Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,5,Mod(703,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.703");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.b (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: | \(119.082197473\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.3 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.703 |
Dual form | 1152.5.b.k.703.6 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 23.7490i | − 0.949961i | −0.879996 | − | 0.474980i | \(-0.842455\pi\) | ||||
0.879996 | − | 0.474980i | \(-0.157545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 9.38251i | − 0.191480i | −0.995406 | − | 0.0957399i | \(-0.969478\pi\) | ||||
0.995406 | − | 0.0957399i | \(-0.0305217\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 112.001 | 0.925631 | 0.462816 | − | 0.886455i | \(-0.346839\pi\) | ||||
0.462816 | + | 0.886455i | \(0.346839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.5020i | 0.334331i | 0.985929 | + | 0.167166i | \(0.0534615\pi\) | ||||
−0.985929 | + | 0.167166i | \(0.946539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 79.9921 | 0.276789 | 0.138395 | − | 0.990377i | \(-0.455806\pi\) | ||||
0.138395 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −211.297 | −0.585309 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 217.355i | − 0.410880i | −0.978670 | − | 0.205440i | \(-0.934138\pi\) | ||||
0.978670 | − | 0.205440i | \(-0.0658625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.9843 | 0.0975748 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 616.753i | − 0.733357i | −0.930348 | − | 0.366678i | \(-0.880495\pi\) | ||||
0.930348 | − | 0.366678i | \(-0.119505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1111.81i | − 1.15693i | −0.815707 | − | 0.578465i | \(-0.803652\pi\) | ||||
0.815707 | − | 0.578465i | \(-0.196348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −222.825 | −0.181898 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 802.980i | 0.586545i | 0.956029 | + | 0.293273i | \(0.0947443\pi\) | ||||
−0.956029 | + | 0.293273i | \(0.905256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2411.93 | 1.43482 | 0.717409 | − | 0.696652i | \(-0.245328\pi\) | ||||
0.717409 | + | 0.696652i | \(0.245328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2130.38 | 1.15218 | 0.576090 | − | 0.817386i | \(-0.304578\pi\) | ||||
0.576090 | + | 0.817386i | \(0.304578\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3596.58i | 1.62815i | 0.580761 | + | 0.814074i | \(0.302755\pi\) | ||||
−0.580761 | + | 0.814074i | \(0.697245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2312.97 | 0.963335 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 833.725i | 0.296805i | 0.988927 | + | 0.148403i | \(0.0474131\pi\) | ||||
−0.988927 | + | 0.148403i | \(0.952587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2659.92i | − 0.879313i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1309.43 | −0.376165 | −0.188083 | − | 0.982153i | \(-0.560227\pi\) | ||||
−0.188083 | + | 0.982153i | \(0.560227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4785.91i | − 1.28619i | −0.765786 | − | 0.643095i | \(-0.777650\pi\) | ||||
0.765786 | − | 0.643095i | \(-0.222350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1341.87 | 0.317601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4025.23 | −0.896688 | −0.448344 | − | 0.893861i | \(-0.647986\pi\) | ||||
−0.448344 | + | 0.893861i | \(0.647986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9487.13i | 1.88199i | 0.338416 | + | 0.940997i | \(0.390109\pi\) | ||||
−0.338416 | + | 0.940997i | \(0.609891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −266.031 | −0.0499215 | −0.0249607 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249607 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1050.85i | − 0.177240i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 5756.11i | − 0.922306i | −0.887321 | − | 0.461153i | \(-0.847436\pi\) | ||||
0.887321 | − | 0.461153i | \(-0.152564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7287.16 | 1.05780 | 0.528898 | − | 0.848685i | \(-0.322605\pi\) | ||||
0.528898 | + | 0.848685i | \(0.322605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1899.73i | − 0.262939i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1414.08 | 0.178523 | 0.0892614 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892614 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 530.130 | 0.0640177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5018.09i | 0.556021i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3110.08 | −0.330543 | −0.165271 | − | 0.986248i | \(-0.552850\pi\) | ||||
−0.165271 | + | 0.986248i | \(0.552850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 488.501i | 0.0478876i | 0.999713 | + | 0.0239438i | \(0.00762227\pi\) | ||||
−0.999713 | + | 0.0239438i | \(0.992378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 20097.0i | − 1.89434i | −0.320739 | − | 0.947168i | \(-0.603931\pi\) | ||||
0.320739 | − | 0.947168i | \(-0.396069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12383.0 | −1.08158 | −0.540790 | − | 0.841158i | \(-0.681874\pi\) | ||||
−0.540790 | + | 0.841158i | \(0.681874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 15542.1i | − 1.30814i | −0.756433 | − | 0.654072i | \(-0.773059\pi\) | ||||
0.756433 | − | 0.654072i | \(-0.226941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11653.6 | −0.912651 | −0.456325 | − | 0.889813i | \(-0.650835\pi\) | ||||
−0.456325 | + | 0.889813i | \(0.650835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5161.98 | −0.390319 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 750.527i | − 0.0529996i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2096.69 | −0.143206 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 16291.5i | − 1.04265i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4724.04i | − 0.292891i | −0.989219 | − | 0.146445i | \(-0.953217\pi\) | ||||
0.989219 | − | 0.146445i | \(-0.0467833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9632.86 | 0.561323 | 0.280661 | − | 0.959807i | \(-0.409446\pi\) | ||||
0.280661 | + | 0.959807i | \(0.409446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1982.49i | 0.112075i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16407.6 | −0.874185 | −0.437093 | − | 0.899417i | \(-0.643992\pi\) | ||||
−0.437093 | + | 0.899417i | \(0.643992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25544.1 | 1.32209 | 0.661046 | − | 0.750346i | \(-0.270113\pi\) | ||||
0.661046 | + | 0.750346i | \(0.270113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6328.30i | 0.309467i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14647.3 | −0.696660 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18716.6i | − 0.843054i | −0.906816 | − | 0.421527i | \(-0.861494\pi\) | ||||
0.906816 | − | 0.421527i | \(-0.138506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 28860.0i | 1.26574i | 0.774260 | + | 0.632868i | \(0.218122\pi\) | ||||
−0.774260 | + | 0.632868i | \(0.781878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26404.4 | −1.09904 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 23963.1i | − 0.972172i | −0.873911 | − | 0.486086i | \(-0.838424\pi\) | ||||
0.873911 | − | 0.486086i | \(-0.161576\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2039.34 | −0.0786752 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24424.8 | −0.919297 | −0.459648 | − | 0.888101i | \(-0.652025\pi\) | ||||
−0.459648 | + | 0.888101i | \(0.652025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3088.40i | − 0.110739i | −0.998466 | − | 0.0553696i | \(-0.982366\pi\) | ||||
0.998466 | − | 0.0553696i | \(-0.0176337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25368.5 | 0.888223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18621.0i | − 0.622171i | −0.950382 | − | 0.311085i | \(-0.899307\pi\) | ||||
0.950382 | − | 0.311085i | \(-0.100693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 572.185i | − 0.0186836i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 50739.3 | 1.58357 | 0.791787 | − | 0.610797i | \(-0.209151\pi\) | ||||
0.791787 | + | 0.610797i | \(0.209151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 58050.5i | − 1.77194i | −0.463742 | − | 0.885970i | \(-0.653494\pi\) | ||||
0.463742 | − | 0.885970i | \(-0.346506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19070.0 | 0.557195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8959.23 | 0.256205 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 21285.6i | − 0.583471i | −0.956499 | − | 0.291736i | \(-0.905767\pi\) | ||||
0.956499 | − | 0.291736i | \(-0.0942327\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26074.3 | −0.700001 | −0.350001 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350001 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4731.26i | − 0.121911i | −0.998140 | − | 0.0609557i | \(-0.980585\pi\) | ||||
0.998140 | − | 0.0609557i | \(-0.0194149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 38561.7i | 0.973756i | 0.873470 | + | 0.486878i | \(0.161864\pi\) | ||||
−0.873470 | + | 0.486878i | \(0.838136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5786.69 | −0.140423 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 57280.9i | − 1.36302i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23665.5 | −0.541780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −48656.4 | −1.09289 | −0.546444 | − | 0.837496i | \(-0.684019\pi\) | ||||
−0.546444 | + | 0.837496i | \(0.684019\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 50594.5i | − 1.09453i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10431.6 | −0.221529 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4519.71i | 0.0925393i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 73299.7i | 1.47398i | 0.675902 | + | 0.736992i | \(0.263754\pi\) | ||||
−0.675902 | + | 0.736992i | \(0.736246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14996.0 | −0.291020 | −0.145510 | − | 0.989357i | \(-0.546482\pi\) | ||||
−0.145510 | + | 0.989357i | \(0.546482\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 74694.9i | − 1.42436i | −0.701996 | − | 0.712181i | \(-0.747708\pi\) | ||||
0.701996 | − | 0.712181i | \(-0.252292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 69476.6 | 1.27975 | 0.639877 | − | 0.768477i | \(-0.278985\pi\) | ||||
0.639877 | + | 0.768477i | \(0.278985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 85415.2 | 1.54668 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 87478.2i | − 1.53145i | −0.643166 | − | 0.765727i | \(-0.722380\pi\) | ||||
0.643166 | − | 0.765727i | \(-0.277620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 74951.4 | 1.29046 | 0.645232 | − | 0.763987i | \(-0.276761\pi\) | ||||
0.645232 | + | 0.763987i | \(0.276761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 54930.7i | − 0.915131i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 11938.7i | − 0.195687i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −43677.8 | −0.693287 | −0.346643 | − | 0.937997i | \(-0.612679\pi\) | ||||
−0.346643 | + | 0.937997i | \(0.612679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 24344.1i | − 0.380323i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1164.55 | 0.0176316 | 0.00881581 | − | 0.999961i | \(-0.497194\pi\) | ||||
0.00881581 | + | 0.999961i | \(0.497194\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7533.97 | 0.112312 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 35001.0i | − 0.506021i | −0.967464 | − | 0.253010i | \(-0.918579\pi\) | ||||
0.967464 | − | 0.253010i | \(-0.0814207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19800.2 | 0.281953 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 41077.9i | − 0.567681i | −0.958872 | − | 0.283840i | \(-0.908391\pi\) | ||||
0.958872 | − | 0.283840i | \(-0.0916085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46419.1i | 0.632060i | 0.948749 | + | 0.316030i | \(0.102350\pi\) | ||||
−0.948749 | + | 0.316030i | \(0.897650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6830.32 | 0.0903183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 150297.i | − 1.95881i | −0.201907 | − | 0.979405i | \(-0.564714\pi\) | ||||
0.201907 | − | 0.979405i | \(-0.435286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 117793. | 1.49179 | 0.745895 | − | 0.666063i | \(-0.232022\pi\) | ||||
0.745895 | + | 0.666063i | \(0.232022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −41243.6 | −0.514973 | −0.257486 | − | 0.966282i | \(-0.582894\pi\) | ||||
−0.257486 | + | 0.966282i | \(0.582894\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 22629.9i | − 0.274739i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77122.3 | −0.923388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 71937.8i | − 0.837957i | −0.907996 | − | 0.418979i | \(-0.862388\pi\) | ||||
0.907996 | − | 0.418979i | \(-0.137612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31097.7i | 0.357342i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12281.0 | 0.137370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 19988.3i | − 0.220619i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −113661. | −1.22183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −54572.7 | −0.579027 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 60945.8i | 0.630119i | 0.949072 | + | 0.315060i | \(0.102025\pi\) | ||||
−0.949072 | + | 0.315060i | \(0.897975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 102774. | 1.04904 | 0.524521 | − | 0.851397i | \(-0.324244\pi\) | ||||
0.524521 | + | 0.851397i | \(0.324244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 39779.2i | − 0.395857i | −0.980217 | − | 0.197928i | \(-0.936579\pi\) | ||||
0.980217 | − | 0.197928i | \(-0.0634213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 69077.2i | − 0.678818i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16902.1 | −0.162007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3445.73i | 0.0326223i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33744.9 | 0.311758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −87804.6 | −0.801422 | −0.400711 | − | 0.916204i | \(-0.631237\pi\) | ||||
−0.400711 | + | 0.916204i | \(0.631237\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 95595.3i | 0.851818i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −57972.0 | −0.510456 | −0.255228 | − | 0.966881i | \(-0.582151\pi\) | ||||
−0.255228 | + | 0.966881i | \(0.582151\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 124524.i | − 1.07089i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 44228.9i | − 0.375939i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 159188. | 1.32206 | 0.661031 | − | 0.750359i | \(-0.270119\pi\) | ||||
0.661031 | + | 0.750359i | \(0.270119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17396.8i | − 0.142830i | −0.997447 | − | 0.0714149i | \(-0.977249\pi\) | ||||
0.997447 | − | 0.0714149i | \(-0.0227514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −150532. | −1.20803 | −0.604017 | − | 0.796972i | \(-0.706434\pi\) | ||||
−0.604017 | + | 0.796972i | \(0.706434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 225310. | 1.78782 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24818.5i | 0.192569i | 0.995354 | + | 0.0962846i | \(0.0306959\pi\) | ||||
−0.995354 | + | 0.0962846i | \(0.969304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −85674.8 | −0.657413 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6317.99i | 0.0474234i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 89484.6i | − 0.664379i | −0.943213 | − | 0.332190i | \(-0.892213\pi\) | ||||
0.943213 | − | 0.332190i | \(-0.107787\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7822.44 | 0.0568322 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 168536.i | − 1.21137i | −0.795705 | − | 0.605684i | \(-0.792900\pi\) | ||||
0.795705 | − | 0.605684i | \(-0.207100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34847.8 | 0.245184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −126865. | −0.883208 | −0.441604 | − | 0.897210i | \(-0.645590\pi\) | ||||
−0.441604 | + | 0.897210i | \(0.645590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 257277.i | 1.75389i | 0.480587 | + | 0.876947i | \(0.340424\pi\) | ||||
−0.480587 | + | 0.876947i | \(0.659576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24956.8 | −0.168371 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 150562.i | 0.994983i | 0.867469 | + | 0.497492i | \(0.165745\pi\) | ||||
−0.867469 | + | 0.497492i | \(0.834255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 17386.7i | − 0.113727i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −136702. | −0.876155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 185402.i | − 1.17634i | −0.808736 | − | 0.588171i | \(-0.799848\pi\) | ||||
0.808736 | − | 0.588171i | \(-0.200152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −167681. | −1.04279 | −0.521393 | − | 0.853317i | \(-0.674587\pi\) | ||||
−0.521393 | + | 0.853317i | \(0.674587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 62819.4 | 0.386798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 89934.9i | 0.542925i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 60544.6 | 0.361934 | 0.180967 | − | 0.983489i | \(-0.442077\pi\) | ||||
0.180967 | + | 0.983489i | \(0.442077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12285.7i | 0.0720280i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 173063.i | − 1.00486i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −307306. | −1.75042 | −0.875211 | − | 0.483741i | \(-0.839277\pi\) | ||||
−0.875211 | + | 0.483741i | \(0.839277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 172189.i | 0.971496i | 0.874099 | + | 0.485748i | \(0.161453\pi\) | ||||
−0.874099 | + | 0.485748i | \(0.838547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4878.26 | 0.0270077 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44903.9 | −0.246279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28153.8i | 0.151559i | 0.997125 | + | 0.0757797i | \(0.0241446\pi\) | ||||
−0.997125 | + | 0.0757797i | \(0.975855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −322037. | −1.71763 | −0.858815 | − | 0.512285i | \(-0.828799\pi\) | ||||
−0.858815 | + | 0.512285i | \(0.828799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45926.4i | 0.240492i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 292438.i | − 1.51742i | −0.651430 | − | 0.758709i | \(-0.725830\pi\) | ||||
0.651430 | − | 0.758709i | \(-0.274170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 227681. | 1.16016 | 0.580082 | − | 0.814558i | \(-0.303020\pi\) | ||||
0.580082 | + | 0.814558i | \(0.303020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 33583.0i | − 0.169590i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −159097. | −0.789169 | −0.394585 | − | 0.918860i | \(-0.629111\pi\) | ||||
−0.394585 | + | 0.918860i | \(0.629111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 270139. | 1.32811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 12590.1i | − 0.0608143i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 340590. | 1.63079 | 0.815397 | − | 0.578902i | \(-0.196519\pi\) | ||||
0.815397 | + | 0.578902i | \(0.196519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 178561.i | − 0.840204i | −0.907477 | − | 0.420102i | \(-0.861994\pi\) | ||||
0.907477 | − | 0.420102i | \(-0.138006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4179.11i | 0.0194950i | 0.999952 | + | 0.00974748i | \(0.00310277\pi\) | ||||
−0.999952 | + | 0.00974748i | \(0.996897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 160583. | 0.736318 | 0.368159 | − | 0.929763i | \(-0.379988\pi\) | ||||
0.368159 | + | 0.929763i | \(0.379988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37766.8i | 0.171698i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 238606. | 1.06649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12885.8 | −0.0571114 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 153260.i | − 0.667970i | −0.942578 | − | 0.333985i | \(-0.891607\pi\) | ||||
0.942578 | − | 0.333985i | \(-0.108393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45370.0 | −0.196100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 73861.3i | 0.314003i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 113347.i | − 0.477917i | −0.971030 | − | 0.238958i | \(-0.923194\pi\) | ||||
0.971030 | − | 0.238958i | \(-0.0768059\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 248336. | 1.03009 | 0.515046 | − | 0.857162i | \(-0.327775\pi\) | ||||
0.515046 | + | 0.857162i | \(0.327775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 49335.4i | − 0.202985i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 89013.1 | 0.360364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −378612. | −1.52052 | −0.760262 | − | 0.649617i | \(-0.774929\pi\) | ||||
−0.760262 | + | 0.649617i | \(0.774929\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 255639.i | 1.01040i | 0.863004 | + | 0.505198i | \(0.168580\pi\) | ||||
−0.863004 | + | 0.505198i | \(0.831420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11601.4 | 0.0454913 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 204106.i | 0.787809i | 0.919151 | + | 0.393904i | \(0.128876\pi\) | ||||
−0.919151 | + | 0.393904i | \(0.871124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2496.04i | 0.00955895i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −477284. | −1.79954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 402822.i | 1.50707i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 295131. | 1.08727 | 0.543637 | − | 0.839320i | \(-0.317047\pi\) | ||||
0.543637 | + | 0.839320i | \(0.317047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −212950. | −0.778527 | −0.389263 | − | 0.921127i | \(-0.627270\pi\) | ||||
−0.389263 | + | 0.921127i | \(0.627270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 88936.0i | − 0.320226i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232598. | 0.831178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 136279.i | 0.479704i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 294084.i | 1.02746i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 259056. | 0.891694 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 387756.i | 1.32484i | 0.749132 | + | 0.662421i | \(0.230471\pi\) | ||||
−0.749132 | + | 0.662421i | \(0.769529\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −369108. | −1.24268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 241227. | 0.806215 | 0.403107 | − | 0.915153i | \(-0.367930\pi\) | ||||
0.403107 | + | 0.915153i | \(0.367930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130318.i | 0.429240i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54006.8 | −0.176603 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 86454.9i | − 0.278663i | −0.990246 | − | 0.139331i | \(-0.955505\pi\) | ||||
0.990246 | − | 0.139331i | \(-0.0444954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 120371.i | 0.385210i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 99585.2 | 0.314179 | 0.157090 | − | 0.987584i | \(-0.449789\pi\) | ||||
0.157090 | + | 0.987584i | \(0.449789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 276762.i | 0.866982i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 524085. | 1.61874 | 0.809371 | − | 0.587298i | \(-0.199808\pi\) | ||||
0.809371 | + | 0.587298i | \(0.199808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32749.2 | −0.100445 | −0.0502225 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502225 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 13255.3i | − 0.0400915i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −140276. | −0.421338 | −0.210669 | − | 0.977557i | \(-0.567564\pi\) | ||||
−0.210669 | + | 0.977557i | \(0.567564\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 68371.8i | − 0.202547i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 93378.4i | 0.274732i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −303094. | −0.879634 | −0.439817 | − | 0.898087i | \(-0.644957\pi\) | ||||
−0.439817 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 234921.i | 0.677161i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −117438. | −0.333963 | −0.166981 | − | 0.985960i | \(-0.553402\pi\) | ||||
−0.166981 | + | 0.985960i | \(0.553402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17824.3 | −0.0503475 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 537187.i | − 1.49717i | −0.663037 | − | 0.748587i | \(-0.730733\pi\) | ||||
0.663037 | − | 0.748587i | \(-0.269267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 382705. | 1.05953 | 0.529767 | − | 0.848143i | \(-0.322279\pi\) | ||||
0.529767 | + | 0.848143i | \(0.322279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49794.2i | 0.136040i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 578934.i | 1.57127i | 0.618688 | + | 0.785637i | \(0.287664\pi\) | ||||
−0.618688 | + | 0.785637i | \(0.712336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −203214. | −0.544341 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 287542.i | 0.765209i | 0.923912 | + | 0.382605i | \(0.124973\pi\) | ||||
−0.923912 | + | 0.382605i | \(0.875027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 400806. | 1.05284 | 0.526422 | − | 0.850223i | \(-0.323533\pi\) | ||||
0.526422 | + | 0.850223i | \(0.323533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 233469. | 0.609323 | 0.304661 | − | 0.952461i | \(-0.401457\pi\) | ||||
0.304661 | + | 0.952461i | \(0.401457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 13267.6i | − 0.0341835i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −348791. | −0.892904 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64232.1i | 0.162349i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 499538.i | 1.25461i | 0.778773 | + | 0.627306i | \(0.215843\pi\) | ||||
−0.778773 | + | 0.627306i | \(0.784157\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −112191. | −0.278235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 130687.i | 0.322073i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −405774. | −0.987571 | −0.493786 | − | 0.869584i | \(-0.664387\pi\) | ||||
−0.493786 | + | 0.869584i | \(0.664387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 550571. | 1.33165 | 0.665827 | − | 0.746106i | \(-0.268079\pi\) | ||||
0.665827 | + | 0.746106i | \(0.268079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 428220.i | − 1.02296i | −0.859295 | − | 0.511480i | \(-0.829097\pi\) | ||||
0.859295 | − | 0.511480i | \(-0.170903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −146658. | −0.348190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 802147.i | 1.88117i | 0.339561 | + | 0.940584i | \(0.389721\pi\) | ||||
−0.339561 | + | 0.940584i | \(0.610279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 228771.i | − 0.533234i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 662958. | 1.52656 | 0.763282 | − | 0.646065i | \(-0.223586\pi\) | ||||
0.763282 | + | 0.646065i | \(0.223586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 231396.i | 0.529607i | 0.964302 | + | 0.264804i | \(0.0853071\pi\) | ||||
−0.964302 | + | 0.264804i | \(0.914693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 47082.2 | 0.106467 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −134055. | −0.301321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 536029.i | − 1.19054i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 311867. | 0.688557 | 0.344278 | − | 0.938868i | \(-0.388124\pi\) | ||||
0.344278 | + | 0.938868i | \(0.388124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 655173.i | 1.42948i | 0.699389 | + | 0.714741i | \(0.253455\pi\) | ||||
−0.699389 | + | 0.714741i | \(0.746545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29180.3i | 0.0632923i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −358002. | −0.767439 | −0.383719 | − | 0.923450i | \(-0.625357\pi\) | ||||
−0.383719 | + | 0.923450i | \(0.625357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 389664.i | 0.830442i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47107.1 | −0.0992312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −826006. | −1.72992 | −0.864962 | − | 0.501838i | \(-0.832657\pi\) | ||||
−0.864962 | + | 0.501838i | \(0.832657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 606648.i | − 1.25593i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 192935. | 0.397142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 229057.i | − 0.466130i | −0.972461 | − | 0.233065i | \(-0.925124\pi\) | ||||
0.972461 | − | 0.233065i | \(-0.0748756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 169667.i | − 0.343310i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4583.37 | 0.00916950 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6312.88i | 0.0125584i | 0.999980 | + | 0.00627921i | \(0.00199875\pi\) | ||||
−0.999980 | + | 0.00627921i | \(0.998001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −241658. | −0.475359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 150291. | 0.293982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 179483.i | − 0.347189i | −0.984817 | − | 0.173594i | \(-0.944462\pi\) | ||||
0.984817 | − | 0.173594i | \(-0.0555382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −188560. | −0.362727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 37612.2i | − 0.0715571i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 310931.i | 0.588295i | 0.955760 | + | 0.294147i | \(0.0950357\pi\) | ||||
−0.955760 | + | 0.294147i | \(0.904964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 170414. | 0.318911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 602271.i | 1.12094i | 0.828173 | + | 0.560472i | \(0.189380\pi\) | ||||
−0.828173 | + | 0.560472i | \(0.810620\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −450832. | −0.830002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 64180.3 | 0.117520 | 0.0587602 | − | 0.998272i | \(-0.481285\pi\) | ||||
0.0587602 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 525793.i | 0.952440i | 0.879326 | + | 0.476220i | \(0.157993\pi\) | ||||
−0.879326 | + | 0.476220i | \(0.842007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −444502. | −0.800868 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 116184.i | 0.207101i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 405381.i | 0.718759i | 0.933191 | + | 0.359380i | \(0.117012\pi\) | ||||
−0.933191 | + | 0.359380i | \(0.882988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 685398. | 1.20240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5071.58i | 0.00885016i | 0.999990 | + | 0.00442508i | \(0.00140855\pi\) | ||||
−0.999990 | + | 0.00442508i | \(0.998591\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29104.4 | 0.0502561 | 0.0251280 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251280 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −145823. | −0.250483 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 73985.4i | − 0.125764i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −235095. | −0.397548 | −0.198774 | − | 0.980045i | \(-0.563696\pi\) | ||||
−0.198774 | + | 0.980045i | \(0.563696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 89776.8i | − 0.150247i | −0.997174 | − | 0.0751234i | \(-0.976065\pi\) | ||||
0.997174 | − | 0.0751234i | \(-0.0239351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 67802.8i | − 0.112887i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −509632. | −0.839812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06257e6i | 1.74203i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −569099. | −0.923525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −406715. | −0.656660 | −0.328330 | − | 0.944563i | \(-0.606486\pi\) | ||||
−0.328330 | + | 0.944563i | \(0.606486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 109340.i | 0.174754i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 270414. | 0.430013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02634e6i | 1.61576i | 0.589350 | + | 0.807878i | \(0.299384\pi\) | ||||
−0.589350 | + | 0.807878i | \(0.700616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 287698.i | 0.450654i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29795.9 | −0.0462089 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48432.3i | 0.0747383i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −245306. | −0.374810 | −0.187405 | − | 0.982283i | \(-0.560008\pi\) | ||||
−0.187405 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26760e6 | 1.92726 | 0.963628 | − | 0.267246i | \(-0.0861137\pi\) | ||||
0.963628 | + | 0.267246i | \(0.0861137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 580065.i | 0.873296i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −450142. | −0.674382 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 163484.i | 0.242542i | 0.992619 | + | 0.121271i | \(0.0386971\pi\) | ||||
−0.992619 | + | 0.121271i | \(0.961303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 913000.i | − 1.34794i | −0.738758 | − | 0.673971i | \(-0.764587\pi\) | ||||
0.738758 | − | 0.673971i | \(-0.235413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −378235. | −0.553032 | −0.276516 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276516 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 70195.3i | − 0.102141i | −0.998695 | − | 0.0510704i | \(-0.983737\pi\) | ||||
0.998695 | − | 0.0510704i | \(-0.0162633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 185019. | 0.266641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −73346.5 | −0.105198 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 410513.i | 0.583180i | 0.956543 | + | 0.291590i | \(0.0941843\pi\) | ||||
−0.956543 | + | 0.291590i | \(0.905816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 326897. | 0.462188 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 602478.i | − 0.843777i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19672.2i | 0.0274211i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 174532. | 0.240999 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 577725.i | 0.794005i | 0.917817 | + | 0.397003i | \(0.129950\pi\) | ||||
−0.917817 | + | 0.397003i | \(0.870050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 388294. | 0.528687 | 0.264344 | − | 0.964429i | \(-0.414845\pi\) | ||||
0.264344 | + | 0.964429i | \(0.414845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 124443. | 0.168650 | 0.0843248 | − | 0.996438i | \(-0.473127\pi\) | ||||
0.0843248 | + | 0.996438i | \(0.473127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 652166.i | 0.875662i | 0.899057 | + | 0.437831i | \(0.144253\pi\) | ||||
−0.899057 | + | 0.437831i | \(0.855747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −442229. | −0.591038 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 644693.i | − 0.853716i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 227434.i | − 0.299791i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −152855. | −0.199647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 75235.9i | 0.0978196i | 0.998803 | + | 0.0489098i | \(0.0155747\pi\) | ||||
−0.998803 | + | 0.0489098i | \(0.984425\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 916209. | 1.18044 | 0.590218 | − | 0.807244i | \(-0.299042\pi\) | ||||
0.590218 | + | 0.807244i | \(0.299042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.14981e6 | −1.47471 | −0.737354 | − | 0.675506i | \(-0.763925\pi\) | ||||
−0.737354 | + | 0.675506i | \(0.763925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.01630e6i | 1.29174i | 0.763448 | + | 0.645870i | \(0.223505\pi\) | ||||
−0.763448 | + | 0.645870i | \(0.776495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44323.3 | −0.0560827 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 759945.i | − 0.952970i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.20501e6i | − 1.50433i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −685711. | −0.848442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66691.5i | 0.0821525i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.37864e6 | −1.68327 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00415e6 | 1.22063 | 0.610315 | − | 0.792159i | \(-0.291043\pi\) | ||||
0.610315 | + | 0.792159i | \(0.291043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 231087.i | 0.278444i | 0.990261 | + | 0.139222i | \(0.0444602\pi\) | ||||
−0.990261 | + | 0.139222i | \(0.955540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 816172. | 0.979129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 90380.4i | − 0.107482i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 545658.i | − 0.646084i | −0.946385 | − | 0.323042i | \(-0.895294\pi\) | ||||
0.946385 | − | 0.323042i | \(-0.104706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −536041. | −0.629209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48969.2i | 0.0572320i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 243550. | 0.282200 | 0.141100 | − | 0.989995i | \(-0.454936\pi\) | ||||
0.141100 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −488722. | −0.563849 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 212773.i | − 0.243385i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 479076. | 0.545664 | 0.272832 | − | 0.962062i | \(-0.412040\pi\) | ||||
0.272832 | + | 0.962062i | \(0.412040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25655e6i | 1.41906i | 0.704675 | + | 0.709530i | \(0.251093\pi\) | ||||
−0.704675 | + | 0.709530i | \(0.748907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 524246.i | − 0.589538i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.22304e6 | 1.36377 | 0.681886 | − | 0.731459i | \(-0.261160\pi\) | ||||
0.681886 | + | 0.731459i | \(0.261160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15031.3i | − 0.0166903i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.12329e6 | 1.23682 | 0.618409 | − | 0.785856i | \(-0.287777\pi\) | ||||
0.618409 | + | 0.785856i | \(0.287777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −505512. | −0.554275 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 153944.i | 0.167389i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −312598. | −0.338485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 619240.i | 0.664974i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 310108.i | − 0.331635i | −0.986156 | − | 0.165818i | \(-0.946974\pi\) | ||||
0.986156 | − | 0.165818i | \(-0.0530263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 459519. | 0.487376 | 0.243688 | − | 0.969854i | \(-0.421643\pi\) | ||||
0.243688 | + | 0.969854i | \(0.421643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 239668.i | − 0.253154i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 645770. | 0.676532 | 0.338266 | − | 0.941050i | \(-0.390160\pi\) | ||||
0.338266 | + | 0.941050i | \(0.390160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 158379. | 0.165246 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 828941.i | 0.857860i | 0.903338 | + | 0.428930i | \(0.141109\pi\) | ||||
−0.903338 | + | 0.428930i | \(0.858891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −112363. | −0.115811 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 463050.i | − 0.473407i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 460245.i | − 0.468642i | −0.972159 | − | 0.234321i | \(-0.924713\pi\) | ||||
0.972159 | − | 0.234321i | \(-0.0752867\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 915803. | 0.925030 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.82730e6i | − 1.83831i | −0.393894 | − | 0.919156i | \(-0.628872\pi\) | ||||
0.393894 | − | 0.919156i | \(-0.371128\pi\) | |||||||
\(998\) | 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 | 1152.5.b.k.703.3 | 8 | ||
3.2 | odd | 2 | 384.5.b.c.319.3 | yes | 8 | ||
4.3 | odd | 2 | inner | 1152.5.b.k.703.4 | 8 | ||
8.3 | odd | 2 | inner | 1152.5.b.k.703.6 | 8 | ||
8.5 | even | 2 | inner | 1152.5.b.k.703.5 | 8 | ||
12.11 | even | 2 | 384.5.b.c.319.7 | yes | 8 | ||
24.5 | odd | 2 | 384.5.b.c.319.6 | yes | 8 | ||
24.11 | even | 2 | 384.5.b.c.319.2 | ✓ | 8 | ||
48.5 | odd | 4 | 768.5.g.g.511.3 | 4 | |||
48.11 | even | 4 | 768.5.g.g.511.1 | 4 | |||
48.29 | odd | 4 | 768.5.g.c.511.2 | 4 | |||
48.35 | even | 4 | 768.5.g.c.511.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.c.319.2 | ✓ | 8 | 24.11 | even | 2 | ||
384.5.b.c.319.3 | yes | 8 | 3.2 | odd | 2 | ||
384.5.b.c.319.6 | yes | 8 | 24.5 | odd | 2 | ||
384.5.b.c.319.7 | yes | 8 | 12.11 | even | 2 | ||
768.5.g.c.511.2 | 4 | 48.29 | odd | 4 | |||
768.5.g.c.511.4 | 4 | 48.35 | even | 4 | |||
768.5.g.g.511.1 | 4 | 48.11 | even | 4 | |||
768.5.g.g.511.3 | 4 | 48.5 | odd | 4 | |||
1152.5.b.k.703.3 | 8 | 1.1 | even | 1 | trivial | ||
1152.5.b.k.703.4 | 8 | 4.3 | odd | 2 | inner | ||
1152.5.b.k.703.5 | 8 | 8.5 | even | 2 | inner | ||
1152.5.b.k.703.6 | 8 | 8.3 | odd | 2 | inner |