Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [83,13,Mod(82,83)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(83, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.82");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 83 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 83.b (of order \(2\), degree \(1\), 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: | \(75.8614868339\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 82.3 | ||
Character | \(\chi\) | \(=\) | 83.82 |
Dual form | 83.13.b.c.82.78 |
$q$-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 \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 118.839i | − | 1.85687i | −0.371499 | − | 0.928433i | \(-0.621156\pi\) | ||
0.371499 | − | 0.928433i | \(-0.378844\pi\) | |||||||
\(3\) | 844.819 | 1.15887 | 0.579437 | − | 0.815017i | \(-0.303273\pi\) | ||||
0.579437 | + | 0.815017i | \(0.303273\pi\) | |||||||
\(4\) | −10026.8 | −2.44795 | ||||||||
\(5\) | − | 13361.5i | − | 0.855133i | −0.903984 | − | 0.427567i | \(-0.859371\pi\) | ||
0.903984 | − | 0.427567i | \(-0.140629\pi\) | |||||||
\(6\) | − | 100398.i | − | 2.15187i | ||||||
\(7\) | −171650. | −1.45900 | −0.729500 | − | 0.683981i | \(-0.760247\pi\) | ||||
−0.729500 | + | 0.683981i | \(0.760247\pi\) | |||||||
\(8\) | 704815.i | 2.68866i | ||||||||
\(9\) | 182277. | 0.342987 | ||||||||
\(10\) | −1.58787e6 | −1.58787 | ||||||||
\(11\) | −2.15926e6 | −1.21885 | −0.609423 | − | 0.792845i | \(-0.708599\pi\) | ||||
−0.609423 | + | 0.792845i | \(0.708599\pi\) | |||||||
\(12\) | −8.47084e6 | −2.83687 | ||||||||
\(13\) | 1.84444e6i | 0.382125i | 0.981578 | + | 0.191063i | \(0.0611933\pi\) | ||||
−0.981578 | + | 0.191063i | \(0.938807\pi\) | |||||||
\(14\) | 2.03988e7i | 2.70917i | ||||||||
\(15\) | − | 1.12880e7i | − | 0.990991i | ||||||
\(16\) | 4.26900e7 | 2.54452 | ||||||||
\(17\) | 3.93307e7 | 1.62944 | 0.814719 | − | 0.579857i | \(-0.196891\pi\) | ||||
0.814719 | + | 0.579857i | \(0.196891\pi\) | |||||||
\(18\) | − | 2.16618e7i | − | 0.636882i | ||||||
\(19\) | − | 3.06545e7i | − | 0.651587i | −0.945441 | − | 0.325794i | \(-0.894369\pi\) | ||
0.945441 | − | 0.325794i | \(-0.105631\pi\) | |||||||
\(20\) | 1.33973e8i | 2.09333i | ||||||||
\(21\) | −1.45013e8 | −1.69080 | ||||||||
\(22\) | 2.56605e8i | 2.26323i | ||||||||
\(23\) | −1.60765e8 | −1.08598 | −0.542992 | − | 0.839738i | \(-0.682709\pi\) | ||||
−0.542992 | + | 0.839738i | \(0.682709\pi\) | |||||||
\(24\) | 5.95441e8i | 3.11581i | ||||||||
\(25\) | 6.56122e7 | 0.268748 | ||||||||
\(26\) | 2.19193e8 | 0.709555 | ||||||||
\(27\) | −2.94980e8 | −0.761395 | ||||||||
\(28\) | 1.72110e9 | 3.57157 | ||||||||
\(29\) | −1.30484e8 | −0.219366 | −0.109683 | − | 0.993967i | \(-0.534984\pi\) | ||||
−0.109683 | + | 0.993967i | \(0.534984\pi\) | |||||||
\(30\) | −1.34146e9 | −1.84014 | ||||||||
\(31\) | 7.79629e7 | 0.0878452 | 0.0439226 | − | 0.999035i | \(-0.486015\pi\) | ||||
0.0439226 | + | 0.999035i | \(0.486015\pi\) | |||||||
\(32\) | − | 2.18634e9i | − | 2.03619i | ||||||
\(33\) | −1.82418e9 | −1.41249 | ||||||||
\(34\) | − | 4.67403e9i | − | 3.02565i | ||||||
\(35\) | 2.29349e9i | 1.24764i | ||||||||
\(36\) | −1.82766e9 | −0.839617 | ||||||||
\(37\) | 2.07818e9 | 0.809978 | 0.404989 | − | 0.914322i | \(-0.367275\pi\) | ||||
0.404989 | + | 0.914322i | \(0.367275\pi\) | |||||||
\(38\) | −3.64296e9 | −1.20991 | ||||||||
\(39\) | 1.55822e9i | 0.442835i | ||||||||
\(40\) | 9.41736e9 | 2.29916 | ||||||||
\(41\) | 1.11963e9 | 0.235707 | 0.117853 | − | 0.993031i | \(-0.462399\pi\) | ||||
0.117853 | + | 0.993031i | \(0.462399\pi\) | |||||||
\(42\) | 1.72333e10i | 3.13958i | ||||||||
\(43\) | − | 8.39804e9i | − | 1.32852i | −0.747503 | − | 0.664259i | \(-0.768747\pi\) | ||
0.747503 | − | 0.664259i | \(-0.231253\pi\) | |||||||
\(44\) | 2.16505e10 | 2.98368 | ||||||||
\(45\) | − | 2.43549e9i | − | 0.293300i | ||||||
\(46\) | 1.91052e10i | 2.01653i | ||||||||
\(47\) | − | 5.29114e8i | − | 0.0490865i | −0.999699 | − | 0.0245433i | \(-0.992187\pi\) | ||
0.999699 | − | 0.0245433i | \(-0.00781315\pi\) | |||||||
\(48\) | 3.60653e10 | 2.94878 | ||||||||
\(49\) | 1.56224e10 | 1.12868 | ||||||||
\(50\) | − | 7.79732e9i | − | 0.499028i | ||||||
\(51\) | 3.32273e10 | 1.88831 | ||||||||
\(52\) | − | 1.84939e10i | − | 0.935425i | ||||||
\(53\) | 4.10466e10i | 1.85192i | 0.377622 | + | 0.925960i | \(0.376742\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(54\) | 3.50552e10i | 1.41381i | ||||||||
\(55\) | 2.88509e10i | 1.04228i | ||||||||
\(56\) | − | 1.20982e11i | − | 3.92275i | ||||||
\(57\) | − | 2.58975e10i | − | 0.755107i | ||||||
\(58\) | 1.55066e10i | 0.407333i | ||||||||
\(59\) | −1.85109e10 | −0.438850 | −0.219425 | − | 0.975629i | \(-0.570418\pi\) | ||||
−0.219425 | + | 0.975629i | \(0.570418\pi\) | |||||||
\(60\) | 1.13183e11i | 2.42590i | ||||||||
\(61\) | 5.15512e10 | 1.00060 | 0.500299 | − | 0.865853i | \(-0.333223\pi\) | ||||
0.500299 | + | 0.865853i | \(0.333223\pi\) | |||||||
\(62\) | − | 9.26507e9i | − | 0.163117i | ||||||
\(63\) | −3.12879e10 | −0.500419 | ||||||||
\(64\) | −8.49648e10 | −1.23640 | ||||||||
\(65\) | 2.46445e10 | 0.326768 | ||||||||
\(66\) | 2.16785e11i | 2.62280i | ||||||||
\(67\) | 3.45570e10i | 0.382021i | 0.981588 | + | 0.191010i | \(0.0611764\pi\) | ||||
−0.981588 | + | 0.191010i | \(0.938824\pi\) | |||||||
\(68\) | −3.94361e11 | −3.98879 | ||||||||
\(69\) | −1.35817e11 | −1.25852 | ||||||||
\(70\) | 2.72557e11 | 2.31670 | ||||||||
\(71\) | 2.62776e10i | 0.205133i | 0.994726 | + | 0.102567i | \(0.0327055\pi\) | ||||
−0.994726 | + | 0.102567i | \(0.967295\pi\) | |||||||
\(72\) | 1.28472e11i | 0.922175i | ||||||||
\(73\) | 6.18428e10i | 0.408651i | 0.978903 | + | 0.204325i | \(0.0655000\pi\) | ||||
−0.978903 | + | 0.204325i | \(0.934500\pi\) | |||||||
\(74\) | − | 2.46970e11i | − | 1.50402i | ||||||
\(75\) | 5.54304e10 | 0.311444 | ||||||||
\(76\) | 3.07367e11i | 1.59506i | ||||||||
\(77\) | 3.70637e11 | 1.77830 | ||||||||
\(78\) | 1.85178e11 | 0.822285 | ||||||||
\(79\) | 1.40174e11i | 0.576640i | 0.957534 | + | 0.288320i | \(0.0930966\pi\) | ||||
−0.957534 | + | 0.288320i | \(0.906903\pi\) | |||||||
\(80\) | − | 5.70401e11i | − | 2.17591i | ||||||
\(81\) | −3.46074e11 | −1.22535 | ||||||||
\(82\) | − | 1.33057e11i | − | 0.437676i | ||||||
\(83\) | 2.46839e11 | + | 2.14384e11i | 0.754998 | + | 0.655727i | ||||
\(84\) | 1.45402e12 | 4.13899 | ||||||||
\(85\) | − | 5.25515e11i | − | 1.39339i | ||||||
\(86\) | −9.98019e11 | −2.46688 | ||||||||
\(87\) | −1.10235e11 | −0.254217 | ||||||||
\(88\) | − | 1.52188e12i | − | 3.27706i | ||||||
\(89\) | − | 8.28753e11i | − | 1.66757i | −0.552087 | − | 0.833787i | \(-0.686168\pi\) | ||
0.552087 | − | 0.833787i | \(-0.313832\pi\) | |||||||
\(90\) | −2.89433e11 | −0.544618 | ||||||||
\(91\) | − | 3.16599e11i | − | 0.557521i | ||||||
\(92\) | 1.61196e12 | 2.65844 | ||||||||
\(93\) | 6.58645e10 | 0.101801 | ||||||||
\(94\) | −6.28797e10 | −0.0911472 | ||||||||
\(95\) | −4.09589e11 | −0.557194 | ||||||||
\(96\) | − | 1.84706e12i | − | 2.35968i | ||||||
\(97\) | 5.97811e11i | 0.717685i | 0.933398 | + | 0.358842i | \(0.116828\pi\) | ||||
−0.933398 | + | 0.358842i | \(0.883172\pi\) | |||||||
\(98\) | − | 1.85656e12i | − | 2.09581i | ||||||
\(99\) | −3.93584e11 | −0.418049 | ||||||||
\(100\) | −6.57882e11 | −0.657882 | ||||||||
\(101\) | − | 1.21055e12i | − | 1.14039i | −0.821508 | − | 0.570197i | \(-0.806867\pi\) | ||
0.821508 | − | 0.570197i | \(-0.193133\pi\) | |||||||
\(102\) | − | 3.94871e12i | − | 3.50634i | ||||||
\(103\) | 1.62356e12i | 1.35971i | 0.733348 | + | 0.679853i | \(0.237956\pi\) | ||||
−0.733348 | + | 0.679853i | \(0.762044\pi\) | |||||||
\(104\) | −1.29999e12 | −1.02740 | ||||||||
\(105\) | 1.93759e12i | 1.44586i | ||||||||
\(106\) | 4.87796e12 | 3.43877 | ||||||||
\(107\) | 2.53420e12i | 1.68864i | 0.535836 | + | 0.844322i | \(0.319997\pi\) | ||||
−0.535836 | + | 0.844322i | \(0.680003\pi\) | |||||||
\(108\) | 2.95771e12 | 1.86386 | ||||||||
\(109\) | −2.99841e12 | −1.78785 | −0.893927 | − | 0.448212i | \(-0.852061\pi\) | ||||
−0.893927 | + | 0.448212i | \(0.852061\pi\) | |||||||
\(110\) | 3.42862e12 | 1.93537 | ||||||||
\(111\) | 1.75569e12 | 0.938662 | ||||||||
\(112\) | −7.32774e12 | −3.71246 | ||||||||
\(113\) | 2.58513e11 | 0.124169 | 0.0620843 | − | 0.998071i | \(-0.480225\pi\) | ||||
0.0620843 | + | 0.998071i | \(0.480225\pi\) | |||||||
\(114\) | −3.07764e12 | −1.40213 | ||||||||
\(115\) | 2.14805e12i | 0.928661i | ||||||||
\(116\) | 1.30834e12 | 0.536997 | ||||||||
\(117\) | 3.36201e11i | 0.131064i | ||||||||
\(118\) | 2.19983e12i | 0.814887i | ||||||||
\(119\) | −6.75110e12 | −2.37735 | ||||||||
\(120\) | 7.95596e12 | 2.66443 | ||||||||
\(121\) | 1.52398e12 | 0.485586 | ||||||||
\(122\) | − | 6.12632e12i | − | 1.85798i | ||||||
\(123\) | 9.45886e11 | 0.273154 | ||||||||
\(124\) | −7.81720e11 | −0.215041 | ||||||||
\(125\) | − | 4.13875e12i | − | 1.08495i | ||||||
\(126\) | 3.71824e12i | 0.929210i | ||||||||
\(127\) | −6.54207e12 | −1.55917 | −0.779584 | − | 0.626298i | \(-0.784569\pi\) | ||||
−0.779584 | + | 0.626298i | \(0.784569\pi\) | |||||||
\(128\) | 1.14193e12i | 0.259646i | ||||||||
\(129\) | − | 7.09482e12i | − | 1.53958i | ||||||
\(130\) | − | 2.92873e12i | − | 0.606764i | ||||||
\(131\) | −4.37005e12 | −0.864687 | −0.432343 | − | 0.901709i | \(-0.642313\pi\) | ||||
−0.432343 | + | 0.901709i | \(0.642313\pi\) | |||||||
\(132\) | 1.82908e13 | 3.45771 | ||||||||
\(133\) | 5.26184e12i | 0.950666i | ||||||||
\(134\) | 4.10673e12 | 0.709361 | ||||||||
\(135\) | 3.94136e12i | 0.651094i | ||||||||
\(136\) | 2.77209e13i | 4.38100i | ||||||||
\(137\) | 8.58649e12i | 1.29865i | 0.760511 | + | 0.649325i | \(0.224949\pi\) | ||||
−0.760511 | + | 0.649325i | \(0.775051\pi\) | |||||||
\(138\) | 1.61404e13i | 2.33690i | ||||||||
\(139\) | − | 4.08815e12i | − | 0.566811i | −0.959000 | − | 0.283405i | \(-0.908536\pi\) | ||
0.959000 | − | 0.283405i | \(-0.0914642\pi\) | |||||||
\(140\) | − | 2.29964e13i | − | 3.05416i | ||||||
\(141\) | − | 4.47006e11i | − | 0.0568851i | ||||||
\(142\) | 3.12282e12 | 0.380905 | ||||||||
\(143\) | − | 3.98264e12i | − | 0.465752i | ||||||
\(144\) | 7.78143e12 | 0.872740 | ||||||||
\(145\) | 1.74345e12i | 0.187587i | ||||||||
\(146\) | 7.34937e12 | 0.758810 | ||||||||
\(147\) | 1.31981e13 | 1.30800 | ||||||||
\(148\) | −2.08376e13 | −1.98279 | ||||||||
\(149\) | − | 3.85057e12i | − | 0.351891i | −0.984400 | − | 0.175945i | \(-0.943702\pi\) | ||
0.984400 | − | 0.175945i | \(-0.0562982\pi\) | |||||||
\(150\) | − | 6.58732e12i | − | 0.578311i | ||||||
\(151\) | 1.93265e13 | 1.63039 | 0.815196 | − | 0.579186i | \(-0.196629\pi\) | ||||
0.815196 | + | 0.579186i | \(0.196629\pi\) | |||||||
\(152\) | 2.16058e13 | 1.75190 | ||||||||
\(153\) | 7.16909e12 | 0.558876 | ||||||||
\(154\) | − | 4.40463e13i | − | 3.30206i | ||||||
\(155\) | − | 1.04170e12i | − | 0.0751193i | ||||||
\(156\) | − | 1.56240e13i | − | 1.08404i | ||||||
\(157\) | − | 1.79822e13i | − | 1.20073i | −0.799726 | − | 0.600365i | \(-0.795022\pi\) | ||
0.799726 | − | 0.600365i | \(-0.204978\pi\) | |||||||
\(158\) | 1.66582e13 | 1.07074 | ||||||||
\(159\) | 3.46769e13i | 2.14614i | ||||||||
\(160\) | −2.92127e13 | −1.74121 | ||||||||
\(161\) | 2.75953e13 | 1.58445 | ||||||||
\(162\) | 4.11273e13i | 2.27531i | ||||||||
\(163\) | 3.63775e13i | 1.93958i | 0.243945 | + | 0.969789i | \(0.421558\pi\) | ||||
−0.243945 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(164\) | −1.12264e13 | −0.577000 | ||||||||
\(165\) | 2.43737e13i | 1.20787i | ||||||||
\(166\) | 2.54772e13 | − | 2.93343e13i | 1.21760 | − | 1.40193i | ||||
\(167\) | −3.86195e13 | −1.78036 | −0.890180 | − | 0.455608i | \(-0.849422\pi\) | ||||
−0.890180 | + | 0.455608i | \(0.849422\pi\) | |||||||
\(168\) | − | 1.02207e14i | − | 4.54597i | ||||||
\(169\) | 1.98961e13 | 0.853980 | ||||||||
\(170\) | −6.24519e13 | −2.58733 | ||||||||
\(171\) | − | 5.58763e12i | − | 0.223486i | ||||||
\(172\) | 8.42057e13i | 3.25215i | ||||||||
\(173\) | 1.21863e13 | 0.454565 | 0.227282 | − | 0.973829i | \(-0.427016\pi\) | ||||
0.227282 | + | 0.973829i | \(0.427016\pi\) | |||||||
\(174\) | 1.31003e13i | 0.472047i | ||||||||
\(175\) | −1.12623e13 | −0.392103 | ||||||||
\(176\) | −9.21789e13 | −3.10138 | ||||||||
\(177\) | −1.56384e13 | −0.508572 | ||||||||
\(178\) | −9.84885e13 | −3.09646 | ||||||||
\(179\) | 3.55533e13i | 1.08084i | 0.841395 | + | 0.540420i | \(0.181735\pi\) | ||||
−0.841395 | + | 0.540420i | \(0.818265\pi\) | |||||||
\(180\) | 2.44202e13i | 0.717984i | ||||||||
\(181\) | 3.32330e13i | 0.945143i | 0.881292 | + | 0.472572i | \(0.156674\pi\) | ||||
−0.881292 | + | 0.472572i | \(0.843326\pi\) | |||||||
\(182\) | −3.76244e13 | −1.03524 | ||||||||
\(183\) | 4.35514e13 | 1.15957 | ||||||||
\(184\) | − | 1.13309e14i | − | 2.91984i | ||||||
\(185\) | − | 2.77675e13i | − | 0.692639i | ||||||
\(186\) | − | 7.82730e12i | − | 0.189032i | ||||||
\(187\) | −8.49251e13 | −1.98603 | ||||||||
\(188\) | 5.30533e12i | 0.120162i | ||||||||
\(189\) | 5.06333e13 | 1.11087 | ||||||||
\(190\) | 4.86753e13i | 1.03463i | ||||||||
\(191\) | 5.91788e13 | 1.21889 | 0.609447 | − | 0.792827i | \(-0.291392\pi\) | ||||
0.609447 | + | 0.792827i | \(0.291392\pi\) | |||||||
\(192\) | −7.17799e13 | −1.43283 | ||||||||
\(193\) | 3.88589e12 | 0.0751877 | 0.0375939 | − | 0.999293i | \(-0.488031\pi\) | ||||
0.0375939 | + | 0.999293i | \(0.488031\pi\) | |||||||
\(194\) | 7.10436e13 | 1.33264 | ||||||||
\(195\) | 2.08201e13 | 0.378682 | ||||||||
\(196\) | −1.56643e14 | −2.76296 | ||||||||
\(197\) | 8.53223e13 | 1.45971 | 0.729853 | − | 0.683605i | \(-0.239589\pi\) | ||||
0.729853 | + | 0.683605i | \(0.239589\pi\) | |||||||
\(198\) | 4.67734e13i | 0.776261i | ||||||||
\(199\) | −8.51346e13 | −1.37084 | −0.685421 | − | 0.728147i | \(-0.740382\pi\) | ||||
−0.685421 | + | 0.728147i | \(0.740382\pi\) | |||||||
\(200\) | 4.62445e13i | 0.722570i | ||||||||
\(201\) | 2.91944e13i | 0.442713i | ||||||||
\(202\) | −1.43861e14 | −2.11756 | ||||||||
\(203\) | 2.23975e13 | 0.320055 | ||||||||
\(204\) | −3.33164e14 | −4.62250 | ||||||||
\(205\) | − | 1.49599e13i | − | 0.201561i | ||||||
\(206\) | 1.92943e14 | 2.52479 | ||||||||
\(207\) | −2.93038e13 | −0.372479 | ||||||||
\(208\) | 7.87394e13i | 0.972327i | ||||||||
\(209\) | 6.61910e13i | 0.794185i | ||||||||
\(210\) | 2.30262e14 | 2.68476 | ||||||||
\(211\) | − | 3.73191e13i | − | 0.422899i | −0.977389 | − | 0.211449i | \(-0.932182\pi\) | ||
0.977389 | − | 0.211449i | \(-0.0678184\pi\) | |||||||
\(212\) | − | 4.11567e14i | − | 4.53341i | ||||||
\(213\) | 2.21998e13i | 0.237723i | ||||||||
\(214\) | 3.01163e14 | 3.13559 | ||||||||
\(215\) | −1.12210e14 | −1.13606 | ||||||||
\(216\) | − | 2.07906e14i | − | 2.04713i | ||||||
\(217\) | −1.33823e13 | −0.128166 | ||||||||
\(218\) | 3.56330e14i | 3.31981i | ||||||||
\(219\) | 5.22460e13i | 0.473574i | ||||||||
\(220\) | − | 2.89282e14i | − | 2.55144i | ||||||
\(221\) | 7.25432e13i | 0.622649i | ||||||||
\(222\) | − | 2.08645e14i | − | 1.74297i | ||||||
\(223\) | 8.90915e13i | 0.724448i | 0.932091 | + | 0.362224i | \(0.117982\pi\) | ||||
−0.932091 | + | 0.362224i | \(0.882018\pi\) | |||||||
\(224\) | 3.75285e14i | 2.97080i | ||||||||
\(225\) | 1.19596e13 | 0.0921770 | ||||||||
\(226\) | − | 3.07216e13i | − | 0.230565i | ||||||
\(227\) | 8.71919e13 | 0.637267 | 0.318633 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318633 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(228\) | 2.59670e14i | 1.84847i | ||||||||
\(229\) | 6.84383e13 | 0.474555 | 0.237277 | − | 0.971442i | \(-0.423745\pi\) | ||||
0.237277 | + | 0.971442i | \(0.423745\pi\) | |||||||
\(230\) | 2.55273e14 | 1.72440 | ||||||||
\(231\) | 3.13121e14 | 2.06082 | ||||||||
\(232\) | − | 9.19670e13i | − | 0.589799i | ||||||
\(233\) | 1.02919e14i | 0.643218i | 0.946873 | + | 0.321609i | \(0.104224\pi\) | ||||
−0.946873 | + | 0.321609i | \(0.895776\pi\) | |||||||
\(234\) | 3.99539e13 | 0.243368 | ||||||||
\(235\) | −7.06974e12 | −0.0419755 | ||||||||
\(236\) | 1.85606e14 | 1.07429 | ||||||||
\(237\) | 1.18421e14i | 0.668252i | ||||||||
\(238\) | 8.02298e14i | 4.41442i | ||||||||
\(239\) | − | 1.78792e13i | − | 0.0959312i | −0.998849 | − | 0.0479656i | \(-0.984726\pi\) | ||
0.998849 | − | 0.0479656i | \(-0.0152738\pi\) | |||||||
\(240\) | − | 4.81885e14i | − | 2.52160i | ||||||
\(241\) | −1.67618e14 | −0.855497 | −0.427748 | − | 0.903898i | \(-0.640693\pi\) | ||||
−0.427748 | + | 0.903898i | \(0.640693\pi\) | |||||||
\(242\) | − | 1.81108e14i | − | 0.901668i | ||||||
\(243\) | −1.35606e14 | −0.658627 | ||||||||
\(244\) | −5.16895e14 | −2.44942 | ||||||||
\(245\) | − | 2.08738e14i | − | 0.965173i | ||||||
\(246\) | − | 1.12409e14i | − | 0.507211i | ||||||
\(247\) | 5.65405e13 | 0.248988 | ||||||||
\(248\) | 5.49495e13i | 0.236186i | ||||||||
\(249\) | 2.08535e14 | + | 1.81115e14i | 0.874947 | + | 0.759904i | ||||
\(250\) | −4.91847e14 | −2.01460 | ||||||||
\(251\) | 2.57841e13i | 0.103112i | 0.998670 | + | 0.0515560i | \(0.0164181\pi\) | ||||
−0.998670 | + | 0.0515560i | \(0.983582\pi\) | |||||||
\(252\) | 3.13718e14 | 1.22500 | ||||||||
\(253\) | 3.47133e14 | 1.32365 | ||||||||
\(254\) | 7.77456e14i | 2.89517i | ||||||||
\(255\) | − | 4.43965e14i | − | 1.61476i | ||||||
\(256\) | −2.12309e14 | −0.754273 | ||||||||
\(257\) | − | 3.59703e14i | − | 1.24838i | −0.781274 | − | 0.624189i | \(-0.785430\pi\) | ||
0.781274 | − | 0.624189i | \(-0.214570\pi\) | |||||||
\(258\) | −8.43145e14 | −2.85880 | ||||||||
\(259\) | −3.56720e14 | −1.18176 | ||||||||
\(260\) | −2.47106e14 | −0.799912 | ||||||||
\(261\) | −2.37843e13 | −0.0752396 | ||||||||
\(262\) | 5.19335e14i | 1.60561i | ||||||||
\(263\) | 6.52934e14i | 1.97303i | 0.163659 | + | 0.986517i | \(0.447670\pi\) | ||||
−0.163659 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(264\) | − | 1.28571e15i | − | 3.79770i | ||||||
\(265\) | 5.48442e14 | 1.58364 | ||||||||
\(266\) | 6.25315e14 | 1.76526 | ||||||||
\(267\) | − | 7.00146e14i | − | 1.93251i | ||||||
\(268\) | − | 3.46496e14i | − | 0.935169i | ||||||
\(269\) | 4.72061e13i | 0.124590i | 0.998058 | + | 0.0622951i | \(0.0198420\pi\) | ||||
−0.998058 | + | 0.0622951i | \(0.980158\pi\) | |||||||
\(270\) | 4.68389e14 | 1.20899 | ||||||||
\(271\) | 4.78882e14i | 1.20896i | 0.796619 | + | 0.604481i | \(0.206620\pi\) | ||||
−0.796619 | + | 0.604481i | \(0.793380\pi\) | |||||||
\(272\) | 1.67903e15 | 4.14614 | ||||||||
\(273\) | − | 2.67469e14i | − | 0.646096i | ||||||
\(274\) | 1.02041e15 | 2.41142 | ||||||||
\(275\) | −1.41674e14 | −0.327562 | ||||||||
\(276\) | 1.36181e15 | 3.08080 | ||||||||
\(277\) | −4.75040e14 | −1.05160 | −0.525802 | − | 0.850607i | \(-0.676235\pi\) | ||||
−0.525802 | + | 0.850607i | \(0.676235\pi\) | |||||||
\(278\) | −4.85834e14 | −1.05249 | ||||||||
\(279\) | 1.42109e13 | 0.0301298 | ||||||||
\(280\) | −1.61649e15 | −3.35448 | ||||||||
\(281\) | − | 7.73695e14i | − | 1.57156i | −0.618504 | − | 0.785782i | \(-0.712261\pi\) | ||
0.618504 | − | 0.785782i | \(-0.287739\pi\) | |||||||
\(282\) | −5.31219e13 | −0.105628 | ||||||||
\(283\) | 9.80496e14i | 1.90865i | 0.298764 | + | 0.954327i | \(0.403426\pi\) | ||||
−0.298764 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(284\) | − | 2.63481e14i | − | 0.502157i | ||||||
\(285\) | −3.46028e14 | −0.645717 | ||||||||
\(286\) | −4.73294e14 | −0.864839 | ||||||||
\(287\) | −1.92185e14 | −0.343896 | ||||||||
\(288\) | − | 3.98520e14i | − | 0.698386i | ||||||
\(289\) | 9.64278e14 | 1.65507 | ||||||||
\(290\) | 2.07191e14 | 0.348324 | ||||||||
\(291\) | 5.05042e14i | 0.831706i | ||||||||
\(292\) | − | 6.20087e14i | − | 1.00036i | ||||||
\(293\) | −9.86102e13 | −0.155853 | −0.0779267 | − | 0.996959i | \(-0.524830\pi\) | ||||
−0.0779267 | + | 0.996959i | \(0.524830\pi\) | |||||||
\(294\) | − | 1.56846e15i | − | 2.42878i | ||||||
\(295\) | 2.47333e14i | 0.375275i | ||||||||
\(296\) | 1.46473e15i | 2.17775i | ||||||||
\(297\) | 6.36938e14 | 0.928023 | ||||||||
\(298\) | −4.57600e14 | −0.653414 | ||||||||
\(299\) | − | 2.96522e14i | − | 0.414982i | ||||||
\(300\) | −5.55791e14 | −0.762401 | ||||||||
\(301\) | 1.44152e15i | 1.93831i | ||||||||
\(302\) | − | 2.29675e15i | − | 3.02742i | ||||||
\(303\) | − | 1.02270e15i | − | 1.32157i | ||||||
\(304\) | − | 1.30864e15i | − | 1.65798i | ||||||
\(305\) | − | 6.88799e14i | − | 0.855645i | ||||||
\(306\) | − | 8.51971e14i | − | 1.03776i | ||||||
\(307\) | − | 6.04520e14i | − | 0.722071i | −0.932552 | − | 0.361036i | \(-0.882423\pi\) | ||
0.932552 | − | 0.361036i | \(-0.117577\pi\) | |||||||
\(308\) | −3.71631e15 | −4.35319 | ||||||||
\(309\) | 1.37161e15i | 1.57573i | ||||||||
\(310\) | −1.23795e14 | −0.139487 | ||||||||
\(311\) | 2.10845e14i | 0.233024i | 0.993189 | + | 0.116512i | \(0.0371714\pi\) | ||||
−0.993189 | + | 0.116512i | \(0.962829\pi\) | |||||||
\(312\) | −1.09826e15 | −1.19063 | ||||||||
\(313\) | −1.23727e14 | −0.131582 | −0.0657912 | − | 0.997833i | \(-0.520957\pi\) | ||||
−0.0657912 | + | 0.997833i | \(0.520957\pi\) | |||||||
\(314\) | −2.13700e15 | −2.22959 | ||||||||
\(315\) | 4.18052e14i | 0.427924i | ||||||||
\(316\) | − | 1.40550e15i | − | 1.41159i | ||||||
\(317\) | −1.82391e15 | −1.79742 | −0.898708 | − | 0.438548i | \(-0.855493\pi\) | ||||
−0.898708 | + | 0.438548i | \(0.855493\pi\) | |||||||
\(318\) | 4.12099e15 | 3.98510 | ||||||||
\(319\) | 2.81749e14 | 0.267373 | ||||||||
\(320\) | 1.13525e15i | 1.05729i | ||||||||
\(321\) | 2.14094e15i | 1.95692i | ||||||||
\(322\) | − | 3.27941e15i | − | 2.94212i | ||||||
\(323\) | − | 1.20566e15i | − | 1.06172i | ||||||
\(324\) | 3.47002e15 | 2.99959 | ||||||||
\(325\) | 1.21018e14i | 0.102695i | ||||||||
\(326\) | 4.32308e15 | 3.60154 | ||||||||
\(327\) | −2.53311e15 | −2.07190 | ||||||||
\(328\) | 7.89134e14i | 0.633735i | ||||||||
\(329\) | 9.08225e13i | 0.0716173i | ||||||||
\(330\) | 2.89656e15 | 2.24284 | ||||||||
\(331\) | 2.50773e15i | 1.90684i | 0.301654 | + | 0.953418i | \(0.402461\pi\) | ||||
−0.301654 | + | 0.953418i | \(0.597539\pi\) | |||||||
\(332\) | −2.47501e15 | − | 2.14959e15i | −1.84820 | − | 1.60519i | ||||
\(333\) | 3.78806e14 | 0.277812 | ||||||||
\(334\) | 4.58952e15i | 3.30589i | ||||||||
\(335\) | 4.61731e14 | 0.326678 | ||||||||
\(336\) | −6.19061e15 | −4.30227 | ||||||||
\(337\) | − | 7.68904e14i | − | 0.524920i | −0.964943 | − | 0.262460i | \(-0.915466\pi\) | ||
0.964943 | − | 0.262460i | \(-0.0845338\pi\) | |||||||
\(338\) | − | 2.36444e15i | − | 1.58573i | ||||||
\(339\) | 2.18397e14 | 0.143896 | ||||||||
\(340\) | 5.26924e15i | 3.41094i | ||||||||
\(341\) | −1.68342e14 | −0.107070 | ||||||||
\(342\) | −6.64030e14 | −0.414984 | ||||||||
\(343\) | −3.05730e14 | −0.187747 | ||||||||
\(344\) | 5.91907e15 | 3.57193 | ||||||||
\(345\) | 1.81471e15i | 1.07620i | ||||||||
\(346\) | − | 1.44822e15i | − | 0.844066i | ||||||
\(347\) | − | 3.17159e14i | − | 0.181677i | −0.995866 | − | 0.0908386i | \(-0.971045\pi\) | ||
0.995866 | − | 0.0908386i | \(-0.0289547\pi\) | |||||||
\(348\) | 1.10531e15 | 0.622312 | ||||||||
\(349\) | −9.46396e13 | −0.0523746 | −0.0261873 | − | 0.999657i | \(-0.508337\pi\) | ||||
−0.0261873 | + | 0.999657i | \(0.508337\pi\) | |||||||
\(350\) | 1.33841e15i | 0.728083i | ||||||||
\(351\) | − | 5.44074e14i | − | 0.290948i | ||||||
\(352\) | 4.72087e15i | 2.48180i | ||||||||
\(353\) | 1.39545e15 | 0.721219 | 0.360610 | − | 0.932717i | \(-0.382569\pi\) | ||||
0.360610 | + | 0.932717i | \(0.382569\pi\) | |||||||
\(354\) | 1.85846e15i | 0.944350i | ||||||||
\(355\) | 3.51107e14 | 0.175416 | ||||||||
\(356\) | 8.30975e15i | 4.08214i | ||||||||
\(357\) | −5.70346e15 | −2.75505 | ||||||||
\(358\) | 4.22513e15 | 2.00698 | ||||||||
\(359\) | 5.60158e14 | 0.261664 | 0.130832 | − | 0.991405i | \(-0.458235\pi\) | ||||
0.130832 | + | 0.991405i | \(0.458235\pi\) | |||||||
\(360\) | 1.71657e15 | 0.788583 | ||||||||
\(361\) | 1.27362e15 | 0.575434 | ||||||||
\(362\) | 3.94939e15 | 1.75500 | ||||||||
\(363\) | 1.28748e15 | 0.562732 | ||||||||
\(364\) | 3.17448e15i | 1.36478i | ||||||||
\(365\) | 8.26310e14 | 0.349451 | ||||||||
\(366\) | − | 5.17563e15i | − | 2.15316i | ||||||
\(367\) | − | 8.60328e14i | − | 0.352101i | −0.984381 | − | 0.176051i | \(-0.943668\pi\) | ||
0.984381 | − | 0.176051i | \(-0.0563322\pi\) | |||||||
\(368\) | −6.86305e15 | −2.76332 | ||||||||
\(369\) | 2.04084e14 | 0.0808445 | ||||||||
\(370\) | −3.29988e15 | −1.28614 | ||||||||
\(371\) | − | 7.04565e15i | − | 2.70195i | ||||||
\(372\) | −6.60412e14 | −0.249205 | ||||||||
\(373\) | −5.27027e15 | −1.95695 | −0.978475 | − | 0.206364i | \(-0.933837\pi\) | ||||
−0.978475 | + | 0.206364i | \(0.933837\pi\) | |||||||
\(374\) | 1.00925e16i | 3.68780i | ||||||||
\(375\) | − | 3.49649e15i | − | 1.25732i | ||||||
\(376\) | 3.72928e14 | 0.131977 | ||||||||
\(377\) | − | 2.40670e14i | − | 0.0838251i | ||||||
\(378\) | − | 6.01723e15i | − | 2.06275i | ||||||
\(379\) | − | 3.72384e15i | − | 1.25648i | −0.778019 | − | 0.628241i | \(-0.783775\pi\) | ||
0.778019 | − | 0.628241i | \(-0.216225\pi\) | |||||||
\(380\) | 4.10687e15 | 1.36399 | ||||||||
\(381\) | −5.52686e15 | −1.80688 | ||||||||
\(382\) | − | 7.03277e15i | − | 2.26332i | ||||||
\(383\) | −1.79701e15 | −0.569322 | −0.284661 | − | 0.958628i | \(-0.591881\pi\) | ||||
−0.284661 | + | 0.958628i | \(0.591881\pi\) | |||||||
\(384\) | 9.64728e14i | 0.300897i | ||||||||
\(385\) | − | 4.95225e15i | − | 1.52068i | ||||||
\(386\) | − | 4.61798e14i | − | 0.139614i | ||||||
\(387\) | − | 1.53077e15i | − | 0.455665i | ||||||
\(388\) | − | 5.99415e15i | − | 1.75686i | ||||||
\(389\) | 6.69572e15i | 1.93241i | 0.257774 | + | 0.966205i | \(0.417011\pi\) | ||||
−0.257774 | + | 0.966205i | \(0.582989\pi\) | |||||||
\(390\) | − | 2.47425e15i | − | 0.703163i | ||||||
\(391\) | −6.32298e15 | −1.76954 | ||||||||
\(392\) | 1.10109e16i | 3.03464i | ||||||||
\(393\) | −3.69190e15 | −1.00206 | ||||||||
\(394\) | − | 1.01397e16i | − | 2.71048i | ||||||
\(395\) | 1.87293e15 | 0.493104 | ||||||||
\(396\) | 3.94640e15 | 1.02336 | ||||||||
\(397\) | −2.15715e15 | −0.550981 | −0.275490 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275490 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(398\) | 1.01173e16i | 2.54547i | ||||||||
\(399\) | 4.44530e15i | 1.10170i | ||||||||
\(400\) | 2.80099e15 | 0.683835 | ||||||||
\(401\) | 8.21528e13 | 0.0197586 | 0.00987929 | − | 0.999951i | \(-0.496855\pi\) | ||||
0.00987929 | + | 0.999951i | \(0.496855\pi\) | |||||||
\(402\) | 3.46944e15 | 0.822060 | ||||||||
\(403\) | 1.43798e14i | 0.0335678i | ||||||||
\(404\) | 1.21380e16i | 2.79163i | ||||||||
\(405\) | 4.62405e15i | 1.04783i | ||||||||
\(406\) | − | 2.66171e15i | − | 0.594299i | ||||||
\(407\) | −4.48734e15 | −0.987239 | ||||||||
\(408\) | 2.34191e16i | 5.07702i | ||||||||
\(409\) | −2.04697e15 | −0.437293 | −0.218646 | − | 0.975804i | \(-0.570164\pi\) | ||||
−0.218646 | + | 0.975804i | \(0.570164\pi\) | |||||||
\(410\) | −1.77783e15 | −0.374271 | ||||||||
\(411\) | 7.25402e15i | 1.50497i | ||||||||
\(412\) | − | 1.62791e16i | − | 3.32850i | ||||||
\(413\) | 3.17740e15 | 0.640283 | ||||||||
\(414\) | 3.48245e15i | 0.691644i | ||||||||
\(415\) | 2.86448e15 | − | 3.29813e15i | 0.560734 | − | 0.645624i | ||||
\(416\) | 4.03258e15 | 0.778078 | ||||||||
\(417\) | − | 3.45375e15i | − | 0.656862i | ||||||
\(418\) | 7.86611e15 | 1.47470 | ||||||||
\(419\) | −1.01743e15 | −0.188027 | −0.0940136 | − | 0.995571i | \(-0.529970\pi\) | ||||
−0.0940136 | + | 0.995571i | \(0.529970\pi\) | |||||||
\(420\) | − | 1.94278e16i | − | 3.53939i | ||||||
\(421\) | 6.38091e15i | 1.14601i | 0.819550 | + | 0.573007i | \(0.194223\pi\) | ||||
−0.819550 | + | 0.573007i | \(0.805777\pi\) | |||||||
\(422\) | −4.43498e15 | −0.785267 | ||||||||
\(423\) | − | 9.64456e13i | − | 0.0168361i | ||||||
\(424\) | −2.89303e16 | −4.97918 | ||||||||
\(425\) | 2.58057e15 | 0.437907 | ||||||||
\(426\) | 2.63821e15 | 0.441421 | ||||||||
\(427\) | −8.84876e15 | −1.45987 | ||||||||
\(428\) | − | 2.54100e16i | − | 4.13372i | ||||||
\(429\) | − | 3.36460e15i | − | 0.539747i | ||||||
\(430\) | 1.33350e16i | 2.10951i | ||||||||
\(431\) | 5.76442e15 | 0.899274 | 0.449637 | − | 0.893211i | \(-0.351553\pi\) | ||||
0.449637 | + | 0.893211i | \(0.351553\pi\) | |||||||
\(432\) | −1.25927e16 | −1.93739 | ||||||||
\(433\) | − | 5.86172e15i | − | 0.889401i | −0.895679 | − | 0.444701i | \(-0.853310\pi\) | ||
0.895679 | − | 0.444701i | \(-0.146690\pi\) | |||||||
\(434\) | 1.59035e15i | 0.237987i | ||||||||
\(435\) | 1.47290e15i | 0.217389i | ||||||||
\(436\) | 3.00645e16 | 4.37659 | ||||||||
\(437\) | 4.92816e15i | 0.707614i | ||||||||
\(438\) | 6.20888e15 | 0.879364 | ||||||||
\(439\) | − | 3.25761e15i | − | 0.455105i | −0.973766 | − | 0.227553i | \(-0.926928\pi\) | ||
0.973766 | − | 0.227553i | \(-0.0730724\pi\) | |||||||
\(440\) | −2.03345e16 | −2.80232 | ||||||||
\(441\) | 2.84761e15 | 0.387124 | ||||||||
\(442\) | 8.62100e15 | 1.15618 | ||||||||
\(443\) | −1.27860e16 | −1.69165 | −0.845826 | − | 0.533459i | \(-0.820892\pi\) | ||||
−0.845826 | + | 0.533459i | \(0.820892\pi\) | |||||||
\(444\) | −1.76040e16 | −2.29780 | ||||||||
\(445\) | −1.10733e16 | −1.42600 | ||||||||
\(446\) | 1.05876e16 | 1.34520 | ||||||||
\(447\) | − | 3.25304e15i | − | 0.407797i | ||||||
\(448\) | 1.45842e16 | 1.80391 | ||||||||
\(449\) | − | 8.57615e15i | − | 1.04668i | −0.852124 | − | 0.523340i | \(-0.824686\pi\) | ||
0.852124 | − | 0.523340i | \(-0.175314\pi\) | |||||||
\(450\) | − | 1.42128e15i | − | 0.171160i | ||||||
\(451\) | −2.41758e15 | −0.287290 | ||||||||
\(452\) | −2.59206e15 | −0.303959 | ||||||||
\(453\) | 1.63274e16 | 1.88942 | ||||||||
\(454\) | − | 1.03618e16i | − | 1.18332i | ||||||
\(455\) | −4.23022e15 | −0.476754 | ||||||||
\(456\) | 1.82530e16 | 2.03022 | ||||||||
\(457\) | 1.72254e15i | 0.189092i | 0.995521 | + | 0.0945459i | \(0.0301399\pi\) | ||||
−0.995521 | + | 0.0945459i | \(0.969860\pi\) | |||||||
\(458\) | − | 8.13317e15i | − | 0.881185i | ||||||
\(459\) | −1.16017e16 | −1.24064 | ||||||||
\(460\) | − | 2.15381e16i | − | 2.27332i | ||||||
\(461\) | 6.71326e15i | 0.699404i | 0.936861 | + | 0.349702i | \(0.113717\pi\) | ||||
−0.936861 | + | 0.349702i | \(0.886283\pi\) | |||||||
\(462\) | − | 3.72111e16i | − | 3.82667i | ||||||
\(463\) | 1.42783e16 | 1.44941 | 0.724705 | − | 0.689059i | \(-0.241976\pi\) | ||||
0.724705 | + | 0.689059i | \(0.241976\pi\) | |||||||
\(464\) | −5.57036e15 | −0.558182 | ||||||||
\(465\) | − | 8.80046e14i | − | 0.0870537i | ||||||
\(466\) | 1.22308e16 | 1.19437 | ||||||||
\(467\) | 7.28270e15i | 0.702087i | 0.936359 | + | 0.351044i | \(0.114173\pi\) | ||||
−0.936359 | + | 0.351044i | \(0.885827\pi\) | |||||||
\(468\) | − | 3.37102e15i | − | 0.320839i | ||||||
\(469\) | − | 5.93170e15i | − | 0.557368i | ||||||
\(470\) | 8.40164e14i | 0.0779430i | ||||||||
\(471\) | − | 1.51917e16i | − | 1.39149i | ||||||
\(472\) | − | 1.30468e16i | − | 1.17992i | ||||||
\(473\) | 1.81336e16i | 1.61926i | ||||||||
\(474\) | 1.40731e16 | 1.24086 | ||||||||
\(475\) | − | 2.01131e15i | − | 0.175112i | ||||||
\(476\) | 6.76921e16 | 5.81964 | ||||||||
\(477\) | 7.48187e15i | 0.635185i | ||||||||
\(478\) | −2.12475e15 | −0.178131 | ||||||||
\(479\) | 1.64745e16 | 1.36395 | 0.681975 | − | 0.731376i | \(-0.261121\pi\) | ||||
0.681975 | + | 0.731376i | \(0.261121\pi\) | |||||||
\(480\) | −2.46794e16 | −2.01784 | ||||||||
\(481\) | 3.83309e15i | 0.309513i | ||||||||
\(482\) | 1.99196e16i | 1.58854i | ||||||||
\(483\) | 2.33130e16 | 1.83618 | ||||||||
\(484\) | −1.52806e16 | −1.18869 | ||||||||
\(485\) | 7.98763e15 | 0.613716 | ||||||||
\(486\) | 1.61153e16i | 1.22298i | ||||||||
\(487\) | 2.13245e16i | 1.59847i | 0.601019 | + | 0.799235i | \(0.294762\pi\) | ||||
−0.601019 | + | 0.799235i | \(0.705238\pi\) | |||||||
\(488\) | 3.63341e16i | 2.69027i | ||||||||
\(489\) | 3.07324e16i | 2.24773i | ||||||||
\(490\) | −2.48063e16 | −1.79220 | ||||||||
\(491\) | − | 7.18491e15i | − | 0.512782i | −0.966573 | − | 0.256391i | \(-0.917467\pi\) | ||
0.966573 | − | 0.256391i | \(-0.0825334\pi\) | |||||||
\(492\) | −9.48423e15 | −0.668669 | ||||||||
\(493\) | −5.13201e15 | −0.357443 | ||||||||
\(494\) | − | 6.71925e15i | − | 0.462337i | ||||||
\(495\) | 5.25886e15i | 0.357487i | ||||||||
\(496\) | 3.32824e15 | 0.223524 | ||||||||
\(497\) | − | 4.51055e15i | − | 0.299289i | ||||||
\(498\) | 2.15236e16 | − | 2.47821e16i | 1.41104 | − | 1.62466i | ||||
\(499\) | 5.21234e15 | 0.337621 | 0.168810 | − | 0.985649i | \(-0.446007\pi\) | ||||
0.168810 | + | 0.985649i | \(0.446007\pi\) | |||||||
\(500\) | 4.14985e16i | 2.65590i | ||||||||
\(501\) | −3.26265e16 | −2.06321 | ||||||||
\(502\) | 3.06417e15 | 0.191465 | ||||||||
\(503\) | 1.18370e16i | 0.730858i | 0.930839 | + | 0.365429i | \(0.119078\pi\) | ||||
−0.930839 | + | 0.365429i | \(0.880922\pi\) | |||||||
\(504\) | − | 2.20522e16i | − | 1.34545i | ||||||
\(505\) | −1.61747e16 | −0.975189 | ||||||||
\(506\) | − | 4.12531e16i | − | 2.45784i | ||||||
\(507\) | 1.68086e16 | 0.989655 | ||||||||
\(508\) | 6.55961e16 | 3.81677 | ||||||||
\(509\) | −6.07670e15 | −0.349431 | −0.174715 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174715 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(510\) | −5.27605e16 | −2.99839 | ||||||||
\(511\) | − | 1.06153e16i | − | 0.596221i | ||||||
\(512\) | 2.99081e16i | 1.66023i | ||||||||
\(513\) | 9.04246e15i | 0.496115i | ||||||||
\(514\) | −4.27470e16 | −2.31807 | ||||||||
\(515\) | 2.16931e16 | 1.16273 | ||||||||
\(516\) | 7.11385e16i | 3.76883i | ||||||||
\(517\) | 1.14250e15i | 0.0598289i | ||||||||
\(518\) | 4.23924e16i | 2.19437i | ||||||||
\(519\) | 1.02952e16 | 0.526783 | ||||||||
\(520\) | 1.73698e16i | 0.878567i | ||||||||
\(521\) | −1.73245e16 | −0.866231 | −0.433116 | − | 0.901338i | \(-0.642586\pi\) | ||||
−0.433116 | + | 0.901338i | \(0.642586\pi\) | |||||||
\(522\) | 2.82651e15i | 0.139710i | ||||||||
\(523\) | −7.23137e15 | −0.353354 | −0.176677 | − | 0.984269i | \(-0.556535\pi\) | ||||
−0.176677 | + | 0.984269i | \(0.556535\pi\) | |||||||
\(524\) | 4.38177e16 | 2.11671 | ||||||||
\(525\) | −9.51462e15 | −0.454397 | ||||||||
\(526\) | 7.75943e16 | 3.66366 | ||||||||
\(527\) | 3.06633e15 | 0.143138 | ||||||||
\(528\) | −7.78745e16 | −3.59411 | ||||||||
\(529\) | 3.93067e15 | 0.179363 | ||||||||
\(530\) | − | 6.51766e16i | − | 2.94060i | ||||||
\(531\) | −3.37413e15 | −0.150520 | ||||||||
\(532\) | − | 5.27596e16i | − | 2.32719i | ||||||
\(533\) | 2.06510e15i | 0.0900695i | ||||||||
\(534\) | −8.32049e16 | −3.58841 | ||||||||
\(535\) | 3.38606e16 | 1.44402 | ||||||||
\(536\) | −2.43563e16 | −1.02712 | ||||||||
\(537\) | 3.00361e16i | 1.25256i | ||||||||
\(538\) | 5.60994e15 | 0.231347 | ||||||||
\(539\) | −3.37329e16 | −1.37569 | ||||||||
\(540\) | − | 3.95193e16i | − | 1.59385i | ||||||
\(541\) | − | 2.71530e16i | − | 1.08302i | −0.840696 | − | 0.541508i | \(-0.817854\pi\) | ||
0.840696 | − | 0.541508i | \(-0.182146\pi\) | |||||||
\(542\) | 5.69101e16 | 2.24488 | ||||||||
\(543\) | 2.80758e16i | 1.09530i | ||||||||
\(544\) | − | 8.59901e16i | − | 3.31784i | ||||||
\(545\) | 4.00631e16i | 1.52885i | ||||||||
\(546\) | −3.17858e16 | −1.19971 | ||||||||
\(547\) | 1.88442e16 | 0.703484 | 0.351742 | − | 0.936097i | \(-0.385589\pi\) | ||||
0.351742 | + | 0.936097i | \(0.385589\pi\) | |||||||
\(548\) | − | 8.60952e16i | − | 3.17904i | ||||||
\(549\) | 9.39662e15 | 0.343192 | ||||||||
\(550\) | 1.68364e16i | 0.608239i | ||||||||
\(551\) | 3.99992e15i | 0.142936i | ||||||||
\(552\) | − | 9.57259e16i | − | 3.38373i | ||||||
\(553\) | − | 2.40608e16i | − | 0.841317i | ||||||
\(554\) | 5.64536e16i | 1.95269i | ||||||||
\(555\) | − | 2.34585e16i | − | 0.802681i | ||||||
\(556\) | 4.09912e16i | 1.38753i | ||||||||
\(557\) | 2.01451e16 | 0.674588 | 0.337294 | − | 0.941399i | \(-0.390488\pi\) | ||||
0.337294 | + | 0.941399i | \(0.390488\pi\) | |||||||
\(558\) | − | 1.68881e15i | − | 0.0559470i | ||||||
\(559\) | 1.54897e16 | 0.507660 | ||||||||
\(560\) | 9.79093e16i | 3.17465i | ||||||||
\(561\) | −7.17463e16 | −2.30156 | ||||||||
\(562\) | −9.19455e16 | −2.91818 | ||||||||
\(563\) | −4.95890e16 | −1.55716 | −0.778582 | − | 0.627542i | \(-0.784061\pi\) | ||||
−0.778582 | + | 0.627542i | \(0.784061\pi\) | |||||||
\(564\) | 4.48205e15i | 0.139252i | ||||||||
\(565\) | − | 3.45411e15i | − | 0.106181i | ||||||
\(566\) | 1.16522e17 | 3.54412 | ||||||||
\(567\) | 5.94036e16 | 1.78778 | ||||||||
\(568\) | −1.85209e16 | −0.551533 | ||||||||
\(569\) | 3.06515e16i | 0.903187i | 0.892224 | + | 0.451594i | \(0.149144\pi\) | ||||
−0.892224 | + | 0.451594i | \(0.850856\pi\) | |||||||
\(570\) | 4.11218e16i | 1.19901i | ||||||||
\(571\) | − | 3.02745e16i | − | 0.873495i | −0.899584 | − | 0.436748i | \(-0.856130\pi\) | ||
0.899584 | − | 0.436748i | \(-0.143870\pi\) | |||||||
\(572\) | 3.99332e16i | 1.14014i | ||||||||
\(573\) | 4.99953e16 | 1.41254 | ||||||||
\(574\) | 2.28391e16i | 0.638570i | ||||||||
\(575\) | −1.05481e16 | −0.291856 | ||||||||
\(576\) | −1.54872e16 | −0.424070 | ||||||||
\(577\) | − | 1.73130e16i | − | 0.469156i | −0.972097 | − | 0.234578i | \(-0.924629\pi\) | ||
0.972097 | − | 0.234578i | \(-0.0753708\pi\) | |||||||
\(578\) | − | 1.14594e17i | − | 3.07324i | ||||||
\(579\) | 3.28288e15 | 0.0871331 | ||||||||
\(580\) | − | 1.74813e16i | − | 0.459204i | ||||||
\(581\) | −4.23700e16 | − | 3.67989e16i | −1.10154 | − | 0.956706i | ||||
\(582\) | 6.00189e16 | 1.54437 | ||||||||
\(583\) | − | 8.86303e16i | − | 2.25721i | ||||||
\(584\) | −4.35878e16 | −1.09872 | ||||||||
\(585\) | 4.49213e15 | 0.112077 | ||||||||
\(586\) | 1.17188e16i | 0.289399i | ||||||||
\(587\) | − | 6.26769e16i | − | 1.53207i | −0.642799 | − | 0.766035i | \(-0.722227\pi\) | ||
0.642799 | − | 0.766035i | \(-0.277773\pi\) | |||||||
\(588\) | −1.32335e17 | −3.20192 | ||||||||
\(589\) | − | 2.38991e15i | − | 0.0572388i | ||||||
\(590\) | 2.93929e16 | 0.696836 | ||||||||
\(591\) | 7.20819e16 | 1.69161 | ||||||||
\(592\) | 8.87177e16 | 2.06101 | ||||||||
\(593\) | 9.06460e15 | 0.208459 | 0.104229 | − | 0.994553i | \(-0.466762\pi\) | ||||
0.104229 | + | 0.994553i | \(0.466762\pi\) | |||||||
\(594\) | − | 7.56934e16i | − | 1.72321i | ||||||
\(595\) | 9.02046e16i | 2.03295i | ||||||||
\(596\) | 3.86090e16i | 0.861412i | ||||||||
\(597\) | −7.19233e16 | −1.58863 | ||||||||
\(598\) | −3.52385e16 | −0.770566 | ||||||||
\(599\) | − | 2.72962e16i | − | 0.590938i | −0.955352 | − | 0.295469i | \(-0.904524\pi\) | ||
0.955352 | − | 0.295469i | \(-0.0954759\pi\) | |||||||
\(600\) | 3.90682e16i | 0.837367i | ||||||||
\(601\) | 3.44890e16i | 0.731869i | 0.930641 | + | 0.365935i | \(0.119251\pi\) | ||||
−0.930641 | + | 0.365935i | \(0.880749\pi\) | |||||||
\(602\) | 1.71310e17 | 3.59918 | ||||||||
\(603\) | 6.29896e15i | 0.131028i | ||||||||
\(604\) | −1.93783e17 | −3.99112 | ||||||||
\(605\) | − | 2.03625e16i | − | 0.415240i | ||||||
\(606\) | −1.21537e17 | −2.45398 | ||||||||
\(607\) | −5.10224e16 | −1.02007 | −0.510034 | − | 0.860154i | \(-0.670367\pi\) | ||||
−0.510034 | + | 0.860154i | \(0.670367\pi\) | |||||||
\(608\) | −6.70211e16 | −1.32675 | ||||||||
\(609\) | 1.89219e16 | 0.370903 | ||||||||
\(610\) | −8.18565e16 | −1.58882 | ||||||||
\(611\) | 9.75922e14 | 0.0187572 | ||||||||
\(612\) | −7.18832e16 | −1.36810 | ||||||||
\(613\) | 5.53492e16i | 1.04315i | 0.853204 | + | 0.521577i | \(0.174656\pi\) | ||||
−0.853204 | + | 0.521577i | \(0.825344\pi\) | |||||||
\(614\) | −7.18408e16 | −1.34079 | ||||||||
\(615\) | − | 1.26384e16i | − | 0.233583i | ||||||
\(616\) | 2.61231e17i | 4.78123i | ||||||||
\(617\) | −1.21775e16 | −0.220723 | −0.110362 | − | 0.993891i | \(-0.535201\pi\) | ||||
−0.110362 | + | 0.993891i | \(0.535201\pi\) | |||||||
\(618\) | 1.63002e17 | 2.92591 | ||||||||
\(619\) | 5.58277e16 | 0.992444 | 0.496222 | − | 0.868196i | \(-0.334720\pi\) | ||||
0.496222 | + | 0.868196i | \(0.334720\pi\) | |||||||
\(620\) | 1.04449e16i | 0.183889i | ||||||||
\(621\) | 4.74223e16 | 0.826863 | ||||||||
\(622\) | 2.50567e16 | 0.432695 | ||||||||
\(623\) | 1.42255e17i | 2.43299i | ||||||||
\(624\) | 6.65205e16i | 1.12680i | ||||||||
\(625\) | −3.92811e16 | −0.659027 | ||||||||
\(626\) | 1.47036e16i | 0.244331i | ||||||||
\(627\) | 5.59194e16i | 0.920359i | ||||||||
\(628\) | 1.80304e17i | 2.93933i | ||||||||
\(629\) | 8.17363e16 | 1.31981 | ||||||||
\(630\) | 4.96811e16 | 0.794599 | ||||||||
\(631\) | − | 3.85729e16i | − | 0.611092i | −0.952177 | − | 0.305546i | \(-0.901161\pi\) | ||
0.952177 | − | 0.305546i | \(-0.0988389\pi\) | |||||||
\(632\) | −9.87967e16 | −1.55039 | ||||||||
\(633\) | − | 3.15279e16i | − | 0.490086i | ||||||
\(634\) | 2.16753e17i | 3.33756i | ||||||||
\(635\) | 8.74115e16i | 1.33330i | ||||||||
\(636\) | − | 3.47700e17i | − | 5.25365i | ||||||
\(637\) | 2.88147e16i | 0.431298i | ||||||||
\(638\) | − | 3.34829e16i | − | 0.496476i | ||||||
\(639\) | 4.78982e15i | 0.0703581i | ||||||||
\(640\) | 1.52579e16 | 0.222032 | ||||||||
\(641\) | − | 7.93407e16i | − | 1.14379i | −0.820326 | − | 0.571897i | \(-0.806208\pi\) | ||
0.820326 | − | 0.571897i | \(-0.193792\pi\) | |||||||
\(642\) | 2.54428e17 | 3.63375 | ||||||||
\(643\) | − | 4.46023e16i | − | 0.631091i | −0.948910 | − | 0.315545i | \(-0.897813\pi\) | ||
0.948910 | − | 0.315545i | \(-0.102187\pi\) | |||||||
\(644\) | −2.76693e17 | −3.87867 | ||||||||
\(645\) | −9.47972e16 | −1.31655 | ||||||||
\(646\) | −1.43280e17 | −1.97147 | ||||||||
\(647\) | 6.95026e16i | 0.947491i | 0.880662 | + | 0.473746i | \(0.157098\pi\) | ||||
−0.880662 | + | 0.473746i | \(0.842902\pi\) | |||||||
\(648\) | − | 2.43918e17i | − | 3.29454i | ||||||
\(649\) | 3.99699e16 | 0.534891 | ||||||||
\(650\) | 1.43817e16 | 0.190691 | ||||||||
\(651\) | −1.13056e16 | −0.148528 | ||||||||
\(652\) | − | 3.64751e17i | − | 4.74800i | ||||||
\(653\) | − | 9.60289e16i | − | 1.23858i | −0.785164 | − | 0.619288i | \(-0.787421\pi\) | ||
0.785164 | − | 0.619288i | \(-0.212579\pi\) | |||||||
\(654\) | 3.01034e17i | 3.84724i | ||||||||
\(655\) | 5.83902e16i | 0.739422i | ||||||||
\(656\) | 4.77972e16 | 0.599762 | ||||||||
\(657\) | 1.12726e16i | 0.140162i | ||||||||
\(658\) | 1.07933e16 | 0.132984 | ||||||||
\(659\) | −5.88008e16 | −0.717911 | −0.358956 | − | 0.933355i | \(-0.616867\pi\) | ||||
−0.358956 | + | 0.933355i | \(0.616867\pi\) | |||||||
\(660\) | − | 2.44391e17i | − | 2.95680i | ||||||
\(661\) | 9.31680e16i | 1.11701i | 0.829500 | + | 0.558506i | \(0.188625\pi\) | ||||
−0.829500 | + | 0.558506i | \(0.811375\pi\) | |||||||
\(662\) | 2.98018e17 | 3.54074 | ||||||||
\(663\) | 6.12859e16i | 0.721571i | ||||||||
\(664\) | −1.51101e17 | + | 1.73976e17i | −1.76303 | + | 2.02993i | ||||
\(665\) | 7.03059e16 | 0.812946 | ||||||||
\(666\) | − | 4.50171e16i | − | 0.515860i | ||||||
\(667\) | 2.09772e16 | 0.238228 | ||||||||
\(668\) | 3.87231e17 | 4.35824 | ||||||||
\(669\) | 7.52661e16i | 0.839543i | ||||||||
\(670\) | − | 5.48719e16i | − | 0.606598i | ||||||
\(671\) | −1.11312e17 | −1.21958 | ||||||||
\(672\) | 3.17048e17i | 3.44278i | ||||||||
\(673\) | −8.41391e15 | −0.0905539 | −0.0452770 | − | 0.998974i | \(-0.514417\pi\) | ||||
−0.0452770 | + | 0.998974i | \(0.514417\pi\) | |||||||
\(674\) | −9.13762e16 | −0.974706 | ||||||||
\(675\) | −1.93543e16 | −0.204623 | ||||||||
\(676\) | −1.99495e17 | −2.09050 | ||||||||
\(677\) | 4.74659e15i | 0.0493003i | 0.999696 | + | 0.0246502i | \(0.00784719\pi\) | ||||
−0.999696 | + | 0.0246502i | \(0.992153\pi\) | |||||||
\(678\) | − | 2.59541e16i | − | 0.267195i | ||||||
\(679\) | − | 1.02614e17i | − | 1.04710i | ||||||
\(680\) | 3.70391e17 | 3.74634 | ||||||||
\(681\) | 7.36614e16 | 0.738511 | ||||||||
\(682\) | 2.00057e16i | 0.198814i | ||||||||
\(683\) | − | 3.02791e16i | − | 0.298276i | −0.988816 | − | 0.149138i | \(-0.952350\pi\) | ||
0.988816 | − | 0.149138i | \(-0.0476498\pi\) | |||||||
\(684\) | 5.60261e16i | 0.547084i | ||||||||
\(685\) | 1.14728e17 | 1.11052 | ||||||||
\(686\) | 3.63328e16i | 0.348622i | ||||||||
\(687\) | 5.78180e16 | 0.549949 | ||||||||
\(688\) | − | 3.58513e17i | − | 3.38045i | ||||||
\(689\) | −7.57082e16 | −0.707665 | ||||||||
\(690\) | 2.15660e17 | 1.99836 | ||||||||
\(691\) | 1.30429e17 | 1.19813 | 0.599066 | − | 0.800699i | \(-0.295539\pi\) | ||||
0.599066 | + | 0.800699i | \(0.295539\pi\) | |||||||
\(692\) | −1.22190e17 | −1.11275 | ||||||||
\(693\) | 6.75588e16 | 0.609933 | ||||||||
\(694\) | −3.76910e16 | −0.337350 | ||||||||
\(695\) | −5.46237e16 | −0.484699 | ||||||||
\(696\) | − | 7.76955e16i | − | 0.683503i | ||||||
\(697\) | 4.40359e16 | 0.384070 | ||||||||
\(698\) | 1.12469e16i | 0.0972526i | ||||||||
\(699\) | 8.69476e16i | 0.745409i | ||||||||
\(700\) | 1.12925e17 | 0.959849 | ||||||||
\(701\) | −1.24581e17 | −1.04989 | −0.524947 | − | 0.851135i | \(-0.675915\pi\) | ||||
−0.524947 | + | 0.851135i | \(0.675915\pi\) | |||||||
\(702\) | −6.46575e16 | −0.540252 | ||||||||
\(703\) | − | 6.37056e16i | − | 0.527772i | ||||||
\(704\) | 1.83461e17 | 1.50698 | ||||||||
\(705\) | −5.97265e15 | −0.0486443 | ||||||||
\(706\) | − | 1.65835e17i | − | 1.33921i | ||||||
\(707\) | 2.07791e17i | 1.66384i | ||||||||
\(708\) | 1.56803e17 | 1.24496 | ||||||||
\(709\) | − | 3.77878e16i | − | 0.297491i | −0.988875 | − | 0.148746i | \(-0.952476\pi\) | ||
0.988875 | − | 0.148746i | \(-0.0475236\pi\) | |||||||
\(710\) | − | 4.17254e16i | − | 0.325724i | ||||||
\(711\) | 2.55505e16i | 0.197780i | ||||||||
\(712\) | 5.84118e17 | 4.48353 | ||||||||
\(713\) | −1.25337e16 | −0.0953985 | ||||||||
\(714\) | 6.77796e17i | 5.11575i | ||||||||
\(715\) | −5.32138e16 | −0.398280 | ||||||||
\(716\) | − | 3.56486e17i | − | 2.64585i | ||||||
\(717\) | − | 1.51046e16i | − | 0.111172i | ||||||
\(718\) | − | 6.65689e16i | − | 0.485875i | ||||||
\(719\) | − | 1.62645e17i | − | 1.17724i | −0.808409 | − | 0.588622i | \(-0.799671\pi\) | ||
0.808409 | − | 0.588622i | \(-0.200329\pi\) | |||||||
\(720\) | − | 1.03971e17i | − | 0.746308i | ||||||
\(721\) | − | 2.78684e17i | − | 1.98381i | ||||||
\(722\) | − | 1.51356e17i | − | 1.06850i | ||||||
\(723\) | −1.41607e17 | −0.991412 | ||||||||
\(724\) | − | 3.33221e17i | − | 2.31367i | ||||||
\(725\) | −8.56133e15 | −0.0589540 | ||||||||
\(726\) | − | 1.53004e17i | − | 1.04492i | ||||||
\(727\) | −1.39320e17 | −0.943638 | −0.471819 | − | 0.881695i | \(-0.656402\pi\) | ||||
−0.471819 | + | 0.881695i | \(0.656402\pi\) | |||||||
\(728\) | 2.23144e17 | 1.49898 | ||||||||
\(729\) | 6.93559e16 | 0.462081 | ||||||||
\(730\) | − | 9.81982e16i | − | 0.648883i | ||||||
\(731\) | − | 3.30301e17i | − | 2.16474i | ||||||
\(732\) | −4.36682e17 | −2.83857 | ||||||||
\(733\) | −8.26984e16 | −0.533179 | −0.266590 | − | 0.963810i | \(-0.585897\pi\) | ||||
−0.266590 | + | 0.963810i | \(0.585897\pi\) | |||||||
\(734\) | −1.02241e17 | −0.653805 | ||||||||
\(735\) | − | 1.76346e17i | − | 1.11851i | ||||||
\(736\) | 3.51486e17i | 2.21127i | ||||||||
\(737\) | − | 7.46175e16i | − | 0.465624i | ||||||
\(738\) | − | 2.42532e16i | − | 0.150117i | ||||||
\(739\) | −2.61294e17 | −1.60422 | −0.802109 | − | 0.597178i | \(-0.796289\pi\) | ||||
−0.802109 | + | 0.597178i | \(0.796289\pi\) | |||||||
\(740\) | 2.78420e17i | 1.69555i | ||||||||
\(741\) | 4.77665e16 | 0.288545 | ||||||||
\(742\) | −8.37301e17 | −5.01716 | ||||||||
\(743\) | − | 8.11764e16i | − | 0.482499i | −0.970463 | − | 0.241250i | \(-0.922443\pi\) | ||
0.970463 | − | 0.241250i | \(-0.0775573\pi\) | |||||||
\(744\) | 4.64223e16i | 0.273709i | ||||||||
\(745\) | −5.14492e16 | −0.300913 | ||||||||
\(746\) | 6.26316e17i | 3.63380i | ||||||||
\(747\) | 4.49933e16 | + | 3.90773e16i | 0.258955 | + | 0.224906i | ||||
\(748\) | 8.51529e17 | 4.86172 | ||||||||
\(749\) | − | 4.34995e17i | − | 2.46373i | ||||||
\(750\) | −4.15521e17 | −2.33467 | ||||||||
\(751\) | −6.90851e16 | −0.385074 | −0.192537 | − | 0.981290i | \(-0.561672\pi\) | ||||
−0.192537 | + | 0.981290i | \(0.561672\pi\) | |||||||
\(752\) | − | 2.25879e16i | − | 0.124902i | ||||||
\(753\) | 2.17829e16i | 0.119494i | ||||||||
\(754\) | −2.86011e16 | −0.155652 | ||||||||
\(755\) | − | 2.58230e17i | − | 1.39420i | ||||||
\(756\) | −5.07691e17 | −2.71937 | ||||||||
\(757\) | 8.38383e16 | 0.445520 | 0.222760 | − | 0.974873i | \(-0.428493\pi\) | ||||
0.222760 | + | 0.974873i | \(0.428493\pi\) | |||||||
\(758\) | −4.42540e17 | −2.33312 | ||||||||
\(759\) | 2.93264e17 | 1.53394 | ||||||||
\(760\) | − | 2.88684e17i | − | 1.49810i | ||||||
\(761\) | 5.84528e16i | 0.300952i | 0.988614 | + | 0.150476i | \(0.0480807\pi\) | ||||
−0.988614 | + | 0.150476i | \(0.951919\pi\) | |||||||
\(762\) | 6.56809e17i | 3.35513i | ||||||||
\(763\) | 5.14677e17 | 2.60848 | ||||||||
\(764\) | −5.93375e17 | −2.98379 | ||||||||
\(765\) | − | 9.57895e16i | − | 0.477913i | ||||||
\(766\) | 2.13556e17i | 1.05716i | ||||||||
\(767\) | − | 3.41424e16i | − | 0.167696i | ||||||
\(768\) | −1.79363e17 | −0.874107 | ||||||||
\(769\) | − | 1.73611e16i | − | 0.0839498i | −0.999119 | − | 0.0419749i | \(-0.986635\pi\) | ||
0.999119 | − | 0.0419749i | \(-0.0133649\pi\) | |||||||
\(770\) | −5.88522e17 | −2.82370 | ||||||||
\(771\) | − | 3.03884e17i | − | 1.44671i | ||||||
\(772\) | −3.89632e16 | −0.184056 | ||||||||
\(773\) | −3.54239e16 | −0.166043 | −0.0830213 | − | 0.996548i | \(-0.526457\pi\) | ||||
−0.0830213 | + | 0.996548i | \(0.526457\pi\) | |||||||
\(774\) | −1.81916e17 | −0.846109 | ||||||||
\(775\) | 5.11532e15 | 0.0236082 | ||||||||
\(776\) | −4.21347e17 | −1.92961 | ||||||||
\(777\) | −3.01364e17 | −1.36951 | ||||||||
\(778\) | 7.95715e17 | 3.58823 | ||||||||
\(779\) | − | 3.43218e16i | − | 0.153584i | ||||||
\(780\) | −2.08759e17 | −0.926997 | ||||||||
\(781\) | − | 5.67402e16i | − | 0.250026i | ||||||
\(782\) | 7.51420e17i | 3.28581i | ||||||||
\(783\) | 3.84901e16 | 0.167024 | ||||||||
\(784\) | 6.66921e17 | 2.87196 | ||||||||
\(785\) | −2.40268e17 | −1.02678 | ||||||||
\(786\) | 4.38744e17i | 1.86070i | ||||||||
\(787\) | 1.73853e17 | 0.731702 | 0.365851 | − | 0.930673i | \(-0.380778\pi\) | ||||
0.365851 | + | 0.930673i | \(0.380778\pi\) | |||||||
\(788\) | −8.55511e17 | −3.57329 | ||||||||
\(789\) | 5.51610e17i | 2.28650i | ||||||||
\(790\) | − | 2.22578e17i | − | 0.915628i | ||||||
\(791\) | −4.43737e16 | −0.181162 | ||||||||
\(792\) | − | 2.77404e17i | − | 1.12399i | ||||||
\(793\) | 9.50833e16i | 0.382354i | ||||||||
\(794\) | 2.56354e17i | 1.02310i | ||||||||
\(795\) | 4.63334e17 | 1.83524 | ||||||||
\(796\) | 8.53629e17 | 3.35576 | ||||||||
\(797\) | − | 1.42743e17i | − | 0.556935i | −0.960446 | − | 0.278467i | \(-0.910174\pi\) | ||
0.960446 | − | 0.278467i | \(-0.0898264\pi\) | |||||||
\(798\) | 5.28277e17 | 2.04571 | ||||||||
\(799\) | − | 2.08104e16i | − | 0.0799834i | ||||||
\(800\) | − | 1.43450e17i | − | 0.547220i | ||||||
\(801\) | − | 1.51063e17i | − | 0.571956i | ||||||
\(802\) | − | 9.76299e15i | − | 0.0366891i | ||||||
\(803\) | − | 1.33535e17i | − | 0.498082i | ||||||
\(804\) | − | 2.92727e17i | − | 1.08374i | ||||||
\(805\) | − | 3.68713e17i | − | 1.35492i | ||||||
\(806\) | 1.70889e16 | 0.0623310 | ||||||||
\(807\) | 3.98806e16i | 0.144384i | ||||||||
\(808\) | 8.53215e17 | 3.06613 | ||||||||
\(809\) | − | 8.77739e16i | − | 0.313094i | −0.987671 | − | 0.156547i | \(-0.949964\pi\) | ||
0.987671 | − | 0.156547i | \(-0.0500362\pi\) | |||||||
\(810\) | 5.49520e17 | 1.94569 | ||||||||
\(811\) | 1.86891e17 | 0.656845 | 0.328423 | − | 0.944531i | \(-0.393483\pi\) | ||||
0.328423 | + | 0.944531i | \(0.393483\pi\) | |||||||
\(812\) | −2.24576e17 | −0.783479 | ||||||||
\(813\) | 4.04568e17i | 1.40103i | ||||||||
\(814\) | 5.33273e17i | 1.83317i | ||||||||
\(815\) | 4.86056e17 | 1.65860 | ||||||||
\(816\) | 1.41847e18 | 4.80485 | ||||||||
\(817\) | −2.57438e17 | −0.865645 | ||||||||
\(818\) | 2.43261e17i | 0.811994i | ||||||||
\(819\) | − | 5.77088e16i | − | 0.191222i | ||||||
\(820\) | 1.50000e17i | 0.493411i | ||||||||
\(821\) | − | 2.33519e17i | − | 0.762540i | −0.924464 | − | 0.381270i | \(-0.875487\pi\) | ||
0.924464 | − | 0.381270i | \(-0.124513\pi\) | |||||||
\(822\) | 8.62064e17 | 2.79453 | ||||||||
\(823\) | − | 5.39826e17i | − | 1.73722i | −0.495495 | − | 0.868611i | \(-0.665013\pi\) | ||
0.495495 | − | 0.868611i | \(-0.334987\pi\) | |||||||
\(824\) | −1.14431e18 | −3.65578 | ||||||||
\(825\) | −1.19689e17 | −0.379603 | ||||||||
\(826\) | − | 3.77601e17i | − | 1.18892i | ||||||
\(827\) | 9.87890e16i | 0.308799i | 0.988009 | + | 0.154399i | \(0.0493443\pi\) | ||||
−0.988009 | + | 0.154399i | \(0.950656\pi\) | |||||||
\(828\) | 2.93824e17 | 0.911811 | ||||||||
\(829\) | 5.70217e17i | 1.75676i | 0.477961 | + | 0.878381i | \(0.341376\pi\) | ||||
−0.477961 | + | 0.878381i | \(0.658624\pi\) | |||||||
\(830\) | −3.91948e17 | − | 3.40413e17i | −1.19884 | − | 1.04121i | ||||
\(831\) | −4.01323e17 | −1.21868 | ||||||||
\(832\) | − | 1.56713e17i | − | 0.472460i | ||||||
\(833\) | 6.14440e17 | 1.83912 | ||||||||
\(834\) | −4.10441e17 | −1.21971 | ||||||||
\(835\) | 5.16013e17i | 1.52245i | ||||||||
\(836\) | − | 6.63686e17i | − | 1.94413i | ||||||
\(837\) | −2.29975e16 | −0.0668848 | ||||||||
\(838\) | 1.20911e17i | 0.349142i | ||||||||
\(839\) | −4.61102e17 | −1.32198 | −0.660990 | − | 0.750394i | \(-0.729864\pi\) | ||||
−0.660990 | + | 0.750394i | \(0.729864\pi\) | |||||||
\(840\) | −1.36564e18 | −3.88741 | ||||||||
\(841\) | −3.36789e17 | −0.951879 | ||||||||
\(842\) | 7.58304e17 | 2.12800 | ||||||||
\(843\) | − | 6.53632e17i | − | 1.82124i | ||||||
\(844\) | 3.74192e17i | 1.03524i | ||||||||
\(845\) | − | 2.65841e17i | − | 0.730267i | ||||||
\(846\) | −1.14615e16 | −0.0312623 | ||||||||
\(847\) | −2.61590e17 | −0.708470 | ||||||||
\(848\) | 1.75228e18i | 4.71226i | ||||||||
\(849\) | 8.28341e17i | 2.21189i | ||||||||
\(850\) | − | 3.06674e17i | − | 0.813135i | ||||||
\(851\) | −3.34098e17 | −0.879624 | ||||||||
\(852\) | − | 2.22594e17i | − | 0.581936i | ||||||
\(853\) | 3.76065e17 | 0.976268 | 0.488134 | − | 0.872769i | \(-0.337678\pi\) | ||||
0.488134 | + | 0.872769i | \(0.337678\pi\) | |||||||
\(854\) | 1.05158e18i | 2.71079i | ||||||||
\(855\) | −7.46588e16 | −0.191110 | ||||||||
\(856\) | −1.78614e18 | −4.54019 | ||||||||
\(857\) | 1.20139e17 | 0.303250 | 0.151625 | − | 0.988438i | \(-0.451549\pi\) | ||||
0.151625 | + | 0.988438i | \(0.451549\pi\) | |||||||
\(858\) | −3.99848e17 | −1.00224 | ||||||||
\(859\) | −3.66071e17 | −0.911184 | −0.455592 | − | 0.890189i | \(-0.650572\pi\) | ||||
−0.455592 | + | 0.890189i | \(0.650572\pi\) | |||||||
\(860\) | 1.12511e18 | 2.78102 | ||||||||
\(861\) | −1.62361e17 | −0.398532 | ||||||||
\(862\) | − | 6.85040e17i | − | 1.66983i | ||||||
\(863\) | −5.51779e17 | −1.33567 | −0.667837 | − | 0.744307i | \(-0.732780\pi\) | ||||
−0.667837 | + | 0.744307i | \(0.732780\pi\) | |||||||
\(864\) | 6.44926e17i | 1.55034i | ||||||||
\(865\) | − | 1.62827e17i | − | 0.388713i | ||||||
\(866\) | −6.96604e17 | −1.65150 | ||||||||
\(867\) | 8.14640e17 | 1.91801 | ||||||||
\(868\) | 1.34182e17 | 0.313745 | ||||||||
\(869\) | − | 3.02672e17i | − | 0.702835i | ||||||
\(870\) | 1.75039e17 | 0.403663 | ||||||||
\(871\) | −6.37384e16 | −0.145980 | ||||||||
\(872\) | − | 2.11333e18i | − | 4.80693i | ||||||
\(873\) | 1.08968e17i | 0.246157i | ||||||||
\(874\) | 5.85660e17 | 1.31394 | ||||||||
\(875\) | 7.10416e17i | 1.58294i | ||||||||
\(876\) | − | 5.23861e17i | − | 1.15929i | ||||||
\(877\) | − | 3.89314e17i | − | 0.855661i | −0.903859 | − | 0.427831i | \(-0.859278\pi\) | ||
0.903859 | − | 0.427831i | \(-0.140722\pi\) | |||||||
\(878\) | −3.87133e17 | −0.845070 | ||||||||
\(879\) | −8.33077e16 | −0.180614 | ||||||||
\(880\) | 1.23164e18i | 2.65210i | ||||||||
\(881\) | 1.94636e17 | 0.416264 | 0.208132 | − | 0.978101i | \(-0.433262\pi\) | ||||
0.208132 | + | 0.978101i | \(0.433262\pi\) | |||||||
\(882\) | − | 3.38409e17i | − | 0.718837i | ||||||
\(883\) | − | 4.09135e17i | − | 0.863181i | −0.902070 | − | 0.431591i | \(-0.857953\pi\) | ||
0.902070 | − | 0.431591i | \(-0.142047\pi\) | |||||||
\(884\) | − | 7.27378e17i | − | 1.52422i | ||||||
\(885\) | 2.08952e17i | 0.434897i | ||||||||
\(886\) | 1.51948e18i | 3.14117i | ||||||||
\(887\) | 7.71233e17i | 1.58359i | 0.610785 | + | 0.791797i | \(0.290854\pi\) | ||||
−0.610785 | + | 0.791797i | \(0.709146\pi\) | |||||||
\(888\) | 1.23744e18i | 2.52374i | ||||||||
\(889\) | 1.12295e18 | 2.27483 | ||||||||
\(890\) | 1.31595e18i | 2.64789i | ||||||||
\(891\) | 7.47264e17 | 1.49351 | ||||||||
\(892\) | − | 8.93304e17i | − | 1.77341i | ||||||
\(893\) | −1.62197e16 | −0.0319842 | ||||||||
\(894\) | −3.86589e17 | −0.757224 | ||||||||
\(895\) | 4.75043e17 | 0.924262 | ||||||||
\(896\) | − | 1.96013e17i | − | 0.378824i | ||||||
\(897\) | − | 2.50507e17i | − | 0.480912i | ||||||
\(898\) | −1.01918e18 | −1.94355 | ||||||||
\(899\) | −1.01729e16 | −0.0192702 | ||||||||
\(900\) | −1.19917e17 | −0.225645 | ||||||||
\(901\) | 1.61439e18i | 3.01759i | ||||||||
\(902\) | 2.87304e17i | 0.533460i | ||||||||
\(903\) | 1.21783e18i | 2.24625i | ||||||||
\(904\) | 1.82204e17i | 0.333847i | ||||||||
\(905\) | 4.44041e17 | 0.808223 | ||||||||
\(906\) | − | 1.94034e18i | − | 3.50839i | ||||||
\(907\) | 1.74730e17 | 0.313852 | 0.156926 | − | 0.987610i | \(-0.449842\pi\) | ||||
0.156926 | + | 0.987610i | \(0.449842\pi\) | |||||||
\(908\) | −8.74258e17 | −1.56000 | ||||||||
\(909\) | − | 2.20656e17i | − | 0.391141i | ||||||
\(910\) | 5.02717e17i | 0.885269i | ||||||||
\(911\) | 7.85468e14 | 0.00137410 | 0.000687050 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000687050 | 1.00000i | \(0.499781\pi\) | ||||||||
\(912\) | − | 1.10557e18i | − | 1.92139i | ||||||
\(913\) | −5.32990e17 | − | 4.62910e17i | −0.920227 | − | 0.799230i | ||||
\(914\) | 2.04706e17 | 0.351118 | ||||||||
\(915\) | − | 5.81910e17i | − | 0.991584i | ||||||
\(916\) | −6.86219e17 | −1.16169 | ||||||||
\(917\) | 7.50119e17 | 1.26158 | ||||||||
\(918\) | 1.37875e18i | 2.30371i | ||||||||
\(919\) | 3.44048e17i | 0.571119i | 0.958361 | + | 0.285559i | \(0.0921794\pi\) | ||||
−0.958361 | + | 0.285559i | \(0.907821\pi\) | |||||||
\(920\) | −1.51398e18 | −2.49685 | ||||||||
\(921\) | − | 5.10709e17i | − | 0.836789i | ||||||
\(922\) | 7.97800e17 | 1.29870 | ||||||||
\(923\) | −4.84676e16 | −0.0783865 | ||||||||
\(924\) | −3.13961e18 | −5.04479 | ||||||||
\(925\) | 1.36354e17 | 0.217680 | ||||||||
\(926\) | − | 1.69683e18i | − | 2.69136i | ||||||
\(927\) | 2.95938e17i | 0.466362i | ||||||||
\(928\) | 2.85282e17i | 0.446669i | ||||||||
\(929\) | 1.06336e18 | 1.65419 | 0.827095 | − | 0.562063i | \(-0.189992\pi\) | ||||
0.827095 | + | 0.562063i | \(0.189992\pi\) | |||||||
\(930\) | −1.04584e17 | −0.161647 | ||||||||
\(931\) | − | 4.78897e17i | − | 0.735435i | ||||||
\(932\) | − | 1.03195e18i | − | 1.57457i | ||||||
\(933\) | 1.78126e17i | 0.270046i | ||||||||
\(934\) | 8.65472e17 | 1.30368 | ||||||||
\(935\) | 1.13472e18i | 1.69832i | ||||||||
\(936\) | −2.36959e17 | −0.352386 | ||||||||
\(937\) | 5.99788e17i | 0.886258i | 0.896458 | + | 0.443129i | \(0.146132\pi\) | ||||
−0.896458 | + | 0.443129i | \(0.853868\pi\) | |||||||
\(938\) | −7.04920e17 | −1.03496 | ||||||||
\(939\) | −1.04527e17 | −0.152487 | ||||||||
\(940\) | 7.08870e16 | 0.102754 | ||||||||
\(941\) | −5.91926e16 | −0.0852569 | −0.0426284 | − | 0.999091i | \(-0.513573\pi\) | ||||
−0.0426284 | + | 0.999091i | \(0.513573\pi\) | |||||||
\(942\) | −1.80537e18 | −2.58382 | ||||||||
\(943\) | −1.79997e17 | −0.255974 | ||||||||
\(944\) | −7.90233e17 | −1.11667 | ||||||||
\(945\) | − | 6.76534e17i | − | 0.949946i | ||||||
\(946\) | 2.15498e18 | 3.00675 | ||||||||
\(947\) | − | 7.98630e17i | − | 1.10725i | −0.832766 | − | 0.553625i | \(-0.813244\pi\) | ||
0.832766 | − | 0.553625i | \(-0.186756\pi\) | |||||||
\(948\) | − | 1.18739e18i | − | 1.63585i | ||||||
\(949\) | −1.14066e17 | −0.156156 | ||||||||
\(950\) | −2.39023e17 | −0.325161 | ||||||||
\(951\) | −1.54088e18 | −2.08298 | ||||||||
\(952\) | − | 4.75828e18i | − | 6.39188i | ||||||
\(953\) | 9.91381e17 | 1.32338 | 0.661688 | − | 0.749779i | \(-0.269840\pi\) | ||||
0.661688 | + | 0.749779i | \(0.269840\pi\) | |||||||
\(954\) | 8.89142e17 | 1.17945 | ||||||||
\(955\) | − | 7.90714e17i | − | 1.04232i | ||||||
\(956\) | 1.79271e17i | 0.234835i | ||||||||
\(957\) | 2.38026e17 | 0.309851 | ||||||||
\(958\) | − | 1.95782e18i | − | 2.53267i | ||||||
\(959\) | − | 1.47387e18i | − | 1.89473i | ||||||
\(960\) | 9.59083e17i | 1.22526i | ||||||||
\(961\) | −7.81585e17 | −0.992283 | ||||||||
\(962\) | 4.55523e17 | 0.574724 | ||||||||
\(963\) | 4.61928e17i | 0.579183i | ||||||||
\(964\) | 1.68068e18 | 2.09422 | ||||||||
\(965\) | − | 5.19212e16i | − | 0.0642955i | ||||||
\(966\) | − | 2.77050e18i | − | 3.40954i | ||||||
\(967\) | 1.09903e18i | 1.34415i | 0.740481 | + | 0.672077i | \(0.234598\pi\) | ||||
−0.740481 | + | 0.672077i | \(0.765402\pi\) | |||||||
\(968\) | 1.07412e18i | 1.30557i | ||||||||
\(969\) | − | 1.01857e18i | − | 1.23040i | ||||||
\(970\) | − | 9.49245e17i | − | 1.13959i | ||||||
\(971\) | − | 4.00487e17i | − | 0.477830i | −0.971040 | − | 0.238915i | \(-0.923208\pi\) | ||
0.971040 | − | 0.238915i | \(-0.0767917\pi\) | |||||||
\(972\) | 1.35969e18 | 1.61229 | ||||||||
\(973\) | 7.01731e17i | 0.826977i | ||||||||
\(974\) | 2.53419e18 | 2.96815 | ||||||||
\(975\) | 1.02238e17i | 0.119011i | ||||||||
\(976\) | 2.20072e18 | 2.54605 | ||||||||
\(977\) | 3.72887e17 | 0.428756 | 0.214378 | − | 0.976751i | \(-0.431228\pi\) | ||||
0.214378 | + | 0.976751i | \(0.431228\pi\) | |||||||
\(978\) | 3.65222e18 | 4.17373 | ||||||||
\(979\) | 1.78949e18i | 2.03252i | ||||||||
\(980\) | 2.09298e18i | 2.36270i | ||||||||
\(981\) | −5.46543e17 | −0.613211 | ||||||||
\(982\) | −8.53851e17 | −0.952168 | ||||||||
\(983\) | −1.57247e18 | −1.74286 | −0.871428 | − | 0.490524i | \(-0.836806\pi\) | ||||
−0.871428 | + | 0.490524i | \(0.836806\pi\) | |||||||
\(984\) | 6.66675e17i | 0.734419i | ||||||||
\(985\) | − | 1.14003e18i | − | 1.24824i | ||||||
\(986\) | 6.09886e17i | 0.663723i | ||||||||
\(987\) | 7.67285e16i | 0.0829954i | ||||||||
\(988\) | −5.66922e17 | −0.609511 | ||||||||
\(989\) | 1.35011e18i | 1.44275i | ||||||||
\(990\) | 6.24960e17 | 0.663806 | ||||||||
\(991\) | −7.20299e17 | −0.760451 | −0.380225 | − | 0.924894i | \(-0.624154\pi\) | ||||
−0.380225 | + | 0.924894i | \(0.624154\pi\) | |||||||
\(992\) | − | 1.70453e17i | − | 0.178869i | ||||||
\(993\) | 2.11858e18i | 2.20978i | ||||||||
\(994\) | −5.36031e17 | −0.555740 | ||||||||
\(995\) | 1.13752e18i | 1.17225i | ||||||||
\(996\) | −2.09094e18 | − | 1.81601e18i | −2.14183 | − | 1.86021i | ||||
\(997\) | −1.28675e18 | −1.31015 | −0.655077 | − | 0.755562i | \(-0.727364\pi\) | ||||
−0.655077 | + | 0.755562i | \(0.727364\pi\) | |||||||
\(998\) | − | 6.19432e17i | − | 0.626917i | ||||||
\(999\) | −6.13022e17 | −0.616713 |
(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 | 83.13.b.c.82.3 | ✓ | 80 | |
83.82 | odd | 2 | inner | 83.13.b.c.82.78 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
83.13.b.c.82.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
83.13.b.c.82.78 | yes | 80 | 83.82 | odd | 2 | inner |