Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), 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: | \(51.9643576194\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 11x^{2} + 10x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(1.85078 + 3.20565i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.6.e.f.109.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −28.8141 | − | 49.9074i | −0.515442 | − | 0.892771i | −0.999839 | − | 0.0179231i | \(-0.994295\pi\) |
0.484398 | − | 0.874848i | \(-0.339039\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −78.4422 | + | 135.866i | −0.605068 | + | 1.04801i | 0.386972 | + | 0.922091i | \(0.373521\pi\) |
−0.992041 | + | 0.125918i | \(0.959812\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 109.012 | − | 188.815i | 0.271640 | − | 0.470495i | −0.697642 | − | 0.716447i | \(-0.745767\pi\) |
0.969282 | + | 0.245952i | \(0.0791005\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 293.769 | + | 508.822i | 0.482111 | + | 0.835041i | 0.999789 | − | 0.0205346i | \(-0.00653681\pi\) |
−0.517678 | + | 0.855576i | \(0.673203\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2124.56 | 1.78298 | 0.891491 | − | 0.453038i | \(-0.149660\pi\) | ||||
0.891491 | + | 0.453038i | \(0.149660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.7687 | 0.0189180 | 0.00945902 | − | 0.999955i | \(-0.496989\pi\) | ||||
0.00945902 | + | 0.999955i | \(0.496989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1585.74 | − | 2746.59i | −0.625048 | − | 1.08262i | −0.988532 | − | 0.151014i | \(-0.951746\pi\) |
0.363483 | − | 0.931601i | \(-0.381587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.0000 | + | 169.741i | −0.0313600 | + | 0.0543171i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1821.07 | + | 3154.18i | −0.402097 | + | 0.696452i | −0.993979 | − | 0.109573i | \(-0.965052\pi\) |
0.591882 | + | 0.806025i | \(0.298385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3165.94 | − | 5483.57i | −0.591696 | − | 1.02485i | −0.994004 | − | 0.109343i | \(-0.965125\pi\) |
0.402309 | − | 0.915504i | \(-0.368208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9040.95 | 1.24751 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8435.69 | −1.01302 | −0.506508 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506508 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5073.22 | − | 8787.07i | −0.471328 | − | 0.816365i | 0.528134 | − | 0.849161i | \(-0.322892\pi\) |
−0.999462 | + | 0.0327965i | \(0.989559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3427.88 | − | 5937.26i | 0.282718 | − | 0.489683i | −0.689335 | − | 0.724443i | \(-0.742097\pi\) |
0.972053 | + | 0.234760i | \(0.0754305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12223.9 | + | 21172.4i | −0.807171 | + | 1.39806i | 0.107645 | + | 0.994189i | \(0.465669\pi\) |
−0.914816 | + | 0.403872i | \(0.867664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3902.85 | − | 6759.94i | −0.232216 | − | 0.402209i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −25483.2 | −1.24613 | −0.623066 | − | 0.782169i | \(-0.714113\pi\) | ||||
−0.623066 | + | 0.782169i | \(0.714113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12564.4 | −0.560059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10348.1 | + | 17923.4i | 0.387017 | + | 0.670333i | 0.992047 | − | 0.125870i | \(-0.0401721\pi\) |
−0.605030 | + | 0.796203i | \(0.706839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22790.1 | + | 39473.7i | −0.784191 | + | 1.35826i | 0.145290 | + | 0.989389i | \(0.453589\pi\) |
−0.929481 | + | 0.368870i | \(0.879745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16929.3 | − | 29322.5i | 0.497000 | − | 0.860830i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9549.67 | − | 16540.5i | −0.259897 | − | 0.450155i | 0.706317 | − | 0.707896i | \(-0.250355\pi\) |
−0.966214 | + | 0.257741i | \(0.917022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23055.0 | 0.542773 | 0.271387 | − | 0.962470i | \(-0.412518\pi\) | ||||
0.271387 | + | 0.962470i | \(0.412518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −89651.6 | −1.96902 | −0.984511 | − | 0.175320i | \(-0.943904\pi\) | ||||
−0.984511 | + | 0.175320i | \(0.943904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17102.4 | + | 29622.1i | 0.328722 | + | 0.569364i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17011.8 | − | 29465.3i | 0.306678 | − | 0.531182i | −0.670955 | − | 0.741498i | \(-0.734116\pi\) |
0.977634 | + | 0.210316i | \(0.0674492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 54248.7 | − | 93961.6i | 0.864359 | − | 1.49711i | −0.00332246 | − | 0.999994i | \(-0.501058\pi\) |
0.867682 | − | 0.497120i | \(-0.165609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −61217.3 | − | 106031.i | −0.919023 | − | 1.59180i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −110055. | −1.47277 | −0.736384 | − | 0.676564i | \(-0.763468\pi\) | ||||
−0.736384 | + | 0.676564i | \(0.763468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −92175.4 | −1.16684 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −857.757 | − | 1485.68i | −0.00975114 | − | 0.0168895i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14416.0 | − | 24969.2i | 0.155566 | − | 0.269448i | −0.777699 | − | 0.628637i | \(-0.783613\pi\) |
0.933265 | + | 0.359189i | \(0.116947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20145.2 | − | 34892.5i | 0.196502 | − | 0.340352i | −0.750890 | − | 0.660428i | \(-0.770375\pi\) |
0.947392 | + | 0.320076i | \(0.103708\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −102274. | − | 177143.i | −0.949885 | − | 1.64525i | −0.745662 | − | 0.666324i | \(-0.767867\pi\) |
−0.204223 | − | 0.978924i | \(-0.565467\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 164042. | 1.38515 | 0.692573 | − | 0.721348i | \(-0.256477\pi\) | ||||
0.692573 | + | 0.721348i | \(0.256477\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −131554. | −1.06057 | −0.530285 | − | 0.847819i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847819i | \(0.677915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 47161.0 | + | 81685.2i | 0.347446 | + | 0.601793i | 0.985795 | − | 0.167953i | \(-0.0537158\pi\) |
−0.638349 | + | 0.769747i | \(0.720382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −91383.4 | + | 158281.i | −0.644352 | + | 1.11605i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −166655. | + | 288655.i | −1.07883 | + | 1.86858i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56758.1 | + | 98307.8i | 0.352423 | + | 0.610414i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −168793. | −0.966226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −303144. | −1.66778 | −0.833891 | − | 0.551929i | \(-0.813892\pi\) | ||||
−0.833891 | + | 0.551929i | \(0.813892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −158286. | − | 274160.i | −0.805871 | − | 1.39581i | −0.915701 | − | 0.401859i | \(-0.868364\pi\) |
0.109830 | − | 0.993950i | \(-0.464969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2335.12 | + | 4044.55i | −0.0114467 | + | 0.0198263i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 491.479 | − | 851.266i | 0.00223719 | − | 0.00387493i | −0.864905 | − | 0.501936i | \(-0.832621\pi\) |
0.867142 | + | 0.498061i | \(0.165955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38766.9 | − | 67146.3i | −0.170186 | − | 0.294771i | 0.768299 | − | 0.640091i | \(-0.221104\pi\) |
−0.938485 | + | 0.345320i | \(0.887770\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 128098. | 0.523844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 209889. | 0.829030 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −59604.6 | − | 103238.i | −0.219945 | − | 0.380956i | 0.734846 | − | 0.678234i | \(-0.237255\pi\) |
−0.954791 | + | 0.297278i | \(0.903921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29784.4 | − | 51588.1i | 0.106303 | − | 0.184123i | −0.807967 | − | 0.589228i | \(-0.799432\pi\) |
0.914270 | + | 0.405105i | \(0.132765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −182447. | + | 316008.i | −0.609969 | + | 1.05650i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −148781. | − | 257696.i | −0.481723 | − | 0.834368i | 0.518057 | − | 0.855346i | \(-0.326655\pi\) |
−0.999780 | + | 0.0209776i | \(0.993322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 497557. | 1.51279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −98681.9 | −0.290917 | −0.145458 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145458 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9276.51 | + | 16067.4i | 0.0257391 | + | 0.0445814i | 0.878608 | − | 0.477544i | \(-0.158473\pi\) |
−0.852869 | + | 0.522125i | \(0.825139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13046.4 | − | 22597.0i | 0.0351377 | − | 0.0608603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 248326. | − | 430113.i | 0.630822 | − | 1.09262i | −0.356561 | − | 0.934272i | \(-0.616051\pi\) |
0.987384 | − | 0.158345i | \(-0.0506157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15374.7 | − | 26629.7i | −0.0379499 | − | 0.0657311i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −150072. | −0.350080 | −0.175040 | − | 0.984561i | \(-0.556005\pi\) | ||||
−0.175040 | + | 0.984561i | \(0.556005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −73515.6 | −0.166795 | −0.0833976 | − | 0.996516i | \(-0.526577\pi\) | ||||
−0.0833976 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 243066. | + | 421003.i | 0.522150 | + | 0.904391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 231604. | − | 401150.i | 0.484330 | − | 0.838885i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 299659. | − | 519025.i | 0.594353 | − | 1.02945i | −0.399285 | − | 0.916827i | \(-0.630742\pi\) |
0.993638 | − | 0.112622i | \(-0.0359251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 361873. | + | 626783.i | 0.699299 | + | 1.21122i | 0.968710 | + | 0.248196i | \(0.0798378\pi\) |
−0.269411 | + | 0.963025i | \(0.586829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −416589. | −0.764790 | −0.382395 | − | 0.923999i | \(-0.624901\pi\) | ||||
−0.382395 | + | 0.923999i | \(0.624901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 688177. | 1.23188 | 0.615938 | − | 0.787794i | \(-0.288777\pi\) | ||||
0.615938 | + | 0.787794i | \(0.288777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −285697. | − | 494841.i | −0.486592 | − | 0.842802i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −292360. | + | 506382.i | −0.485885 | + | 0.841577i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3245.16 | − | 5620.78i | 0.00513890 | − | 0.00890084i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 160937. | + | 278751.i | 0.248857 | + | 0.431033i | 0.963209 | − | 0.268753i | \(-0.0866117\pi\) |
−0.714352 | + | 0.699787i | \(0.753278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −395084. | −0.582899 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 993373. | 1.43207 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 624130. | + | 1.08102e6i | 0.859596 | + | 1.48886i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 177237. | − | 306983.i | 0.238667 | − | 0.413383i | −0.721665 | − | 0.692242i | \(-0.756623\pi\) |
0.960332 | + | 0.278859i | \(0.0899563\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 113261. | − | 196174.i | 0.145887 | − | 0.252684i | −0.783816 | − | 0.620993i | \(-0.786730\pi\) |
0.929704 | + | 0.368309i | \(0.120063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 727154. | + | 1.25947e6i | 0.916299 | + | 1.58708i | 0.804988 | + | 0.593292i | \(0.202172\pi\) |
0.111312 | + | 0.993786i | \(0.464495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −423642. | −0.511221 | −0.255611 | − | 0.966780i | \(-0.582277\pi\) | ||||
−0.255611 | + | 0.966780i | \(0.582277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.40888e6 | 1.66420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 373526. | + | 646966.i | 0.422986 | + | 0.732633i | 0.996230 | − | 0.0867515i | \(-0.0276486\pi\) |
−0.573244 | + | 0.819385i | \(0.694315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −305937. | + | 529899.i | −0.339305 | + | 0.587693i | −0.984302 | − | 0.176492i | \(-0.943525\pi\) |
0.644998 | + | 0.764185i | \(0.276858\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −224914. | + | 389562.i | −0.239387 | + | 0.414631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8745.12 | + | 15147.0i | 0.00912059 | + | 0.0157973i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −985152. | −0.987004 | −0.493502 | − | 0.869745i | \(-0.664283\pi\) | ||||
−0.493502 | + | 0.869745i | \(0.664283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −691463. | −0.679153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −693891. | − | 1.20185e6i | −0.655327 | − | 1.13506i | −0.981812 | − | 0.189857i | \(-0.939197\pi\) |
0.326485 | − | 0.945203i | \(-0.394136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 661714. | − | 1.14612e6i | 0.612944 | − | 1.06165i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −438768. | + | 759968.i | −0.391152 | + | 0.677495i | −0.992602 | − | 0.121415i | \(-0.961257\pi\) |
0.601450 | + | 0.798911i | \(0.294590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 734274. | + | 1.27180e6i | 0.642308 | + | 1.11251i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 911089. | 0.767680 | 0.383840 | − | 0.923400i | \(-0.374601\pi\) | ||||
0.383840 | + | 0.923400i | \(0.374601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 620129. | 0.512931 | 0.256465 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256465 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21366.4 | + | 37007.8i | 0.0170373 | + | 0.0295095i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 118364. | − | 205012.i | 0.0926871 | − | 0.160539i | −0.815954 | − | 0.578117i | \(-0.803788\pi\) |
0.908641 | + | 0.417578i | \(0.137121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −538457. | + | 932636.i | −0.406804 | + | 0.704606i | −0.994530 | − | 0.104455i | \(-0.966690\pi\) |
0.587725 | + | 0.809061i | \(0.300024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.02658e6 | − | 1.77809e6i | −0.761953 | − | 1.31974i | −0.941843 | − | 0.336054i | \(-0.890908\pi\) |
0.179890 | − | 0.983687i | \(-0.442426\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.59182e6 | 1.14074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.09391e6 | 2.17903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.06433e6 | − | 1.84347e6i | −0.724280 | − | 1.25449i | −0.959270 | − | 0.282492i | \(-0.908839\pi\) |
0.234990 | − | 0.971998i | \(-0.424494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 596341. | − | 1.03289e6i | 0.398969 | − | 0.691035i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 931684. | − | 1.61372e6i | 0.602685 | − | 1.04388i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 537780. | + | 931463.i | 0.342128 | + | 0.592583i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.62670e6 | 1.61682 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.54154e6 | −0.933489 | −0.466744 | − | 0.884392i | \(-0.654573\pi\) | ||||
−0.466744 | + | 0.884392i | \(0.654573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 868197. | + | 1.50376e6i | 0.508999 | + | 0.881612i | 0.999946 | + | 0.0104227i | \(0.00331772\pi\) |
−0.490946 | + | 0.871190i | \(0.663349\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.13707e6 | + | 1.96946e6i | −0.656034 | + | 1.13628i | 0.325600 | + | 0.945508i | \(0.394434\pi\) |
−0.981634 | + | 0.190776i | \(0.938900\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 158418. | − | 274388.i | 0.0885435 | − | 0.153362i | −0.818352 | − | 0.574717i | \(-0.805112\pi\) |
0.906896 | + | 0.421355i | \(0.138445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 397038. | + | 687690.i | 0.218452 | + | 0.378369i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 63245.5 | 0.0337305 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −115157. | −0.0604760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.91774e6 | − | 3.32162e6i | −0.976787 | − | 1.69185i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 224396. | − | 388664.i | 0.112576 | − | 0.194987i | −0.804232 | − | 0.594315i | \(-0.797423\pi\) |
0.916808 | + | 0.399328i | \(0.130757\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −550330. | + | 953199.i | −0.267924 | + | 0.464057i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 929347. | + | 1.60968e6i | 0.445762 | + | 0.772083i | 0.998105 | − | 0.0615344i | \(-0.0195994\pi\) |
−0.552343 | + | 0.833617i | \(0.686266\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.38051e6 | −0.642914 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.41216e6 | −0.648111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 111822. | + | 193681.i | 0.0498542 | + | 0.0863500i | 0.889876 | − | 0.456203i | \(-0.150791\pi\) |
−0.840021 | + | 0.542553i | \(0.817458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −669904. | + | 1.16031e6i | −0.294407 | + | 0.509929i | −0.974847 | − | 0.222876i | \(-0.928456\pi\) |
0.680439 | + | 0.732804i | \(0.261789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.69842e6 | + | 2.94174e6i | −0.725449 | + | 1.25652i | 0.233339 | + | 0.972395i | \(0.425035\pi\) |
−0.958789 | + | 0.284120i | \(0.908299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −664307. | − | 1.15061e6i | −0.279768 | − | 0.484572i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −761965. | −0.312032 | −0.156016 | − | 0.987755i | \(-0.549865\pi\) | ||||
−0.156016 | + | 0.987755i | \(0.549865\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47521e6 | −0.999642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.58323e6 | + | 4.47428e6i | 1.01492 | + | 1.75789i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −698558. | + | 1.20994e6i | −0.270730 | + | 0.468919i | −0.969049 | − | 0.246868i | \(-0.920599\pi\) |
0.698319 | + | 0.715787i | \(0.253932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.99896e6 | − | 3.46229e6i | 0.753995 | − | 1.30596i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.62621e6 | − | 2.81668e6i | −0.605209 | − | 1.04825i | −0.992018 | − | 0.126093i | \(-0.959756\pi\) |
0.386809 | − | 0.922160i | \(-0.373577\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.13989e6 | −0.775421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −700188. | −0.250390 | −0.125195 | − | 0.992132i | \(-0.539956\pi\) | ||||
−0.125195 | + | 0.992132i | \(0.539956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.15361e6 | + | 1.99810e6i | 0.401847 | + | 0.696019i | 0.993949 | − | 0.109844i | \(-0.0350352\pi\) |
−0.592102 | + | 0.805863i | \(0.701702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 985576. | − | 1.70707e6i | 0.338874 | − | 0.586947i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00563e6 | − | 1.74180e6i | 0.336950 | − | 0.583614i | −0.646908 | − | 0.762568i | \(-0.723938\pi\) |
0.983857 | + | 0.178955i | \(0.0572715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.36901e6 | − | 5.83530e6i | −1.11445 | − | 1.93028i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.96072e6 | −0.632299 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −165619. | −0.0527392 | −0.0263696 | − | 0.999652i | \(-0.508395\pi\) | ||||
−0.0263696 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −547270. | − | 947900.i | −0.169958 | − | 0.294375i | 0.768447 | − | 0.639913i | \(-0.221030\pi\) |
−0.938405 | + | 0.345538i | \(0.887696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.86011e6 | − | 3.22180e6i | 0.570526 | − | 0.988180i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −919595. | + | 1.59279e6i | −0.275176 | + | 0.476619i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 536465. | + | 929184.i | 0.158574 | + | 0.274659i | 0.934355 | − | 0.356344i | \(-0.115977\pi\) |
−0.775780 | + | 0.631003i | \(0.782644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.24691e6 | −0.936687 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.25250e6 | −1.78211 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −426090. | − | 738010.i | −0.118568 | − | 0.205365i | 0.800633 | − | 0.599156i | \(-0.204497\pi\) |
−0.919200 | + | 0.393790i | \(0.871164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.59392e6 | + | 2.76075e6i | −0.438290 | + | 0.759140i | −0.997558 | − | 0.0698468i | \(-0.977749\pi\) |
0.559268 | + | 0.828987i | \(0.311082\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −208207. | + | 360625.i | −0.0559143 | + | 0.0968465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.57541e6 | − | 6.19280e6i | −0.948979 | − | 1.64368i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.54409e6 | −1.17829 | −0.589147 | − | 0.808026i | \(-0.700536\pi\) | ||||
−0.589147 | + | 0.808026i | \(0.700536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.16131e6 | −1.57926 | −0.789629 | − | 0.613585i | \(-0.789727\pi\) | ||||
−0.789629 | + | 0.613585i | \(0.789727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −47205.5 | − | 81762.4i | −0.0118247 | − | 0.0204809i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −451417. | + | 781877.i | −0.111793 | + | 0.193632i | −0.916493 | − | 0.400050i | \(-0.868993\pi\) |
0.804700 | + | 0.593682i | \(0.202326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.84356e6 | − | 3.19314e6i | 0.446321 | − | 0.773051i | −0.551822 | − | 0.833962i | \(-0.686067\pi\) |
0.998143 | + | 0.0609110i | \(0.0194006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.17113e6 | + | 5.49255e6i | 0.759126 | + | 1.31484i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.71368e6 | 1.80570 | 0.902851 | − | 0.429954i | \(-0.141470\pi\) | ||||
0.902851 | + | 0.429954i | \(0.141470\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.21218e6 | −0.512128 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.65595e6 | + | 4.60024e6i | 0.601438 | + | 1.04172i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.89634e6 | + | 3.28455e6i | −0.424742 | + | 0.735674i | −0.996396 | − | 0.0848200i | \(-0.972968\pi\) |
0.571654 | + | 0.820494i | \(0.306302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.38949e6 | − | 4.13871e6i | 0.523664 | − | 0.907012i | −0.475957 | − | 0.879469i | \(-0.657898\pi\) |
0.999621 | − | 0.0275435i | \(-0.00876848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.27951e6 | − | 2.21618e6i | −0.277391 | − | 0.480456i | 0.693344 | − | 0.720606i | \(-0.256136\pi\) |
−0.970736 | + | 0.240151i | \(0.922803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.22563e6 | 1.74533 | 0.872664 | − | 0.488321i | \(-0.162390\pi\) | ||||
0.872664 | + | 0.488321i | \(0.162390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.99639e6 | 0.629022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −747363. | − | 1.29447e6i | −0.153596 | − | 0.266035i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2917.33 | + | 5052.97i | −0.000593270 | + | 0.00102757i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.27184e6 | + | 2.20290e6i | −0.253277 | + | 0.438688i | −0.964426 | − | 0.264353i | \(-0.914842\pi\) |
0.711149 | + | 0.703041i | \(0.248175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.47814e6 | − | 4.29227e6i | −0.488386 | − | 0.845910i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.66153e6 | −0.320741 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.25686e6 | 0.240139 | 0.120070 | − | 0.992765i | \(-0.461688\pi\) | ||||
0.120070 | + | 0.992765i | \(0.461688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.94983e6 | − | 8.57336e6i | −0.926588 | − | 1.60490i | −0.788987 | − | 0.614410i | \(-0.789394\pi\) |
−0.137601 | − | 0.990488i | \(-0.543939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.86897e6 | + | 6.70125e6i | −0.716932 | + | 1.24176i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.80848e6 | + | 3.13238e6i | −0.328415 | + | 0.568831i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.52076e6 | + | 2.63403e6i | 0.273406 | + | 0.473553i | 0.969732 | − | 0.244173i | \(-0.0785164\pi\) |
−0.696326 | + | 0.717726i | \(0.745183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.75985e6 | 0.486368 | 0.243184 | − | 0.969980i | \(-0.421808\pi\) | ||||
0.243184 | + | 0.969980i | \(0.421808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.32186e6 | −0.405142 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 722539. | + | 1.25147e6i | 0.123614 | + | 0.214105i | 0.921190 | − | 0.389113i | \(-0.127218\pi\) |
−0.797577 | + | 0.603218i | \(0.793885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.03246e6 | − | 1.21806e7i | 1.19139 | − | 2.06355i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.89384e6 | + | 1.02084e7i | −0.979220 | + | 1.69606i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.66512e6 | + | 4.61612e6i | 0.438521 | + | 0.759540i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.28492e6 | 0.207388 | 0.103694 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103694 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.38275e6 | −0.380912 | −0.190456 | − | 0.981696i | \(-0.560997\pi\) | ||||
−0.190456 | + | 0.981696i | \(0.560997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.72623e6 | − | 1.16502e7i | −1.05498 | − | 1.82728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.81100e6 | + | 3.13674e6i | −0.281370 | + | 0.487347i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.98070e6 | − | 5.16273e6i | 0.454465 | − | 0.787157i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.72671e6 | − | 8.18691e6i | −0.713961 | − | 1.23662i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.70184e6 | −0.252317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.22158e6 | 0.326339 | 0.163170 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163170 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.79062e6 | + | 6.56554e6i | 0.546662 | + | 0.946846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 908447. | − | 1.57348e6i | 0.129817 | − | 0.224850i | −0.793789 | − | 0.608194i | \(-0.791894\pi\) |
0.923606 | + | 0.383344i | \(0.125228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54210.8 | + | 93895.8i | −0.00760688 | + | 0.0131755i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.66889e6 | + | 4.62265e6i | 0.371123 | + | 0.642803i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.53109e6 | −0.482248 | −0.241124 | − | 0.970494i | \(-0.577516\pi\) | ||||
−0.241124 | + | 0.970494i | \(0.577516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.02801e6 | 0.545207 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 163728. | + | 283585.i | 0.0217697 | + | 0.0377062i | 0.876705 | − | 0.481028i | \(-0.159737\pi\) |
−0.854935 | + | 0.518735i | \(0.826403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.71780e6 | − | 4.70737e6i | 0.358176 | − | 0.620379i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.03386e6 | + | 6.98686e6i | −0.522325 | + | 0.904693i | 0.477338 | + | 0.878720i | \(0.341602\pi\) |
−0.999663 | + | 0.0259731i | \(0.991732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 105674. | + | 183033.i | 0.0135637 | + | 0.0234931i | 0.872728 | − | 0.488207i | \(-0.162349\pi\) |
−0.859164 | + | 0.511701i | \(0.829016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 621612. | 0.0784060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.60363e6 | −0.200523 | −0.100261 | − | 0.994961i | \(-0.531968\pi\) | ||||
−0.100261 | + | 0.994961i | \(0.531968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.51078e6 | + | 1.47411e7i | 1.04599 | + | 1.81171i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.77799e6 | + | 4.81161e6i | −0.338500 | + | 0.586299i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.96240e6 | + | 8.59513e6i | −0.594424 | + | 1.02957i | 0.399203 | + | 0.916862i | \(0.369287\pi\) |
−0.993628 | + | 0.112711i | \(0.964047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −94245.9 | − | 163239.i | −0.0111937 | − | 0.0193881i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.74316e6 | 0.670678 | 0.335339 | − | 0.942098i | \(-0.391149\pi\) | ||||
0.335339 | + | 0.942098i | \(0.391149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.92081e7 | 2.22429 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.63787e6 | − | 4.56892e6i | −0.300391 | − | 0.520292i | 0.675834 | − | 0.737054i | \(-0.263784\pi\) |
−0.976224 | + | 0.216762i | \(0.930450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.07476e6 | + | 3.59359e6i | −0.234305 | + | 0.405828i | −0.959070 | − | 0.283167i | \(-0.908615\pi\) |
0.724765 | + | 0.688996i | \(0.241948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.27086e6 | − | 5.66530e6i | 0.363307 | − | 0.629266i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.92504e6 | + | 1.37266e7i | 0.873031 | + | 1.51213i | 0.858846 | + | 0.512234i | \(0.171182\pi\) |
0.0141852 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.43640e7 | −1.55658 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.48963e7 | 1.60113 | 0.800565 | − | 0.599246i | \(-0.204533\pi\) | ||||
0.800565 | + | 0.599246i | \(0.204533\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.23952e6 | − | 1.25392e7i | −0.765591 | − | 1.32604i | −0.939934 | − | 0.341357i | \(-0.889113\pi\) |
0.174343 | − | 0.984685i | \(-0.444220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.29461e6 | − | 9.17053e6i | 0.555402 | − | 0.961984i | −0.442471 | − | 0.896783i | \(-0.645898\pi\) |
0.997872 | − | 0.0652007i | \(-0.0207688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.63294e6 | − | 1.49527e7i | 0.891125 | − | 1.54347i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.16985e6 | + | 8.95445e6i | 0.529393 | + | 0.916936i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.79221e7 | −1.80619 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.93118e6 | −0.493035 | −0.246517 | − | 0.969138i | \(-0.579286\pi\) | ||||
−0.246517 | + | 0.969138i | \(0.579286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.73480e6 | + | 1.51291e7i | 0.859644 | + | 1.48895i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.29307e6 | − | 3.97171e6i | 0.223908 | − | 0.387819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.50299e6 | − | 1.64597e7i | 0.913514 | − | 1.58225i | 0.104452 | − | 0.994530i | \(-0.466691\pi\) |
0.809062 | − | 0.587723i | \(-0.199975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.34869e6 | + | 5.80010e6i | 0.319409 | + | 0.553233i | 0.980365 | − | 0.197192i | \(-0.0631822\pi\) |
−0.660956 | + | 0.750425i | \(0.729849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.62821e7 | 1.52915 | 0.764574 | − | 0.644536i | \(-0.222949\pi\) | ||||
0.764574 | + | 0.644536i | \(0.222949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.51228e6 | 0.420518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.76043e6 | + | 4.78121e6i | 0.253334 | + | 0.438788i | 0.964442 | − | 0.264296i | \(-0.0851394\pi\) |
−0.711108 | + | 0.703083i | \(0.751806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.12175e6 | + | 1.57993e7i | −0.830759 | + | 1.43892i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −69588.1 | + | 120530.i | −0.00624197 | + | 0.0108114i | −0.869130 | − | 0.494585i | \(-0.835320\pi\) |
0.862888 | + | 0.505396i | \(0.168654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.72751e6 | + | 1.68485e7i | 0.865960 | + | 1.49989i | 0.866090 | + | 0.499887i | \(0.166625\pi\) |
−0.000129981 | 1.00000i | \(0.500041\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 269137. | 0.0236004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.15510e7 | 1.00532 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.96882e6 | + | 8.60624e6i | 0.426036 | + | 0.737916i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.57506e6 | − | 7.92423e6i | 0.389367 | − | 0.674403i | −0.602998 | − | 0.797743i | \(-0.706027\pi\) |
0.992364 | + | 0.123340i | \(0.0393605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.96358e6 | − | 8.59717e6i | 0.416220 | − | 0.720915i | −0.579335 | − | 0.815089i | \(-0.696688\pi\) |
0.995556 | + | 0.0941744i | \(0.0300211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.26164e6 | + | 3.91728e6i | 0.188256 | + | 0.326069i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.27969e7 | 1.04967 | 0.524835 | − | 0.851204i | \(-0.324127\pi\) | ||||
0.524835 | + | 0.851204i | \(0.324127\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56646.0 | −0.00461257 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.48616e6 | − | 1.29664e7i | −0.600774 | − | 1.04057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.02846e6 | + | 6.97749e6i | −0.320955 | + | 0.555910i | −0.980685 | − | 0.195592i | \(-0.937337\pi\) |
0.659731 | + | 0.751502i | \(0.270670\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.23406e6 | + | 3.86951e6i | −0.175442 | + | 0.303874i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.07784e7 | − | 1.86687e7i | −0.840371 | − | 1.45556i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.05658e7 | −0.812100 | −0.406050 | − | 0.913851i | \(-0.633094\pi\) | ||||
−0.406050 | + | 0.913851i | \(0.633094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −251120. | −0.0191643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.16046e6 | + | 5.47408e6i | 0.237795 | + | 0.411872i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.59109e6 | − | 1.31482e7i | 0.567138 | − | 0.982312i | −0.429709 | − | 0.902967i | \(-0.641384\pi\) |
0.996847 | − | 0.0793445i | \(-0.0252827\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.00407e7 | + | 1.73911e7i | −0.739676 | + | 1.28116i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.69102e6 | − | 6.39303e6i | −0.270011 | − | 0.467672i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.93525e6 | 0.211750 | 0.105875 | − | 0.994379i | \(-0.466236\pi\) | ||||
0.105875 | + | 0.994379i | \(0.466236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.20903e7 | 2.29898 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −356929. | − | 618219.i | −0.0252195 | − | 0.0436815i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.66682e6 | − | 8.08316e6i | 0.327480 | − | 0.567212i | −0.654531 | − | 0.756035i | \(-0.727134\pi\) |
0.982011 | + | 0.188823i | \(0.0604673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.28274e6 | − | 1.26141e7i | 0.504082 | − | 0.873096i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.36625e6 | + | 4.09846e6i | 0.162667 | + | 0.281748i | 0.935824 | − | 0.352466i | \(-0.114657\pi\) |
−0.773157 | + | 0.634215i | \(0.781324\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.16413e6 | −0.282394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.42162e7 | −1.63115 | −0.815575 | − | 0.578651i | \(-0.803579\pi\) | ||||
−0.815575 | + | 0.578651i | \(0.803579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.23724e7 | − | 2.14296e7i | −0.822207 | − | 1.42410i | −0.904035 | − | 0.427458i | \(-0.859409\pi\) |
0.0818282 | − | 0.996646i | \(-0.473924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.43490e6 | + | 5.94943e6i | −0.226738 | + | 0.392721i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.28678e7 | + | 2.22877e7i | −0.838108 | + | 1.45165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.78532e6 | + | 4.82432e6i | 0.180209 | + | 0.312131i | 0.941952 | − | 0.335749i | \(-0.108989\pi\) |
−0.761743 | + | 0.647880i | \(0.775656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.43284e6 | −0.219173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.72203e6 | −0.172645 | −0.0863224 | − | 0.996267i | \(-0.527511\pi\) | ||||
−0.0863224 | + | 0.996267i | \(0.527511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.53087e6 | + | 1.30438e7i | 0.471393 | + | 0.816477i | 0.999464 | − | 0.0327230i | \(-0.0104179\pi\) |
−0.528071 | + | 0.849200i | \(0.677085\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.03194e7 | − | 1.78738e7i | 0.641718 | − | 1.11149i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.07989e6 | + | 1.05307e7i | −0.373170 | + | 0.646350i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.56946e6 | − | 7.91454e6i | −0.278644 | − | 0.482625i | 0.692404 | − | 0.721510i | \(-0.256552\pi\) |
−0.971048 | + | 0.238885i | \(0.923218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.35738e7 | 0.817060 | 0.408530 | − | 0.912745i | \(-0.366041\pi\) | ||||
0.408530 | + | 0.912745i | \(0.366041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.24105e6 | 0.0742223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −151023. | − | 261580.i | −0.00891661 | − | 0.0154440i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.51328e6 | − | 4.35312e6i | 0.147439 | − | 0.255372i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.57395e6 | + | 1.48505e7i | −0.496600 | + | 0.860136i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.02146e7 | + | 1.76922e7i | 0.587875 | + | 1.01823i | 0.994510 | + | 0.104639i | \(0.0333686\pi\) |
−0.406635 | + | 0.913591i | \(0.633298\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.47976e7 | −0.840913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67801e7 | −1.51227 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.51983e7 | − | 2.63242e7i | −0.847518 | − | 1.46794i | −0.883416 | − | 0.468589i | \(-0.844762\pi\) |
0.0358980 | − | 0.999355i | \(-0.488571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.59705e7 | + | 4.49822e7i | −1.43917 | + | 2.49272i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.77314e6 | + | 1.69276e7i | −0.534866 | + | 0.926416i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.43366e7 | − | 2.48318e7i | −0.779754 | − | 1.35057i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.50428e7 | 1.88247 | 0.941234 | − | 0.337755i | \(-0.109667\pi\) | ||||
0.941234 | + | 0.337755i | \(0.109667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55069e7 | 0.827893 | 0.413946 | − | 0.910301i | \(-0.364150\pi\) | ||||
0.413946 | + | 0.910301i | \(0.364150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.84343e6 | + | 4.92496e6i | 0.149951 | + | 0.259722i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 102043. | − | 176745.i | 0.00534848 | − | 0.00926383i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.58087e6 | − | 1.31304e7i | 0.392519 | − | 0.679863i | −0.600262 | − | 0.799804i | \(-0.704937\pi\) |
0.992781 | + | 0.119940i | \(0.0382703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.32661e6 | + | 1.09580e7i | 0.325590 | + | 0.563939i | 0.981632 | − | 0.190786i | \(-0.0611037\pi\) |
−0.656041 | + | 0.754725i | \(0.727770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.21240e7 | 0.616427 | 0.308213 | − | 0.951317i | \(-0.400269\pi\) | ||||
0.308213 | + | 0.951317i | \(0.400269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.79003e7 | −0.904634 | −0.452317 | − | 0.891857i | \(-0.649402\pi\) | ||||
−0.452317 | + | 0.891857i | \(0.649402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.29185e6 | − | 1.43619e7i | −0.414037 | − | 0.717133i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 534588. | − | 925933.i | 0.0265340 | − | 0.0459583i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17183e7 | − | 2.02966e7i | 0.574723 | − | 0.995449i | −0.421349 | − | 0.906899i | \(-0.638443\pi\) |
0.996072 | − | 0.0885507i | \(-0.0282235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.62301e6 | + | 6.27524e6i | 0.176636 | + | 0.305943i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50368e6 | −0.0724458 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.78089e7 | −0.852960 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.33768e7 | + | 2.31694e7i | 0.633183 | + | 1.09671i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.44546e7 | + | 2.50361e7i | −0.680196 | + | 1.17813i | 0.294725 | + | 0.955582i | \(0.404772\pi\) |
−0.974921 | + | 0.222552i | \(0.928561\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.34804e6 | + | 9.26307e6i | −0.248738 | + | 0.430827i | −0.963176 | − | 0.268872i | \(-0.913349\pi\) |
0.714438 | + | 0.699699i | \(0.246682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.84851e7 | − | 3.20172e7i | −0.854752 | − | 1.48047i | −0.876875 | − | 0.480718i | \(-0.840376\pi\) |
0.0221237 | − | 0.999755i | \(-0.492957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.83720e7 | −1.75383 | −0.876914 | − | 0.480646i | \(-0.840402\pi\) | ||||
−0.876914 | + | 0.480646i | \(0.840402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.86211e7 | −1.30061 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.70900e6 | − | 6.42417e6i | −0.166612 | − | 0.288581i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.61079e6 | − | 9.71817e6i | 0.250599 | − | 0.434050i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.32405e7 | − | 2.29332e7i | 0.584633 | − | 1.01261i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.83104e7 | − | 3.17146e7i | −0.803895 | − | 1.39239i | −0.917035 | − | 0.398808i | \(-0.869424\pi\) |
0.113140 | − | 0.993579i | \(-0.463909\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.70223e7 | −0.738889 | −0.369445 | − | 0.929253i | \(-0.620452\pi\) | ||||
−0.369445 | + | 0.929253i | \(0.620452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.54409e7 | 1.52969 | 0.764844 | − | 0.644215i | \(-0.222816\pi\) | ||||
0.764844 | + | 0.644215i | \(0.222816\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00360e6 | + | 1.03985e7i | 0.256214 | + | 0.443776i | 0.965225 | − | 0.261422i | \(-0.0841915\pi\) |
−0.709011 | + | 0.705198i | \(0.750858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.37793e7 | − | 4.11869e7i | 1.00912 | − | 1.74785i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −363890. | + | 630276.i | −0.0152701 | + | 0.0264486i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.32418e6 | + | 7.48971e6i | 0.180446 | + | 0.312541i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.30615e7 | 0.951676 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.41406e7 | −2.22183 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.11828e6 | + | 3.66898e6i | 0.0859731 | + | 0.148910i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.21452e6 | − | 7.29977e6i | 0.170110 | − | 0.294639i | −0.768348 | − | 0.640032i | \(-0.778921\pi\) |
0.938458 | + | 0.345393i | \(0.112254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.24424e7 | − | 2.15508e7i | 0.496715 | − | 0.860335i | −0.503278 | − | 0.864125i | \(-0.667873\pi\) |
0.999993 | + | 0.00378921i | \(0.00120614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.18276e7 | − | 2.04860e7i | −0.469590 | − | 0.813354i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.96653e7 | 1.95043 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68789e7 | −1.44042 | −0.720210 | − | 0.693757i | \(-0.755954\pi\) | ||||
−0.720210 | + | 0.693757i | \(0.755954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.77282e6 | + | 1.17309e7i | 0.261677 | + | 0.453238i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 826697. | − | 1.43188e6i | 0.0317682 | − | 0.0550241i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.30455e7 | − | 2.25955e7i | 0.495932 | − | 0.858979i | −0.504057 | − | 0.863670i | \(-0.668160\pi\) |
0.999989 | + | 0.00469142i | \(0.00149333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −116183. | − | 201235.i | −0.00439307 | − | 0.00760901i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.66938e7 | −0.998576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.84259e6 | 0.291817 | 0.145908 | − | 0.989298i | \(-0.453390\pi\) | ||||
0.145908 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.68082e7 | + | 2.91127e7i | 0.618796 | + | 1.07179i | 0.989706 | + | 0.143117i | \(0.0457126\pi\) |
−0.370910 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60896e7 | + | 2.78681e7i | −0.589206 | + | 1.02053i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.88767e6 | + | 1.36619e7i | −0.285808 | + | 0.495034i | −0.972805 | − | 0.231627i | \(-0.925595\pi\) |
0.686997 | + | 0.726660i | \(0.258929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.63368e7 | − | 4.56167e7i | −0.949288 | − | 1.64421i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.32737e7 | −0.830104 | −0.415052 | − | 0.909798i | \(-0.636237\pi\) | ||||
−0.415052 | + | 0.909798i | \(0.636237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.45376e7 | −1.22542 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77105.3 | + | 133550.i | 0.00270731 | + | 0.00468920i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.73176e6 | + | 9.92770e6i | −0.200207 | + | 0.346769i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.08541e7 | − | 3.61203e7i | 0.720896 | − | 1.24863i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.77148e6 | − | 1.69247e7i | −0.336043 | − | 0.582043i | 0.647642 | − | 0.761945i | \(-0.275755\pi\) |
−0.983685 | + | 0.179902i | \(0.942422\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.59842e7 | −1.90554 | −0.952768 | − | 0.303700i | \(-0.901778\pi\) | ||||
−0.952768 | + | 0.303700i | \(0.901778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.21638e7 | 0.411897 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.10112e6 | − | 3.63925e6i | −0.0704231 | − | 0.121976i | 0.828664 | − | 0.559747i | \(-0.189102\pi\) |
−0.899087 | + | 0.437770i | \(0.855768\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.19974e7 | + | 2.07800e7i | −0.400063 | + | 0.692930i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.07877e6 | + | 1.57249e7i | −0.299670 | + | 0.519044i | −0.976060 | − | 0.217500i | \(-0.930210\pi\) |
0.676390 | + | 0.736543i | \(0.263543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.20036e7 | + | 2.07909e7i | 0.394205 | + | 0.682782i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.17429e7 | −0.706851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.51450e6 | 0.210716 | 0.105358 | − | 0.994434i | \(-0.466401\pi\) | ||||
0.105358 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.98292e7 | − | 3.43451e7i | −0.634960 | − | 1.09978i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.44585e7 | − | 2.50428e7i | 0.460664 | − | 0.797894i | −0.538330 | − | 0.842734i | \(-0.680944\pi\) |
0.998994 | + | 0.0448401i | \(0.0142778\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.6.e.f.217.1 | 4 | ||
3.2 | odd | 2 | 324.6.e.g.217.2 | 4 | |||
9.2 | odd | 6 | 108.6.a.b.1.1 | ✓ | 2 | ||
9.4 | even | 3 | inner | 324.6.e.f.109.1 | 4 | ||
9.5 | odd | 6 | 324.6.e.g.109.2 | 4 | |||
9.7 | even | 3 | 108.6.a.c.1.2 | yes | 2 | ||
36.7 | odd | 6 | 432.6.a.q.1.2 | 2 | |||
36.11 | even | 6 | 432.6.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.b.1.1 | ✓ | 2 | 9.2 | odd | 6 | ||
108.6.a.c.1.2 | yes | 2 | 9.7 | even | 3 | ||
324.6.e.f.109.1 | 4 | 9.4 | even | 3 | inner | ||
324.6.e.f.217.1 | 4 | 1.1 | even | 1 | trivial | ||
324.6.e.g.109.2 | 4 | 9.5 | odd | 6 | |||
324.6.e.g.217.2 | 4 | 3.2 | odd | 2 | |||
432.6.a.q.1.2 | 2 | 36.7 | odd | 6 | |||
432.6.a.r.1.1 | 2 | 36.11 | even | 6 |