Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.12 | ||
Root | \(-6.14819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.b.383.11 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.67629 | + | 15.4981i | −0.107534 | + | 0.994201i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.76651i | 0.121043i | 0.998167 | + | 0.0605215i | \(0.0192764\pi\) | ||||
−0.998167 | + | 0.0605215i | \(0.980724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 132.568i | 1.02257i | 0.859412 | + | 0.511284i | \(0.170830\pi\) | ||||
−0.859412 | + | 0.511284i | \(0.829170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −237.380 | − | 51.9584i | −0.976873 | − | 0.213820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 687.674 | 1.71357 | 0.856783 | − | 0.515677i | \(-0.172459\pi\) | ||||
0.856783 | + | 0.515677i | \(0.172459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 609.929 | 1.00097 | 0.500485 | − | 0.865745i | \(-0.333155\pi\) | ||||
0.500485 | + | 0.865745i | \(0.333155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −104.868 | − | 11.3426i | −0.120341 | − | 0.0130162i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 550.567i | − | 0.462049i | −0.972948 | − | 0.231024i | \(-0.925792\pi\) | ||
0.972948 | − | 0.231024i | \(-0.0742077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 232.742i | 0.147908i | 0.997262 | + | 0.0739538i | \(0.0235617\pi\) | ||||
−0.997262 | + | 0.0739538i | \(0.976438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2054.54 | − | 222.221i | −1.01664 | − | 0.109961i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4487.15 | 1.76869 | 0.884343 | − | 0.466838i | \(-0.154607\pi\) | ||||
0.884343 | + | 0.466838i | \(0.154607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3079.21 | 0.985349 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1203.17 | − | 3591.84i | 0.317627 | − | 0.948216i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2046.54i | − | 0.451882i | −0.974141 | − | 0.225941i | \(-0.927454\pi\) | ||
0.974141 | − | 0.225941i | \(-0.0725457\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6671.05i | − | 1.24678i | −0.781911 | − | 0.623391i | \(-0.785755\pi\) | ||
0.781911 | − | 0.623391i | \(-0.214245\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1152.74 | + | 10657.6i | −0.184266 | + | 1.70363i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −897.020 | −0.123775 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2608.75 | 0.313277 | 0.156639 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156639 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1022.42 | + | 9452.73i | −0.107638 | + | 0.995166i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12755.2i | 1.18502i | 0.805563 | + | 0.592511i | \(0.201863\pi\) | ||||
−0.805563 | + | 0.592511i | \(0.798137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9781.38i | 0.806732i | 0.915039 | + | 0.403366i | \(0.132160\pi\) | ||||
−0.915039 | + | 0.403366i | \(0.867840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 351.577 | − | 1606.23i | 0.0258815 | − | 0.118244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16955.6 | 1.11961 | 0.559807 | − | 0.828623i | \(-0.310875\pi\) | ||||
0.559807 | + | 0.828623i | \(0.310875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −767.166 | −0.0456456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8532.72 | + | 922.907i | 0.459370 | + | 0.0496858i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 22440.7i | − | 1.09735i | −0.836034 | − | 0.548677i | \(-0.815132\pi\) | ||
0.836034 | − | 0.548677i | \(-0.184868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4653.15i | 0.207415i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3607.05 | − | 390.142i | −0.147050 | − | 0.0159051i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16109.1 | −0.602477 | −0.301239 | − | 0.953549i | \(-0.597400\pi\) | ||||
−0.301239 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8678.41 | −0.298618 | −0.149309 | − | 0.988791i | \(-0.547705\pi\) | ||||
−0.149309 | + | 0.988791i | \(0.547705\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6888.00 | − | 31468.9i | 0.218646 | − | 0.998919i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4127.09i | 0.121160i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 53373.9i | − | 1.45259i | −0.687385 | − | 0.726293i | \(-0.741241\pi\) | ||
0.687385 | − | 0.726293i | \(-0.258759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7521.74 | + | 69542.1i | −0.190193 | + | 1.75843i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45069.3 | 1.06105 | 0.530524 | − | 0.847670i | \(-0.321995\pi\) | ||||
0.530524 | + | 0.847670i | \(0.321995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7818.42 | 0.171716 | 0.0858582 | − | 0.996307i | \(-0.472637\pi\) | ||||
0.0858582 | + | 0.996307i | \(0.472637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5161.64 | + | 47721.9i | −0.105958 | + | 0.979635i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 91163.3i | 1.75224i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6497.77i | 0.117138i | 0.998283 | + | 0.0585688i | \(0.0186537\pi\) | ||||
−0.998283 | + | 0.0585688i | \(0.981346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 53649.7 | + | 24667.8i | 0.908562 | + | 0.417751i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101487. | −1.61701 | −0.808506 | − | 0.588488i | \(-0.799723\pi\) | ||||
−0.808506 | + | 0.588488i | \(0.799723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3725.42 | 0.0559278 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 31717.4 | + | 3430.59i | 0.449262 | + | 0.0485926i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 59204.9i | 0.792288i | 0.918188 | + | 0.396144i | \(0.129652\pi\) | ||||
−0.918188 | + | 0.396144i | \(0.870348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 80856.9i | 1.02356i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 103388. | + | 11182.6i | 1.23955 | + | 0.134071i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1574.85 | −0.0179032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −146508. | −1.58100 | −0.790500 | − | 0.612462i | \(-0.790179\pi\) | ||||
−0.790500 | + | 0.612462i | \(0.790179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −163240. | − | 35730.4i | −1.67394 | − | 0.366396i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 168923.i | 1.64773i | 0.566789 | + | 0.823863i | \(0.308186\pi\) | ||||
−0.566789 | + | 0.823863i | \(0.691814\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 65641.0i | 0.609652i | 0.952408 | + | 0.304826i | \(0.0985983\pi\) | ||||
−0.952408 | + | 0.304826i | \(0.901402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1503.66 | − | 13902.1i | 0.0133100 | − | 0.123057i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −115602. | −0.976128 | −0.488064 | − | 0.872808i | \(-0.662297\pi\) | ||||
−0.488064 | + | 0.872808i | \(0.662297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 45690.7 | 0.368351 | 0.184175 | − | 0.982893i | \(-0.441039\pi\) | ||||
0.184175 | + | 0.982893i | \(0.441039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4373.02 | + | 40430.6i | −0.0336879 | + | 0.311461i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 141844.i | 1.04500i | 0.852641 | + | 0.522498i | \(0.175000\pi\) | ||||
−0.852641 | + | 0.522498i | \(0.825000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30362.3i | 0.214087i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −144785. | − | 31690.9i | −0.977821 | − | 0.214028i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 72987.3 | 0.472476 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 311845. | 1.93631 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −197680. | − | 21381.3i | −1.17815 | − | 0.127430i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41980.9i | 0.240312i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 228668.i | − | 1.25804i | −0.777387 | − | 0.629022i | \(-0.783455\pi\) | ||
0.777387 | − | 0.629022i | \(-0.216545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −151593. | − | 16396.4i | −0.802054 | − | 0.0867509i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 94798.2 | 0.482638 | 0.241319 | − | 0.970446i | \(-0.422420\pi\) | ||||
0.241319 | + | 0.970446i | \(0.422420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30854.0 | −0.151246 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24304.2 | + | 8141.27i | 0.114775 | + | 0.0384466i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 229049.i | 1.04262i | 0.853367 | + | 0.521311i | \(0.174557\pi\) | ||||
−0.853367 | + | 0.521311i | \(0.825443\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 156067.i | − | 0.685133i | −0.939494 | − | 0.342566i | \(-0.888704\pi\) | ||
0.939494 | − | 0.342566i | \(-0.111296\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28422.4 | + | 262779.i | −0.120396 | + | 1.11312i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 419433. | 1.71523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13847.9 | 0.0546972 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1285.99 | − | 11889.6i | 0.00490845 | − | 0.0453810i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 299333.i | 1.10456i | 0.833659 | + | 0.552279i | \(0.186242\pi\) | ||||
−0.833659 | + | 0.552279i | \(0.813758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 70935.1i | − | 0.253174i | −0.991956 | − | 0.126587i | \(-0.959598\pi\) | ||
0.991956 | − | 0.126587i | \(-0.0404023\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28606.6 | + | 130694.i | −0.0987955 | + | 0.451363i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 45139.7 | 0.150914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 387310. | 1.25403 | 0.627017 | − | 0.779006i | \(-0.284276\pi\) | ||||
0.627017 | + | 0.779006i | \(0.284276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 347788. | + | 37617.0i | 1.09099 | + | 0.118003i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 594850.i | 1.80860i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 520550.i | 1.53459i | 0.641291 | + | 0.767297i | \(0.278399\pi\) | ||||
−0.641291 | + | 0.767297i | \(0.721601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −72114.9 | − | 7800.01i | −0.206212 | − | 0.0223041i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 474775. | 1.31734 | 0.658668 | − | 0.752434i | \(-0.271120\pi\) | ||||
0.658668 | + | 0.752434i | \(0.271120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 720.801 | 0.00194133 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12092.9 | − | 55248.3i | 0.0316257 | − | 0.144487i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 428218.i | − | 1.08780i | −0.839149 | − | 0.543901i | \(-0.816947\pi\) | ||
0.839149 | − | 0.543901i | \(-0.183053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 408204.i | 1.00759i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27003.4 | − | 249660.i | 0.0647867 | − | 0.598984i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −68071.9 | −0.158794 | −0.0793972 | − | 0.996843i | \(-0.525300\pi\) | ||||
−0.0793972 | + | 0.996843i | \(0.525300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −607181. | −1.37760 | −0.688798 | − | 0.724953i | \(-0.741861\pi\) | ||||
−0.688798 | + | 0.724953i | \(0.741861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14547.5 | − | 134499.i | 0.0321115 | − | 0.296886i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17652.2i | 0.0379200i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 378611.i | − | 0.791751i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 476161. | + | 159502.i | 0.969615 | + | 0.324796i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −188197. | −0.373275 | −0.186637 | − | 0.982429i | \(-0.559759\pi\) | ||||
−0.186637 | + | 0.982429i | \(0.559759\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −597386. | −1.15441 | −0.577207 | − | 0.816598i | \(-0.695857\pi\) | ||||
−0.577207 | + | 0.816598i | \(0.695857\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −63961.9 | − | 6918.18i | −0.120458 | − | 0.0130288i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 983345.i | − | 1.80526i | −0.430416 | − | 0.902631i | \(-0.641633\pi\) | ||
0.430416 | − | 0.902631i | \(-0.358367\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 698819.i | − | 1.25093i | −0.780254 | − | 0.625463i | \(-0.784910\pi\) | ||
0.780254 | − | 0.625463i | \(-0.215090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 827193. | + | 89469.9i | 1.44416 | + | 0.156202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 271305. | 0.462080 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −86307.9 | −0.143439 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.06516e6 | − | 233145.i | −1.72778 | − | 0.378181i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160051.i | 0.253450i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 558698.i | − | 0.863915i | −0.901894 | − | 0.431957i | \(-0.857823\pi\) | ||
0.901894 | − | 0.431957i | \(-0.142177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −75549.0 | + | 698487.i | −0.114098 | + | 1.05489i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −66185.8 | −0.0976492 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 884366. | 1.27492 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13105.9 | + | 121170.i | −0.0184653 | + | 0.170721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 335807.i | − | 0.462497i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.31975e6i | 1.77717i | 0.458710 | + | 0.888586i | \(0.348312\pi\) | ||||
−0.458710 | + | 0.888586i | \(0.651688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −730944. | − | 159991.i | −0.962560 | − | 0.210688i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 473989. | 0.610526 | 0.305263 | − | 0.952268i | \(-0.401256\pi\) | ||||
0.305263 | + | 0.952268i | \(0.401256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −891437. | −1.12332 | −0.561658 | − | 0.827369i | \(-0.689836\pi\) | ||||
−0.561658 | + | 0.827369i | \(0.689836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41285e6 | − | 152816.i | −1.74208 | − | 0.188425i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 726371.i | − | 0.876534i | −0.898845 | − | 0.438267i | \(-0.855592\pi\) | ||
0.898845 | − | 0.438267i | \(-0.144408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 114730.i | 0.135521i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −100703. | − | 10892.1i | −0.116458 | − | 0.0125962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 870021. | 0.985224 | 0.492612 | − | 0.870249i | \(-0.336042\pi\) | ||||
0.492612 | + | 0.870249i | \(0.336042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.14608e6 | −1.27108 | −0.635538 | − | 0.772070i | \(-0.719221\pi\) | ||||
−0.635538 | + | 0.772070i | \(0.719221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −472235. | + | 790116.i | −0.513030 | + | 0.858371i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 5191.04i | − | 0.00552508i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 141956.i | 0.148051i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 170120. | − | 1.57284e6i | 0.173883 | − | 1.60763i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 138933. | 0.139194 | 0.0695969 | − | 0.997575i | \(-0.477829\pi\) | ||||
0.0695969 | + | 0.997575i | \(0.477829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.08569e6 | 3.03076 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6244.86 | + | 57736.7i | −0.00601412 | + | 0.0556035i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.75878e6i | − | 1.66103i | −0.556994 | − | 0.830517i | \(-0.688045\pi\) | ||
0.556994 | − | 0.830517i | \(-0.311955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 345836.i | 0.320347i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −106335. | + | 485808.i | −0.0966217 | + | 0.441432i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −636768. | −0.567665 | −0.283832 | − | 0.958874i | \(-0.591606\pi\) | ||||
−0.283832 | + | 0.958874i | \(0.591606\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 151845. | 0.132827 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −917562. | − | 99244.4i | −0.787694 | − | 0.0851977i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 330293.i | − | 0.278304i | −0.990271 | − | 0.139152i | \(-0.955562\pi\) | ||
0.990271 | − | 0.139152i | \(-0.0444376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.31762e6i | − | 1.08985i | −0.838485 | − | 0.544925i | \(-0.816558\pi\) | ||
0.838485 | − | 0.544925i | \(-0.183442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.25313e6 | − | 135539.i | −1.01763 | − | 0.110067i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.11750e6 | 1.68846 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.99956e6 | −1.56579 | −0.782897 | − | 0.622152i | \(-0.786259\pi\) | ||||
−0.782897 | + | 0.622152i | \(0.786259\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −346617. | + | 1.58358e6i | −0.266587 | + | 1.21795i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 755636.i | 0.570882i | 0.958396 | + | 0.285441i | \(0.0921401\pi\) | ||||
−0.958396 | + | 0.285441i | \(0.907860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 500952.i | 0.371817i | 0.982567 | + | 0.185909i | \(0.0595229\pi\) | ||||
−0.982567 | + | 0.185909i | \(0.940477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2639.90 | − | 24407.1i | 0.00192520 | − | 0.0177994i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.69092e6 | −1.21177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.11673e6 | 0.786511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 245589. | − | 2.27059e6i | 0.170011 | − | 1.57183i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.43780e6i | − | 0.978431i | −0.872163 | − | 0.489215i | \(-0.837283\pi\) | ||
0.872163 | − | 0.489215i | \(-0.162717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 109002.i | − | 0.0729257i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 827390. | − | 2.47001e6i | 0.544276 | − | 1.62483i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.73684e6 | 1.77040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29669e6 | −0.824938 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.61798e6 | − | 283163.i | −1.63817 | − | 0.177186i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 58722.6i | − | 0.0361456i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 730785.i | 0.442531i | 0.975214 | + | 0.221266i | \(0.0710188\pi\) | ||||
−0.975214 | + | 0.221266i | \(0.928981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.01731e6 | − | 110033.i | −0.606117 | − | 0.0655582i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −648099. | −0.379962 | −0.189981 | − | 0.981788i | \(-0.560843\pi\) | ||||
−0.189981 | + | 0.981788i | \(0.560843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 131249. | 0.0757243 | 0.0378622 | − | 0.999283i | \(-0.487945\pi\) | ||||
0.0378622 | + | 0.999283i | \(0.487945\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 212935. | + | 46607.7i | 0.120912 | + | 0.0264656i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.23573e6i | − | 1.80852i | −0.426978 | − | 0.904262i | \(-0.640422\pi\) | ||
0.426978 | − | 0.904262i | \(-0.359578\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.40735e6i | − | 0.774330i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 193782. | − | 1.79161e6i | 0.104967 | − | 0.970468i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 128140. | 0.0683406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.87810e6 | 0.986305 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −76590.6 | + | 708117.i | −0.0396101 | + | 0.366215i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.24776e6i | 1.14488i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.75600e6i | − | 0.880956i | −0.897763 | − | 0.440478i | \(-0.854809\pi\) | ||
0.897763 | − | 0.440478i | \(-0.145191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −619266. | − | 135547.i | −0.306032 | − | 0.0669851i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 361155. | 0.175825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.56913e6 | −1.23229 | −0.616143 | − | 0.787634i | \(-0.711306\pi\) | ||||
−0.616143 | + | 0.787634i | \(0.711306\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.19830e6 | − | 237771.i | −1.03894 | − | 0.112372i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.58751e6i | − | 2.13644i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.12636e6i | 0.975892i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −470557. | − | 50895.9i | −0.212846 | − | 0.0230216i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.29984e6 | 1.47119 | 0.735596 | − | 0.677420i | \(-0.236902\pi\) | ||||
0.735596 | + | 0.677420i | \(0.236902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40218e6 | 0.616227 | 0.308113 | − | 0.951350i | \(-0.400302\pi\) | ||||
0.308113 | + | 0.951350i | \(0.400302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 733849. | − | 2.19077e6i | 0.317936 | − | 0.949136i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.52203e6i | 1.93151i | 0.259456 | + | 0.965755i | \(0.416457\pi\) | ||||
−0.259456 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 304962.i | 0.128432i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −122348. | + | 1.13116e6i | −0.0508072 | + | 0.469737i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.40082e6 | 1.39267 | 0.696335 | − | 0.717717i | \(-0.254813\pi\) | ||||
0.696335 | + | 0.717717i | \(0.254813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.42193e6 | 0.978123 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −522741. | + | 4.83299e6i | −0.208219 | + | 1.92508i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52903.4i | 0.0207851i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.90470e6i | 1.12573i | 0.826547 | + | 0.562867i | \(0.190302\pi\) | ||||
−0.826547 | + | 0.562867i | \(0.809698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 662737. | − | 3.02782e6i | 0.253382 | − | 1.15762i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.97491e6 | 1.12212 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58294e6 | −0.589104 | −0.294552 | − | 0.955635i | \(-0.595170\pi\) | ||||
−0.294552 | + | 0.955635i | \(0.595170\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −650622. | − | 70371.9i | −0.238919 | − | 0.0258417i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.24824e6i | − | 0.452321i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 112527.i | − | 0.0402401i | −0.999798 | − | 0.0201201i | \(-0.993595\pi\) | ||
0.999798 | − | 0.0201201i | \(-0.00640485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.54391e6 | + | 383313.i | 1.25075 | + | 0.135282i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.84859e6 | 0.643937 | 0.321969 | − | 0.946750i | \(-0.395655\pi\) | ||||
0.321969 | + | 0.946750i | \(0.395655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −616857. | −0.212096 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 508225. | − | 2.32191e6i | 0.172496 | − | 0.788074i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.58651e6i | 1.20171i | 0.799360 | + | 0.600853i | \(0.205172\pi\) | ||||
−0.799360 | + | 0.600853i | \(0.794828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.47047e6i | − | 0.817219i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −158909. | + | 1.46919e6i | −0.0518999 | + | 0.479840i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −43967.2 | −0.0141787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.21573e6 | −1.02401 | −0.512004 | − | 0.858983i | \(-0.671097\pi\) | ||||
−0.512004 | + | 0.858983i | \(0.671097\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 51720.2 | − | 478178.i | 0.0162640 | − | 0.150369i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.52639e6i | 0.784583i | 0.919841 | + | 0.392291i | \(0.128318\pi\) | ||||
−0.919841 | + | 0.392291i | \(0.871682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.06887e6i | − | 1.24799i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −166915. | + | 363021.i | −0.0505658 | + | 0.109975i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.79397e6 | 0.536821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.17254e6 | −0.346594 | −0.173297 | − | 0.984870i | \(-0.555442\pi\) | ||||
−0.173297 | + | 0.984870i | \(0.555442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.54982e6 | − | 383952.i | −1.03658 | − | 0.112117i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.13554e6i | − | 0.616074i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 686709.i | − | 0.195728i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.41874e6 | + | 261613.i | 0.681160 | + | 0.0736749i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.27821e6 | 0.355685 | 0.177842 | − | 0.984059i | \(-0.443088\pi\) | ||||
0.177842 | + | 0.984059i | \(0.443088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02494e6 | −0.281834 | −0.140917 | − | 0.990021i | \(-0.545005\pi\) | ||||
−0.140917 | + | 0.990021i | \(0.545005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.02492e6 | − | 880985.i | −1.09372 | − | 0.239396i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.69531e6i | − | 0.455279i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.15048e6i | − | 0.305357i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −703089. | + | 6.50039e6i | −0.184445 | + | 1.70528i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.06484e6 | 1.57263 | 0.786315 | − | 0.617826i | \(-0.211986\pi\) | ||||
0.786315 | + | 0.617826i | \(0.211986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 924491. | 0.236964 | 0.118482 | − | 0.992956i | \(-0.462197\pi\) | ||||
0.118482 | + | 0.992956i | \(0.462197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23213.1 | + | 214616.i | −0.00588179 | + | 0.0543800i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.04435e6i | 0.261602i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.18052e6i | − | 0.540007i | −0.962859 | − | 0.270004i | \(-0.912975\pi\) | ||
0.962859 | − | 0.270004i | \(-0.0870249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 182110. | + | 39860.7i | 0.0445900 | + | 0.00975997i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.19111e6 | −0.530463 | −0.265231 | − | 0.964185i | \(-0.585448\pi\) | ||||
−0.265231 | + | 0.964185i | \(0.585448\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −400611. | −0.0959009 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.63908e6 | − | 501767.i | −1.09815 | − | 0.118777i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.31214e6i | − | 0.541252i | −0.962685 | − | 0.270626i | \(-0.912769\pi\) | ||
0.962685 | − | 0.270626i | \(-0.0872306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.77139e6i | 2.03061i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.09936e6 | + | 118907.i | 0.251706 | + | 0.0272247i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −547119. | −0.123895 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.20376e6 | −0.493599 | −0.246799 | − | 0.969067i | \(-0.579379\pi\) | ||||
−0.246799 | + | 0.969067i | \(0.579379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.97755e6 | − | 662426.i | −0.438122 | − | 0.146759i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.43150e6i | − | 0.313718i | −0.987621 | − | 0.156859i | \(-0.949863\pi\) | ||
0.987621 | − | 0.156859i | \(-0.0501369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.31236e6i | 1.58528i | 0.609692 | + | 0.792639i | \(0.291293\pi\) | ||||
−0.609692 | + | 0.792639i | \(0.708707\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −75667.1 | + | 699579.i | −0.0162284 | + | 0.150039i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.26234e6 | −1.75312 | −0.876559 | − | 0.481295i | \(-0.840167\pi\) | ||||
−0.876559 | + | 0.481295i | \(0.840167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.07565e6 | 1.48537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −649241. | + | 6.00255e6i | −0.134851 | + | 1.24676i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.72640e6i | 1.38239i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 716662.i | 0.145741i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.16598e6 | + | 5.32698e6i | −0.234637 | + | 1.07198i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.73045e6 | 0.344604 | 0.172302 | − | 0.985044i | \(-0.444879\pi\) | ||||
0.172302 | + | 0.985044i | \(0.444879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.59116e6 | 0.313581 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.21903e6 | − | 997139.i | −1.79811 | − | 0.194486i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 991348.i | − | 0.191369i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.85313e6i | − | 1.50045i | −0.661185 | − | 0.750223i | \(-0.729946\pi\) | ||
0.661185 | − | 0.750223i | \(-0.270054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.06752e6 | − | 872591.i | −1.52570 | − | 0.165021i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.99056e6 | −1.30860 | −0.654302 | − | 0.756233i | \(-0.727037\pi\) | ||||
−0.654302 | + | 0.756233i | \(0.727037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.12676e6 | −0.208792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 241770. | − | 1.10457e6i | 0.0443496 | − | 0.202618i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.97473e6i | 1.08499i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.17073e6i | 0.929609i | 0.885413 | + | 0.464805i | \(0.153875\pi\) | ||||
−0.885413 | + | 0.464805i | \(0.846125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −795858. | + | 7.35809e6i | −0.141658 | + | 1.30970i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.39136e6 | 1.30258 | 0.651290 | − | 0.758829i | \(-0.274228\pi\) | ||||
0.651290 | + | 0.758829i | \(0.274228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.14302e6 | −0.199446 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1208.27 | + | 11171.0i | −0.000208758 | + | 0.00193007i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.05541e6i | 1.37814i | 0.724695 | + | 0.689070i | \(0.241981\pi\) | ||||
−0.724695 | + | 0.689070i | \(0.758019\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.03647e6i | 0.175592i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 835971. | + | 280028.i | 0.140248 | + | 0.0469795i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −444160. | −0.0737941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.16599e7 | 1.91853 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.63655e6 | + | 717816.i | 1.08149 | + | 0.116975i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.37512e6i | 1.02895i | 0.857506 | + | 0.514475i | \(0.172013\pi\) | ||||
−0.857506 | + | 0.514475i | \(0.827987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.99175e6i | − | 1.59730i | −0.601794 | − | 0.798651i | \(-0.705547\pi\) | ||
0.601794 | − | 0.798651i | \(-0.294453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.32637e6 | − | 684267.i | −1.00174 | − | 0.108350i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.67286e6 | −0.576074 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.36981e7 | 2.12825 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.82398e6 | + | 837002.i | 0.588544 | + | 0.128822i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.77975e6i | 1.18617i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 782223.i | − | 0.118153i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 114108. | − | 1.05498e6i | 0.0170758 | − | 0.157874i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −527560. | −0.0782169 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.10975e7 | −1.63017 | −0.815087 | − | 0.579339i | \(-0.803311\pi\) | ||||
−0.815087 | + | 0.579339i | \(0.803311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.01781e6 | − | 9.41014e6i | 0.148138 | − | 1.36961i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 309166.i | 0.0445862i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.87837e6i | 1.12582i | 0.826519 | + | 0.562909i | \(0.190318\pi\) | ||||
−0.826519 | + | 0.562909i | \(0.809682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.06008e6 | + | 450916.i | 0.291712 | + | 0.0638506i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 476316. | 0.0668369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −861393. | −0.119781 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −273574. | − | 29590.0i | −0.0377001 | − | 0.00407768i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.96402e6i | 0.404802i | 0.979303 | + | 0.202401i | \(0.0648744\pi\) | ||||
−0.979303 | + | 0.202401i | \(0.935126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.96595e6i | 0.807514i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.86773e6 | + | 634660.i | 0.787160 | + | 0.0851400i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.10467e6 | 0.146879 | 0.0734395 | − | 0.997300i | \(-0.476602\pi\) | ||||
0.0734395 | + | 0.997300i | \(0.476602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −959787. | −0.126489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.27015e6 | + | 7.11221e6i | −0.427179 | + | 0.929066i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 706266.i | 0.0914509i | 0.998954 | + | 0.0457254i | \(0.0145599\pi\) | ||||
−0.998954 | + | 0.0457254i | \(0.985440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.81546e6i | − | 1.13150i | −0.824577 | − | 0.565750i | \(-0.808587\pi\) | ||
0.824577 | − | 0.565750i | \(-0.191413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 315471. | − | 2.91668e6i | 0.0401396 | − | 0.371110i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.38169e7 | 1.74277 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.30662e6 | −0.788601 | −0.394300 | − | 0.918982i | \(-0.629013\pi\) | ||||
−0.394300 | + | 0.918982i | \(0.629013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00139e6 | − | 9.25832e6i | 0.124138 | − | 1.14772i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.34538e7i | − | 1.65350i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.54319e7i | − | 1.88039i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 214437. | − | 979690.i | 0.0259066 | − | 0.118358i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.68327e6 | 0.560988 | 0.280494 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280494 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55263e6 | 0.184409 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.52399e7 | + | 1.64837e6i | 1.79479 | + | 0.194127i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.23289e6i | − | 0.611089i | −0.952178 | − | 0.305545i | \(-0.901161\pi\) | ||
0.952178 | − | 0.305545i | \(-0.0988385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 493869.i | 0.0571899i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.08303e7 | + | 1.17142e6i | 1.24367 | + | 0.134517i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 370351. | 0.0421741 | 0.0210871 | − | 0.999778i | \(-0.493287\pi\) | ||||
0.0210871 | + | 0.999778i | \(0.493287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.55229e7 | −1.75302 | −0.876511 | − | 0.481382i | \(-0.840135\pi\) | ||||
−0.876511 | + | 0.481382i | \(0.840135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.77322e6 | + | 1.26699e7i | −0.310593 | + | 1.41899i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.11010e6i | 0.234377i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.07624e6i | 0.449043i | 0.974469 | + | 0.224522i | \(0.0720820\pi\) | ||||
−0.974469 | + | 0.224522i | \(0.927918\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −454784. | + | 4.20470e6i | −0.0496892 | + | 0.459401i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.03417e7 | 1.12070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.13469e7 | −1.21962 | −0.609811 | − | 0.792547i | \(-0.708755\pi\) | ||||
−0.609811 | + | 0.792547i | \(0.708755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 144677. | − | 1.33761e6i | 0.0154245 | − | 0.142607i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.85036e6i | 0.830188i | 0.909779 | + | 0.415094i | \(0.136251\pi\) | ||||
−0.909779 | + | 0.415094i | \(0.863749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.05257e6i | 0.530012i | 0.964247 | + | 0.265006i | \(0.0853740\pi\) | ||||
−0.964247 | + | 0.265006i | \(0.914626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.39880e6 | − | 1.61171e7i | 0.561783 | − | 1.67710i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.84866e6 | −0.810168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.33848e6 | 0.956260 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.48048e6 | − | 268291.i | −0.251980 | − | 0.0272544i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.43629e6i | − | 0.144749i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.88223e7i | 1.88191i | 0.338530 | + | 0.940956i | \(0.390070\pi\) | ||||
−0.338530 | + | 0.940956i | \(0.609930\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.65874e6 | + | 936537.i | 0.858905 | + | 0.0929000i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.54728e6 | 0.152277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −467917. | −0.0456899 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.06986e7 | − | 2.34173e6i | −1.03651 | − | 0.226874i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.21548e7i | 1.16843i | 0.811597 | + | 0.584217i | \(0.198598\pi\) | ||||
−0.811597 | + | 0.584217i | \(0.801402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.75899e6i | − | 0.644695i | −0.946621 | − | 0.322348i | \(-0.895528\pi\) | ||
0.946621 | − | 0.322348i | \(-0.104472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 110946. | − | 1.02575e6i | 0.0105006 | − | 0.0970830i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.10161e6 | −0.666954 | −0.333477 | − | 0.942758i | \(-0.608222\pi\) | ||||
−0.333477 | + | 0.942758i | \(0.608222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.10778e7 | −1.03239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.48245e6 | + | 1.37060e7i | −0.137097 | + | 1.26753i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.87673e6i | 0.355781i | 0.984050 | + | 0.177891i | \(0.0569273\pi\) | ||||
−0.984050 | + | 0.177891i | \(0.943073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 641453.i | 0.0584200i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.85594e6 | − | 406232.i | −0.167745 | − | 0.0367165i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.63662e6 | 0.326201 | 0.163100 | − | 0.986609i | \(-0.447851\pi\) | ||||
0.163100 | + | 0.986609i | \(0.447851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.07769e6 | 0.719091 | 0.359545 | − | 0.933128i | \(-0.382932\pi\) | ||||
0.359545 | + | 0.933128i | \(0.382932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.20436e6 | + | 562908.i | 0.459815 | + | 0.0497341i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 208774.i | − | 0.0183072i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.18313e6i | − | 0.799238i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.04536e7 | − | 2.21228e6i | −1.76687 | − | 0.191106i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.96792e6 | −0.511702 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.48594e7 | 1.26463 | 0.632317 | − | 0.774710i | \(-0.282104\pi\) | ||||
0.632317 | + | 0.774710i | \(0.282104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.70482e6 | − | 1.10600e7i | 0.312974 | − | 0.934323i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.98129e6i | 0.753125i | 0.926391 | + | 0.376562i | \(0.122894\pi\) | ||||
−0.926391 | + | 0.376562i | \(0.877106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.94222e7i | − | 1.61668i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −794542. | + | 7.34592e6i | −0.0656521 | + | 0.606986i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.64006e6 | 0.216552 | 0.108276 | − | 0.994121i | \(-0.465467\pi\) | ||||
0.108276 | + | 0.994121i | \(0.465467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.54986e6 | −0.126202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.49430e6 | − | 1.38156e7i | 0.120794 | − | 1.11680i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.36872e7i | − | 1.09842i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.95325e6i | 0.314963i | 0.987522 | + | 0.157482i | \(0.0503375\pi\) | ||||
−0.987522 | + | 0.157482i | \(0.949663\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.73670e6 | − | 2.16404e7i | 0.374664 | − | 1.71171i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.05603e6 | 0.0829305 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.02257e6 | 0.547538 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.12573e7 | + | 1.21761e6i | 0.871451 | + | 0.0942570i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.18289e6i | − | 0.475222i | −0.971360 | − | 0.237611i | \(-0.923636\pi\) | ||
0.971360 | − | 0.237611i | \(-0.0763643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 607166.i | 0.0463361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.77809e6 | − | 192320.i | −0.134736 | − | 0.0145731i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.23937e7 | −1.68491 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.01154e7 | 0.755734 | 0.377867 | − | 0.925860i | \(-0.376658\pi\) | ||||
0.377867 | + | 0.925860i | \(0.376658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 337613. | − | 1.54244e6i | 0.0250464 | − | 0.114429i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.99340e7i | − | 2.20516i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.83809e6i | 0.207616i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.45840e6 | + | 1.34836e7i | −0.105945 | + | 0.979511i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.51532e7 | −1.81456 | −0.907279 | − | 0.420530i | \(-0.861844\pi\) | ||||
−0.907279 | + | 0.420530i | \(0.861844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.70187e6 | −0.623411 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.92115e6 | − | 1.77620e7i | 0.136683 | − | 1.26370i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.30174e6i | − | 0.445262i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.70218e7i | 1.19445i | 0.802072 | + | 0.597227i | \(0.203731\pi\) | ||||
−0.802072 | + | 0.597227i | \(0.796269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.14537e7 | − | 8.64319e6i | −0.798226 | − | 0.602359i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.38531e6 | 0.372749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.61715e7 | −1.11171 | −0.555853 | − | 0.831281i | \(-0.687608\pi\) | ||||
−0.555853 | + | 0.831281i | \(0.687608\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 80451.0 | + | 8701.66i | 0.00549305 | + | 0.000594133i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.67039e7i | − | 2.48910i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.81667e6i | 0.257083i | 0.991704 | + | 0.128542i | \(0.0410296\pi\) | ||||
−0.991704 | + | 0.128542i | \(0.958970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.20005e6 | − | 237959.i | −0.147193 | − | 0.0159205i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.59769e7 | −1.06175 | −0.530873 | − | 0.847451i | \(-0.678136\pi\) | ||||
−0.530873 | + | 0.847451i | \(0.678136\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.02544e6 | −0.133699 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.40909e7 | + | 5.27307e6i | 1.57961 | + | 0.345750i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.53251e7i | − | 0.998157i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.48347e6i | 0.160679i | 0.996768 | + | 0.0803395i | \(0.0256005\pi\) | ||||
−0.996768 | + | 0.0803395i | \(0.974400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −232891. | + | 2.15319e6i | −0.0149680 | + | 0.138387i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 479983. | 0.0306449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.17289e6 | 0.137815 | 0.0689077 | − | 0.997623i | \(-0.478049\pi\) | ||||
0.0689077 | + | 0.997623i | \(0.478049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.17250e6 | + | 4.78223e7i | −0.325909 | + | 3.01319i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.95287e7i | − | 1.22240i | −0.791478 | − | 0.611198i | \(-0.790688\pi\) | ||
0.791478 | − | 0.611198i | \(-0.209312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.05710e6i | 0.376664i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −884340. | − | 193567.i | −0.0546343 | − | 0.0119585i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.82540e6 | −0.603062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.16573e6 | −0.0710857 | −0.0355428 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355428 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.72577e7 | + | 2.94822e6i | 1.65140 | + | 0.178617i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.92482e7i | 1.15862i | 0.815107 | + | 0.579311i | \(0.196678\pi\) | ||||
−0.815107 | + | 0.579311i | \(0.803322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.05416e7i | − | 1.22851i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.35979e6 | − | 579720.i | −0.318490 | − | 0.0344481i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.96866e6 | −0.175274 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.09930e7 | 1.81818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.35084e6 | − | 2.46234e6i | −0.428482 | − | 0.143530i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.62073e6i | 0.151792i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.41154e7i | 1.38790i | 0.720024 | + | 0.693949i | \(0.244131\pi\) | ||||
−0.720024 | + | 0.693949i | \(0.755869\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.06741e6 | − | 9.86867e6i | 0.0610431 | − | 0.564373i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.88039e7 | −1.06858 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.29322e6 | −0.298908 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −254536. | + | 2.35331e6i | −0.0142834 | + | 0.132057i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.46187e6i | 0.137284i | 0.997641 | + | 0.0686420i | \(0.0218666\pi\) | ||||
−0.997641 | + | 0.0686420i | \(0.978133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.33519e6i | − | 0.517316i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.07619e6 | − | 1.40541e7i | 0.169407 | − | 0.773965i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.37653e6 | 0.294248 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.02506e6 | −0.218919 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.11891e6 | + | 553666.i | 0.276690 | + | 0.0299270i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.92214e6i | − | 0.533008i | −0.963834 | − | 0.266504i | \(-0.914131\pi\) | ||
0.963834 | − | 0.266504i | \(-0.0858686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.34389e7i | − | 1.25137i | −0.780076 | − | 0.625684i | \(-0.784820\pi\) | ||
0.780076 | − | 0.625684i | \(-0.215180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.04206e7 | + | 2.20871e6i | 1.08353 | + | 0.117196i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.52231e6 | −0.185752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.27654e6 | −0.119322 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.20119e6 | − | 1.91938e7i | 0.218858 | − | 0.999888i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.50269e7i | − | 0.778059i | −0.921225 | − | 0.389029i | \(-0.872810\pi\) | ||
0.921225 | − | 0.389029i | \(-0.127190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.54090e6i | 0.182228i | 0.995840 | + | 0.0911138i | \(0.0290427\pi\) | ||||
−0.995840 | + | 0.0911138i | \(0.970957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.54953e6 | + | 3.28171e7i | −0.181567 | + | 1.67867i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.15599e7 | −1.60462 | −0.802308 | − | 0.596910i | \(-0.796395\pi\) | ||||
−0.802308 | + | 0.596910i | \(0.796395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.34618e7 | −0.680326 | −0.340163 | − | 0.940367i | \(-0.610482\pi\) | ||||
−0.340163 | + | 0.940367i | \(0.610482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.35183e6 | − | 3.09893e7i | 0.168376 | − | 1.55671i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 422376.i | 0.0210905i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.21257e6i | 0.159454i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.39613e7 | − | 8.02642e6i | −1.18222 | − | 0.396012i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.65806e7 | −0.813199 | −0.406599 | − | 0.913607i | \(-0.633285\pi\) | ||||
−0.406599 | + | 0.913607i | \(0.633285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.63228e7 | 0.795802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.17109e7 | − | 1.26666e6i | −0.567572 | − | 0.0613891i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4877.30i | 0.000234984i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.13405e7i | 1.98001i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.76378e6 | − | 839738.i | −0.369661 | − | 0.0399829i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17059e7 | 0.554089 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.35123e7 | −1.10643 | −0.553214 | − | 0.833039i | \(-0.686599\pi\) | ||||
−0.553214 | + | 0.833039i | \(0.686599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 373838. | + | 81826.7i | 0.0174891 | + | 0.00382807i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.12776e7i | − | 0.989627i | −0.868999 | − | 0.494813i | \(-0.835236\pi\) | ||
0.868999 | − | 0.494813i | \(-0.164764\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.20510e6i | − | 0.425643i | −0.977091 | − | 0.212821i | \(-0.931735\pi\) | ||
0.977091 | − | 0.212821i | \(-0.0682653\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.83447e6 | − | 2.62060e7i | 0.130306 | − | 1.20474i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.62622e6 | −0.348564 | −0.174282 | − | 0.984696i | \(-0.555760\pi\) | ||||
−0.174282 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89754e6 | 0.131671 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.87196e6 | + | 1.73072e7i | −0.0845765 | + | 0.781950i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.46835e6i | 0.200723i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.25543e7i | − | 1.45400i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.47781e7 | + | 7.61232e6i | 1.54444 | + | 0.338050i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.56530e6 | −0.245736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.68055e6 | 0.161590 | 0.0807948 | − | 0.996731i | \(-0.474254\pi\) | ||||
0.0807948 | + | 0.996731i | \(0.474254\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.22832e7 | + | 2.41017e6i | 0.972757 | + | 0.105214i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.12805e7i | 0.489653i | 0.969567 | + | 0.244826i | \(0.0787310\pi\) | ||||
−0.969567 | + | 0.244826i | \(0.921269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9.26250e6i | − | 0.399785i | −0.979818 | − | 0.199893i | \(-0.935941\pi\) | ||
0.979818 | − | 0.199893i | \(-0.0640593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.68932e6 | + | 182719.i | 0.0725028 | + | 0.00784197i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.85163e6 | 0.0790216 | 0.0395108 | − | 0.999219i | \(-0.487420\pi\) | ||||
0.0395108 | + | 0.999219i | \(0.487420\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.03140e7 | 1.28644 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.68935e7 | + | 1.69634e7i | 1.55688 | + | 0.715844i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.94628e6i | 0.165599i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 460609.i | − | 0.0192209i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.58773e6 | + | 4.24158e7i | −0.190378 | + | 1.76014i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.36526e7 | −0.563398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.23551e7 | −0.507031 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.17363e6 | − | 2.00963e7i | 0.0887087 | − | 0.820155i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.10850e6i | − | 0.166748i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.81822e7i | − | 0.733886i | −0.930243 | − | 0.366943i | \(-0.880404\pi\) | ||
0.930243 | − | 0.366943i | \(-0.119596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.77696e6 | − | 4.00989e7i | 0.352318 | − | 1.60962i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.97211e7 | 1.18650 | 0.593251 | − | 0.805018i | \(-0.297844\pi\) | ||||
0.593251 | + | 0.805018i | \(0.297844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.97896e7 | −2.77086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 910086. | + | 98435.8i | 0.0359360 | + | 0.00388687i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25672e7i | 0.493531i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.67014e7i | 0.652325i | 0.945314 | + | 0.326163i | \(0.105756\pi\) | ||||
−0.945314 | + | 0.326163i | \(0.894244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13258e7 | − | 1.22501e6i | −0.439965 | − | 0.0475871i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.74891e7 | 1.06208 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.03291e6 | 0.308687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.41060e6 | − | 1.55819e7i | 0.130356 | − | 0.595553i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.30629e6i | − | 0.277752i | −0.990310 | − | 0.138876i | \(-0.955651\pi\) | ||
0.990310 | − | 0.138876i | \(-0.0443490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 178552.i | − | 0.00675134i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.08640e6 | − | 1.00443e7i | 0.0408588 | − | 0.377759i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.56187e6 | 0.0958359 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.58175e7 | 0.588558 | 0.294279 | − | 0.955720i | \(-0.404921\pi\) | ||||
0.294279 | + | 0.955720i | \(0.404921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −220011. | + | 2.03411e6i | −0.00814292 | + | 0.0752852i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.17746e7i | 0.801633i | 0.916158 | + | 0.400816i | \(0.131273\pi\) | ||||
−0.916158 | + | 0.400816i | \(0.868727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.72343e7i | 2.09593i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.07927e6 | + | 3.22195e6i | −0.0393142 | + | 0.117365i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.81364e7 | −0.657169 | −0.328584 | − | 0.944475i | \(-0.606572\pi\) | ||||
−0.328584 | + | 0.944475i | \(0.606572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.76869e6 | 0.171883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.01476e7 | + | 5.42401e6i | 1.79804 | + | 0.194477i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.50157e7i | 0.892239i | 0.894973 | + | 0.446119i | \(0.147194\pi\) | ||||
−0.894973 | + | 0.446119i | \(0.852806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.27343e6i | − | 0.0451823i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.18112e7 | + | 2.35913e6i | 0.769840 | + | 0.0832667i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.03645e7 | −1.06615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.58738e7 | −0.554463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.74417e7 | + | 6.00650e6i | 0.953553 | + | 0.208716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.04221e6i | − | 0.139734i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.10696e7i | − | 1.75629i | −0.478395 | − | 0.878145i | \(-0.658781\pi\) | ||
0.478395 | − | 0.878145i | \(-0.341219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −214799. | + | 1.98592e6i | −0.00734892 | + | 0.0679443i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.26999e7 | 1.11301 | 0.556505 | − | 0.830844i | \(-0.312142\pi\) | ||||
0.556505 | + | 0.830844i | \(0.312142\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.06895e7 | 0.700595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.14824e6 | + | 2.91070e7i | −0.106061 | + | 0.980585i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.15607e7i | − | 1.05782i | −0.848679 | − | 0.528909i | \(-0.822601\pi\) | ||
0.848679 | − | 0.528909i | \(-0.177399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.07137e7i | 1.35764i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.08461e7 | − | 2.37401e6i | −0.359832 | − | 0.0787609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.82318e7 | 0.601791 | 0.300896 | − | 0.953657i | \(-0.402714\pi\) | ||||
0.300896 | + | 0.953657i | \(0.402714\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.65381e6 | 0.218514 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.48360e7 | − | 3.76789e6i | −1.13824 | − | 0.123113i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.38905e7i | 1.42685i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.46491e7i | − | 0.473836i | −0.971530 | − | 0.236918i | \(-0.923863\pi\) | ||
0.971530 | − | 0.236918i | \(-0.0761372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.72146e7 | + | 2.94356e6i | 0.875848 | + | 0.0947325i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.72856e6 | 0.151416 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.14521e7 | −0.683490 | −0.341745 | − | 0.939793i | \(-0.611018\pi\) | ||||
−0.341745 | + | 0.939793i | \(0.611018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.13878e6 | − | 9.37021e6i | 0.0995054 | − | 0.297054i |
(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 | 384.6.c.b.383.12 | yes | 20 | |
3.2 | odd | 2 | 384.6.c.c.383.10 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.c.383.9 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.a.383.12 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.d.383.9 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.b.383.11 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.a.383.11 | ✓ | 20 | ||
24.11 | even | 2 | 384.6.c.d.383.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.11 | ✓ | 20 | 24.5 | odd | 2 | ||
384.6.c.a.383.12 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.11 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.12 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.c.c.383.9 | yes | 20 | 4.3 | odd | 2 | ||
384.6.c.c.383.10 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.9 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.10 | yes | 20 | 24.11 | even | 2 |