Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,6,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.0671684673\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 33x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(4.53113i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.6.b.d.99.1 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53113i | 0.800998i | 0.916297 | + | 0.400499i | \(0.131163\pi\) | ||||
−0.916297 | + | 0.400499i | \(0.868837\pi\) | |||||||
\(3\) | 10.5934i | 0.679566i | 0.940504 | + | 0.339783i | \(0.110354\pi\) | ||||
−0.940504 | + | 0.339783i | \(0.889646\pi\) | |||||||
\(4\) | 11.4689 | 0.358402 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −48.0000 | −0.544331 | ||||||||
\(7\) | − 49.0000i | − 0.377964i | ||||||||
\(8\) | 196.963i | 1.08808i | ||||||||
\(9\) | 130.780 | 0.538190 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 90.5195 | 0.225559 | 0.112780 | − | 0.993620i | \(-0.464025\pi\) | ||||
0.112780 | + | 0.993620i | \(0.464025\pi\) | |||||||
\(12\) | 121.494i | 0.243558i | ||||||||
\(13\) | 74.8502i | 0.122838i | 0.998112 | + | 0.0614192i | \(0.0195627\pi\) | ||||
−0.998112 | + | 0.0614192i | \(0.980437\pi\) | |||||||
\(14\) | 222.025 | 0.302749 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −525.461 | −0.513146 | ||||||||
\(17\) | 1032.31i | 0.866342i | 0.901312 | + | 0.433171i | \(0.142605\pi\) | ||||
−0.901312 | + | 0.433171i | \(0.857395\pi\) | |||||||
\(18\) | 592.582i | 0.431089i | ||||||||
\(19\) | 31.6771 | 0.0201308 | 0.0100654 | − | 0.999949i | \(-0.496796\pi\) | ||||
0.0100654 | + | 0.999949i | \(0.496796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 519.076 | 0.256852 | ||||||||
\(22\) | 410.156i | 0.180672i | ||||||||
\(23\) | 3857.08i | 1.52033i | 0.649728 | + | 0.760167i | \(0.274883\pi\) | ||||
−0.649728 | + | 0.760167i | \(0.725117\pi\) | |||||||
\(24\) | −2086.51 | −0.739421 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −339.156 | −0.0983934 | ||||||||
\(27\) | 3959.60i | 1.04530i | ||||||||
\(28\) | − 561.975i | − 0.135463i | ||||||||
\(29\) | 866.917 | 0.191418 | 0.0957089 | − | 0.995409i | \(-0.469488\pi\) | ||||
0.0957089 | + | 0.995409i | \(0.469488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3526.76 | 0.659131 | 0.329566 | − | 0.944133i | \(-0.393098\pi\) | ||||
0.329566 | + | 0.944133i | \(0.393098\pi\) | |||||||
\(32\) | 3921.89i | 0.677049i | ||||||||
\(33\) | 958.908i | 0.153282i | ||||||||
\(34\) | −4677.54 | −0.693938 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1499.90 | 0.192888 | ||||||||
\(37\) | − 9531.22i | − 1.14458i | −0.820053 | − | 0.572288i | \(-0.806056\pi\) | ||||
0.820053 | − | 0.572288i | \(-0.193944\pi\) | |||||||
\(38\) | 143.533i | 0.0161247i | ||||||||
\(39\) | −792.917 | −0.0834769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14503.9 | −1.34748 | −0.673742 | − | 0.738967i | \(-0.735314\pi\) | ||||
−0.673742 | + | 0.738967i | \(0.735314\pi\) | |||||||
\(42\) | 2352.00i | 0.205738i | ||||||||
\(43\) | 9844.30i | 0.811921i | 0.913891 | + | 0.405960i | \(0.133063\pi\) | ||||
−0.913891 | + | 0.405960i | \(0.866937\pi\) | |||||||
\(44\) | 1038.16 | 0.0808409 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17476.9 | −1.21778 | ||||||||
\(47\) | − 16993.5i | − 1.12212i | −0.827775 | − | 0.561059i | \(-0.810394\pi\) | ||||
0.827775 | − | 0.561059i | \(-0.189606\pi\) | |||||||
\(48\) | − 5566.41i | − 0.348716i | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10935.7 | −0.588736 | ||||||||
\(52\) | 858.447i | 0.0440256i | ||||||||
\(53\) | 29621.1i | 1.44848i | 0.689549 | + | 0.724239i | \(0.257809\pi\) | ||||
−0.689549 | + | 0.724239i | \(0.742191\pi\) | |||||||
\(54\) | −17941.4 | −0.837285 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9651.19 | 0.411255 | ||||||||
\(57\) | 335.568i | 0.0136802i | ||||||||
\(58\) | 3928.11i | 0.153325i | ||||||||
\(59\) | −50697.4 | −1.89607 | −0.948037 | − | 0.318159i | \(-0.896935\pi\) | ||||
−0.948037 | + | 0.318159i | \(0.896935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2921.38 | −0.100522 | −0.0502612 | − | 0.998736i | \(-0.516005\pi\) | ||||
−0.0502612 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(62\) | 15980.2i | 0.527963i | ||||||||
\(63\) | − 6408.23i | − 0.203417i | ||||||||
\(64\) | −34585.3 | −1.05546 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4344.94 | −0.122779 | ||||||||
\(67\) | − 41086.2i | − 1.11817i | −0.829109 | − | 0.559086i | \(-0.811152\pi\) | ||||
0.829109 | − | 0.559086i | \(-0.188848\pi\) | |||||||
\(68\) | 11839.5i | 0.310499i | ||||||||
\(69\) | −40859.5 | −1.03317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61753.1 | 1.45383 | 0.726914 | − | 0.686729i | \(-0.240954\pi\) | ||||
0.726914 | + | 0.686729i | \(0.240954\pi\) | |||||||
\(72\) | 25758.9i | 0.585592i | ||||||||
\(73\) | 23664.5i | 0.519745i | 0.965643 | + | 0.259872i | \(0.0836805\pi\) | ||||
−0.965643 | + | 0.259872i | \(0.916320\pi\) | |||||||
\(74\) | 43187.2 | 0.916802 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 363.300 | 0.00721493 | ||||||||
\(77\) | − 4435.46i | − 0.0852533i | ||||||||
\(78\) | − 3592.81i | − 0.0668648i | ||||||||
\(79\) | −45191.5 | −0.814683 | −0.407341 | − | 0.913276i | \(-0.633544\pi\) | ||||
−0.407341 | + | 0.913276i | \(0.633544\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10166.0 | −0.172162 | ||||||||
\(82\) | − 65718.8i | − 1.07933i | ||||||||
\(83\) | − 39095.9i | − 0.622925i | −0.950259 | − | 0.311462i | \(-0.899181\pi\) | ||||
0.950259 | − | 0.311462i | \(-0.100819\pi\) | |||||||
\(84\) | 5953.22 | 0.0920563 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −44605.8 | −0.650347 | ||||||||
\(87\) | 9183.58i | 0.130081i | ||||||||
\(88\) | 17829.0i | 0.245426i | ||||||||
\(89\) | 41891.1 | 0.560592 | 0.280296 | − | 0.959914i | \(-0.409567\pi\) | ||||
0.280296 | + | 0.959914i | \(0.409567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3667.66 | 0.0464286 | ||||||||
\(92\) | 44236.3i | 0.544891i | ||||||||
\(93\) | 37360.4i | 0.447923i | ||||||||
\(94\) | 76999.9 | 0.898815 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −41546.1 | −0.460099 | ||||||||
\(97\) | 8036.53i | 0.0867240i | 0.999059 | + | 0.0433620i | \(0.0138069\pi\) | ||||
−0.999059 | + | 0.0433620i | \(0.986193\pi\) | |||||||
\(98\) | − 10879.2i | − 0.114428i | ||||||||
\(99\) | 11838.2 | 0.121394 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 124979. | 1.21908 | 0.609542 | − | 0.792754i | \(-0.291353\pi\) | ||||
0.609542 | + | 0.792754i | \(0.291353\pi\) | |||||||
\(102\) | − 49551.0i | − 0.471577i | ||||||||
\(103\) | 76635.1i | 0.711762i | 0.934531 | + | 0.355881i | \(0.115819\pi\) | ||||
−0.934531 | + | 0.355881i | \(0.884181\pi\) | |||||||
\(104\) | −14742.7 | −0.133658 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −134217. | −1.16023 | ||||||||
\(107\) | 135296.i | 1.14242i | 0.820804 | + | 0.571209i | \(0.193526\pi\) | ||||
−0.820804 | + | 0.571209i | \(0.806474\pi\) | |||||||
\(108\) | 45412.1i | 0.374638i | ||||||||
\(109\) | 199508. | 1.60840 | 0.804202 | − | 0.594356i | \(-0.202593\pi\) | ||||
0.804202 | + | 0.594356i | \(0.202593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100968. | 0.777814 | ||||||||
\(112\) | 25747.6i | 0.193951i | ||||||||
\(113\) | − 122569.i | − 0.902991i | −0.892273 | − | 0.451496i | \(-0.850891\pi\) | ||||
0.892273 | − | 0.451496i | \(-0.149109\pi\) | |||||||
\(114\) | −1520.50 | −0.0109578 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9942.56 | 0.0686046 | ||||||||
\(117\) | 9788.92i | 0.0661104i | ||||||||
\(118\) | − 229716.i | − 1.51875i | ||||||||
\(119\) | 50583.4 | 0.327446 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152857. | −0.949123 | ||||||||
\(122\) | − 13237.1i | − 0.0805183i | ||||||||
\(123\) | − 153645.i | − 0.915704i | ||||||||
\(124\) | 40448.0 | 0.236234 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29036.5 | 0.162936 | ||||||||
\(127\) | 40046.2i | 0.220319i | 0.993914 | + | 0.110160i | \(0.0351362\pi\) | ||||
−0.993914 | + | 0.110160i | \(0.964864\pi\) | |||||||
\(128\) | − 31210.2i | − 0.168373i | ||||||||
\(129\) | −104284. | −0.551754 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 211963. | 1.07915 | 0.539576 | − | 0.841937i | \(-0.318585\pi\) | ||||
0.539576 | + | 0.841937i | \(0.318585\pi\) | |||||||
\(132\) | 10997.6i | 0.0549367i | ||||||||
\(133\) | − 1552.18i | − 0.00760873i | ||||||||
\(134\) | 186167. | 0.895654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −203328. | −0.942647 | ||||||||
\(137\) | 40980.5i | 0.186542i | 0.995641 | + | 0.0932709i | \(0.0297323\pi\) | ||||
−0.995641 | + | 0.0932709i | \(0.970268\pi\) | |||||||
\(138\) | − 185140.i | − 0.827565i | ||||||||
\(139\) | 418948. | 1.83917 | 0.919587 | − | 0.392886i | \(-0.128523\pi\) | ||||
0.919587 | + | 0.392886i | \(0.128523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180019. | 0.762554 | ||||||||
\(142\) | 279811.i | 1.16451i | ||||||||
\(143\) | 6775.40i | 0.0277073i | ||||||||
\(144\) | −68719.9 | −0.276170 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −107227. | −0.416314 | ||||||||
\(147\) | − 25434.7i | − 0.0970809i | ||||||||
\(148\) | − 109312.i | − 0.410218i | ||||||||
\(149\) | 64962.7 | 0.239717 | 0.119858 | − | 0.992791i | \(-0.461756\pi\) | ||||
0.119858 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 379801. | 1.35554 | 0.677772 | − | 0.735272i | \(-0.262946\pi\) | ||||
0.677772 | + | 0.735272i | \(0.262946\pi\) | |||||||
\(152\) | 6239.22i | 0.0219039i | ||||||||
\(153\) | 135006.i | 0.466256i | ||||||||
\(154\) | 20097.6 | 0.0682878 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9093.86 | −0.0299183 | ||||||||
\(157\) | − 281546.i | − 0.911590i | −0.890085 | − | 0.455795i | \(-0.849355\pi\) | ||||
0.890085 | − | 0.455795i | \(-0.150645\pi\) | |||||||
\(158\) | − 204768.i | − 0.652559i | ||||||||
\(159\) | −313788. | −0.984337 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 188997. | 0.574632 | ||||||||
\(162\) | − 46063.3i | − 0.137901i | ||||||||
\(163\) | 382587.i | 1.12788i | 0.825817 | + | 0.563938i | \(0.190714\pi\) | ||||
−0.825817 | + | 0.563938i | \(0.809286\pi\) | |||||||
\(164\) | −166343. | −0.482941 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 177148. | 0.498961 | ||||||||
\(167\) | − 388635.i | − 1.07833i | −0.842201 | − | 0.539164i | \(-0.818740\pi\) | ||||
0.842201 | − | 0.539164i | \(-0.181260\pi\) | |||||||
\(168\) | 102239.i | 0.279475i | ||||||||
\(169\) | 365690. | 0.984911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4142.73 | 0.0108342 | ||||||||
\(172\) | 112903.i | 0.290994i | ||||||||
\(173\) | 389693.i | 0.989936i | 0.868911 | + | 0.494968i | \(0.164820\pi\) | ||||
−0.868911 | + | 0.494968i | \(0.835180\pi\) | |||||||
\(174\) | −41612.0 | −0.104195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −47564.5 | −0.115745 | ||||||||
\(177\) | − 537057.i | − 1.28851i | ||||||||
\(178\) | 189814.i | 0.449033i | ||||||||
\(179\) | 149812. | 0.349473 | 0.174737 | − | 0.984615i | \(-0.444093\pi\) | ||||
0.174737 | + | 0.984615i | \(0.444093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −821019. | −1.86276 | −0.931380 | − | 0.364049i | \(-0.881394\pi\) | ||||
−0.931380 | + | 0.364049i | \(0.881394\pi\) | |||||||
\(182\) | 16618.6i | 0.0371892i | ||||||||
\(183\) | − 30947.3i | − 0.0683117i | ||||||||
\(184\) | −759702. | −1.65424 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −169285. | −0.358786 | ||||||||
\(187\) | 93444.5i | 0.195411i | ||||||||
\(188\) | − 194897.i | − 0.402170i | ||||||||
\(189\) | 194020. | 0.395087 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 286619. | 0.568487 | 0.284244 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284244 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(192\) | − 366376.i | − 0.717255i | ||||||||
\(193\) | − 993573.i | − 1.92002i | −0.279959 | − | 0.960012i | \(-0.590321\pi\) | ||||
0.279959 | − | 0.960012i | \(-0.409679\pi\) | |||||||
\(194\) | −36414.6 | −0.0694657 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −27536.8 | −0.0512003 | ||||||||
\(197\) | − 38209.0i | − 0.0701456i | −0.999385 | − | 0.0350728i | \(-0.988834\pi\) | ||||
0.999385 | − | 0.0350728i | \(-0.0111663\pi\) | |||||||
\(198\) | 53640.2i | 0.0972361i | ||||||||
\(199\) | −730487. | −1.30761 | −0.653807 | − | 0.756661i | \(-0.726829\pi\) | ||||
−0.653807 | + | 0.756661i | \(0.726829\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 435242. | 0.759872 | ||||||||
\(202\) | 566296.i | 0.976484i | ||||||||
\(203\) | − 42478.9i | − 0.0723491i | ||||||||
\(204\) | −125420. | −0.211004 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −347244. | −0.570120 | ||||||||
\(207\) | 504429.i | 0.818228i | ||||||||
\(208\) | − 39330.9i | − 0.0630340i | ||||||||
\(209\) | 2867.39 | 0.00454069 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 194286. | 0.300424 | 0.150212 | − | 0.988654i | \(-0.452004\pi\) | ||||
0.150212 | + | 0.988654i | \(0.452004\pi\) | |||||||
\(212\) | 339721.i | 0.519138i | ||||||||
\(213\) | 654175.i | 0.987972i | ||||||||
\(214\) | −613043. | −0.915075 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −779894. | −1.13737 | ||||||||
\(217\) | − 172811.i | − 0.249128i | ||||||||
\(218\) | 903999.i | 1.28833i | ||||||||
\(219\) | −250687. | −0.353201 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −77268.8 | −0.106420 | ||||||||
\(222\) | 457499.i | 0.623028i | ||||||||
\(223\) | − 1.13569e6i | − 1.52931i | −0.644438 | − | 0.764656i | \(-0.722909\pi\) | ||||
0.644438 | − | 0.764656i | \(-0.277091\pi\) | |||||||
\(224\) | 192172. | 0.255900 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 555375. | 0.723294 | ||||||||
\(227\) | − 143806.i | − 0.185231i | −0.995702 | − | 0.0926155i | \(-0.970477\pi\) | ||||
0.995702 | − | 0.0926155i | \(-0.0295227\pi\) | |||||||
\(228\) | 3848.58i | 0.00490302i | ||||||||
\(229\) | 3832.50 | 0.00482940 | 0.00241470 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241470 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 46986.5 | 0.0579353 | ||||||||
\(232\) | 170751.i | 0.208277i | ||||||||
\(233\) | 1.35599e6i | 1.63631i | 0.574995 | + | 0.818157i | \(0.305004\pi\) | ||||
−0.574995 | + | 0.818157i | \(0.694996\pi\) | |||||||
\(234\) | −44354.8 | −0.0529543 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −581442. | −0.679557 | ||||||||
\(237\) | − 478731.i | − 0.553631i | ||||||||
\(238\) | 229200.i | 0.262284i | ||||||||
\(239\) | 478372. | 0.541716 | 0.270858 | − | 0.962619i | \(-0.412693\pi\) | ||||
0.270858 | + | 0.962619i | \(0.412693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31082e6 | −1.45379 | −0.726894 | − | 0.686750i | \(-0.759037\pi\) | ||||
−0.726894 | + | 0.686750i | \(0.759037\pi\) | |||||||
\(242\) | − 692616.i | − 0.760246i | ||||||||
\(243\) | 854490.i | 0.928307i | ||||||||
\(244\) | −33504.9 | −0.0360275 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 696185. | 0.733477 | ||||||||
\(247\) | 2371.04i | 0.00247284i | ||||||||
\(248\) | 694642.i | 0.717186i | ||||||||
\(249\) | 414157. | 0.423318 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 340113. | 0.340753 | 0.170376 | − | 0.985379i | \(-0.445502\pi\) | ||||
0.170376 | + | 0.985379i | \(0.445502\pi\) | |||||||
\(252\) | − 73495.1i | − 0.0729050i | ||||||||
\(253\) | 349141.i | 0.342925i | ||||||||
\(254\) | −181454. | −0.176475 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −965313. | −0.920594 | ||||||||
\(257\) | − 58839.6i | − 0.0555696i | −0.999614 | − | 0.0277848i | \(-0.991155\pi\) | ||||
0.999614 | − | 0.0277848i | \(-0.00884531\pi\) | |||||||
\(258\) | − 472526.i | − 0.441954i | ||||||||
\(259\) | −467030. | −0.432609 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 113376. | 0.103019 | ||||||||
\(262\) | 960433.i | 0.864398i | ||||||||
\(263\) | 1380.79i | 0.00123095i | 1.00000 | 0.000615473i | \(0.000195911\pi\) | |||||
−1.00000 | 0.000615473i | \(0.999804\pi\) | ||||||||
\(264\) | −188869. | −0.166783 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7033.11 | 0.00609458 | ||||||||
\(267\) | 443769.i | 0.380959i | ||||||||
\(268\) | − 471212.i | − 0.400756i | ||||||||
\(269\) | −886839. | −0.747247 | −0.373624 | − | 0.927580i | \(-0.621885\pi\) | ||||
−0.373624 | + | 0.927580i | \(0.621885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −376955. | −0.311793 | −0.155897 | − | 0.987773i | \(-0.549827\pi\) | ||||
−0.155897 | + | 0.987773i | \(0.549827\pi\) | |||||||
\(272\) | − 542441.i | − 0.444559i | ||||||||
\(273\) | 38852.9i | 0.0315513i | ||||||||
\(274\) | −185688. | −0.149420 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −468613. | −0.370289 | ||||||||
\(277\) | − 880363.i | − 0.689386i | −0.938716 | − | 0.344693i | \(-0.887983\pi\) | ||||
0.938716 | − | 0.344693i | \(-0.112017\pi\) | |||||||
\(278\) | 1.89831e6i | 1.47317i | ||||||||
\(279\) | 461231. | 0.354738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.08492e6 | 1.57515 | 0.787577 | − | 0.616217i | \(-0.211335\pi\) | ||||
0.787577 | + | 0.616217i | \(0.211335\pi\) | |||||||
\(282\) | 815689.i | 0.610804i | ||||||||
\(283\) | − 692401.i | − 0.513915i | −0.966423 | − | 0.256958i | \(-0.917280\pi\) | ||||
0.966423 | − | 0.256958i | \(-0.0827201\pi\) | |||||||
\(284\) | 708238. | 0.521055 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −30700.2 | −0.0221935 | ||||||||
\(287\) | 710689.i | 0.509301i | ||||||||
\(288\) | 512905.i | 0.364381i | ||||||||
\(289\) | 354186. | 0.249452 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −85134.1 | −0.0589347 | ||||||||
\(292\) | 271405.i | 0.186278i | ||||||||
\(293\) | − 2.27624e6i | − 1.54899i | −0.632580 | − | 0.774495i | \(-0.718004\pi\) | ||||
0.632580 | − | 0.774495i | \(-0.281996\pi\) | |||||||
\(294\) | 115248. | 0.0777616 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.87730e6 | 1.24539 | ||||||||
\(297\) | 358421.i | 0.235777i | ||||||||
\(298\) | 294354.i | 0.192013i | ||||||||
\(299\) | −288703. | −0.186755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 482371. | 0.306877 | ||||||||
\(302\) | 1.72093e6i | 1.08579i | ||||||||
\(303\) | 1.32395e6i | 0.828448i | ||||||||
\(304\) | −16645.1 | −0.0103300 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −611730. | −0.373470 | ||||||||
\(307\) | − 2.65187e6i | − 1.60586i | −0.596076 | − | 0.802928i | \(-0.703274\pi\) | ||||
0.596076 | − | 0.802928i | \(-0.296726\pi\) | |||||||
\(308\) | − 50869.7i | − 0.0305550i | ||||||||
\(309\) | −811825. | −0.483689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.57626e6 | 1.51039 | 0.755195 | − | 0.655501i | \(-0.227542\pi\) | ||||
0.755195 | + | 0.655501i | \(0.227542\pi\) | |||||||
\(312\) | − 156175.i | − 0.0908293i | ||||||||
\(313\) | − 2.51549e6i | − 1.45131i | −0.688057 | − | 0.725657i | \(-0.741536\pi\) | ||||
0.688057 | − | 0.725657i | \(-0.258464\pi\) | |||||||
\(314\) | 1.27572e6 | 0.730182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −518295. | −0.291984 | ||||||||
\(317\) | − 2.30397e6i | − 1.28774i | −0.765135 | − | 0.643870i | \(-0.777328\pi\) | ||||
0.765135 | − | 0.643870i | \(-0.222672\pi\) | |||||||
\(318\) | − 1.42181e6i | − 0.788452i | ||||||||
\(319\) | 78472.9 | 0.0431760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.43324e6 | −0.776349 | ||||||||
\(322\) | 856369.i | 0.460279i | ||||||||
\(323\) | 32700.7i | 0.0174402i | ||||||||
\(324\) | −116592. | −0.0617031 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.73355e6 | −0.903427 | ||||||||
\(327\) | 2.11347e6i | 1.09302i | ||||||||
\(328\) | − 2.85672e6i | − 1.46617i | ||||||||
\(329\) | −832683. | −0.424121 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 697305. | 0.349827 | 0.174913 | − | 0.984584i | \(-0.444035\pi\) | ||||
0.174913 | + | 0.984584i | \(0.444035\pi\) | |||||||
\(332\) | − 448385.i | − 0.223258i | ||||||||
\(333\) | − 1.24649e6i | − 0.615999i | ||||||||
\(334\) | 1.76096e6 | 0.863739 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −272754. | −0.131802 | ||||||||
\(337\) | − 1.14848e6i | − 0.550868i | −0.961320 | − | 0.275434i | \(-0.911178\pi\) | ||||
0.961320 | − | 0.275434i | \(-0.0888216\pi\) | |||||||
\(338\) | 1.65699e6i | 0.788911i | ||||||||
\(339\) | 1.29842e6 | 0.613642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 319241. | 0.148673 | ||||||||
\(342\) | 18771.3i | 0.00867817i | ||||||||
\(343\) | 117649.i | 0.0539949i | ||||||||
\(344\) | −1.93896e6 | −0.883433 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.76575e6 | −0.792937 | ||||||||
\(347\) | − 2.43716e6i | − 1.08658i | −0.839546 | − | 0.543289i | \(-0.817179\pi\) | ||||
0.839546 | − | 0.543289i | \(-0.182821\pi\) | |||||||
\(348\) | 105325.i | 0.0466213i | ||||||||
\(349\) | −896801. | −0.394124 | −0.197062 | − | 0.980391i | \(-0.563140\pi\) | ||||
−0.197062 | + | 0.980391i | \(0.563140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −296377. | −0.128403 | ||||||||
\(352\) | 355007.i | 0.152715i | ||||||||
\(353\) | − 4.33422e6i | − 1.85129i | −0.378396 | − | 0.925644i | \(-0.623524\pi\) | ||||
0.378396 | − | 0.925644i | \(-0.376476\pi\) | |||||||
\(354\) | 2.43347e6 | 1.03209 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 480444. | 0.200917 | ||||||||
\(357\) | 535849.i | 0.222521i | ||||||||
\(358\) | 678817.i | 0.279927i | ||||||||
\(359\) | 3.59167e6 | 1.47082 | 0.735411 | − | 0.677621i | \(-0.236989\pi\) | ||||
0.735411 | + | 0.677621i | \(0.236989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47510e6 | −0.999595 | ||||||||
\(362\) | − 3.72014e6i | − 1.49207i | ||||||||
\(363\) | − 1.61928e6i | − 0.644992i | ||||||||
\(364\) | 42063.9 | 0.0166401 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 140226. | 0.0547175 | ||||||||
\(367\) | 361791.i | 0.140215i | 0.997539 | + | 0.0701073i | \(0.0223342\pi\) | ||||
−0.997539 | + | 0.0701073i | \(0.977666\pi\) | |||||||
\(368\) | − 2.02674e6i | − 0.780152i | ||||||||
\(369\) | −1.89682e6 | −0.725202 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.45144e6 | 0.547473 | ||||||||
\(372\) | 428481.i | 0.160537i | ||||||||
\(373\) | 3.08325e6i | 1.14746i | 0.819045 | + | 0.573729i | \(0.194504\pi\) | ||||
−0.819045 | + | 0.573729i | \(0.805496\pi\) | |||||||
\(374\) | −423409. | −0.156524 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.34710e6 | 1.22095 | ||||||||
\(377\) | 64888.9i | 0.0235135i | ||||||||
\(378\) | 879131.i | 0.316464i | ||||||||
\(379\) | 5.04227e6 | 1.80313 | 0.901567 | − | 0.432639i | \(-0.142418\pi\) | ||||
0.901567 | + | 0.432639i | \(0.142418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −424225. | −0.149721 | ||||||||
\(382\) | 1.29871e6i | 0.455357i | ||||||||
\(383\) | 3.11928e6i | 1.08657i | 0.839548 | + | 0.543285i | \(0.182820\pi\) | ||||
−0.839548 | + | 0.543285i | \(0.817180\pi\) | |||||||
\(384\) | 330622. | 0.114420 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.50201e6 | 1.53794 | ||||||||
\(387\) | 1.28744e6i | 0.436968i | ||||||||
\(388\) | 92169.9i | 0.0310821i | ||||||||
\(389\) | 1.64560e6 | 0.551378 | 0.275689 | − | 0.961247i | \(-0.411094\pi\) | ||||
0.275689 | + | 0.961247i | \(0.411094\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.98171e6 | −1.31713 | ||||||||
\(392\) | − 472908.i | − 0.155440i | ||||||||
\(393\) | 2.24541e6i | 0.733355i | ||||||||
\(394\) | 173130. | 0.0561865 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 135770. | 0.0435078 | ||||||||
\(397\) | 3.72727e6i | 1.18690i | 0.804870 | + | 0.593451i | \(0.202235\pi\) | ||||
−0.804870 | + | 0.593451i | \(0.797765\pi\) | |||||||
\(398\) | − 3.30993e6i | − 1.04740i | ||||||||
\(399\) | 16442.8 | 0.00517063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.84820e6 | 1.50564 | 0.752818 | − | 0.658229i | \(-0.228694\pi\) | ||||
0.752818 | + | 0.658229i | \(0.228694\pi\) | |||||||
\(402\) | 1.97214e6i | 0.608656i | ||||||||
\(403\) | 263979.i | 0.0809667i | ||||||||
\(404\) | 1.43337e6 | 0.436923 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 192477. | 0.0579515 | ||||||||
\(407\) | − 862761.i | − 0.258169i | ||||||||
\(408\) | − 2.15393e6i | − 0.640591i | ||||||||
\(409\) | 3.03126e6 | 0.896014 | 0.448007 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448007 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −434123. | −0.126768 | ||||||||
\(412\) | 878918.i | 0.255097i | ||||||||
\(413\) | 2.48417e6i | 0.716649i | ||||||||
\(414\) | −2.28563e6 | −0.655399 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −293554. | −0.0831676 | ||||||||
\(417\) | 4.43808e6i | 1.24984i | ||||||||
\(418\) | 12992.5i | 0.00363708i | ||||||||
\(419\) | −1.66905e6 | −0.464444 | −0.232222 | − | 0.972663i | \(-0.574600\pi\) | ||||
−0.232222 | + | 0.972663i | \(0.574600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.76031e6 | −0.484043 | −0.242022 | − | 0.970271i | \(-0.577810\pi\) | ||||
−0.242022 | + | 0.970271i | \(0.577810\pi\) | |||||||
\(422\) | 880335.i | 0.240639i | ||||||||
\(423\) | − 2.22242e6i | − 0.603913i | ||||||||
\(424\) | −5.83427e6 | −1.57606 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.96415e6 | −0.791364 | ||||||||
\(427\) | 143148.i | 0.0379939i | ||||||||
\(428\) | 1.55169e6i | 0.409445i | ||||||||
\(429\) | −71774.4 | −0.0188290 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −648832. | −0.168244 | −0.0841219 | − | 0.996455i | \(-0.526809\pi\) | ||||
−0.0841219 | + | 0.996455i | \(0.526809\pi\) | |||||||
\(432\) | − 2.08061e6i | − 0.536392i | ||||||||
\(433\) | 360993.i | 0.0925293i | 0.998929 | + | 0.0462646i | \(0.0147318\pi\) | ||||
−0.998929 | + | 0.0462646i | \(0.985268\pi\) | |||||||
\(434\) | 783031. | 0.199551 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.28814e6 | 0.576455 | ||||||||
\(437\) | 122181.i | 0.0306055i | ||||||||
\(438\) | − 1.13590e6i | − 0.282913i | ||||||||
\(439\) | −1.07021e6 | −0.265038 | −0.132519 | − | 0.991180i | \(-0.542307\pi\) | ||||
−0.132519 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −314003. | −0.0768843 | ||||||||
\(442\) | − 350115.i | − 0.0852423i | ||||||||
\(443\) | 797145.i | 0.192987i | 0.995334 | + | 0.0964935i | \(0.0307627\pi\) | ||||
−0.995334 | + | 0.0964935i | \(0.969237\pi\) | |||||||
\(444\) | 1.15799e6 | 0.278770 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.14594e6 | 1.22498 | ||||||||
\(447\) | 688175.i | 0.162903i | ||||||||
\(448\) | 1.69468e6i | 0.398927i | ||||||||
\(449\) | −6.40103e6 | −1.49842 | −0.749211 | − | 0.662331i | \(-0.769567\pi\) | ||||
−0.749211 | + | 0.662331i | \(0.769567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.31288e6 | −0.303937 | ||||||||
\(452\) | − 1.40572e6i | − 0.323634i | ||||||||
\(453\) | 4.02338e6i | 0.921181i | ||||||||
\(454\) | 651605. | 0.148370 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −66094.4 | −0.0148851 | ||||||||
\(457\) | 5.91843e6i | 1.32561i | 0.748791 | + | 0.662806i | \(0.230634\pi\) | ||||
−0.748791 | + | 0.662806i | \(0.769366\pi\) | |||||||
\(458\) | 17365.5i | 0.00386834i | ||||||||
\(459\) | −4.08755e6 | −0.905588 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.84337e6 | −1.93805 | −0.969026 | − | 0.246960i | \(-0.920569\pi\) | ||||
−0.969026 | + | 0.246960i | \(0.920569\pi\) | |||||||
\(462\) | 212902.i | 0.0464060i | ||||||||
\(463\) | 6.76858e6i | 1.46739i | 0.679479 | + | 0.733695i | \(0.262206\pi\) | ||||
−0.679479 | + | 0.733695i | \(0.737794\pi\) | |||||||
\(464\) | −455531. | −0.0982252 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.14416e6 | −1.31068 | ||||||||
\(467\) | − 1.04740e6i | − 0.222239i | −0.993807 | − | 0.111120i | \(-0.964556\pi\) | ||||
0.993807 | − | 0.111120i | \(-0.0354437\pi\) | |||||||
\(468\) | 112268.i | 0.0236941i | ||||||||
\(469\) | −2.01322e6 | −0.422630 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.98252e6 | 0.619486 | ||||||||
\(472\) | − 9.98551e6i | − 2.06308i | ||||||||
\(473\) | 891101.i | 0.183136i | ||||||||
\(474\) | 2.16919e6 | 0.443457 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 580134. | 0.117358 | ||||||||
\(477\) | 3.87386e6i | 0.779556i | ||||||||
\(478\) | 2.16757e6i | 0.433913i | ||||||||
\(479\) | 9.37725e6 | 1.86740 | 0.933699 | − | 0.358060i | \(-0.116562\pi\) | ||||
0.933699 | + | 0.358060i | \(0.116562\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 713414. | 0.140598 | ||||||||
\(482\) | − 5.93950e6i | − 1.16448i | ||||||||
\(483\) | 2.00212e6i | 0.390500i | ||||||||
\(484\) | −1.75310e6 | −0.340168 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.87181e6 | −0.743572 | ||||||||
\(487\) | − 2.88960e6i | − 0.552098i | −0.961144 | − | 0.276049i | \(-0.910975\pi\) | ||||
0.961144 | − | 0.276049i | \(-0.0890251\pi\) | |||||||
\(488\) | − 575404.i | − 0.109376i | ||||||||
\(489\) | −4.05290e6 | −0.766467 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04845e6 | −0.196265 | −0.0981324 | − | 0.995173i | \(-0.531287\pi\) | ||||
−0.0981324 | + | 0.995173i | \(0.531287\pi\) | |||||||
\(492\) | − 1.76213e6i | − 0.328191i | ||||||||
\(493\) | 894930.i | 0.165833i | ||||||||
\(494\) | −10743.5 | −0.00198074 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.85318e6 | −0.338230 | ||||||||
\(497\) | − 3.02590e6i | − 0.549495i | ||||||||
\(498\) | 1.87660e6i | 0.339077i | ||||||||
\(499\) | −6.38524e6 | −1.14796 | −0.573979 | − | 0.818870i | \(-0.694601\pi\) | ||||
−0.573979 | + | 0.818870i | \(0.694601\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.11696e6 | 0.732795 | ||||||||
\(502\) | 1.54110e6i | 0.272942i | ||||||||
\(503\) | − 1.35497e6i | − 0.238787i | −0.992847 | − | 0.119394i | \(-0.961905\pi\) | ||||
0.992847 | − | 0.119394i | \(-0.0380950\pi\) | |||||||
\(504\) | 1.26218e6 | 0.221333 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.58200e6 | −0.274682 | ||||||||
\(507\) | 3.87390e6i | 0.669312i | ||||||||
\(508\) | 459285.i | 0.0789628i | ||||||||
\(509\) | −6.43410e6 | −1.10076 | −0.550381 | − | 0.834914i | \(-0.685518\pi\) | ||||
−0.550381 | + | 0.834914i | \(0.685518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.15956e6 | 0.196445 | ||||||||
\(512\) | − 5.37268e6i | − 0.905767i | ||||||||
\(513\) | 125429.i | 0.0210428i | ||||||||
\(514\) | 266610. | 0.0445111 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.19603e6 | −0.197750 | ||||||||
\(517\) | − 1.53825e6i | − 0.253104i | ||||||||
\(518\) | − 2.11617e6i | − 0.346519i | ||||||||
\(519\) | −4.12817e6 | −0.672727 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.16552e6 | 0.995120 | 0.497560 | − | 0.867430i | \(-0.334229\pi\) | ||||
0.497560 | + | 0.867430i | \(0.334229\pi\) | |||||||
\(522\) | 513719.i | 0.0825181i | ||||||||
\(523\) | − 7.12400e6i | − 1.13886i | −0.822040 | − | 0.569429i | \(-0.807164\pi\) | ||||
0.822040 | − | 0.569429i | \(-0.192836\pi\) | |||||||
\(524\) | 2.43098e6 | 0.386770 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6256.55 | −0.000985985 0 | ||||||||
\(527\) | 3.64072e6i | 0.571033i | ||||||||
\(528\) | − 503869.i | − 0.0786562i | ||||||||
\(529\) | −8.44071e6 | −1.31141 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.63021e6 | −1.02045 | ||||||||
\(532\) | − 17801.7i | − 0.00272699i | ||||||||
\(533\) | − 1.08562e6i | − 0.165523i | ||||||||
\(534\) | −2.01077e6 | −0.305148 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.09246e6 | 1.21666 | ||||||||
\(537\) | 1.58702e6i | 0.237490i | ||||||||
\(538\) | − 4.01838e6i | − 0.598544i | ||||||||
\(539\) | −217337. | −0.0322227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.51129e6 | −1.39716 | −0.698580 | − | 0.715532i | \(-0.746184\pi\) | ||||
−0.698580 | + | 0.715532i | \(0.746184\pi\) | |||||||
\(542\) | − 1.70803e6i | − 0.249746i | ||||||||
\(543\) | − 8.69737e6i | − 1.26587i | ||||||||
\(544\) | −4.04862e6 | −0.586556 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −176048. | −0.0252725 | ||||||||
\(547\) | 1.48406e6i | 0.212071i | 0.994362 | + | 0.106036i | \(0.0338158\pi\) | ||||
−0.994362 | + | 0.106036i | \(0.966184\pi\) | |||||||
\(548\) | 470001.i | 0.0668570i | ||||||||
\(549\) | −382058. | −0.0541002 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27461.4 | 0.00385340 | ||||||||
\(552\) | − 8.04782e6i | − 1.12417i | ||||||||
\(553\) | 2.21438e6i | 0.307921i | ||||||||
\(554\) | 3.98904e6 | 0.552197 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.80486e6 | 0.659164 | ||||||||
\(557\) | − 7.72192e6i | − 1.05460i | −0.849680 | − | 0.527299i | \(-0.823205\pi\) | ||||
0.849680 | − | 0.527299i | \(-0.176795\pi\) | |||||||
\(558\) | 2.08990e6i | 0.284144i | ||||||||
\(559\) | −736847. | −0.0997351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −989894. | −0.132795 | ||||||||
\(562\) | 9.44703e6i | 1.26169i | ||||||||
\(563\) | − 3.41747e6i | − 0.454395i | −0.973849 | − | 0.227198i | \(-0.927044\pi\) | ||||
0.973849 | − | 0.227198i | \(-0.0729563\pi\) | |||||||
\(564\) | 2.06461e6 | 0.273301 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.13736e6 | 0.411645 | ||||||||
\(567\) | 498133.i | 0.0650710i | ||||||||
\(568\) | 1.21631e7i | 1.58188i | ||||||||
\(569\) | 2.42117e6 | 0.313505 | 0.156752 | − | 0.987638i | \(-0.449898\pi\) | ||||
0.156752 | + | 0.987638i | \(0.449898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.31941e6 | 0.297705 | 0.148853 | − | 0.988859i | \(-0.452442\pi\) | ||||
0.148853 | + | 0.988859i | \(0.452442\pi\) | |||||||
\(572\) | 77706.2i | 0.00993037i | ||||||||
\(573\) | 3.03626e6i | 0.386325i | ||||||||
\(574\) | −3.22022e6 | −0.407949 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.52307e6 | −0.568038 | ||||||||
\(577\) | 2.56645e6i | 0.320917i | 0.987043 | + | 0.160459i | \(0.0512973\pi\) | ||||
−0.987043 | + | 0.160459i | \(0.948703\pi\) | |||||||
\(578\) | 1.60486e6i | 0.199811i | ||||||||
\(579\) | 1.05253e7 | 1.30478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.91570e6 | −0.235443 | ||||||||
\(582\) | − 385753.i | − 0.0472066i | ||||||||
\(583\) | 2.68129e6i | 0.326718i | ||||||||
\(584\) | −4.66103e6 | −0.565522 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.03139e7 | 1.24074 | ||||||||
\(587\) | 2.09851e6i | 0.251371i | 0.992070 | + | 0.125685i | \(0.0401130\pi\) | ||||
−0.992070 | + | 0.125685i | \(0.959887\pi\) | |||||||
\(588\) | − 291708.i | − 0.0347940i | ||||||||
\(589\) | 111718. | 0.0132688 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 404763. | 0.0476686 | ||||||||
\(592\) | 5.00829e6i | 0.587334i | ||||||||
\(593\) | 5.11831e6i | 0.597709i | 0.954299 | + | 0.298854i | \(0.0966045\pi\) | ||||
−0.954299 | + | 0.298854i | \(0.903396\pi\) | |||||||
\(594\) | −1.62405e6 | −0.188857 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 745048. | 0.0859150 | ||||||||
\(597\) | − 7.73833e6i | − 0.888610i | ||||||||
\(598\) | − 1.30815e6i | − 0.149591i | ||||||||
\(599\) | 2.61775e6 | 0.298099 | 0.149049 | − | 0.988830i | \(-0.452379\pi\) | ||||
0.149049 | + | 0.988830i | \(0.452379\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.49925e6 | 1.07276 | 0.536381 | − | 0.843976i | \(-0.319791\pi\) | ||||
0.536381 | + | 0.843976i | \(0.319791\pi\) | |||||||
\(602\) | 2.18568e6i | 0.245808i | ||||||||
\(603\) | − 5.37326e6i | − 0.601789i | ||||||||
\(604\) | 4.35589e6 | 0.485830 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.99899e6 | −0.663586 | ||||||||
\(607\) | 6.07366e6i | 0.669081i | 0.942381 | + | 0.334541i | \(0.108581\pi\) | ||||
−0.942381 | + | 0.334541i | \(0.891419\pi\) | |||||||
\(608\) | 124234.i | 0.0136295i | ||||||||
\(609\) | 449996. | 0.0491660 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.27197e6 | 0.137839 | ||||||||
\(612\) | 1.54837e6i | 0.167107i | ||||||||
\(613\) | 9.20907e6i | 0.989839i | 0.868939 | + | 0.494920i | \(0.164802\pi\) | ||||
−0.868939 | + | 0.494920i | \(0.835198\pi\) | |||||||
\(614\) | 1.20160e7 | 1.28629 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 873621. | 0.0927622 | ||||||||
\(617\) | 1.37224e7i | 1.45117i | 0.688133 | + | 0.725585i | \(0.258431\pi\) | ||||
−0.688133 | + | 0.725585i | \(0.741569\pi\) | |||||||
\(618\) | − 3.67848e6i | − 0.387434i | ||||||||
\(619\) | 6.80356e6 | 0.713690 | 0.356845 | − | 0.934164i | \(-0.383852\pi\) | ||||
0.356845 | + | 0.934164i | \(0.383852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52725e7 | −1.58921 | ||||||||
\(622\) | 1.16734e7i | 1.20982i | ||||||||
\(623\) | − 2.05266e6i | − 0.211884i | ||||||||
\(624\) | 416647. | 0.0428358 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.13980e7 | 1.16250 | ||||||||
\(627\) | 30375.4i | 0.00308570i | ||||||||
\(628\) | − 3.22901e6i | − 0.326716i | ||||||||
\(629\) | 9.83921e6 | 0.991593 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.80897e6 | −0.280850 | −0.140425 | − | 0.990091i | \(-0.544847\pi\) | ||||
−0.140425 | + | 0.990091i | \(0.544847\pi\) | |||||||
\(632\) | − 8.90105e6i | − 0.886438i | ||||||||
\(633\) | 2.05815e6i | 0.204158i | ||||||||
\(634\) | 1.04396e7 | 1.03148 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.59880e6 | −0.352788 | ||||||||
\(637\) | − 179715.i | − 0.0175484i | ||||||||
\(638\) | 355571.i | 0.0345839i | ||||||||
\(639\) | 8.07608e6 | 0.782435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.83494e6 | −0.368649 | −0.184325 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184325 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(642\) | − 6.49420e6i | − 0.621854i | ||||||||
\(643\) | − 1.59562e7i | − 1.52195i | −0.648779 | − | 0.760977i | \(-0.724720\pi\) | ||||
0.648779 | − | 0.760977i | \(-0.275280\pi\) | |||||||
\(644\) | 2.16758e6 | 0.205949 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −148171. | −0.0139695 | ||||||||
\(647\) | − 7.48025e6i | − 0.702514i | −0.936279 | − | 0.351257i | \(-0.885754\pi\) | ||||
0.936279 | − | 0.351257i | \(-0.114246\pi\) | |||||||
\(648\) | − 2.00232e6i | − 0.187325i | ||||||||
\(649\) | −4.58910e6 | −0.427677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.83066e6 | 0.169299 | ||||||||
\(652\) | 4.38785e6i | 0.404234i | ||||||||
\(653\) | − 2.62102e6i | − 0.240540i | −0.992741 | − | 0.120270i | \(-0.961624\pi\) | ||||
0.992741 | − | 0.120270i | \(-0.0383760\pi\) | |||||||
\(654\) | −9.57641e6 | −0.875504 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.62121e6 | 0.691456 | ||||||||
\(657\) | 3.09485e6i | 0.279721i | ||||||||
\(658\) | − 3.77299e6i | − 0.339720i | ||||||||
\(659\) | 8.01276e6 | 0.718734 | 0.359367 | − | 0.933196i | \(-0.382993\pi\) | ||||
0.359367 | + | 0.933196i | \(0.382993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.21439e6 | −0.642238 | −0.321119 | − | 0.947039i | \(-0.604059\pi\) | ||||
−0.321119 | + | 0.947039i | \(0.604059\pi\) | |||||||
\(662\) | 3.15958e6i | 0.280210i | ||||||||
\(663\) | − 818539.i | − 0.0723195i | ||||||||
\(664\) | 7.70044e6 | 0.677790 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.64803e6 | 0.493414 | ||||||||
\(667\) | 3.34377e6i | 0.291019i | ||||||||
\(668\) | − 4.45721e6i | − 0.386475i | ||||||||
\(669\) | 1.20308e7 | 1.03927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −264442. | −0.0226738 | ||||||||
\(672\) | 2.03576e6i | 0.173901i | ||||||||
\(673\) | − 1.43323e7i | − 1.21977i | −0.792488 | − | 0.609887i | \(-0.791215\pi\) | ||||
0.792488 | − | 0.609887i | \(-0.208785\pi\) | |||||||
\(674\) | 5.20390e6 | 0.441244 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.19406e6 | 0.352994 | ||||||||
\(677\) | − 4.94781e6i | − 0.414898i | −0.978246 | − | 0.207449i | \(-0.933484\pi\) | ||||
0.978246 | − | 0.207449i | \(-0.0665161\pi\) | |||||||
\(678\) | 5.88330e6i | 0.491526i | ||||||||
\(679\) | 393790. | 0.0327786 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.52340e6 | 0.125877 | ||||||||
\(682\) | 1.44652e6i | 0.119087i | ||||||||
\(683\) | − 7.77331e6i | − 0.637608i | −0.947821 | − | 0.318804i | \(-0.896719\pi\) | ||||
0.947821 | − | 0.318804i | \(-0.103281\pi\) | |||||||
\(684\) | 47512.5 | 0.00388300 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −533083. | −0.0432498 | ||||||||
\(687\) | 40599.1i | 0.00328190i | ||||||||
\(688\) | − 5.17280e6i | − 0.416634i | ||||||||
\(689\) | −2.21715e6 | −0.177929 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.69151e6 | −0.612797 | −0.306398 | − | 0.951903i | \(-0.599124\pi\) | ||||
−0.306398 | + | 0.951903i | \(0.599124\pi\) | |||||||
\(692\) | 4.46934e6i | 0.354795i | ||||||||
\(693\) | − 580070.i | − 0.0458825i | ||||||||
\(694\) | 1.10431e7 | 0.870347 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.80883e6 | −0.141538 | ||||||||
\(697\) | − 1.49725e7i | − 1.16738i | ||||||||
\(698\) | − 4.06352e6i | − 0.315692i | ||||||||
\(699\) | −1.43645e7 | −1.11198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.53139e7 | 1.17704 | 0.588521 | − | 0.808482i | \(-0.299711\pi\) | ||||
0.588521 | + | 0.808482i | \(0.299711\pi\) | |||||||
\(702\) | − 1.34292e6i | − 0.102851i | ||||||||
\(703\) | − 301921.i | − 0.0230412i | ||||||||
\(704\) | −3.13065e6 | −0.238069 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.96389e7 | 1.48288 | ||||||||
\(707\) | − 6.12397e6i | − 0.460771i | ||||||||
\(708\) | − 6.15944e6i | − 0.461804i | ||||||||
\(709\) | −1.84381e7 | −1.37753 | −0.688764 | − | 0.724986i | \(-0.741846\pi\) | ||||
−0.688764 | + | 0.724986i | \(0.741846\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.91015e6 | −0.438454 | ||||||||
\(712\) | 8.25100e6i | 0.609968i | ||||||||
\(713\) | 1.36030e7i | 1.00210i | ||||||||
\(714\) | −2.42800e6 | −0.178239 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.71817e6 | 0.125252 | ||||||||
\(717\) | 5.06758e6i | 0.368132i | ||||||||
\(718\) | 1.62743e7i | 1.17813i | ||||||||
\(719\) | 99951.2 | 0.00721051 | 0.00360525 | − | 0.999994i | \(-0.498852\pi\) | ||||
0.00360525 | + | 0.999994i | \(0.498852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.75512e6 | 0.269021 | ||||||||
\(722\) | − 1.12150e7i | − 0.800673i | ||||||||
\(723\) | − 1.38860e7i | − 0.987945i | ||||||||
\(724\) | −9.41616e6 | −0.667617 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.33715e6 | 0.516637 | ||||||||
\(727\) | 1.25198e7i | 0.878538i | 0.898356 | + | 0.439269i | \(0.144762\pi\) | ||||
−0.898356 | + | 0.439269i | \(0.855238\pi\) | |||||||
\(728\) | 722393.i | 0.0505179i | ||||||||
\(729\) | −1.15223e7 | −0.803007 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.01624e7 | −0.703401 | ||||||||
\(732\) | − 354931.i | − 0.0244831i | ||||||||
\(733\) | 1.72341e7i | 1.18476i | 0.805660 | + | 0.592378i | \(0.201811\pi\) | ||||
−0.805660 | + | 0.592378i | \(0.798189\pi\) | |||||||
\(734\) | −1.63932e6 | −0.112312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.51270e7 | −1.02934 | ||||||||
\(737\) | − 3.71910e6i | − 0.252214i | ||||||||
\(738\) | − 8.59472e6i | − 0.580886i | ||||||||
\(739\) | 1.83842e7 | 1.23832 | 0.619160 | − | 0.785265i | \(-0.287473\pi\) | ||||
0.619160 | + | 0.785265i | \(0.287473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25117.3 | −0.00168046 | ||||||||
\(742\) | 6.57664e6i | 0.438525i | ||||||||
\(743\) | − 2.79507e7i | − 1.85746i | −0.370752 | − | 0.928732i | \(-0.620900\pi\) | ||||
0.370752 | − | 0.928732i | \(-0.379100\pi\) | |||||||
\(744\) | −7.35861e6 | −0.487375 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.39706e7 | −0.919111 | ||||||||
\(747\) | − 5.11296e6i | − 0.335252i | ||||||||
\(748\) | 1.07170e6i | 0.0700358i | ||||||||
\(749\) | 6.62950e6 | 0.431794 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.70136e7 | 1.10077 | 0.550383 | − | 0.834912i | \(-0.314482\pi\) | ||||
0.550383 | + | 0.834912i | \(0.314482\pi\) | |||||||
\(752\) | 8.92944e6i | 0.575810i | ||||||||
\(753\) | 3.60295e6i | 0.231564i | ||||||||
\(754\) | −294020. | −0.0188342 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.22519e6 | 0.141600 | ||||||||
\(757\) | − 1.91600e7i | − 1.21522i | −0.794234 | − | 0.607611i | \(-0.792128\pi\) | ||||
0.794234 | − | 0.607611i | \(-0.207872\pi\) | |||||||
\(758\) | 2.28472e7i | 1.44431i | ||||||||
\(759\) | −3.69858e6 | −0.233040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.06404e7 | −1.29198 | −0.645992 | − | 0.763344i | \(-0.723556\pi\) | ||||
−0.645992 | + | 0.763344i | \(0.723556\pi\) | |||||||
\(762\) | − 1.92222e6i | − 0.119926i | ||||||||
\(763\) | − 9.77592e6i | − 0.607919i | ||||||||
\(764\) | 3.28719e6 | 0.203747 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.41339e7 | −0.870341 | ||||||||
\(767\) | − 3.79471e6i | − 0.232911i | ||||||||
\(768\) | − 1.02259e7i | − 0.625605i | ||||||||
\(769\) | −1.11748e7 | −0.681432 | −0.340716 | − | 0.940166i | \(-0.610669\pi\) | ||||
−0.340716 | + | 0.940166i | \(0.610669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 623311. | 0.0377632 | ||||||||
\(772\) | − 1.13952e7i | − 0.688141i | ||||||||
\(773\) | 3.07555e7i | 1.85129i | 0.378394 | + | 0.925645i | \(0.376477\pi\) | ||||
−0.378394 | + | 0.925645i | \(0.623523\pi\) | |||||||
\(774\) | −5.83355e6 | −0.350010 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.58290e6 | −0.0943624 | ||||||||
\(777\) | − 4.94743e6i | − 0.293986i | ||||||||
\(778\) | 7.45641e6i | 0.441653i | ||||||||
\(779\) | −459440. | −0.0271259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.58986e6 | 0.327924 | ||||||||
\(782\) | − 1.80417e7i | − 1.05502i | ||||||||
\(783\) | 3.43264e6i | 0.200089i | ||||||||
\(784\) | 1.26163e6 | 0.0733065 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.01742e7 | −0.587416 | ||||||||
\(787\) | 3.52357e6i | 0.202790i | 0.994846 | + | 0.101395i | \(0.0323305\pi\) | ||||
−0.994846 | + | 0.101395i | \(0.967669\pi\) | |||||||
\(788\) | − 438214.i | − 0.0251403i | ||||||||
\(789\) | −14627.3 | −0.000836509 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00587e6 | −0.341299 | ||||||||
\(792\) | 2.33168e6i | 0.132086i | ||||||||
\(793\) | − 218666.i | − 0.0123480i | ||||||||
\(794\) | −1.68887e7 | −0.950706 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.37786e6 | −0.468652 | ||||||||
\(797\) | − 3.57469e6i | − 0.199339i | −0.995021 | − | 0.0996695i | \(-0.968221\pi\) | ||||
0.995021 | − | 0.0996695i | \(-0.0317785\pi\) | |||||||
\(798\) | 74504.5i | 0.00414167i | ||||||||
\(799\) | 1.75426e7 | 0.972139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.47853e6 | 0.301705 | ||||||||
\(802\) | 2.19678e7i | 1.20601i | ||||||||
\(803\) | 2.14210e6i | 0.117233i | ||||||||
\(804\) | 4.99173e6 | 0.272340 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.19612e6 | −0.0648542 | ||||||||
\(807\) | − 9.39463e6i | − 0.507804i | ||||||||
\(808\) | 2.46163e7i | 1.32646i | ||||||||
\(809\) | −3.38466e7 | −1.81821 | −0.909104 | − | 0.416569i | \(-0.863233\pi\) | ||||
−0.909104 | + | 0.416569i | \(0.863233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.21058e7 | 1.71408 | 0.857042 | − | 0.515247i | \(-0.172300\pi\) | ||||
0.857042 | + | 0.515247i | \(0.172300\pi\) | |||||||
\(812\) | − 487185.i | − 0.0259301i | ||||||||
\(813\) | − 3.99323e6i | − 0.211884i | ||||||||
\(814\) | 3.90928e6 | 0.206793 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.74628e6 | 0.302108 | ||||||||
\(817\) | 311839.i | 0.0163446i | ||||||||
\(818\) | 1.37350e7i | 0.717706i | ||||||||
\(819\) | 479657. | 0.0249874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.04076e6 | 0.157443 | 0.0787216 | − | 0.996897i | \(-0.474916\pi\) | ||||
0.0787216 | + | 0.996897i | \(0.474916\pi\) | |||||||
\(822\) | − 1.96707e6i | − 0.101541i | ||||||||
\(823\) | − 3.72147e6i | − 0.191520i | −0.995404 | − | 0.0957601i | \(-0.969472\pi\) | ||||
0.995404 | − | 0.0957601i | \(-0.0305282\pi\) | |||||||
\(824\) | −1.50943e7 | −0.774452 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.12561e7 | −0.574034 | ||||||||
\(827\) | − 8.77895e6i | − 0.446354i | −0.974778 | − | 0.223177i | \(-0.928357\pi\) | ||||
0.974778 | − | 0.223177i | \(-0.0716427\pi\) | |||||||
\(828\) | 5.78523e6i | 0.293255i | ||||||||
\(829\) | −6.61553e6 | −0.334332 | −0.167166 | − | 0.985929i | \(-0.553462\pi\) | ||||
−0.167166 | + | 0.985929i | \(0.553462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.32602e6 | 0.468483 | ||||||||
\(832\) | − 2.58872e6i | − 0.129651i | ||||||||
\(833\) | − 2.47858e6i | − 0.123763i | ||||||||
\(834\) | −2.01095e7 | −1.00112 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32885.8 | 0.00162739 | ||||||||
\(837\) | 1.39646e7i | 0.688991i | ||||||||
\(838\) | − 7.56267e6i | − 0.372019i | ||||||||
\(839\) | 4.67110e6 | 0.229094 | 0.114547 | − | 0.993418i | \(-0.463458\pi\) | ||||
0.114547 | + | 0.993418i | \(0.463458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.97596e7 | −0.963359 | ||||||||
\(842\) | − 7.97619e6i | − 0.387718i | ||||||||
\(843\) | 2.20863e7i | 1.07042i | ||||||||
\(844\) | 2.22824e6 | 0.107673 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.00701e7 | 0.483733 | ||||||||
\(847\) | 7.49000e6i | 0.358735i | ||||||||
\(848\) | − 1.55648e7i | − 0.743280i | ||||||||
\(849\) | 7.33487e6 | 0.349239 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.67627e7 | 1.74014 | ||||||||
\(852\) | 7.50264e6i | 0.354091i | ||||||||
\(853\) | 3.66146e7i | 1.72299i | 0.507768 | + | 0.861494i | \(0.330471\pi\) | ||||
−0.507768 | + | 0.861494i | \(0.669529\pi\) | |||||||
\(854\) | −648620. | −0.0304331 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.66483e7 | −1.24304 | ||||||||
\(857\) | 1.15520e7i | 0.537288i | 0.963240 | + | 0.268644i | \(0.0865755\pi\) | ||||
−0.963240 | + | 0.268644i | \(0.913425\pi\) | |||||||
\(858\) | − 325219.i | − 0.0150820i | ||||||||
\(859\) | −3.53878e7 | −1.63633 | −0.818165 | − | 0.574983i | \(-0.805009\pi\) | ||||
−0.818165 | + | 0.574983i | \(0.805009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.52860e6 | −0.346104 | ||||||||
\(862\) | − 2.93994e6i | − 0.134763i | ||||||||
\(863\) | − 1.07433e7i | − 0.491034i | −0.969392 | − | 0.245517i | \(-0.921042\pi\) | ||||
0.969392 | − | 0.245517i | \(-0.0789577\pi\) | |||||||
\(864\) | −1.55291e7 | −0.707720 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.63571e6 | −0.0741158 | ||||||||
\(867\) | 3.75203e6i | 0.169519i | ||||||||
\(868\) | − 1.98195e6i | − 0.0892881i | ||||||||
\(869\) | −4.09071e6 | −0.183759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.07531e6 | 0.137355 | ||||||||
\(872\) | 3.92958e7i | 1.75007i | ||||||||
\(873\) | 1.05102e6i | 0.0466740i | ||||||||
\(874\) | −553618. | −0.0245150 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.87510e6 | −0.126588 | ||||||||
\(877\) | 4.58293e6i | 0.201208i | 0.994927 | + | 0.100604i | \(0.0320775\pi\) | ||||
−0.994927 | + | 0.100604i | \(0.967923\pi\) | |||||||
\(878\) | − 4.84927e6i | − 0.212295i | ||||||||
\(879\) | 2.41131e7 | 1.05264 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.68070e7 | 0.729543 | 0.364772 | − | 0.931097i | \(-0.381147\pi\) | ||||
0.364772 | + | 0.931097i | \(0.381147\pi\) | |||||||
\(882\) | − 1.42279e6i | − 0.0615842i | ||||||||
\(883\) | 5.28260e6i | 0.228006i | 0.993480 | + | 0.114003i | \(0.0363673\pi\) | ||||
−0.993480 | + | 0.114003i | \(0.963633\pi\) | |||||||
\(884\) | −886186. | −0.0381412 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.61197e6 | −0.154582 | ||||||||
\(887\) | 4.43107e7i | 1.89104i | 0.325569 | + | 0.945518i | \(0.394444\pi\) | ||||
−0.325569 | + | 0.945518i | \(0.605556\pi\) | |||||||
\(888\) | 1.98870e7i | 0.846322i | ||||||||
\(889\) | 1.96226e6 | 0.0832728 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −920219. | −0.0388326 | ||||||||
\(892\) | − 1.30250e7i | − 0.548109i | ||||||||
\(893\) | − 538305.i | − 0.0225892i | ||||||||
\(894\) | −3.11821e6 | −0.130485 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.52930e6 | −0.0636389 | ||||||||
\(897\) | − 3.05834e6i | − 0.126913i | ||||||||
\(898\) | − 2.90039e7i | − 1.20023i | ||||||||
\(899\) | 3.05741e6 | 0.126170 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.05783e7 | −1.25488 | ||||||||
\(902\) | − 5.94883e6i | − 0.243453i | ||||||||
\(903\) | 5.10994e6i | 0.208543i | ||||||||
\(904\) | 2.41415e7 | 0.982524 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.82304e7 | −0.737865 | ||||||||
\(907\) | − 3.95608e7i | − 1.59679i | −0.602135 | − | 0.798394i | \(-0.705683\pi\) | ||||
0.602135 | − | 0.798394i | \(-0.294317\pi\) | |||||||
\(908\) | − 1.64930e6i | − 0.0663872i | ||||||||
\(909\) | 1.63448e7 | 0.656099 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.40982e7 | −0.962030 | −0.481015 | − | 0.876712i | \(-0.659732\pi\) | ||||
−0.481015 | + | 0.876712i | \(0.659732\pi\) | |||||||
\(912\) | − 176328.i | − 0.00701994i | ||||||||
\(913\) | − 3.53894e6i | − 0.140506i | ||||||||
\(914\) | −2.68172e7 | −1.06181 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43954.4 | 0.00173087 | ||||||||
\(917\) | − 1.03862e7i | − 0.407881i | ||||||||
\(918\) | − 1.85212e7i | − 0.725375i | ||||||||
\(919\) | 2.24660e7 | 0.877480 | 0.438740 | − | 0.898614i | \(-0.355425\pi\) | ||||
0.438740 | + | 0.898614i | \(0.355425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.80923e7 | 1.09129 | ||||||||
\(922\) | − 4.00704e7i | − 1.55238i | ||||||||
\(923\) | 4.62223e6i | 0.178586i | ||||||||
\(924\) | 538882. | 0.0207641 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.06693e7 | −1.17538 | ||||||||
\(927\) | 1.00224e7i | 0.383063i | ||||||||
\(928\) | 3.39995e6i | 0.129599i | ||||||||
\(929\) | 1.16280e7 | 0.442043 | 0.221021 | − | 0.975269i | \(-0.429061\pi\) | ||||
0.221021 | + | 0.975269i | \(0.429061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −76056.7 | −0.00287583 | ||||||||
\(932\) | 1.55517e7i | 0.586458i | ||||||||
\(933\) | 2.72913e7i | 1.02641i | ||||||||
\(934\) | 4.74591e6 | 0.178013 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.92806e6 | −0.0719333 | ||||||||
\(937\) | − 2.40956e7i | − 0.896580i | −0.893888 | − | 0.448290i | \(-0.852033\pi\) | ||||
0.893888 | − | 0.448290i | \(-0.147967\pi\) | |||||||
\(938\) | − 9.12218e6i | − 0.338525i | ||||||||
\(939\) | 2.66475e7 | 0.986264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −567590. | −0.0208959 | −0.0104479 | − | 0.999945i | \(-0.503326\pi\) | ||||
−0.0104479 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(942\) | 1.35142e7i | 0.496207i | ||||||||
\(943\) | − 5.59425e7i | − 2.04863i | ||||||||
\(944\) | 2.66395e7 | 0.972962 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.03769e6 | −0.146692 | ||||||||
\(947\) | 9.04501e6i | 0.327743i | 0.986482 | + | 0.163872i | \(0.0523983\pi\) | ||||
−0.986482 | + | 0.163872i | \(0.947602\pi\) | |||||||
\(948\) | − 5.49050e6i | − 0.198423i | ||||||||
\(949\) | −1.77129e6 | −0.0638446 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.44068e7 | 0.875105 | ||||||||
\(952\) | 9.96305e6i | 0.356287i | ||||||||
\(953\) | 1.48053e7i | 0.528063i | 0.964514 | + | 0.264032i | \(0.0850524\pi\) | ||||
−0.964514 | + | 0.264032i | \(0.914948\pi\) | |||||||
\(954\) | −1.75529e7 | −0.624423 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.48639e6 | 0.194152 | ||||||||
\(957\) | 831294.i | 0.0293410i | ||||||||
\(958\) | 4.24895e7i | 1.49578i | ||||||||
\(959\) | 2.00805e6 | 0.0705062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.61911e7 | −0.565546 | ||||||||
\(962\) | 3.23257e6i | 0.112619i | ||||||||
\(963\) | 1.76940e7i | 0.614838i | ||||||||
\(964\) | −1.50336e7 | −0.521041 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.07185e6 | −0.312790 | ||||||||
\(967\) | − 2.02304e7i | − 0.695726i | −0.937545 | − | 0.347863i | \(-0.886907\pi\) | ||||
0.937545 | − | 0.347863i | \(-0.113093\pi\) | |||||||
\(968\) | − 3.01072e7i | − 1.03272i | ||||||||
\(969\) | −346411. | −0.0118517 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −255216. | −0.00868679 | −0.00434340 | − | 0.999991i | \(-0.501383\pi\) | ||||
−0.00434340 | + | 0.999991i | \(0.501383\pi\) | |||||||
\(972\) | 9.80004e6i | 0.332707i | ||||||||
\(973\) | − 2.05284e7i | − 0.695142i | ||||||||
\(974\) | 1.30932e7 | 0.442229 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.53507e6 | 0.0515827 | ||||||||
\(977\) | 3.15610e7i | 1.05783i | 0.848675 | + | 0.528914i | \(0.177401\pi\) | ||||
−0.848675 | + | 0.528914i | \(0.822599\pi\) | |||||||
\(978\) | − 1.83642e7i | − 0.613938i | ||||||||
\(979\) | 3.79196e6 | 0.126447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.60917e7 | 0.865627 | ||||||||
\(982\) | − 4.75064e6i | − 0.157208i | ||||||||
\(983\) | 5.24054e7i | 1.72978i | 0.501958 | + | 0.864892i | \(0.332613\pi\) | ||||
−0.501958 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(984\) | 3.02624e7 | 0.996357 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.05504e6 | −0.132832 | ||||||||
\(987\) | − 8.82093e6i | − 0.288218i | ||||||||
\(988\) | 27193.1i | 0 0.000886270i | ||||||||
\(989\) | −3.79702e7 | −1.23439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.73103e7 | 1.20683 | 0.603413 | − | 0.797429i | \(-0.293807\pi\) | ||||
0.603413 | + | 0.797429i | \(0.293807\pi\) | |||||||
\(992\) | 1.38316e7i | 0.446264i | ||||||||
\(993\) | 7.38682e6i | 0.237730i | ||||||||
\(994\) | 1.37108e7 | 0.440145 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.74992e6 | 0.151718 | ||||||||
\(997\) | − 2.27918e7i | − 0.726174i | −0.931755 | − | 0.363087i | \(-0.881723\pi\) | ||||
0.931755 | − | 0.363087i | \(-0.118277\pi\) | |||||||
\(998\) | − 2.89323e7i | − 0.919512i | ||||||||
\(999\) | 3.77398e7 | 1.19643 |
(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 | 175.6.b.d.99.4 | 4 | ||
5.2 | odd | 4 | 175.6.a.d.1.1 | 2 | |||
5.3 | odd | 4 | 35.6.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 175.6.b.d.99.1 | 4 | ||
15.8 | even | 4 | 315.6.a.c.1.1 | 2 | |||
20.3 | even | 4 | 560.6.a.l.1.2 | 2 | |||
35.13 | even | 4 | 245.6.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
175.6.a.d.1.1 | 2 | 5.2 | odd | 4 | |||
175.6.b.d.99.1 | 4 | 5.4 | even | 2 | inner | ||
175.6.b.d.99.4 | 4 | 1.1 | even | 1 | trivial | ||
245.6.a.c.1.2 | 2 | 35.13 | even | 4 | |||
315.6.a.c.1.1 | 2 | 15.8 | even | 4 | |||
560.6.a.l.1.2 | 2 | 20.3 | even | 4 |