Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,4,Mod(49,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("300.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.d (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: | \(17.7005730017\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.49 |
Dual form | 300.4.d.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 32.0000i | − 1.72784i | −0.503631 | − | 0.863919i | \(-0.668003\pi\) | ||||
0.503631 | − | 0.863919i | \(-0.331997\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 10.0000i | − 0.213346i | −0.994294 | − | 0.106673i | \(-0.965980\pi\) | ||||
0.994294 | − | 0.106673i | \(-0.0340198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 78.0000i | 1.11281i | 0.830911 | + | 0.556405i | \(0.187820\pi\) | ||||
−0.830911 | + | 0.556405i | \(0.812180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −140.000 | −1.69043 | −0.845216 | − | 0.534425i | \(-0.820528\pi\) | ||||
−0.845216 | + | 0.534425i | \(0.820528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.0000 | −0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 192.000i | − 1.74064i | −0.492485 | − | 0.870321i | \(-0.663911\pi\) | ||||
0.492485 | − | 0.870321i | \(-0.336089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −0.0384197 | −0.0192099 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192099 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0000 | −0.0926995 | −0.0463498 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463498 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 108.000i | − 0.569709i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.0000i | 0.151069i | 0.997143 | + | 0.0755347i | \(0.0240664\pi\) | ||||
−0.997143 | + | 0.0755347i | \(0.975934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −30.0000 | −0.123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 52.0000i | − 0.184417i | −0.995740 | − | 0.0922084i | \(-0.970607\pi\) | ||||
0.995740 | − | 0.0922084i | \(-0.0293926\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 408.000i | − 1.26623i | −0.774057 | − | 0.633116i | \(-0.781776\pi\) | ||||
0.774057 | − | 0.633116i | \(-0.218224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −681.000 | −1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 234.000 | 0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 114.000i | − 0.295455i | −0.989028 | − | 0.147727i | \(-0.952804\pi\) | ||||
0.989028 | − | 0.147727i | \(-0.0471958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 420.000i | 0.975971i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −516.000 | −1.13860 | −0.569301 | − | 0.822129i | \(-0.692786\pi\) | ||||
−0.569301 | + | 0.822129i | \(0.692786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.0000 | −0.121740 | −0.0608700 | − | 0.998146i | \(-0.519388\pi\) | ||||
−0.0608700 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.000i | 0.575946i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 892.000i | 1.62649i | 0.581918 | + | 0.813247i | \(0.302302\pi\) | ||||
−0.581918 | + | 0.813247i | \(0.697698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −576.000 | −1.00496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 646.000i | − 1.03573i | −0.855461 | − | 0.517867i | \(-0.826726\pi\) | ||||
0.855461 | − | 0.517867i | \(-0.173274\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1152.00i | − 1.70497i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1168.00 | 1.66342 | 0.831711 | − | 0.555209i | \(-0.187362\pi\) | ||||
0.831711 | + | 0.555209i | \(0.187362\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 732.000i | − 0.968041i | −0.875057 | − | 0.484021i | \(-0.839176\pi\) | ||||
0.875057 | − | 0.484021i | \(-0.160824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000i | 0.0221816i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1590.00 | 1.89370 | 0.946852 | − | 0.321669i | \(-0.104244\pi\) | ||||
0.946852 | + | 0.321669i | \(0.104244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −320.000 | −0.368628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.0000i | 0.0535201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 194.000i | − 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −324.000 | −0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 798.000 | 0.786178 | 0.393089 | − | 0.919500i | \(-0.371406\pi\) | ||||
0.393089 | + | 0.919500i | \(0.371406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 272.000i | 0.260203i | 0.991501 | + | 0.130102i | \(0.0415304\pi\) | ||||
−0.991501 | + | 0.130102i | \(0.958470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 156.000i | − 0.140945i | −0.997514 | − | 0.0704724i | \(-0.977549\pi\) | ||||
0.997514 | − | 0.0704724i | \(-0.0224507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1622.00 | −1.42532 | −0.712658 | − | 0.701512i | \(-0.752509\pi\) | ||||
−0.712658 | + | 0.701512i | \(0.752509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.000 | 0.0872199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1074.00i | 0.894101i | 0.894509 | + | 0.447051i | \(0.147526\pi\) | ||||
−0.894509 | + | 0.447051i | \(0.852474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 90.0000i | 0.0711154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2496.00 | 1.92276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1170.00i | 0.857686i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1528.00i | 1.06762i | 0.845604 | + | 0.533811i | \(0.179241\pi\) | ||||
−0.845604 | + | 0.533811i | \(0.820759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −156.000 | −0.106473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2412.00 | 1.60868 | 0.804341 | − | 0.594168i | \(-0.202518\pi\) | ||||
0.804341 | + | 0.594168i | \(0.202518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4480.00i | 2.92079i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2106.00i | − 1.31334i | −0.754178 | − | 0.656671i | \(-0.771964\pi\) | ||||
0.754178 | − | 0.656671i | \(-0.228036\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 556.000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1224.00 | −0.731060 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 360.000i | − 0.210522i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2043.00i | 1.14628i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2418.00 | 1.32946 | 0.664732 | − | 0.747081i | \(-0.268546\pi\) | ||||
0.664732 | + | 0.747081i | \(0.268546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2840.00 | 1.53057 | 0.765285 | − | 0.643692i | \(-0.222598\pi\) | ||||
0.765285 | + | 0.643692i | \(0.222598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 702.000i | − 0.370937i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2054.00i | − 1.04412i | −0.852908 | − | 0.522061i | \(-0.825163\pi\) | ||||
0.852908 | − | 0.522061i | \(-0.174837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −342.000 | −0.170581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6144.00 | −3.00755 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 460.000i | − 0.221043i | −0.993874 | − | 0.110521i | \(-0.964748\pi\) | ||||
0.993874 | − | 0.110521i | \(-0.0352521\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2016.00i | − 0.934148i | −0.884218 | − | 0.467074i | \(-0.845308\pi\) | ||||
0.884218 | − | 0.467074i | \(-0.154692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2097.00 | 0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1260.00 | 0.563477 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 618.000i | − 0.271593i | −0.990737 | − | 0.135797i | \(-0.956641\pi\) | ||||
0.990737 | − | 0.135797i | \(-0.0433594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1548.00i | 0.657372i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2964.00 | 1.23765 | 0.618826 | − | 0.785528i | \(-0.287609\pi\) | ||||
0.618826 | + | 0.785528i | \(0.287609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −370.000 | −0.151944 | −0.0759721 | − | 0.997110i | \(-0.524206\pi\) | ||||
−0.0759721 | + | 0.997110i | \(0.524206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 174.000i | 0.0702866i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2808.00i | 1.09808i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1104.00 | 0.418234 | 0.209117 | − | 0.977891i | \(-0.432941\pi\) | ||||
0.209117 | + | 0.977891i | \(0.432941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 2398.00i | − 0.894362i | −0.894444 | − | 0.447181i | \(-0.852428\pi\) | ||||
0.894444 | − | 0.447181i | \(-0.147572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1278.00i | − 0.462202i | −0.972930 | − | 0.231101i | \(-0.925767\pi\) | ||||
0.972930 | − | 0.231101i | \(-0.0742327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4472.00 | −1.59302 | −0.796512 | − | 0.604623i | \(-0.793324\pi\) | ||||
−0.796512 | + | 0.604623i | \(0.793324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2676.00 | 0.939057 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 192.000i | 0.0663830i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1728.00i | 0.580214i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5040.00 | −1.66806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1340.00 | 0.437201 | 0.218600 | − | 0.975814i | \(-0.429851\pi\) | ||||
0.218600 | + | 0.975814i | \(0.429851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 360.000i | 0.115807i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 512.000i | 0.160170i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1938.00 | −0.597981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 780.000 | 0.237414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2360.00i | 0.708687i | 0.935115 | + | 0.354344i | \(0.115296\pi\) | ||||
−0.935115 | + | 0.354344i | \(0.884704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1380.00i | − 0.403497i | −0.979437 | − | 0.201748i | \(-0.935338\pi\) | ||||
0.979437 | − | 0.201748i | \(-0.0646624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1694.00 | −0.488833 | −0.244416 | − | 0.969670i | \(-0.578596\pi\) | ||||
−0.244416 | + | 0.969670i | \(0.578596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3456.00 | −0.984364 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 5190.00i | − 1.45926i | −0.683841 | − | 0.729631i | \(-0.739692\pi\) | ||||
0.683841 | − | 0.729631i | \(-0.260308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3504.00i | − 0.960377i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2352.00 | −0.636562 | −0.318281 | − | 0.947996i | \(-0.603105\pi\) | ||||
−0.318281 | + | 0.947996i | \(0.603105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3502.00 | −0.936032 | −0.468016 | − | 0.883720i | \(-0.655031\pi\) | ||||
−0.468016 | + | 0.883720i | \(0.655031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1400.00i | 0.360647i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2196.00 | −0.558899 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4788.00 | 1.20405 | 0.602024 | − | 0.798478i | \(-0.294361\pi\) | ||||
0.602024 | + | 0.798478i | \(0.294361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6912.00i | − 1.71760i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1506.00i | − 0.365532i | −0.983156 | − | 0.182766i | \(-0.941495\pi\) | ||||
0.983156 | − | 0.182766i | \(-0.0585051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1088.00 | 0.261023 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.0000 | 0.0128066 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 432.000i | − 0.101286i | −0.998717 | − | 0.0506431i | \(-0.983873\pi\) | ||||
0.998717 | − | 0.0506431i | \(-0.0161271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4770.00i | − 1.09333i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −54.0000 | −0.0122395 | −0.00611977 | − | 0.999981i | \(-0.501948\pi\) | ||||
−0.00611977 | + | 0.999981i | \(0.501948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6496.00 | −1.45610 | −0.728051 | − | 0.685522i | \(-0.759574\pi\) | ||||
−0.728051 | + | 0.685522i | \(0.759574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 960.000i | 0.212827i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 466.000i | 0.101080i | 0.998722 | + | 0.0505401i | \(0.0160943\pi\) | ||||
−0.998722 | + | 0.0505401i | \(0.983906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 144.000 | 0.0308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4854.00 | −1.03048 | −0.515241 | − | 0.857045i | \(-0.672298\pi\) | ||||
−0.515241 | + | 0.857045i | \(0.672298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4516.00i | − 0.948581i | −0.880368 | − | 0.474290i | \(-0.842705\pi\) | ||||
0.880368 | − | 0.474290i | \(-0.157295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12480.0i | 2.56680i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1171.00 | −0.238347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −582.000 | −0.117242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8574.00i | 1.70955i | 0.518998 | + | 0.854775i | \(0.326305\pi\) | ||||
−0.518998 | + | 0.854775i | \(0.673695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 972.000i | 0.189903i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1920.00 | −0.371359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1664.00 | −0.318642 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2394.00i | − 0.453900i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3476.00i | − 0.646208i | −0.946363 | − | 0.323104i | \(-0.895274\pi\) | ||||
0.946363 | − | 0.323104i | \(-0.104726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 816.000 | 0.150229 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2424.00 | 0.441969 | 0.220985 | − | 0.975277i | \(-0.429073\pi\) | ||||
0.220985 | + | 0.975277i | \(0.429073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1558.00i | − 0.281353i | −0.990056 | − | 0.140676i | \(-0.955072\pi\) | ||||
0.990056 | − | 0.140676i | \(-0.0449277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8538.00i | 1.51275i | 0.654138 | + | 0.756375i | \(0.273032\pi\) | ||||
−0.654138 | + | 0.756375i | \(0.726968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −216.000 | −0.0379112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −468.000 | −0.0813745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 10920.0i | − 1.88113i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4866.00i | 0.822906i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13056.0 | −2.18784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −988.000 | −0.164065 | −0.0820323 | − | 0.996630i | \(-0.526141\pi\) | ||||
−0.0820323 | + | 0.996630i | \(0.526141\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 306.000i | − 0.0503564i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2546.00i | − 0.411541i | −0.978600 | − | 0.205771i | \(-0.934030\pi\) | ||||
0.978600 | − | 0.205771i | \(-0.0659701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3222.00 | 0.516209 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576.000 | −0.0914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0i | 1.70265i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8556.00i | − 1.32366i | −0.749654 | − | 0.661830i | \(-0.769780\pi\) | ||||
0.749654 | − | 0.661830i | \(-0.230220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3706.00 | 0.568417 | 0.284209 | − | 0.958762i | \(-0.408269\pi\) | ||||
0.284209 | + | 0.958762i | \(0.408269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 270.000 | 0.0410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11394.0i | 1.71796i | 0.512005 | + | 0.858982i | \(0.328903\pi\) | ||||
−0.512005 | + | 0.858982i | \(0.671097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 7488.00i | − 1.11010i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 264.000 | 0.0388117 | 0.0194058 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194058 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12741.0 | 1.85756 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000i | 0.0151820i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10232.0i | − 1.45533i | −0.685933 | − | 0.727665i | \(-0.740606\pi\) | ||||
0.685933 | − | 0.727665i | \(-0.259394\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3510.00 | 0.495185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3648.00 | −0.510498 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 562.000i | − 0.0780141i | −0.999239 | − | 0.0390070i | \(-0.987581\pi\) | ||||
0.999239 | − | 0.0390070i | \(-0.0124195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 60.0000i | 0.00819670i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7228.00 | 0.979624 | 0.489812 | − | 0.871828i | \(-0.337065\pi\) | ||||
0.489812 | + | 0.871828i | \(0.337065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4584.00 | 0.616392 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 5736.00i | − 0.765263i | −0.923901 | − | 0.382632i | \(-0.875018\pi\) | ||||
0.923901 | − | 0.382632i | \(-0.124982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 468.000i | 0.0614723i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9186.00 | 1.19730 | 0.598649 | − | 0.801012i | \(-0.295705\pi\) | ||||
0.598649 | + | 0.801012i | \(0.295705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14976.0 | 1.93700 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 7236.00i | − 0.928773i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 394.000i | 0.0498093i | 0.999690 | + | 0.0249047i | \(0.00792822\pi\) | ||||
−0.999690 | + | 0.0249047i | \(0.992072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13440.0 | 1.68632 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1614.00 | −0.200996 | −0.100498 | − | 0.994937i | \(-0.532044\pi\) | ||||
−0.100498 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 160.000i | 0.0197771i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1224.00i | 0.149070i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1034.00 | −0.125007 | −0.0625037 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625037 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6318.00 | −0.758258 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16512.0i | 1.96732i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 1668.00i | − 0.195881i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3708.00 | −0.432333 | −0.216167 | − | 0.976356i | \(-0.569355\pi\) | ||||
−0.216167 | + | 0.976356i | \(0.569355\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4930.00 | −0.570721 | −0.285360 | − | 0.958420i | \(-0.592113\pi\) | ||||
−0.285360 | + | 0.958420i | \(0.592113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3672.00i | 0.422077i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1856.00i | 0.210347i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1080.00 | −0.121545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2592.00 | −0.289680 | −0.144840 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144840 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2162.00i | 0.239952i | 0.992777 | + | 0.119976i | \(0.0382817\pi\) | ||||
−0.992777 | + | 0.119976i | \(0.961718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26880.0i | 2.94244i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1352.00 | −0.146987 | −0.0734937 | − | 0.997296i | \(-0.523415\pi\) | ||||
−0.0734937 | + | 0.997296i | \(0.523415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5532.00i | 0.593303i | 0.954986 | + | 0.296652i | \(0.0958700\pi\) | ||||
−0.954986 | + | 0.296652i | \(0.904130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 7254.00i | − 0.767567i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3198.00 | 0.336131 | 0.168066 | − | 0.985776i | \(-0.446248\pi\) | ||||
0.168066 | + | 0.985776i | \(0.446248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14040.0 | −1.46589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 8520.00i | − 0.883674i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1510.00i | 0.154562i | 0.997009 | + | 0.0772810i | \(0.0246239\pi\) | ||||
−0.997009 | + | 0.0772810i | \(0.975376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2106.00 | −0.214160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16086.0 | 1.62516 | 0.812581 | − | 0.582848i | \(-0.198062\pi\) | ||||
0.812581 | + | 0.582848i | \(0.198062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5384.00i | 0.540423i | 0.962801 | + | 0.270211i | \(0.0870936\pi\) | ||||
−0.962801 | + | 0.270211i | \(0.912906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2604.00i | 0.258027i | 0.991643 | + | 0.129014i | \(0.0411811\pi\) | ||||
−0.991643 | + | 0.129014i | \(0.958819\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28544.0 | 2.81032 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6162.00 | −0.602824 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1872.00i | − 0.181976i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1026.00i | 0.0984849i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11136.0 | −1.06225 | −0.531124 | − | 0.847294i | \(-0.678230\pi\) | ||||
−0.531124 | + | 0.847294i | \(0.678230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 340.000 | 0.0322301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18432.0i | 1.73641i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 14624.0i | − 1.36073i | −0.732872 | − | 0.680366i | \(-0.761821\pi\) | ||||
0.732872 | − | 0.680366i | \(-0.238179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1380.00 | −0.127619 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11844.0 | 1.08862 | 0.544310 | − | 0.838884i | \(-0.316792\pi\) | ||||
0.544310 | + | 0.838884i | \(0.316792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 468.000i | − 0.0427539i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3840.00i | 0.346575i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11284.0 | 1.01231 | 0.506154 | − | 0.862443i | \(-0.331067\pi\) | ||||
0.506154 | + | 0.862443i | \(0.331067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6048.00 | −0.539331 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4032.00i | 0.357412i | 0.983903 | + | 0.178706i | \(0.0571910\pi\) | ||||
−0.983903 | + | 0.178706i | \(0.942809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6291.00i | − 0.551071i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17562.0 | 1.52932 | 0.764658 | − | 0.644436i | \(-0.222908\pi\) | ||||
0.764658 | + | 0.644436i | \(0.222908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20672.0 | −1.78958 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 3780.00i | − 0.325324i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14688.0i | − 1.24947i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1854.00 | −0.156805 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3162.00 | 0.265892 | 0.132946 | − | 0.991123i | \(-0.457556\pi\) | ||||
0.132946 | + | 0.991123i | \(0.457556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6764.00i | 0.565524i | 0.959190 | + | 0.282762i | \(0.0912507\pi\) | ||||
−0.959190 | + | 0.282762i | \(0.908749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1248.00i | − 0.103157i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24697.0 | −2.02983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4644.00 | 0.379534 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3900.00i | 0.316938i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 8892.00i | − 0.714559i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24516.0 | −1.95914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17798.0 | 1.41441 | 0.707205 | − | 0.707009i | \(-0.249956\pi\) | ||||
0.707205 | + | 0.707009i | \(0.249956\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1110.00i | 0.0877250i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19996.0i | 1.56301i | 0.623898 | + | 0.781506i | \(0.285548\pi\) | ||||
−0.623898 | + | 0.781506i | \(0.714452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 522.000 | 0.0405800 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 840.000 | 0.0649459 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 37376.0i | − 2.87412i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11094.0i | − 0.843928i | −0.906613 | − | 0.421964i | \(-0.861341\pi\) | ||||
0.906613 | − | 0.421964i | \(-0.138659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −520.000 | −0.0393446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8424.00 | 0.633978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 900.000i | 0.0673721i | 0.999432 | + | 0.0336860i | \(0.0107246\pi\) | ||||
−0.999432 | + | 0.0336860i | \(0.989275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2592.00i | − 0.191982i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7914.00 | −0.583079 | −0.291540 | − | 0.956559i | \(-0.594168\pi\) | ||||
−0.291540 | + | 0.956559i | \(0.594168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2380.00 | −0.174431 | −0.0872153 | − | 0.996189i | \(-0.527797\pi\) | ||||
−0.0872153 | + | 0.996189i | \(0.527797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3312.00i | − 0.241467i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25726.0i | 1.85613i | 0.372417 | + | 0.928065i | \(0.378529\pi\) | ||||
−0.372417 | + | 0.928065i | \(0.621471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7194.00 | −0.516360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23424.0 | −1.67262 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4104.00i | − 0.291544i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3612.00i | − 0.253975i | −0.991904 | − | 0.126987i | \(-0.959469\pi\) | ||||
0.991904 | − | 0.126987i | \(-0.0405308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2240.00 | 0.156702 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3834.00 | −0.266852 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2898.00i | 0.200686i | 0.994953 | + | 0.100343i | \(0.0319940\pi\) | ||||
−0.994953 | + | 0.100343i | \(0.968006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13416.0i | 0.919733i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2664.00 | −0.181716 | −0.0908582 | − | 0.995864i | \(-0.528961\pi\) | ||||
−0.0908582 | + | 0.995864i | \(0.528961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −502.000 | −0.0340716 | −0.0170358 | − | 0.999855i | \(-0.505423\pi\) | ||||
−0.0170358 | + | 0.999855i | \(0.505423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8028.00i | − 0.542165i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 7976.00i | − 0.533337i | −0.963788 | − | 0.266669i | \(-0.914077\pi\) | ||||
0.963788 | − | 0.266669i | \(-0.0859230\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 576.000 | 0.0383263 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4080.00 | −0.270146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20414.0i | 1.34505i | 0.740076 | + | 0.672523i | \(0.234790\pi\) | ||||
−0.740076 | + | 0.672523i | \(0.765210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6342.00i | 0.413808i | 0.978361 | + | 0.206904i | \(0.0663387\pi\) | ||||
−0.978361 | + | 0.206904i | \(0.933661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22676.0 | −1.47242 | −0.736208 | − | 0.676755i | \(-0.763385\pi\) | ||||
−0.736208 | + | 0.676755i | \(0.763385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5184.00 | 0.334987 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 50880.0i | − 3.27201i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15120.0i | 0.963054i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2652.00 | −0.168112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7048.00 | −0.444654 | −0.222327 | − | 0.974972i | \(-0.571365\pi\) | ||||
−0.222327 | + | 0.974972i | \(0.571365\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4020.00i | − 0.252418i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6810.00i | 0.423582i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1080.00 | 0.0668609 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20286.0 | −1.25000 | −0.624999 | − | 0.780625i | \(-0.714901\pi\) | ||||
−0.624999 | + | 0.780625i | \(0.714901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 16108.0i | − 0.987928i | −0.869482 | − | 0.493964i | \(-0.835548\pi\) | ||||
0.869482 | − | 0.493964i | \(-0.164452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 27456.0i | − 1.66833i | −0.551518 | − | 0.834163i | \(-0.685951\pi\) | ||||
0.551518 | − | 0.834163i | \(-0.314049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18576.0 | −1.12353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1536.00 | 0.0924740 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 12522.0i | − 0.750419i | −0.926940 | − | 0.375210i | \(-0.877571\pi\) | ||||
0.926940 | − | 0.375210i | \(-0.122429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5814.00i | 0.345245i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16308.0 | 0.963990 | 0.481995 | − | 0.876174i | \(-0.339912\pi\) | ||||
0.481995 | + | 0.876174i | \(0.339912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32078.0 | 1.88758 | 0.943789 | − | 0.330547i | \(-0.107233\pi\) | ||||
0.943789 | + | 0.330547i | \(0.107233\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2340.00i | − 0.137071i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1152.00i | 0.0668750i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7080.00 | 0.409161 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2088.00 | −0.120129 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4610.00i | 0.264045i | 0.991247 | + | 0.132023i | \(0.0421472\pi\) | ||||
−0.991247 | + | 0.132023i | \(0.957853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10782.0i | − 0.612091i | −0.952017 | − | 0.306046i | \(-0.900994\pi\) | ||||
0.952017 | − | 0.306046i | \(-0.0990060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6208.00 | −0.350871 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4140.00 | −0.232959 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2892.00i | 0.162019i | 0.996713 | + | 0.0810097i | \(0.0258145\pi\) | ||||
−0.996713 | + | 0.0810097i | \(0.974186\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5082.00i | 0.282228i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1140.00 | −0.0630342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29572.0 | −1.62803 | −0.814017 | − | 0.580841i | \(-0.802724\pi\) | ||||
−0.814017 | + | 0.580841i | \(0.802724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10368.0i | 0.568323i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 30420.0i | − 1.65314i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15570.0 | −0.842506 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5766.00 | 0.310669 | 0.155334 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4760.00i | − 0.255372i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 25536.0i | − 1.35839i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3326.00 | −0.176178 | −0.0880892 | − | 0.996113i | \(-0.528076\pi\) | ||||
−0.0880892 | + | 0.996113i | \(0.528076\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10512.0 | −0.554474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3072.00i | 0.161357i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7056.00i | 0.367519i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7728.00 | 0.400843 | 0.200421 | − | 0.979710i | \(-0.435769\pi\) | ||||
0.200421 | + | 0.979710i | \(0.435769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8704.00 | 0.449589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10506.0i | 0.540418i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21616.0i | 1.10274i | 0.834260 | + | 0.551371i | \(0.185895\pi\) | ||||
−0.834260 | + | 0.551371i | \(0.814105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4056.00 | 0.205221 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10118.0i | 0.509846i | 0.966961 | + | 0.254923i | \(0.0820501\pi\) | ||||
−0.966961 | + | 0.254923i | \(0.917950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32112.0i | 1.60497i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10460.0 | −0.520673 | −0.260336 | − | 0.965518i | \(-0.583833\pi\) | ||||
−0.260336 | + | 0.965518i | \(0.583833\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4200.00 | 0.208220 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17232.0i | 0.850849i | 0.904994 | + | 0.425424i | \(0.139875\pi\) | ||||
−0.904994 | + | 0.425424i | \(0.860125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6588.00i | 0.322680i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4992.00 | −0.243530 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26912.0 | 1.30763 | 0.653817 | − | 0.756653i | \(-0.273167\pi\) | ||||
0.653817 | + | 0.756653i | \(0.273167\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 14364.0i | − 0.695157i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 13838.0i | − 0.664400i | −0.943209 | − | 0.332200i | \(-0.892209\pi\) | ||||
0.943209 | − | 0.332200i | \(-0.107791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20736.0 | −0.991659 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17238.0 | −0.821126 | −0.410563 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410563 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51904.0i | 2.46271i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5160.00i | 0.242916i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21698.0 | −1.01749 | −0.508745 | − | 0.860917i | \(-0.669890\pi\) | ||||
−0.508745 | + | 0.860917i | \(0.669890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4518.00 | −0.211040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18366.0i | 0.854565i | 0.904118 | + | 0.427283i | \(0.140529\pi\) | ||||
−0.904118 | + | 0.427283i | \(0.859471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3264.00i | − 0.150702i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54600.0 | 2.51123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4320.00 | −0.197928 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 162.000i | − 0.00739388i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30316.0i | 1.37312i | 0.727071 | + | 0.686562i | \(0.240881\pi\) | ||||
−0.727071 | + | 0.686562i | \(0.759119\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1296.00 | −0.0584776 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34368.0 | 1.54486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 580.000i | 0.0259728i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7494.00i | − 0.333063i | −0.986036 | − | 0.166531i | \(-0.946743\pi\) | ||||
0.986036 | − | 0.166531i | \(-0.0532567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31824.0 | 1.40908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14310.0 | −0.631235 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 23256.0i | − 1.02203i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 162.000i | 0.00706651i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11526.0 | 0.500906 | 0.250453 | − | 0.968129i | \(-0.419421\pi\) | ||||
0.250453 | + | 0.968129i | \(0.419421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33820.0 | −1.46434 | −0.732171 | − | 0.681121i | \(-0.761493\pi\) | ||||
−0.732171 | + | 0.681121i | \(0.761493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19488.0i | 0.840681i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7280.00i | 0.311744i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2880.00 | 0.122876 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19566.0 | 0.831739 | 0.415870 | − | 0.909424i | \(-0.363477\pi\) | ||||
0.415870 | + | 0.909424i | \(0.363477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 40096.0i | − 1.69825i | −0.528193 | − | 0.849124i | \(-0.677130\pi\) | ||||
0.528193 | − | 0.849124i | \(-0.322870\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 31884.0i | − 1.34065i | −0.742069 | − | 0.670324i | \(-0.766155\pi\) | ||||
0.742069 | − | 0.670324i | \(-0.233845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24442.0 | 1.02401 | 0.512006 | − | 0.858982i | \(-0.328903\pi\) | ||||
0.512006 | + | 0.858982i | \(0.328903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1398.00 | 0.0583587 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 53118.0i | − 2.20940i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 432.000i | − 0.0178400i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31944.0 | 1.31446 | 0.657228 | − | 0.753691i | \(-0.271729\pi\) | ||||
0.657228 | + | 0.753691i | \(0.271729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14562.0i | 0.594949i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1120.00i | 0.0454352i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13548.0 | −0.547663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6528.00 | 0.262958 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17486.0i | 0.701887i | 0.936397 | + | 0.350943i | \(0.114139\pi\) | ||||
−0.936397 | + | 0.350943i | \(0.885861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 43434.0i | − 1.73125i | −0.500697 | − | 0.865623i | \(-0.666923\pi\) | ||||
0.500697 | − | 0.865623i | \(-0.333077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10820.0 | −0.429771 | −0.214886 | − | 0.976639i | \(-0.568938\pi\) | ||||
−0.214886 | + | 0.976639i | \(0.568938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37440.0 | 1.48194 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29976.0i | 1.18238i | 0.806532 | + | 0.591191i | \(0.201342\pi\) | ||||
−0.806532 | + | 0.591191i | \(0.798658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3513.00i | 0.137610i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42048.0 | 1.64140 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8920.00 | 0.347007 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1746.00i | 0.0676897i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40522.0i | 1.56024i | 0.625630 | + | 0.780120i | \(0.284842\pi\) | ||||
−0.625630 | + | 0.780120i | \(0.715158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25722.0 | 0.987010 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15570.0 | 0.595422 | 0.297711 | − | 0.954656i | \(-0.403777\pi\) | ||||
0.297711 | + | 0.954656i | \(0.403777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1084.00i | − 0.0413131i | −0.999787 | − | 0.0206566i | \(-0.993424\pi\) | ||||
0.999787 | − | 0.0206566i | \(-0.00657566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8208.00i | 0.310708i | 0.987859 | + | 0.155354i | \(0.0496518\pi\) | ||||
−0.987859 | + | 0.155354i | \(0.950348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48896.0 | 1.84468 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00 | 0.109640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57120.0i | 2.14048i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5760.00i | 0.214404i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 96.0000 | 0.00356149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8892.00 | 0.328785 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4992.00i | 0.183968i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 34076.0i | − 1.24749i | −0.781627 | − | 0.623746i | \(-0.785610\pi\) | ||||
0.781627 | − | 0.623746i | \(-0.214390\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7182.00 | −0.262059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15072.0 | −0.548142 | −0.274071 | − | 0.961709i | \(-0.588370\pi\) | ||||
−0.274071 | + | 0.961709i | \(0.588370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 26352.0i | − 0.955229i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 77184.0i | − 2.77954i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24392.0 | −0.875536 | −0.437768 | − | 0.899088i | \(-0.644231\pi\) | ||||
−0.437768 | + | 0.899088i | \(0.644231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10428.0 | −0.373088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1200.00i | 0.0427936i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2448.00i | − 0.0867345i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13602.0 | −0.480374 | −0.240187 | − | 0.970727i | \(-0.577209\pi\) | ||||
−0.240187 | + | 0.970727i | \(0.577209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95340.0 | 3.35622 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7272.00i | − 0.255171i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47974.0i | 1.67262i | 0.548259 | + | 0.836309i | \(0.315291\pi\) | ||||
−0.548259 | + | 0.836309i | \(0.684709\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4674.00 | −0.162439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48330.0 | −1.67430 | −0.837148 | − | 0.546976i | \(-0.815779\pi\) | ||||
−0.837148 | + | 0.546976i | \(0.815779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74880.0i | 2.58582i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9324.00i | 0.319946i | 0.987121 | + | 0.159973i | \(0.0511408\pi\) | ||||
−0.987121 | + | 0.159973i | \(0.948859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6460.00 | −0.220970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25614.0 | 0.873387 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 14838.0i | − 0.504355i | −0.967681 | − | 0.252177i | \(-0.918853\pi\) | ||||
0.967681 | − | 0.252177i | \(-0.0811466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 648.000i | 0.0218881i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −67392.0 | −2.26924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29535.0 | −0.991407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1404.00i | 0.0469816i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 11360.0i | − 0.377780i | −0.981998 | − | 0.188890i | \(-0.939511\pi\) | ||||
0.981998 | − | 0.188890i | \(-0.0604889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32760.0 | −1.08607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6972.00 | −0.230424 | −0.115212 | − | 0.993341i | \(-0.536755\pi\) | ||||
−0.115212 | + | 0.993341i | \(0.536755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17792.0i | − 0.586213i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41166.0i | 1.34802i | 0.738722 | + | 0.674011i | \(0.235430\pi\) | ||||
−0.738722 | + | 0.674011i | \(0.764570\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57240.0 | 1.86864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14598.0 | 0.475105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22464.0i | 0.728881i | 0.931227 | + | 0.364441i | \(0.118740\pi\) | ||||
−0.931227 | + | 0.364441i | \(0.881260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39168.0i | 1.26315i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9984.00 | −0.321004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10192.0 | −0.326700 | −0.163350 | − | 0.986568i | \(-0.552230\pi\) | ||||
−0.163350 | + | 0.986568i | \(0.552230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2964.00i | 0.0947228i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 322.000i | 0.0102285i | 0.999987 | + | 0.00511426i | \(0.00162793\pi\) | ||||
−0.999987 | + | 0.00511426i | \(0.998372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −918.000 | −0.0290733 |
(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 | 300.4.d.d.49.1 | 2 | ||
3.2 | odd | 2 | 900.4.d.b.649.1 | 2 | |||
4.3 | odd | 2 | 1200.4.f.e.49.2 | 2 | |||
5.2 | odd | 4 | 60.4.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 300.4.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 300.4.d.d.49.2 | 2 | ||
15.2 | even | 4 | 180.4.a.c.1.1 | 1 | |||
15.8 | even | 4 | 900.4.a.b.1.1 | 1 | |||
15.14 | odd | 2 | 900.4.d.b.649.2 | 2 | |||
20.3 | even | 4 | 1200.4.a.s.1.1 | 1 | |||
20.7 | even | 4 | 240.4.a.j.1.1 | 1 | |||
20.19 | odd | 2 | 1200.4.f.e.49.1 | 2 | |||
40.27 | even | 4 | 960.4.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 960.4.a.bb.1.1 | 1 | |||
45.2 | even | 12 | 1620.4.i.g.1081.1 | 2 | |||
45.7 | odd | 12 | 1620.4.i.a.1081.1 | 2 | |||
45.22 | odd | 12 | 1620.4.i.a.541.1 | 2 | |||
45.32 | even | 12 | 1620.4.i.g.541.1 | 2 | |||
60.47 | odd | 4 | 720.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
180.4.a.c.1.1 | 1 | 15.2 | even | 4 | |||
240.4.a.j.1.1 | 1 | 20.7 | even | 4 | |||
300.4.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
300.4.d.d.49.1 | 2 | 1.1 | even | 1 | trivial | ||
300.4.d.d.49.2 | 2 | 5.4 | even | 2 | inner | ||
720.4.a.c.1.1 | 1 | 60.47 | odd | 4 | |||
900.4.a.b.1.1 | 1 | 15.8 | even | 4 | |||
900.4.d.b.649.1 | 2 | 3.2 | odd | 2 | |||
900.4.d.b.649.2 | 2 | 15.14 | odd | 2 | |||
960.4.a.a.1.1 | 1 | 40.27 | even | 4 | |||
960.4.a.bb.1.1 | 1 | 40.37 | odd | 4 | |||
1200.4.a.s.1.1 | 1 | 20.3 | even | 4 | |||
1200.4.f.e.49.1 | 2 | 20.19 | odd | 2 | |||
1200.4.f.e.49.2 | 2 | 4.3 | odd | 2 | |||
1620.4.i.a.541.1 | 2 | 45.22 | odd | 12 | |||
1620.4.i.a.1081.1 | 2 | 45.7 | odd | 12 | |||
1620.4.i.g.541.1 | 2 | 45.32 | even | 12 | |||
1620.4.i.g.1081.1 | 2 | 45.2 | even | 12 |