Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (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: | \(21.5545667584\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8869743.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{3} + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 68.2 | ||
Root | \(1.33454 + 0.467979i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.8.c.a.68.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 15.9248i | − | 1.40757i | −0.710413 | − | 0.703785i | \(-0.751492\pi\) | ||
0.710413 | − | 0.703785i | \(-0.248508\pi\) | |||||||
\(3\) | 37.2603 | − | 28.2607i | 0.796751 | − | 0.604308i | ||||
\(4\) | −125.600 | −0.981251 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −450.047 | − | 593.365i | −0.850605 | − | 1.12148i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | − | 38.2170i | − | 0.0263901i | ||||||
\(9\) | 589.667 | − | 2106.01i | 0.269624 | − | 0.962966i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −4679.91 | + | 3549.55i | −0.781813 | + | 0.592978i | ||||
\(13\) | −13940.2 | −1.75982 | −0.879908 | − | 0.475143i | \(-0.842396\pi\) | ||||
−0.879908 | + | 0.475143i | \(0.842396\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16685.4 | −1.01840 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −33537.8 | − | 9390.34i | −1.35544 | − | 0.379514i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 58350.9i | − | 1.00000i | ||||||
\(24\) | −1080.04 | − | 1423.98i | −0.0159478 | − | 0.0210264i | ||||
\(25\) | −78125.0 | −1.00000 | ||||||||
\(26\) | 221995.i | 2.47706i | ||||||||
\(27\) | −37546.0 | − | 95134.9i | −0.367105 | − | 0.930179i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2688.67i | − | 0.0204712i | −0.999948 | − | 0.0102356i | \(-0.996742\pi\) | ||
0.999948 | − | 0.0102356i | \(-0.00325815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 325469. | 1.96220 | 0.981101 | − | 0.193498i | \(-0.0619832\pi\) | ||||
0.981101 | + | 0.193498i | \(0.0619832\pi\) | |||||||
\(32\) | 260821.i | 1.40707i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −74062.2 | + | 264515.i | −0.264568 | + | 0.944911i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −519417. | + | 393960.i | −1.40214 | + | 1.06347i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 525376.i | 1.19049i | 0.803543 | + | 0.595246i | \(0.202946\pi\) | ||||
−0.803543 | + | 0.595246i | \(0.797054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −929228. | −1.40757 | ||||||||
\(47\) | − | 487652.i | − | 0.685121i | −0.939496 | − | 0.342561i | \(-0.888706\pi\) | ||
0.939496 | − | 0.342561i | \(-0.111294\pi\) | |||||||
\(48\) | −621705. | + | 471541.i | −0.811409 | + | 0.615426i | ||||
\(49\) | 823543. | 1.00000 | ||||||||
\(50\) | 1.24413e6i | 1.40757i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.75089e6 | 1.72682 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −1.51501e6 | + | 597914.i | −1.30929 | + | 0.516726i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −42816.6 | −0.0288147 | ||||||||
\(59\) | − | 3.15500e6i | − | 1.99994i | −0.00783115 | − | 0.999969i | \(-0.502493\pi\) | ||
0.00783115 | − | 0.999969i | \(-0.497507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | − | 5.18304e6i | − | 2.76193i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.01779e6 | 0.962158 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.64904e6 | − | 2.17417e6i | −0.604308 | − | 0.796751i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.47759e6i | − | 1.15312i | −0.817055 | − | 0.576559i | \(-0.804395\pi\) | ||
0.817055 | − | 0.576559i | \(-0.195605\pi\) | |||||||
\(72\) | −80485.2 | − | 22535.3i | −0.0254128 | − | 0.00711540i | ||||
\(73\) | −600932. | −0.180799 | −0.0903993 | − | 0.995906i | \(-0.528814\pi\) | ||||
−0.0903993 | + | 0.995906i | \(0.528814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.91096e6 | + | 2.20787e6i | −0.796751 | + | 0.604308i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.27374e6 | + | 8.27163e6i | 1.49691 | + | 1.97360i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.08756e6 | − | 2.48368e6i | −0.854606 | − | 0.519277i | ||||
\(82\) | 8.36652e6 | 1.67570 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −75983.6 | − | 100181.i | −0.0123709 | − | 0.0163105i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.32888e6i | 0.981251i | ||||||||
\(93\) | 1.21271e7 | − | 9.19798e6i | 1.56339 | − | 1.18577i | ||||
\(94\) | −7.76577e6 | −0.964356 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.37097e6 | + | 9.71827e6i | 0.850306 | + | 1.12109i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 1.31148e7i | − | 1.40757i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.81251e6 | 0.981251 | ||||||||
\(101\) | − | 1.08442e7i | − | 1.04730i | −0.851933 | − | 0.523650i | \(-0.824570\pi\) | ||
0.851933 | − | 0.523650i | \(-0.175430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 532753.i | 0.0464418i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 4.71578e6 | + | 1.19490e7i | 0.360222 | + | 0.912740i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 337697.i | 0.0200874i | ||||||||
\(117\) | −8.22008e6 | + | 2.93582e7i | −0.474488 | + | 1.69464i | ||||
\(118\) | −5.02428e7 | −2.81505 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94872e7 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.48475e7 | + | 1.95757e7i | 0.719424 | + | 0.948526i | ||||
\(124\) | −4.08790e7 | −1.92541 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.08122e7 | −0.901580 | −0.450790 | − | 0.892630i | \(-0.648858\pi\) | ||||
−0.450790 | + | 0.892630i | \(0.648858\pi\) | |||||||
\(128\) | 1.25207e6i | 0.0527710i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.90964e7i | − | 1.51945i | −0.650243 | − | 0.759727i | \(-0.725333\pi\) | ||
0.650243 | − | 0.759727i | \(-0.274667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −3.46233e7 | + | 2.62606e7i | −1.12148 | + | 0.850605i | ||||
\(139\) | 6.16654e7 | 1.94755 | 0.973777 | − | 0.227505i | \(-0.0730566\pi\) | ||||
0.973777 | + | 0.227505i | \(0.0730566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.37814e7 | − | 1.81701e7i | −0.414024 | − | 0.545871i | ||||
\(142\) | −5.53800e7 | −1.62309 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.83884e6 | + | 3.51396e7i | −0.274584 | + | 0.980682i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.56973e6i | 0.254487i | ||||||||
\(147\) | 3.06855e7 | − | 2.32739e7i | 0.796751 | − | 0.604308i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 3.51599e7 | + | 4.63566e7i | 0.850605 | + | 1.12148i | ||||
\(151\) | 7.35151e7 | 1.73763 | 0.868815 | − | 0.495137i | \(-0.164882\pi\) | ||||
0.868815 | + | 0.495137i | \(0.164882\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.52388e7 | − | 4.94814e7i | 1.37585 | − | 1.04353i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.95522e7 | + | 6.50936e7i | −0.730918 | + | 1.20292i | ||||
\(163\) | 1.01017e8 | 1.82699 | 0.913497 | − | 0.406845i | \(-0.133371\pi\) | ||||
0.913497 | + | 0.406845i | \(0.133371\pi\) | |||||||
\(164\) | − | 6.59873e7i | − | 1.16817i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.56023e7i | 0.923815i | 0.886928 | + | 0.461907i | \(0.152835\pi\) | ||||
−0.886928 | + | 0.461907i | \(0.847165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.31581e8 | 2.09696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.26618e7i | 1.06695i | 0.845815 | + | 0.533476i | \(0.179114\pi\) | ||||
−0.845815 | + | 0.533476i | \(0.820886\pi\) | |||||||
\(174\) | −1.59536e6 | + | 1.21003e6i | −0.0229581 | + | 0.0174129i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.91623e7 | − | 1.17556e8i | −1.20858 | − | 1.59345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.42600e8i | − | 1.85837i | −0.369611 | − | 0.929186i | \(-0.620509\pi\) | ||
0.369611 | − | 0.929186i | \(-0.379491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.23000e6 | −0.0263901 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.46476e8 | − | 1.93122e8i | −1.66906 | − | 2.20057i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.12492e7i | 0.672276i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 7.51836e7 | − | 5.70242e7i | 0.766600 | − | 0.581440i | ||||
\(193\) | 1.32545e7 | 0.132712 | 0.0663562 | − | 0.997796i | \(-0.478863\pi\) | ||||
0.0663562 | + | 0.997796i | \(0.478863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.03437e8 | −0.981251 | ||||||||
\(197\) | 4.99985e7i | 0.465935i | 0.972484 | + | 0.232968i | \(0.0748436\pi\) | ||||
−0.972484 | + | 0.232968i | \(0.925156\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 2.98570e6i | 0.0263901i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.72691e8 | −1.47415 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.22887e8 | − | 3.44076e7i | −0.962966 | − | 0.269624i | ||||
\(208\) | 2.32598e8 | 1.79219 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.24635e8 | 1.64623 | 0.823113 | − | 0.567878i | \(-0.192235\pi\) | ||||
0.823113 | + | 0.567878i | \(0.192235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.82791e7 | − | 1.29576e8i | −0.696839 | − | 0.918748i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.63577e6 | + | 1.43490e6i | −0.0245476 | + | 0.00968796i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.23909e7 | + | 1.69827e7i | −0.144051 | + | 0.109258i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.13612e8 | −1.89376 | −0.946881 | − | 0.321583i | \(-0.895785\pi\) | ||||
−0.946881 | + | 0.321583i | \(0.895785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.60677e7 | + | 1.64532e8i | −0.269624 | + | 0.962966i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −102753. | −0.000540239 | ||||||||
\(233\) | − | 2.26864e8i | − | 1.17495i | −0.809241 | − | 0.587476i | \(-0.800122\pi\) | ||
0.809241 | − | 0.587476i | \(-0.199878\pi\) | |||||||
\(234\) | 4.67524e8 | + | 1.30903e8i | 2.38533 | + | 0.667875i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.96268e8i | 1.96244i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.97272e8i | 1.88233i | 0.337948 | + | 0.941165i | \(0.390267\pi\) | ||||
−0.337948 | + | 0.941165i | \(0.609733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 3.10330e8i | 1.40757i | ||||||||
\(243\) | −2.22494e8 | + | 2.29742e7i | −0.994711 | + | 0.102711i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.11740e8 | − | 2.36444e8i | 1.33512 | − | 1.01264i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 1.24384e7i | − | 0.0517828i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.31430e8i | 1.26904i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.78216e8 | 1.03644 | ||||||||
\(257\) | 5.41979e8i | 1.99167i | 0.0911942 | + | 0.995833i | \(0.470932\pi\) | ||||
−0.0911942 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.66235e6 | − | 1.58542e6i | −0.0197131 | − | 0.00551953i | ||||
\(262\) | −6.22604e8 | −2.13874 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.16125e8i | − | 1.92990i | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||
0.262427 | − | 0.964952i | \(-0.415477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.61606e8 | −0.798464 | −0.399232 | − | 0.916850i | \(-0.630723\pi\) | ||||
−0.399232 | + | 0.916850i | \(0.630723\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.07119e8 | + | 2.73077e8i | 0.592978 | + | 0.781813i | ||||
\(277\) | −7.06389e8 | −1.99694 | −0.998469 | − | 0.0553055i | \(-0.982387\pi\) | ||||
−0.998469 | + | 0.0553055i | \(0.982387\pi\) | |||||||
\(278\) | − | 9.82010e8i | − | 2.74132i | ||||||
\(279\) | 1.91918e8 | − | 6.85440e8i | 0.529056 | − | 1.88953i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −2.89355e8 | + | 2.19466e8i | −0.768351 | + | 0.582768i | ||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 4.36786e8i | 1.13150i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.49290e8 | + | 1.53797e8i | 1.35496 | + | 0.379380i | ||||
\(289\) | −4.10339e8 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.54771e7 | 0.177409 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −3.70633e8 | − | 4.88661e8i | −0.850605 | − | 1.12148i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.13423e8i | 1.75982i | ||||||||
\(300\) | 3.65618e8 | − | 2.77308e8i | 0.781813 | − | 0.592978i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1.17072e9i | − | 2.44583i | ||||||
\(303\) | −3.06463e8 | − | 4.04057e8i | −0.632892 | − | 0.834437i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.08266e8 | 1.79155 | 0.895775 | − | 0.444509i | \(-0.146622\pi\) | ||||
0.895775 | + | 0.444509i | \(0.146622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.69412e8i | 0.507873i | 0.967221 | + | 0.253937i | \(0.0817255\pi\) | ||||
−0.967221 | + | 0.253937i | \(0.918275\pi\) | |||||||
\(312\) | 1.50560e7 | + | 1.98506e7i | 0.0280652 | + | 0.0370025i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.45302e8i | 1.49041i | 0.666838 | + | 0.745203i | \(0.267647\pi\) | ||||
−0.666838 | + | 0.745203i | \(0.732353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.13398e8 | + | 3.11951e8i | 0.838583 | + | 0.509541i | ||||
\(325\) | 1.08908e9 | 1.75982 | ||||||||
\(326\) | − | 1.60868e9i | − | 2.57162i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00783e7 | 0.0314173 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.53397e8 | −0.990329 | −0.495164 | − | 0.868799i | \(-0.664892\pi\) | ||||
−0.495164 | + | 0.868799i | \(0.664892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.85457e8 | 1.30033 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 2.09540e9i | − | 2.95161i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.15713e9 | 1.50181 | ||||||||
\(347\) | 1.50749e9i | 1.93688i | 0.249251 | + | 0.968439i | \(0.419816\pi\) | ||||
−0.249251 | + | 0.968439i | \(0.580184\pi\) | |||||||
\(348\) | 9.54355e6 | + | 1.25827e7i | 0.0121390 | + | 0.0160047i | ||||
\(349\) | 1.46751e9 | 1.84796 | 0.923978 | − | 0.382445i | \(-0.124918\pi\) | ||||
0.923978 | + | 0.382445i | \(0.124918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.23399e8 | + | 1.32620e9i | 0.646038 | + | 1.63695i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.49711e9i | − | 1.81152i | −0.423792 | − | 0.905760i | \(-0.639301\pi\) | ||
0.423792 | − | 0.905760i | \(-0.360699\pi\) | |||||||
\(354\) | −1.87206e9 | + | 1.41990e9i | −2.24290 | + | 1.70116i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.27088e9 | −2.61579 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.93872e8 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.26099e8 | + | 5.50721e8i | −0.796751 | + | 0.604308i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 9.73609e8i | 1.01840i | ||||||||
\(369\) | 1.10645e9 | + | 3.09797e8i | 1.14640 | + | 0.320985i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.52316e9 | + | 1.15527e9i | −1.53407 | + | 1.16354i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.86366e7 | −0.0180804 | ||||||||
\(377\) | 3.74806e7i | 0.0360256i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.75469e8 | + | 5.88166e8i | −0.718335 | + | 0.544832i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 3.53845e7 | + | 4.66527e7i | 0.0318899 | + | 0.0420453i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.11075e8i | − | 0.186802i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 3.14733e7i | − | 0.0263901i | ||||||
\(393\) | −1.10489e9 | − | 1.45675e9i | −0.918218 | − | 1.21063i | ||||
\(394\) | 7.96218e8 | 0.655836 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.88167e9 | −1.50930 | −0.754651 | − | 0.656126i | \(-0.772194\pi\) | ||||
−0.754651 | + | 0.656126i | \(0.772194\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.30355e9 | 1.01840 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.53710e9 | −3.45312 | ||||||||
\(404\) | 1.36203e9i | 1.02766i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.71588e9 | 1.96282 | 0.981408 | − | 0.191935i | \(-0.0614762\pi\) | ||||
0.981408 | + | 0.191935i | \(0.0614762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.47935e8 | + | 1.95696e9i | −0.379514 | + | 1.35544i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 3.63589e9i | − | 2.47619i | ||||||
\(417\) | 2.29767e9 | − | 1.74271e9i | 1.55172 | − | 1.17692i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | − | 3.57728e9i | − | 2.31718i | ||||||
\(423\) | −1.02700e9 | − | 2.87552e8i | −0.659748 | − | 0.184725i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.06348e9 | + | 1.56508e9i | −1.29320 | + | 0.980849i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 6.26471e8 | + | 1.58737e9i | 0.373859 | + | 0.947292i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.70447e8 | + | 3.56572e8i | 0.153788 | + | 0.202762i | ||||
\(439\) | −2.88478e9 | −1.62737 | −0.813685 | − | 0.581306i | \(-0.802542\pi\) | ||||
−0.813685 | + | 0.581306i | \(0.802542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.85616e8 | − | 1.73439e9i | 0.269624 | − | 0.962966i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.59756e9i | 1.96605i | 0.183462 | + | 0.983027i | \(0.441270\pi\) | ||||
−0.183462 | + | 0.983027i | \(0.558730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.99422e9i | 2.66560i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.82648e9i | 1.99498i | 0.0708395 | + | 0.997488i | \(0.477432\pi\) | ||||
−0.0708395 | + | 0.997488i | \(0.522568\pi\) | |||||||
\(450\) | 2.62014e9 | + | 7.33621e8i | 1.35544 | + | 0.379514i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.73920e9 | − | 2.07759e9i | 1.38446 | − | 1.05006i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.27874e9i | − | 1.55867i | −0.626609 | − | 0.779334i | \(-0.715558\pi\) | ||
0.626609 | − | 0.779334i | \(-0.284442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.71939e9 | 0.805085 | 0.402543 | − | 0.915401i | \(-0.368126\pi\) | ||||
0.402543 | + | 0.915401i | \(0.368126\pi\) | |||||||
\(464\) | 4.48615e7i | 0.0208478i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.61277e9 | −1.65383 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 1.03244e9 | − | 3.68739e9i | 0.465592 | − | 1.66287i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.20574e8 | −0.0527787 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.32649e9 | 2.64951 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.44759e9 | 0.981251 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.65860e8 | + | 3.54318e9i | 0.144573 | + | 1.40012i | ||||
\(487\) | −2.19042e9 | −0.859362 | −0.429681 | − | 0.902981i | \(-0.641374\pi\) | ||||
−0.429681 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.76392e9 | − | 2.85481e9i | 1.45566 | − | 1.10407i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.53523e9i | − | 1.34782i | −0.738812 | − | 0.673912i | \(-0.764613\pi\) | ||
0.738812 | − | 0.673912i | \(-0.235387\pi\) | |||||||
\(492\) | −1.86485e9 | − | 2.45871e9i | −0.705936 | − | 0.930743i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.43059e9 | −1.99830 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.41765e9 | −0.510761 | −0.255380 | − | 0.966841i | \(-0.582201\pi\) | ||||
−0.255380 | + | 0.966841i | \(0.582201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.57136e9 | + | 2.07176e9i | 0.558269 | + | 0.736050i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.90275e9 | − | 3.71857e9i | 1.67075 | − | 1.26721i | ||||
\(508\) | 2.61401e9 | 0.884677 | ||||||||
\(509\) | − | 1.77233e9i | − | 0.595707i | −0.954612 | − | 0.297853i | \(-0.903729\pi\) | ||
0.954612 | − | 0.297853i | \(-0.0962706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 4.27028e9i | − | 1.40609i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.63092e9 | 2.80341 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05347e9 | + | 2.70740e9i | 0.644767 | + | 0.850094i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | −2.52475e7 | + | 9.01719e7i | −0.00776912 | + | 0.0277476i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 4.91052e9i | 1.49097i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.40483e9 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.64444e9 | − | 1.86040e9i | −1.92587 | − | 0.539231i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.32385e9i | − | 2.09505i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.02996e9 | − | 5.31331e9i | −1.12303 | − | 1.48066i | ||||
\(538\) | −9.81168e9 | −2.71647 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.37199e8 | −0.173015 | −0.0865076 | − | 0.996251i | \(-0.527571\pi\) | ||||
−0.0865076 | + | 0.996251i | \(0.527571\pi\) | |||||||
\(542\) | 4.16603e9i | 1.12389i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.56469e9 | 0.408765 | 0.204382 | − | 0.978891i | \(-0.434481\pi\) | ||||
0.204382 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −8.30904e7 | + | 6.30212e7i | −0.0210264 | + | 0.0159478i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.12491e10i | 2.81083i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.74518e9 | −1.91104 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | −1.09155e10 | − | 3.05626e9i | −2.65965 | − | 0.744683i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 1.73094e9 | + | 2.28216e9i | 0.406262 | + | 0.535637i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.32903e8 | −0.0304310 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.55866e9i | 1.00000i | ||||||||
\(576\) | 1.18982e9 | − | 4.24948e9i | 0.259420 | − | 0.926525i | ||||
\(577\) | 8.05760e9 | 1.74619 | 0.873093 | − | 0.487554i | \(-0.162111\pi\) | ||||
0.873093 | + | 0.487554i | \(0.162111\pi\) | |||||||
\(578\) | 6.53457e9i | 1.40757i | ||||||||
\(579\) | 4.93866e8 | − | 3.74580e8i | 0.105739 | − | 0.0801991i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.29658e7i | 0.00477130i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.31368e9i | 1.28840i | 0.764859 | + | 0.644198i | \(0.222809\pi\) | ||||
−0.764859 | + | 0.644198i | \(0.777191\pi\) | |||||||
\(588\) | −3.85410e9 | + | 2.92320e9i | −0.781813 | + | 0.592978i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.41299e9 | + | 1.86296e9i | 0.281568 | + | 0.371234i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.80116e8i | 0.133934i | 0.997755 | + | 0.0669671i | \(0.0213323\pi\) | ||||
−0.997755 | + | 0.0669671i | \(0.978668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.29536e10 | 2.47706 | ||||||||
\(599\) | 1.03305e10i | 1.96393i | 0.189052 | + | 0.981967i | \(0.439459\pi\) | ||||
−0.189052 | + | 0.981967i | \(0.560541\pi\) | |||||||
\(600\) | 8.43780e7 | + | 1.11248e8i | 0.0159478 | + | 0.0210264i | ||||
\(601\) | 9.07724e9 | 1.70566 | 0.852831 | − | 0.522187i | \(-0.174884\pi\) | ||||
0.852831 | + | 0.522187i | \(0.174884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.23351e9 | −1.70505 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.43454e9 | + | 4.88038e9i | −1.17453 | + | 0.890839i | ||||
\(607\) | 3.74889e9 | 0.680365 | 0.340183 | − | 0.940359i | \(-0.389511\pi\) | ||||
0.340183 | + | 0.940359i | \(0.389511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.79797e9i | 1.20569i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | − | 1.44640e10i | − | 2.52173i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.55121e9 | + | 2.19084e9i | −0.930179 | + | 0.367105i | ||||
\(622\) | 4.29034e9 | 0.714867 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.66669e9 | − | 6.57339e9i | 1.42793 | − | 1.08304i | ||||
\(625\) | 6.10352e9 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.36999e9 | − | 6.34835e9i | 1.31163 | − | 0.994828i | ||||
\(634\) | 1.34613e10 | 2.09785 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14804e10 | −1.75982 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.32383e9 | − | 2.05062e9i | −1.11041 | − | 0.310908i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.06840e10i | 1.55085i | 0.631441 | + | 0.775424i | \(0.282464\pi\) | ||||
−0.631441 | + | 0.775424i | \(0.717536\pi\) | |||||||
\(648\) | −9.49190e7 | + | 1.56214e8i | −0.0137038 | + | 0.0225532i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 1.73434e10i | − | 2.47706i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.26877e10 | −1.79274 | ||||||||
\(653\) | − | 1.57744e9i | − | 0.221696i | −0.993837 | − | 0.110848i | \(-0.964643\pi\) | ||
0.993837 | − | 0.110848i | \(-0.0353566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.76612e9i | − | 1.21239i | ||||||
\(657\) | −3.54349e8 | + | 1.26557e9i | −0.0487476 | + | 0.174103i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 1.04052e10i | 1.39396i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.56886e8 | −0.0204712 | ||||||||
\(668\) | − | 6.98365e9i | − | 0.906494i | ||||||
\(669\) | −1.16853e10 | + | 8.86289e9i | −1.50886 | + | 1.14442i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.94077e9 | −0.245426 | −0.122713 | − | 0.992442i | \(-0.539160\pi\) | ||||
−0.122713 | + | 0.992442i | \(0.539160\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.93328e9 | + | 7.43241e9i | 0.367105 | + | 0.930179i | ||||
\(676\) | −1.65266e10 | −2.05764 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.10695e10i | − | 1.32940i | −0.747109 | − | 0.664701i | \(-0.768559\pi\) | ||
0.747109 | − | 0.664701i | \(-0.231441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.06109e10 | −1.22343 | −0.611716 | − | 0.791078i | \(-0.709520\pi\) | ||||
−0.611716 | + | 0.791078i | \(0.709520\pi\) | |||||||
\(692\) | − | 9.12633e9i | − | 1.04695i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.40066e10 | 2.72629 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.82860e6 | + | 2.90386e6i | −0.000430436 | + | 0.000326471i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 2.33698e10i | − | 2.60113i | ||||||
\(699\) | −6.41134e9 | − | 8.45304e9i | −0.710033 | − | 0.936144i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 2.11195e10 | − | 8.33504e9i | 2.30411 | − | 0.909343i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.38413e10 | −2.54984 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.11988e10 | + | 1.47651e10i | 1.18592 | + | 1.56358i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.89914e10i | − | 1.96220i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.79105e10i | 1.82353i | ||||||||
\(717\) | 1.12272e10 | + | 1.48025e10i | 1.13751 | + | 1.49975i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.98207e10i | − | 1.98870i | −0.106173 | − | 0.994348i | \(-0.533860\pi\) | ||
0.106173 | − | 0.994348i | \(-0.466140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.42348e10i | − | 1.40757i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.10052e8i | 0.0204712i | ||||||||
\(726\) | 8.77014e9 | + | 1.15630e10i | 0.850605 | + | 1.12148i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.64095e9 | + | 7.14387e9i | −0.730468 | + | 0.682947i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.52191e10 | 1.40707 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.93346e9 | − | 1.76200e10i | 0.451809 | − | 1.61364i | ||||
\(739\) | 1.98085e10 | 1.80549 | 0.902746 | − | 0.430174i | \(-0.141548\pi\) | ||||
0.902746 | + | 0.430174i | \(0.141548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | −3.51519e8 | − | 4.63461e8i | −0.0312927 | − | 0.0412580i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 8.13668e9i | 0.697726i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.96872e8 | 0.0507086 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.37612e9i | 0.359951i | 0.983671 | + | 0.179975i | \(0.0576018\pi\) | ||||
−0.983671 | + | 0.179975i | \(0.942398\pi\) | |||||||
\(762\) | 9.36645e9 | + | 1.23492e10i | 0.766889 | + | 1.01111i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.39813e10i | 3.51953i | ||||||||
\(768\) | 1.03664e10 | − | 7.86258e9i | 0.825782 | − | 0.626327i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.53167e10 | + | 2.01943e10i | 1.20358 | + | 1.58686i | ||||
\(772\) | −1.66476e9 | −0.130224 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.54273e10 | −1.96220 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.55786e8 | + | 1.00949e8i | −0.0190419 | + | 0.00751510i | ||||
\(784\) | −1.37412e10 | −1.01840 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.31984e10 | + | 1.75952e10i | −1.70404 | + | 1.29246i | ||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | − | 6.27982e9i | − | 0.457200i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2.99652e10i | 2.12445i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 2.03766e10i | − | 1.40707i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.22526e10i | 4.86050i | ||||||||
\(807\) | −1.74121e10 | − | 2.29570e10i | −1.16626 | − | 1.53765i | ||||
\(808\) | −4.14431e8 | −0.0276384 | ||||||||
\(809\) | − | 2.68654e10i | − | 1.78391i | −0.452125 | − | 0.891955i | \(-0.649334\pi\) | ||
0.452125 | − | 0.891955i | \(-0.350666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.33600e10 | −1.53780 | −0.768898 | − | 0.639371i | \(-0.779195\pi\) | ||||
−0.768898 | + | 0.639371i | \(0.779195\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.74754e9 | + | 7.39317e9i | −0.636177 | + | 0.482519i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 4.32500e10i | − | 2.76280i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.16676e10i | − | 1.36650i | −0.730185 | − | 0.683249i | \(-0.760566\pi\) | ||
0.730185 | − | 0.683249i | \(-0.239434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.98569e10 | 1.86700 | 0.933501 | − | 0.358574i | \(-0.116737\pi\) | ||||
0.933501 | + | 0.358574i | \(0.116737\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 1.54347e10 | + | 4.32160e9i | 0.944911 | + | 0.264568i | ||||
\(829\) | −7.89933e9 | −0.481559 | −0.240780 | − | 0.970580i | \(-0.577403\pi\) | ||||
−0.240780 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.63203e10 | + | 1.99630e10i | −1.59106 | + | 1.20677i | ||||
\(832\) | −2.81284e10 | −1.69322 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.77523e10 | − | 3.65900e10i | −1.65660 | − | 2.18415i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.22201e10 | − | 3.09635e10i | −0.720334 | − | 1.82520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.72426e10 | 0.999581 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.82142e10 | −1.61536 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.57922e9 | + | 1.63548e10i | −0.260013 | + | 0.928641i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.23439e10 | + | 1.62748e10i | 0.683774 | + | 0.901523i | ||||
\(853\) | 3.38461e10 | 1.86718 | 0.933592 | − | 0.358338i | \(-0.116656\pi\) | ||||
0.933592 | + | 0.358338i | \(0.116656\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.52479e10i | 1.91294i | 0.291834 | + | 0.956469i | \(0.405734\pi\) | ||||
−0.291834 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.75816e10 | −0.946416 | −0.473208 | − | 0.880951i | \(-0.656904\pi\) | ||||
−0.473208 | + | 0.880951i | \(0.656904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.75427e10i | − | 1.98832i | −0.107897 | − | 0.994162i | \(-0.534412\pi\) | ||
0.107897 | − | 0.994162i | \(-0.465588\pi\) | |||||||
\(864\) | 2.48132e10 | − | 9.79277e9i | 1.30883 | − | 0.516544i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.52894e10 | + | 1.15965e10i | −0.796751 | + | 0.604308i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.81230e9 | − | 2.13304e9i | 0.141351 | − | 0.107210i | ||||
\(877\) | −3.97530e10 | −1.99008 | −0.995042 | − | 0.0994600i | \(-0.968288\pi\) | ||||
−0.995042 | + | 0.0994600i | \(0.968288\pi\) | |||||||
\(878\) | 4.59396e10i | 2.29064i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −2.76198e10 | − | 7.73335e9i | −1.35544 | − | 0.379514i | ||||
\(883\) | 3.77437e10 | 1.84494 | 0.922469 | − | 0.386072i | \(-0.126168\pi\) | ||||
0.922469 | + | 0.386072i | \(0.126168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.72906e10 | 2.76736 | ||||||||
\(887\) | − | 1.69785e10i | − | 0.816896i | −0.912781 | − | 0.408448i | \(-0.866070\pi\) | ||
0.912781 | − | 0.408448i | \(-0.133930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.93897e10 | 1.85826 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.29879e10 | + | 3.03084e10i | 1.06347 | + | 1.40214i | ||||
\(898\) | 6.09361e10 | 2.80807 | ||||||||
\(899\) | − | 8.75078e8i | − | 0.0401687i | ||||||
\(900\) | 5.78611e9 | − | 2.06652e10i | 0.264568 | − | 0.944911i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.30852e10 | − | 4.36213e10i | −1.47804 | − | 1.94872i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.28379e10 | − | 6.39444e9i | −1.00851 | − | 0.282377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.38423e10 | − | 2.56682e10i | 1.42742 | − | 1.08265i | ||||
\(922\) | −5.22134e10 | −2.19393 | ||||||||
\(923\) | 4.84783e10i | 2.02928i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 2.73811e10i | − | 1.13321i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.01260e8 | 0.0288046 | ||||||||
\(929\) | − | 4.53220e10i | − | 1.85462i | −0.374300 | − | 0.927308i | \(-0.622117\pi\) | ||
0.374300 | − | 0.927308i | \(-0.377883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.84942e10i | 1.15292i | ||||||||
\(933\) | 7.61377e9 | + | 1.00384e10i | 0.306912 | + | 0.404648i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.12198e9 | + | 3.14147e8i | 0.0447219 | + | 0.0125218i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.06562e10 | 1.19049 | ||||||||
\(944\) | 5.26424e10i | 2.03673i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 5.04672e10i | − | 1.93101i | −0.260385 | − | 0.965505i | \(-0.583849\pi\) | ||
0.260385 | − | 0.965505i | \(-0.416151\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.37711e9 | 0.318172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.38888e10 | + | 3.14962e10i | 0.900664 | + | 1.18748i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 4.98975e10i | − | 1.84704i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.84174e10 | 2.85023 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.82955e10 | −0.650658 | −0.325329 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325329 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(968\) | 7.44741e8i | 0.0263901i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 2.79453e10 | − | 2.88556e9i | 0.976062 | − | 0.100786i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.48821e10i | 1.20961i | ||||||||
\(975\) | 4.05794e10 | − | 3.07781e10i | 1.40214 | − | 1.06347i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −4.54623e10 | − | 5.99398e10i | −1.55405 | − | 2.04894i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.62980e10 | −1.89715 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 7.48124e8 | − | 5.67427e8i | 0.0250317 | − | 0.0189857i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.02745e10 | −1.96732 | −0.983662 | − | 0.180023i | \(-0.942383\pi\) | ||||
−0.983662 | + | 0.180023i | \(0.942383\pi\) | |||||||
\(992\) | 8.48890e10i | 2.76096i | ||||||||
\(993\) | −2.43458e10 | + | 1.84655e10i | −0.789045 | + | 0.598464i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.06654e10 | −0.340835 | −0.170417 | − | 0.985372i | \(-0.554512\pi\) | ||||
−0.170417 | + | 0.985372i | \(0.554512\pi\) | |||||||
\(998\) | 2.25758e10i | 0.718931i | ||||||||
\(999\) | 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 | 69.8.c.a.68.2 | ✓ | 6 | |
3.2 | odd | 2 | inner | 69.8.c.a.68.5 | yes | 6 | |
23.22 | odd | 2 | CM | 69.8.c.a.68.2 | ✓ | 6 | |
69.68 | even | 2 | inner | 69.8.c.a.68.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.c.a.68.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
69.8.c.a.68.2 | ✓ | 6 | 23.22 | odd | 2 | CM | |
69.8.c.a.68.5 | yes | 6 | 3.2 | odd | 2 | inner | |
69.8.c.a.68.5 | yes | 6 | 69.68 | even | 2 | inner |