Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.4 | ||
Root | \(2.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.ba.649.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.7477i | 1.01228i | 0.862451 | + | 0.506141i | \(0.168928\pi\) | ||||
−0.862451 | + | 0.506141i | \(0.831072\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.9909 | −1.09616 | −0.548078 | − | 0.836427i | \(-0.684640\pi\) | ||||
−0.548078 | + | 0.836427i | \(0.684640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 33.7477i | − 0.719995i | −0.932953 | − | 0.359998i | \(-0.882778\pi\) | ||||
0.932953 | − | 0.359998i | \(-0.117222\pi\) | |||||||
\(14\) | −37.4955 | −0.715792 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 53.7386i | − 0.766678i | −0.923608 | − | 0.383339i | \(-0.874774\pi\) | ||||
0.923608 | − | 0.383339i | \(-0.125226\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −91.7386 | −1.10770 | −0.553850 | − | 0.832617i | \(-0.686842\pi\) | ||||
−0.553850 | + | 0.832617i | \(0.686842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 79.9818i | − 0.775099i | ||||||||
\(23\) | 80.7386i | 0.731964i | 0.930622 | + | 0.365982i | \(0.119267\pi\) | ||||
−0.930622 | + | 0.365982i | \(0.880733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 67.4955 | 0.509113 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 74.9909i | − 0.506141i | ||||||||
\(29\) | −141.234 | −0.904362 | −0.452181 | − | 0.891926i | \(-0.649354\pi\) | ||||
−0.452181 | + | 0.891926i | \(0.649354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 264.955 | 1.53507 | 0.767536 | − | 0.641006i | \(-0.221483\pi\) | ||||
0.767536 | + | 0.641006i | \(0.221483\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 107.477 | 0.542124 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 61.2432i | 0.272117i | 0.990701 | + | 0.136058i | \(0.0434435\pi\) | ||||
−0.990701 | + | 0.136058i | \(0.956557\pi\) | |||||||
\(38\) | − 183.477i | − 0.783262i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 314.973 | 1.19977 | 0.599884 | − | 0.800087i | \(-0.295213\pi\) | ||||
0.599884 | + | 0.800087i | \(0.295213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 236.261i | − 0.837896i | −0.908010 | − | 0.418948i | \(-0.862399\pi\) | ||||
0.908010 | − | 0.418948i | \(-0.137601\pi\) | |||||||
\(44\) | 159.964 | 0.548078 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −161.477 | −0.517577 | ||||||||
\(47\) | − 243.261i | − 0.754964i | −0.926017 | − | 0.377482i | \(-0.876790\pi\) | ||||
0.926017 | − | 0.377482i | \(-0.123210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.47727 | −0.0247151 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 134.991i | 0.359998i | ||||||||
\(53\) | − 191.739i | − 0.496931i | −0.968641 | − | 0.248465i | \(-0.920074\pi\) | ||||
0.968641 | − | 0.248465i | \(-0.0799262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 149.982 | 0.357896 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 282.468i | − 0.639481i | ||||||||
\(59\) | 312.441 | 0.689430 | 0.344715 | − | 0.938707i | \(-0.387976\pi\) | ||||
0.344715 | + | 0.938707i | \(0.387976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −550.648 | −1.15579 | −0.577895 | − | 0.816111i | \(-0.696126\pi\) | ||||
−0.577895 | + | 0.816111i | \(0.696126\pi\) | |||||||
\(62\) | 529.909i | 1.08546i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 571.270i | 1.04167i | 0.853658 | + | 0.520834i | \(0.174379\pi\) | ||||
−0.853658 | + | 0.520834i | \(0.825621\pi\) | |||||||
\(68\) | 214.955i | 0.383339i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 183.784 | 0.307199 | 0.153600 | − | 0.988133i | \(-0.450913\pi\) | ||||
0.153600 | + | 0.988133i | \(0.450913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 125.027i | − 0.200457i | −0.994964 | − | 0.100228i | \(-0.968043\pi\) | ||||
0.994964 | − | 0.100228i | \(-0.0319573\pi\) | |||||||
\(74\) | −122.486 | −0.192416 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 366.955 | 0.553850 | ||||||||
\(77\) | − 749.739i | − 1.10962i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 429.216 | 0.611273 | 0.305636 | − | 0.952148i | \(-0.401131\pi\) | ||||
0.305636 | + | 0.952148i | \(0.401131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 629.945i | 0.848364i | ||||||||
\(83\) | − 1091.48i | − 1.44344i | −0.692187 | − | 0.721718i | \(-0.743353\pi\) | ||||
0.692187 | − | 0.721718i | \(-0.256647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 472.523 | 0.592482 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 319.927i | 0.387550i | ||||||||
\(89\) | −1233.59 | −1.46922 | −0.734610 | − | 0.678489i | \(-0.762635\pi\) | ||||
−0.734610 | + | 0.678489i | \(0.762635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 632.693 | 0.728838 | ||||||||
\(92\) | − 322.955i | − 0.365982i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 486.523 | 0.533840 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1532.44i | 1.60408i | 0.597270 | + | 0.802040i | \(0.296252\pi\) | ||||
−0.597270 | + | 0.802040i | \(0.703748\pi\) | |||||||
\(98\) | − 16.9545i | − 0.0174762i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −358.639 | −0.353326 | −0.176663 | − | 0.984271i | \(-0.556530\pi\) | ||||
−0.176663 | + | 0.984271i | \(0.556530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 437.514i | 0.418539i | 0.977858 | + | 0.209269i | \(0.0671086\pi\) | ||||
−0.977858 | + | 0.209269i | \(0.932891\pi\) | |||||||
\(104\) | −269.982 | −0.254557 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 383.477 | 0.351383 | ||||||||
\(107\) | − 922.818i | − 0.833759i | −0.908962 | − | 0.416879i | \(-0.863124\pi\) | ||||
0.908962 | − | 0.416879i | \(-0.136876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1219.39 | 1.07152 | 0.535762 | − | 0.844369i | \(-0.320025\pi\) | ||||
0.535762 | + | 0.844369i | \(0.320025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 299.964i | 0.253071i | ||||||||
\(113\) | − 463.045i | − 0.385484i | −0.981250 | − | 0.192742i | \(-0.938262\pi\) | ||||
0.981250 | − | 0.192742i | \(-0.0617380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 564.936 | 0.452181 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 624.882i | 0.487500i | ||||||||
\(119\) | 1007.48 | 0.776095 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 268.273 | 0.201557 | ||||||||
\(122\) | − 1101.30i | − 0.817267i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1059.82 | −0.767536 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 207.677i | 0.145105i | 0.997365 | + | 0.0725527i | \(0.0231145\pi\) | ||||
−0.997365 | + | 0.0725527i | \(0.976885\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2567.34 | 1.71229 | 0.856144 | − | 0.516738i | \(-0.172854\pi\) | ||||
0.856144 | + | 0.516738i | \(0.172854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1719.89i | − 1.12130i | ||||||||
\(134\) | −1142.54 | −0.736571 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −429.909 | −0.271062 | ||||||||
\(137\) | − 15.9205i | − 0.00992830i | −0.999988 | − | 0.00496415i | \(-0.998420\pi\) | ||||
0.999988 | − | 0.00496415i | \(-0.00158014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2839.65 | 1.73278 | 0.866388 | − | 0.499372i | \(-0.166436\pi\) | ||||
0.866388 | + | 0.499372i | \(0.166436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 367.568i | 0.217223i | ||||||||
\(143\) | 1349.60i | 0.789227i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 250.055 | 0.141744 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 244.973i | − 0.136058i | ||||||||
\(149\) | 202.377 | 0.111271 | 0.0556355 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556355 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3657.81 | 1.97131 | 0.985656 | − | 0.168767i | \(-0.0539786\pi\) | ||||
0.985656 | + | 0.168767i | \(0.0539786\pi\) | |||||||
\(152\) | 733.909i | 0.391631i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1499.48 | 0.784619 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2272.29i | 1.15508i | 0.816361 | + | 0.577542i | \(0.195988\pi\) | ||||
−0.816361 | + | 0.577542i | \(0.804012\pi\) | |||||||
\(158\) | 858.432i | 0.432235i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1513.67 | −0.740954 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2754.68i | − 1.32370i | −0.749636 | − | 0.661851i | \(-0.769771\pi\) | ||||
0.749636 | − | 0.661851i | \(-0.230229\pi\) | |||||||
\(164\) | −1259.89 | −0.599884 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2182.95 | 1.02066 | ||||||||
\(167\) | 1067.85i | 0.494808i | 0.968912 | + | 0.247404i | \(0.0795774\pi\) | ||||
−0.968912 | + | 0.247404i | \(0.920423\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1058.09 | 0.481607 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 945.045i | 0.418948i | ||||||||
\(173\) | − 2963.47i | − 1.30236i | −0.758924 | − | 0.651180i | \(-0.774274\pi\) | ||||
0.758924 | − | 0.651180i | \(-0.225726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −639.855 | −0.274039 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2467.19i | − 1.03890i | ||||||||
\(179\) | 3087.14 | 1.28907 | 0.644536 | − | 0.764574i | \(-0.277051\pi\) | ||||
0.644536 | + | 0.764574i | \(0.277051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4080.03 | 1.67551 | 0.837753 | − | 0.546050i | \(-0.183869\pi\) | ||||
0.837753 | + | 0.546050i | \(0.183869\pi\) | |||||||
\(182\) | 1265.39i | 0.515366i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 645.909 | 0.258788 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2149.06i | 0.840399i | ||||||||
\(188\) | 973.045i | 0.377482i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2672.01 | 1.01225 | 0.506126 | − | 0.862460i | \(-0.331077\pi\) | ||||
0.506126 | + | 0.862460i | \(0.331077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4509.45i | 1.68185i | 0.541149 | + | 0.840927i | \(0.317989\pi\) | ||||
−0.541149 | + | 0.840927i | \(0.682011\pi\) | |||||||
\(194\) | −3064.88 | −1.13426 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 33.9091 | 0.0123575 | ||||||||
\(197\) | 2251.82i | 0.814393i | 0.913341 | + | 0.407196i | \(0.133494\pi\) | ||||
−0.913341 | + | 0.407196i | \(0.866506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1548.93 | −0.551763 | −0.275882 | − | 0.961192i | \(-0.588970\pi\) | ||||
−0.275882 | + | 0.961192i | \(0.588970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 717.277i | − 0.249839i | ||||||||
\(203\) | − 2647.82i | − 0.915470i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −875.027 | −0.295952 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 539.964i | − 0.179999i | ||||||||
\(209\) | 3668.71 | 1.21421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2230.61 | 0.727781 | 0.363890 | − | 0.931442i | \(-0.381448\pi\) | ||||
0.363890 | + | 0.931442i | \(0.381448\pi\) | |||||||
\(212\) | 766.955i | 0.248465i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1845.64 | 0.589557 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4967.30i | 1.55393i | ||||||||
\(218\) | 2438.77i | 0.757681i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1813.56 | −0.552005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2069.04i | − 0.621314i | −0.950522 | − | 0.310657i | \(-0.899451\pi\) | ||||
0.950522 | − | 0.310657i | \(-0.100549\pi\) | |||||||
\(224\) | −599.927 | −0.178948 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 926.091 | 0.272578 | ||||||||
\(227\) | − 5240.45i | − 1.53225i | −0.642690 | − | 0.766126i | \(-0.722182\pi\) | ||||
0.642690 | − | 0.766126i | \(-0.277818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3557.69 | 1.02663 | 0.513317 | − | 0.858199i | \(-0.328417\pi\) | ||||
0.513317 | + | 0.858199i | \(0.328417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1129.87i | 0.319740i | ||||||||
\(233\) | 35.4887i | 0.00997828i | 0.999988 | + | 0.00498914i | \(0.00158810\pi\) | ||||
−0.999988 | + | 0.00498914i | \(0.998412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1249.76 | −0.344715 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2014.95i | 0.548782i | ||||||||
\(239\) | −1170.62 | −0.316826 | −0.158413 | − | 0.987373i | \(-0.550638\pi\) | ||||
−0.158413 | + | 0.987373i | \(0.550638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3319.50 | −0.887252 | −0.443626 | − | 0.896212i | \(-0.646308\pi\) | ||||
−0.443626 | + | 0.896212i | \(0.646308\pi\) | |||||||
\(242\) | 536.545i | 0.142523i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2202.59 | 0.577895 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3095.97i | 0.797538i | ||||||||
\(248\) | − 2119.64i | − 0.542730i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5852.48 | −1.47173 | −0.735867 | − | 0.677126i | \(-0.763225\pi\) | ||||
−0.735867 | + | 0.677126i | \(0.763225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3228.81i | − 0.802346i | ||||||||
\(254\) | −415.355 | −0.102605 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 4239.62i | − 1.02903i | −0.857482 | − | 0.514515i | \(-0.827972\pi\) | ||||
0.857482 | − | 0.514515i | \(-0.172028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1148.17 | −0.275459 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5134.68i | 1.21077i | ||||||||
\(263\) | 6702.60i | 1.57148i | 0.618555 | + | 0.785742i | \(0.287719\pi\) | ||||
−0.618555 | + | 0.785742i | \(0.712281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3439.78 | 0.792882 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2285.08i | − 0.520834i | ||||||||
\(269\) | 3182.94 | 0.721440 | 0.360720 | − | 0.932674i | \(-0.382531\pi\) | ||||
0.360720 | + | 0.932674i | \(0.382531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2349.73 | −0.526700 | −0.263350 | − | 0.964700i | \(-0.584827\pi\) | ||||
−0.263350 | + | 0.964700i | \(0.584827\pi\) | |||||||
\(272\) | − 859.818i | − 0.191670i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.8409 | 0.00702037 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6654.79i | 1.44349i | 0.692157 | + | 0.721747i | \(0.256660\pi\) | ||||
−0.692157 | + | 0.721747i | \(0.743340\pi\) | |||||||
\(278\) | 5679.30i | 1.22526i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6245.88 | −1.32597 | −0.662986 | − | 0.748632i | \(-0.730711\pi\) | ||||
−0.662986 | + | 0.748632i | \(0.730711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2360.43i | − 0.495806i | −0.968785 | − | 0.247903i | \(-0.920258\pi\) | ||||
0.968785 | − | 0.247903i | \(-0.0797415\pi\) | |||||||
\(284\) | −735.136 | −0.153600 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2699.20 | −0.558068 | ||||||||
\(287\) | 5905.02i | 1.21450i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2025.16 | 0.412204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 500.109i | 0.100228i | ||||||||
\(293\) | − 5834.08i | − 1.16324i | −0.813459 | − | 0.581622i | \(-0.802418\pi\) | ||||
0.813459 | − | 0.581622i | \(-0.197582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 489.945 | 0.0962078 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 404.755i | 0.0786805i | ||||||||
\(299\) | 2724.75 | 0.527010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4429.36 | 0.848187 | ||||||||
\(302\) | 7315.61i | 1.39393i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1467.82 | −0.276925 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1460.05i | 0.271432i | 0.990748 | + | 0.135716i | \(0.0433335\pi\) | ||||
−0.990748 | + | 0.135716i | \(0.956666\pi\) | |||||||
\(308\) | 2998.95i | 0.554809i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4200.24 | −0.765833 | −0.382916 | − | 0.923783i | \(-0.625080\pi\) | ||||
−0.382916 | + | 0.923783i | \(0.625080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5890.15i | − 1.06368i | −0.846846 | − | 0.531838i | \(-0.821501\pi\) | ||||
0.846846 | − | 0.531838i | \(-0.178499\pi\) | |||||||
\(314\) | −4544.57 | −0.816768 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1716.86 | −0.305636 | ||||||||
\(317\) | 1507.03i | 0.267014i | 0.991048 | + | 0.133507i | \(0.0426239\pi\) | ||||
−0.991048 | + | 0.133507i | \(0.957376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5648.08 | 0.991322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3027.33i | − 0.523934i | ||||||||
\(323\) | 4929.91i | 0.849249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5509.36 | 0.935998 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 2519.78i | − 0.424182i | ||||||||
\(329\) | 4560.60 | 0.764237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3256.75 | −0.540807 | −0.270404 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270404 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(332\) | 4365.91i | 0.721718i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2135.70 | −0.349882 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 7698.71i | − 1.24444i | −0.782843 | − | 0.622219i | \(-0.786231\pi\) | ||||
0.782843 | − | 0.622219i | \(-0.213769\pi\) | |||||||
\(338\) | 2116.18i | 0.340548i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10595.8 | −1.68268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6271.54i | 0.987263i | ||||||||
\(344\) | −1890.09 | −0.296241 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5926.93 | 0.920907 | ||||||||
\(347\) | − 9545.73i | − 1.47678i | −0.674376 | − | 0.738388i | \(-0.735587\pi\) | ||||
0.674376 | − | 0.738388i | \(-0.264413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2926.48 | 0.448856 | 0.224428 | − | 0.974491i | \(-0.427949\pi\) | ||||
0.224428 | + | 0.974491i | \(0.427949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1279.71i | − 0.193775i | ||||||||
\(353\) | − 4679.69i | − 0.705595i | −0.935700 | − | 0.352797i | \(-0.885231\pi\) | ||||
0.935700 | − | 0.352797i | \(-0.114769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4934.37 | 0.734610 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6174.28i | 0.911511i | ||||||||
\(359\) | 12252.8 | 1.80133 | 0.900667 | − | 0.434509i | \(-0.143078\pi\) | ||||
0.900667 | + | 0.434509i | \(0.143078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1556.98 | 0.226998 | ||||||||
\(362\) | 8160.07i | 1.18476i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2530.77 | −0.364419 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11666.1i | 1.65931i | 0.558280 | + | 0.829653i | \(0.311462\pi\) | ||||
−0.558280 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(368\) | 1291.82i | 0.182991i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3594.66 | 0.503034 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1543.32i | 0.214237i | 0.994246 | + | 0.107118i | \(0.0341623\pi\) | ||||
−0.994246 | + | 0.107118i | \(0.965838\pi\) | |||||||
\(374\) | −4298.11 | −0.594252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1946.09 | −0.266920 | ||||||||
\(377\) | 4766.33i | 0.651136i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1421.25 | 0.192625 | 0.0963123 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963123 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5344.03i | 0.715770i | ||||||||
\(383\) | − 8785.42i | − 1.17210i | −0.810275 | − | 0.586050i | \(-0.800682\pi\) | ||||
0.810275 | − | 0.586050i | \(-0.199318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9018.91 | −1.18925 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6129.76i | − 0.802040i | ||||||||
\(389\) | −5555.06 | −0.724043 | −0.362022 | − | 0.932170i | \(-0.617913\pi\) | ||||
−0.362022 | + | 0.932170i | \(0.617913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4338.78 | 0.561181 | ||||||||
\(392\) | 67.8182i | 0.00873810i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4503.64 | −0.575863 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11483.1i | − 1.45169i | −0.687856 | − | 0.725847i | \(-0.741448\pi\) | ||||
0.687856 | − | 0.725847i | \(-0.258552\pi\) | |||||||
\(398\) | − 3097.86i | − 0.390155i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12002.9 | 1.49475 | 0.747376 | − | 0.664401i | \(-0.231313\pi\) | ||||
0.747376 | + | 0.664401i | \(0.231313\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8941.61i | − 1.10524i | ||||||||
\(404\) | 1434.55 | 0.176663 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5295.64 | 0.647335 | ||||||||
\(407\) | − 2449.17i | − 0.298282i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9770.32 | −1.18120 | −0.590600 | − | 0.806964i | \(-0.701109\pi\) | ||||
−0.590600 | + | 0.806964i | \(0.701109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 1750.05i | − 0.209269i | ||||||||
\(413\) | 5857.56i | 0.697897i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1079.93 | 0.127278 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7337.42i | 0.858577i | ||||||||
\(419\) | −8055.79 | −0.939262 | −0.469631 | − | 0.882863i | \(-0.655613\pi\) | ||||
−0.469631 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4967.99 | 0.575119 | 0.287559 | − | 0.957763i | \(-0.407156\pi\) | ||||
0.287559 | + | 0.957763i | \(0.407156\pi\) | |||||||
\(422\) | 4461.23i | 0.514619i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1533.91 | −0.175692 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10323.4i | − 1.16999i | ||||||||
\(428\) | 3691.27i | 0.416879i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10826.5 | −1.20997 | −0.604984 | − | 0.796238i | \(-0.706821\pi\) | ||||
−0.604984 | + | 0.796238i | \(0.706821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 2038.63i | − 0.226259i | −0.993580 | − | 0.113130i | \(-0.963912\pi\) | ||||
0.993580 | − | 0.113130i | \(-0.0360875\pi\) | |||||||
\(434\) | −9934.59 | −1.09879 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4877.55 | −0.535762 | ||||||||
\(437\) | − 7406.85i | − 0.810796i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11648.4 | −1.26640 | −0.633200 | − | 0.773988i | \(-0.718259\pi\) | ||||
−0.633200 | + | 0.773988i | \(0.718259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 3627.11i | − 0.390326i | ||||||||
\(443\) | − 4156.59i | − 0.445791i | −0.974842 | − | 0.222896i | \(-0.928449\pi\) | ||||
0.974842 | − | 0.222896i | \(-0.0715509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4138.08 | 0.439336 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1199.85i | − 0.126535i | ||||||||
\(449\) | 14987.5 | 1.57529 | 0.787645 | − | 0.616129i | \(-0.211300\pi\) | ||||
0.787645 | + | 0.616129i | \(0.211300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12596.0 | −1.31513 | ||||||||
\(452\) | 1852.18i | 0.192742i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10480.9 | 1.08347 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 13215.5i | − 1.35272i | −0.736571 | − | 0.676361i | \(-0.763556\pi\) | ||||
0.736571 | − | 0.676361i | \(-0.236444\pi\) | |||||||
\(458\) | 7115.39i | 0.725939i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6365.55 | −0.643109 | −0.321554 | − | 0.946891i | \(-0.604205\pi\) | ||||
−0.321554 | + | 0.946891i | \(0.604205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13954.3i | 1.40068i | 0.713811 | + | 0.700338i | \(0.246967\pi\) | ||||
−0.713811 | + | 0.700338i | \(0.753033\pi\) | |||||||
\(464\) | −2259.75 | −0.226091 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −70.9773 | −0.00705571 | ||||||||
\(467\) | − 15289.1i | − 1.51498i | −0.652848 | − | 0.757489i | \(-0.726426\pi\) | ||||
0.652848 | − | 0.757489i | \(-0.273574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10710.0 | −1.05446 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 2499.53i | − 0.243750i | ||||||||
\(473\) | 9448.31i | 0.918464i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4029.91 | −0.388047 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 2341.25i | − 0.224030i | ||||||||
\(479\) | 8268.35 | 0.788706 | 0.394353 | − | 0.918959i | \(-0.370969\pi\) | ||||
0.394353 | + | 0.918959i | \(0.370969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2066.82 | 0.195923 | ||||||||
\(482\) | − 6639.00i | − 0.627382i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1073.09 | −0.100779 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7144.78i | − 0.664806i | −0.943137 | − | 0.332403i | \(-0.892141\pi\) | ||||
0.943137 | − | 0.332403i | \(-0.107859\pi\) | |||||||
\(488\) | 4405.18i | 0.408634i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19527.2 | 1.79481 | 0.897405 | − | 0.441209i | \(-0.145450\pi\) | ||||
0.897405 | + | 0.441209i | \(0.145450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7589.73i | 0.693355i | ||||||||
\(494\) | −6191.94 | −0.563945 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4239.27 | 0.383768 | ||||||||
\(497\) | 3445.53i | 0.310972i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12923.7 | 1.15941 | 0.579704 | − | 0.814827i | \(-0.303168\pi\) | ||||
0.579704 | + | 0.814827i | \(0.303168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 11705.0i | − 1.04067i | ||||||||
\(503\) | − 14125.0i | − 1.25209i | −0.779787 | − | 0.626045i | \(-0.784672\pi\) | ||||
0.779787 | − | 0.626045i | \(-0.215328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6457.62 | 0.567345 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 830.709i | − 0.0725527i | ||||||||
\(509\) | 13955.7 | 1.21527 | 0.607636 | − | 0.794215i | \(-0.292118\pi\) | ||||
0.607636 | + | 0.794215i | \(0.292118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2343.98 | 0.202919 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8479.25 | 0.727634 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9728.24i | 0.827558i | ||||||||
\(518\) | − 2296.34i | − 0.194779i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19825.1 | −1.66709 | −0.833544 | − | 0.552452i | \(-0.813692\pi\) | ||||
−0.833544 | + | 0.552452i | \(0.813692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14258.7i | 1.19214i | 0.802933 | + | 0.596070i | \(0.203272\pi\) | ||||
−0.802933 | + | 0.596070i | \(0.796728\pi\) | |||||||
\(524\) | −10269.4 | −0.856144 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13405.2 | −1.11121 | ||||||||
\(527\) | − 14238.3i | − 1.17691i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5648.27 | 0.464229 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6879.56i | 0.560652i | ||||||||
\(533\) | − 10629.6i | − 0.863827i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4570.16 | 0.368285 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6365.88i | 0.510135i | ||||||||
\(539\) | 339.014 | 0.0270916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19037.6 | −1.51292 | −0.756462 | − | 0.654037i | \(-0.773074\pi\) | ||||
−0.756462 | + | 0.654037i | \(0.773074\pi\) | |||||||
\(542\) | − 4699.45i | − 0.372433i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1719.64 | 0.135531 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 11176.9i | − 0.873657i | −0.899545 | − | 0.436828i | \(-0.856102\pi\) | ||||
0.899545 | − | 0.436828i | \(-0.143898\pi\) | |||||||
\(548\) | 63.6819i | 0.00496415i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12956.6 | 1.00176 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8046.82i | 0.618781i | ||||||||
\(554\) | −13309.6 | −1.02070 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11358.6 | −0.866388 | ||||||||
\(557\) | 19583.4i | 1.48972i | 0.667219 | + | 0.744862i | \(0.267485\pi\) | ||||
−0.667219 | + | 0.744862i | \(0.732515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7973.28 | −0.603281 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 12491.8i | − 0.937603i | ||||||||
\(563\) | − 26341.1i | − 1.97184i | −0.167230 | − | 0.985918i | \(-0.553482\pi\) | ||||
0.167230 | − | 0.985918i | \(-0.446518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4720.87 | 0.350588 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 1470.27i | − 0.108611i | ||||||||
\(569\) | −5794.46 | −0.426918 | −0.213459 | − | 0.976952i | \(-0.568473\pi\) | ||||
−0.213459 | + | 0.976952i | \(0.568473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17512.7 | −1.28351 | −0.641756 | − | 0.766909i | \(-0.721794\pi\) | ||||
−0.641756 | + | 0.766909i | \(0.721794\pi\) | |||||||
\(572\) | − 5398.41i | − 0.394613i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11810.0 | −0.858784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 7908.96i | − 0.570631i | −0.958434 | − | 0.285316i | \(-0.907902\pi\) | ||||
0.958434 | − | 0.285316i | \(-0.0920984\pi\) | |||||||
\(578\) | 4050.32i | 0.291472i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20462.7 | 1.46116 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7667.80i | 0.544713i | ||||||||
\(584\) | −1000.22 | −0.0708721 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11668.2 | 0.822538 | ||||||||
\(587\) | 769.500i | 0.0541067i | 0.999634 | + | 0.0270534i | \(0.00861241\pi\) | ||||
−0.999634 | + | 0.0270534i | \(0.991388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24306.6 | −1.70040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 979.891i | 0.0680292i | ||||||||
\(593\) | 13608.5i | 0.942385i | 0.882030 | + | 0.471192i | \(0.156176\pi\) | ||||
−0.882030 | + | 0.471192i | \(0.843824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −809.509 | −0.0556355 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5449.49i | 0.372653i | ||||||||
\(599\) | 1242.90 | 0.0847805 | 0.0423902 | − | 0.999101i | \(-0.486503\pi\) | ||||
0.0423902 | + | 0.999101i | \(0.486503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8879.95 | −0.602697 | −0.301349 | − | 0.953514i | \(-0.597437\pi\) | ||||
−0.301349 | + | 0.953514i | \(0.597437\pi\) | |||||||
\(602\) | 8858.73i | 0.599759i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14631.2 | −0.985656 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 17859.3i | − 1.19421i | −0.802163 | − | 0.597106i | \(-0.796317\pi\) | ||||
0.802163 | − | 0.597106i | \(-0.203683\pi\) | |||||||
\(608\) | − 2935.64i | − 0.195815i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8209.52 | −0.543570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8241.30i | 0.543006i | 0.962438 | + | 0.271503i | \(0.0875207\pi\) | ||||
−0.962438 | + | 0.271503i | \(0.912479\pi\) | |||||||
\(614\) | −2920.11 | −0.191932 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5997.91 | −0.392309 | ||||||||
\(617\) | − 6854.93i | − 0.447276i | −0.974672 | − | 0.223638i | \(-0.928207\pi\) | ||||
0.974672 | − | 0.223638i | \(-0.0717933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1857.93 | 0.120641 | 0.0603203 | − | 0.998179i | \(-0.480788\pi\) | ||||
0.0603203 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 8400.49i | − 0.541525i | ||||||||
\(623\) | − 23127.1i | − 1.48727i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11780.3 | 0.752133 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 9089.15i | − 0.577542i | ||||||||
\(629\) | 3291.12 | 0.208626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8079.78 | −0.509748 | −0.254874 | − | 0.966974i | \(-0.582034\pi\) | ||||
−0.254874 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(632\) | − 3433.73i | − 0.216118i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3014.07 | −0.188807 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 286.089i | 0.0177947i | ||||||||
\(638\) | 11296.2i | 0.700971i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21810.4 | 1.34393 | 0.671966 | − | 0.740582i | \(-0.265450\pi\) | ||||
0.671966 | + | 0.740582i | \(0.265450\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 10487.6i | − 0.643220i | −0.946872 | − | 0.321610i | \(-0.895776\pi\) | ||||
0.946872 | − | 0.321610i | \(-0.104224\pi\) | |||||||
\(644\) | 6054.66 | 0.370477 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9859.82 | −0.600510 | ||||||||
\(647\) | 23644.5i | 1.43672i | 0.695669 | + | 0.718362i | \(0.255108\pi\) | ||||
−0.695669 | + | 0.718362i | \(0.744892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12494.8 | −0.755722 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11018.7i | 0.661851i | ||||||||
\(653\) | − 9685.08i | − 0.580408i | −0.956965 | − | 0.290204i | \(-0.906277\pi\) | ||||
0.956965 | − | 0.290204i | \(-0.0937232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5039.56 | 0.299942 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9121.20i | 0.540397i | ||||||||
\(659\) | −15248.7 | −0.901374 | −0.450687 | − | 0.892682i | \(-0.648821\pi\) | ||||
−0.450687 | + | 0.892682i | \(0.648821\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1423.58 | −0.0837683 | −0.0418841 | − | 0.999122i | \(-0.513336\pi\) | ||||
−0.0418841 | + | 0.999122i | \(0.513336\pi\) | |||||||
\(662\) | − 6513.50i | − 0.382408i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8731.82 | −0.510332 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11403.0i | − 0.661961i | ||||||||
\(668\) | − 4271.41i | − 0.247404i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22020.9 | 1.26693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 16652.6i | − 0.953805i | −0.878956 | − | 0.476902i | \(-0.841760\pi\) | ||||
0.878956 | − | 0.476902i | \(-0.158240\pi\) | |||||||
\(674\) | 15397.4 | 0.879950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4232.36 | −0.240804 | ||||||||
\(677\) | − 30296.0i | − 1.71989i | −0.510384 | − | 0.859947i | \(-0.670497\pi\) | ||||
0.510384 | − | 0.859947i | \(-0.329503\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28729.8 | −1.62378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 21191.5i | − 1.18983i | ||||||||
\(683\) | 21943.5i | 1.22935i | 0.788780 | + | 0.614675i | \(0.210713\pi\) | ||||
−0.788780 | + | 0.614675i | \(0.789287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12543.1 | −0.698101 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 3780.18i | − 0.209474i | ||||||||
\(689\) | −6470.74 | −0.357788 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16153.5 | 0.889300 | 0.444650 | − | 0.895704i | \(-0.353328\pi\) | ||||
0.444650 | + | 0.895704i | \(0.353328\pi\) | |||||||
\(692\) | 11853.9i | 0.651180i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19091.5 | 1.04424 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 16926.2i | − 0.919836i | ||||||||
\(698\) | 5852.95i | 0.317389i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31969.9 | −1.72252 | −0.861261 | − | 0.508163i | \(-0.830325\pi\) | ||||
−0.861261 | + | 0.508163i | \(0.830325\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5618.37i | − 0.301423i | ||||||||
\(704\) | 2559.42 | 0.137019 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9359.39 | 0.498931 | ||||||||
\(707\) | − 6723.66i | − 0.357665i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27367.1 | 1.44964 | 0.724819 | − | 0.688939i | \(-0.241923\pi\) | ||||
0.724819 | + | 0.688939i | \(0.241923\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9868.75i | 0.519448i | ||||||||
\(713\) | 21392.1i | 1.12362i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12348.6 | −0.644536 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24505.6i | 1.27374i | ||||||||
\(719\) | 3379.36 | 0.175283 | 0.0876417 | − | 0.996152i | \(-0.472067\pi\) | ||||
0.0876417 | + | 0.996152i | \(0.472067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8202.39 | −0.423679 | ||||||||
\(722\) | 3113.95i | 0.160512i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16320.1 | −0.837753 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2831.94i | 0.144472i | 0.997388 | + | 0.0722358i | \(0.0230134\pi\) | ||||
−0.997388 | + | 0.0722358i | \(0.976987\pi\) | |||||||
\(728\) | − 5061.55i | − 0.257683i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12696.4 | −0.642397 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 25298.0i | − 1.27476i | −0.770548 | − | 0.637382i | \(-0.780017\pi\) | ||||
0.770548 | − | 0.637382i | \(-0.219983\pi\) | |||||||
\(734\) | −23332.2 | −1.17331 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2583.64 | −0.129394 | ||||||||
\(737\) | − 22845.6i | − 1.14183i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7545.60 | −0.375601 | −0.187801 | − | 0.982207i | \(-0.560136\pi\) | ||||
−0.187801 | + | 0.982207i | \(0.560136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7189.33i | 0.355699i | ||||||||
\(743\) | − 26471.0i | − 1.30704i | −0.756911 | − | 0.653518i | \(-0.773293\pi\) | ||||
0.756911 | − | 0.653518i | \(-0.226707\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3086.65 | −0.151488 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 8596.23i | − 0.420199i | ||||||||
\(749\) | 17300.7 | 0.843999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20997.8 | −1.02027 | −0.510133 | − | 0.860095i | \(-0.670404\pi\) | ||||
−0.510133 | + | 0.860095i | \(0.670404\pi\) | |||||||
\(752\) | − 3892.18i | − 0.188741i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9532.66 | −0.460423 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 37735.2i | − 1.81177i | −0.423524 | − | 0.905885i | \(-0.639207\pi\) | ||||
0.423524 | − | 0.905885i | \(-0.360793\pi\) | |||||||
\(758\) | 2842.50i | 0.136206i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4449.85 | 0.211967 | 0.105984 | − | 0.994368i | \(-0.466201\pi\) | ||||
0.105984 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22860.7i | 1.08468i | ||||||||
\(764\) | −10688.1 | −0.506126 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17570.8 | 0.828799 | ||||||||
\(767\) | − 10544.2i | − 0.496386i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6269.70 | −0.294007 | −0.147003 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147003 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 18037.8i | − 0.840927i | ||||||||
\(773\) | 23242.7i | 1.08148i | 0.841190 | + | 0.540739i | \(0.181855\pi\) | ||||
−0.841190 | + | 0.540739i | \(0.818145\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12259.5 | 0.567128 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 11110.1i | − 0.511976i | ||||||||
\(779\) | −28895.2 | −1.32898 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7349.69 | −0.336738 | ||||||||
\(782\) | 8677.57i | 0.396815i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −135.636 | −0.00617877 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 32584.4i | − 1.47587i | −0.674873 | − | 0.737934i | \(-0.735802\pi\) | ||||
0.674873 | − | 0.737934i | \(-0.264198\pi\) | |||||||
\(788\) | − 9007.27i | − 0.407196i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8681.05 | 0.390218 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18583.1i | 0.832163i | ||||||||
\(794\) | 22966.3 | 1.02650 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6195.73 | 0.275882 | ||||||||
\(797\) | − 6338.31i | − 0.281699i | −0.990031 | − | 0.140850i | \(-0.955017\pi\) | ||||
0.990031 | − | 0.140850i | \(-0.0449834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13072.5 | −0.578815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24005.8i | 1.05695i | ||||||||
\(803\) | 4999.95i | 0.219732i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17883.2 | 0.781526 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2869.11i | 0.124919i | ||||||||
\(809\) | 17364.4 | 0.754635 | 0.377317 | − | 0.926084i | \(-0.376847\pi\) | ||||
0.377317 | + | 0.926084i | \(0.376847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8146.53 | 0.352729 | 0.176365 | − | 0.984325i | \(-0.443566\pi\) | ||||
0.176365 | + | 0.984325i | \(0.443566\pi\) | |||||||
\(812\) | 10591.3i | 0.457735i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4898.34 | 0.210917 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21674.3i | 0.928137i | ||||||||
\(818\) | − 19540.6i | − 0.835235i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17433.3 | −0.741078 | −0.370539 | − | 0.928817i | \(-0.620827\pi\) | ||||
−0.370539 | + | 0.928817i | \(0.620827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 29692.7i | − 1.25762i | −0.777559 | − | 0.628810i | \(-0.783542\pi\) | ||||
0.777559 | − | 0.628810i | \(-0.216458\pi\) | |||||||
\(824\) | 3500.11 | 0.147976 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11715.1 | −0.493488 | ||||||||
\(827\) | 9694.27i | 0.407621i | 0.979010 | + | 0.203811i | \(0.0653327\pi\) | ||||
−0.979010 | + | 0.203811i | \(0.934667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10975.2 | 0.459814 | 0.229907 | − | 0.973213i | \(-0.426158\pi\) | ||||
0.229907 | + | 0.973213i | \(0.426158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2159.85i | 0.0899994i | ||||||||
\(833\) | 455.557i | 0.0189485i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14674.8 | −0.607105 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 16111.6i | − 0.664159i | ||||||||
\(839\) | 5314.17 | 0.218671 | 0.109336 | − | 0.994005i | \(-0.465128\pi\) | ||||
0.109336 | + | 0.994005i | \(0.465128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4441.93 | −0.182128 | ||||||||
\(842\) | 9935.98i | 0.406670i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8922.45 | −0.363890 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5029.50i | 0.204033i | ||||||||
\(848\) | − 3067.82i | − 0.124233i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4944.69 | −0.199180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12904.3i | 0.517978i | 0.965880 | + | 0.258989i | \(0.0833893\pi\) | ||||
−0.965880 | + | 0.258989i | \(0.916611\pi\) | |||||||
\(854\) | 20646.8 | 0.827305 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7382.55 | −0.294778 | ||||||||
\(857\) | 33810.1i | 1.34764i | 0.738893 | + | 0.673822i | \(0.235349\pi\) | ||||
−0.738893 | + | 0.673822i | \(0.764651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13512.0 | 0.536698 | 0.268349 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268349 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 21653.1i | − 0.855577i | ||||||||
\(863\) | 8599.41i | 0.339197i | 0.985513 | + | 0.169599i | \(0.0542471\pi\) | ||||
−0.985513 | + | 0.169599i | \(0.945753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4077.25 | 0.159989 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 19869.2i | − 0.776963i | ||||||||
\(869\) | −17164.7 | −0.670050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19279.1 | 0.749996 | ||||||||
\(872\) | − 9755.09i | − 0.378841i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14813.7 | 0.573319 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35722.7i | 1.37545i | 0.725971 | + | 0.687725i | \(0.241390\pi\) | ||||
−0.725971 | + | 0.687725i | \(0.758610\pi\) | |||||||
\(878\) | − 23296.9i | − 0.895480i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44841.2 | −1.71480 | −0.857400 | − | 0.514650i | \(-0.827922\pi\) | ||||
−0.857400 | + | 0.514650i | \(0.827922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22688.4i | − 0.864694i | −0.901707 | − | 0.432347i | \(-0.857685\pi\) | ||||
0.901707 | − | 0.432347i | \(-0.142315\pi\) | |||||||
\(884\) | 7254.23 | 0.276002 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8313.18 | 0.315222 | ||||||||
\(887\) | 14717.2i | 0.557110i | 0.960420 | + | 0.278555i | \(0.0898554\pi\) | ||||
−0.960420 | + | 0.278555i | \(0.910145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3893.48 | −0.146888 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8276.15i | 0.310657i | ||||||||
\(893\) | 22316.5i | 0.836273i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2399.71 | 0.0894739 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29975.1i | 1.11390i | ||||||||
\(899\) | −37420.6 | −1.38826 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10303.8 | −0.380986 | ||||||||
\(902\) | − 25192.1i | − 0.929939i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3704.36 | −0.136289 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43973.3i | 1.60982i | 0.593394 | + | 0.804912i | \(0.297787\pi\) | ||||
−0.593394 | + | 0.804912i | \(0.702213\pi\) | |||||||
\(908\) | 20961.8i | 0.766126i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46506.3 | 1.69135 | 0.845677 | − | 0.533695i | \(-0.179197\pi\) | ||||
0.845677 | + | 0.533695i | \(0.179197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43649.2i | 1.58223i | ||||||||
\(914\) | 26430.9 | 0.956518 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14230.8 | −0.513317 | ||||||||
\(917\) | 48131.8i | 1.73332i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22676.1 | −0.813945 | −0.406973 | − | 0.913440i | \(-0.633416\pi\) | ||||
−0.406973 | + | 0.913440i | \(0.633416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 12731.1i | − 0.454747i | ||||||||
\(923\) | − 6202.30i | − 0.221182i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27908.7 | −0.990427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 4519.49i | − 0.159870i | ||||||||
\(929\) | 31583.2 | 1.11541 | 0.557703 | − | 0.830040i | \(-0.311683\pi\) | ||||
0.557703 | + | 0.830040i | \(0.311683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 777.693 | 0.0273769 | ||||||||
\(932\) | − 141.955i | − 0.00498914i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30578.2 | 1.07125 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 6038.94i | − 0.210548i | −0.994443 | − | 0.105274i | \(-0.966428\pi\) | ||||
0.994443 | − | 0.105274i | \(-0.0335720\pi\) | |||||||
\(938\) | − 21420.0i | − 0.745618i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40751.5 | −1.41175 | −0.705877 | − | 0.708335i | \(-0.749447\pi\) | ||||
−0.705877 | + | 0.708335i | \(0.749447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25430.5i | 0.878187i | ||||||||
\(944\) | 4999.05 | 0.172357 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18896.6 | −0.649452 | ||||||||
\(947\) | − 18283.2i | − 0.627377i | −0.949526 | − | 0.313688i | \(-0.898435\pi\) | ||||
0.949526 | − | 0.313688i | \(-0.101565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4219.39 | −0.144328 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 8059.82i | − 0.274391i | ||||||||
\(953\) | 31486.4i | 1.07025i | 0.844774 | + | 0.535123i | \(0.179735\pi\) | ||||
−0.844774 | + | 0.535123i | \(0.820265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4682.50 | 0.158413 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16536.7i | 0.557700i | ||||||||
\(959\) | 298.473 | 0.0100502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40409.9 | 1.35645 | ||||||||
\(962\) | 4133.64i | 0.138538i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13278.0 | 0.443626 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30578.2i | 1.01689i | 0.861096 | + | 0.508443i | \(0.169779\pi\) | ||||
−0.861096 | + | 0.508443i | \(0.830221\pi\) | |||||||
\(968\) | − 2146.18i | − 0.0712613i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8854.87 | −0.292653 | −0.146327 | − | 0.989236i | \(-0.546745\pi\) | ||||
−0.146327 | + | 0.989236i | \(0.546745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53236.9i | 1.75406i | ||||||||
\(974\) | 14289.6 | 0.470089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8810.36 | −0.288948 | ||||||||
\(977\) | 24452.9i | 0.800736i | 0.916355 | + | 0.400368i | \(0.131118\pi\) | ||||
−0.916355 | + | 0.400368i | \(0.868882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49332.5 | 1.61049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39054.4i | 1.26912i | ||||||||
\(983\) | − 5512.42i | − 0.178860i | −0.995993 | − | 0.0894298i | \(-0.971496\pi\) | ||||
0.995993 | − | 0.0894298i | \(-0.0285045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15179.5 | −0.490276 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 12383.9i | − 0.398769i | ||||||||
\(989\) | 19075.4 | 0.613309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22724.4 | 0.728420 | 0.364210 | − | 0.931317i | \(-0.381339\pi\) | ||||
0.364210 | + | 0.931317i | \(0.381339\pi\) | |||||||
\(992\) | 8478.55i | 0.271365i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6891.07 | −0.219891 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10218.0i | 0.324582i | 0.986743 | + | 0.162291i | \(0.0518883\pi\) | ||||
−0.986743 | + | 0.162291i | \(0.948112\pi\) | |||||||
\(998\) | 25847.4i | 0.819825i | ||||||||
\(999\) | 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 | 1350.4.c.ba.649.4 | 4 | ||
3.2 | odd | 2 | 1350.4.c.v.649.2 | 4 | |||
5.2 | odd | 4 | 1350.4.a.be.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1350.4.a.bn.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 1350.4.c.ba.649.1 | 4 | ||
15.2 | even | 4 | 1350.4.a.bl.1.1 | yes | 2 | ||
15.8 | even | 4 | 1350.4.a.bg.1.2 | yes | 2 | ||
15.14 | odd | 2 | 1350.4.c.v.649.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.4.a.be.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1350.4.a.bg.1.2 | yes | 2 | 15.8 | even | 4 | ||
1350.4.a.bl.1.1 | yes | 2 | 15.2 | even | 4 | ||
1350.4.a.bn.1.2 | yes | 2 | 5.3 | odd | 4 | ||
1350.4.c.v.649.2 | 4 | 3.2 | odd | 2 | |||
1350.4.c.v.649.3 | 4 | 15.14 | odd | 2 | |||
1350.4.c.ba.649.1 | 4 | 5.4 | even | 2 | inner | ||
1350.4.c.ba.649.4 | 4 | 1.1 | even | 1 | trivial |