Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,18,Mod(17,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.17");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6310679503\) |
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: | \( x^{16} - 8 x^{15} + 83403052 x^{14} - 583821224 x^{13} + \cdots + 21\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{240}\cdot 3^{14}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.8 | ||
Root | \(0.500000 + 409.736i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.17 |
Dual form | 32.18.b.a.17.9 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1638.94i | − 0.144223i | −0.997397 | − | 0.0721113i | \(-0.977026\pi\) | ||||
0.997397 | − | 0.0721113i | \(-0.0229737\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21254e6i | 1.38820i | 0.719879 | + | 0.694100i | \(0.244197\pi\) | ||||
−0.719879 | + | 0.694100i | \(0.755803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.76580e7 | −1.15773 | −0.578866 | − | 0.815423i | \(-0.696505\pi\) | ||||
−0.578866 | + | 0.815423i | \(0.696505\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.26454e8 | 0.979200 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 7.26817e8i | − 1.02232i | −0.859485 | − | 0.511161i | \(-0.829216\pi\) | ||||
0.859485 | − | 0.511161i | \(-0.170784\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.16645e9i | − 1.07660i | −0.842753 | − | 0.538300i | \(-0.819067\pi\) | ||||
0.842753 | − | 0.538300i | \(-0.180933\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.98729e9 | 0.200210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56030e10 | 1.58554 | 0.792771 | − | 0.609520i | \(-0.208638\pi\) | ||||
0.792771 | + | 0.609520i | \(0.208638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.55789e10i | 0.210441i | 0.994449 | + | 0.105220i | \(0.0335548\pi\) | ||||
−0.994449 | + | 0.105220i | \(0.966445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.89404e10i | 0.166971i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.09250e11 | −1.08969 | −0.544843 | − | 0.838538i | \(-0.683411\pi\) | ||||
−0.544843 | + | 0.838538i | \(0.683411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.07318e11 | −0.927096 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.18904e11i | − 0.285445i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.11338e12i | 1.15571i | 0.816139 | + | 0.577855i | \(0.196110\pi\) | ||||
−0.816139 | + | 0.577855i | \(0.803890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.57077e12 | 1.38370 | 0.691850 | − | 0.722041i | \(-0.256796\pi\) | ||||
0.691850 | + | 0.722041i | \(0.256796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.19121e12 | −0.147442 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.14111e13i | − 1.60716i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36898e13i | 0.640739i | 0.947293 | + | 0.320369i | \(0.103807\pi\) | ||||
−0.947293 | + | 0.320369i | \(0.896193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.18964e12 | −0.155270 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.81830e12 | −0.0551220 | −0.0275610 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275610 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.36024e13i | 0.177474i | 0.996055 | + | 0.0887369i | \(0.0282830\pi\) | ||||
−0.996055 | + | 0.0887369i | \(0.971717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.53331e14i | 1.35932i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.84132e11 | −0.00419091 | −0.00209545 | − | 0.999998i | \(-0.500667\pi\) | ||||
−0.00209545 | + | 0.999998i | \(0.500667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.91743e13 | 0.340343 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 7.47407e13i | − 0.228671i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.47869e14i | − 0.546862i | −0.961892 | − | 0.273431i | \(-0.911841\pi\) | ||||
0.961892 | − | 0.273431i | \(-0.0881585\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.81297e14 | 1.41919 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.55329e13 | 0.0303503 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.03296e15i | 1.80255i | 0.433245 | + | 0.901276i | \(0.357368\pi\) | ||||
−0.433245 | + | 0.901276i | \(0.642632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92495e14i | 0.596077i | 0.954554 | + | 0.298038i | \(0.0963324\pi\) | ||||
−0.954554 | + | 0.298038i | \(0.903668\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.23292e15 | −1.13365 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.83946e15 | 1.49454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.06693e15i | 1.52444i | 0.647321 | + | 0.762218i | \(0.275889\pi\) | ||||
−0.647321 | + | 0.762218i | \(0.724111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.70737e14i | 0.157157i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.85113e15 | 1.25912 | 0.629559 | − | 0.776953i | \(-0.283236\pi\) | ||||
0.629559 | + | 0.776953i | \(0.283236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.37250e15 | 0.199191 | 0.0995954 | − | 0.995028i | \(-0.468245\pi\) | ||||
0.0995954 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.15925e15i | 0.133708i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.28341e16i | 1.18357i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.78556e16 | 1.32417 | 0.662085 | − | 0.749429i | \(-0.269672\pi\) | ||||
0.662085 | + | 0.749429i | \(0.269672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.56437e16 | 0.938032 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.48017e15i | − 0.0721354i | −0.999349 | − | 0.0360677i | \(-0.988517\pi\) | ||||
0.999349 | − | 0.0360677i | \(-0.0114832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52955e16i | 2.20105i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.10265e15 | 0.166680 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.78700e16 | −1.01972 | −0.509859 | − | 0.860258i | \(-0.670303\pi\) | ||||
−0.509859 | + | 0.860258i | \(0.670303\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59132e16i | 1.24642i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.07691e16i | − 0.199561i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.88900e16 | −0.292134 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.28098e17 | 1.65952 | 0.829760 | − | 0.558121i | \(-0.188477\pi\) | ||||
0.829760 | + | 0.558121i | \(0.188477\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 9.19090e16i | − 1.00106i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.82139e16i | − 0.626818i | −0.949618 | − | 0.313409i | \(-0.898529\pi\) | ||||
0.949618 | − | 0.313409i | \(-0.101471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.08715e16 | 0.240127 | 0.120063 | − | 0.992766i | \(-0.461690\pi\) | ||||
0.120063 | + | 0.992766i | \(0.461690\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.50915e16 | −0.231789 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.71861e17i | 1.52962i | 0.644253 | + | 0.764812i | \(0.277168\pi\) | ||||
−0.644253 | + | 0.764812i | \(0.722832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.32808e17i | − 0.638407i | −0.947686 | − | 0.319203i | \(-0.896585\pi\) | ||||
0.947686 | − | 0.319203i | \(-0.103415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24367e16 | 0.0924090 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.78953e17 | −1.34097 | −0.670484 | − | 0.741924i | \(-0.733913\pi\) | ||||
−0.670484 | + | 0.741924i | \(0.733913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.96232e17i | − 1.51270i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.00411e17i | − 1.05421i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.05257e17 | −1.83563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.28165e16 | −0.0451413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.61904e15i | 0.00794983i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.74428e16i | 0.101205i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.56390e17 | 0.336179 | 0.168089 | − | 0.985772i | \(-0.446240\pi\) | ||||
0.168089 | + | 0.985772i | \(0.446240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.22936e16 | 0.0255957 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.61862e18i | − 1.63057i | −0.579060 | − | 0.815285i | \(-0.696580\pi\) | ||||
0.579060 | − | 0.815285i | \(-0.303420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.75092e17i | − 0.243634i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.07939e17 | 0.396255 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.32494e17 | −0.228907 | −0.114453 | − | 0.993429i | \(-0.536512\pi\) | ||||
−0.114453 | + | 0.993429i | \(0.536512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 6.37994e17i | − 0.388321i | −0.980970 | − | 0.194161i | \(-0.937802\pi\) | ||||
0.980970 | − | 0.194161i | \(-0.0621983\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12125e15i | 0 0.000604423i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.30143e18 | −1.10063 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.77510e18 | −1.60436 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.29762e17i | − 0.0490852i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.77142e18i | 0.934585i | 0.884103 | + | 0.467293i | \(0.154771\pi\) | ||||
−0.884103 | + | 0.467293i | \(0.845229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.43299e18 | 1.33473 | 0.667364 | − | 0.744732i | \(-0.267423\pi\) | ||||
0.667364 | + | 0.744732i | \(0.267423\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.76668e18 | 1.55256 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.96734e18i | 1.92085i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.50626e18i | − 0.758048i | −0.925387 | − | 0.379024i | \(-0.876260\pi\) | ||||
0.925387 | − | 0.379024i | \(-0.123740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.06244e17 | −0.0788698 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.22653e18 | 1.26157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.12490e18i | 0.333998i | 0.985957 | + | 0.166999i | \(0.0534076\pi\) | ||||
−0.985957 | + | 0.166999i | \(0.946592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.44439e18i | − 0.204679i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.81083e18 | −0.487450 | −0.243725 | − | 0.969844i | \(-0.578369\pi\) | ||||
−0.243725 | + | 0.969844i | \(0.578369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.37601e18 | −0.159069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.97001e18i | 0.206064i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.51874e18i | 0.807204i | 0.914935 | + | 0.403602i | \(0.132242\pi\) | ||||
−0.914935 | + | 0.403602i | \(0.867758\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.24898e19 | 1.07333 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.33191e18 | 0.259969 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.98628e19i | 1.40860i | 0.709900 | + | 0.704302i | \(0.248740\pi\) | ||||
−0.709900 | + | 0.704302i | \(0.751260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34430e19i | 1.51267i | 0.654182 | + | 0.756337i | \(0.273013\pi\) | ||||
−0.654182 | + | 0.756337i | \(0.726987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.46275e18 | 0.0859677 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.65994e19 | −0.889473 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.31451e19i | − 1.62093i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.39701e18i | 0.330469i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50710e19 | 0.615686 | 0.307843 | − | 0.951437i | \(-0.400393\pi\) | ||||
0.307843 | + | 0.951437i | \(0.400393\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.30819e18 | 0.348039 | 0.174020 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174020 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 6.29265e18i | − 0.215546i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.15016e19i | − 1.30347i | −0.758445 | − | 0.651737i | \(-0.774041\pi\) | ||||
0.758445 | − | 0.651737i | \(-0.225959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.63945e19 | −0.472550 | −0.236275 | − | 0.971686i | \(-0.575927\pi\) | ||||
−0.236275 | + | 0.971686i | \(0.575927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.30440e18 | 0.219858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.49760e19i | − 1.33800i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.41731e18i | − 0.0765203i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.17513e19 | −1.06702 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.13230e19 | 0.215138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.37209e19i | 1.29178i | 0.763429 | + | 0.645892i | \(0.223514\pi\) | ||||
−0.763429 | + | 0.645892i | \(0.776486\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.12286e19i | − 0.181593i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.64935e19 | −0.246369 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.16027e20 | −1.60195 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.24946e18i | − 0.0287278i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.44400e20i | − 1.70699i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.21618e19 | −0.352167 | −0.176083 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176083 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.94433e19 | −0.907813 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.66411e19i | − 0.909792i | −0.890545 | − | 0.454896i | \(-0.849677\pi\) | ||||
0.890545 | − | 0.454896i | \(-0.150323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.07436e16i | 0 0.000268629i | 1.00000 | 0.000134314i | \(4.27536e-5\pi\) | |||||
−1.00000 | 0.000134314i | \(0.999957\pi\) | ||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.10344e19 | 0.170698 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.21535e20 | 1.67077 | 0.835385 | − | 0.549666i | \(-0.185245\pi\) | ||||
0.835385 | + | 0.549666i | \(0.185245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.29539e17i | − 0.00581781i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.92643e19i | − 0.190975i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.51465e18 | 0.0274310 | 0.0137155 | − | 0.999906i | \(-0.495634\pi\) | ||||
0.0137155 | + | 0.999906i | \(0.495634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.81683e19 | −0.102842 | −0.0514209 | − | 0.998677i | \(-0.516375\pi\) | ||||
−0.0514209 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 7.97365e19i | − 0.420731i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.60021e19i | 0.472464i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.93298e19 | 0.226561 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.42592e18 | −0.0104035 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.26192e20i | 1.30691i | 0.756964 | + | 0.653456i | \(0.226682\pi\) | ||||
−0.756964 | + | 0.653456i | \(0.773318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.97450e20i | 1.11401i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.06262e19 | 0.317441 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.22717e20 | −0.402228 | −0.201114 | − | 0.979568i | \(-0.564456\pi\) | ||||
−0.201114 | + | 0.979568i | \(0.564456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.41734e20i | − 0.741804i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.93699e20i | 1.13167i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.35733e18 | −0.00904420 | −0.00452210 | − | 0.999990i | \(-0.501439\pi\) | ||||
−0.00452210 | + | 0.999990i | \(0.501439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00552e20 | 0.759153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.20668e19i | 0.147066i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.42496e20i | 0.539275i | 0.962962 | + | 0.269637i | \(0.0869038\pi\) | ||||
−0.962962 | + | 0.269637i | \(0.913096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.38962e20 | 0.498988 | 0.249494 | − | 0.968376i | \(-0.419736\pi\) | ||||
0.249494 | + | 0.968376i | \(0.419736\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.16386e19 | 0.179761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.14091e20i | 0.947791i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.05700e20i | − 0.876628i | −0.898822 | − | 0.438314i | \(-0.855576\pi\) | ||||
0.898822 | − | 0.438314i | \(-0.144424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.30901e20 | 1.35492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.23986e20 | −0.343730 | −0.171865 | − | 0.985120i | \(-0.554979\pi\) | ||||
−0.171865 | + | 0.985120i | \(0.554979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.21843e20i | 0.753971i | 0.926219 | + | 0.376986i | \(0.123039\pi\) | ||||
−0.926219 | + | 0.376986i | \(0.876961\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.09597e19i | 0.0421323i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.97656e19 | 0.0638165 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.25239e21 | 1.51394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2.09945e20i | − 0.239340i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4.94662e20i | − 0.532027i | −0.963969 | − | 0.266014i | \(-0.914293\pi\) | ||||
0.963969 | − | 0.266014i | \(-0.0857066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.46506e21 | −2.50230 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.04467e20 | −0.291817 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.29587e21i | 1.17316i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.40191e20i | − 0.205467i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.11799e20 | −0.0904012 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.08219e21 | −0.827473 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.86234e21i | − 1.34705i | −0.739166 | − | 0.673523i | \(-0.764780\pi\) | ||||
0.739166 | − | 0.673523i | \(-0.235220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 5.05965e19i | − 0.0346317i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.47522e20 | 0.419557 | 0.209779 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209779 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.62295e21 | −0.995817 | −0.497909 | − | 0.867230i | \(-0.665898\pi\) | ||||
−0.497909 | + | 0.867230i | \(0.665898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.70751e21i | − 1.57373i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.11436e21i | − 1.16460i | −0.812976 | − | 0.582298i | \(-0.802154\pi\) | ||||
0.812976 | − | 0.582298i | \(-0.197846\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.26286e21 | 1.18151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.45565e20 | 0.220606 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.10443e20i | 0.333663i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.23969e21i | 0.998113i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.17664e20 | −0.0920726 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.20804e19 | 0.00485195 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.36509e21i | − 1.66516i | −0.553908 | − | 0.832578i | \(-0.686864\pi\) | ||||
0.553908 | − | 0.832578i | \(-0.313136\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.73112e21i | 0.627411i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.14386e21 | −2.11622 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.59518e21 | −0.849792 | −0.424896 | − | 0.905242i | \(-0.639689\pi\) | ||||
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.21082e20i | 0.193398i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.77575e21i | − 1.41459i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.70973e21 | 0.763706 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.13296e20 | −0.218166 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.40818e20i | 0.189195i | 0.995516 | + | 0.0945977i | \(0.0301565\pi\) | ||||
−0.995516 | + | 0.0945977i | \(0.969844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.81507e20i | 0.0441446i | 0.999756 | + | 0.0220723i | \(0.00702640\pi\) | ||||
−0.999756 | + | 0.0220723i | \(0.992974\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.32644e21 | −0.307310 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.26526e21 | 0.720830 | 0.360415 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360415 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.30728e21i | 1.74791i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.31977e21i | 0.264739i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.19419e21 | −0.419732 | −0.209866 | − | 0.977730i | \(-0.567303\pi\) | ||||
−0.209866 | + | 0.977730i | \(0.567303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.23769e21 | 0.955715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.73950e19i | 0.00651040i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.66422e21i | 0.276516i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.08265e22 | 1.71723 | 0.858615 | − | 0.512621i | \(-0.171325\pi\) | ||||
0.858615 | + | 0.512621i | \(0.171325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.56386e20 | −0.0539755 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.37687e21i | 0.633120i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.20618e20i | − 0.0719439i | −0.999353 | − | 0.0359719i | \(-0.988547\pi\) | ||||
0.999353 | − | 0.0359719i | \(-0.0114527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.10535e20 | 0.0145960 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.85837e21 | 1.24424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.99720e21i | − 0.361645i | −0.983516 | − | 0.180823i | \(-0.942124\pi\) | ||||
0.983516 | − | 0.180823i | \(-0.0578760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4.20209e20i | − 0.0484845i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.22679e22 | 1.35388 | 0.676939 | − | 0.736039i | \(-0.263306\pi\) | ||||
0.676939 | + | 0.736039i | \(0.263306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55619e22 | −1.64304 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.72008e21i | 0.173782i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.60002e21i | 0.154722i | 0.997003 | + | 0.0773612i | \(0.0246495\pi\) | ||||
−0.997003 | + | 0.0773612i | \(0.975351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.86630e22 | −1.72774 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.65283e21 | −0.235165 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.16506e22i | 1.83821i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.44521e22i | 1.98883i | 0.105546 | + | 0.994414i | \(0.466341\pi\) | ||||
−0.105546 | + | 0.994414i | \(0.533659\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.50859e20 | −0.0351375 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.46119e22 | 1.83830 | 0.919152 | − | 0.393903i | \(-0.128875\pi\) | ||||
0.919152 | + | 0.393903i | \(0.128875\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.08061e22i | − 1.48969i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.89687e22i | 1.30218i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.94995e21 | 0.655041 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.67464e21 | −0.358336 | −0.179168 | − | 0.983819i | \(-0.557341\pi\) | ||||
−0.179168 | + | 0.983819i | \(0.557341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.44938e20i | 0.0330135i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.58981e22i | − 2.08687i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.79477e21 | 0.100138 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.04564e21 | −0.0560047 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.70146e22i | − 1.38925i | −0.719374 | − | 0.694623i | \(-0.755571\pi\) | ||||
0.719374 | − | 0.694623i | \(-0.244429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.26169e22i | − 0.623094i | −0.950231 | − | 0.311547i | \(-0.899153\pi\) | ||||
0.950231 | − | 0.311547i | \(-0.100847\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.65113e19 | −0.00410374 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.22558e22 | −1.46995 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.57597e22i | − 0.690097i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.77192e21i | 0.158736i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.26128e21 | −0.172378 | −0.0861892 | − | 0.996279i | \(-0.527469\pi\) | ||||
−0.0861892 | + | 0.996279i | \(0.527469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.62172e21 | −0.0630707 | −0.0315353 | − | 0.999503i | \(-0.510040\pi\) | ||||
−0.0315353 | + | 0.999503i | \(0.510040\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.18718e21i | 0.231384i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.37565e21i | − 0.229315i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.56475e22 | −0.541375 | −0.270687 | − | 0.962667i | \(-0.587251\pi\) | ||||
−0.270687 | + | 0.962667i | \(0.587251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00119e22 | 0.333264 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.08815e22i | 0.989161i | 0.869132 | + | 0.494581i | \(0.164678\pi\) | ||||
−0.869132 | + | 0.494581i | \(0.835322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4.59190e22i | − 1.41557i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.54220e21 | 0.134788 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.44678e22 | −0.413340 | −0.206670 | − | 0.978411i | \(-0.566263\pi\) | ||||
−0.206670 | + | 0.978411i | \(0.566263\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.04839e21i | 0.0563524i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7.26542e21i | − 0.192498i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.77971e22 | −1.73027 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.09366e22 | −0.268903 | −0.134452 | − | 0.990920i | \(-0.542927\pi\) | ||||
−0.134452 | + | 0.990920i | \(0.542927\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.91033e22i | − 0.452585i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.78938e22i | 0.865187i | 0.901589 | + | 0.432594i | \(0.142402\pi\) | ||||
−0.901589 | + | 0.432594i | \(0.857598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.34510e21 | −0.117630 | −0.0588149 | − | 0.998269i | \(-0.518732\pi\) | ||||
−0.0588149 | + | 0.998269i | \(0.518732\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.30580e22 | 0.277030 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.81699e21i | − 0.0576224i | −0.999585 | − | 0.0288112i | \(-0.990828\pi\) | ||||
0.999585 | − | 0.0288112i | \(-0.00917216\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.94718e22i | − 1.76489i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.74655e21 | −0.109328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.88647e21 | 0.181435 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.10192e22i | − 0.195099i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.13441e22i | − 0.535487i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.05318e22 | 1.49262 | 0.746310 | − | 0.665598i | \(-0.231823\pi\) | ||||
0.746310 | + | 0.665598i | \(0.231823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.33480e22 | 0.689820 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.18439e22i | − 0.181946i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.55324e23i | 2.30374i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.07462e22 | 0.440347 | 0.220173 | − | 0.975461i | \(-0.429338\pi\) | ||||
0.220173 | + | 0.975461i | \(0.429338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.48259e21 | 0.0481700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.94168e22i | − 0.259409i | −0.991553 | − | 0.129704i | \(-0.958597\pi\) | ||||
0.991553 | − | 0.129704i | \(-0.0414028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.41979e23i | 1.83243i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.11444e23 | 1.38967 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.20977e23 | −1.45772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.79434e22i | 0.907664i | 0.891087 | + | 0.453832i | \(0.149943\pi\) | ||||
−0.891087 | + | 0.453832i | \(0.850057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.24573e21i | 0.0703012i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.18157e23 | −1.28568 | −0.642838 | − | 0.766002i | \(-0.722243\pi\) | ||||
−0.642838 | + | 0.766002i | \(0.722243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.27122e22 | 0.870148 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.25521e21i | 0.0229413i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.87932e21i | − 0.0283262i | −0.999900 | − | 0.0141631i | \(-0.995492\pi\) | ||||
0.999900 | − | 0.0141631i | \(-0.00450841\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.42357e22 | −0.230610 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.52605e21 | 0.0600694 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.74329e22i | 0.333344i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.97239e20i | 0.00428446i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.39617e22 | 0.116417 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.28391e23 | 1.03613 | 0.518066 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518066 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.89027e22i | − 0.147659i | −0.997271 | − | 0.0738293i | \(-0.976478\pi\) | ||||
0.997271 | − | 0.0738293i | \(-0.0235220\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2.04701e22i | − 0.154798i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.99647e23 | 2.19391 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.64353e22 | 0.187418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.57077e23i | 1.76506i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.92403e21i | 0.0593444i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.29643e23 | −2.12342 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.25539e22 | 0.203152 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.75452e22i | − 0.347940i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.25660e23i | − 1.90804i | −0.299744 | − | 0.954020i | \(-0.596901\pi\) | ||||
0.299744 | − | 0.954020i | \(-0.403099\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.84218e22 | 0.218162 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.61035e23 | 0.886236 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.90295e22i | − 0.261556i | −0.991412 | − | 0.130778i | \(-0.958252\pi\) | ||||
0.991412 | − | 0.130778i | \(-0.0417476\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.12860e23i | 0.583679i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.85029e22 | −0.243209 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.15294e23 | −1.53303 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.72055e22i | 0.128282i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.60011e23i | 1.18911i | 0.804054 | + | 0.594556i | \(0.202672\pi\) | ||||
−0.804054 | + | 0.594556i | \(0.797328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.30714e22 | 0.191068 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.43228e22 | −0.233775 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.80701e23i | − 0.754467i | −0.926118 | − | 0.377233i | \(-0.876875\pi\) | ||||
0.926118 | − | 0.377233i | \(-0.123125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.59496e23i | − 1.86153i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.76237e23 | −1.08599 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.54026e23 | −1.35077 | −0.675384 | − | 0.737467i | \(-0.736022\pi\) | ||||
−0.675384 | + | 0.737467i | \(0.736022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.77850e23i | − 0.658637i | −0.944219 | − | 0.329318i | \(-0.893181\pi\) | ||||
0.944219 | − | 0.329318i | \(-0.106819\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.47006e22i | − 0.0887958i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.89470e23 | 1.01024 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.55869e23 | −1.20586 | −0.602928 | − | 0.797796i | \(-0.705999\pi\) | ||||
−0.602928 | + | 0.797796i | \(0.705999\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.52556e22i | − 0.0501951i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.61369e22i | 0.0835134i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.80156e23 | −0.559069 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.85515e23 | 1.46345 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.22604e23i | − 0.651791i | −0.945406 | − | 0.325896i | \(-0.894334\pi\) | ||||
0.945406 | − | 0.325896i | \(-0.105666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.02365e23i | 0.291187i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.80188e22 | −0.187990 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.01922e23 | 1.61650 | 0.808250 | − | 0.588840i | \(-0.200415\pi\) | ||||
0.808250 | + | 0.588840i | \(0.200415\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 9.76408e23i | − 2.54822i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.68697e22i | 0.0681523i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.83674e23 | −0.699346 | −0.349673 | − | 0.936872i | \(-0.613707\pi\) | ||||
−0.349673 | + | 0.936872i | \(0.613707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.18303e23 | −1.00244 | −0.501220 | − | 0.865320i | \(-0.667115\pi\) | ||||
−0.501220 | + | 0.865320i | \(0.667115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.40734e23i | 1.49273i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.76660e22i | − 0.0626651i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.31638e23 | 0.510159 | 0.255080 | − | 0.966920i | \(-0.417898\pi\) | ||||
0.255080 | + | 0.966920i | \(0.417898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.01026e22 | −0.192970 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.16627e21i | 0.00451193i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.79613e23i | − 0.566425i | −0.959057 | − | 0.283213i | \(-0.908600\pi\) | ||||
0.959057 | − | 0.283213i | \(-0.0914002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.60078e21 | −0.0110360 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.73444e23 | −0.332457 | −0.166229 | − | 0.986087i | \(-0.553159\pi\) | ||||
−0.166229 | + | 0.986087i | \(0.553159\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.77105e23i | 1.26266i | 0.775515 | + | 0.631329i | \(0.217490\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.71436e23i | 0.311046i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.68708e23 | 1.18056 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.21418e23 | −1.06759 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.85577e22i | − 0.0310278i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.24294e23i | 1.01592i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.02867e24 | −1.62940 | −0.814698 | − | 0.579885i | \(-0.803097\pi\) | ||||
−0.814698 | + | 0.579885i | \(0.803097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.20824e23 | 0.186304 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.10884e23i | 0.466683i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.50702e23i | − 0.366414i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.66353e23 | 1.23293 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.31083e23 | 1.01315 | 0.506575 | − | 0.862196i | \(-0.330911\pi\) | ||||
0.506575 | + | 0.862196i | \(0.330911\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.31860e23i | 0.717801i | 0.933376 | + | 0.358901i | \(0.116848\pi\) | ||||
−0.933376 | + | 0.358901i | \(0.883152\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.70319e22i | 0.0355319i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.87216e23 | −1.00788 | −0.503939 | − | 0.863740i | \(-0.668116\pi\) | ||||
−0.503939 | + | 0.863740i | \(0.668116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.47759e24 | 1.84279 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.90161e23i | 0.231038i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.77252e22i | − 0.0328180i | −0.999865 | − | 0.0164090i | \(-0.994777\pi\) | ||||
0.999865 | − | 0.0164090i | \(-0.00522338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.96265e24 | 2.26356 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.73559e23 | 0.195048 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.48992e24i | 1.63169i | 0.578273 | + | 0.815843i | \(0.303727\pi\) | ||||
−0.578273 | + | 0.815843i | \(0.696273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.01553e22i | 0.0215118i | 0.999942 | + | 0.0107559i | \(0.00342377\pi\) | ||||
−0.999942 | + | 0.0107559i | \(0.996576\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.36663e23 | −0.246187 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.33560e23 | 0.338213 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.27415e24i | − 1.25936i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.27113e22i | 0.0507904i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.48681e23 | 0.609382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.70622e23 | −0.705851 | −0.352926 | − | 0.935651i | \(-0.614813\pi\) | ||||
−0.352926 | + | 0.935651i | \(0.614813\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.96299e23i | 0.264635i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.03721e23i | 0.700006i | 0.936749 | + | 0.350003i | \(0.113819\pi\) | ||||
−0.936749 | + | 0.350003i | \(0.886181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.26195e24 | −1.92128 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.58389e23 | −0.131212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3.12264e23i | − 0.252317i | −0.992010 | − | 0.126158i | \(-0.959735\pi\) | ||||
0.992010 | − | 0.126158i | \(-0.0402647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4.03163e23i | − 0.317768i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.03869e19 | 3.87423e−5 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.84867e23 | −0.588752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.46577e24i | − 1.07276i | −0.843977 | − | 0.536379i | \(-0.819792\pi\) | ||||
0.843977 | − | 0.536379i | \(-0.180208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.62293e24i | 1.15896i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.73595e23 | 0.539067 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.28523e23 | −0.0873982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 3.63083e23i | − 0.240963i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.04249e24i | 1.32299i | 0.749950 | + | 0.661495i | \(0.230078\pi\) | ||||
−0.749950 | + | 0.661495i | \(0.769922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.13271e23 | −0.134838 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.35957e21 | −0.000839060 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.20452e24i | 0.725687i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 2.96920e24i | − 1.74641i | −0.487352 | − | 0.873206i | \(-0.662037\pi\) | ||||
0.487352 | − | 0.873206i | \(-0.337963\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25791e24 | 1.29663 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.68909e24 | −1.50780 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.79058e24i | − 1.52790i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7.39925e21i | − 0.00395617i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.13376e23 | −0.215849 | −0.107924 | − | 0.994159i | \(-0.534420\pi\) | ||||
−0.107924 | + | 0.994159i | \(0.534420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.45128e23 | −0.278003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.97768e22i | 0.0148321i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.20215e24i | − 1.07146i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.92465e24 | −1.39005 | −0.695027 | − | 0.718983i | \(-0.744608\pi\) | ||||
−0.695027 | + | 0.718983i | \(0.744608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.88955e24 | 0.877353 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.20311e23i | 0.281392i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 3.06846e24i | − 1.35999i | −0.733216 | − | 0.679996i | \(-0.761982\pi\) | ||||
0.733216 | − | 0.679996i | \(-0.238018\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.57342e23 | 0.0681400 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.68273e24 | 1.55846 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 3.06955e24i | − 1.26939i | −0.772761 | − | 0.634697i | \(-0.781125\pi\) | ||||
0.772761 | − | 0.634697i | \(-0.218875\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 8.08486e22i | − 0.0326752i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.34334e24 | −1.71561 | −0.857805 | − | 0.513975i | \(-0.828172\pi\) | ||||
−0.857805 | + | 0.513975i | \(0.828172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.36046e24 | −1.29739 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.87174e23i | − 0.0706350i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.80052e24i | − 1.77090i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.59956e23 | −0.274062 | −0.137031 | − | 0.990567i | \(-0.543756\pi\) | ||||
−0.137031 | + | 0.990567i | \(0.543756\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.34610e23 | 0.188486 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.37519e24i | 1.85287i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.36037e24i | 0.795544i | 0.917484 | + | 0.397772i | \(0.130217\pi\) | ||||
−0.917484 | + | 0.397772i | \(0.869783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.87503e23 | 0.160665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.99857e23 | −0.128865 | −0.0644326 | − | 0.997922i | \(-0.520524\pi\) | ||||
−0.0644326 | + | 0.997922i | \(0.520524\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.34511e24i | 0.739104i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.99234e24i | 2.15526i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.43729e24 | 1.94063 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.40521e24 | −1.00408 | −0.502042 | − | 0.864843i | \(-0.667418\pi\) | ||||
−0.502042 | + | 0.864843i | \(0.667418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.01126e23i | 0.0580103i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 9.20037e23i | − 0.259585i | −0.991541 | − | 0.129793i | \(-0.958569\pi\) | ||||
0.991541 | − | 0.129793i | \(-0.0414311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.64763e24 | −1.28282 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.96188e23 | −0.106985 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.39060e22i | − 0.0115999i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 4.97952e24i | − 1.28722i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.30421e24 | 0.329892 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.25148e24 | 1.05232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.43784e24i | − 1.80161i | −0.434220 | − | 0.900807i | \(-0.642976\pi\) | ||||
0.434220 | − | 0.900807i | \(-0.357024\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.50247e21i | 0.00130438i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.69154e24 | 1.55248 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.82605e24 | 0.641737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 4.92587e23i | − 0.109487i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.58511e24i | 1.43274i | 0.697721 | + | 0.716369i | \(0.254197\pi\) | ||||
−0.697721 | + | 0.716369i | \(0.745803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.11985e22 | −0.00664486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.78881e24 | −0.998508 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.97560e23i | − 0.203637i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.76247e24i | 1.75130i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.97437e23 | 0.0777755 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.49816e24 | 1.24517 | 0.622584 | − | 0.782553i | \(-0.286083\pi\) | ||||
0.622584 | + | 0.782553i | \(0.286083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.42750e24i | 1.01841i | 0.860645 | + | 0.509205i | \(0.170060\pi\) | ||||
−0.860645 | + | 0.509205i | \(0.829940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.91645e23i | − 0.0719653i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.57653e24 | −0.463655 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.11910e23 | −0.0373477 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.07045e24i | 1.22049i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.44666e24i | 0.244595i | 0.992493 | + | 0.122298i | \(0.0390263\pi\) | ||||
−0.992493 | + | 0.122298i | \(0.960974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.56998e24 | 0.922476 | 0.461238 | − | 0.887276i | \(-0.347405\pi\) | ||||
0.461238 | + | 0.887276i | \(0.347405\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.42566e23 | 0.136693 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.21332e24i | 0.828548i | 0.910152 | + | 0.414274i | \(0.135964\pi\) | ||||
−0.910152 | + | 0.414274i | \(0.864036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.83347e24i | 0.596869i | 0.954430 | + | 0.298434i | \(0.0964644\pi\) | ||||
−0.954430 | + | 0.298434i | \(0.903536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.28814e23 | −0.126429 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.61058e24 | 0.539628 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.62079e24i | − 0.676677i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.75252e24i | − 0.394971i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.72339e24 | −0.664167 | −0.332083 | − | 0.943250i | \(-0.607752\pi\) | ||||
−0.332083 | + | 0.943250i | \(0.607752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.43599e24 | −0.335667 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.67101e23i | 0.0495737i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.66847e24i | − 0.220819i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.02894e23 | 0.0522616 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.55270e23 | 0.108740 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.60253e24i | − 0.698205i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.83079e24i | − 0.956619i | −0.878191 | − | 0.478309i | \(-0.841250\pi\) | ||||
0.878191 | − | 0.478309i | \(-0.158750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.38872e24 | −0.286057 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.64085e24 | −0.544830 | −0.272415 | − | 0.962180i | \(-0.587822\pi\) | ||||
−0.272415 | + | 0.962180i | \(0.587822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.90901e24i | 0.795195i | 0.917560 | + | 0.397598i | \(0.130156\pi\) | ||||
−0.917560 | + | 0.397598i | \(0.869844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 8.15629e22i | − 0.00920378i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.17194e24 | −0.461579 | −0.230790 | − | 0.973004i | \(-0.574131\pi\) | ||||
−0.230790 | + | 0.973004i | \(0.574131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03293e25 | −1.12056 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.05260e24i | − 0.218344i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.29778e25i | − 1.35373i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.60442e25 | 1.64121 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.61985e25 | 1.62500 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.19090e24i | − 0.117168i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.21294e24i | − 0.213537i | −0.994284 | − | 0.106768i | \(-0.965950\pi\) | ||||
0.994284 | − | 0.106768i | \(-0.0340504\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.10723e23 | −0.0767303 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.30646e24 | −0.121283 | −0.0606415 | − | 0.998160i | \(-0.519315\pi\) | ||||
−0.0606415 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.46757e24i | − 0.224700i | −0.993669 | − | 0.112350i | \(-0.964162\pi\) | ||||
0.993669 | − | 0.112350i | \(-0.0358378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.04008e24i | 0.360888i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.19751e24 | −0.192567 | −0.0962833 | − | 0.995354i | \(-0.530695\pi\) | ||||
−0.0962833 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.52734e24 | −0.389205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.13701e25i | − 0.958971i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.06580e22i | 0 0.000881939i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.40844e25 | −1.95542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.12386e24 | 0.169196 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.04573e25i | 1.59916i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.13036e25i | − 0.867073i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.93660e23 | −0.0296330 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.84256e25 | −2.09989 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.67764e25i | − 1.94129i | −0.240512 | − | 0.970646i | \(-0.577315\pi\) | ||||
0.240512 | − | 0.970646i | \(-0.422685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 8.62592e24i | − 0.613780i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.35546e25 | −1.64501 | −0.822506 | − | 0.568757i | \(-0.807424\pi\) | ||||
−0.822506 | + | 0.568757i | \(0.807424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.07581e24 | −0.0737456 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.77364e24i | 0.119340i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.85816e25i | 1.88776i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.71735e24 | 0.370692 | 0.185346 | − | 0.982673i | \(-0.440659\pi\) | ||||
0.185346 | + | 0.982673i | \(0.440659\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.05227e24 | −0.194274 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.16938e25i | − 1.35557i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.68302e24i | − 0.594027i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.90382e24 | 0.235132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.14170e25 | 1.26656 | 0.633278 | − | 0.773925i | \(-0.281709\pi\) | ||||
0.633278 | + | 0.773925i | \(0.281709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.23345e24i | 0.0716222i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.06125e24i | − 0.0605096i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.01898e25 | 2.25018 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.03504e25 | 0.569076 | 0.284538 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284538 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.65993e24i | 0.143619i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.49549e25i | 0.792997i | 0.918035 | + | 0.396498i | \(0.129775\pi\) | ||||
−0.918035 | + | 0.396498i | \(0.870225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15339e24 | 0.0600657 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.96918e24 | −0.458757 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.05139e25i | − 1.03056i | −0.857021 | − | 0.515281i | \(-0.827688\pi\) | ||||
0.857021 | − | 0.515281i | \(-0.172312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.34597e24i | − 0.214449i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.46531e24 | −0.167961 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.91249e25 | −0.910563 | −0.455281 | − | 0.890348i | \(-0.650461\pi\) | ||||
−0.455281 | + | 0.890348i | \(0.650461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.82743e25i | 0.854695i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 3.70870e24i | − 0.170400i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.87117e24 | 0.265013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.06250e25 | 0.914627 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.43779e25i | 1.49781i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.12866e25i | 0.483148i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.63419e24 | 0.363159 | 0.181579 | − | 0.983376i | \(-0.441879\pi\) | ||||
0.181579 | + | 0.983376i | \(0.441879\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.16438e24 | 0.0481217 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.31893e24i | 0.297224i | 0.988896 | + | 0.148612i | \(0.0474806\pi\) | ||||
−0.988896 | + | 0.148612i | \(0.952519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.12657e25i | 0.449572i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.67073e24 | 0.143950 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.91796e25 | −0.739154 | −0.369577 | − | 0.929200i | \(-0.620497\pi\) | ||||
−0.369577 | + | 0.929200i | \(0.620497\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.75246e25i | 1.04248i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.67940e25i | − 0.625128i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.21150e24 | −0.336996 | −0.168498 | − | 0.985702i | \(-0.553892\pi\) | ||||
−0.168498 | + | 0.985702i | \(0.553892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.03225e25 | 1.80948 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.97991e22i | 0 0.000699760i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 5.56678e24i | − 0.193391i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.52241e25 | −1.88583 | −0.942915 | − | 0.333034i | \(-0.891927\pi\) | ||||
−0.942915 | + | 0.333034i | \(0.891927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.15413e24 | −0.240153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.98790e25i | − 0.655993i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.29322e25i | 1.06835i | 0.845375 | + | 0.534174i | \(0.179377\pi\) | ||||
−0.845375 | + | 0.534174i | \(0.820623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.73470e24 | 0.182896 |
(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 | 32.18.b.a.17.8 | 16 | ||
4.3 | odd | 2 | 8.18.b.a.5.11 | ✓ | 16 | ||
8.3 | odd | 2 | 8.18.b.a.5.12 | yes | 16 | ||
8.5 | even | 2 | inner | 32.18.b.a.17.9 | 16 | ||
12.11 | even | 2 | 72.18.d.b.37.6 | 16 | |||
24.11 | even | 2 | 72.18.d.b.37.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.11 | ✓ | 16 | 4.3 | odd | 2 | ||
8.18.b.a.5.12 | yes | 16 | 8.3 | odd | 2 | ||
32.18.b.a.17.8 | 16 | 1.1 | even | 1 | trivial | ||
32.18.b.a.17.9 | 16 | 8.5 | even | 2 | inner | ||
72.18.d.b.37.5 | 16 | 24.11 | even | 2 | |||
72.18.d.b.37.6 | 16 | 12.11 | even | 2 |