Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 384x^{6} + 506x^{5} + 49869x^{4} + 29654x^{3} - 2235516x^{2} - 1528906x + 34180205 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.1 | ||
Root | \(14.2856 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.b.161.8 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 27.5713i | − 1.76870i | −0.466828 | − | 0.884348i | \(-0.654603\pi\) | ||||
0.466828 | − | 0.884348i | \(-0.345397\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 220.359 | 1.69975 | 0.849875 | − | 0.526985i | \(-0.176678\pi\) | ||||
0.849875 | + | 0.526985i | \(0.176678\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −517.174 | −2.12829 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.4115i | 0.160503i | 0.996775 | + | 0.0802513i | \(0.0255723\pi\) | ||||
−0.996775 | + | 0.0802513i | \(0.974428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 703.006i | 1.15372i | 0.816843 | + | 0.576860i | \(0.195722\pi\) | ||||
−0.816843 | + | 0.576860i | \(0.804278\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 689.281 | 0.790985 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −207.573 | −0.174200 | −0.0871001 | − | 0.996200i | \(-0.527760\pi\) | ||||
−0.0871001 | + | 0.996200i | \(0.527760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2790.91i | − 1.77363i | −0.462127 | − | 0.886814i | \(-0.652913\pi\) | ||||
0.462127 | − | 0.886814i | \(-0.347087\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 6075.56i | − 3.00634i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3258.47 | 1.28438 | 0.642192 | − | 0.766544i | \(-0.278025\pi\) | ||||
0.642192 | + | 0.766544i | \(0.278025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7559.32i | 1.99560i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7896.13i | − 1.74349i | −0.489961 | − | 0.871745i | \(-0.662989\pi\) | ||||
0.489961 | − | 0.871745i | \(-0.337011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5051.23 | −0.944046 | −0.472023 | − | 0.881586i | \(-0.656476\pi\) | ||||
−0.472023 | + | 0.881586i | \(0.656476\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1775.91 | 0.283880 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5508.96i | 0.760151i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4915.89i | − 0.590334i | −0.955446 | − | 0.295167i | \(-0.904625\pi\) | ||||
0.955446 | − | 0.295167i | \(-0.0953753\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19382.8 | 2.04058 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7036.16 | 0.653696 | 0.326848 | − | 0.945077i | \(-0.394013\pi\) | ||||
0.326848 | + | 0.945077i | \(0.394013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 15147.0i | − 1.24927i | −0.780918 | − | 0.624633i | \(-0.785248\pi\) | ||||
0.780918 | − | 0.624633i | \(-0.214752\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 12929.4i | − 0.951799i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9305.48 | 0.614461 | 0.307230 | − | 0.951635i | \(-0.400598\pi\) | ||||
0.307230 | + | 0.951635i | \(0.400598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31750.9 | 1.88915 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5723.05i | 0.308107i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4938.18i | − 0.241478i | −0.992684 | − | 0.120739i | \(-0.961474\pi\) | ||||
0.992684 | − | 0.120739i | \(-0.0385264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1610.29 | −0.0717789 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −76949.0 | −3.13701 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 38441.5i | − 1.43771i | −0.695162 | − | 0.718853i | \(-0.744667\pi\) | ||||
0.695162 | − | 0.718853i | \(-0.255333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27779.9i | 0.955886i | 0.878391 | + | 0.477943i | \(0.158618\pi\) | ||||
−0.878391 | + | 0.477943i | \(0.841382\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −113964. | −3.61756 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17575.2 | −0.515960 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7780.18i | 0.211740i | 0.994380 | + | 0.105870i | \(0.0337627\pi\) | ||||
−0.994380 | + | 0.105870i | \(0.966237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 89840.2i | − 2.27168i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60101.8 | −1.41495 | −0.707476 | − | 0.706737i | \(-0.750166\pi\) | ||||
−0.707476 | + | 0.706737i | \(0.750166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 36397.3 | 0.799396 | 0.399698 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399698 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17232.0i | 0.353739i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14193.6i | 0.272814i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −36768.7 | −0.662843 | −0.331421 | − | 0.943483i | \(-0.607528\pi\) | ||||
−0.331421 | + | 0.943483i | \(0.607528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 82746.7 | 1.40132 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 21132.9i | 0.336716i | 0.985726 | + | 0.168358i | \(0.0538465\pi\) | ||||
−0.985726 | + | 0.168358i | \(0.946153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5189.32i | − 0.0779047i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −217706. | −3.08370 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −63887.8 | −0.854955 | −0.427477 | − | 0.904026i | \(-0.640598\pi\) | ||||
−0.427477 | + | 0.904026i | \(0.640598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 154913.i | 1.96104i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 139269.i | 1.66973i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 69772.9 | 0.793190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14388.5 | −0.155269 | −0.0776346 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776346 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 33312.0i | − 0.341596i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 73761.5i | − 0.719493i | −0.933050 | − | 0.359747i | \(-0.882863\pi\) | ||||
0.933050 | − | 0.359747i | \(-0.117137\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13374.5 | 0.124218 | 0.0621090 | − | 0.998069i | \(-0.480217\pi\) | ||||
0.0621090 | + | 0.998069i | \(0.480217\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 151889. | 1.34448 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 206058.i | − 1.73992i | −0.493120 | − | 0.869961i | \(-0.664144\pi\) | ||||
0.493120 | − | 0.869961i | \(-0.335856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 73086.1i | − 0.589208i | −0.955619 | − | 0.294604i | \(-0.904812\pi\) | ||||
0.955619 | − | 0.294604i | \(-0.0951877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −135537. | −1.04412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −154909. | −1.14125 | −0.570626 | − | 0.821210i | \(-0.693299\pi\) | ||||
−0.570626 | + | 0.821210i | \(0.693299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 81461.8i | 0.574394i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 363577.i | − 2.45545i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −45740.5 | −0.296097 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 156902. | 0.974239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 193996.i | − 1.15619i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 156780. | 0.862545 | 0.431273 | − | 0.902222i | \(-0.358065\pi\) | ||||
0.431273 | + | 0.902222i | \(0.358065\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −417621. | −2.20957 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 241597.i | 1.23002i | 0.788518 | + | 0.615012i | \(0.210849\pi\) | ||||
−0.788518 | + | 0.615012i | \(0.789151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 615002.i | − 3.01472i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −188983. | −0.892459 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −34718.4 | −0.158037 | −0.0790184 | − | 0.996873i | \(-0.525179\pi\) | ||||
−0.0790184 | + | 0.996873i | \(0.525179\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 148522.i | 0.652008i | 0.945368 | + | 0.326004i | \(0.105702\pi\) | ||||
−0.945368 | + | 0.326004i | \(0.894298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 256564.i | − 1.08680i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −45281.7 | −0.185175 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 197403. | 0.779712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 875412.i | − 3.34133i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 95567.9i | − 0.352652i | −0.984332 | − | 0.176326i | \(-0.943579\pi\) | ||||
0.984332 | − | 0.176326i | \(-0.0564213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 445946. | 1.59162 | 0.795810 | − | 0.605546i | \(-0.207045\pi\) | ||||
0.795810 | + | 0.605546i | \(0.207045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 107351. | 0.370748 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 126281.i | − 0.422190i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 534503.i | 1.73062i | 0.501240 | + | 0.865308i | \(0.332877\pi\) | ||||
−0.501240 | + | 0.865308i | \(0.667123\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −136152. | −0.427101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 718033. | 2.18313 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 509438.i | 1.50184i | 0.660396 | + | 0.750918i | \(0.270389\pi\) | ||||
−0.660396 | + | 0.750918i | \(0.729611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 44397.7i | 0.126955i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 658419. | 1.82689 | 0.913443 | − | 0.406967i | \(-0.133414\pi\) | ||||
0.913443 | + | 0.406967i | \(0.133414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −122925. | −0.331072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.44339e6i | 3.77479i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 233004.i | − 0.591900i | −0.955203 | − | 0.295950i | \(-0.904364\pi\) | ||||
0.955203 | − | 0.295950i | \(-0.0956362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −137724. | −0.339950 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.05988e6 | −2.54287 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 300920.i | − 0.701970i | −0.936381 | − | 0.350985i | \(-0.885847\pi\) | ||||
0.936381 | − | 0.350985i | \(-0.114153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 54124.5i | 0.122800i | 0.998113 | + | 0.0613998i | \(0.0195565\pi\) | ||||
−0.998113 | + | 0.0613998i | \(0.980444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 765927. | 1.69067 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 122897. | 0.264006 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 13370.1i | − 0.0279596i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.66576e6i | 3.39202i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −417470. | −0.828021 | −0.414011 | − | 0.910272i | \(-0.635872\pi\) | ||||
−0.414011 | + | 0.910272i | \(0.635872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 430941. | 0.832769 | 0.416384 | − | 0.909189i | \(-0.363297\pi\) | ||||
0.416384 | + | 0.909189i | \(0.363297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 484569.i | 0.912576i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 289267.i | − 0.531047i | −0.964104 | − | 0.265523i | \(-0.914455\pi\) | ||||
0.964104 | − | 0.265523i | \(-0.0855448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −812396. | −1.45424 | −0.727119 | − | 0.686512i | \(-0.759141\pi\) | ||||
−0.727119 | + | 0.686512i | \(0.759141\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 214509. | 0.374504 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.73998e6i | − 2.96349i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 175904.i | 0.292342i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.68520e6 | −2.73354 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 179767. | 0.284672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 227948.i | − 0.352476i | −0.984348 | − | 0.176238i | \(-0.943607\pi\) | ||||
0.984348 | − | 0.176238i | \(-0.0563928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.65708e6i | 2.50262i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 378675. | 0.558689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.11308e6 | −1.60464 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.00352e6i | − 1.41389i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 145925.i | − 0.200978i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 371367. | 0.500082 | 0.250041 | − | 0.968235i | \(-0.419556\pi\) | ||||
0.250041 | + | 0.968235i | \(0.419556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 323234. | 0.425658 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 761652.i | 0.981052i | 0.871427 | + | 0.490526i | \(0.163195\pi\) | ||||
−0.871427 | + | 0.490526i | \(0.836805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 325400.i | − 0.410043i | −0.978757 | − | 0.205021i | \(-0.934274\pi\) | ||||
0.978757 | − | 0.205021i | \(-0.0657264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 391336. | 0.482525 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −527689. | −0.636778 | −0.318389 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318389 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 232637.i | 0.274795i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.01376e6i | 1.17237i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.09227e6 | 1.23691 | 0.618454 | − | 0.785821i | \(-0.287759\pi\) | ||||
0.618454 | + | 0.785821i | \(0.287759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −63366.4 | −0.0702776 | −0.0351388 | − | 0.999382i | \(-0.511187\pi\) | ||||
−0.0351388 | + | 0.999382i | \(0.511187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 444515.i | − 0.482915i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 793772.i | 0.844852i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.96203e6 | 2.04627 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 582661. | 0.595549 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.59819e6i | 1.60120i | 0.599201 | + | 0.800599i | \(0.295485\pi\) | ||||
−0.599201 | + | 0.800599i | \(0.704515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 209883.i | 0.206147i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −143076. | −0.137790 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −478358. | −0.451773 | −0.225886 | − | 0.974154i | \(-0.572528\pi\) | ||||
−0.225886 | + | 0.974154i | \(0.572528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.08326e6i | − 1.00342i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.08367e6i | 3.71065i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −720034. | −0.641895 | −0.320947 | − | 0.947097i | \(-0.604001\pi\) | ||||
−0.320947 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 123454. | 0.107992 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.76147e6i | 1.51216i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.74800e6i | − 1.47286i | −0.676514 | − | 0.736430i | \(-0.736510\pi\) | ||||
0.676514 | − | 0.736430i | \(-0.263490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80305e6 | 1.49137 | 0.745683 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745683 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.27116e6 | 3.46848 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 40257.2i | − 0.0321005i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 243112.i | − 0.190374i | −0.995459 | − | 0.0951869i | \(-0.969655\pi\) | ||||
0.995459 | − | 0.0951869i | \(-0.0303449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.61237e6 | 2.00920 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −377345. | −0.285084 | −0.142542 | − | 0.989789i | \(-0.545528\pi\) | ||||
−0.142542 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 904709.i | − 0.671495i | −0.941952 | − | 0.335748i | \(-0.891011\pi\) | ||||
0.941952 | − | 0.335748i | \(-0.108989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.92373e6i | − 1.40291i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.55048e6 | 1.11112 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37677e6 | −0.969654 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 396708.i | 0.274624i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.57254e6i | − 1.07012i | −0.844814 | − | 0.535060i | \(-0.820289\pi\) | ||||
0.844814 | − | 0.535060i | \(-0.179711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 961037. | 0.642962 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −486907. | −0.320299 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.29073e6i | 1.48182i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.33777e6i | − 2.12344i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.03370e6 | −1.27256 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −694498. | −0.427485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.50494e6i | − 0.911326i | −0.890152 | − | 0.455663i | \(-0.849402\pi\) | ||||
0.890152 | − | 0.455663i | \(-0.150598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 368752.i | − 0.219704i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 50915.6 | 0.0298504 | 0.0149252 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149252 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.05135e6 | −0.606581 | −0.303290 | − | 0.952898i | \(-0.598085\pi\) | ||||
−0.303290 | + | 0.952898i | \(0.598085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.84909e6i | − 1.61782i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 591005.i | − 0.330326i | −0.986266 | − | 0.165163i | \(-0.947185\pi\) | ||||
0.986266 | − | 0.165163i | \(-0.0528151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 508602. | 0.279834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.68128e6 | −3.07740 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 579318.i | 0.308966i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 439379.i | − 0.230744i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.01508e6 | −1.04213 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.05054e6 | 1.04443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.47751e6i | − 0.741242i | −0.928784 | − | 0.370621i | \(-0.879145\pi\) | ||||
0.928784 | − | 0.370621i | \(-0.120855\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.54237e6i | 1.25640i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −194505. | −0.0946930 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.32321e6 | 1.59398 | 0.796990 | − | 0.603993i | \(-0.206425\pi\) | ||||
0.796990 | + | 0.603993i | \(0.206425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.27104e6i | 2.01853i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 325357.i | − 0.151522i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29301e6 | 1.51133 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.24600e6 | 1.01593 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 602144.i | − 0.268458i | −0.990950 | − | 0.134229i | \(-0.957144\pi\) | ||||
0.990950 | − | 0.134229i | \(-0.0428558\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.58858e6i | − 0.698147i | −0.937095 | − | 0.349073i | \(-0.886496\pi\) | ||||
0.937095 | − | 0.349073i | \(-0.113504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.31425e6 | −2.30237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 319264. | 0.136368 | 0.0681841 | − | 0.997673i | \(-0.478279\pi\) | ||||
0.0681841 | + | 0.997673i | \(0.478279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.50255e6i | − 0.632786i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.26112e6i | 0.523705i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.83807e6 | 1.57173 | 0.785863 | − | 0.618401i | \(-0.212219\pi\) | ||||
0.785863 | + | 0.618401i | \(0.212219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.31310e6 | −2.14576 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4.32599e6i | − 1.72313i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 909932.i | 0.357501i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.02410e6 | −0.784455 | −0.392227 | − | 0.919868i | \(-0.628295\pi\) | ||||
−0.392227 | + | 0.919868i | \(0.628295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.63892e6 | −1.39125 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.08817e6i | − 0.410451i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.39562e6i | 1.63587i | 0.575311 | + | 0.817935i | \(0.304881\pi\) | ||||
−0.575311 | + | 0.817935i | \(0.695119\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −430801. | −0.158197 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.55103e6 | 2.01150 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.04075e6i | 0.729780i | 0.931051 | + | 0.364890i | \(0.118893\pi\) | ||||
−0.931051 | + | 0.364890i | \(0.881107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4.32263e6i | − 1.52558i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.64545e6 | −0.921516 | −0.460758 | − | 0.887526i | \(-0.652422\pi\) | ||||
−0.460758 | + | 0.887526i | \(0.652422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −354841. | −0.122006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.83363e6i | 2.65880i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.90022e6i | 0.636693i | 0.947974 | + | 0.318346i | \(0.103127\pi\) | ||||
−0.947974 | + | 0.318346i | \(0.896873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −676371. | −0.223740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.66113e6 | 2.17554 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 919217.i | − 0.296432i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 716277.i | 0.228089i | 0.993476 | + | 0.114045i | \(0.0363807\pi\) | ||||
−0.993476 | + | 0.114045i | \(0.963619\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.69564e7 | −5.33213 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.77803e6 | −0.552175 | −0.276088 | − | 0.961132i | \(-0.589038\pi\) | ||||
−0.276088 | + | 0.961132i | \(0.589038\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.55105e6i | − 1.08917i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.06867e6i | 0.626690i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 316640. | 0.0947502 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.15560e6 | 0.932767 | 0.466384 | − | 0.884583i | \(-0.345557\pi\) | ||||
0.466384 | + | 0.884583i | \(0.345557\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 957230.i | 0.279519i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.47091e6i | − 2.44374i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −528323. | −0.150584 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.09493e6 | 1.15320 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.73881e6i | − 0.483857i | −0.970294 | − | 0.241929i | \(-0.922220\pi\) | ||||
0.970294 | − | 0.241929i | \(-0.0777800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.05279e6i | 1.11442i | 0.830371 | + | 0.557210i | \(0.188128\pi\) | ||||
−0.830371 | + | 0.557210i | \(0.811872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.81255e6 | −1.30775 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 129733. | 0.0348400 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.12154e6i | 1.62477i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.24847e6i | 0.327519i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.04038e6 | −1.04768 | −0.523840 | − | 0.851817i | \(-0.675501\pi\) | ||||
−0.523840 | + | 0.851817i | \(0.675501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.95477e6 | 1.27000 | 0.634999 | − | 0.772513i | \(-0.281000\pi\) | ||||
0.634999 | + | 0.772513i | \(0.281000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 5.44265e6i | − 1.37907i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 9.09412e6i | − 2.27802i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.27775e6 | 0.564086 | 0.282043 | − | 0.959402i | \(-0.408988\pi\) | ||||
0.282043 | + | 0.959402i | \(0.408988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.64207e7 | −4.02065 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.88598e6i | 0.698688i | 0.936995 | + | 0.349344i | \(0.113596\pi\) | ||||
−0.936995 | + | 0.349344i | \(0.886404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.59720e6i | − 0.382347i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.63493e6 | −0.623735 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.01250e6 | −0.939288 | −0.469644 | − | 0.882856i | \(-0.655618\pi\) | ||||
−0.469644 | + | 0.882856i | \(0.655618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 453210.i | 0.104920i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.22953e7i | − 2.81509i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.87284e6 | −0.877002 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.10953e6 | −1.36841 | −0.684206 | − | 0.729288i | \(-0.739851\pi\) | ||||
−0.684206 | + | 0.729288i | \(0.739851\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.56911e6i | − 0.347634i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.59208e6i | 1.44467i | 0.691541 | + | 0.722337i | \(0.256932\pi\) | ||||
−0.691541 | + | 0.722337i | \(0.743068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.37278e6 | 0.514406 | 0.257203 | − | 0.966357i | \(-0.417199\pi\) | ||||
0.257203 | + | 0.966357i | \(0.417199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.48172e6 | −0.746726 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.30012e6i | 1.33677i | 0.743816 | + | 0.668385i | \(0.233014\pi\) | ||||
−0.743816 | + | 0.668385i | \(0.766986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71443e6i | 0.359905i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.47369e7 | 3.06094 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 975641. | 0.200510 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.74432e6i | 0.354726i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.55390e6i | 0.513934i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.28649e6 | 0.455334 | 0.227667 | − | 0.973739i | \(-0.426890\pi\) | ||||
0.227667 | + | 0.973739i | \(0.426890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.45590e6 | 0.681081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.97971e7i | − 3.86129i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 359712.i | − 0.0694385i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.28593e6 | −0.436758 | −0.218379 | − | 0.975864i | \(-0.570077\pi\) | ||||
−0.218379 | + | 0.975864i | \(0.570077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.40458e7 | 2.65629 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7.08998e6i | − 1.32721i | −0.748081 | − | 0.663607i | \(-0.769025\pi\) | ||||
0.748081 | − | 0.663607i | \(-0.230975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.63902e6i | 0.303716i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 832799. | 0.152766 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.32440e7 | −2.40506 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.60881e6i | 0.648804i | 0.945919 | + | 0.324402i | \(0.105163\pi\) | ||||
−0.945919 | + | 0.324402i | \(0.894837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.81534e7i | − 3.23121i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.01067e7 | 1.78111 | 0.890554 | − | 0.454878i | \(-0.150317\pi\) | ||||
0.890554 | + | 0.454878i | \(0.150317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84404e6 | 0.321767 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.38919e6i | 0.585566i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.49518e6i | 0.426882i | 0.976956 | + | 0.213441i | \(0.0684670\pi\) | ||||
−0.976956 | + | 0.213441i | \(0.931533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.02045e6 | 1.35877 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.10974e7 | 3.53945 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 334363.i | 0.0555520i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 599380.i | 0.0986225i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.42422e6 | −1.04689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.37259e6 | −1.51274 | −0.756371 | − | 0.654142i | \(-0.773030\pi\) | ||||
−0.756371 | + | 0.654142i | \(0.773030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.96213e6i | 0.313670i | 0.987625 | + | 0.156835i | \(0.0501291\pi\) | ||||
−0.987625 | + | 0.156835i | \(0.949871\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.79723e6i | 0.601268i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.04850e6 | 0.164453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.18131e6 | 0.649640 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.98809e7i | 3.05985i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.94646e6i | 0.754183i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.15145e6 | 0.778117 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.29674e6 | −1.24157 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.04512e6i | 0.303213i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.57325e6i | − 0.377998i | −0.981977 | − | 0.188999i | \(-0.939476\pi\) | ||||
0.981977 | − | 0.188999i | \(-0.0605243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.49228e6 | 0.217195 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.82715e6 | 0.263502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.99737e6i | 0.999923i | 0.866048 | + | 0.499962i | \(0.166653\pi\) | ||||
−0.866048 | + | 0.499962i | \(0.833347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.43670e7i | − 2.03440i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.20374e7 | −3.09230 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.10230e6 | −1.12667 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3.38843e6i | − 0.466946i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.11329e7i | − 1.52044i | −0.649665 | − | 0.760221i | \(-0.725091\pi\) | ||||
0.649665 | − | 0.760221i | \(-0.274909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.06484e7 | 1.44130 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −368630. | −0.0494520 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.19654e6i | − 0.956870i | −0.878123 | − | 0.478435i | \(-0.841204\pi\) | ||||
0.878123 | − | 0.478435i | \(-0.158796\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.87273e6i | − 0.510383i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.82339e7 | 2.38190 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.80510e6 | 0.492703 | 0.246352 | − | 0.969181i | \(-0.420768\pi\) | ||||
0.246352 | + | 0.969181i | \(0.420768\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.56459e6i | 0.457530i | 0.973482 | + | 0.228765i | \(0.0734687\pi\) | ||||
−0.973482 | + | 0.228765i | \(0.926531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.15102e7i | 1.46452i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.03655e6 | −0.256877 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.33424e7 | 1.66837 | 0.834187 | − | 0.551482i | \(-0.185937\pi\) | ||||
0.834187 | + | 0.551482i | \(0.185937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.18816e7i | − 1.47292i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.65682e6i | 0.572333i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 318075. | 0.0387578 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.08941e6 | 1.09811 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.02312e7i | − 1.22555i | −0.790257 | − | 0.612775i | \(-0.790053\pi\) | ||||
0.790257 | − | 0.612775i | \(-0.209947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.40976e7i | 1.67439i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.97545e6 | −0.939261 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.50572e7 | 1.75836 | 0.879181 | − | 0.476487i | \(-0.158090\pi\) | ||||
0.879181 | + | 0.476487i | \(0.158090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.14351e6i | − 0.132418i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.23988e7i | 2.57211i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 994780. | 0.113282 | 0.0566409 | − | 0.998395i | \(-0.481961\pi\) | ||||
0.0566409 | + | 0.998395i | \(0.481961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.59335e6 | 0.744595 | 0.372297 | − | 0.928113i | \(-0.378570\pi\) | ||||
0.372297 | + | 0.928113i | \(0.378570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.02371e6i | − 0.450644i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.92255e6i | 0.435693i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.09559e6 | −1.00198 | −0.500990 | − | 0.865453i | \(-0.667031\pi\) | ||||
−0.500990 | + | 0.865453i | \(0.667031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.79734e7 | −5.24152 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.54181e6i | 0.708916i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.08785e7i | 1.16927i | 0.811295 | + | 0.584637i | \(0.198763\pi\) | ||||
−0.811295 | + | 0.584637i | \(0.801237\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.84989e6 | 0.517064 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.35827e6 | −0.249391 | −0.124696 | − | 0.992195i | \(-0.539795\pi\) | ||||
−0.124696 | + | 0.992195i | \(0.539795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 2.95345e6i | − 0.309815i | −0.987929 | − | 0.154907i | \(-0.950492\pi\) | ||||
0.987929 | − | 0.154907i | \(-0.0495079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.46318e7i | 2.56311i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.40782e7 | −1.45321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.95640e6i | − 0.503498i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.02041e6i | 0.102836i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.49811e7 | 1.49785 | 0.748927 | − | 0.662653i | \(-0.230570\pi\) | ||||
0.748927 | + | 0.662653i | \(0.230570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.28481e6 | −0.623423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.91950e6i | 0.385742i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.23211e7i | 2.17955i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.10831e7 | 3.01143 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.70605e6 | −0.452388 | −0.226194 | − | 0.974082i | \(-0.572628\pi\) | ||||
−0.226194 | + | 0.974082i | \(0.572628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.00759e7i | − 0.961074i | −0.876974 | − | 0.480537i | \(-0.840442\pi\) | ||||
0.876974 | − | 0.480537i | \(-0.159558\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.04405e7i | − 0.988151i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.69585e6 | 0.159267 | 0.0796337 | − | 0.996824i | \(-0.474625\pi\) | ||||
0.0796337 | + | 0.996824i | \(0.474625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.47607e6 | 0.230755 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.06891e7i | 2.83812i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.63786e6i | 0.884500i | 0.896892 | + | 0.442250i | \(0.145820\pi\) | ||||
−0.896892 | + | 0.442250i | \(0.854180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.03993e6 | −0.550083 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.88237e7 | −1.70134 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.50539e6i | 0.852622i | 0.904577 | + | 0.426311i | \(0.140187\pi\) | ||||
−0.904577 | + | 0.426311i | \(0.859813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.34346e7i | 1.19597i | 0.801507 | + | 0.597986i | \(0.204032\pi\) | ||||
−0.801507 | + | 0.597986i | \(0.795968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.02334e6 | −0.355470 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.53750e7 | 1.34822 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.57293e7i | − 2.23931i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.02390e7i | − 0.884493i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.78935e6 | −0.153422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 930663. | 0.0792054 | 0.0396027 | − | 0.999216i | \(-0.487391\pi\) | ||||
0.0396027 | + | 0.999216i | \(0.487391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4.72458e6i | − 0.399120i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.87737e6i | − 0.576701i | −0.957525 | − | 0.288350i | \(-0.906893\pi\) | ||||
0.957525 | − | 0.288350i | \(-0.0931068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.17062e6 | −0.263919 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.09997e7 | 1.73518 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 909803.i | − 0.0746269i | −0.999304 | − | 0.0373135i | \(-0.988120\pi\) | ||||
0.999304 | − | 0.0373135i | \(-0.0118800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 867960.i | − 0.0706762i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.97169e6 | −0.725241 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.47157e6 | 0.278598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.04678e7i | 1.63071i | 0.578961 | + | 0.815355i | \(0.303458\pi\) | ||||
−0.578961 | + | 0.815355i | \(0.696542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.34058e6i | − 0.580627i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.71304e6 | −0.291587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.46052e6 | −0.113874 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.45490e7i | 1.12627i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.75532e7i | 1.34916i | 0.738203 | + | 0.674578i | \(0.235674\pi\) | ||||
−0.738203 | + | 0.674578i | \(0.764326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.37198e7 | −1.04703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.41410e6 | 0.486030 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.62540e7i | − 1.22296i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.23525e7i | 1.66997i | 0.550270 | + | 0.834987i | \(0.314525\pi\) | ||||
−0.550270 | + | 0.834987i | \(0.685475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.90158e7 | 1.41072 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.64593e7 | −1.21252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.13204e6i | − 0.0828128i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.01154e7i | − 2.18771i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.84982e7 | −1.33447 | −0.667234 | − | 0.744848i | \(-0.732522\pi\) | ||||
−0.667234 | + | 0.744848i | \(0.732522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.94719e6 | 0.211140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.74709e6i | 0.124300i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.93508e6i | 0.348698i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.77823e6 | 0.405470 | 0.202735 | − | 0.979234i | \(-0.435017\pi\) | ||||
0.202735 | + | 0.979234i | \(0.435017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.85162e6 | 0.547193 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.14410e6i | 0.217622i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00639e6i | 0.0691839i | 0.999402 | + | 0.0345920i | \(0.0110132\pi\) | ||||
−0.999402 | + | 0.0345920i | \(0.988987\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.18853e7 | 1.49429 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −501133. | −0.0339848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.10508e7i | 0.744357i | 0.928161 | + | 0.372179i | \(0.121389\pi\) | ||||
−0.928161 | + | 0.372179i | \(0.878611\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 5.40956e7i | − 3.61923i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.91879e6 | 0.459789 | 0.229894 | − | 0.973216i | \(-0.426162\pi\) | ||||
0.229894 | + | 0.973216i | \(0.426162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.38920e6 | 0.157711 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.09294e7i | − 0.716630i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.54066e7i | − 2.95743i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.79833e7 | 1.16351 | 0.581756 | − | 0.813364i | \(-0.302366\pi\) | ||||
0.581756 | + | 0.813364i | \(0.302366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.40642e7 | 2.83203 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.11486e7i | 0.711795i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.59762e7i | 1.64754i | 0.566923 | + | 0.823771i | \(0.308134\pi\) | ||||
−0.566923 | + | 0.823771i | \(0.691866\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.78674e6 | 0.364611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.18122e6 | 0.512102 | 0.256051 | − | 0.966663i | \(-0.417579\pi\) | ||||
0.256051 | + | 0.966663i | \(0.417579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.61052e7i | − 1.00151i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.68378e6i | 0.165804i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.70246e7 | 1.65871 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85187e7 | −1.12926 | −0.564630 | − | 0.825344i | \(-0.690981\pi\) | ||||
−0.564630 | + | 0.825344i | \(0.690981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.31889e7i | 0.799049i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.07043e7i | 0.644329i | 0.946684 | + | 0.322164i | \(0.104410\pi\) | ||||
−0.946684 | + | 0.322164i | \(0.895590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.15702e6 | 0.188809 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.98668e7 | −1.77475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.96373e7i | − 1.15941i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3.87125e6i | − 0.227104i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.96894e7 | 3.47931 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.33626e7 | −0.773955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 68571.9i | − 0.00394648i | −0.999998 | − | 0.00197324i | \(-0.999372\pi\) | ||||
0.999998 | − | 0.00197324i | \(-0.000628102\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.98523e7i | 1.13532i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.41356e7 | −1.93984 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.95294e7 | −1.10283 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 3.40379e6i | − 0.191005i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.51343e7i | − 1.40159i | −0.713363 | − | 0.700794i | \(-0.752829\pi\) | ||||
0.713363 | − | 0.700794i | \(-0.247171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.93157e6 | −0.107039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.30411e7 | 1.81959 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.34440e6i | 0.128305i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.79508e7i | 0.976325i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.81946e7 | −2.60504 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.45606e7 | 1.31937 | 0.659687 | − | 0.751540i | \(-0.270689\pi\) | ||||
0.659687 | + | 0.751540i | \(0.270689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.94878e6i | 0.104043i | 0.998646 | + | 0.0520213i | \(0.0165664\pi\) | ||||
−0.998646 | + | 0.0520213i | \(0.983434\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 4.97123e7i | − 2.63778i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.27360e7 | −0.671641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.22739e7 | −2.21573 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 8.01172e7i | − 4.17365i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.02265e7i | 1.04728i | 0.851940 | + | 0.523639i | \(0.175426\pi\) | ||||
−0.851940 | + | 0.523639i | \(0.824574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.57978e7 | 0.813010 | 0.406505 | − | 0.913649i | \(-0.366747\pi\) | ||||
0.406505 | + | 0.913649i | \(0.366747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.10994e6 | −0.0567761 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.99880e7i | 1.52470i | 0.647167 | + | 0.762348i | \(0.275954\pi\) | ||||
−0.647167 | + | 0.762348i | \(0.724046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.30834e7i | 0.661201i | 0.943771 | + | 0.330601i | \(0.107251\pi\) | ||||
−0.943771 | + | 0.330601i | \(0.892749\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.70290e6 | −0.336713 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.59063e6 | −0.329090 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.64605e7i | 0.817008i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.81839e7i | − 1.88394i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.58503e7 | −0.777378 | −0.388689 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388689 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.18377e7 | −2.03975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.04039e7i | 0.504227i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.07312e6i | − 0.148060i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.45747e7 | 1.65596 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.49440e7 | −1.18767 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.60183e7i | − 0.758215i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.25379e6i | − 0.388402i | −0.980962 | − | 0.194201i | \(-0.937789\pi\) | ||||
0.980962 | − | 0.194201i | \(-0.0622113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.60847e7 | −1.68814 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.20306e7 | 0.559546 | 0.279773 | − | 0.960066i | \(-0.409741\pi\) | ||||
0.279773 | + | 0.960066i | \(0.409741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.28563e6i | 0.336887i | 0.985711 | + | 0.168443i | \(0.0538741\pi\) | ||||
−0.985711 | + | 0.168443i | \(0.946126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 4.27486e7i | − 1.96523i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.70168e7 | −1.23483 | −0.617415 | − | 0.786638i | \(-0.711820\pi\) | ||||
−0.617415 | + | 0.786638i | \(0.711820\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.82511e6 | 0.264706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.79593e7i | 1.71502i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.36833e6i | − 0.106388i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.46952e6 | −0.244289 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.44134e6 | 0.330458 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.44310e6i | − 0.152030i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.20510e7i | 0.529082i | 0.964374 | + | 0.264541i | \(0.0852204\pi\) | ||||
−0.964374 | + | 0.264541i | \(0.914780\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.33569e7 | −1.89272 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.10240e7 | 1.78073 | 0.890366 | − | 0.455245i | \(-0.150448\pi\) | ||||
0.890366 | + | 0.455245i | \(0.150448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.77485e6i | 0.119767i | 0.998205 | + | 0.0598835i | \(0.0190729\pi\) | ||||
−0.998205 | + | 0.0598835i | \(0.980927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.64970e7i | − 1.13720i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.74930e7 | −1.17331 | −0.586655 | − | 0.809837i | \(-0.699556\pi\) | ||||
−0.586655 | + | 0.809837i | \(0.699556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.45479e7 | 1.46611 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.32984e6i | 0.224916i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.59708e7i | − 1.08982i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.52300e6 | 0.313931 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.31582e7 | 2.62089 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.98852e7i | 1.64593i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.02503e6i | 0.0420654i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.20264e7 | −3.75572 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.35311e6 | −0.0549177 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.59931e7i | 0.645525i | 0.946480 | + | 0.322763i | \(0.104612\pi\) | ||||
−0.946480 | + | 0.322763i | \(0.895388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.81476e7i | 1.53129i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.65270e6 | 0.265584 | 0.132792 | − | 0.991144i | \(-0.457606\pi\) | ||||
0.132792 | + | 0.991144i | \(0.457606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.36120e6 | −0.0540438 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.91482e7i | 0.756092i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.32380e7i | 2.09073i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.78769e7 | −1.08882 | −0.544409 | − | 0.838820i | \(-0.683246\pi\) | ||||
−0.544409 | + | 0.838820i | \(0.683246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.14931e7 | −1.61186 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.22520e7i | − 1.63246i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.07243e6i | 0.118067i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.91695e6 | −0.264372 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.07437e7 | 0.788581 | 0.394290 | − | 0.918986i | \(-0.370990\pi\) | ||||
0.394290 | + | 0.918986i | \(0.370990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8.86140e7i | − 3.35064i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.40381e6i | − 0.0527963i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 334252. | 0.0125039 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.13976e7 | −0.424097 | −0.212049 | − | 0.977259i | \(-0.568014\pi\) | ||||
−0.212049 | + | 0.977259i | \(0.568014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.89872e7i | 1.07286i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 995880.i | 0.0366634i | 0.999832 | + | 0.0183317i | \(0.00583549\pi\) | ||||
−0.999832 | + | 0.0183317i | \(0.994165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.29271e7 | 0.839596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.16440e7 | −1.51696 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.26122e6i | 0.190639i | 0.995447 | + | 0.0953194i | \(0.0303872\pi\) | ||||
−0.995447 | + | 0.0953194i | \(0.969613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.55875e7i | 0.922280i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.62948e7 | −0.584247 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.85407e7 | −1.01797 | −0.508983 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508983 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.04367e7i | − 0.370302i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.40228e7i | − 0.494942i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.65050e6 | −0.268623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.11422e6 | −0.108778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.06568e8i | 3.70306i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.07735e7i | 0.372426i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.62711e6 | 0.296688 | 0.148344 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148344 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.59725e7 | 0.546467 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.69141e7i | 0.575706i | 0.957675 | + | 0.287853i | \(0.0929415\pi\) | ||||
−0.957675 | + | 0.287853i | \(0.907058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.27280e7i | 1.10825i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.21142e7 | −0.408117 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.09583e7 | −0.367288 | −0.183644 | − | 0.982993i | \(-0.558789\pi\) | ||||
−0.183644 | + | 0.982993i | \(0.558789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.11511e6i | − 0.137222i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.77982e7i | 1.25400i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.08936e7 | 0.359573 | 0.179787 | − | 0.983706i | \(-0.442459\pi\) | ||||
0.179787 | + | 0.983706i | \(0.442459\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.23167e6 | 0.237491 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.65360e7i | − 1.84728i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.93561e7i | − 1.60454i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.60015e6 | 0.0517578 | 0.0258789 | − | 0.999665i | \(-0.491762\pi\) | ||||
0.0258789 | + | 0.999665i | \(0.491762\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.07367e7 | −1.31103 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.03099e7i | − 0.650355i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.42051e7i | 0.452593i | 0.974059 | + | 0.226296i | \(0.0726618\pi\) | ||||
−0.974059 | + | 0.226296i | \(0.927338\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.71608e7 | 1.17807 |
(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 | 320.6.d.b.161.1 | yes | 8 | |
4.3 | odd | 2 | 320.6.d.a.161.8 | yes | 8 | ||
8.3 | odd | 2 | 320.6.d.a.161.1 | ✓ | 8 | ||
8.5 | even | 2 | inner | 320.6.d.b.161.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.a.161.1 | ✓ | 8 | 8.3 | odd | 2 | ||
320.6.d.a.161.8 | yes | 8 | 4.3 | odd | 2 | ||
320.6.d.b.161.1 | yes | 8 | 1.1 | even | 1 | trivial | |
320.6.d.b.161.8 | yes | 8 | 8.5 | even | 2 | inner |