Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{15}\cdot 7^{9} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.7 | ||
Root | \(10810.2 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.12.k.d.109.7 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5539.86 | − | 9595.32i | 0.792801 | − | 1.37317i | −0.131426 | − | 0.991326i | \(-0.541956\pi\) |
0.924226 | − | 0.381845i | \(-0.124711\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32020.8 | − | 30854.4i | −0.720100 | − | 0.693870i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −451860. | − | 782645.i | −0.845949 | − | 1.46523i | −0.884794 | − | 0.465982i | \(-0.845701\pi\) |
0.0388451 | − | 0.999245i | \(-0.487632\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −761355. | −0.568721 | −0.284360 | − | 0.958717i | \(-0.591781\pi\) | ||||
−0.284360 | + | 0.958717i | \(0.591781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.39149e6 | − | 4.14219e6i | −0.408508 | − | 0.707556i | 0.586215 | − | 0.810155i | \(-0.300617\pi\) |
−0.994723 | + | 0.102599i | \(0.967284\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.25438e6 | + | 3.90470e6i | −0.208873 | + | 0.361779i | −0.951360 | − | 0.308082i | \(-0.900313\pi\) |
0.742487 | + | 0.669861i | \(0.233646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.38885e7 | − | 4.13761e7i | 0.773901 | − | 1.34044i | −0.161509 | − | 0.986871i | \(-0.551636\pi\) |
0.935410 | − | 0.353565i | \(-0.115031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.69661e7 | − | 6.40271e7i | −0.757065 | − | 1.31128i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.65205e8 | −1.49567 | −0.747833 | − | 0.663887i | \(-0.768905\pi\) | ||||
−0.747833 | + | 0.663887i | \(0.768905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.95464e7 | − | 5.11759e7i | −0.185360 | − | 0.321053i | 0.758338 | − | 0.651862i | \(-0.226012\pi\) |
−0.943698 | + | 0.330809i | \(0.892678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.73449e8 | + | 1.36321e8i | −1.52370 | + | 0.438720i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.08530e8 | − | 1.87980e8i | 0.257301 | − | 0.445658i | −0.708217 | − | 0.705995i | \(-0.750500\pi\) |
0.965518 | + | 0.260337i | \(0.0838335\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.52269e8 | 0.744456 | 0.372228 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372228 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.04028e9 | −1.07913 | −0.539563 | − | 0.841945i | \(-0.681411\pi\) | ||||
−0.539563 | + | 0.841945i | \(0.681411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.93035e7 | − | 1.20037e8i | 0.0440775 | − | 0.0763445i | −0.843145 | − | 0.537686i | \(-0.819298\pi\) |
0.887222 | + | 0.461342i | \(0.152632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.33368e7 | + | 1.97597e9i | 0.0370889 | + | 0.999312i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.34318e9 | − | 4.05851e9i | −0.769641 | − | 1.33306i | −0.937758 | − | 0.347290i | \(-0.887102\pi\) |
0.168117 | − | 0.985767i | \(-0.446232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00130e10 | −2.68268 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.49535e9 | + | 7.78617e9i | 0.818610 | + | 1.41787i | 0.906706 | + | 0.421763i | \(0.138588\pi\) |
−0.0880959 | + | 0.996112i | \(0.528078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08443e8 | + | 1.87828e8i | −0.0164394 | + | 0.0284739i | −0.874128 | − | 0.485695i | \(-0.838566\pi\) |
0.857689 | + | 0.514169i | \(0.171900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.21780e9 | + | 7.30545e9i | −0.450882 | + | 0.780951i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.64085e9 | − | 1.49664e10i | −0.781889 | − | 1.35427i | −0.930840 | − | 0.365426i | \(-0.880923\pi\) |
0.148952 | − | 0.988844i | \(-0.452410\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.28267e9 | 0.347482 | 0.173741 | − | 0.984791i | \(-0.444414\pi\) | ||||
0.173741 | + | 0.984791i | \(0.444414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55061e9 | − | 9.61394e9i | −0.313375 | − | 0.542782i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.979091 | + | 0.203424i | \(0.934793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.67912e9 | + | 3.90028e10i | −0.407509 | + | 1.64209i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.14340e9 | − | 3.71248e9i | 0.0783709 | − | 0.135742i | −0.824176 | − | 0.566333i | \(-0.808361\pi\) |
0.902547 | + | 0.430591i | \(0.141695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.61200e10 | 1.28517 | 0.642584 | − | 0.766216i | \(-0.277863\pi\) | ||||
0.642584 | + | 0.766216i | \(0.277863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.29942e10 | −1.29546 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.53894e9 | − | 1.47899e10i | 0.162091 | − | 0.280750i | −0.773527 | − | 0.633763i | \(-0.781510\pi\) |
0.935618 | + | 0.353013i | \(0.114843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.43792e10 | + | 2.34912e10i | 0.409536 | + | 0.394618i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.49779e10 | + | 4.32631e10i | 0.331190 | + | 0.573637i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.57413e11 | 1.86121 | 0.930605 | − | 0.366026i | \(-0.119282\pi\) | ||||
0.930605 | + | 0.366026i | \(0.119282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.77841e10 | + | 1.34726e11i | 0.736416 | + | 1.27551i | 0.954099 | + | 0.299490i | \(0.0968166\pi\) |
−0.217683 | + | 0.976019i | \(0.569850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.88269e10 | − | 1.19212e11i | 0.584997 | − | 1.01324i | −0.409879 | − | 0.912140i | \(-0.634429\pi\) |
0.994876 | − | 0.101105i | \(-0.0322377\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.51994e10 | − | 1.64890e11i | 0.656181 | − | 1.13654i | −0.325416 | − | 0.945571i | \(-0.605504\pi\) |
0.981596 | − | 0.190967i | \(-0.0611624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.45648e10 | − | 1.63791e11i | −0.588686 | − | 1.01963i | −0.994405 | − | 0.105636i | \(-0.966312\pi\) |
0.405719 | − | 0.913998i | \(-0.367021\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.29301e11 | 0.660190 | 0.330095 | − | 0.943948i | \(-0.392919\pi\) | ||||
0.330095 | + | 0.943948i | \(0.392919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.64678e11 | − | 4.58436e11i | −1.22710 | − | 2.12540i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.12273e10 | + | 2.06424e11i | −0.196785 | + | 0.792962i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65699e11 | + | 4.60205e11i | −0.931260 | + | 1.61299i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.78146e11 | −0.815206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.94863e10 | 0.0523369 | 0.0261685 | − | 0.999658i | \(-0.491669\pi\) | ||||
0.0261685 | + | 0.999658i | \(0.491669\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.37802e10 | − | 2.38680e10i | 0.0312078 | − | 0.0540535i | −0.850000 | − | 0.526783i | \(-0.823398\pi\) |
0.881207 | + | 0.472730i | \(0.156731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.92665e11 | − | 5.54741e10i | 0.401437 | − | 0.115586i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.55036e11 | − | 2.68531e11i | −0.274454 | − | 0.475369i | 0.695543 | − | 0.718485i | \(-0.255164\pi\) |
−0.969997 | + | 0.243116i | \(0.921831\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.28928e11 | 0.864600 | 0.432300 | − | 0.901730i | \(-0.357702\pi\) | ||||
0.432300 | + | 0.901730i | \(0.357702\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.44026e11 | + | 5.95871e11i | 0.481109 | + | 0.833305i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.15213e11 | + | 1.58520e12i | −1.18576 | + | 2.05380i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.21201e11 | + | 3.83131e11i | −0.246753 | + | 0.427389i | −0.962623 | − | 0.270845i | \(-0.912697\pi\) |
0.715870 | + | 0.698234i | \(0.246030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.75046e11 | + | 1.51562e12i | 0.907105 | + | 1.57115i | 0.818066 | + | 0.575124i | \(0.195046\pi\) |
0.0890393 | + | 0.996028i | \(0.471620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.54733e11 | −0.587814 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.97856e11 | − | 1.20872e12i | −0.583872 | − | 1.01130i | −0.995015 | − | 0.0997250i | \(-0.968204\pi\) |
0.411143 | − | 0.911571i | \(-0.365130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.04156e12 | + | 5.87830e11i | −1.48738 | + | 0.428262i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.83315e11 | − | 1.18354e12i | 0.465146 | − | 0.805656i | −0.534062 | − | 0.845445i | \(-0.679335\pi\) |
0.999208 | + | 0.0397888i | \(0.0126685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.20052e11 | −0.369392 | −0.184696 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184696 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.21250e12 | −0.676557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.99102e11 | − | 6.91264e11i | 0.195808 | − | 0.339149i | −0.751357 | − | 0.659896i | \(-0.770600\pi\) |
0.947165 | + | 0.320747i | \(0.103934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.91836e11 | + | 3.19077e12i | −0.364692 | + | 1.46955i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.98673e11 | − | 6.90522e11i | −0.162153 | − | 0.280857i | 0.773488 | − | 0.633811i | \(-0.218510\pi\) |
−0.935641 | + | 0.352954i | \(0.885177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.89173e12 | 1.48906 | 0.744528 | − | 0.667591i | \(-0.232675\pi\) | ||||
0.744528 | + | 0.667591i | \(0.232675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.20249e12 | − | 2.08277e12i | −0.407977 | − | 0.706636i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.16124e12 | + | 3.74338e12i | −0.691153 | + | 1.19711i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.64431e12 | − | 2.84803e12i | 0.468059 | − | 0.810701i | −0.531275 | − | 0.847199i | \(-0.678287\pi\) |
0.999334 | + | 0.0364981i | \(0.0116203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.74782e12 | − | 3.02731e12i | −0.469819 | − | 0.813750i | 0.529586 | − | 0.848257i | \(-0.322347\pi\) |
−0.999404 | + | 0.0345062i | \(0.989014\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.58940e12 | −1.34215 | −0.671074 | − | 0.741390i | \(-0.734167\pi\) | ||||
−0.671074 | + | 0.741390i | \(0.734167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.69940e12 | + | 4.67549e12i | 0.613162 | + | 1.06203i | 0.990704 | + | 0.136035i | \(0.0434359\pi\) |
−0.377542 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.29000e12 | + | 5.09731e12i | 1.07703 | + | 1.03780i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.05949e12 | − | 5.29920e12i | 0.590205 | − | 1.02227i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.07466e12 | 0.706785 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.02377e12 | 1.32076 | 0.660381 | − | 0.750930i | \(-0.270395\pi\) | ||||
0.660381 | + | 0.750930i | \(0.270395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.76299e12 | + | 9.98179e12i | −0.855532 | + | 1.48182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.32903e11 | + | 2.55033e12i | −0.0892912 | + | 0.359806i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.82078e12 | + | 3.15368e12i | 0.232327 | + | 0.402402i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.85492e10 | 0.00346671 | 0.00173336 | − | 0.999998i | \(-0.499448\pi\) | ||||
0.00173336 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.93582e12 | + | 1.20132e13i | 0.763757 | + | 1.32287i | 0.940901 | + | 0.338682i | \(0.109981\pi\) |
−0.177144 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.91500e12 | + | 5.04892e12i | −0.305874 | + | 0.529790i | −0.977456 | − | 0.211141i | \(-0.932282\pi\) |
0.671581 | + | 0.740931i | \(0.265615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.68712e12 | + | 1.33145e13i | −0.733341 | + | 1.27018i | 0.222107 | + | 0.975022i | \(0.428707\pi\) |
−0.955447 | + | 0.295161i | \(0.904627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.67864e11 | − | 1.32998e12i | −0.0698893 | − | 0.121052i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.72983e13 | −1.43488 | −0.717438 | − | 0.696622i | \(-0.754686\pi\) | ||||
−0.717438 | + | 0.696622i | \(0.754686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.79662e12 | + | 3.11184e12i | 0.142352 | + | 0.246560i | 0.928382 | − | 0.371628i | \(-0.121200\pi\) |
−0.786030 | + | 0.618188i | \(0.787867\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.93663e13 | + | 1.02429e13i | 1.40163 | + | 0.741326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.71639e12 | − | 2.97287e12i | 0.118791 | − | 0.205751i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.07857e12 | 0.131692 | 0.0658461 | − | 0.997830i | \(-0.479025\pi\) | ||||
0.0658461 | + | 0.997830i | \(0.479025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.31770e13 | −2.61872 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.77704e12 | + | 8.27408e12i | −0.265783 | + | 0.460350i | −0.967768 | − | 0.251842i | \(-0.918964\pi\) |
0.701986 | + | 0.712191i | \(0.252297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.27524e12 | + | 2.67063e12i | −0.494511 | + | 0.142385i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.62484e13 | + | 2.81431e13i | 0.796259 | + | 1.37916i | 0.922036 | + | 0.387103i | \(0.126524\pi\) |
−0.125777 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.19236e13 | −2.44069 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.57863e12 | − | 9.66247e12i | −0.241485 | − | 0.418264i | 0.719653 | − | 0.694334i | \(-0.244301\pi\) |
−0.961137 | + | 0.276070i | \(0.910968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.81340e12 | + | 1.18012e13i | −0.283161 | + | 0.490449i | −0.972161 | − | 0.234312i | \(-0.924716\pi\) |
0.689001 | + | 0.724761i | \(0.258050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.34070e13 | + | 5.78626e13i | −1.28088 | + | 2.21855i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.14769e13 | + | 1.98786e13i | 0.422850 | + | 0.732397i | 0.996217 | − | 0.0869014i | \(-0.0276965\pi\) |
−0.573367 | + | 0.819298i | \(0.694363\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.32538e13 | 0.451291 | 0.225645 | − | 0.974210i | \(-0.427551\pi\) | ||||
0.225645 | + | 0.974210i | \(0.427551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.36242e13 | − | 4.09183e13i | −0.773627 | − | 1.33996i | −0.935563 | − | 0.353161i | \(-0.885107\pi\) |
0.161935 | − | 0.986801i | \(-0.448226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.76841e13 | − | 1.70399e13i | −0.536083 | − | 0.516556i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.69746e12 | − | 9.86829e12i | 0.166243 | − | 0.287941i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50335e13 | −1.21833 | −0.609164 | − | 0.793045i | \(-0.708495\pi\) | ||||
−0.609164 | + | 0.793045i | \(0.708495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.96144e13 | 2.59598 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.81876e13 | + | 3.15019e13i | −0.440134 | + | 0.762334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33105e13 | + | 3.20971e13i | 0.777079 | + | 0.748773i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.20152e12 | + | 2.08109e12i | 0.0260664 | + | 0.0451483i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.11886e13 | −1.69916 | −0.849580 | − | 0.527460i | \(-0.823144\pi\) | ||||
−0.849580 | + | 0.527460i | \(0.823144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.56233e13 | + | 7.90218e13i | 0.889210 | + | 1.54016i | 0.840811 | + | 0.541329i | \(0.182078\pi\) |
0.0483988 | + | 0.998828i | \(0.484588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.75443e13 | + | 3.03876e13i | −0.330097 | + | 0.571745i | −0.982531 | − | 0.186101i | \(-0.940415\pi\) |
0.652433 | + | 0.757846i | \(0.273748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.71054e13 | − | 6.42684e13i | 0.651045 | − | 1.12764i | −0.331825 | − | 0.943341i | \(-0.607664\pi\) |
0.982870 | − | 0.184301i | \(-0.0590022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.46496e13 | + | 1.29297e14i | 1.26526 | + | 2.19149i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.15654e13 | 0.341305 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.81443e13 | + | 4.87474e13i | 0.430559 | + | 0.745750i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.92283e12 | + | 1.70537e12i | −0.0847133 | + | 0.0243916i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.12968e12 | + | 8.88487e12i | −0.0709637 | + | 0.122913i | −0.899324 | − | 0.437283i | \(-0.855941\pi\) |
0.828360 | + | 0.560196i | \(0.189274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.91476e14 | −2.47953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.27820e13 | 0.661487 | 0.330743 | − | 0.943721i | \(-0.392701\pi\) | ||||
0.330743 | + | 0.943721i | \(0.392701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.67017e13 | + | 4.62487e13i | −0.313610 | + | 0.543189i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.86190e13 | − | 6.55348e13i | 0.666685 | − | 0.745340i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.11874e13 | + | 1.05980e14i | 0.652905 | + | 1.13086i | 0.982415 | + | 0.186712i | \(0.0597831\pi\) |
−0.329510 | + | 0.944152i | \(0.606884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.45906e13 | 0.254232 | 0.127116 | − | 0.991888i | \(-0.459428\pi\) | ||||
0.127116 | + | 0.991888i | \(0.459428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.31490e13 | − | 4.00952e13i | −0.224787 | − | 0.389343i | 0.731468 | − | 0.681875i | \(-0.238835\pi\) |
−0.956256 | + | 0.292533i | \(0.905502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.92653e13 | − | 5.06889e13i | 0.275484 | − | 0.477153i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.74265e13 | − | 1.68748e14i | 0.862298 | − | 1.49354i | −0.00740641 | − | 0.999973i | \(-0.502358\pi\) |
0.869705 | − | 0.493572i | \(-0.164309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.80807e13 | + | 8.32781e13i | 0.412744 | + | 0.714893i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.22998e14 | −0.993777 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.70186e13 | − | 1.33400e14i | −0.603854 | − | 1.04591i | −0.992231 | − | 0.124406i | \(-0.960298\pi\) |
0.388377 | − | 0.921501i | \(-0.373036\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.01923e13 | + | 2.02254e14i | −0.370750 | + | 1.49397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.42105e13 | + | 1.28536e14i | −0.532190 | + | 0.921780i | 0.467104 | + | 0.884203i | \(0.345297\pi\) |
−0.999294 | + | 0.0375776i | \(0.988036\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.25780e14 | 0.850616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.63905e14 | −1.73353 | −0.866766 | − | 0.498715i | \(-0.833805\pi\) | ||||
−0.866766 | + | 0.498715i | \(0.833805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.31627e13 | + | 4.01190e13i | −0.143614 | + | 0.248746i | −0.928855 | − | 0.370444i | \(-0.879206\pi\) |
0.785241 | + | 0.619190i | \(0.212539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.20623e14 | + | 3.08944e14i | 1.93180 | + | 1.86143i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.12486e12 | + | 5.41242e12i | 0.0177872 | + | 0.0308084i | 0.874782 | − | 0.484517i | \(-0.161005\pi\) |
−0.856995 | + | 0.515325i | \(0.827671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.28517e14 | −1.26458 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.37483e13 | − | 4.11333e13i | −0.124265 | − | 0.215233i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.83142e13 | + | 8.36827e13i | −0.245882 | + | 0.425880i | −0.962379 | − | 0.271710i | \(-0.912411\pi\) |
0.716497 | + | 0.697590i | \(0.245744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00607e13 | − | 1.04028e14i | 0.289265 | − | 0.501022i | −0.684369 | − | 0.729136i | \(-0.739922\pi\) |
0.973635 | + | 0.228113i | \(0.0732556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.24953e13 | + | 3.89631e13i | 0.105418 | + | 0.182589i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.96162e14 | −0.870654 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.06240e14 | − | 1.84013e14i | −0.458998 | − | 0.795007i | 0.539911 | − | 0.841722i | \(-0.318458\pi\) |
−0.998908 | + | 0.0467150i | \(0.985125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.62931e13 | − | 3.88021e14i | 0.394339 | − | 1.58902i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.55498e14 | − | 4.42536e14i | 1.01888 | − | 1.76475i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.70399e13 | −0.291433 | −0.145716 | − | 0.989326i | \(-0.546549\pi\) | ||||
−0.145716 | + | 0.989326i | \(0.546549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.49104e14 | −1.28648 | −0.643241 | − | 0.765664i | \(-0.722411\pi\) | ||||
−0.643241 | + | 0.765664i | \(0.722411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.76808e14 | + | 3.06241e14i | −0.618534 | + | 1.07133i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.26776e12 | − | 2.66848e12i | 0.0315952 | − | 0.00909726i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.54794e13 | + | 6.14522e13i | 0.114908 | + | 0.199027i | 0.917743 | − | 0.397174i | \(-0.130009\pi\) |
−0.802835 | + | 0.596202i | \(0.796676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.57341e14 | −1.75969 | −0.879847 | − | 0.475256i | \(-0.842355\pi\) | ||||
−0.879847 | + | 0.475256i | \(0.842355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.07708e14 | + | 1.86555e14i | 0.323295 | + | 0.559963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.90654e14 | − | 3.30223e14i | 0.558074 | − | 0.966613i | −0.439583 | − | 0.898202i | \(-0.644874\pi\) |
0.997657 | − | 0.0684109i | \(-0.0217929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.88095e13 | + | 1.19182e14i | −0.191614 | + | 0.331886i | −0.945785 | − | 0.324792i | \(-0.894706\pi\) |
0.754171 | + | 0.656678i | \(0.228039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.46091e13 | − | 1.63868e14i | −0.257012 | − | 0.445157i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.91960e14 | 0.496429 | 0.248214 | − | 0.968705i | \(-0.420156\pi\) | ||||
0.248214 | + | 0.968705i | \(0.420156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.49548e14 | − | 4.32230e14i | −0.629772 | − | 1.09080i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.60463e14 | − | 1.03789e14i | 0.866558 | − | 0.249509i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.61232e14 | − | 6.25673e14i | 0.847711 | − | 1.46828i | −0.0355355 | − | 0.999368i | \(-0.511314\pi\) |
0.883246 | − | 0.468910i | \(-0.155353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.28898e14 | 0.959398 | 0.479699 | − | 0.877433i | \(-0.340746\pi\) | ||||
0.479699 | + | 0.877433i | \(0.340746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.20134e14 | 1.35453 | 0.677267 | − | 0.735737i | \(-0.263164\pi\) | ||||
0.677267 | + | 0.735737i | \(0.263164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.53364e14 | − | 6.12045e14i | 0.736173 | − | 1.27509i | −0.218033 | − | 0.975941i | \(-0.569964\pi\) |
0.954207 | − | 0.299148i | \(-0.0967025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.85092e14 | + | 7.45844e14i | −0.376650 | + | 1.51774i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.70059e14 | + | 8.14167e14i | 0.912886 | + | 1.58116i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.33343e14 | 0.632523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.76957e13 | − | 1.34573e14i | −0.140783 | − | 0.243844i | 0.787008 | − | 0.616942i | \(-0.211629\pi\) |
−0.927792 | + | 0.373098i | \(0.878295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.26301e13 | + | 1.43120e14i | −0.146332 | + | 0.253455i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.72045e14 | − | 1.51043e15i | 1.47557 | − | 2.55576i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.67311e14 | − | 2.89791e14i | −0.276767 | − | 0.479375i | 0.693812 | − | 0.720156i | \(-0.255930\pi\) |
−0.970579 | + | 0.240781i | \(0.922596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.46129e14 | −0.863668 | −0.431834 | − | 0.901953i | \(-0.642133\pi\) | ||||
−0.431834 | + | 0.901953i | \(0.642133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.95087e14 | + | 6.84311e14i | 0.610991 | + | 1.05827i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.69155e14 | − | 1.62994e14i | −0.250222 | − | 0.241108i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.26652e14 | − | 5.65778e14i | 0.472642 | − | 0.818640i | −0.526868 | − | 0.849947i | \(-0.676634\pi\) |
0.999510 | + | 0.0313069i | \(0.00996694\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.29756e15 | 1.79682 | 0.898409 | − | 0.439161i | \(-0.144724\pi\) | ||||
0.898409 | + | 0.439161i | \(0.144724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.72365e15 | 2.33532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.20168e14 | + | 9.00957e14i | −0.674832 | + | 1.16884i | 0.301686 | + | 0.953407i | \(0.402451\pi\) |
−0.976518 | + | 0.215436i | \(0.930883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.18897e14 | + | 4.79107e14i | −0.150959 | + | 0.608300i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.62583e14 | − | 1.32083e15i | −0.927572 | − | 1.60660i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.25262e14 | −0.149149 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.26924e14 | − | 1.43227e15i | −0.943752 | − | 1.63463i | −0.758231 | − | 0.651986i | \(-0.773936\pi\) |
−0.185522 | − | 0.982640i | \(-0.559397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.37190e14 | + | 4.10824e14i | −0.265055 | + | 0.459089i | −0.967578 | − | 0.252572i | \(-0.918724\pi\) |
0.702523 | + | 0.711661i | \(0.252057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.41320e14 | + | 2.44774e14i | −0.151442 | + | 0.262305i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.64915e14 | − | 1.15167e15i | −0.697847 | − | 1.20871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.20473e14 | −0.423388 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.05478e15 | − | 1.82694e15i | −1.04044 | − | 1.80210i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.51334e15 | − | 9.50257e14i | 1.43284 | − | 0.899711i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.57042e14 | + | 4.45210e14i | −0.238462 | + | 0.413028i | −0.960273 | − | 0.279062i | \(-0.909977\pi\) |
0.721811 | + | 0.692090i | \(0.243310\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.09550e15 | −1.86684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.36242e14 | 0.380888 | 0.190444 | − | 0.981698i | \(-0.439007\pi\) | ||||
0.190444 | + | 0.981698i | \(0.439007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72435e14 | − | 6.45077e14i | 0.312404 | − | 0.541100i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.83180e14 | + | 5.27433e13i | −0.150623 | + | 0.0433689i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.08792e15 | − | 1.88434e15i | −0.859795 | − | 1.48921i | −0.872124 | − | 0.489285i | \(-0.837258\pi\) |
0.0123289 | − | 0.999924i | \(-0.496075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.92020e14 | 0.613721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.45391e14 | + | 7.71439e14i | 0.331852 | + | 0.574785i | 0.982875 | − | 0.184273i | \(-0.0589931\pi\) |
−0.651023 | + | 0.759058i | \(0.725660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.16307e14 | − | 1.24068e15i | 0.523399 | − | 0.906554i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.25020e15 | − | 2.16542e15i | 0.878747 | − | 1.52203i | 0.0260291 | − | 0.999661i | \(-0.491714\pi\) |
0.852717 | − | 0.522372i | \(-0.174953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.20063e15 | + | 2.07955e15i | 0.827773 | + | 1.43374i | 0.899782 | + | 0.436341i | \(0.143726\pi\) |
−0.0720088 | + | 0.997404i | \(0.522941\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.53226e15 | −2.34358 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.01843e14 | − | 1.38883e15i | −0.521942 | − | 0.904031i | −0.999674 | − | 0.0255249i | \(-0.991874\pi\) |
0.477732 | − | 0.878506i | \(-0.341459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.47680e15 | − | 1.42301e15i | −0.925449 | − | 0.891739i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.11758e15 | + | 3.66775e15i | −1.30215 | + | 2.25540i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.58598e15 | 1.53150 | 0.765749 | − | 0.643140i | \(-0.222369\pi\) | ||||
0.765749 | + | 0.643140i | \(0.222369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.66436e14 | 0.154867 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.43649e14 | − | 1.28804e15i | 0.416454 | − | 0.721320i | −0.579126 | − | 0.815238i | \(-0.696606\pi\) |
0.995580 | + | 0.0939186i | \(0.0299394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.69692e15 | + | 1.63510e15i | 0.932861 | + | 0.898881i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.28520e14 | + | 9.15423e14i | 0.280036 | + | 0.485036i | 0.971393 | − | 0.237477i | \(-0.0763203\pi\) |
−0.691357 | + | 0.722513i | \(0.742987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.15911e15 | −1.12322 | −0.561610 | − | 0.827402i | \(-0.689818\pi\) | ||||
−0.561610 | + | 0.827402i | \(0.689818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.94388e15 | + | 5.09894e15i | 1.47661 | + | 2.55756i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.50659e14 | + | 1.64659e15i | −0.468260 | + | 0.811050i | −0.999342 | − | 0.0362702i | \(-0.988452\pi\) |
0.531082 | + | 0.847320i | \(0.321786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.27646e13 | + | 9.13909e13i | −0.0250678 | + | 0.0434187i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.85740e14 | − | 8.41326e14i | −0.226658 | − | 0.392583i | 0.730158 | − | 0.683279i | \(-0.239447\pi\) |
−0.956816 | + | 0.290696i | \(0.906113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.39104e15 | 0.626282 | 0.313141 | − | 0.949707i | \(-0.398619\pi\) | ||||
0.313141 | + | 0.949707i | \(0.398619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.56881e15 | − | 2.71726e15i | −0.693859 | − | 1.20180i | −0.970564 | − | 0.240844i | \(-0.922576\pi\) |
0.276705 | − | 0.960955i | \(-0.410758\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.29757e14 | + | 2.10120e14i | −0.311526 | + | 0.0896979i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.64095e14 | − | 4.57426e14i | 0.110769 | − | 0.191858i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.03820e15 | −0.420438 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.42265e15 | 1.76003 | 0.880017 | − | 0.474942i | \(-0.157531\pi\) | ||||
0.880017 | + | 0.474942i | \(0.157531\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.07951e14 | − | 1.86977e14i | 0.0414927 | − | 0.0718675i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.58354e13 | − | 1.50441e15i | −0.0210932 | − | 0.568329i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.94254e14 | + | 8.56073e14i | 0.180398 | + | 0.312458i | 0.942016 | − | 0.335568i | \(-0.108928\pi\) |
−0.761618 | + | 0.648026i | \(0.775595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.69033e15 | 0.965262 | 0.482631 | − | 0.875824i | \(-0.339681\pi\) | ||||
0.482631 | + | 0.875824i | \(0.339681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47451e15 | + | 2.55393e15i | 0.511299 | + | 0.885595i | 0.999914 | + | 0.0130960i | \(0.00416870\pi\) |
−0.488616 | + | 0.872499i | \(0.662498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.06254e15 | − | 7.03652e15i | 1.38501 | − | 2.39890i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.17965e15 | + | 2.04321e15i | −0.388803 | + | 0.673427i | −0.992289 | − | 0.123947i | \(-0.960445\pi\) |
0.603486 | + | 0.797374i | \(0.293778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.52681e14 | − | 2.64451e14i | −0.0494831 | − | 0.0857072i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.40458e14 | 0.138050 | 0.0690248 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690248 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.68645e14 | + | 1.33133e15i | 0.236929 | + | 0.410373i | 0.959831 | − | 0.280577i | \(-0.0905259\pi\) |
−0.722903 | + | 0.690950i | \(0.757193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.35043e14 | − | 2.15600e15i | 0.159540 | − | 0.642879i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.94650e15 | + | 6.83554e15i | −1.15750 | + | 2.00484i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.96004e14 | 0.0556277 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.83410e14 | −0.107048 | −0.0535242 | − | 0.998567i | \(-0.517045\pi\) | ||||
−0.0535242 | + | 0.998567i | \(0.517045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.52818e15 | + | 2.64688e15i | −0.412986 | + | 0.715313i | −0.995215 | − | 0.0977120i | \(-0.968848\pi\) |
0.582228 | + | 0.813025i | \(0.302181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.04048e15 | − | 4.85688e15i | −1.34026 | − | 1.29144i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.24318e15 | + | 2.15324e15i | 0.320051 | + | 0.554344i | 0.980498 | − | 0.196528i | \(-0.0629667\pi\) |
−0.660447 | + | 0.750872i | \(0.729633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.43552e15 | −0.870350 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.78399e15 | + | 3.08997e15i | 0.437711 | + | 0.758137i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.75214e15 | − | 3.03479e15i | 0.423096 | − | 0.732823i | −0.573145 | − | 0.819454i | \(-0.694277\pi\) |
0.996240 | + | 0.0866310i | \(0.0276101\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.93019e15 | − | 5.07523e15i | 0.685455 | − | 1.18724i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.32075e15 | − | 2.28760e15i | −0.304116 | − | 0.526745i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.93387e15 | −1.32400 | −0.662001 | − | 0.749503i | \(-0.730293\pi\) | ||||
−0.662001 | + | 0.749503i | \(0.730293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89337e14 | + | 8.47557e14i | 0.107487 | + | 0.186172i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.66618e15 | − | 6.71402e15i | 0.354745 | − | 1.42947i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.66852e15 | + | 4.62202e15i | −0.559393 | + | 0.968896i | 0.438155 | + | 0.898900i | \(0.355632\pi\) |
−0.997547 | + | 0.0699967i | \(0.977701\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.82328e15 | −0.573801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.62343e15 | 1.52569 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.51335e15 | + | 2.62120e15i | −0.293718 | + | 0.508735i | −0.974686 | − | 0.223579i | \(-0.928226\pi\) |
0.680968 | + | 0.732313i | \(0.261559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.88210e15 | + | 1.69364e15i | −1.12432 | + | 0.323726i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.10699e15 | + | 1.05776e16i | 1.13232 | + | 1.96123i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.66738e15 | −0.304506 | −0.152253 | − | 0.988342i | \(-0.548653\pi\) | ||||
−0.152253 | + | 0.988342i | \(0.548653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.48781e15 | + | 4.30902e15i | 0.440831 | + | 0.763542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.19667e15 | + | 3.80474e15i | −0.383436 | + | 0.664130i | −0.991551 | − | 0.129719i | \(-0.958593\pi\) |
0.608115 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.80891e15 | + | 1.35254e16i | −1.32288 | + | 2.29129i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.77656e14 | − | 1.69335e15i | −0.163170 | − | 0.282620i | 0.772834 | − | 0.634609i | \(-0.218839\pi\) |
−0.936004 | + | 0.351989i | \(0.885505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.66464e15 | −1.24180 | −0.620902 | − | 0.783888i | \(-0.713234\pi\) | ||||
−0.620902 | + | 0.783888i | \(0.713234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.45085e15 | + | 4.24499e15i | 0.391252 | + | 0.677668i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.13595e15 | + | 2.34259e15i | −1.26113 | + | 0.363117i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.89846e15 | + | 8.48439e15i | −0.748239 | + | 1.29599i | 0.200427 | + | 0.979709i | \(0.435767\pi\) |
−0.948666 | + | 0.316279i | \(0.897566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.93905e16 | 2.87661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.58148e15 | 0.231226 | 0.115613 | − | 0.993294i | \(-0.463117\pi\) | ||||
0.115613 | + | 0.993294i | \(0.463117\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.93379e15 | + | 6.81352e15i | −0.558722 | + | 0.967734i | 0.438882 | + | 0.898545i | \(0.355375\pi\) |
−0.997604 | + | 0.0691896i | \(0.977959\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.02564e15 | + | 8.16246e15i | −0.283580 | + | 1.14271i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.42256e15 | − | 5.92804e15i | −0.465561 | − | 0.806375i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.27927e15 | 0.842005 | 0.421002 | − | 0.907060i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907060i | \(0.361678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.66695e15 | − | 2.88725e15i | −0.217238 | − | 0.376268i | 0.736724 | − | 0.676193i | \(-0.236372\pi\) |
−0.953963 | + | 0.299925i | \(0.903038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.18443e15 | + | 3.78355e15i | −0.280659 | + | 0.486116i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.24503e15 | + | 2.15645e15i | −0.155497 | + | 0.269329i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.38703e15 | − | 4.13446e15i | −0.293952 | − | 0.509140i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.54641e16 | −1.85158 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.18067e15 | − | 7.24113e15i | −0.493611 | − | 0.854960i | 0.506362 | − | 0.862321i | \(-0.330990\pi\) |
−0.999973 | + | 0.00736161i | \(0.997657\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.14031e15 | − | 3.98949e15i | −0.475403 | − | 0.458086i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.25635e13 | − | 1.43004e14i | 0.00934944 | − | 0.0161937i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.02626e15 | 0.553636 | 0.276818 | − | 0.960922i | \(-0.410720\pi\) | ||||
0.276818 | + | 0.960922i | \(0.410720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.62955e14 | −0.0720240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.01620e15 | + | 8.68831e15i | −0.530199 | + | 0.918332i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.66956e15 | + | 2.28460e16i | −0.591115 | + | 2.38195i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.22897e15 | − | 5.59275e15i | −0.327603 | − | 0.567425i | 0.654433 | − | 0.756120i | \(-0.272907\pi\) |
−0.982036 | + | 0.188695i | \(0.939574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.75664e15 | 0.676264 | 0.338132 | − | 0.941099i | \(-0.390205\pi\) | ||||
0.338132 | + | 0.941099i | \(0.390205\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.57094e15 | − | 1.31133e16i | −0.737536 | − | 1.27745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34518e15 | − | 4.06197e15i | 0.225401 | − | 0.390405i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.36313e15 | − | 2.36101e15i | 0.127541 | − | 0.220907i | −0.795182 | − | 0.606370i | \(-0.792625\pi\) |
0.922723 | + | 0.385463i | \(0.125958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.57340e15 | − | 4.45726e15i | −0.237579 | − | 0.411499i | 0.722440 | − | 0.691434i | \(-0.243021\pi\) |
−0.960019 | + | 0.279934i | \(0.909687\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.44595e16 | 1.29979 | 0.649896 | − | 0.760023i | \(-0.274812\pi\) | ||||
0.649896 | + | 0.760023i | \(0.274812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.58791e15 | + | 9.67854e15i | 0.495677 | + | 0.858538i | 0.999988 | − | 0.00498412i | \(-0.00158650\pi\) |
−0.504310 | + | 0.863523i | \(0.668253\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.00944e15 | − | 5.02929e15i | 0.691918 | − | 0.434469i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.43500e15 | + | 5.94960e15i | −0.292854 | + | 0.507238i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.90990e15 | −0.407739 | −0.203869 | − | 0.978998i | \(-0.565352\pi\) | ||||
−0.203869 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.50922e16 | 1.23702 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.71707e15 | + | 1.16343e16i | −0.536375 | + | 0.929028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27073e16 | − | 6.53813e15i | 1.78981 | − | 0.515341i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.18525e15 | − | 8.98111e15i | −0.398251 | − | 0.689791i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.08977e16 | 0.826259 | 0.413130 | − | 0.910672i | \(-0.364436\pi\) | ||||
0.413130 | + | 0.910672i | \(0.364436\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.46459e15 | + | 1.29291e16i | 0.551584 | + | 0.955372i | 0.998161 | + | 0.0606261i | \(0.0193097\pi\) |
−0.446577 | + | 0.894745i | \(0.647357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.26814e15 | − | 1.60529e16i | 0.676130 | − | 1.17109i | −0.300007 | − | 0.953937i | \(-0.596989\pi\) |
0.976137 | − | 0.217155i | \(-0.0696776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.01520e15 | + | 1.38827e16i | −0.569974 | + | 0.987223i | 0.426594 | + | 0.904443i | \(0.359713\pi\) |
−0.996568 | + | 0.0827802i | \(0.973620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.42194e15 | − | 7.65902e15i | −0.310473 | − | 0.537755i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.87408e15 | −0.265191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.57875e15 | + | 1.13947e16i | 0.444676 | + | 0.770202i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.90645e15 | + | 8.58203e15i | 0.587030 | + | 0.565647i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.71479e13 | + | 6.43421e13i | −0.00241789 | + | 0.00418791i | −0.867232 | − | 0.497905i | \(-0.834103\pi\) |
0.864814 | + | 0.502092i | \(0.167436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.09340e14 | −0.0196367 | −0.00981834 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981834 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.33039e16 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.87138e15 | − | 8.43749e15i | 0.297901 | − | 0.515980i | −0.677754 | − | 0.735288i | \(-0.737047\pi\) |
0.975656 | + | 0.219308i | \(0.0703800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.23966e14 | − | 6.01237e14i | −0.0376878 | − | 0.0363150i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.12473e14 | + | 5.41219e14i | 0.0184132 | + | 0.0318926i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.83437e15 | −0.514220 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.88122e15 | + | 8.45453e15i | 0.277236 | + | 0.480188i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12074e16 | + | 1.94118e16i | −0.628809 | + | 1.08913i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.15597e16 | − | 3.73424e16i | 1.18052 | − | 2.04473i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.21611e15 | − | 2.10636e15i | −0.0657857 | − | 0.113944i | 0.831257 | − | 0.555889i | \(-0.187622\pi\) |
−0.897042 | + | 0.441945i | \(0.854289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.60045e15 | 0.295714 | 0.147857 | − | 0.989009i | \(-0.452762\pi\) | ||||
0.147857 | + | 0.989009i | \(0.452762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.08398e16 | − | 3.60956e16i | −1.08719 | − | 1.88306i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.17769e15 | + | 3.39092e14i | −0.0599788 | + | 0.0172698i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.67446e15 | + | 6.36435e15i | −0.184909 | + | 0.320272i | −0.943546 | − | 0.331242i | \(-0.892532\pi\) |
0.758637 | + | 0.651514i | \(0.225866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.02199e15 | −0.197620 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.60478e16 | −0.779175 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.59318e16 | − | 2.75947e16i | 0.755404 | − | 1.30840i | −0.189769 | − | 0.981829i | \(-0.560774\pi\) |
0.945173 | − | 0.326569i | \(-0.105893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.88089e15 | − | 4.16822e15i | −0.369277 | − | 0.195312i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.39460e16 | + | 4.14756e16i | 1.09589 | + | 1.89814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.96022e14 | 0.0314815 | 0.0157407 | − | 0.999876i | \(-0.494989\pi\) | ||||
0.0157407 | + | 0.999876i | \(0.494989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00499e15 | + | 3.47274e15i | 0.0885866 | + | 0.153437i | 0.906914 | − | 0.421316i | \(-0.138432\pi\) |
−0.818327 | + | 0.574753i | \(0.805098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.31929e16 | − | 2.28507e16i | 0.576136 | − | 0.997897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.41225e16 | − | 2.44609e16i | 0.602542 | − | 1.04363i | −0.389893 | − | 0.920860i | \(-0.627488\pi\) |
0.992435 | − | 0.122773i | \(-0.0391787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.22599e15 | + | 7.31962e15i | 0.178223 | + | 0.308691i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.94290e16 | −0.800645 | −0.400322 | − | 0.916374i | \(-0.631102\pi\) | ||||
−0.400322 | + | 0.916374i | \(0.631102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.82185e16 | − | 3.15554e16i | −0.742154 | − | 1.28545i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.32097e15 | + | 1.33821e16i | −0.132210 | + | 0.532749i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.09583e16 | − | 1.89803e16i | 0.431283 | − | 0.747005i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.87306e16 | −1.48989 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.43128e14 | −0.0320662 | −0.0160331 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160331 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.41094e16 | + | 2.44382e16i | −0.524569 | + | 0.908580i | 0.475022 | + | 0.879974i | \(0.342440\pi\) |
−0.999591 | + | 0.0286063i | \(0.990893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.69367e16 | − | 1.63198e16i | −0.622599 | − | 0.599920i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.52194e16 | − | 2.63608e16i | −0.546988 | − | 0.947411i | −0.998479 | − | 0.0551353i | \(-0.982441\pi\) |
0.451491 | − | 0.892276i | \(-0.350892\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.54336e16 | −0.548483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.50449e15 | + | 9.53406e15i | 0.191282 | + | 0.331309i | 0.945675 | − | 0.325113i | \(-0.105402\pi\) |
−0.754394 | + | 0.656422i | \(0.772069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.09645e16 | + | 5.36321e16i | −1.06406 | + | 1.84300i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.48506e16 | + | 4.30426e16i | −0.835137 | + | 1.44650i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.82372e15 | + | 8.35493e15i | 0.160316 | + | 0.277676i | 0.934982 | − | 0.354695i | \(-0.115415\pi\) |
−0.774666 | + | 0.632371i | \(0.782082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.98172e16 | 1.94446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.25892e15 | − | 9.10872e15i | −0.169073 | − | 0.292843i | 0.769021 | − | 0.639223i | \(-0.220744\pi\) |
−0.938094 | + | 0.346381i | \(0.887411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.12.k.d.37.7 | 16 | ||
3.2 | odd | 2 | 84.12.i.b.37.2 | yes | 16 | ||
7.4 | even | 3 | inner | 252.12.k.d.109.7 | 16 | ||
21.11 | odd | 6 | 84.12.i.b.25.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.i.b.25.2 | ✓ | 16 | 21.11 | odd | 6 | ||
84.12.i.b.37.2 | yes | 16 | 3.2 | odd | 2 | ||
252.12.k.d.37.7 | 16 | 1.1 | even | 1 | trivial | ||
252.12.k.d.109.7 | 16 | 7.4 | even | 3 | inner |