(212\) | 8.03487e27i | 0.0669546i | ||||||||
\(213\) | 2.18363e28i | 0.171567i | ||||||||
\(214\) | −8.08517e27 | −0.0599124 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.86687e28 | −0.123152 | ||||||||
\(217\) | 7.43790e28i | 0.463131i | ||||||||
\(218\) | 1.99169e29i | 1.17089i | ||||||||
\(219\) | −3.64455e28 | −0.202345 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.82702e27 | −0.0239208 | ||||||||
\(222\) | − 1.61222e28i | − 0.0755112i | ||||||||
\(223\) | 1.55992e28i | 0.0690704i | 0.999403 | + | 0.0345352i | \(0.0109951\pi\) | ||||
−0.999403 | + | 0.0345352i | \(0.989005\pi\) | |||||||
\(224\) | 2.02924e28 | 0.0849639 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.87765e29 | 0.703491 | ||||||||
\(227\) | 3.57748e29i | 1.26839i | 0.773171 | + | 0.634197i | \(0.218669\pi\) | ||||
−0.773171 | + | 0.634197i | \(0.781331\pi\) | |||||||
\(228\) | 8.16947e27i | 0.0274163i | ||||||||
\(229\) | 6.16468e29 | 1.95870 | 0.979348 | − | 0.202179i | \(-0.0648024\pi\) | ||||
0.979348 | + | 0.202179i | \(0.0648024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.22211e28 | 0.0918313 | ||||||||
\(232\) | 1.45718e29i | 0.393472i | ||||||||
\(233\) | 5.68344e29i | 1.45433i | 0.686464 | + | 0.727163i | \(0.259162\pi\) | ||||
−0.686464 | + | 0.727163i | \(0.740838\pi\) | |||||||
\(234\) | 1.42617e28 | 0.0345917 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.03732e29 | 0.444283 | ||||||||
\(237\) | − 6.22710e28i | − 0.128805i | ||||||||
\(238\) | 8.20317e28i | 0.160979i | ||||||||
\(239\) | 5.96388e29 | 1.11059 | 0.555296 | − | 0.831653i | \(-0.312605\pi\) | ||||
0.555296 | + | 0.831653i | \(0.312605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.97938e29 | −0.835530 | −0.417765 | − | 0.908555i | \(-0.637187\pi\) | ||||
−0.417765 | + | 0.908555i | \(0.637187\pi\) | |||||||
\(242\) | − 7.37237e28i | − 0.117467i | ||||||||
\(243\) | 3.36233e29i | 0.508817i | ||||||||
\(244\) | 3.41128e29 | 0.490393 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.07778e29 | −0.139908 | ||||||||
\(247\) | − 1.26835e28i | − 0.0156505i | ||||||||
\(248\) | 2.90399e29i | 0.340682i | ||||||||
\(249\) | 1.25701e29 | 0.140232 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.75610e30 | 1.77267 | 0.886335 | − | 0.463044i | \(-0.153243\pi\) | ||||
0.886335 | + | 0.463044i | \(0.153243\pi\) | |||||||
\(252\) | − 2.42367e29i | − 0.232791i | ||||||||
\(253\) | 1.37476e30i | 1.25667i | ||||||||
\(254\) | 5.39531e29 | 0.469456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | − 1.22065e30i | − 0.917123i | −0.888663 | − | 0.458562i | \(-0.848365\pi\) | ||||
0.888663 | − | 0.458562i | \(-0.151635\pi\) | |||||||
\(258\) | − 2.07874e29i | − 0.148783i | ||||||||
\(259\) | 4.25376e29 | 0.290086 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.74041e30 | 1.07807 | ||||||||
\(262\) | 3.01581e29i | 0.178089i | ||||||||
\(263\) | 2.27827e30i | 1.28280i | 0.767207 | + | 0.641399i | \(0.221646\pi\) | ||||
−0.767207 | + | 0.641399i | \(0.778354\pi\) | |||||||
\(264\) | 1.25801e29 | 0.0675518 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.15548e29 | −0.105323 | ||||||||
\(267\) | 1.36900e29i | 0.0638284i | ||||||||
\(268\) | 1.03289e30i | 0.459590i | ||||||||
\(269\) | 3.12815e30 | 1.32857 | 0.664284 | − | 0.747480i | \(-0.268736\pi\) | ||||
0.664284 | + | 0.747480i | \(0.268736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.31818e30 | 0.510339 | 0.255170 | − | 0.966896i | \(-0.417869\pi\) | ||||
0.255170 | + | 0.966896i | \(0.417869\pi\) | |||||||
\(272\) | 3.20278e29i | 0.118417i | ||||||||
\(273\) | − 1.21605e28i | − 0.00429456i | ||||||||
\(274\) | 3.92528e30 | 1.32431 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.34188e29 | −0.102950 | ||||||||
\(277\) | − 2.11862e30i | − 0.623815i | −0.950112 | − | 0.311908i | \(-0.899032\pi\) | ||||
0.950112 | − | 0.311908i | \(-0.100968\pi\) | |||||||
\(278\) | − 2.00936e30i | − 0.565585i | ||||||||
\(279\) | 3.46844e30 | 0.933429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.37141e30 | −1.56822 | −0.784109 | − | 0.620623i | \(-0.786880\pi\) | ||||
−0.784109 | + | 0.620623i | \(0.786880\pi\) | |||||||
\(282\) | 8.17758e29i | 0.192536i | ||||||||
\(283\) | 3.00725e30i | 0.677391i | 0.940896 | + | 0.338695i | \(0.109986\pi\) | ||||
−0.940896 | + | 0.338695i | \(0.890014\pi\) | |||||||
\(284\) | −2.24943e30 | −0.484835 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.95314e29 | −0.0385618 | ||||||||
\(287\) | − 2.84368e30i | − 0.537473i | ||||||||
\(288\) | − 9.46276e29i | − 0.171243i | ||||||||
\(289\) | 4.47591e30 | 0.775637 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00840e30 | −0.160313 | ||||||||
\(292\) | − 3.75438e30i | − 0.571811i | ||||||||
\(293\) | − 7.19334e30i | − 1.04975i | −0.851180 | − | 0.524875i | \(-0.824112\pi\) | ||||
0.851180 | − | 0.524875i | \(-0.175888\pi\) | |||||||
\(294\) | 6.87956e29 | 0.0962097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.66080e30 | 0.213389 | ||||||||
\(297\) | − 3.05362e30i | − 0.376149i | ||||||||
\(298\) | 3.72578e30i | 0.440063i | ||||||||
\(299\) | 5.18845e29 | 0.0587690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.48465e30 | 0.571568 | ||||||||
\(302\) | − 3.37740e30i | − 0.337672i | ||||||||
\(303\) | 1.08197e30i | 0.103797i | ||||||||
\(304\) | −8.41567e29 | −0.0774763 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.82530e30 | 0.324450 | ||||||||
\(307\) | 6.08638e30i | 0.495597i | 0.968812 | + | 0.247799i | \(0.0797072\pi\) | ||||
−0.968812 | + | 0.247799i | \(0.920293\pi\) | |||||||
\(308\) | 3.31921e30i | 0.259508i | ||||||||
\(309\) | −2.22702e30 | −0.167203 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.60168e30 | 0.249460 | 0.124730 | − | 0.992191i | \(-0.460194\pi\) | ||||
0.124730 | + | 0.992191i | \(0.460194\pi\) | |||||||
\(312\) | − 4.74785e28i | − 0.00315911i | ||||||||
\(313\) | 3.07166e30i | 0.196367i | 0.995168 | + | 0.0981835i | \(0.0313032\pi\) | ||||
−0.995168 | + | 0.0981835i | \(0.968697\pi\) | |||||||
\(314\) | −3.98503e30 | −0.244800 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.41476e30 | 0.363992 | ||||||||
\(317\) | 2.80660e31i | 1.53088i | 0.643510 | + | 0.765438i | \(0.277478\pi\) | ||||
−0.643510 | + | 0.765438i | \(0.722522\pi\) | |||||||
\(318\) | − 3.19480e29i | − 0.0167535i | ||||||||
\(319\) | −2.38349e31 | −1.20180 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.21480e29 | 0.0149914 | ||||||||
\(322\) | − 8.81740e30i | − 0.395496i | ||||||||
\(323\) | − 3.40201e30i | − 0.146793i | ||||||||
\(324\) | −1.09250e31 | −0.453532 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.04437e31 | −0.401453 | ||||||||
\(327\) | − 7.91929e30i | − 0.292981i | ||||||||
\(328\) | − 1.11026e31i | − 0.395369i | ||||||||
\(329\) | −2.15762e31 | −0.739649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.79893e31 | −0.571694 | −0.285847 | − | 0.958275i | \(-0.592275\pi\) | ||||
−0.285847 | + | 0.958275i | \(0.592275\pi\) | |||||||
\(332\) | 1.29490e31i | 0.396286i | ||||||||
\(333\) | − 1.98361e31i | − 0.584661i | ||||||||
\(334\) | −3.31394e31 | −0.940835 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.06863e29 | −0.0212598 | ||||||||
\(337\) | 3.37680e31i | 0.857296i | 0.903472 | + | 0.428648i | \(0.141010\pi\) | ||||
−0.903472 | + | 0.428648i | \(0.858990\pi\) | |||||||
\(338\) | − 2.88293e31i | − 0.705303i | ||||||||
\(339\) | −7.46585e30 | −0.176028 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.75003e31 | −1.04056 | ||||||||
\(342\) | 1.00514e31i | 0.212276i | ||||||||
\(343\) | 4.17554e31i | 0.850230i | ||||||||
\(344\) | 2.14138e31 | 0.420450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.84957e31 | 0.337769 | ||||||||
\(347\) | 3.07070e30i | 0.0540902i | 0.999634 | + | 0.0270451i | \(0.00860977\pi\) | ||||
−0.999634 | + | 0.0270451i | \(0.991390\pi\) | |||||||
\(348\) | − 5.79400e30i | − 0.0984550i | ||||||||
\(349\) | −4.73553e31 | −0.776338 | −0.388169 | − | 0.921588i | \(-0.626892\pi\) | ||||
−0.388169 | + | 0.921588i | \(0.626892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.15246e30 | −0.0175909 | ||||||||
\(352\) | 1.29593e31i | 0.190896i | ||||||||
\(353\) | − 1.13735e32i | − 1.61700i | −0.588496 | − | 0.808500i | \(-0.700280\pi\) | ||||
0.588496 | − | 0.808500i | \(-0.299720\pi\) | |||||||
\(354\) | −8.10074e30 | −0.111169 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.41026e31 | −0.180374 | ||||||||
\(357\) | − 3.26172e30i | − 0.0402805i | ||||||||
\(358\) | − 7.97467e31i | − 0.950988i | ||||||||
\(359\) | −7.58317e31 | −0.873313 | −0.436656 | − | 0.899628i | \(-0.643837\pi\) | ||||
−0.436656 | + | 0.899628i | \(0.643837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.41373e31 | −0.903959 | ||||||||
\(362\) | 4.99517e31i | 0.518434i | ||||||||
\(363\) | 2.93138e30i | 0.0293927i | ||||||||
\(364\) | 1.25270e30 | 0.0121361 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.35638e31 | −0.122707 | ||||||||
\(367\) | − 6.65888e31i | − 0.582205i | −0.956692 | − | 0.291102i | \(-0.905978\pi\) | ||||
0.956692 | − | 0.291102i | \(-0.0940220\pi\) | |||||||
\(368\) | − 3.44259e31i | − 0.290930i | ||||||||
\(369\) | −1.32606e32 | −1.08326 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.42934e30 | 0.0643605 | ||||||||
\(372\) | − 1.15468e31i | − 0.0852459i | ||||||||
\(373\) | 4.03892e31i | 0.288340i | 0.989553 | + | 0.144170i | \(0.0460512\pi\) | ||||
−0.989553 | + | 0.144170i | \(0.953949\pi\) | |||||||
\(374\) | −5.23875e31 | −0.361687 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.42403e31 | −0.544091 | ||||||||
\(377\) | 8.99550e30i | 0.0562029i | ||||||||
\(378\) | 1.95853e31i | 0.118381i | ||||||||
\(379\) | −3.00036e32 | −1.75462 | −0.877309 | − | 0.479926i | \(-0.840664\pi\) | ||||
−0.877309 | + | 0.479926i | \(0.840664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.14527e31 | −0.117468 | ||||||||
\(382\) | − 2.50314e32i | − 1.32646i | ||||||||
\(383\) | − 5.83515e31i | − 0.299273i | −0.988741 | − | 0.149636i | \(-0.952190\pi\) | ||||
0.988741 | − | 0.149636i | \(-0.0478103\pi\) | |||||||
\(384\) | −3.15025e30 | −0.0156388 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.65804e32 | 1.23657 | ||||||||
\(387\) | − 2.55760e32i | − 1.15198i | ||||||||
\(388\) | − 1.03879e32i | − 0.453032i | ||||||||
\(389\) | 4.65526e32 | 1.96595 | 0.982977 | − | 0.183726i | \(-0.0588161\pi\) | ||||
0.982977 | + | 0.183726i | \(0.0588161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39166e32 | 0.551218 | ||||||||
\(392\) | 7.08688e31i | 0.271881i | ||||||||
\(393\) | − 1.19914e31i | − 0.0445617i | ||||||||
\(394\) | 1.30058e32 | 0.468204 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.54781e32 | 0.523033 | ||||||||
\(397\) | 3.57088e32i | 1.16922i | 0.811316 | + | 0.584608i | \(0.198752\pi\) | ||||
−0.811316 | + | 0.584608i | \(0.801248\pi\) | |||||||
\(398\) | − 3.02791e32i | − 0.960737i | ||||||||
\(399\) | 8.57055e30 | 0.0263540 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.85410e32 | −1.69105 | −0.845523 | − | 0.533940i | \(-0.820711\pi\) | ||||
−0.845523 | + | 0.533940i | \(0.820711\pi\) | |||||||
\(402\) | − 4.10696e31i | − 0.114999i | ||||||||
\(403\) | 1.79270e31i | 0.0486625i | ||||||||
\(404\) | −1.11458e32 | −0.293322 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.52872e32 | 0.378227 | ||||||||
\(407\) | 2.71656e32i | 0.651762i | ||||||||
\(408\) | − 1.27348e31i | − 0.0296306i | ||||||||
\(409\) | 5.85778e32 | 1.32188 | 0.660939 | − | 0.750439i | \(-0.270158\pi\) | ||||
0.660939 | + | 0.750439i | \(0.270158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.56076e32 | −0.331370 | ||||||||
\(412\) | − 2.29413e32i | − 0.472502i | ||||||||
\(413\) | − 2.13734e32i | − 0.427070i | ||||||||
\(414\) | −4.11172e32 | −0.797113 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.89093e30 | 0.00892740 | ||||||||
\(417\) | 7.98956e31i | 0.141521i | ||||||||
\(418\) | − 1.37654e32i | − 0.236639i | ||||||||
\(419\) | 2.15945e32 | 0.360303 | 0.180152 | − | 0.983639i | \(-0.442341\pi\) | ||||
0.180152 | + | 0.983639i | \(0.442341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.57301e32 | −0.404497 | −0.202249 | − | 0.979334i | \(-0.564825\pi\) | ||||
−0.202249 | + | 0.979334i | \(0.564825\pi\) | |||||||
\(422\) | − 4.83394e31i | − 0.0737727i | ||||||||
\(423\) | 1.00614e33i | 1.49075i | ||||||||
\(424\) | 3.29108e31 | 0.0473441 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.94413e31 | 0.121316 | ||||||||
\(427\) | − 3.57876e32i | − 0.471394i | ||||||||
\(428\) | 3.31169e31i | 0.0423645i | ||||||||
\(429\) | 7.76601e30 | 0.00964899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.87420e32 | −0.571396 | −0.285698 | − | 0.958320i | \(-0.592225\pi\) | ||||
−0.285698 | + | 0.958320i | \(0.592225\pi\) | |||||||
\(432\) | 7.64671e31i | 0.0870819i | ||||||||
\(433\) | 1.34127e33i | 1.48394i | 0.670433 | + | 0.741970i | \(0.266108\pi\) | ||||
−0.670433 | + | 0.741970i | \(0.733892\pi\) | |||||||
\(434\) | 3.04656e32 | 0.327483 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.15795e32 | 0.827942 | ||||||||
\(437\) | 3.65674e32i | 0.360642i | ||||||||
\(438\) | 1.49281e32i | 0.143079i | ||||||||
\(439\) | −3.20033e32 | −0.298118 | −0.149059 | − | 0.988828i | \(-0.547624\pi\) | ||||
−0.149059 | + | 0.988828i | \(0.547624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.46435e32 | 0.744923 | ||||||||
\(442\) | 1.97715e31i | 0.0169146i | ||||||||
\(443\) | 1.50899e33i | 1.25499i | 0.778622 | + | 0.627494i | \(0.215919\pi\) | ||||
−0.778622 | + | 0.627494i | \(0.784081\pi\) | |||||||
\(444\) | −6.60364e31 | −0.0533945 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.38944e31 | 0.0488402 | ||||||||
\(447\) | − 1.48144e32i | − 0.110113i | ||||||||
\(448\) | − 8.31179e31i | − 0.0600785i | ||||||||
\(449\) | 7.32432e32 | 0.514859 | 0.257429 | − | 0.966297i | \(-0.417125\pi\) | ||||
0.257429 | + | 0.966297i | \(0.417125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.81604e33 | 1.20759 | ||||||||
\(452\) | − 7.69084e32i | − 0.497443i | ||||||||
\(453\) | 1.34291e32i | 0.0844928i | ||||||||
\(454\) | 1.46534e33 | 0.896890 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.34621e31 | 0.0193862 | ||||||||
\(457\) | 1.80848e33i | 1.01944i | 0.860341 | + | 0.509718i | \(0.170250\pi\) | ||||
−0.860341 | + | 0.509718i | \(0.829750\pi\) | |||||||
\(458\) | − 2.52505e33i | − 1.38501i | ||||||||
\(459\) | −3.09116e32 | −0.164992 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.02348e33 | −1.02291 | −0.511454 | − | 0.859311i | \(-0.670893\pi\) | ||||
−0.511454 | + | 0.859311i | \(0.670893\pi\) | |||||||
\(462\) | − 1.31978e32i | − 0.0649345i | ||||||||
\(463\) | 4.00896e33i | 1.91986i | 0.280239 | + | 0.959930i | \(0.409586\pi\) | ||||
−0.280239 | + | 0.959930i | \(0.590414\pi\) | |||||||
\(464\) | 5.96861e32 | 0.278226 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.32794e33 | 1.02836 | ||||||||
\(467\) | 1.11951e33i | 0.481466i | 0.970591 | + | 0.240733i | \(0.0773878\pi\) | ||||
−0.970591 | + | 0.240733i | \(0.922612\pi\) | |||||||
\(468\) | − 5.84158e31i | − 0.0244600i | ||||||||
\(469\) | 1.08360e33 | 0.441784 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.58452e32 | 0.0612541 | ||||||||
\(472\) | − 8.34487e32i | − 0.314155i | ||||||||
\(473\) | 3.50264e33i | 1.28420i | ||||||||
\(474\) | −2.55062e32 | −0.0910786 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.36002e32 | 0.113830 | ||||||||
\(477\) | − 3.93077e32i | − 0.129717i | ||||||||
\(478\) | − 2.44280e33i | − 0.785308i | ||||||||
\(479\) | 5.66968e33 | 1.77568 | 0.887841 | − | 0.460151i | \(-0.152205\pi\) | ||||
0.887841 | + | 0.460151i | \(0.152205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.02525e32 | 0.0304802 | ||||||||
\(482\) | 2.03955e33i | 0.590809i | ||||||||
\(483\) | 3.50595e32i | 0.0989616i | ||||||||
\(484\) | −3.01972e32 | −0.0830615 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.37721e33 | 0.359788 | ||||||||
\(487\) | − 1.76093e33i | − 0.448363i | −0.974547 | − | 0.224182i | \(-0.928029\pi\) | ||||
0.974547 | − | 0.224182i | \(-0.0719709\pi\) | |||||||
\(488\) | − 1.39726e33i | − 0.346760i | ||||||||
\(489\) | 4.15260e32 | 0.100452 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.58354e33 | −1.28348 | −0.641742 | − | 0.766920i | \(-0.721788\pi\) | ||||
−0.641742 | + | 0.766920i | \(0.721788\pi\) | |||||||
\(492\) | 4.41459e32i | 0.0989297i | ||||||||
\(493\) | 2.41280e33i | 0.527150i | ||||||||
\(494\) | −5.19518e31 | −0.0110666 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.18947e33 | 0.240899 | ||||||||
\(497\) | 2.35987e33i | 0.466050i | ||||||||
\(498\) | − 5.14873e32i | − 0.0991593i | ||||||||
\(499\) | 4.37368e33 | 0.821468 | 0.410734 | − | 0.911755i | \(-0.365273\pi\) | ||||
0.410734 | + | 0.911755i | \(0.365273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31768e33 | 0.235417 | ||||||||
\(502\) | − 7.19299e33i | − 1.25347i | ||||||||
\(503\) | − 4.32379e33i | − 0.734962i | −0.930031 | − | 0.367481i | \(-0.880220\pi\) | ||||
0.930031 | − | 0.367481i | \(-0.119780\pi\) | |||||||
\(504\) | −9.92734e32 | −0.164608 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.63101e33 | 0.888597 | ||||||||
\(507\) | 1.14630e33i | 0.176482i | ||||||||
\(508\) | − 2.20992e33i | − 0.331955i | ||||||||
\(509\) | −1.81736e33 | −0.266360 | −0.133180 | − | 0.991092i | \(-0.542519\pi\) | ||||
−0.133180 | + | 0.991092i | \(0.542519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.93870e33 | −0.549657 | ||||||||
\(512\) | − 3.24519e32i | − 0.0441942i | ||||||||
\(513\) | − 8.12238e32i | − 0.107948i | ||||||||
\(514\) | −4.99979e33 | −0.648504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.51451e32 | −0.105205 | ||||||||
\(517\) | − 1.37791e34i | − 1.66184i | ||||||||
\(518\) | − 1.74234e33i | − 0.205121i | ||||||||
\(519\) | −7.35420e32 | −0.0845169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.48131e33 | −0.819419 | −0.409710 | − | 0.912216i | \(-0.634370\pi\) | ||||
−0.409710 | + | 0.912216i | \(0.634370\pi\) | |||||||
\(522\) | − 7.12872e33i | − 0.762308i | ||||||||
\(523\) | 1.34405e34i | 1.40328i | 0.712531 | + | 0.701641i | \(0.247549\pi\) | ||||
−0.712531 | + | 0.701641i | \(0.752451\pi\) | |||||||
\(524\) | 1.23527e33 | 0.125928 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.33180e33 | 0.907076 | ||||||||
\(527\) | 4.80842e33i | 0.456426i | ||||||||
\(528\) | − 5.15283e32i | − 0.0477663i | ||||||||
\(529\) | −3.91286e33 | −0.354240 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.96685e33 | −0.860749 | ||||||||
\(532\) | 8.82883e32i | 0.0744746i | ||||||||
\(533\) | − 6.85390e32i | − 0.0564739i | ||||||||
\(534\) | 5.60744e32 | 0.0451335 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.23073e33 | 0.324979 | ||||||||
\(537\) | 3.17087e33i | 0.237958i | ||||||||
\(538\) | − 1.28129e34i | − 0.939440i | ||||||||
\(539\) | −1.15919e34 | −0.830418 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.16620e33 | −0.626937 | −0.313468 | − | 0.949599i | \(-0.601491\pi\) | ||||
−0.313468 | + | 0.949599i | \(0.601491\pi\) | |||||||
\(542\) | − 5.39927e33i | − 0.360864i | ||||||||
\(543\) | − 1.98617e33i | − 0.129723i | ||||||||
\(544\) | 1.31186e33 | 0.0837338 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.98095e31 | −0.00303671 | ||||||||
\(547\) | 2.47403e34i | 1.47423i | 0.675770 | + | 0.737113i | \(0.263811\pi\) | ||||
−0.675770 | + | 0.737113i | \(0.736189\pi\) | |||||||
\(548\) | − 1.60779e34i | − 0.936426i | ||||||||
\(549\) | −1.66884e34 | −0.950082 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.33989e33 | −0.344895 | ||||||||
\(552\) | 1.36883e33i | 0.0727968i | ||||||||
\(553\) | − 6.72970e33i | − 0.349890i | ||||||||
\(554\) | −8.67787e33 | −0.441104 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.23034e33 | −0.399929 | ||||||||
\(557\) | 2.03083e34i | 0.964905i | 0.875922 | + | 0.482452i | \(0.160254\pi\) | ||||
−0.875922 | + | 0.482452i | \(0.839746\pi\) | |||||||
\(558\) | − 1.42067e34i | − 0.660034i | ||||||||
\(559\) | 1.32192e33 | 0.0600564 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.08302e33 | 0.0905018 | ||||||||
\(562\) | 2.60973e34i | 1.10890i | ||||||||
\(563\) | − 3.26297e34i | − 1.35599i | −0.735064 | − | 0.677997i | \(-0.762848\pi\) | ||||
0.735064 | − | 0.677997i | \(-0.237152\pi\) | |||||||
\(564\) | 3.34954e33 | 0.136143 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.23177e34 | 0.478988 | ||||||||
\(567\) | 1.14613e34i | 0.435960i | ||||||||
\(568\) | 9.21368e33i | 0.342830i | ||||||||
\(569\) | −3.41443e34 | −1.24284 | −0.621419 | − | 0.783478i | \(-0.713444\pi\) | ||||
−0.621419 | + | 0.783478i | \(0.713444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.36450e33 | 0.0475359 | 0.0237679 | − | 0.999718i | \(-0.492434\pi\) | ||||
0.0237679 | + | 0.999718i | \(0.492434\pi\) | |||||||
\(572\) | 8.00005e32i | 0.0272673i | ||||||||
\(573\) | 9.95293e33i | 0.331908i | ||||||||
\(574\) | −1.16477e34 | −0.380051 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.87595e33 | −0.121087 | ||||||||
\(577\) | − 3.92987e34i | − 1.20138i | −0.799481 | − | 0.600691i | \(-0.794892\pi\) | ||||
0.799481 | − | 0.600691i | \(-0.205108\pi\) | |||||||
\(578\) | − 1.83333e34i | − 0.548458i | ||||||||
\(579\) | −1.05688e34 | −0.309417 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.35847e34 | 0.380933 | ||||||||
\(582\) | 4.13039e33i | 0.113358i | ||||||||
\(583\) | 5.38319e33i | 0.144605i | ||||||||
\(584\) | −1.53780e34 | −0.404332 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.94639e34 | −0.742285 | ||||||||
\(587\) | − 3.72718e34i | − 0.919187i | −0.888129 | − | 0.459594i | \(-0.847995\pi\) | ||||
0.888129 | − | 0.459594i | \(-0.152005\pi\) | |||||||
\(588\) | − 2.81787e33i | − 0.0680305i | ||||||||
\(589\) | −1.26347e34 | −0.298623 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.17134e33 | −0.117155 | ||||||||
\(592\) | − 6.80265e33i | − 0.150889i | ||||||||
\(593\) | 7.75169e34i | 1.68350i | 0.539870 | + | 0.841749i | \(0.318474\pi\) | ||||
−0.539870 | + | 0.841749i | \(0.681526\pi\) | |||||||
\(594\) | −1.25076e34 | −0.265978 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.52608e34 | 0.311171 | ||||||||
\(597\) | 1.20395e34i | 0.240397i | ||||||||
\(598\) | − 2.12519e33i | − 0.0415559i | ||||||||
\(599\) | −6.18820e34 | −1.18503 | −0.592515 | − | 0.805559i | \(-0.701865\pi\) | ||||
−0.592515 | + | 0.805559i | \(0.701865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.95852e34 | −0.543430 | −0.271715 | − | 0.962378i | \(-0.587591\pi\) | ||||
−0.271715 | + | 0.962378i | \(0.587591\pi\) | |||||||
\(602\) | − 2.24651e34i | − 0.404160i | ||||||||
\(603\) | − 5.05305e34i | − 0.890405i | ||||||||
\(604\) | −1.38338e34 | −0.238770 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.43177e33 | 0.0733954 | ||||||||
\(607\) | 1.00617e35i | 1.63234i | 0.577810 | + | 0.816171i | \(0.303907\pi\) | ||||
−0.577810 | + | 0.816171i | \(0.696093\pi\) | |||||||
\(608\) | 3.44706e33i | 0.0547840i | ||||||||
\(609\) | −6.07845e33 | −0.0946405 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.20034e33 | −0.0777171 | ||||||||
\(612\) | − 1.56684e34i | − 0.229421i | ||||||||
\(613\) | − 4.47446e34i | − 0.641926i | −0.947092 | − | 0.320963i | \(-0.895993\pi\) | ||||
0.947092 | − | 0.320963i | \(-0.104007\pi\) | |||||||
\(614\) | 2.49298e34 | 0.350440 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.35955e34 | 0.183500 | ||||||||
\(617\) | − 2.58799e34i | − 0.342293i | −0.985246 | − | 0.171147i | \(-0.945253\pi\) | ||||
0.985246 | − | 0.171147i | \(-0.0547472\pi\) | |||||||
\(618\) | 9.12187e33i | 0.118230i | ||||||||
\(619\) | 1.37687e35 | 1.74889 | 0.874443 | − | 0.485129i | \(-0.161227\pi\) | ||||
0.874443 | + | 0.485129i | \(0.161227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.32262e34 | 0.405355 | ||||||||
\(622\) | − 1.47525e34i | − 0.176395i | ||||||||
\(623\) | 1.47950e34i | 0.173386i | ||||||||
\(624\) | −1.94472e32 | −0.00223383 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.25815e34 | 0.138852 | ||||||||
\(627\) | 5.47337e33i | 0.0592121i | ||||||||
\(628\) | 1.63227e34i | 0.173099i | ||||||||
\(629\) | 2.74996e34 | 0.285886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.83484e34 | −0.283244 | −0.141622 | − | 0.989921i | \(-0.545232\pi\) | ||||
−0.141622 | + | 0.989921i | \(0.545232\pi\) | |||||||
\(632\) | − 2.62749e34i | − 0.257381i | ||||||||
\(633\) | 1.92206e33i | 0.0184595i | ||||||||
\(634\) | 1.14958e35 | 1.08249 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.30859e33 | −0.0118465 | ||||||||
\(637\) | 4.37489e33i | 0.0388351i | ||||||||
\(638\) | 9.76279e34i | 0.849798i | ||||||||
\(639\) | 1.10045e35 | 0.939314 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.36368e34 | −0.111940 | −0.0559701 | − | 0.998432i | \(-0.517825\pi\) | ||||
−0.0559701 | + | 0.998432i | \(0.517825\pi\) | |||||||
\(642\) | − 1.31678e33i | − 0.0106005i | ||||||||
\(643\) | 8.47939e32i | 0.00669464i | 0.999994 | + | 0.00334732i | \(0.00106549\pi\) | ||||
−0.999994 | + | 0.00334732i | \(0.998935\pi\) | |||||||
\(644\) | −3.61161e34 | −0.279658 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.39346e34 | −0.103798 | ||||||||
\(647\) | − 2.50478e35i | − 1.83007i | −0.403379 | − | 0.915033i | \(-0.632164\pi\) | ||||
0.403379 | − | 0.915033i | \(-0.367836\pi\) | |||||||
\(648\) | 4.47487e34i | 0.320696i | ||||||||
\(649\) | 1.36496e35 | 0.959537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.21137e34 | −0.0819432 | ||||||||
\(652\) | 4.27774e34i | 0.283870i | ||||||||
\(653\) | − 1.55775e35i | − 1.01410i | −0.861916 | − | 0.507051i | \(-0.830735\pi\) | ||||
0.861916 | − | 0.507051i | \(-0.169265\pi\) | |||||||
\(654\) | −3.24374e34 | −0.207169 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.54763e34 | −0.279568 | ||||||||
\(657\) | 1.83669e35i | 1.10782i | ||||||||
\(658\) | 8.83760e34i | 0.523011i | ||||||||
\(659\) | 1.85485e35 | 1.07706 | 0.538531 | − | 0.842605i | \(-0.318979\pi\) | ||||
0.538531 | + | 0.842605i | \(0.318979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.92623e35 | 1.63602 | 0.818012 | − | 0.575202i | \(-0.195076\pi\) | ||||
0.818012 | + | 0.575202i | \(0.195076\pi\) | |||||||
\(662\) | 7.36840e34i | 0.404248i | ||||||||
\(663\) | − 7.86148e32i | − 0.00423239i | ||||||||
\(664\) | 5.30389e34 | 0.280217 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.12488e34 | −0.413417 | ||||||||
\(667\) | − 2.59346e35i | − 1.29511i | ||||||||
\(668\) | 1.35739e35i | 0.665271i | ||||||||
\(669\) | −2.54055e33 | −0.0122209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.28548e35 | 1.05912 | ||||||||
\(672\) | 3.30491e33i | 0.0150329i | ||||||||
\(673\) | 2.13829e35i | 0.954724i | 0.878707 | + | 0.477362i | \(0.158407\pi\) | ||||
−0.878707 | + | 0.477362i | \(0.841593\pi\) | |||||||
\(674\) | 1.38314e35 | 0.606200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.18085e35 | −0.498725 | ||||||||
\(677\) | − 1.59208e35i | − 0.660096i | −0.943964 | − | 0.330048i | \(-0.892935\pi\) | ||||
0.943964 | − | 0.330048i | \(-0.107065\pi\) | |||||||
\(678\) | 3.05801e34i | 0.124471i | ||||||||
\(679\) | −1.08978e35 | −0.435480 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.82643e34 | −0.224421 | ||||||||
\(682\) | 1.94561e35i | 0.735786i | ||||||||
\(683\) | 4.23003e35i | 1.57067i | 0.619071 | + | 0.785335i | \(0.287509\pi\) | ||||
−0.619071 | + | 0.785335i | \(0.712491\pi\) | |||||||
\(684\) | 4.11706e34 | 0.150102 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.71030e35 | 0.601203 | ||||||||
\(687\) | 1.00401e35i | 0.346559i | ||||||||
\(688\) | − 8.77111e34i | − 0.297303i | ||||||||
\(689\) | 2.03166e33 | 0.00676255 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.02759e35 | 0.971899 | 0.485950 | − | 0.873987i | \(-0.338474\pi\) | ||||
0.485950 | + | 0.873987i | \(0.338474\pi\) | |||||||
\(692\) | − 7.57584e34i | − 0.238838i | ||||||||
\(693\) | − 1.62380e35i | − 0.502769i | ||||||||
\(694\) | 1.25776e34 | 0.0382476 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.37322e34 | −0.0696182 | ||||||||
\(697\) | − 1.83837e35i | − 0.529692i | ||||||||
\(698\) | 1.93967e35i | 0.548954i | ||||||||
\(699\) | −9.25627e34 | −0.257319 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.66145e35 | 0.713909 | 0.356954 | − | 0.934122i | \(-0.383815\pi\) | ||||
0.356954 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(702\) | 4.72049e33i | 0.0124386i | ||||||||
\(703\) | 7.22582e34i | 0.187045i | ||||||||
\(704\) | 5.30812e34 | 0.134984 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.65859e35 | −1.14339 | ||||||||
\(707\) | 1.16930e35i | 0.281958i | ||||||||
\(708\) | 3.31806e34i | 0.0786084i | ||||||||
\(709\) | −2.81745e34 | −0.0655810 | −0.0327905 | − | 0.999462i | \(-0.510439\pi\) | ||||
−0.0327905 | + | 0.999462i | \(0.510439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.13819e35 | −0.705195 | ||||||||
\(712\) | 5.77643e34i | 0.127544i | ||||||||
\(713\) | − 5.16846e35i | − 1.12135i | ||||||||
\(714\) | −1.33600e34 | −0.0284826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.26643e35 | −0.672450 | ||||||||
\(717\) | 9.71301e34i | 0.196501i | ||||||||
\(718\) | 3.10606e35i | 0.617526i | ||||||||
\(719\) | −2.87441e35 | −0.561613 | −0.280806 | − | 0.959764i | \(-0.590602\pi\) | ||||
−0.280806 | + | 0.959764i | \(0.590602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.40676e35 | −0.454195 | ||||||||
\(722\) | 3.44626e35i | 0.639195i | ||||||||
\(723\) | − 8.10962e34i | − 0.147833i | ||||||||
\(724\) | 2.04602e35 | 0.366588 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.20069e34 | 0.0207838 | ||||||||
\(727\) | 4.98046e35i | 0.847402i | 0.905802 | + | 0.423701i | \(0.139269\pi\) | ||||
−0.905802 | + | 0.423701i | \(0.860731\pi\) | |||||||
\(728\) | − 5.13105e33i | − 0.00858152i | ||||||||
\(729\) | 4.96977e35 | 0.817037 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.54570e35 | 0.563293 | ||||||||
\(732\) | 5.55575e34i | 0.0867668i | ||||||||
\(733\) | − 8.47339e35i | − 1.30094i | −0.759531 | − | 0.650471i | \(-0.774572\pi\) | ||||
0.759531 | − | 0.650471i | \(-0.225428\pi\) | |||||||
\(734\) | −2.72748e35 | −0.411681 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.41009e35 | −0.205718 | ||||||||
\(737\) | 6.92016e35i | 0.992597i | ||||||||
\(738\) | 5.43155e35i | 0.765983i | ||||||||
\(739\) | −7.12136e35 | −0.987433 | −0.493716 | − | 0.869623i | \(-0.664362\pi\) | ||||
−0.493716 | + | 0.869623i | \(0.664362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.06569e33 | 0.00276910 | ||||||||
\(742\) | − 3.45266e34i | − 0.0455098i | ||||||||
\(743\) | − 6.18867e35i | − 0.802116i | −0.916053 | − | 0.401058i | \(-0.868643\pi\) | ||||
0.916053 | − | 0.401058i | \(-0.131357\pi\) | |||||||
\(744\) | −4.72956e34 | −0.0602780 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.65434e35 | 0.203887 | ||||||||
\(747\) | − 6.33481e35i | − 0.767761i | ||||||||
\(748\) | 2.14579e35i | 0.255751i | ||||||||
\(749\) | 3.47427e34 | 0.0407231 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.34082e36 | 1.52009 | 0.760046 | − | 0.649869i | \(-0.225176\pi\) | ||||
0.760046 | + | 0.649869i | \(0.225176\pi\) | |||||||
\(752\) | 3.45048e35i | 0.384731i | ||||||||
\(753\) | 2.86006e35i | 0.313644i | ||||||||
\(754\) | 3.68456e34 | 0.0397414 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.02213e34 | 0.0837080 | ||||||||
\(757\) | − 8.81045e35i | − 0.904274i | −0.891949 | − | 0.452137i | \(-0.850662\pi\) | ||||
0.891949 | − | 0.452137i | \(-0.149338\pi\) | |||||||
\(758\) | 1.22895e36i | 1.24070i | ||||||||
\(759\) | −2.23899e35 | −0.222346 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.08045e35 | −0.872568 | −0.436284 | − | 0.899809i | \(-0.643706\pi\) | ||||
−0.436284 | + | 0.899809i | \(0.643706\pi\) | |||||||
\(762\) | 8.78701e34i | 0.0830623i | ||||||||
\(763\) | − 8.55847e35i | − 0.795865i | ||||||||
\(764\) | −1.02529e36 | −0.937948 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.39008e35 | −0.211618 | ||||||||
\(767\) | − 5.15148e34i | − 0.0448735i | ||||||||
\(768\) | 1.29034e34i | 0.0110583i | ||||||||
\(769\) | −1.57427e36 | −1.32739 | −0.663696 | − | 0.748003i | \(-0.731013\pi\) | ||||
−0.663696 | + | 0.748003i | \(0.731013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.98800e35 | 0.162270 | ||||||||
\(772\) | − 1.08873e36i | − 0.874389i | ||||||||
\(773\) | − 1.97307e36i | − 1.55919i | −0.626284 | − | 0.779595i | \(-0.715425\pi\) | ||||
0.626284 | − | 0.779595i | \(-0.284575\pi\) | |||||||
\(774\) | −1.04759e36 | −0.814574 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.25486e35 | −0.320342 | ||||||||
\(777\) | 6.92785e34i | 0.0513258i | ||||||||
\(778\) | − 1.90679e36i | − 1.39014i | ||||||||
\(779\) | 4.83052e35 | 0.346558 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.50707e36 | −1.04712 | ||||||||
\(782\) | − 5.70024e35i | − 0.389770i | ||||||||
\(783\) | 5.76061e35i | 0.387656i | ||||||||
\(784\) | 2.90279e35 | 0.192249 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.91166e34 | −0.0315099 | ||||||||
\(787\) | − 9.52553e35i | − 0.601458i | −0.953710 | − | 0.300729i | \(-0.902770\pi\) | ||||
0.953710 | − | 0.300729i | \(-0.0972299\pi\) | |||||||
\(788\) | − 5.32719e35i | − 0.331070i | ||||||||
\(789\) | −3.71048e35 | −0.226970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.06842e35 | −0.478170 | ||||||||
\(792\) | − 6.33985e35i | − 0.369840i | ||||||||
\(793\) | − 8.62560e34i | − 0.0495307i | ||||||||
\(794\) | 1.46263e36 | 0.826760 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.24023e36 | −0.679344 | ||||||||
\(797\) | − 3.70863e35i | − 0.199979i | −0.994989 | − | 0.0999894i | \(-0.968119\pi\) | ||||
0.994989 | − | 0.0999894i | \(-0.0318809\pi\) | |||||||
\(798\) | − 3.51050e34i | − 0.0186351i | ||||||||
\(799\) | −1.39485e36 | −0.728941 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.89918e35 | 0.349455 | ||||||||
\(802\) | 2.39784e36i | 1.19575i | ||||||||
\(803\) | − 2.51536e36i | − 1.23497i | ||||||||
\(804\) | −1.68221e35 | −0.0813168 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.34290e34 | 0.0344096 | ||||||||
\(807\) | 5.09463e35i | 0.235068i | ||||||||
\(808\) | 4.56532e35i | 0.207410i | ||||||||
\(809\) | 2.08152e36 | 0.931159 | 0.465580 | − | 0.885006i | \(-0.345846\pi\) | ||||
0.465580 | + | 0.885006i | \(0.345846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.20046e34 | −0.0399070 | −0.0199535 | − | 0.999801i | \(-0.506352\pi\) | ||||
−0.0199535 | + | 0.999801i | \(0.506352\pi\) | |||||||
\(812\) | − 6.26164e35i | − 0.267447i | ||||||||
\(813\) | 2.14684e35i | 0.0902960i | ||||||||
\(814\) | 1.11270e36 | 0.460865 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.21618e34 | −0.0209520 | ||||||||
\(817\) | 9.31673e35i | 0.368543i | ||||||||
\(818\) | − 2.39935e36i | − 0.934709i | ||||||||
\(819\) | −6.12837e34 | −0.0235124 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.64905e35 | 0.359083 | 0.179542 | − | 0.983750i | \(-0.442539\pi\) | ||||
0.179542 | + | 0.983750i | \(0.442539\pi\) | |||||||
\(822\) | 6.39286e35i | 0.234314i | ||||||||
\(823\) | 4.33977e35i | 0.156664i | 0.996927 | + | 0.0783319i | \(0.0249594\pi\) | ||||
−0.996927 | + | 0.0783319i | \(0.975041\pi\) | |||||||
\(824\) | −9.39677e35 | −0.334109 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.75456e35 | −0.301984 | ||||||||
\(827\) | − 1.42223e36i | − 0.483227i | −0.970373 | − | 0.241614i | \(-0.922323\pi\) | ||||
0.970373 | − | 0.241614i | \(-0.0776766\pi\) | |||||||
\(828\) | 1.68416e36i | 0.563644i | ||||||||
\(829\) | −4.07234e36 | −1.34249 | −0.671247 | − | 0.741234i | \(-0.734241\pi\) | ||||
−0.671247 | + | 0.741234i | \(0.734241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.45047e35 | 0.110374 | ||||||||
\(832\) | − 2.00333e34i | − 0.00631263i | ||||||||
\(833\) | 1.17344e36i | 0.364251i | ||||||||
\(834\) | 3.27252e35 | 0.100071 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.63832e35 | −0.167329 | ||||||||
\(837\) | 1.14802e36i | 0.335646i | ||||||||
\(838\) | − 8.84511e35i | − 0.254773i | ||||||||
\(839\) | −1.54259e36 | −0.437750 | −0.218875 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218875 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.66055e35 | 0.238559 | ||||||||
\(842\) | 1.05391e36i | 0.286023i | ||||||||
\(843\) | − 1.03767e36i | − 0.277470i | ||||||||
\(844\) | −1.97998e35 | −0.0521652 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.12115e36 | 1.05412 | ||||||||
\(847\) | 3.16798e35i | 0.0798434i | ||||||||
\(848\) | − 1.34803e35i | − 0.0334773i | ||||||||
\(849\) | −4.89773e35 | −0.119853 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.95586e36 | −0.702368 | ||||||||
\(852\) | − 3.66352e35i | − 0.0857834i | ||||||||
\(853\) | 7.94652e36i | 1.83364i | 0.399300 | + | 0.916820i | \(0.369253\pi\) | ||||
−0.399300 | + | 0.916820i | \(0.630747\pi\) | |||||||
\(854\) | −1.46586e36 | −0.333326 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.35647e35 | 0.0299562 | ||||||||
\(857\) | 7.37212e35i | 0.160447i | 0.996777 | + | 0.0802236i | \(0.0255634\pi\) | ||||
−0.996777 | + | 0.0802236i | \(0.974437\pi\) | |||||||
\(858\) | − 3.18096e34i | − 0.00682286i | ||||||||
\(859\) | 6.08537e36 | 1.28639 | 0.643195 | − | 0.765703i | \(-0.277609\pi\) | ||||
0.643195 | + | 0.765703i | \(0.277609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.63133e35 | 0.0950968 | ||||||||
\(862\) | 1.99647e36i | 0.404038i | ||||||||
\(863\) | 3.30325e36i | 0.658880i | 0.944177 | + | 0.329440i | \(0.106860\pi\) | ||||
−0.944177 | + | 0.329440i | \(0.893140\pi\) | |||||||
\(864\) | 3.13209e35 | 0.0615762 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.49382e36 | 1.04930 | ||||||||
\(867\) | 7.28965e35i | 0.137236i | ||||||||
\(868\) | − 1.24787e36i | − 0.231565i | ||||||||
\(869\) | 4.29775e36 | 0.786130 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.61173e35 | 0.0464195 | ||||||||
\(872\) | − 3.34150e36i | − 0.585444i | ||||||||
\(873\) | 5.08188e36i | 0.877700i | ||||||||
\(874\) | 1.49780e36 | 0.255013 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.11454e35 | 0.101172 | ||||||||
\(877\) | 2.53964e35i | 0.0414264i | 0.999785 | + | 0.0207132i | \(0.00659369\pi\) | ||||
−0.999785 | + | 0.0207132i | \(0.993406\pi\) | |||||||
\(878\) | 1.31085e36i | 0.210801i | ||||||||
\(879\) | 1.17154e36 | 0.185736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.01270e35 | 0.108065 | 0.0540327 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540327 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(882\) | − 3.46700e36i | − 0.526740i | ||||||||
\(883\) | 7.67538e36i | 1.14972i | 0.818253 | + | 0.574858i | \(0.194943\pi\) | ||||
−0.818253 | + | 0.574858i | \(0.805057\pi\) | |||||||
\(884\) | 8.09840e34 | 0.0119604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.18082e36 | 0.887410 | ||||||||
\(887\) | 1.19088e37i | 1.68586i | 0.538024 | + | 0.842929i | \(0.319171\pi\) | ||||
−0.538024 | + | 0.842929i | \(0.680829\pi\) | |||||||
\(888\) | 2.70485e35i | 0.0377556i | ||||||||
\(889\) | −2.31841e36 | −0.319094 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.31950e36 | −0.979513 | ||||||||
\(892\) | − 2.61712e35i | − 0.0345352i | ||||||||
\(893\) | − 3.66512e36i | − 0.476920i | ||||||||
\(894\) | −6.06796e35 | −0.0778617 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.40451e35 | −0.0424819 | ||||||||
\(897\) | 8.45012e34i | 0.0103982i | ||||||||
\(898\) | − 3.00004e36i | − 0.364060i | ||||||||
\(899\) | 8.96084e36 | 1.07239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.44937e35 | 0.0634288 | ||||||||
\(902\) | − 7.43851e36i | − 0.853895i | ||||||||
\(903\) | 8.93253e35i | 0.101129i | ||||||||
\(904\) | −3.15017e36 | −0.351745 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.50056e35 | 0.0597454 | ||||||||
\(907\) | − 6.98769e36i | − 0.748587i | −0.927310 | − | 0.374294i | \(-0.877885\pi\) | ||||
0.927310 | − | 0.374294i | \(-0.122115\pi\) | |||||||
\(908\) | − 6.00202e36i | − 0.634197i | ||||||||
\(909\) | 5.45268e36 | 0.568279 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.23719e36 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(912\) | − 1.37061e35i | − 0.0137081i | ||||||||
\(913\) | 8.67553e36i | 0.855877i | ||||||||
\(914\) | 7.40751e36 | 0.720850 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.03426e37 | −0.979348 | ||||||||
\(917\) | − 1.29592e36i | − 0.121049i | ||||||||
\(918\) | 1.26614e36i | 0.116667i | ||||||||
\(919\) | 8.31177e36 | 0.755526 | 0.377763 | − | 0.925902i | \(-0.376693\pi\) | ||||
0.377763 | + | 0.925902i | \(0.376693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.91251e35 | −0.0876877 | ||||||||
\(922\) | 8.28816e36i | 0.723305i | ||||||||
\(923\) | 5.68781e35i | 0.0489693i | ||||||||
\(924\) | −5.40581e35 | −0.0459157 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.64207e37 | 1.35755 | ||||||||
\(927\) | 1.12232e37i | 0.915420i | ||||||||
\(928\) | − 2.44474e36i | − 0.196736i | ||||||||
\(929\) | 1.48672e37 | 1.18041 | 0.590205 | − | 0.807253i | \(-0.299047\pi\) | ||||
0.590205 | + | 0.807253i | \(0.299047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.08336e36 | −0.238316 | ||||||||
\(932\) | − 9.53522e36i | − 0.727163i | ||||||||
\(933\) | 5.86585e35i | 0.0441378i | ||||||||
\(934\) | 4.58550e36 | 0.340448 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.39271e35 | −0.0172959 | ||||||||
\(937\) | − 2.25559e37i | − 1.60885i | −0.594055 | − | 0.804424i | \(-0.702474\pi\) | ||||
0.594055 | − | 0.804424i | \(-0.297526\pi\) | |||||||
\(938\) | − 4.43844e36i | − 0.312388i | ||||||||
\(939\) | −5.00263e35 | −0.0347439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.40580e37 | 1.62701 | 0.813504 | − | 0.581559i | \(-0.197557\pi\) | ||||
0.813504 | + | 0.581559i | \(0.197557\pi\) | |||||||
\(942\) | − 6.49017e35i | − 0.0433132i | ||||||||
\(943\) | 1.97602e37i | 1.30135i | ||||||||
\(944\) | −3.41806e36 | −0.222141 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.43468e37 | 0.908063 | ||||||||
\(947\) | 2.05868e35i | 0.0128592i | 0.999979 | + | 0.00642962i | \(0.00204662\pi\) | ||||
−0.999979 | + | 0.00642962i | \(0.997953\pi\) | |||||||
\(948\) | 1.04473e36i | 0.0644023i | ||||||||
\(949\) | −9.49316e35 | −0.0577541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.57094e36 | −0.270863 | ||||||||
\(952\) | − 1.37626e36i | − 0.0804896i | ||||||||
\(953\) | 7.96109e36i | 0.459528i | 0.973246 | + | 0.229764i | \(0.0737954\pi\) | ||||
−0.973246 | + | 0.229764i | \(0.926205\pi\) | |||||||
\(954\) | −1.61004e36 | −0.0917239 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.00057e37 | −0.555296 | ||||||||
\(957\) | − 3.88185e36i | − 0.212638i | ||||||||
\(958\) | − 2.32230e37i | − 1.25560i | ||||||||
\(959\) | −1.68673e37 | −0.900145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37487e36 | −0.0714859 | ||||||||
\(962\) | − 4.19943e35i | − 0.0215527i | ||||||||
\(963\) | − 1.62012e36i | − 0.0820765i | ||||||||
\(964\) | 8.35401e36 | 0.417765 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.43604e36 | 0.0699764 | ||||||||
\(967\) | − 4.83856e36i | − 0.232748i | −0.993205 | − | 0.116374i | \(-0.962873\pi\) | ||||
0.993205 | − | 0.116374i | \(-0.0371271\pi\) | |||||||
\(968\) | 1.23688e36i | 0.0587334i | ||||||||
\(969\) | 5.54066e35 | 0.0259725 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.24060e37 | 0.566749 | 0.283375 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283375 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(972\) | − 5.64105e36i | − 0.254409i | ||||||||
\(973\) | 8.63441e36i | 0.384434i | ||||||||
\(974\) | −7.21277e36 | −0.317041 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.72318e36 | −0.245197 | ||||||||
\(977\) | − 5.52484e36i | − 0.233688i | −0.993150 | − | 0.116844i | \(-0.962722\pi\) | ||||
0.993150 | − | 0.116844i | \(-0.0372778\pi\) | |||||||
\(978\) | − 1.70090e36i | − 0.0710303i | ||||||||
\(979\) | −9.44844e36 | −0.389562 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.99098e37 | −1.60405 | ||||||||
\(982\) | 2.28702e37i | 0.907561i | ||||||||
\(983\) | − 3.62327e37i | − 1.41965i | −0.704377 | − | 0.709826i | \(-0.748774\pi\) | ||||
0.704377 | − | 0.709826i | \(-0.251226\pi\) | |||||||
\(984\) | 1.80822e36 | 0.0699539 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.88281e36 | 0.372751 | ||||||||
\(987\) | − 3.51398e36i | − 0.130869i | ||||||||
\(988\) | 2.12795e35i | 0.00782526i | ||||||||
\(989\) | −3.81119e37 | −1.38391 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.55999e37 | −0.552334 | −0.276167 | − | 0.961110i | \(-0.589064\pi\) | ||||
−0.276167 | + | 0.961110i | \(0.589064\pi\) | |||||||
\(992\) | − 4.87209e36i | − 0.170341i | ||||||||
\(993\) | − 2.92980e36i | − 0.101152i | ||||||||
\(994\) | 9.66602e36 | 0.329547 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.10892e36 | −0.0701162 | ||||||||
\(997\) | 5.89404e37i | 1.93519i | 0.252505 | + | 0.967596i | \(0.418746\pi\) | ||||
−0.252505 | + | 0.967596i | \(0.581254\pi\) | |||||||
\(998\) | − 1.79146e37i | − 0.580865i | ||||||||
\(999\) | 6.56558e36 | 0.210235 |
(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 | 50.26.b.b.49.1 | 2 | ||
5.2 | odd | 4 | 10.26.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 50.26.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 50.26.b.b.49.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
50.26.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
50.26.b.b.49.1 | 2 | 1.1 | even | 1 | trivial | ||
50.26.b.b.49.2 | 2 | 5.4 | even | 2 | inner |