Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,9,Mod(44,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.44");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.d (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: | \(18.3320374528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1982 x^{14} + 1579736 x^{12} + 654647506 x^{10} + 151540734566 x^{8} + 19474609444738 x^{6} + \cdots + 29\!\cdots\!09 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{42}\cdot 5^{10}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 44.14 | ||
Root | \(6.77659i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.44 |
Dual form | 45.9.d.a.44.13 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.2774 | 1.39234 | 0.696168 | − | 0.717879i | \(-0.254887\pi\) | ||||
0.696168 | + | 0.717879i | \(0.254887\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 240.281 | 0.938598 | ||||||||
\(5\) | −622.133 | + | 59.7978i | −0.995412 | + | 0.0956765i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2644.18i | − | 1.10128i | −0.834742 | − | 0.550642i | \(-0.814383\pi\) | ||
0.834742 | − | 0.550642i | \(-0.185617\pi\) | |||||||
\(8\) | −350.176 | −0.0854921 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −13859.5 | + | 1332.14i | −1.38595 | + | 0.133214i | ||||
\(11\) | − | 22455.9i | − | 1.53377i | −0.641786 | − | 0.766884i | \(-0.721806\pi\) | ||
0.641786 | − | 0.766884i | \(-0.278194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11076.3i | − | 0.387811i | −0.981020 | − | 0.193905i | \(-0.937885\pi\) | ||
0.981020 | − | 0.193905i | \(-0.0621155\pi\) | |||||||
\(14\) | − | 58905.4i | − | 1.53336i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −69313.0 | −1.05763 | ||||||||
\(17\) | 35513.3 | 0.425201 | 0.212601 | − | 0.977139i | \(-0.431807\pi\) | ||||
0.212601 | + | 0.977139i | \(0.431807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3033.68 | 0.0232785 | 0.0116393 | − | 0.999932i | \(-0.496295\pi\) | ||||
0.0116393 | + | 0.999932i | \(0.496295\pi\) | |||||||
\(20\) | −149487. | + | 14368.3i | −0.934292 | + | 0.0898018i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 500258.i | − | 2.13552i | ||||||
\(23\) | −352929. | −1.26118 | −0.630589 | − | 0.776117i | \(-0.717186\pi\) | ||||
−0.630589 | + | 0.776117i | \(0.717186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 383473. | − | 74404.4i | 0.981692 | − | 0.190475i | ||||
\(26\) | − | 246750.i | − | 0.539963i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 635347.i | − | 1.03366i | ||||||
\(29\) | 1.14240e6i | 1.61521i | 0.589726 | + | 0.807603i | \(0.299236\pi\) | ||||
−0.589726 | + | 0.807603i | \(0.700764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 317106. | 0.343367 | 0.171683 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171683 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(32\) | −1.45447e6 | −1.38709 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 791142. | 0.592023 | ||||||||
\(35\) | 158116. | + | 1.64503e6i | 0.105367 | + | 1.09623i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.94595e6i | − | 1.03831i | −0.854681 | − | 0.519153i | \(-0.826247\pi\) | ||
0.854681 | − | 0.519153i | \(-0.173753\pi\) | |||||||
\(38\) | 67582.4 | 0.0324115 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 217856. | − | 20939.8i | 0.0850999 | − | 0.00817959i | ||||
\(41\) | − | 3.08883e6i | − | 1.09310i | −0.837428 | − | 0.546548i | \(-0.815941\pi\) | ||
0.837428 | − | 0.546548i | \(-0.184059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 255669.i | − | 0.0747833i | −0.999301 | − | 0.0373916i | \(-0.988095\pi\) | ||
0.999301 | − | 0.0373916i | \(-0.0119049\pi\) | |||||||
\(44\) | − | 5.39573e6i | − | 1.43959i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.86233e6 | −1.75598 | ||||||||
\(47\) | −5.90149e6 | −1.20940 | −0.604701 | − | 0.796453i | \(-0.706707\pi\) | ||||
−0.604701 | + | 0.796453i | \(0.706707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.22689e6 | −0.212824 | ||||||||
\(50\) | 8.54278e6 | − | 1.65753e6i | 1.36684 | − | 0.265205i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.66142e6i | − | 0.363998i | ||||||
\(53\) | 9.19732e6 | 1.16562 | 0.582811 | − | 0.812608i | \(-0.301953\pi\) | ||||
0.582811 | + | 0.812608i | \(0.301953\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.34281e6 | + | 1.39705e7i | 0.146746 | + | 1.52673i | ||||
\(56\) | 925928.i | 0.0941510i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.54498e7i | 2.24891i | ||||||||
\(59\) | 1.32577e7i | 1.09411i | 0.837096 | + | 0.547056i | \(0.184251\pi\) | ||||
−0.837096 | + | 0.547056i | \(0.815749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.48813e7 | 1.79703 | 0.898513 | − | 0.438946i | \(-0.144648\pi\) | ||||
0.898513 | + | 0.438946i | \(0.144648\pi\) | |||||||
\(62\) | 7.06429e6 | 0.478082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.46575e7 | −0.873657 | ||||||||
\(65\) | 662337. | + | 6.89091e6i | 0.0371044 | + | 0.386032i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.54713e7i | − | 1.76026i | −0.474729 | − | 0.880132i | \(-0.657454\pi\) | ||
0.474729 | − | 0.880132i | \(-0.342546\pi\) | |||||||
\(68\) | 8.53316e6 | 0.399093 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.52241e6 | + | 3.66470e7i | 0.146706 | + | 1.52632i | ||||
\(71\) | 4.67255e7i | 1.83874i | 0.393394 | + | 0.919370i | \(0.371301\pi\) | ||||
−0.393394 | + | 0.919370i | \(0.628699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.36638e6i | 0.153755i | 0.997041 | + | 0.0768777i | \(0.0244951\pi\) | ||||
−0.997041 | + | 0.0768777i | \(0.975505\pi\) | |||||||
\(74\) | − | 4.33507e7i | − | 1.44567i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 728936. | 0.0218492 | ||||||||
\(77\) | −5.93774e7 | −1.68911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73568e7 | 0.445617 | 0.222808 | − | 0.974862i | \(-0.428478\pi\) | ||||
0.222808 | + | 0.974862i | \(0.428478\pi\) | |||||||
\(80\) | 4.31219e7 | − | 4.14477e6i | 1.05278 | − | 0.101191i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.88110e7i | − | 1.52196i | ||||||
\(83\) | 5.54885e6 | 0.116921 | 0.0584603 | − | 0.998290i | \(-0.481381\pi\) | ||||
0.0584603 | + | 0.998290i | \(0.481381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.20940e7 | + | 2.12362e6i | −0.423251 | + | 0.0406818i | ||||
\(86\) | − | 5.69564e6i | − | 0.104123i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.86351e6i | 0.131125i | ||||||||
\(89\) | − | 9.75180e7i | − | 1.55426i | −0.629338 | − | 0.777132i | \(-0.716674\pi\) | ||
0.629338 | − | 0.777132i | \(-0.283326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.92876e7 | −0.427089 | ||||||||
\(92\) | −8.48022e7 | −1.18374 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.31470e8 | −1.68389 | ||||||||
\(95\) | −1.88735e6 | + | 181408.i | −0.0231717 | + | 0.00222721i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.26808e8i | − | 1.43238i | −0.697905 | − | 0.716190i | \(-0.745884\pi\) | ||
0.697905 | − | 0.716190i | \(-0.254116\pi\) | |||||||
\(98\) | −2.73319e7 | −0.296323 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.21414e7 | − | 1.78780e7i | 0.921414 | − | 0.178780i | ||||
\(101\) | − | 7.63212e7i | − | 0.733432i | −0.930333 | − | 0.366716i | \(-0.880482\pi\) | ||
0.930333 | − | 0.366716i | \(-0.119518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.62029e8i | − | 1.43960i | −0.694180 | − | 0.719801i | \(-0.744233\pi\) | ||
0.694180 | − | 0.719801i | \(-0.255767\pi\) | |||||||
\(104\) | 3.87864e6i | 0.0331548i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.04892e8 | 1.62294 | ||||||||
\(107\) | −1.38641e8 | −1.05768 | −0.528842 | − | 0.848720i | \(-0.677374\pi\) | ||||
−0.528842 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.81922e7 | −0.412248 | −0.206124 | − | 0.978526i | \(-0.566085\pi\) | ||||
−0.206124 | + | 0.978526i | \(0.566085\pi\) | |||||||
\(110\) | 2.99144e7 | + | 3.11227e8i | 0.204319 | + | 2.12572i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.83276e8i | 1.16475i | ||||||||
\(113\) | 1.57487e7 | 0.0965899 | 0.0482949 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482949 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19569e8 | − | 2.11044e7i | 1.25539 | − | 0.120665i | ||||
\(116\) | 2.74498e8i | 1.51603i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.95348e8i | 1.52337i | ||||||||
\(119\) | − | 9.39034e7i | − | 0.468267i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.89908e8 | −1.35244 | ||||||||
\(122\) | 5.54291e8 | 2.50206 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.61946e7 | 0.322283 | ||||||||
\(125\) | −2.34122e8 | + | 6.92203e7i | −0.958964 | + | 0.283526i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.56922e7i | 0.329402i | 0.986344 | + | 0.164701i | \(0.0526660\pi\) | ||||
−0.986344 | + | 0.164701i | \(0.947334\pi\) | |||||||
\(128\) | 4.58117e7 | 0.170662 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.47551e7 | + | 1.53511e8i | 0.0516618 | + | 0.537486i | ||||
\(131\) | − | 2.13424e8i | − | 0.724699i | −0.932042 | − | 0.362350i | \(-0.881975\pi\) | ||
0.932042 | − | 0.362350i | \(-0.118025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.02160e6i | − | 0.0256362i | ||||||
\(134\) | − | 7.90207e8i | − | 2.45088i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.24359e7 | −0.0363514 | ||||||||
\(137\) | 4.29184e8 | 1.21832 | 0.609159 | − | 0.793048i | \(-0.291507\pi\) | ||||
0.609159 | + | 0.793048i | \(0.291507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.52255e8 | −1.47938 | −0.739691 | − | 0.672947i | \(-0.765028\pi\) | ||||
−0.739691 | + | 0.672947i | \(0.765028\pi\) | |||||||
\(140\) | 3.79924e7 | + | 3.95270e8i | 0.0988972 | + | 1.02892i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.04092e9i | 2.56014i | ||||||||
\(143\) | −2.48727e8 | −0.594812 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.83133e7 | − | 7.10727e8i | −0.154537 | − | 1.60780i | ||||
\(146\) | 9.72715e7i | 0.214079i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.67576e8i | − | 0.974553i | ||||||
\(149\) | − | 4.10444e8i | − | 0.832738i | −0.909196 | − | 0.416369i | \(-0.863302\pi\) | ||
0.909196 | − | 0.416369i | \(-0.136698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.42072e8 | 1.61973 | 0.809863 | − | 0.586619i | \(-0.199541\pi\) | ||||
0.809863 | + | 0.586619i | \(0.199541\pi\) | |||||||
\(152\) | −1.06232e6 | −0.00199013 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.32277e9 | −2.35181 | ||||||||
\(155\) | −1.97282e8 | + | 1.89623e7i | −0.341791 | + | 0.0328521i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.77763e8i | 0.621757i | 0.950450 | + | 0.310878i | \(0.100623\pi\) | ||||
−0.950450 | + | 0.310878i | \(0.899377\pi\) | |||||||
\(158\) | 3.86664e8 | 0.620448 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.04870e8 | − | 8.69739e7i | 1.38072 | − | 0.132712i | ||||
\(161\) | 9.33208e8i | 1.38891i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59262e8i | 0.225612i | 0.993617 | + | 0.112806i | \(0.0359839\pi\) | ||||
−0.993617 | + | 0.112806i | \(0.964016\pi\) | |||||||
\(164\) | − | 7.42188e8i | − | 1.02598i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.23614e8 | 0.162793 | ||||||||
\(167\) | −3.89514e7 | −0.0500792 | −0.0250396 | − | 0.999686i | \(-0.507971\pi\) | ||||
−0.0250396 | + | 0.999686i | \(0.507971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.93047e8 | 0.849603 | ||||||||
\(170\) | −4.92195e8 | + | 4.73086e7i | −0.589307 | + | 0.0566427i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6.14325e7i | − | 0.0701914i | ||||||
\(173\) | −9.12788e8 | −1.01903 | −0.509513 | − | 0.860463i | \(-0.670175\pi\) | ||||
−0.509513 | + | 0.860463i | \(0.670175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.96739e8 | − | 1.01397e9i | −0.209767 | − | 1.08112i | ||||
\(176\) | 1.55648e9i | 1.62216i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.17244e9i | − | 2.16406i | ||||||
\(179\) | 1.70075e8i | 0.165664i | 0.996564 | + | 0.0828321i | \(0.0263965\pi\) | ||||
−0.996564 | + | 0.0828321i | \(0.973603\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.47609e8 | 0.696563 | 0.348281 | − | 0.937390i | \(-0.386765\pi\) | ||||
0.348281 | + | 0.937390i | \(0.386765\pi\) | |||||||
\(182\) | −6.52452e8 | −0.594652 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.23587e8 | 0.107821 | ||||||||
\(185\) | 1.16364e8 | + | 1.21064e9i | 0.0993416 | + | 1.03354i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.97482e8i | − | 0.652160i | ||||||
\(188\) | −1.41802e9 | −1.13514 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.20452e7 | + | 4.04128e6i | −0.0322628 | + | 0.00310102i | ||||
\(191\) | − | 1.90973e8i | − | 0.143495i | −0.997423 | − | 0.0717477i | \(-0.977142\pi\) | ||
0.997423 | − | 0.0717477i | \(-0.0228576\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.57576e9i | 1.13569i | 0.823134 | + | 0.567847i | \(0.192224\pi\) | ||||
−0.823134 | + | 0.567847i | \(0.807776\pi\) | |||||||
\(194\) | − | 2.82494e9i | − | 1.99435i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.94798e8 | −0.199756 | ||||||||
\(197\) | −3.35396e7 | −0.0222686 | −0.0111343 | − | 0.999938i | \(-0.503544\pi\) | ||||
−0.0111343 | + | 0.999938i | \(0.503544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.16032e9 | −0.739890 | −0.369945 | − | 0.929054i | \(-0.620623\pi\) | ||||
−0.369945 | + | 0.929054i | \(0.620623\pi\) | |||||||
\(200\) | −1.34283e8 | + | 2.60546e7i | −0.0839269 | + | 0.0162841i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.70024e9i | − | 1.02118i | ||||||
\(203\) | 3.02072e9 | 1.77880 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.84705e8 | + | 1.92166e9i | 0.104584 | + | 1.08808i | ||||
\(206\) | − | 3.60957e9i | − | 2.00441i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.67729e8i | 0.410161i | ||||||||
\(209\) | − | 6.81240e7i | − | 0.0357039i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65320e9 | −0.834059 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(212\) | 2.20994e9 | 1.09405 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.08855e9 | −1.47265 | ||||||||
\(215\) | 1.52885e7 | + | 1.59060e8i | 0.00715501 | + | 0.0744402i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.38486e8i | − | 0.378144i | ||||||
\(218\) | −1.29637e9 | −0.573988 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.22653e8 | + | 3.35686e9i | 0.137735 | + | 1.43299i | ||||
\(221\) | − | 3.93354e8i | − | 0.164898i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.62653e9i | 1.46647i | 0.679977 | + | 0.733233i | \(0.261990\pi\) | ||||
−0.679977 | + | 0.733233i | \(0.738010\pi\) | |||||||
\(224\) | 3.84587e9i | 1.52757i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.50840e8 | 0.134486 | ||||||||
\(227\) | −3.32488e9 | −1.25220 | −0.626099 | − | 0.779744i | \(-0.715349\pi\) | ||||
−0.626099 | + | 0.779744i | \(0.715349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.14773e9 | 1.50823 | 0.754117 | − | 0.656740i | \(-0.228065\pi\) | ||||
0.754117 | + | 0.656740i | \(0.228065\pi\) | |||||||
\(230\) | 4.89141e9 | − | 4.70150e8i | 1.74793 | − | 0.168006i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 4.00042e8i | − | 0.138087i | ||||||
\(233\) | 4.25813e9 | 1.44476 | 0.722380 | − | 0.691496i | \(-0.243048\pi\) | ||||
0.722380 | + | 0.691496i | \(0.243048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.67151e9 | − | 3.52897e8i | 1.20385 | − | 0.115711i | ||||
\(236\) | 3.18559e9i | 1.02693i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.09192e9i | − | 0.651985i | ||||||
\(239\) | 3.02690e9i | 0.927698i | 0.885914 | + | 0.463849i | \(0.153532\pi\) | ||||
−0.885914 | + | 0.463849i | \(0.846468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.38816e9 | −1.00438 | −0.502188 | − | 0.864758i | \(-0.667471\pi\) | ||||
−0.502188 | + | 0.864758i | \(0.667471\pi\) | |||||||
\(242\) | −6.45840e9 | −1.88306 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.97852e9 | 1.68669 | ||||||||
\(245\) | 7.63288e8 | − | 7.33653e7i | 0.211848 | − | 0.0203623i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.36018e7i | − | 0.00902766i | ||||||
\(248\) | −1.11043e8 | −0.0293551 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.21563e9 | + | 1.54205e9i | −1.33520 | + | 0.394764i | ||||
\(251\) | − | 2.21606e9i | − | 0.558324i | −0.960244 | − | 0.279162i | \(-0.909943\pi\) | ||
0.960244 | − | 0.279162i | \(-0.0900566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.92534e9i | 1.93435i | ||||||||
\(254\) | 1.90900e9i | 0.458639i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.77289e9 | 1.11128 | ||||||||
\(257\) | 3.68531e9 | 0.844777 | 0.422388 | − | 0.906415i | \(-0.361192\pi\) | ||||
0.422388 | + | 0.906415i | \(0.361192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.14545e9 | −1.14347 | ||||||||
\(260\) | 1.59147e8 | + | 1.65575e9i | 0.0348261 | + | 0.362329i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 4.75452e9i | − | 1.00902i | ||||||
\(263\) | 2.54121e9 | 0.531151 | 0.265575 | − | 0.964090i | \(-0.414438\pi\) | ||||
0.265575 | + | 0.964090i | \(0.414438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.72196e9 | + | 5.49980e8i | −1.16028 | + | 0.111523i | ||||
\(266\) | − | 1.78700e8i | − | 0.0356942i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 8.52308e9i | − | 1.65218i | ||||||
\(269\) | − | 4.48964e9i | − | 0.857437i | −0.903438 | − | 0.428718i | \(-0.858965\pi\) | ||
0.903438 | − | 0.428718i | \(-0.141035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.36070e8 | −0.0252281 | −0.0126141 | − | 0.999920i | \(-0.504015\pi\) | ||||
−0.0126141 | + | 0.999920i | \(0.504015\pi\) | |||||||
\(272\) | −2.46153e9 | −0.449707 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.56108e9 | 1.69631 | ||||||||
\(275\) | −1.67082e9 | − | 8.61124e9i | −0.292145 | − | 1.50569i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.79752e9i | − | 0.984743i | −0.870385 | − | 0.492372i | \(-0.836130\pi\) | ||
0.870385 | − | 0.492372i | \(-0.163870\pi\) | |||||||
\(278\) | −1.23028e10 | −2.05980 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.53685e7 | − | 5.76050e8i | −0.00900804 | − | 0.0937191i | ||||
\(281\) | − | 4.33689e9i | − | 0.695589i | −0.937571 | − | 0.347794i | \(-0.886931\pi\) | ||
0.937571 | − | 0.347794i | \(-0.113069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.93677e9i | − | 0.457850i | −0.973444 | − | 0.228925i | \(-0.926479\pi\) | ||
0.973444 | − | 0.228925i | \(-0.0735211\pi\) | |||||||
\(284\) | 1.12272e10i | 1.72584i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.54099e9 | −0.828178 | ||||||||
\(287\) | −8.16742e9 | −1.20381 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.71457e9 | −0.819204 | ||||||||
\(290\) | −1.52184e9 | − | 1.58331e10i | −0.215168 | − | 2.23859i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.04916e9i | 0.144314i | ||||||||
\(293\) | 9.39536e9 | 1.27480 | 0.637401 | − | 0.770532i | \(-0.280009\pi\) | ||||
0.637401 | + | 0.770532i | \(0.280009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.92785e8 | − | 8.24808e9i | −0.104681 | − | 1.08909i | ||||
\(296\) | 6.81426e8i | 0.0887670i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.14360e9i | − | 1.15945i | ||||||
\(299\) | 3.90914e9i | 0.489098i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.76035e8 | −0.0823575 | ||||||||
\(302\) | 1.87592e10 | 2.25520 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.10273e8 | −0.0246201 | ||||||||
\(305\) | −1.54795e10 | + | 1.48785e9i | −1.78878 | + | 0.171933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.64974e9i | 0.410874i | 0.978670 | + | 0.205437i | \(0.0658616\pi\) | ||||
−0.978670 | + | 0.205437i | \(0.934138\pi\) | |||||||
\(308\) | −1.42673e10 | −1.58540 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.39493e9 | + | 4.22429e8i | −0.475888 | + | 0.0457412i | ||||
\(311\) | 1.33369e9i | 0.142566i | 0.997456 | + | 0.0712828i | \(0.0227093\pi\) | ||||
−0.997456 | + | 0.0712828i | \(0.977291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.07379e10i | 1.11878i | 0.828906 | + | 0.559389i | \(0.188964\pi\) | ||||
−0.828906 | + | 0.559389i | \(0.811036\pi\) | |||||||
\(314\) | 8.41556e9i | 0.865694i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.17051e9 | 0.418255 | ||||||||
\(317\) | 1.03929e10 | 1.02920 | 0.514602 | − | 0.857429i | \(-0.327940\pi\) | ||||
0.514602 | + | 0.857429i | \(0.327940\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.56537e10 | 2.47735 | ||||||||
\(320\) | 9.11894e9 | − | 8.76489e8i | 0.869649 | − | 0.0835885i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.07894e10i | 1.93383i | ||||||||
\(323\) | 1.07736e8 | 0.00989806 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.24123e8 | − | 4.24745e9i | −0.0738684 | − | 0.380711i | ||||
\(326\) | 3.54794e9i | 0.314128i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.08163e9i | 0.0934512i | ||||||||
\(329\) | 1.56046e10i | 1.33189i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.63188e9 | 0.552491 | 0.276245 | − | 0.961087i | \(-0.410910\pi\) | ||||
0.276245 | + | 0.961087i | \(0.410910\pi\) | |||||||
\(332\) | 1.33328e9 | 0.109741 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.67735e8 | −0.0697270 | ||||||||
\(335\) | 2.12111e9 | + | 2.20679e10i | 0.168416 | + | 1.75219i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.60918e10i | 1.24763i | 0.781574 | + | 0.623813i | \(0.214417\pi\) | ||||
−0.781574 | + | 0.623813i | \(0.785583\pi\) | |||||||
\(338\) | 1.54393e10 | 1.18293 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.30876e9 | + | 5.10265e8i | −0.397262 | + | 0.0381839i | ||||
\(341\) | − | 7.12091e9i | − | 0.526645i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.19991e10i | − | 0.866903i | ||||||
\(344\) | 8.95291e7i | 0.00639338i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.03345e10 | −1.41883 | ||||||||
\(347\) | −7.03461e9 | −0.485201 | −0.242601 | − | 0.970126i | \(-0.578000\pi\) | ||||
−0.242601 | + | 0.970126i | \(0.578000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.52532e9 | 0.507252 | 0.253626 | − | 0.967302i | \(-0.418377\pi\) | ||||
0.253626 | + | 0.967302i | \(0.418377\pi\) | |||||||
\(350\) | −4.38282e9 | − | 2.25886e10i | −0.292066 | − | 1.50528i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.26613e10i | 2.12747i | ||||||||
\(353\) | −7.21191e9 | −0.464464 | −0.232232 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232232 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.79408e9 | − | 2.90694e10i | −0.175924 | − | 1.83030i | ||||
\(356\) | − | 2.34317e10i | − | 1.45883i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.78882e9i | 0.230660i | ||||||||
\(359\) | 3.85025e9i | 0.231799i | 0.993261 | + | 0.115899i | \(0.0369750\pi\) | ||||
−0.993261 | + | 0.115899i | \(0.963025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69744e10 | −0.999458 | ||||||||
\(362\) | 1.66548e10 | 0.969849 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.03727e9 | −0.400865 | ||||||||
\(365\) | −2.61100e8 | − | 2.71647e9i | −0.0147108 | − | 0.153050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.32948e10i | − | 0.732857i | −0.930446 | − | 0.366428i | \(-0.880580\pi\) | ||
0.930446 | − | 0.366428i | \(-0.119420\pi\) | |||||||
\(368\) | 2.44626e10 | 1.33386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.59228e9 | + | 2.69699e10i | 0.138317 | + | 1.43904i | ||||
\(371\) | − | 2.43194e10i | − | 1.28368i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.34647e10i | 1.21221i | 0.795383 | + | 0.606107i | \(0.207270\pi\) | ||||
−0.795383 | + | 0.606107i | \(0.792730\pi\) | |||||||
\(374\) | − | 1.77658e10i | − | 0.908026i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.06656e9 | 0.103394 | ||||||||
\(377\) | 1.26536e10 | 0.626394 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.18561e10 | −1.05929 | −0.529646 | − | 0.848219i | \(-0.677675\pi\) | ||||
−0.529646 | + | 0.848219i | \(0.677675\pi\) | |||||||
\(380\) | −4.53495e8 | + | 4.35888e7i | −0.0217489 | + | 0.00209045i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 4.25437e9i | − | 0.199794i | ||||||
\(383\) | −2.96898e10 | −1.37979 | −0.689894 | − | 0.723911i | \(-0.742343\pi\) | ||||
−0.689894 | + | 0.723911i | \(0.742343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.69407e10 | − | 3.55064e9i | 1.68136 | − | 0.161608i | ||||
\(386\) | 3.51038e10i | 1.58127i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 3.04695e10i | − | 1.34443i | ||||||
\(389\) | 1.55829e10i | 0.680533i | 0.940329 | + | 0.340266i | \(0.110517\pi\) | ||||
−0.940329 | + | 0.340266i | \(0.889483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.25337e10 | −0.536254 | ||||||||
\(392\) | 4.29627e8 | 0.0181948 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.47174e8 | −0.0310054 | ||||||||
\(395\) | −1.07982e10 | + | 1.03790e9i | −0.443572 | + | 0.0426351i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.23824e10i | − | 1.30361i | −0.758388 | − | 0.651803i | \(-0.774013\pi\) | ||
0.758388 | − | 0.651803i | \(-0.225987\pi\) | |||||||
\(398\) | −2.58490e10 | −1.03017 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.65797e10 | + | 5.15719e9i | −1.03827 | + | 0.201453i | ||||
\(401\) | 1.02122e10i | 0.394951i | 0.980308 | + | 0.197475i | \(0.0632743\pi\) | ||||
−0.980308 | + | 0.197475i | \(0.936726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.51235e9i | − | 0.133161i | ||||||
\(404\) | − | 1.83385e10i | − | 0.688398i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.72938e10 | 2.47669 | ||||||||
\(407\) | −4.36981e10 | −1.59252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.75586e9 | 0.0984836 | 0.0492418 | − | 0.998787i | \(-0.484320\pi\) | ||||
0.0492418 | + | 0.998787i | \(0.484320\pi\) | |||||||
\(410\) | 4.11475e9 | + | 4.28096e10i | 0.145616 | + | 1.51498i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 3.89324e10i | − | 1.35121i | ||||||
\(413\) | 3.50559e10 | 1.20493 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.45212e9 | + | 3.31809e8i | −0.116384 | + | 0.0111866i | ||||
\(416\) | 1.61100e10i | 0.537927i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.51762e9i | − | 0.0497117i | ||||||
\(419\) | − | 3.02983e10i | − | 0.983019i | −0.870872 | − | 0.491510i | \(-0.836445\pi\) | ||
0.870872 | − | 0.491510i | \(-0.163555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.76263e10 | 0.879417 | 0.439709 | − | 0.898141i | \(-0.355082\pi\) | ||||
0.439709 | + | 0.898141i | \(0.355082\pi\) | |||||||
\(422\) | −3.68290e10 | −1.16129 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.22068e9 | −0.0996515 | ||||||||
\(425\) | 1.36184e10 | − | 2.64234e9i | 0.417417 | − | 0.0809904i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.57908e10i | − | 1.97903i | ||||||
\(428\) | −3.33128e10 | −0.992740 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.40587e8 | + | 3.54344e9i | 0.00996217 | + | 0.103646i | ||||
\(431\) | 2.12776e10i | 0.616614i | 0.951287 | + | 0.308307i | \(0.0997624\pi\) | ||||
−0.951287 | + | 0.308307i | \(0.900238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.56994e9i | 0.272244i | 0.990692 | + | 0.136122i | \(0.0434638\pi\) | ||||
−0.990692 | + | 0.136122i | \(0.956536\pi\) | |||||||
\(434\) | − | 1.86793e10i | − | 0.526503i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.39825e10 | −0.386935 | ||||||||
\(437\) | −1.07067e9 | −0.0293583 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.49688e10 | 0.672264 | 0.336132 | − | 0.941815i | \(-0.390881\pi\) | ||||
0.336132 | + | 0.941815i | \(0.390881\pi\) | |||||||
\(440\) | −4.70221e8 | − | 4.89215e9i | −0.0125456 | − | 0.130524i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 8.76290e9i | − | 0.229593i | ||||||
\(443\) | 4.80091e9 | 0.124655 | 0.0623273 | − | 0.998056i | \(-0.480148\pi\) | ||||
0.0623273 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.83136e9 | + | 6.06691e10i | 0.148707 | + | 1.54713i | ||||
\(446\) | 8.07896e10i | 2.04181i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.87572e10i | 0.962144i | ||||||||
\(449\) | − | 2.77325e10i | − | 0.682345i | −0.940001 | − | 0.341172i | \(-0.889176\pi\) | ||
0.940001 | − | 0.341172i | \(-0.110824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.93625e10 | −1.67656 | ||||||||
\(452\) | 3.78412e9 | 0.0906591 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.40696e10 | −1.74348 | ||||||||
\(455\) | 1.82208e10 | − | 1.75134e9i | 0.425130 | − | 0.0408624i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.03683e10i | 1.15476i | 0.816475 | + | 0.577381i | \(0.195925\pi\) | ||||
−0.816475 | + | 0.577381i | \(0.804075\pi\) | |||||||
\(458\) | 9.24006e10 | 2.09997 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.27582e10 | − | 5.07099e9i | 1.17831 | − | 0.113256i | ||||
\(461\) | − | 5.32820e10i | − | 1.17971i | −0.807508 | − | 0.589857i | \(-0.799184\pi\) | ||
0.807508 | − | 0.589857i | \(-0.200816\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.43748e10i | − | 0.748025i | −0.927424 | − | 0.374013i | \(-0.877982\pi\) | ||
0.927424 | − | 0.374013i | \(-0.122018\pi\) | |||||||
\(464\) | − | 7.91834e10i | − | 1.70829i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48600e10 | 2.01159 | ||||||||
\(467\) | −5.12262e10 | −1.07702 | −0.538511 | − | 0.842618i | \(-0.681013\pi\) | ||||
−0.538511 | + | 0.842618i | \(0.681013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.37925e10 | −1.93855 | ||||||||
\(470\) | 8.17917e10 | − | 7.86161e9i | 1.67617 | − | 0.161109i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 4.64254e9i | − | 0.0935379i | ||||||
\(473\) | −5.74128e9 | −0.114700 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.16334e9 | − | 2.25719e8i | 0.0228523 | − | 0.00443398i | ||||
\(476\) | − | 2.25632e10i | − | 0.439515i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.74314e10i | 1.29167i | ||||||||
\(479\) | − | 4.70739e10i | − | 0.894208i | −0.894482 | − | 0.447104i | \(-0.852455\pi\) | ||
0.894482 | − | 0.447104i | \(-0.147545\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.15539e10 | −0.402667 | ||||||||
\(482\) | −7.54794e10 | −1.39843 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.96595e10 | −1.26940 | ||||||||
\(485\) | 7.58282e9 | + | 7.88912e10i | 0.137045 | + | 1.42581i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.31750e9i | − | 0.0945348i | −0.998882 | − | 0.0472674i | \(-0.984949\pi\) | ||
0.998882 | − | 0.0472674i | \(-0.0150513\pi\) | |||||||
\(488\) | −8.71284e9 | −0.153632 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.70041e10 | − | 1.63439e9i | 0.294963 | − | 0.0283511i | ||||
\(491\) | − | 8.86772e10i | − | 1.52576i | −0.646540 | − | 0.762880i | \(-0.723785\pi\) | ||
0.646540 | − | 0.762880i | \(-0.276215\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.05705e10i | 0.686788i | ||||||||
\(494\) | − | 7.48561e8i | − | 0.0125695i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.19796e10 | −0.363155 | ||||||||
\(497\) | 1.23551e11 | 2.02497 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.19202e10 | 0.998688 | 0.499344 | − | 0.866404i | \(-0.333574\pi\) | ||||
0.499344 | + | 0.866404i | \(0.333574\pi\) | |||||||
\(500\) | −5.62551e10 | + | 1.66323e10i | −0.900082 | + | 0.266117i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 4.93679e10i | − | 0.777374i | ||||||
\(503\) | 5.89096e10 | 0.920268 | 0.460134 | − | 0.887850i | \(-0.347801\pi\) | ||||
0.460134 | + | 0.887850i | \(0.347801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.56384e9 | + | 4.74819e10i | 0.0701722 | + | 0.730067i | ||||
\(506\) | 1.76556e11i | 2.69327i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.05902e10i | 0.309176i | ||||||||
\(509\) | 8.77959e10i | 1.30799i | 0.756501 | + | 0.653993i | \(0.226907\pi\) | ||||
−0.756501 | + | 0.653993i | \(0.773093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.15455e10 | 0.169328 | ||||||||
\(512\) | 9.45997e10 | 1.37661 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.20991e10 | 1.17621 | ||||||||
\(515\) | 9.68896e9 | + | 1.00803e11i | 0.137736 | + | 1.43300i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.32523e11i | 1.85494i | ||||||||
\(518\) | −1.14627e11 | −1.59209 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.31934e8 | − | 2.41303e9i | −0.00317213 | − | 0.0330027i | ||||
\(521\) | − | 6.67388e10i | − | 0.905790i | −0.891564 | − | 0.452895i | \(-0.850391\pi\) | ||
0.891564 | − | 0.452895i | \(-0.149609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.80448e10i | − | 0.642155i | −0.947053 | − | 0.321078i | \(-0.895955\pi\) | ||
0.947053 | − | 0.321078i | \(-0.104045\pi\) | |||||||
\(524\) | − | 5.12817e10i | − | 0.680201i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.66115e10 | 0.739540 | ||||||||
\(527\) | 1.12615e10 | 0.146000 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.62479e10 | 0.590568 | ||||||||
\(530\) | −1.27470e11 | + | 1.22521e10i | −1.61549 | + | 0.155277i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 1.92744e9i | − | 0.0240621i | ||||||
\(533\) | −3.42127e10 | −0.423915 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.62530e10 | − | 8.29042e9i | 1.05283 | − | 0.101196i | ||||
\(536\) | 1.24212e10i | 0.150489i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.00017e11i | − | 1.19384i | ||||||
\(539\) | 2.75509e10i | 0.326423i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.05776e10 | −0.823906 | −0.411953 | − | 0.911205i | \(-0.635153\pi\) | ||||
−0.411953 | + | 0.911205i | \(0.635153\pi\) | |||||||
\(542\) | −3.03128e9 | −0.0351260 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.16528e10 | −0.589791 | ||||||||
\(545\) | 3.62033e10 | − | 3.47977e9i | 0.410357 | − | 0.0394425i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.29854e10i | 0.368445i | 0.982885 | + | 0.184222i | \(0.0589767\pi\) | ||||
−0.982885 | + | 0.184222i | \(0.941023\pi\) | |||||||
\(548\) | 1.03125e11 | 1.14351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.72214e10 | − | 1.91836e11i | −0.406764 | − | 2.09642i | ||||
\(551\) | 3.46569e9i | 0.0375996i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.58945e10i | − | 0.490750i | ||||||
\(554\) | − | 1.29153e11i | − | 1.37109i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.32696e11 | −1.38855 | ||||||||
\(557\) | −1.44778e10 | −0.150412 | −0.0752060 | − | 0.997168i | \(-0.523961\pi\) | ||||
−0.0752060 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.83186e9 | −0.0290018 | ||||||||
\(560\) | −1.09595e10 | − | 1.14022e11i | −0.111439 | − | 1.15941i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 9.66144e10i | − | 0.968493i | ||||||
\(563\) | −1.90253e11 | −1.89364 | −0.946820 | − | 0.321765i | \(-0.895724\pi\) | ||||
−0.946820 | + | 0.321765i | \(0.895724\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.79780e9 | + | 9.41740e8i | −0.0961468 | + | 0.00924139i | ||||
\(566\) | − | 6.54234e10i | − | 0.637481i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.63621e10i | − | 0.157198i | ||||||
\(569\) | 1.91216e10i | 0.182422i | 0.995832 | + | 0.0912108i | \(0.0290737\pi\) | ||||
−0.995832 | + | 0.0912108i | \(0.970926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.67341e10 | 0.721845 | 0.360923 | − | 0.932596i | \(-0.382462\pi\) | ||||
0.360923 | + | 0.932596i | \(0.382462\pi\) | |||||||
\(572\) | −5.97645e10 | −0.558289 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.81949e11 | −1.67611 | ||||||||
\(575\) | −1.35339e11 | + | 2.62595e10i | −1.23809 | + | 0.240223i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.10167e11i | 0.993910i | 0.867776 | + | 0.496955i | \(0.165549\pi\) | ||||
−0.867776 | + | 0.496955i | \(0.834451\pi\) | |||||||
\(578\) | −1.27305e11 | −1.14061 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.64144e10 | − | 1.70774e11i | −0.145048 | − | 1.50907i | ||||
\(581\) | − | 1.46722e10i | − | 0.128763i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.06534e11i | − | 1.78779i | ||||||
\(584\) | − | 1.52900e9i | − | 0.0131449i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.09304e11 | 1.77495 | ||||||||
\(587\) | 1.70283e11 | 1.43423 | 0.717116 | − | 0.696954i | \(-0.245462\pi\) | ||||
0.717116 | + | 0.696954i | \(0.245462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.61999e8 | 0.00799307 | ||||||||
\(590\) | −1.76612e10 | − | 1.83745e11i | −0.145751 | − | 1.51638i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.34880e11i | 1.09815i | ||||||||
\(593\) | 2.23071e11 | 1.80395 | 0.901976 | − | 0.431785i | \(-0.142116\pi\) | ||||
0.901976 | + | 0.431785i | \(0.142116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.61522e9 | + | 5.84204e10i | 0.0448022 | + | 0.466119i | ||||
\(596\) | − | 9.86218e10i | − | 0.781606i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.70853e10i | 0.680989i | ||||||||
\(599\) | 2.26036e11i | 1.75578i | 0.478862 | + | 0.877890i | \(0.341049\pi\) | ||||
−0.478862 | + | 0.877890i | \(0.658951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.83332e10 | −0.600410 | −0.300205 | − | 0.953875i | \(-0.597055\pi\) | ||||
−0.300205 | + | 0.953875i | \(0.597055\pi\) | |||||||
\(602\) | −1.50603e10 | −0.114669 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.02334e11 | 1.52027 | ||||||||
\(605\) | 1.80362e11 | − | 1.73359e10i | 1.34624 | − | 0.129397i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.42070e11i | 1.04652i | 0.852173 | + | 0.523260i | \(0.175284\pi\) | ||||
−0.852173 | + | 0.523260i | \(0.824716\pi\) | |||||||
\(608\) | −4.41238e9 | −0.0322893 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.44843e11 | + | 3.31454e10i | −2.49059 | + | 0.239389i | ||||
\(611\) | 6.53665e10i | 0.469019i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.77570e10i | 0.409037i | 0.978863 | + | 0.204518i | \(0.0655629\pi\) | ||||
−0.978863 | + | 0.204518i | \(0.934437\pi\) | |||||||
\(614\) | 8.13066e10i | 0.572074i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.07925e10 | 0.144406 | ||||||||
\(617\) | −4.44327e10 | −0.306593 | −0.153296 | − | 0.988180i | \(-0.548989\pi\) | ||||
−0.153296 | + | 0.988180i | \(0.548989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00759e10 | 0.136745 | 0.0683727 | − | 0.997660i | \(-0.478219\pi\) | ||||
0.0683727 | + | 0.997660i | \(0.478219\pi\) | |||||||
\(620\) | −4.74032e10 | + | 4.55628e9i | −0.320805 | + | 0.0308349i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.97112e10i | 0.198499i | ||||||||
\(623\) | −2.57855e11 | −1.71168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.41516e11 | − | 5.70642e10i | 0.927438 | − | 0.373976i | ||||
\(626\) | 2.39213e11i | 1.55771i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.07692e10i | 0.583580i | ||||||||
\(629\) | − | 6.91071e10i | − | 0.441489i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.22887e11 | −0.775153 | −0.387577 | − | 0.921837i | \(-0.626688\pi\) | ||||
−0.387577 | + | 0.921837i | \(0.626688\pi\) | |||||||
\(632\) | −6.07793e9 | −0.0380967 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.31527e11 | 1.43300 | ||||||||
\(635\) | −5.12421e9 | − | 5.33120e10i | −0.0315161 | − | 0.327891i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.35894e10i | 0.0825355i | ||||||||
\(638\) | 5.71497e11 | 3.44930 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.85010e10 | + | 2.73944e9i | −0.169879 | + | 0.0163283i | ||||
\(641\) | 2.11826e10i | 0.125472i | 0.998030 | + | 0.0627362i | \(0.0199827\pi\) | ||||
−0.998030 | + | 0.0627362i | \(0.980017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.09819e10i | − | 0.473744i | −0.971541 | − | 0.236872i | \(-0.923878\pi\) | ||
0.971541 | − | 0.236872i | \(-0.0761223\pi\) | |||||||
\(644\) | 2.24232e11i | 1.30363i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.40007e9 | 0.0137814 | ||||||||
\(647\) | 6.55894e10 | 0.374297 | 0.187149 | − | 0.982332i | \(-0.440075\pi\) | ||||
0.187149 | + | 0.982332i | \(0.440075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.97715e11 | 1.67811 | ||||||||
\(650\) | −1.83593e10 | − | 9.46221e10i | −0.102850 | − | 0.530077i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.82677e10i | 0.211759i | ||||||||
\(653\) | −2.79107e11 | −1.53504 | −0.767518 | − | 0.641028i | \(-0.778508\pi\) | ||||
−0.767518 | + | 0.641028i | \(0.778508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.27623e10 | + | 1.32778e11i | 0.0693367 | + | 0.721375i | ||||
\(656\) | 2.14096e11i | 1.15609i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.47630e11i | 1.85444i | ||||||||
\(659\) | 4.32498e10i | 0.229320i | 0.993405 | + | 0.114660i | \(0.0365779\pi\) | ||||
−0.993405 | + | 0.114660i | \(0.963422\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.31191e11 | −0.687226 | −0.343613 | − | 0.939111i | \(-0.611651\pi\) | ||||
−0.343613 | + | 0.939111i | \(0.611651\pi\) | |||||||
\(662\) | 1.47741e11 | 0.769252 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.94307e9 | −0.00999579 | ||||||||
\(665\) | 4.79674e8 | + | 4.99050e9i | 0.00245279 | + | 0.0255186i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.03188e11i | − | 2.03706i | ||||||
\(668\) | −9.35929e9 | −0.0470042 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.72527e10 | + | 4.91614e11i | 0.234492 | + | 2.43964i | ||||
\(671\) | − | 5.58733e11i | − | 2.75622i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.54815e10i | 0.172958i | 0.996254 | + | 0.0864792i | \(0.0275616\pi\) | ||||
−0.996254 | + | 0.0864792i | \(0.972438\pi\) | |||||||
\(674\) | 3.58482e11i | 1.73711i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.66526e11 | 0.797435 | ||||||||
\(677\) | 5.19019e10 | 0.247075 | 0.123537 | − | 0.992340i | \(-0.460576\pi\) | ||||
0.123537 | + | 0.992340i | \(0.460576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.35302e11 | −1.57746 | ||||||||
\(680\) | 7.73677e9 | − | 7.43639e8i | 0.0361846 | − | 0.00347797i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.58635e11i | − | 0.733266i | ||||||
\(683\) | 4.75602e10 | 0.218555 | 0.109278 | − | 0.994011i | \(-0.465146\pi\) | ||||
0.109278 | + | 0.994011i | \(0.465146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.67009e11 | + | 2.56643e10i | −1.21273 | + | 0.116565i | ||||
\(686\) | − | 2.67307e11i | − | 1.20702i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.77212e10i | 0.0790932i | ||||||||
\(689\) | − | 1.01872e11i | − | 0.452041i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.97123e11 | −0.864618 | −0.432309 | − | 0.901726i | \(-0.642301\pi\) | ||||
−0.432309 | + | 0.901726i | \(0.642301\pi\) | |||||||
\(692\) | −2.19326e11 | −0.956457 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.56713e11 | −0.675563 | ||||||||
\(695\) | 3.43576e11 | − | 3.30236e10i | 1.47260 | − | 0.141542i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.09694e11i | − | 0.464786i | ||||||
\(698\) | 1.67644e11 | 0.706265 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.72726e10 | − | 2.43639e11i | −0.196887 | − | 1.01474i | ||||
\(701\) | − | 4.52903e11i | − | 1.87557i | −0.347220 | − | 0.937784i | \(-0.612874\pi\) | ||
0.347220 | − | 0.937784i | \(-0.387126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.90340e9i | − | 0.0241702i | ||||||
\(704\) | 3.29148e11i | 1.33999i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.60662e11 | −0.646689 | ||||||||
\(707\) | −2.01807e11 | −0.807716 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.64885e11 | 1.44401 | 0.722007 | − | 0.691886i | \(-0.243220\pi\) | ||||
0.722007 | + | 0.691886i | \(0.243220\pi\) | |||||||
\(710\) | −6.22448e10 | − | 6.47591e11i | −0.244946 | − | 2.54840i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.41484e10i | 0.132877i | ||||||||
\(713\) | −1.11916e11 | −0.433046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.54742e11 | − | 1.48734e10i | 0.592083 | − | 0.0569095i | ||||
\(716\) | 4.08658e10i | 0.155492i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.57735e10i | 0.322742i | ||||||||
\(719\) | 1.83828e10i | 0.0687853i | 0.999408 | + | 0.0343927i | \(0.0109497\pi\) | ||||
−0.999408 | + | 0.0343927i | \(0.989050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28433e11 | −1.58541 | ||||||||
\(722\) | −3.78144e11 | −1.39158 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.79636e11 | 0.653792 | ||||||||
\(725\) | 8.49999e10 | + | 4.38082e11i | 0.307657 | + | 1.58564i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.01714e11i | − | 1.43807i | −0.694975 | − | 0.719034i | \(-0.744584\pi\) | ||
0.694975 | − | 0.719034i | \(-0.255416\pi\) | |||||||
\(728\) | 1.02558e10 | 0.0365128 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.81662e9 | − | 6.05158e10i | −0.0204823 | − | 0.213097i | ||||
\(731\) | − | 9.07964e9i | − | 0.0317980i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.34842e11i | − | 1.50632i | −0.657840 | − | 0.753158i | \(-0.728530\pi\) | ||
0.657840 | − | 0.753158i | \(-0.271470\pi\) | |||||||
\(734\) | − | 2.96174e11i | − | 1.02038i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.13323e11 | 1.74936 | ||||||||
\(737\) | −7.96540e11 | −2.69984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.89228e11 | 0.634466 | 0.317233 | − | 0.948348i | \(-0.397246\pi\) | ||||
0.317233 | + | 0.948348i | \(0.397246\pi\) | |||||||
\(740\) | 2.79600e10 | + | 2.90894e11i | 0.0932418 | + | 0.970082i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 5.41772e11i | − | 1.78731i | ||||||
\(743\) | 1.56871e11 | 0.514739 | 0.257369 | − | 0.966313i | \(-0.417144\pi\) | ||||
0.257369 | + | 0.966313i | \(0.417144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.45436e10 | + | 2.55350e11i | 0.0796735 | + | 0.828918i | ||||
\(746\) | 5.22731e11i | 1.68781i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.91620e11i | − | 0.612116i | ||||||
\(749\) | 3.66591e11i | 1.16481i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.09763e11 | 0.345061 | 0.172530 | − | 0.985004i | \(-0.444806\pi\) | ||||
0.172530 | + | 0.985004i | \(0.444806\pi\) | |||||||
\(752\) | 4.09050e11 | 1.27910 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.81888e11 | 0.872151 | ||||||||
\(755\) | −5.23881e11 | + | 5.03541e10i | −1.61230 | + | 0.154970i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7.49572e10i | − | 0.228260i | −0.993466 | − | 0.114130i | \(-0.963592\pi\) | ||
0.993466 | − | 0.114130i | \(-0.0364081\pi\) | |||||||
\(758\) | −4.86897e11 | −1.47489 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.60905e8 | − | 6.35245e7i | 0.00198100 | − | 0.000190409i | ||||
\(761\) | 3.28200e11i | 0.978589i | 0.872119 | + | 0.489295i | \(0.162746\pi\) | ||||
−0.872119 | + | 0.489295i | \(0.837254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.53871e11i | 0.454002i | ||||||||
\(764\) | − | 4.58871e10i | − | 0.134684i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.61411e11 | −1.92113 | ||||||||
\(767\) | 1.46846e11 | 0.424308 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.35427e11 | −0.673210 | −0.336605 | − | 0.941646i | \(-0.609279\pi\) | ||||
−0.336605 | + | 0.941646i | \(0.609279\pi\) | |||||||
\(770\) | 8.22941e11 | − | 7.90990e10i | 2.34102 | − | 0.225013i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.78626e11i | 1.06596i | ||||||||
\(773\) | 2.82657e11 | 0.791666 | 0.395833 | − | 0.918323i | \(-0.370456\pi\) | ||||
0.395833 | + | 0.918323i | \(0.370456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.21602e11 | − | 2.35941e10i | 0.337080 | − | 0.0654028i | ||||
\(776\) | 4.44049e10i | 0.122457i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.47145e11i | 0.947530i | ||||||||
\(779\) | − | 9.37052e9i | − | 0.0254457i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.04926e12 | 2.82020 | ||||||||
\(782\) | −2.79217e11 | −0.746646 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.50393e10 | 0.225090 | ||||||||
\(785\) | −2.25894e10 | − | 2.35019e11i | −0.0594875 | − | 0.618904i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.22808e11i | 1.10216i | 0.834452 | + | 0.551080i | \(0.185784\pi\) | ||||
−0.834452 | + | 0.551080i | \(0.814216\pi\) | |||||||
\(788\) | −8.05894e9 | −0.0209013 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.40556e11 | + | 2.31217e10i | −0.617601 | + | 0.0593623i | ||||
\(791\) | − | 4.16425e10i | − | 0.106373i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.75592e11i | − | 0.696906i | ||||||
\(794\) | − | 7.21394e11i | − | 1.81506i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.78804e11 | −0.694459 | ||||||||
\(797\) | 2.99331e11 | 0.741855 | 0.370927 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370927 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.09581e11 | −0.514239 | ||||||||
\(800\) | −5.57749e11 | + | 1.08219e11i | −1.36169 | + | 0.264206i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.27502e11i | 0.549904i | ||||||||
\(803\) | 9.80510e10 | 0.235825 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.58038e10 | − | 5.80579e11i | −0.132886 | − | 1.38254i | ||||
\(806\) | − | 7.82460e10i | − | 0.185405i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.67258e10i | 0.0627026i | ||||||||
\(809\) | 2.38530e11i | 0.556864i | 0.960456 | + | 0.278432i | \(0.0898147\pi\) | ||||
−0.960456 | + | 0.278432i | \(0.910185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.52223e11 | 0.351883 | 0.175941 | − | 0.984401i | \(-0.443703\pi\) | ||||
0.175941 | + | 0.984401i | \(0.443703\pi\) | |||||||
\(812\) | 7.25823e11 | 1.66958 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.73479e11 | −2.21732 | ||||||||
\(815\) | −9.52354e9 | − | 9.90823e10i | −0.0215858 | − | 0.224577i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.75618e8i | − | 0.00174084i | ||||||
\(818\) | 6.13933e10 | 0.137122 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.43812e10 | + | 4.61739e11i | 0.0981621 | + | 1.02127i | ||||
\(821\) | − | 1.26619e11i | − | 0.278693i | −0.990244 | − | 0.139346i | \(-0.955500\pi\) | ||
0.990244 | − | 0.139346i | \(-0.0445001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.97934e11i | 1.73927i | 0.493694 | + | 0.869636i | \(0.335646\pi\) | ||||
−0.493694 | + | 0.869636i | \(0.664354\pi\) | |||||||
\(824\) | 5.67385e10i | 0.123075i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.80953e11 | 1.67766 | ||||||||
\(827\) | 4.23420e11 | 0.905211 | 0.452605 | − | 0.891711i | \(-0.350495\pi\) | ||||
0.452605 | + | 0.891711i | \(0.350495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.03970e11 | −1.06705 | −0.533527 | − | 0.845783i | \(-0.679134\pi\) | ||||
−0.533527 | + | 0.845783i | \(0.679134\pi\) | |||||||
\(830\) | −7.69042e10 | + | 7.39184e9i | −0.162046 | + | 0.0155754i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.62351e11i | 0.338814i | ||||||||
\(833\) | −4.35708e10 | −0.0904932 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.42330e10 | − | 2.32921e9i | 0.0498495 | − | 0.00479140i | ||||
\(836\) | − | 1.63689e10i | − | 0.0335116i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 6.74966e11i | − | 1.36869i | ||||||
\(839\) | − | 4.10460e11i | − | 0.828367i | −0.910193 | − | 0.414184i | \(-0.864067\pi\) | ||
0.910193 | − | 0.414184i | \(-0.135933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.04842e11 | −1.60889 | ||||||||
\(842\) | 6.15442e11 | 1.22444 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.97234e11 | −0.782846 | ||||||||
\(845\) | −4.31167e11 | + | 4.14427e10i | −0.845705 | + | 0.0812871i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.66570e11i | 1.48942i | ||||||||
\(848\) | −6.37494e11 | −1.23280 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.03382e11 | − | 5.88644e10i | 0.581184 | − | 0.112766i | ||||
\(851\) | 6.86784e11i | 1.30949i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.32498e11i | 0.250273i | 0.992140 | + | 0.125137i | \(0.0399369\pi\) | ||||
−0.992140 | + | 0.125137i | \(0.960063\pi\) | |||||||
\(854\) | − | 1.46565e12i | − | 2.75548i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.85487e10 | 0.0904237 | ||||||||
\(857\) | 4.11482e11 | 0.762830 | 0.381415 | − | 0.924404i | \(-0.375437\pi\) | ||||
0.381415 | + | 0.924404i | \(0.375437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.76431e11 | 1.05870 | 0.529352 | − | 0.848402i | \(-0.322435\pi\) | ||||
0.529352 | + | 0.848402i | \(0.322435\pi\) | |||||||
\(860\) | 3.67353e9 | + | 3.82191e10i | 0.00671567 | + | 0.0698694i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.74009e11i | 0.858534i | ||||||||
\(863\) | 3.26350e11 | 0.588356 | 0.294178 | − | 0.955751i | \(-0.404954\pi\) | ||||
0.294178 | + | 0.955751i | \(0.404954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.67875e11 | − | 5.45828e10i | 1.01435 | − | 0.0974970i | ||||
\(866\) | 2.13193e11i | 0.379054i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 2.01472e11i | − | 0.354925i | ||||||
\(869\) | − | 3.89763e11i | − | 0.683472i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.92890e11 | −0.682650 | ||||||||
\(872\) | 2.03775e10 | 0.0352440 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.38518e10 | −0.0408767 | ||||||||
\(875\) | 1.83031e11 | + | 6.19061e11i | 0.312243 | + | 1.05609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.76864e11i | 0.637069i | 0.947911 | + | 0.318534i | \(0.103191\pi\) | ||||
−0.947911 | + | 0.318534i | \(0.896809\pi\) | |||||||
\(878\) | 5.56239e11 | 0.936017 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.30744e10 | − | 9.68340e11i | −0.155203 | − | 1.61472i | ||||
\(881\) | 3.14014e11i | 0.521250i | 0.965440 | + | 0.260625i | \(0.0839286\pi\) | ||||
−0.965440 | + | 0.260625i | \(0.916071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.57879e11i | 0.424203i | 0.977248 | + | 0.212101i | \(0.0680307\pi\) | ||||
−0.977248 | + | 0.212101i | \(0.931969\pi\) | |||||||
\(884\) | − | 9.45156e10i | − | 0.154773i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.06952e11 | 0.173561 | ||||||||
\(887\) | 1.12112e11 | 0.181117 | 0.0905583 | − | 0.995891i | \(-0.471135\pi\) | ||||
0.0905583 | + | 0.995891i | \(0.471135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.26586e11 | 0.362765 | ||||||||
\(890\) | 1.29907e11 | + | 1.35155e12i | 0.207049 | + | 2.15413i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.71387e11i | 1.37642i | ||||||||
\(893\) | −1.79032e10 | −0.0281531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.01701e10 | − | 1.05809e11i | −0.0158502 | − | 0.164904i | ||||
\(896\) | − | 1.21134e11i | − | 0.187947i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 6.17807e11i | − | 0.950053i | ||||||
\(899\) | 3.62264e11i | 0.554608i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.26627e11 | 0.495624 | ||||||||
\(902\) | −1.54521e12 | −2.33433 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.51482e9 | −0.00825767 | ||||||||
\(905\) | −4.65112e11 | + | 4.47054e10i | −0.693367 | + | 0.0666447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.92285e10i | 0.0875189i | 0.999042 | + | 0.0437594i | \(0.0139335\pi\) | ||||
−0.999042 | + | 0.0437594i | \(0.986066\pi\) | |||||||
\(908\) | −7.98906e11 | −1.17531 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.05912e11 | − | 3.90152e10i | 0.591924 | − | 0.0568942i | ||||
\(911\) | 4.67364e11i | 0.678549i | 0.940687 | + | 0.339275i | \(0.110182\pi\) | ||||
−0.940687 | + | 0.339275i | \(0.889818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.24604e11i | − | 0.179329i | ||||||
\(914\) | 1.12207e12i | 1.60782i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.96622e11 | 1.41563 | ||||||||
\(917\) | −5.64331e11 | −0.798099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.65426e11 | 0.231922 | 0.115961 | − | 0.993254i | \(-0.463005\pi\) | ||||
0.115961 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(920\) | −7.68876e10 | + | 7.39025e9i | −0.107326 | + | 0.0103159i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.18698e12i | − | 1.64256i | ||||||
\(923\) | 5.17544e11 | 0.713083 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.44788e11 | − | 7.46222e11i | −0.197772 | − | 1.01930i | ||||
\(926\) | − | 7.65780e11i | − | 1.04150i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 1.66159e12i | − | 2.24043i | ||||||
\(929\) | − | 4.15075e11i | − | 0.557267i | −0.960398 | − | 0.278633i | \(-0.910119\pi\) | ||
0.960398 | − | 0.278633i | \(-0.0898815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.72199e9 | −0.00495423 | ||||||||
\(932\) | 1.02315e12 | 1.35605 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.14118e12 | −1.49958 | ||||||||
\(935\) | 4.76877e10 | + | 4.96140e11i | 0.0623964 | + | 0.649169i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.22206e11i | − | 1.06665i | −0.845910 | − | 0.533325i | \(-0.820942\pi\) | ||
0.845910 | − | 0.533325i | \(-0.179058\pi\) | |||||||
\(938\) | −2.08945e12 | −2.69911 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.82195e11 | − | 8.47944e10i | 1.12993 | − | 0.108606i | ||||
\(941\) | − | 1.31518e12i | − | 1.67737i | −0.544619 | − | 0.838684i | \(-0.683326\pi\) | ||
0.544619 | − | 0.838684i | \(-0.316674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.09014e12i | 1.37859i | ||||||||
\(944\) | − | 9.18934e11i | − | 1.15717i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.27901e11 | −0.159701 | ||||||||
\(947\) | 3.76228e11 | 0.467791 | 0.233895 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233895 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83632e10 | 0.0596280 | ||||||||
\(950\) | 2.59161e10 | − | 5.02843e9i | 0.0318181 | − | 0.00617359i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.28827e10i | 0.0400331i | ||||||||
\(953\) | 4.73339e11 | 0.573854 | 0.286927 | − | 0.957953i | \(-0.407366\pi\) | ||||
0.286927 | + | 0.957953i | \(0.407366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.14198e10 | + | 1.18810e11i | 0.0137291 | + | 0.142837i | ||||
\(956\) | 7.27307e11i | 0.870736i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.04868e12i | − | 1.24504i | ||||||
\(959\) | − | 1.13484e12i | − | 1.34171i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.52335e11 | −0.882099 | ||||||||
\(962\) | −4.80164e11 | −0.560647 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.14112e11 | −0.942705 | ||||||||
\(965\) | −9.42272e10 | − | 9.80333e11i | −0.108659 | − | 1.13048i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.76879e11i | 0.545384i | 0.962101 | + | 0.272692i | \(0.0879140\pi\) | ||||
−0.962101 | + | 0.272692i | \(0.912086\pi\) | |||||||
\(968\) | 1.01519e11 | 0.115623 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.68925e11 | + | 1.75749e12i | 0.190813 | + | 1.98520i | ||||
\(971\) | − | 8.83200e11i | − | 0.993533i | −0.867884 | − | 0.496766i | \(-0.834521\pi\) | ||
0.867884 | − | 0.496766i | \(-0.165479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.46026e12i | 1.62922i | ||||||||
\(974\) | − | 1.18460e11i | − | 0.131624i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72460e12 | −1.90059 | ||||||||
\(977\) | −7.00113e11 | −0.768405 | −0.384203 | − | 0.923249i | \(-0.625524\pi\) | ||||
−0.384203 | + | 0.923249i | \(0.625524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.18985e12 | −2.38388 | ||||||||
\(980\) | 1.83404e11 | − | 1.76283e10i | 0.198840 | − | 0.0191120i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1.97550e12i | − | 2.12437i | ||||||
\(983\) | 1.59079e12 | 1.70372 | 0.851860 | − | 0.523770i | \(-0.175475\pi\) | ||||
0.851860 | + | 0.523770i | \(0.175475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.08661e10 | − | 2.00560e9i | 0.0221665 | − | 0.00213058i | ||||
\(986\) | 9.03804e11i | 0.956239i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.07389e9i | − | 0.00847335i | ||||||
\(989\) | 9.02331e10i | 0.0943149i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.78061e11 | 0.599348 | 0.299674 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299674 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(992\) | −4.61220e11 | −0.476279 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.75238e12 | 2.81944 | ||||||||
\(995\) | 7.21876e11 | − | 6.93849e10i | 0.736496 | − | 0.0707901i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.39941e12i | − | 1.41633i | −0.706046 | − | 0.708166i | \(-0.749523\pi\) | ||
0.706046 | − | 0.708166i | \(-0.250477\pi\) | |||||||
\(998\) | 1.37942e12 | 1.39051 | ||||||||
\(999\) | 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 | 45.9.d.a.44.14 | yes | 16 | |
3.2 | odd | 2 | inner | 45.9.d.a.44.3 | ✓ | 16 | |
5.2 | odd | 4 | 225.9.c.e.26.14 | 16 | |||
5.3 | odd | 4 | 225.9.c.e.26.3 | 16 | |||
5.4 | even | 2 | inner | 45.9.d.a.44.4 | yes | 16 | |
15.2 | even | 4 | 225.9.c.e.26.4 | 16 | |||
15.8 | even | 4 | 225.9.c.e.26.13 | 16 | |||
15.14 | odd | 2 | inner | 45.9.d.a.44.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.9.d.a.44.3 | ✓ | 16 | 3.2 | odd | 2 | inner | |
45.9.d.a.44.4 | yes | 16 | 5.4 | even | 2 | inner | |
45.9.d.a.44.13 | yes | 16 | 15.14 | odd | 2 | inner | |
45.9.d.a.44.14 | yes | 16 | 1.1 | even | 1 | trivial | |
225.9.c.e.26.3 | 16 | 5.3 | odd | 4 | |||
225.9.c.e.26.4 | 16 | 15.2 | even | 4 | |||
225.9.c.e.26.13 | 16 | 15.8 | even | 4 | |||
225.9.c.e.26.14 | 16 | 5.2 | odd | 4 |