Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), 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: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.14 | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.7.l.b.223.14 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 11.0227 | + | 11.0227i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −128.299 | − | 128.299i | −1.02639 | − | 1.02639i | −0.999642 | − | 0.0267466i | \(-0.991485\pi\) |
−0.0267466 | − | 0.999642i | \(-0.508515\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 76.4178 | 0.222792 | 0.111396 | − | 0.993776i | \(-0.464468\pi\) | ||||
0.111396 | + | 0.993776i | \(0.464468\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 565.739 | − | 565.739i | 0.425048 | − | 0.425048i | −0.461890 | − | 0.886937i | \(-0.652828\pi\) |
0.886937 | + | 0.461890i | \(0.152828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2779.09 | + | 2779.09i | −1.26495 | + | 1.26495i | −0.316283 | + | 0.948665i | \(0.602435\pi\) |
−0.948665 | + | 0.316283i | \(0.897565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2828.39i | − | 0.838043i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5241.26 | 1.06681 | 0.533407 | − | 0.845859i | \(-0.320912\pi\) | ||||
0.533407 | + | 0.845859i | \(0.320912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 46.8386 | + | 46.8386i | 0.00682878 | + | 0.00682878i | 0.710513 | − | 0.703684i | \(-0.248463\pi\) |
−0.703684 | + | 0.710513i | \(0.748463\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 842.331 | + | 842.331i | 0.0909546 | + | 0.0909546i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19532.3 | −1.60535 | −0.802675 | − | 0.596417i | \(-0.796590\pi\) | ||||
−0.802675 | + | 0.596417i | \(0.796590\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17296.1i | 1.10695i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2678.52 | + | 2678.52i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16453.9 | − | 16453.9i | 0.674645 | − | 0.674645i | −0.284138 | − | 0.958783i | \(-0.591707\pi\) |
0.958783 | + | 0.284138i | \(0.0917074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24099.2i | 0.808941i | 0.914551 | + | 0.404470i | \(0.132544\pi\) | ||||
−0.914551 | + | 0.404470i | \(0.867456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12471.9 | 0.347050 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9804.30 | − | 9804.30i | −0.228672 | − | 0.228672i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38199.7 | + | 38199.7i | 0.754144 | + | 0.754144i | 0.975250 | − | 0.221106i | \(-0.0709665\pi\) |
−0.221106 | + | 0.975250i | \(0.570967\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −61266.2 | −1.03283 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66525.2i | 0.965239i | 0.875830 | + | 0.482620i | \(0.160315\pi\) | ||||
−0.875830 | + | 0.482620i | \(0.839685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24959.9 | − | 24959.9i | 0.313934 | − | 0.313934i | −0.532498 | − | 0.846431i | \(-0.678747\pi\) |
0.846431 | + | 0.532498i | \(0.178747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 31176.6 | − | 31176.6i | 0.342130 | − | 0.342130i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 120821.i | − | 1.16372i | −0.813288 | − | 0.581862i | \(-0.802324\pi\) | ||
0.813288 | − | 0.581862i | \(-0.197676\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −111809. | −0.950364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 57772.8 | + | 57772.8i | 0.435525 | + | 0.435525i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −92727.0 | − | 92727.0i | −0.622843 | − | 0.622843i | 0.323415 | − | 0.946257i | \(-0.395169\pi\) |
−0.946257 | + | 0.323415i | \(0.895169\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −145167. | −0.872529 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1032.58i | 0.00557568i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 160301. | − | 160301.i | 0.780511 | − | 0.780511i | −0.199406 | − | 0.979917i | \(-0.563901\pi\) |
0.979917 | + | 0.199406i | \(0.0639013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 178988. | − | 178988.i | 0.788557 | − | 0.788557i | −0.192700 | − | 0.981258i | \(-0.561725\pi\) |
0.981258 | + | 0.192700i | \(0.0617245\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18569.5i | 0.0742642i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 713107. | 2.59666 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 274936. | + | 274936.i | 0.914127 | + | 0.914127i | 0.996594 | − | 0.0824667i | \(-0.0262798\pi\) |
−0.0824667 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −215299. | − | 215299.i | −0.655381 | − | 0.655381i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 631790. | 1.76521 | 0.882607 | − | 0.470111i | \(-0.155786\pi\) | ||||
0.882607 | + | 0.470111i | \(0.155786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 470653.i | − | 1.20985i | −0.796281 | − | 0.604926i | \(-0.793203\pi\) | ||
0.796281 | − | 0.604926i | \(-0.206797\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −190649. | + | 190649.i | −0.451910 | + | 0.451910i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 43232.5 | − | 43232.5i | 0.0946974 | − | 0.0946974i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 535148.i | − | 1.08541i | −0.839924 | − | 0.542704i | \(-0.817401\pi\) | ||
0.839924 | − | 0.542704i | \(-0.182599\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59049.0 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 284269. | + | 284269.i | 0.497159 | + | 0.497159i | 0.910552 | − | 0.413394i | \(-0.135657\pi\) |
−0.413394 | + | 0.910552i | \(0.635657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −672446. | − | 672446.i | −1.09497 | − | 1.09497i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 362733. | 0.550846 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 272304.i | 0.386264i | 0.981173 | + | 0.193132i | \(0.0618645\pi\) | ||||
−0.981173 | + | 0.193132i | \(0.938135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −212372. | + | 212372.i | −0.281821 | + | 0.281821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −265638. | + | 265638.i | −0.330249 | + | 0.330249i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 12018.7i | − | 0.0140180i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 499709. | 0.547523 | 0.273761 | − | 0.961798i | \(-0.411732\pi\) | ||||
0.273761 | + | 0.961798i | \(0.411732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 137474. | + | 137474.i | 0.141683 | + | 0.141683i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 532345. | + | 532345.i | 0.516688 | + | 0.516688i | 0.916568 | − | 0.399879i | \(-0.130948\pi\) |
−0.399879 | + | 0.916568i | \(0.630948\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.15325e6 | −1.05538 | −0.527691 | − | 0.849436i | \(-0.676942\pi\) | ||||
−0.527691 | + | 0.849436i | \(0.676942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 216140.i | − | 0.186710i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 350884. | − | 350884.i | 0.286426 | − | 0.286426i | −0.549239 | − | 0.835665i | \(-0.685082\pi\) |
0.835665 | + | 0.549239i | \(0.185082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 555679. | − | 555679.i | 0.429086 | − | 0.429086i | −0.459231 | − | 0.888317i | \(-0.651875\pi\) |
0.888317 | + | 0.459231i | \(0.151875\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 842127.i | 0.615756i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.30361e6 | 0.903465 | 0.451732 | − | 0.892153i | \(-0.350806\pi\) | ||||
0.451732 | + | 0.892153i | \(0.350806\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.50596e6 | + | 2.50596e6i | 1.64771 | + | 1.64771i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −675319. | − | 675319.i | −0.421649 | − | 0.421649i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 400525. | 0.237678 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.13144e6i | 0.638669i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −733288. | + | 733288.i | −0.394057 | + | 0.394057i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 214395. | − | 214395.i | 0.109770 | − | 0.109770i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55793e6i | 1.24875i | 0.781123 | + | 0.624377i | \(0.214647\pi\) | ||||
−0.781123 | + | 0.624377i | \(0.785353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 550252. | 0.256326 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 28783.5 | + | 28783.5i | 0.0128035 | + | 0.0128035i | 0.713480 | − | 0.700676i | \(-0.247118\pi\) |
−0.700676 | + | 0.713480i | \(0.747118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3579.31 | + | 3579.31i | 0.00152140 | + | 0.00152140i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 687300. | 0.279348 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.78484e6i | − | 1.47192i | −0.677023 | − | 0.735962i | \(-0.736730\pi\) | ||
0.677023 | − | 0.735962i | \(-0.263270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −331261. | + | 331261.i | −0.123346 | + | 0.123346i | −0.766085 | − | 0.642739i | \(-0.777798\pi\) |
0.642739 | + | 0.766085i | \(0.277798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.33178e6 | − | 1.33178e6i | 0.475088 | − | 0.475088i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.14448e6i | 1.07533i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.22203e6 | −1.38490 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.23244e6 | − | 1.23244e6i | −0.387984 | − | 0.387984i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00745e6 | + | 2.00745e6i | 0.606855 | + | 0.606855i | 0.942123 | − | 0.335268i | \(-0.108827\pi\) |
−0.335268 | + | 0.942123i | \(0.608827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.78985e6 | 1.10076 | 0.550378 | − | 0.834916i | \(-0.314484\pi\) | ||||
0.550378 | + | 0.834916i | \(0.314484\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.27363e6i | 0.355605i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.09189e6 | − | 3.09189e6i | 0.830288 | − | 0.830288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.38208e6 | − | 4.38208e6i | 1.13235 | − | 1.13235i | 0.142565 | − | 0.989785i | \(-0.454465\pi\) |
0.989785 | − | 0.142565i | \(-0.0455351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 2.04420e6i | − | 0.508549i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.49261e6 | −0.357660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 502348. | + | 502348.i | 0.115996 | + | 0.115996i | 0.762722 | − | 0.646726i | \(-0.223862\pi\) |
−0.646726 | + | 0.762722i | \(0.723862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.60013e6 | − | 1.60013e6i | −0.356208 | − | 0.356208i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.89436e6 | 1.69499 | 0.847496 | − | 0.530802i | \(-0.178109\pi\) | ||||
0.847496 | + | 0.530802i | \(0.178109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.06199e7i | − | 2.20019i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11381.8 | + | 11381.8i | −0.00227626 | + | 0.00227626i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.35604e6 | − | 3.35604e6i | 0.648170 | − | 0.648170i | −0.304381 | − | 0.952550i | \(-0.598449\pi\) |
0.952550 | + | 0.304381i | \(0.0984495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32173e6i | 0.246620i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.53389e6 | 0.637284 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.48022e6 | + | 1.48022e6i | 0.258087 | + | 0.258087i | 0.824276 | − | 0.566189i | \(-0.191583\pi\) |
−0.566189 | + | 0.824276i | \(0.691583\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.91348e6 | + | 4.91348e6i | 0.828616 | + | 0.828616i | 0.987325 | − | 0.158709i | \(-0.0507332\pi\) |
−0.158709 | + | 0.987325i | \(0.550733\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.94585e6 | 0.643854 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.80193e6i | − | 1.54809i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.96518e6 | − | 2.96518e6i | 0.453447 | − | 0.453447i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −204686. | + | 204686.i | −0.0303182 | + | 0.0303182i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.24457e7i | 1.78615i | 0.449909 | + | 0.893074i | \(0.351456\pi\) | ||||
−0.449909 | + | 0.893074i | \(0.648544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03510e7 | 1.43983 | 0.719913 | − | 0.694064i | \(-0.244182\pi\) | ||||
0.719913 | + | 0.694064i | \(0.244182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.86037e6 | + | 7.86037e6i | 1.06008 | + | 1.06008i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.37780e6 | − | 4.37780e6i | −0.572608 | − | 0.572608i | 0.360248 | − | 0.932856i | \(-0.382692\pi\) |
−0.932856 | + | 0.360248i | \(0.882692\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.15098e6 | 0.399840 | 0.199920 | − | 0.979812i | \(-0.435932\pi\) | ||||
0.199920 | + | 0.979812i | \(0.435932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.06107e6i | 0.746382i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.25737e6 | − | 1.25737e6i | 0.150306 | − | 0.150306i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.53510e6 | − | 8.53510e6i | 0.990711 | − | 0.990711i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.74635e6i | − | 0.535116i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 52996.8 | 0.00580512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.31096e6 | − | 5.31096e6i | −0.565361 | − | 0.565361i | 0.365465 | − | 0.930825i | \(-0.380910\pi\) |
−0.930825 | + | 0.365465i | \(0.880910\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.96403e6 | + | 6.96403e6i | 0.720646 | + | 0.720646i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.40465e6 | −0.644436 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84160e6i | 0.180226i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.18787e6 | − | 5.18787e6i | 0.493920 | − | 0.493920i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.45659e7 | + | 1.45659e7i | −1.34946 | + | 1.34946i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.27496e7i | − | 1.14969i | −0.818261 | − | 0.574847i | \(-0.805062\pi\) | ||
0.818261 | − | 0.574847i | \(-0.194938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.20294e6 | −0.368983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00100e6 | − | 9.00100e6i | −0.769508 | − | 0.769508i | 0.208512 | − | 0.978020i | \(-0.433138\pi\) |
−0.978020 | + | 0.208512i | \(0.933138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.27977e7 | − | 1.27977e7i | −1.06568 | − | 1.06568i | −0.997686 | − | 0.0679892i | \(-0.978342\pi\) |
−0.0679892 | − | 0.997686i | \(-0.521658\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 953078. | 0.0773201 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.59408e7i | − | 1.26021i | −0.776511 | − | 0.630103i | \(-0.783012\pi\) | ||
0.776511 | − | 0.630103i | \(-0.216988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.55012e7 | + | 1.55012e7i | −1.19443 | + | 1.19443i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.89878e6 | − | 5.89878e6i | 0.443116 | − | 0.443116i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36617e7i | 1.00072i | 0.865818 | + | 0.500359i | \(0.166799\pi\) | ||||
−0.865818 | + | 0.500359i | \(0.833201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.16851e6 | 0.226362 | 0.113181 | − | 0.993574i | \(-0.463896\pi\) | ||||
0.113181 | + | 0.993574i | \(0.463896\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −650880. | − | 650880.i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.43450e7 | + | 1.43450e7i | 0.975442 | + | 0.975442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −260338. | −0.0172761 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.26682e6i | 0.405928i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.38815e7 | + | 1.38815e7i | −0.877838 | + | 0.877838i | −0.993311 | − | 0.115473i | \(-0.963162\pi\) |
0.115473 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.10502e7 | + | 1.10502e7i | −0.682350 | + | 0.682350i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.48243e7i | − | 0.894036i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.16993e6 | 0.481304 | 0.240652 | − | 0.970612i | \(-0.422639\pi\) | ||||
0.240652 | + | 0.970612i | \(0.422639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.91914e6 | + | 2.91914e6i | 0.168018 | + | 0.168018i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.99830e6 | + | 3.99830e6i | 0.224882 | + | 0.224882i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.07117e7 | 0.588834 | 0.294417 | − | 0.955677i | \(-0.404875\pi\) | ||||
0.294417 | + | 0.955677i | \(0.404875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.37935e7i | 1.27856i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00153e6 | + | 3.00153e6i | −0.157691 | + | 0.157691i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.98822e6 | − | 3.98822e6i | 0.204891 | − | 0.204891i | −0.597201 | − | 0.802092i | \(-0.703721\pi\) |
0.802092 | + | 0.597201i | \(0.203721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 573671.i | 0.0288240i | 0.999896 | + | 0.0144120i | \(0.00458765\pi\) | ||||
−0.999896 | + | 0.0144120i | \(0.995412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.68183e6 | −0.230106 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.78505e6 | + | 9.78505e6i | 0.470506 | + | 0.470506i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.83692e7 | − | 1.83692e7i | −0.864275 | − | 0.864275i | 0.127556 | − | 0.991831i | \(-0.459287\pi\) |
−0.991831 | + | 0.127556i | \(0.959287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.85609e6 | −0.269647 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.16574e7i | 1.42678i | 0.700769 | + | 0.713388i | \(0.252840\pi\) | ||||
−0.700769 | + | 0.713388i | \(0.747160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −659467. | + | 659467.i | −0.0290960 | + | 0.0290960i | −0.721505 | − | 0.692409i | \(-0.756549\pi\) |
0.692409 | + | 0.721505i | \(0.256549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 132478. | − | 132478.i | 0.00572281 | − | 0.00572281i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.08371e6i | 0.215048i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.33319e6 | 0.138091 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.50814e6 | + | 5.50814e6i | 0.223525 | + | 0.223525i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.40668e6 | + | 4.40668e6i | 0.175190 | + | 0.175190i | 0.789255 | − | 0.614065i | \(-0.210467\pi\) |
−0.614065 | + | 0.789255i | \(0.710467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.11327e7 | −1.60222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.03068e6i | 0.115683i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.42820e7 | − | 5.42820e7i | 2.03068 | − | 2.03068i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.90738e6 | − | 1.90738e6i | 0.0699421 | − | 0.0699421i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.17358e7i | 0.421874i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.59277e7 | −1.61873 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.31828e7 | + | 1.31828e7i | 0.455611 | + | 0.455611i | 0.897212 | − | 0.441601i | \(-0.145589\pi\) |
−0.441601 | + | 0.897212i | \(0.645589\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.27119e7 | − | 1.27119e7i | −0.430858 | − | 0.430858i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.31930e7 | −1.76837 | −0.884185 | − | 0.467137i | \(-0.845286\pi\) | ||||
−0.884185 | + | 0.467137i | \(0.845286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.25409e6i | − | 0.171342i | −0.996323 | − | 0.0856711i | \(-0.972697\pi\) | ||
0.996323 | − | 0.0856711i | \(-0.0273034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.38244e6 | − | 2.38244e6i | 0.0762239 | − | 0.0762239i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.15447e7 | + | 1.15447e7i | −0.362415 | + | 0.362415i | −0.864702 | − | 0.502286i | \(-0.832492\pi\) |
0.502286 | + | 0.864702i | \(0.332492\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.86172e7i | − | 0.573513i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.73539e6 | 0.233866 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 245493. | + | 245493.i | 0.00728504 | + | 0.00728504i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.80673e7 | − | 4.80673e7i | −1.40023 | − | 1.40023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.22502e7 | 0.350347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.23290e6i | − | 0.259269i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.33618e7 | + | 3.33618e7i | −0.919954 | + | 0.919954i | −0.997026 | − | 0.0770720i | \(-0.975443\pi\) |
0.0770720 | + | 0.997026i | \(0.475443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.28252e6 | + | 9.28252e6i | −0.251381 | + | 0.251381i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7.05477e7i | − | 1.87650i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.53546e7 | −0.923753 | −0.461877 | − | 0.886944i | \(-0.652824\pi\) | ||||
−0.461877 | + | 0.886944i | \(0.652824\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.43693e7 | + | 1.43693e7i | 0.368838 | + | 0.368838i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.36338e7 | + | 1.36338e7i | 0.343838 | + | 0.343838i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.75347e7 | −0.434526 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.52450e7i | 1.34535i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.72087e7 | − | 2.72087e7i | 0.651207 | − | 0.651207i | −0.302077 | − | 0.953284i | \(-0.597680\pi\) |
0.953284 | + | 0.302077i | \(0.0976799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.75646e7 | − | 1.75646e7i | 0.413201 | − | 0.413201i | −0.469651 | − | 0.882852i | \(-0.655620\pi\) |
0.882852 | + | 0.469651i | \(0.155620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.48877e7i | − | 0.344275i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.31019e7 | 0.979878 | 0.489939 | − | 0.871757i | \(-0.337019\pi\) | ||||
0.489939 | + | 0.871757i | \(0.337019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.10577e7 | − | 8.10577e7i | −1.81180 | − | 1.81180i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.41487e6 | + | 4.41487e6i | 0.0970317 | + | 0.0970317i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.07426e7 | 1.09670 | 0.548352 | − | 0.836248i | \(-0.315255\pi\) | ||||
0.548352 | + | 0.836248i | \(0.315255\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 4.70415e7i | − | 0.999907i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.24715e7 | + | 1.24715e7i | −0.260735 | + | 0.260735i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.03842e7 | + | 6.03842e7i | −1.24178 | + | 1.24178i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.29504e7i | 1.07120i | 0.844471 | + | 0.535601i | \(0.179915\pi\) | ||||
−0.844471 | + | 0.535601i | \(0.820085\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.61656e7 | −0.321746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.08599e6 | − | 7.08599e6i | −0.138765 | − | 0.138765i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.19127e7 | + | 3.19127e7i | 0.614946 | + | 0.614946i | 0.944231 | − | 0.329285i | \(-0.106808\pi\) |
−0.329285 | + | 0.944231i | \(0.606808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.72642e6 | 0.0896270 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.14539e7i | 1.70678i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.31956e7 | + | 5.31956e7i | −0.977142 | + | 0.977142i | −0.999745 | − | 0.0226024i | \(-0.992805\pi\) |
0.0226024 | + | 0.999745i | \(0.492805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.81953e7 | + | 2.81953e7i | −0.509802 | + | 0.509802i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.34659e7i | − | 0.239685i | −0.992793 | − | 0.119842i | \(-0.961761\pi\) | ||
0.992793 | − | 0.119842i | \(-0.0382389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.10933e7 | −0.194393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.06526e6 | + | 6.06526e6i | 0.104645 | + | 0.104645i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.53726e7 | + | 6.53726e7i | 1.11057 | + | 1.11057i | 0.993073 | + | 0.117499i | \(0.0374878\pi\) |
0.117499 | + | 0.993073i | \(0.462512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.02374e8 | −1.71261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 634545.i | 0.0104541i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.86587e7 | + | 6.86587e7i | −1.11405 | + | 1.11405i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.77960e7 | + | 2.77960e7i | −0.444233 | + | 0.444233i | −0.893432 | − | 0.449199i | \(-0.851709\pi\) |
0.449199 | + | 0.893432i | \(0.351709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 78907.3i | 0.00124222i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.42149e7 | 0.995871 | 0.497935 | − | 0.867214i | \(-0.334092\pi\) | ||||
0.497935 | + | 0.867214i | \(0.334092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.69737e7 | − | 6.69737e7i | −1.02327 | − | 1.02327i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.57590e6 | + | 7.57590e6i | 0.114043 | + | 0.114043i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.32221e7 | 0.641095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.68143e7i | − | 0.976562i | −0.872687 | − | 0.488281i | \(-0.837624\pi\) | ||
0.872687 | − | 0.488281i | \(-0.162376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.17191e7 | − | 4.17191e7i | 0.600910 | − | 0.600910i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.22498e7 | − | 1.22498e7i | 0.173892 | − | 0.173892i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.29426e7i | − | 1.02056i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.30279e6 | −0.100712 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.40014e7 | − | 7.40014e7i | −1.00600 | − | 1.00600i | −0.999982 | − | 0.00601716i | \(-0.998085\pi\) |
−0.00601716 | − | 0.999982i | \(-0.501915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.36241e6 | + | 6.36241e6i | 0.0852659 | + | 0.0852659i | 0.748453 | − | 0.663187i | \(-0.230797\pi\) |
−0.663187 | + | 0.748453i | \(0.730797\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.93596e7 | 0.387908 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.06531e7i | 1.18091i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.36778e7 | − | 1.36778e7i | 0.175685 | − | 0.175685i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.46606e7 | + | 3.46606e7i | −0.439000 | + | 0.439000i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.69859e7i | − | 0.461960i | −0.972959 | − | 0.230980i | \(-0.925807\pi\) | ||
0.972959 | − | 0.230980i | \(-0.0741931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.09232e7 | −0.627266 | −0.313633 | − | 0.949544i | \(-0.601546\pi\) | ||||
−0.313633 | + | 0.949544i | \(0.601546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.65382e7 | − | 4.65382e7i | −0.565382 | − | 0.565382i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −914865. | − | 914865.i | −0.0109626 | − | 0.0109626i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.15508e8 | −1.36527 | −0.682634 | − | 0.730760i | \(-0.739166\pi\) | ||||
−0.682634 | + | 0.730760i | \(0.739166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.71697e7i | − | 0.316788i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.85528e7 | − | 5.85528e7i | 0.673499 | − | 0.673499i | −0.285022 | − | 0.958521i | \(-0.592001\pi\) |
0.958521 | + | 0.285022i | \(0.0920009\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.49362e7 | − | 3.49362e7i | 0.396457 | − | 0.396457i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.42550e7i | 0.495495i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.93732e7 | −0.987344 | −0.493672 | − | 0.869648i | \(-0.664346\pi\) | ||||
−0.493672 | + | 0.869648i | \(0.664346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.76359e7 | + | 3.76359e7i | 0.410273 | + | 0.410273i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.17744e7 | + | 4.17744e7i | 0.449382 | + | 0.449382i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.44941e7 | 0.578516 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.96514e7i | − | 0.939309i | −0.882850 | − | 0.469654i | \(-0.844378\pi\) | ||
0.882850 | − | 0.469654i | \(-0.155622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.40388e7 | + | 1.40388e7i | −0.145175 | + | 0.145175i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.72692e6 | − | 3.72692e6i | 0.0380406 | − | 0.0380406i | −0.687831 | − | 0.725871i | \(-0.741437\pi\) |
0.725871 | + | 0.687831i | \(0.241437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.18637e8i | 1.19530i | 0.801757 | + | 0.597650i | \(0.203899\pi\) | ||||
−0.801757 | + | 0.597650i | \(0.796101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.81619e7 | 0.677927 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.26400e6 | − | 3.26400e6i | −0.0320479 | − | 0.0320479i | 0.690901 | − | 0.722949i | \(-0.257214\pi\) |
−0.722949 | + | 0.690901i | \(0.757214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.10100e7 | + | 2.10100e7i | 0.203661 | + | 0.203661i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.66047e7 | 0.924561 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.82416e7i | − | 0.266874i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −810124. | + | 810124.i | −0.00755911 | + | 0.00755911i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.25327e7 | − | 2.25327e7i | 0.207614 | − | 0.207614i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.56324e7i | 0.688179i | 0.938937 | + | 0.344089i | \(0.111812\pi\) | ||||
−0.938937 | + | 0.344089i | \(0.888188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.12321e8 | −1.90791 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.64526e7 | − | 1.64526e7i | −0.146014 | − | 0.146014i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.41120e7 | − | 6.41120e7i | −0.561971 | − | 0.561971i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.10626e7 | 0.182358 | 0.0911790 | − | 0.995835i | \(-0.470936\pi\) | ||||
0.0911790 | + | 0.995835i | \(0.470936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.10745e7i | 0.0947101i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.57469e7 | + | 4.57469e7i | −0.386471 | + | 0.386471i | −0.873427 | − | 0.486955i | \(-0.838107\pi\) |
0.486955 | + | 0.873427i | \(0.338107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.62392e7 | − | 8.62392e7i | 0.719721 | − | 0.719721i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3.52756e7i | − | 0.290843i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.82800e7 | 0.393277 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.47954e8 | + | 1.47954e8i | 1.19076 | + | 1.19076i | 0.976853 | + | 0.213912i | \(0.0686206\pi\) |
0.213912 | + | 0.976853i | \(0.431379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.70172e7 | + | 8.70172e7i | 0.691977 | + | 0.691977i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.13896e8 | 0.894962 | 0.447481 | − | 0.894293i | \(-0.352321\pi\) | ||||
0.447481 | + | 0.894293i | \(0.352321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.36598e8i | − | 1.06065i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.17060e8 | − | 1.17060e8i | 0.898223 | − | 0.898223i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.31902e7 | − | 6.31902e7i | 0.479177 | − | 0.479177i | −0.425691 | − | 0.904868i | \(-0.639969\pi\) |
0.904868 | + | 0.425691i | \(0.139969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.59663e7i | − | 0.269546i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −250916. | −0.00185856 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.47960e8 | + | 1.47960e8i | 1.08323 | + | 1.08323i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.83533e7 | − | 6.83533e7i | −0.494638 | − | 0.494638i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.39853e7 | 0.529228 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.69906e7i | − | 0.120142i | −0.998194 | − | 0.0600710i | \(-0.980867\pi\) | ||
0.998194 | − | 0.0600710i | \(-0.0191327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.27719e7 | − | 9.27719e7i | 0.648502 | − | 0.648502i | −0.304129 | − | 0.952631i | \(-0.598365\pi\) |
0.952631 | + | 0.304129i | \(0.0983654\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.45690e7 | + | 1.45690e7i | −0.100682 | + | 0.100682i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26310e8i | 0.862989i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.33474e8 | 1.57715 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.89530e7 | + | 3.89530e7i | 0.260170 | + | 0.260170i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.84880e8 | − | 1.84880e8i | −1.22098 | − | 1.22098i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00360e7 | −0.587969 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.26320e7i | 0.210727i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.32548e7 | + | 6.32548e7i | −0.403950 | + | 0.403950i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.86819e7 | − | 3.86819e7i | 0.244296 | − | 0.244296i | −0.574329 | − | 0.818625i | \(-0.694737\pi\) |
0.818625 | + | 0.574329i | \(0.194737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.08320e8i | 0.676562i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.42586e8 | −0.880818 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.18514e8 | − | 2.18514e8i | −1.33511 | − | 1.33511i | −0.900728 | − | 0.434384i | \(-0.856966\pi\) |
−0.434384 | − | 0.900728i | \(-0.643034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.34940e7 | + | 4.34940e7i | 0.262852 | + | 0.262852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.54136e6 | 0.00921401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.08948e7i | − | 0.241821i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.08044e8 | − | 1.08044e8i | 0.632005 | − | 0.632005i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.29193e7 | − | 2.29193e7i | 0.132628 | − | 0.132628i | −0.637676 | − | 0.770304i | \(-0.720104\pi\) |
0.770304 | + | 0.637676i | \(0.220104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38732e8i | 0.794219i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.53686e7 | 0.370238 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.43461e8 | + | 2.43461e8i | 1.36428 | + | 1.36428i | 0.868379 | + | 0.495901i | \(0.165162\pi\) |
0.495901 | + | 0.868379i | \(0.334838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.67251e8 | − | 1.67251e8i | −0.927306 | − | 0.927306i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.51240e6 | −0.0247547 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.46262e7i | 0.296527i | 0.988948 | + | 0.148263i | \(0.0473684\pi\) | ||||
−0.988948 | + | 0.148263i | \(0.952632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.62311e8 | + | 1.62311e8i | −0.871848 | + | 0.871848i | −0.992674 | − | 0.120826i | \(-0.961446\pi\) |
0.120826 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.37185e8 | + | 1.37185e8i | −0.729192 | + | 0.729192i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.37832e8i | − | 1.77704i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.65063e8 | 0.859257 | 0.429629 | − | 0.903006i | \(-0.358644\pi\) | ||||
0.429629 | + | 0.903006i | \(0.358644\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.14096e8 | + | 1.14096e8i | 0.587807 | + | 0.587807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.17232e7 | + | 2.17232e7i | 0.110763 | + | 0.110763i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.04918e8 | −0.529476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.73285e8i | 0.865552i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.58258e8 | + | 1.58258e8i | −0.782441 | + | 0.782441i | −0.980242 | − | 0.197801i | \(-0.936620\pi\) |
0.197801 | + | 0.980242i | \(0.436620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.12877e6 | + | 1.12877e6i | −0.00552408 | + | 0.00552408i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9.65104e7i | − | 0.467532i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.27415e8 | 0.611022 | 0.305511 | − | 0.952189i | \(-0.401173\pi\) | ||||
0.305511 | + | 0.952189i | \(0.401173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.13868e7 | − | 5.13868e7i | −0.243950 | − | 0.243950i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.47323e7 | + | 3.47323e7i | 0.163234 | + | 0.163234i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.41336e8 | −0.657615 | −0.328807 | − | 0.944397i | \(-0.606647\pi\) | ||||
−0.328807 | + | 0.944397i | \(0.606647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.36592e8i | − | 1.55053i | −0.631636 | − | 0.775265i | \(-0.717616\pi\) | ||
0.631636 | − | 0.775265i | \(-0.282384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.68094e7 | + | 6.68094e7i | −0.304709 | + | 0.304709i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.45162e8 | − | 1.45162e8i | 0.655523 | − | 0.655523i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.16255e8i | 0.519810i | 0.965634 | + | 0.259905i | \(0.0836912\pi\) | ||||
−0.965634 | + | 0.259905i | \(0.916309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.77193e7 | 0.122724 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.35773e8 | + | 3.35773e8i | 1.47205 | + | 1.47205i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.25208e8 | + | 1.25208e8i | 0.543563 | + | 0.543563i | 0.924571 | − | 0.381009i | \(-0.124423\pi\) |
−0.381009 | + | 0.924571i | \(0.624423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.88160e8 | 0.808912 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.41424e8i | 1.45358i | 0.686861 | + | 0.726789i | \(0.258988\pi\) | ||||
−0.686861 | + | 0.726789i | \(0.741012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.23598e7 | + | 5.23598e7i | −0.220763 | + | 0.220763i | −0.808820 | − | 0.588057i | \(-0.799893\pi\) |
0.588057 | + | 0.808820i | \(0.299893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.23176e7 | − | 5.23176e7i | 0.218460 | − | 0.218460i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.08089e7i | 0.0860566i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.15238e8 | 0.881614 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 584168. | + | 584168.i | 0.00236993 | + | 0.00236993i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00214e8 | + | 2.00214e8i | 0.804531 | + | 0.804531i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.73769e8 | 1.48770 | 0.743850 | − | 0.668347i | \(-0.232998\pi\) | ||||
0.743850 | + | 0.668347i | \(0.232998\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.17082e8i | − | 0.461615i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.28179e8 | − | 3.28179e8i | 1.28171 | − | 1.28171i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.10728e8 | − | 3.10728e8i | 1.20216 | − | 1.20216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.53525e8i | 0.588405i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.16876e7 | −0.0443763 | −0.0221881 | − | 0.999754i | \(-0.507063\pi\) | ||||
−0.0221881 | + | 0.999754i | \(0.507063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.95708e7 | − | 7.95708e7i | −0.299310 | − | 0.299310i | 0.541434 | − | 0.840743i | \(-0.317882\pi\) |
−0.840743 | + | 0.541434i | \(0.817882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.05965e7 | − | 7.05965e7i | −0.263090 | − | 0.263090i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.53020e8 | 0.564981 | 0.282491 | − | 0.959270i | \(-0.408839\pi\) | ||||
0.282491 | + | 0.959270i | \(0.408839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.81376e8i | − | 0.663509i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.02995e7 | + | 2.02995e7i | −0.0735769 | + | 0.0735769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.21038e7 | + | 4.21038e7i | −0.151210 | + | 0.151210i | −0.778658 | − | 0.627448i | \(-0.784099\pi\) |
0.627448 | + | 0.778658i | \(0.284099\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.38578e6i | − | 0.0262828i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.14369e8 | 0.403284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.81805e8 | − | 1.81805e8i | −0.635256 | − | 0.635256i | 0.314125 | − | 0.949382i | \(-0.398289\pi\) |
−0.949382 | + | 0.314125i | \(0.898289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.69937e8 | − | 2.69937e8i | −0.934669 | − | 0.934669i | 0.0633241 | − | 0.997993i | \(-0.479830\pi\) |
−0.997993 | + | 0.0633241i | \(0.979830\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.21112e8 | −1.10183 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 918440.i | − | 0.00312310i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.21383e8 | + | 3.21383e8i | −1.08304 | + | 1.08304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.40535e8 | − | 1.40535e8i | 0.469360 | − | 0.469360i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.02520e8i | − | 0.670349i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 94641.0 | 0.000310480 | 0.000155240 | − | 1.00000i | \(-0.499951\pi\) | ||||
0.000155240 | 1.00000i | \(0.499951\pi\) | ||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.63278e7 | − | 4.63278e7i | −0.150637 | − | 0.150637i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.76652e8 | − | 1.76652e8i | −0.569314 | − | 0.569314i | 0.362622 | − | 0.931936i | \(-0.381881\pi\) |
−0.931936 | + | 0.362622i | \(0.881881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.81867e7 | 0.121984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.98431e8i | − | 0.628301i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.36247e7 | − | 3.36247e7i | 0.105535 | − | 0.105535i | −0.652368 | − | 0.757903i | \(-0.726224\pi\) |
0.757903 | + | 0.652368i | \(0.226224\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85589e8 | + | 4.85589e8i | −1.51077 | + | 1.51077i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.82130e8i | − | 0.870120i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.15393e8 | 1.57573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.67951e8 | + | 2.67951e8i | 0.812122 | + | 0.812122i | 0.984952 | − | 0.172830i | \(-0.0552912\pi\) |
−0.172830 | + | 0.984952i | \(0.555291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.05055e7 | + | 1.05055e7i | 0.0315658 | + | 0.0315658i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.50007e7 | 0.253203 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.48676e8i | 1.02973i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.75711e8 | − | 1.75711e8i | 0.514477 | − | 0.514477i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.07036e8 | − | 2.07036e8i | 0.601023 | − | 0.601023i | −0.339561 | − | 0.940584i | \(-0.610279\pi\) |
0.940584 | + | 0.339561i | \(0.110279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.57844e6i | 0.0102998i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.41730e8 | −0.975250 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.06806e7 | + | 4.06806e7i | 0.115114 | + | 0.115114i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.86413e8 | − | 2.86413e8i | −0.803626 | − | 0.803626i | 0.180034 | − | 0.983660i | \(-0.442379\pi\) |
−0.983660 | + | 0.180034i | \(0.942379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.30041e8 | 0.361802 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.70712e8i | − | 1.29863i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.03432e8 | − | 4.03432e8i | 1.10370 | − | 1.10370i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.50589e8 | + | 1.50589e8i | −0.408541 | + | 0.408541i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.52364e8i | − | 0.678954i | −0.940614 | − | 0.339477i | \(-0.889750\pi\) | ||
0.940614 | − | 0.339477i | \(-0.110250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.81285e7 | −0.235131 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.49255e7 | + | 3.49255e7i | 0.0924120 | + | 0.0924120i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.84588e8 | + | 2.84588e8i | 0.746797 | + | 0.746797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.87607e8 | −0.488253 | −0.244127 | − | 0.969743i | \(-0.578501\pi\) | ||||
−0.244127 | + | 0.969743i | \(0.578501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.43489e7i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.30821e8 | − | 1.30821e8i | 0.334909 | − | 0.334909i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.14523e8 | − | 2.14523e8i | 0.544705 | − | 0.544705i | −0.380199 | − | 0.924905i | \(-0.624145\pi\) |
0.924905 | + | 0.380199i | \(0.124145\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.16241e8i | 0.796445i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.11083e8 | 0.777095 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.89247e8 | + | 1.89247e8i | 0.468916 | + | 0.468916i | 0.901563 | − | 0.432647i | \(-0.142420\pi\) |
−0.432647 | + | 0.901563i | \(0.642420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.86962e6 | − | 2.86962e6i | −0.00705294 | − | 0.00705294i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.98525e8 | 0.727804 | 0.363902 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363902 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.15105e8i | − | 1.24574i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.90774e7 | + | 6.90774e7i | −0.165720 | + | 0.165720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.68138e7 | − | 2.68138e7i | 0.0638136 | − | 0.0638136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.52347e8i | 0.831860i | 0.909397 | + | 0.415930i | \(0.136544\pi\) | ||||
−0.909397 | + | 0.415930i | \(0.863456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.06023e8 | −0.716752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.86232e8 | − | 4.86232e8i | −1.12980 | − | 1.12980i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50447e8 | + | 1.50447e8i | 0.346814 | + | 0.346814i | 0.858921 | − | 0.512107i | \(-0.171135\pi\) |
−0.512107 | + | 0.858921i | \(0.671135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.43605e8 | −0.557137 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.52589e8i | 0.346233i | 0.984901 | + | 0.173117i | \(0.0553837\pi\) | ||||
−0.984901 | + | 0.173117i | \(0.944616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.24637e7 | − | 4.24637e7i | 0.0955971 | − | 0.0955971i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.63404e8 | − | 1.63404e8i | 0.364989 | − | 0.364989i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.90979e8i | 1.97461i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.19596e8 | −0.922682 | −0.461341 | − | 0.887223i | \(-0.652631\pi\) | ||||
−0.461341 | + | 0.887223i | \(0.652631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.00548e7 | + | 9.00548e7i | 0.196491 | + | 0.196491i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.63380e8 | + | 3.63380e8i | 0.786723 | + | 0.786723i | 0.980956 | − | 0.194232i | \(-0.0622216\pi\) |
−0.194232 | + | 0.980956i | \(0.562222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.16820e8 | −0.895455 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.43535e7i | 0.137186i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.11595e6 | + | 3.11595e6i | −0.00659141 | + | 0.00659141i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.57428e8 | − | 3.57428e8i | 0.750300 | − | 0.750300i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.81442e7i | 0.183615i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.12443e9 | −2.32446 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.05644e8 | − | 2.05644e8i | −0.421884 | − | 0.421884i | 0.463968 | − | 0.885852i | \(-0.346425\pi\) |
−0.885852 | + | 0.463968i | \(0.846425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.18072e8 | + | 1.18072e8i | 0.240391 | + | 0.240391i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.96188e7 | 0.201285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.94845e8i | 1.99497i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.62268e8 | + | 2.62268e8i | −0.521969 | + | 0.521969i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.45649e8 | + | 1.45649e8i | −0.287695 | + | 0.287695i | −0.836168 | − | 0.548473i | \(-0.815209\pi\) |
0.548473 | + | 0.836168i | \(0.315209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.33255e8i | − | 1.24148i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.61699e7 | −0.128755 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.66267e8 | − | 2.66267e8i | −0.514245 | − | 0.514245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.91500e8 | + | 1.91500e8i | 0.367098 | + | 0.367098i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.79219e7 | 0.167292 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.70877e8i | − | 0.511595i | −0.966730 | − | 0.255798i | \(-0.917662\pi\) | ||
0.966730 | − | 0.255798i | \(-0.0823381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.66755e8 | + | 2.66755e8i | −0.500092 | + | 0.500092i | −0.911467 | − | 0.411374i | \(-0.865049\pi\) |
0.411374 | + | 0.911467i | \(0.365049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.32340e6 | + | 6.32340e6i | −0.0117674 | + | 0.0117674i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.28901e8i | − | 0.238113i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.33818e6 | 0.00428757 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.16064e7 | − | 5.16064e7i | −0.0939403 | − | 0.0939403i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.82685e8 | + | 1.82685e8i | 0.330121 | + | 0.330121i | 0.852632 | − | 0.522511i | \(-0.175005\pi\) |
−0.522511 | + | 0.852632i | \(0.675005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.27338e8 | 1.30478 | 0.652389 | − | 0.757884i | \(-0.273767\pi\) | ||||
0.652389 | + | 0.757884i | \(0.273767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.15715e8i | 0.384166i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.81741e8 | − | 3.81741e8i | 0.674919 | − | 0.674919i | −0.283927 | − | 0.958846i | \(-0.591637\pi\) |
0.958846 | + | 0.283927i | \(0.0916372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.84827e8 | + | 5.84827e8i | −1.02651 | + | 1.02651i | −0.0268724 | + | 0.999639i | \(0.508555\pi\) |
−0.999639 | + | 0.0268724i | \(0.991445\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 4.04957e8i | − | 0.705677i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.86021e8 | −1.01386 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.01284e9 | − | 1.01284e9i | −1.73972 | − | 1.73972i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.45500e7 | − | 6.45500e7i | −0.110083 | − | 0.110083i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.40695e8 | −0.915517 | −0.457759 | − | 0.889076i | \(-0.651348\pi\) | ||||
−0.457759 | + | 0.889076i | \(0.651348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.33601e7i | 0.0897074i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.48950e8 | + | 3.48950e8i | −0.582479 | + | 0.582479i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.36252e9 | + | 1.36252e9i | −2.25825 | + | 2.25825i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.64622e7i | 0.142291i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.45382e7 | −0.0237568 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.46127e8 | − | 7.46127e8i | −1.21066 | − | 1.21066i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.16023e8 | + | 8.16023e8i | 1.31479 | + | 1.31479i | 0.917843 | + | 0.396944i | \(0.129929\pi\) |
0.396944 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.92053e6 | 0.00467266 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.99758e8i | 1.42950i | 0.699382 | + | 0.714748i | \(0.253459\pi\) | ||||
−0.699382 | + | 0.714748i | \(0.746541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.05566e8 | + | 5.05566e8i | −0.797624 | + | 0.797624i | −0.982720 | − | 0.185096i | \(-0.940740\pi\) |
0.185096 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.60363e7 | + | 5.60363e7i | −0.0877930 | + | 0.0877930i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.65472e8i | 0.568619i | 0.958733 | + | 0.284310i | \(0.0917643\pi\) | ||||
−0.958733 | + | 0.284310i | \(0.908236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.61150e8 | −1.33055 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.67407e7 | + | 3.67407e7i | 0.0563755 | + | 0.0563755i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.02754e8 | − | 3.02754e8i | −0.461350 | − | 0.461350i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.52814e9 | −2.31265 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.21429e8i | 0.182508i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.63836e7 | − | 1.63836e7i | 0.0244560 | − | 0.0244560i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.17148e8 | + | 1.17148e8i | −0.173674 | + | 0.173674i | −0.788592 | − | 0.614917i | \(-0.789189\pi\) |
0.614917 | + | 0.788592i | \(0.289189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.71471e7i | 0.143042i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.93109e8 | 1.30610 | 0.653050 | − | 0.757314i | \(-0.273489\pi\) | ||||
0.653050 | + | 0.757314i | \(0.273489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.66301e8 | + | 9.66301e8i | 1.40356 | + | 1.40356i | 0.788420 | + | 0.615137i | \(0.210899\pi\) |
0.615137 | + | 0.788420i | \(0.289101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.53393e8 | − | 4.53393e8i | −0.654102 | − | 0.654102i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.37358e8 | −0.340120 | −0.170060 | − | 0.985434i | \(-0.554396\pi\) | ||||
−0.170060 | + | 0.985434i | \(0.554396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.95471e8i | 0.278213i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.34063e7 | + | 3.34063e7i | −0.0472275 | + | 0.0472275i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.65910e6 | − | 5.65910e6i | 0.00794682 | − | 0.00794682i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.79820e8i | − | 0.529796i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.19667e9 | 1.65805 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.96526e8 | + | 3.96526e8i | 0.545748 | + | 0.545748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.86006e8 | − | 4.86006e8i | −0.664457 | − | 0.664457i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.20490e7 | 0.0571074 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.26079e9i | − | 1.70097i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.13327e8 | − | 3.13327e8i | 0.419930 | − | 0.419930i | −0.465250 | − | 0.885179i | \(-0.654035\pi\) |
0.885179 | + | 0.465250i | \(0.154035\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.29360e8 | + | 1.29360e8i | −0.172229 | + | 0.172229i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.43893e8i | 0.454849i | 0.973796 | + | 0.227425i | \(0.0730306\pi\) | ||||
−0.973796 | + | 0.227425i | \(0.926969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.21644e8 | 0.422632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.06247e8 | − | 5.06247e8i | −0.660845 | − | 0.660845i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.19958e6 | + | 2.19958e6i | 0.00285253 | + | 0.00285253i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.23387e9 | 1.58973 | 0.794866 | − | 0.606785i | \(-0.207541\pi\) | ||||
0.794866 | + | 0.606785i | \(0.207541\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.90621e8i | 0.372005i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.75580e9 | + | 1.75580e9i | −2.23290 | + | 2.23290i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.60704e8 | + | 6.60704e8i | −0.834799 | + | 0.834799i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.80239e8i | − | 0.351794i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.33194e8 | 0.166125 | 0.0830627 | − | 0.996544i | \(-0.473530\pi\) | ||||
0.0830627 | + | 0.996544i | \(0.473530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.23699e6 | − | 5.23699e6i | −0.00648983 | − | 0.00648983i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.86331e8 | − | 5.86331e8i | −0.721934 | − | 0.721934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.60857e8 | −0.930825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.04820e9i | 1.27416i | 0.770798 | + | 0.637079i | \(0.219858\pi\) | ||||
−0.770798 | + | 0.637079i | \(0.780142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.79143e7 | − | 5.79143e7i | 0.0699502 | − | 0.0699502i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.82891e8 | − | 4.82891e8i | 0.579536 | − | 0.579536i | −0.355239 | − | 0.934775i | \(-0.615601\pi\) |
0.934775 | + | 0.355239i | \(0.115601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.29939e9i | − | 1.54955i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.25220e7 | 0.0622366 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.94344e8 | − | 1.94344e8i | −0.228835 | − | 0.228835i | 0.583371 | − | 0.812206i | \(-0.301733\pi\) |
−0.812206 | + | 0.583371i | \(0.801733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.30799e9 | + | 1.30799e9i | 1.53040 | + | 1.53040i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.54509e8 | −0.295911 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.33145e9i | − | 1.53832i | −0.639057 | − | 0.769159i | \(-0.720675\pi\) | ||
0.639057 | − | 0.769159i | \(-0.279325\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.59676e9 | − | 1.59676e9i | 1.83328 | − | 1.83328i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.05212e8 | − | 2.05212e8i | 0.234136 | − | 0.234136i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.89229e8i | − | 0.327934i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.06734e8 | 0.345615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.52649e7 | + | 8.52649e7i | 0.0954754 | + | 0.0954754i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.32802e9 | − | 1.32802e9i | −1.47782 | − | 1.47782i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.17954e9 | 1.30447 | 0.652235 | − | 0.758017i | \(-0.273831\pi\) | ||||
0.652235 | + | 0.758017i | \(0.273831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.41200e6i | 0.00594821i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.62523e8 | − | 1.62523e8i | 0.177524 | − | 0.177524i | −0.612752 | − | 0.790276i | \(-0.709937\pi\) |
0.790276 | + | 0.612752i | \(0.209937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.53143e7 | + | 2.53143e7i | −0.0274806 | + | 0.0274806i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.05966e9i | − | 1.14328i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.55049e8 | −0.595179 | −0.297589 | − | 0.954694i | \(-0.596183\pi\) | ||||
−0.297589 | + | 0.954694i | \(0.596183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.54053e8 | + | 1.54053e8i | 0.164181 | + | 0.164181i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.35030e8 | + | 1.35030e8i | 0.143029 | + | 0.143029i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.19931e9 | −1.26262 | −0.631309 | − | 0.775531i | \(-0.717482\pi\) | ||||
−0.631309 | + | 0.775531i | \(0.717482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12333e9i | 1.17544i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.01772e8 | − | 1.01772e8i | 0.105846 | − | 0.105846i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.87524e8 | + | 4.87524e8i | −0.503973 | + | 0.503973i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.74382e7i | − | 0.0487424i | −0.999703 | − | 0.0243712i | \(-0.992242\pi\) | ||
0.999703 | − | 0.0243712i | \(-0.00775837\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.35475e8 | −0.751139 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.04266e8 | − | 4.04266e8i | −0.410391 | − | 0.410391i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.04216e8 | − | 5.04216e8i | −0.508781 | − | 0.508781i | 0.405371 | − | 0.914152i | \(-0.367142\pi\) |
−0.914152 | + | 0.405371i | \(0.867142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.04637e8 | −0.205252 |
(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 | 384.7.l.b.31.14 | 48 | ||
4.3 | odd | 2 | 384.7.l.a.31.11 | 48 | |||
8.3 | odd | 2 | 192.7.l.a.79.14 | 48 | |||
8.5 | even | 2 | 48.7.l.a.43.24 | yes | 48 | ||
16.3 | odd | 4 | inner | 384.7.l.b.223.14 | 48 | ||
16.5 | even | 4 | 192.7.l.a.175.14 | 48 | |||
16.11 | odd | 4 | 48.7.l.a.19.24 | ✓ | 48 | ||
16.13 | even | 4 | 384.7.l.a.223.11 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.l.a.19.24 | ✓ | 48 | 16.11 | odd | 4 | ||
48.7.l.a.43.24 | yes | 48 | 8.5 | even | 2 | ||
192.7.l.a.79.14 | 48 | 8.3 | odd | 2 | |||
192.7.l.a.175.14 | 48 | 16.5 | even | 4 | |||
384.7.l.a.31.11 | 48 | 4.3 | odd | 2 | |||
384.7.l.a.223.11 | 48 | 16.13 | even | 4 | |||
384.7.l.b.31.14 | 48 | 1.1 | even | 1 | trivial | ||
384.7.l.b.223.14 | 48 | 16.3 | odd | 4 | inner |