Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,5,Mod(703,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.703");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(119.082197473\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.7 | ||
Root | \(1.09445 - 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.703 |
Dual form | 1152.5.b.k.703.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 39.7490i | 1.58996i | 0.606635 | + | 0.794980i | \(0.292519\pi\) | ||||
−0.606635 | + | 0.794980i | \(0.707481\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 46.0431i | − 0.939655i | −0.882758 | − | 0.469828i | \(-0.844316\pi\) | ||||
0.882758 | − | 0.469828i | \(-0.155684\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −181.283 | −1.49821 | −0.749105 | − | 0.662451i | \(-0.769516\pi\) | ||||
−0.749105 | + | 0.662451i | \(0.769516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 183.498i | 1.08579i | 0.839801 | + | 0.542894i | \(0.182671\pi\) | ||||
−0.839801 | + | 0.542894i | \(0.817329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −427.992 | −1.48094 | −0.740471 | − | 0.672089i | \(-0.765397\pi\) | ||||
−0.740471 | + | 0.672089i | \(0.765397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 668.558 | 1.85196 | 0.925981 | − | 0.377571i | \(-0.123241\pi\) | ||||
0.925981 | + | 0.377571i | \(0.123241\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 882.463i | 1.66817i | 0.551635 | + | 0.834086i | \(0.314004\pi\) | ||||
−0.551635 | + | 0.834086i | \(0.685996\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −954.984 | −1.52797 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 807.247i | − 0.959866i | −0.877305 | − | 0.479933i | \(-0.840661\pi\) | ||||
0.877305 | − | 0.479933i | \(-0.159339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 391.276i | 0.407155i | 0.979059 | + | 0.203577i | \(0.0652569\pi\) | ||||
−0.979059 | + | 0.203577i | \(0.934743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1830.17 | 1.49402 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 466.980i | − 0.341111i | −0.985348 | − | 0.170555i | \(-0.945444\pi\) | ||||
0.985348 | − | 0.170555i | \(-0.0545561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2159.93 | −1.28491 | −0.642454 | − | 0.766325i | \(-0.722083\pi\) | ||||
−0.642454 | + | 0.766325i | \(0.722083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −509.182 | −0.275382 | −0.137691 | − | 0.990475i | \(-0.543968\pi\) | ||||
−0.137691 | + | 0.990475i | \(0.543968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2056.83i | 0.931116i | 0.885017 | + | 0.465558i | \(0.154146\pi\) | ||||
−0.885017 | + | 0.465558i | \(0.845854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 281.031 | 0.117048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 753.725i | − 0.268325i | −0.990959 | − | 0.134163i | \(-0.957166\pi\) | ||||
0.990959 | − | 0.134163i | \(-0.0428344\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7205.84i | − 2.38210i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1309.43 | −0.376165 | −0.188083 | − | 0.982153i | \(-0.560227\pi\) | ||||
−0.188083 | + | 0.982153i | \(0.560227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 801.913i | 0.215510i | 0.994177 | + | 0.107755i | \(0.0343662\pi\) | ||||
−0.994177 | + | 0.107755i | \(0.965634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7293.87 | −1.72636 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −505.813 | −0.112678 | −0.0563392 | − | 0.998412i | \(-0.517943\pi\) | ||||
−0.0563392 | + | 0.998412i | \(0.517943\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 2170.94i | − 0.430658i | −0.976542 | − | 0.215329i | \(-0.930918\pi\) | ||||
0.976542 | − | 0.215329i | \(-0.0690823\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2297.97 | −0.431219 | −0.215610 | − | 0.976480i | \(-0.569174\pi\) | ||||
−0.215610 | + | 0.976480i | \(0.569174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8346.85i | 1.40780i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 10705.3i | − 1.71532i | −0.514219 | − | 0.857659i | \(-0.671918\pi\) | ||||
0.514219 | − | 0.857659i | \(-0.328082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2977.81 | −0.432256 | −0.216128 | − | 0.976365i | \(-0.569343\pi\) | ||||
−0.216128 | + | 0.976365i | \(0.569343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 17012.3i | − 2.35464i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6493.92 | 0.819836 | 0.409918 | − | 0.912122i | \(-0.365557\pi\) | ||||
0.409918 | + | 0.912122i | \(0.365557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8448.82 | 1.02027 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26574.5i | 2.94455i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8189.92 | −0.870435 | −0.435217 | − | 0.900325i | \(-0.643328\pi\) | ||||
−0.435217 | + | 0.900325i | \(0.643328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15576.5i | − 1.52696i | −0.645833 | − | 0.763479i | \(-0.723490\pi\) | ||||
0.645833 | − | 0.763479i | \(-0.276510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6628.58i | 0.624807i | 0.949950 | + | 0.312403i | \(0.101134\pi\) | ||||
−0.949950 | + | 0.312403i | \(0.898866\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11796.4 | −1.03035 | −0.515173 | − | 0.857086i | \(-0.672272\pi\) | ||||
−0.515173 | + | 0.857086i | \(0.672272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13286.1i | 1.11826i | 0.829080 | + | 0.559130i | \(0.188865\pi\) | ||||
−0.829080 | + | 0.559130i | \(0.811135\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11713.6 | 0.917350 | 0.458675 | − | 0.888604i | \(-0.348324\pi\) | ||||
0.458675 | + | 0.888604i | \(0.348324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −35077.0 | −2.65233 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19706.1i | 1.39157i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18222.7 | 1.24463 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 13116.5i | − 0.839459i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 5640.55i | − 0.349715i | −0.984594 | − | 0.174858i | \(-0.944054\pi\) | ||||
0.984594 | − | 0.174858i | \(-0.0559465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31922.5 | 1.86018 | 0.930089 | − | 0.367335i | \(-0.119730\pi\) | ||||
0.930089 | + | 0.367335i | \(0.119730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 30782.5i | − 1.74021i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10515.6 | 0.560263 | 0.280132 | − | 0.959962i | \(-0.409622\pi\) | ||||
0.280132 | + | 0.959962i | \(0.409622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14985.9 | 0.775626 | 0.387813 | − | 0.921738i | \(-0.373231\pi\) | ||||
0.387813 | + | 0.921738i | \(0.373231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 33265.2i | − 1.62674i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32087.3 | 1.52615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 11795.4i | − 0.531298i | −0.964070 | − | 0.265649i | \(-0.914414\pi\) | ||||
0.964070 | − | 0.265649i | \(-0.0855863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 33792.9i | − 1.48208i | −0.671460 | − | 0.741040i | \(-0.734333\pi\) | ||||
0.671460 | − | 0.741040i | \(-0.265667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15552.8 | −0.647360 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 28788.9i | − 1.16796i | −0.811770 | − | 0.583978i | \(-0.801496\pi\) | ||||
0.811770 | − | 0.583978i | \(-0.198504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 40631.3 | 1.56751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13409.0 | 0.504684 | 0.252342 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252342 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 13206.7i | − 0.473546i | −0.971565 | − | 0.236773i | \(-0.923910\pi\) | ||||
0.971565 | − | 0.236773i | \(-0.0760898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5110.53 | −0.178934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 364.956i | 0.0121940i | 0.999981 | + | 0.00609702i | \(0.00194076\pi\) | ||||
−0.999981 | + | 0.00609702i | \(0.998059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43970.5i | 1.43577i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14372.0 | 0.448549 | 0.224275 | − | 0.974526i | \(-0.427999\pi\) | ||||
0.224275 | + | 0.974526i | \(0.427999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4050.54i | 0.123639i | 0.998087 | + | 0.0618195i | \(0.0196903\pi\) | ||||
−0.998087 | + | 0.0618195i | \(0.980310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18562.0 | 0.542352 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 77587.9 | 2.21876 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 49880.9i | − 1.36731i | −0.729805 | − | 0.683656i | \(-0.760389\pi\) | ||||
0.729805 | − | 0.683656i | \(-0.239611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −48425.7 | −1.30005 | −0.650026 | − | 0.759912i | \(-0.725242\pi\) | ||||
−0.650026 | + | 0.759912i | \(0.725242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5556.74i | − 0.143182i | −0.997434 | − | 0.0715908i | \(-0.977192\pi\) | ||||
0.997434 | − | 0.0715908i | \(-0.0228076\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 60594.7i | 1.53013i | 0.643952 | + | 0.765066i | \(0.277294\pi\) | ||||
−0.643952 | + | 0.765066i | \(0.722706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37168.2 | −0.901943 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 85855.1i | − 2.04295i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −121198. | −2.77463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27539.9 | −0.618583 | −0.309292 | − | 0.950967i | \(-0.600092\pi\) | ||||
−0.309292 | + | 0.950967i | \(0.600092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 20239.5i | − 0.437847i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18015.6 | 0.382585 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 78535.7i | − 1.60799i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3021.35i | 0.0607564i | 0.999538 | + | 0.0303782i | \(0.00967116\pi\) | ||||
−0.999538 | + | 0.0303782i | \(0.990329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7077.28 | −0.137346 | −0.0686728 | − | 0.997639i | \(-0.521876\pi\) | ||||
−0.0686728 | + | 0.997639i | \(0.521876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 102761.i | − 1.95956i | −0.200088 | − | 0.979778i | \(-0.564123\pi\) | ||||
0.200088 | − | 0.979778i | \(-0.435877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22976.6 | −0.423227 | −0.211613 | − | 0.977353i | \(-0.567872\pi\) | ||||
−0.211613 | + | 0.977353i | \(0.567872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −81757.1 | −1.48044 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 35566.7i | − 0.622656i | −0.950303 | − | 0.311328i | \(-0.899226\pi\) | ||||
0.950303 | − | 0.311328i | \(-0.100774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −92683.4 | −1.59576 | −0.797881 | − | 0.602816i | \(-0.794045\pi\) | ||||
−0.797881 | + | 0.602816i | \(0.794045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11170.7i | 0.186101i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 122679.i | 2.01084i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27590.5 | 0.437937 | 0.218968 | − | 0.975732i | \(-0.429731\pi\) | ||||
0.218968 | + | 0.975732i | \(0.429731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 159976.i | − 2.49927i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −92304.6 | −1.39752 | −0.698758 | − | 0.715358i | \(-0.746264\pi\) | ||||
−0.698758 | + | 0.715358i | \(0.746264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21501.2 | −0.320526 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 13884.4i | − 0.200732i | −0.994951 | − | 0.100366i | \(-0.967999\pi\) | ||||
0.994951 | − | 0.100366i | \(-0.0320014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29959.8 | 0.426626 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 52698.1i | − 0.728266i | −0.931347 | − | 0.364133i | \(-0.881365\pi\) | ||||
0.931347 | − | 0.364133i | \(-0.118635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 47028.8i | − 0.640361i | −0.947356 | − | 0.320181i | \(-0.896256\pi\) | ||||
0.947356 | − | 0.320181i | \(-0.103744\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 173123. | 2.28923 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 108393.i | 1.41268i | 0.707873 | + | 0.706340i | \(0.249655\pi\) | ||||
−0.707873 | + | 0.706340i | \(0.750345\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 73090.7 | 0.925656 | 0.462828 | − | 0.886448i | \(-0.346835\pi\) | ||||
0.462828 | + | 0.886448i | \(0.346835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −44763.1 | −0.558917 | −0.279458 | − | 0.960158i | \(-0.590155\pi\) | ||||
−0.279458 | + | 0.960158i | \(0.590155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 99449.9i | 1.20737i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 99656.3 | 1.19319 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 42030.2i | − 0.489583i | −0.969576 | − | 0.244792i | \(-0.921280\pi\) | ||||
0.969576 | − | 0.244792i | \(-0.0787195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 52048.6i | − 0.598088i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −161930. | −1.81128 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23444.3i | 0.258765i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31875.3 | −0.342653 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8820.31 | −0.0935852 | −0.0467926 | − | 0.998905i | \(-0.514900\pi\) | ||||
−0.0467926 | + | 0.998905i | \(0.514900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 155059.i | − 1.60315i | −0.597893 | − | 0.801576i | \(-0.703995\pi\) | ||||
0.597893 | − | 0.801576i | \(-0.296005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −179666. | −1.83390 | −0.916951 | − | 0.398999i | \(-0.869358\pi\) | ||||
−0.916951 | + | 0.398999i | \(0.869358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6188.77i | − 0.0615865i | −0.999526 | − | 0.0307933i | \(-0.990197\pi\) | ||||
0.999526 | − | 0.0307933i | \(-0.00980335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 146341.i | 1.43808i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −286138. | −2.74265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 175238.i | − 1.65906i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 94703.1 | 0.874928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132159. | 1.20626 | 0.603130 | − | 0.797643i | \(-0.293920\pi\) | ||||
0.603130 | + | 0.797643i | \(0.293920\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 20105.6i | − 0.179154i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 70040.0 | 0.616718 | 0.308359 | − | 0.951270i | \(-0.400220\pi\) | ||||
0.308359 | + | 0.951270i | \(0.400220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 70931.8i | − 0.610004i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 123489.i | − 1.04964i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 157722. | 1.30988 | 0.654942 | − | 0.755680i | \(-0.272693\pi\) | ||||
0.654942 | + | 0.755680i | \(0.272693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 198747.i | − 1.63174i | −0.578238 | − | 0.815868i | \(-0.696259\pi\) | ||||
0.578238 | − | 0.815868i | \(-0.303741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13376.1 | −0.107345 | −0.0536724 | − | 0.998559i | \(-0.517093\pi\) | ||||
−0.0536724 | + | 0.998559i | \(0.517093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 86292.9 | 0.684729 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 190011.i | 1.47432i | 0.675721 | + | 0.737158i | \(0.263832\pi\) | ||||
−0.675721 | + | 0.737158i | \(0.736168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 316649. | 2.42976 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 91342.0i | − 0.685622i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 94140.5i | − 0.698947i | −0.936946 | − | 0.349474i | \(-0.886360\pi\) | ||||
0.936946 | − | 0.349474i | \(-0.113640\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34703.9 | −0.252133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 66152.4i | 0.475475i | 0.971329 | + | 0.237738i | \(0.0764058\pi\) | ||||
−0.971329 | + | 0.237738i | \(0.923594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 148128. | 1.04221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −64395.2 | −0.448306 | −0.224153 | − | 0.974554i | \(-0.571962\pi\) | ||||
−0.224153 | + | 0.974554i | \(0.571962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30714.5i | 0.209385i | 0.994505 | + | 0.104693i | \(0.0333859\pi\) | ||||
−0.994505 | + | 0.104693i | \(0.966614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −331779. | −2.23835 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 199122.i | − 1.31589i | −0.753066 | − | 0.657945i | \(-0.771426\pi\) | ||||
0.753066 | − | 0.657945i | \(-0.228574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 377687.i | − 2.47046i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 425525. | 2.72729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 68565.8i | − 0.435037i | −0.976056 | − | 0.217519i | \(-0.930204\pi\) | ||||
0.976056 | − | 0.217519i | \(-0.0697963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21797.1 | 0.135553 | 0.0677765 | − | 0.997701i | \(-0.478410\pi\) | ||||
0.0677765 | + | 0.997701i | \(0.478410\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −71798.3 | −0.442084 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 84655.8i | 0.511055i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 230211. | 1.37620 | 0.688098 | − | 0.725618i | \(-0.258446\pi\) | ||||
0.688098 | + | 0.725618i | \(0.258446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 60290.3i | 0.353465i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 118365.i | − 0.687270i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17360.5 | 0.0988859 | 0.0494430 | − | 0.998777i | \(-0.484255\pi\) | ||||
0.0494430 | + | 0.998777i | \(0.484255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 186829.i | − 1.05410i | −0.849836 | − | 0.527048i | \(-0.823299\pi\) | ||||
0.849836 | − | 0.527048i | \(-0.176701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 408726. | 2.26284 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36922.6 | 0.202505 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 153753.i | 0.827693i | 0.910347 | + | 0.413846i | \(0.135815\pi\) | ||||
−0.910347 | + | 0.413846i | \(0.864185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9168.87 | 0.0489035 | 0.0244517 | − | 0.999701i | \(-0.492216\pi\) | ||||
0.0244517 | + | 0.999701i | \(0.492216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 589978.i | 3.08939i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 178760.i | 0.927561i | 0.885950 | + | 0.463780i | \(0.153507\pi\) | ||||
−0.885950 | + | 0.463780i | \(0.846493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17798.2 | −0.0906920 | −0.0453460 | − | 0.998971i | \(-0.514439\pi\) | ||||
−0.0453460 | + | 0.998971i | \(0.514439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 258127.i | 1.30351i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −242915. | −1.20493 | −0.602464 | − | 0.798146i | \(-0.705814\pi\) | ||||
−0.602464 | + | 0.798146i | \(0.705814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 391559. | 1.92506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 335832.i | 1.62218i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −190762. | −0.913396 | −0.456698 | − | 0.889622i | \(-0.650968\pi\) | ||||
−0.456698 | + | 0.889622i | \(0.650968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 155121.i | 0.729909i | 0.931025 | + | 0.364955i | \(0.118916\pi\) | ||||
−0.931025 | + | 0.364955i | \(0.881084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 230925.i | − 1.07723i | −0.842551 | − | 0.538616i | \(-0.818947\pi\) | ||||
0.842551 | − | 0.538616i | \(-0.181053\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −154112. | −0.706647 | −0.353323 | − | 0.935501i | \(-0.614948\pi\) | ||||
−0.353323 | + | 0.935501i | \(0.614948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23289.2i | 0.105879i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 92306.3 | 0.412581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −638462. | −2.82975 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 405668.i | 1.76807i | 0.467420 | + | 0.884035i | \(0.345184\pi\) | ||||
−0.467420 | + | 0.884035i | \(0.654816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 85690.0 | 0.370373 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 325541.i | − 1.38396i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 426114.i | 1.79667i | 0.439314 | + | 0.898334i | \(0.355222\pi\) | ||||
−0.439314 | + | 0.898334i | \(0.644778\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −273125. | −1.13292 | −0.566459 | − | 0.824090i | \(-0.691687\pi\) | ||||
−0.566459 | + | 0.824090i | \(0.691687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 345495.i | 1.42151i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −99957.1 | −0.404670 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 103548. | 0.415855 | 0.207928 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207928 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 217063.i | − 0.857925i | −0.903322 | − | 0.428963i | \(-0.858879\pi\) | ||||
0.903322 | − | 0.428963i | \(-0.141121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 619151. | 2.42780 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 115098.i | − 0.444256i | −0.975018 | − | 0.222128i | \(-0.928700\pi\) | ||||
0.975018 | − | 0.222128i | \(-0.0713003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 105806.i | 0.405198i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −263479. | −0.993418 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 372870.i | − 1.39501i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −288543. | −1.06300 | −0.531502 | − | 0.847057i | \(-0.678372\pi\) | ||||
−0.531502 | + | 0.847057i | \(0.678372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 176826. | 0.646461 | 0.323231 | − | 0.946320i | \(-0.395231\pi\) | ||||
0.323231 | + | 0.946320i | \(0.395231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 167463.i | − 0.602973i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −498900. | −1.78280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 396343.i | − 1.39514i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 468896.i | − 1.63821i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −50946.4 | −0.175362 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 425220.i | 1.45284i | 0.687249 | + | 0.726422i | \(0.258818\pi\) | ||||
−0.687249 | + | 0.726422i | \(0.741182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −528108. | −1.77799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 495505. | 1.65605 | 0.828024 | − | 0.560692i | \(-0.189465\pi\) | ||||
0.828024 | + | 0.560692i | \(0.189465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 539691.i | − 1.77763i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −492905. | −1.61181 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 257895.i | 0.831251i | 0.909536 | + | 0.415626i | \(0.136437\pi\) | ||||
−0.909536 | + | 0.415626i | \(0.863563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 93433.9i | − 0.299007i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 417799. | 1.31811 | 0.659054 | − | 0.752096i | \(-0.270957\pi\) | ||||
0.659054 | + | 0.752096i | \(0.270957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 465606.i | 1.45855i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 100935. | 0.311756 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −453320. | −1.39038 | −0.695188 | − | 0.718828i | \(-0.744679\pi\) | ||||
−0.695188 | + | 0.718828i | \(0.744679\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 842738.i | − 2.54892i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12119.6 | 0.0364031 | 0.0182015 | − | 0.999834i | \(-0.494206\pi\) | ||||
0.0182015 | + | 0.999834i | \(0.494206\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 137108.i | 0.406172i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 136638.i | 0.402008i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 327468. | 0.950370 | 0.475185 | − | 0.879886i | \(-0.342381\pi\) | ||||
0.475185 | + | 0.879886i | \(0.342381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 261591.i | 0.754035i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −610182. | −1.73520 | −0.867601 | − | 0.497260i | \(-0.834339\pi\) | ||||
−0.867601 | + | 0.497260i | \(0.834339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −783298. | −2.21255 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 499941.i | 1.39337i | 0.717379 | + | 0.696683i | \(0.245342\pi\) | ||||
−0.717379 | + | 0.696683i | \(0.754658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −486965. | −1.34818 | −0.674091 | − | 0.738649i | \(-0.735464\pi\) | ||||
−0.674091 | + | 0.738649i | \(0.735464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 724334.i | 1.97892i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 41693.4i | − 0.113159i | −0.998398 | − | 0.0565796i | \(-0.981981\pi\) | ||||
0.998398 | − | 0.0565796i | \(-0.0180195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −377425. | −1.01099 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 542042.i | 1.44249i | 0.692681 | + | 0.721244i | \(0.256429\pi\) | ||||
−0.692681 | + | 0.721244i | \(0.743571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 146814. | 0.385653 | 0.192827 | − | 0.981233i | \(-0.438235\pi\) | ||||
0.192827 | + | 0.981233i | \(0.438235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −72720.6 | −0.189791 | −0.0948956 | − | 0.995487i | \(-0.530252\pi\) | ||||
−0.0948956 | + | 0.995487i | \(0.530252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 299000.i | − 0.770363i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −75495.2 | −0.193268 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 199864.i | 0.505165i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 568570.i | 1.42799i | 0.700151 | + | 0.713995i | \(0.253116\pi\) | ||||
−0.700151 | + | 0.713995i | \(0.746884\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 224206. | 0.556033 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51568.7i | 0.127089i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −292494. | −0.711870 | −0.355935 | − | 0.934511i | \(-0.615838\pi\) | ||||
−0.355935 | + | 0.934511i | \(0.615838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −103161. | −0.249514 | −0.124757 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124757 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 372569.i | − 0.890017i | −0.895526 | − | 0.445009i | \(-0.853201\pi\) | ||||
0.895526 | − | 0.445009i | \(-0.146799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 237378. | 0.563574 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 85619.0i | − 0.200791i | −0.994948 | − | 0.100395i | \(-0.967989\pi\) | ||||
0.994948 | − | 0.100395i | \(-0.0320108\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.26889e6i | 2.95761i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 258812. | 0.595954 | 0.297977 | − | 0.954573i | \(-0.403688\pi\) | ||||
0.297977 | + | 0.954573i | \(0.403688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 327660.i | 0.749928i | 0.927039 | + | 0.374964i | \(0.122345\pi\) | ||||
−0.927039 | + | 0.374964i | \(0.877655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.22357e6 | 2.76686 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 712366. | 1.60122 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 145374.i | − 0.322880i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 137121. | 0.302742 | 0.151371 | − | 0.988477i | \(-0.451631\pi\) | ||||
0.151371 | + | 0.988477i | \(0.451631\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 573451.i | 1.25118i | 0.780153 | + | 0.625589i | \(0.215141\pi\) | ||||
−0.780153 | + | 0.625589i | \(0.784859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 377089.i | 0.817909i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −175872. | −0.377012 | −0.188506 | − | 0.982072i | \(-0.560364\pi\) | ||||
−0.188506 | + | 0.982072i | \(0.560364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 417984.i | 0.890797i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 138307. | 0.291344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7216.66 | 0.0151140 | 0.00755702 | − | 0.999971i | \(-0.497595\pi\) | ||||
0.00755702 | + | 0.999971i | \(0.497595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 595673.i | 1.23321i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 924433. | 1.90287 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 502543.i | − 1.02267i | −0.859380 | − | 0.511337i | \(-0.829150\pi\) | ||||
0.859380 | − | 0.511337i | \(-0.170850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 312203.i | − 0.631723i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −717191. | −1.43481 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 95591.1i | 0.190163i | 0.995470 | + | 0.0950813i | \(0.0303111\pi\) | ||||
−0.995470 | + | 0.0950813i | \(0.969689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −345286. | −0.679204 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.32226e6 | 2.58645 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 475789.i | 0.920357i | 0.887826 | + | 0.460178i | \(0.152215\pi\) | ||||
−0.887826 | + | 0.460178i | \(0.847785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 305200. | 0.587103 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 770908.i | 1.46665i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 193262.i | − 0.365661i | −0.983144 | − | 0.182830i | \(-0.941474\pi\) | ||||
0.983144 | − | 0.182830i | \(-0.0585259\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 217926. | 0.407825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 650799.i | − 1.21126i | −0.795745 | − | 0.605632i | \(-0.792920\pi\) | ||||
0.795745 | − | 0.605632i | \(-0.207080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 91695.6 | 0.168816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −99472.6 | −0.182144 | −0.0910719 | − | 0.995844i | \(-0.529029\pi\) | ||||
−0.0910719 | + | 0.995844i | \(0.529029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 715681.i | − 1.29641i | −0.761466 | − | 0.648205i | \(-0.775520\pi\) | ||||
0.761466 | − | 0.648205i | \(-0.224480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 468854. | 0.844744 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 543144.i | 0.968170i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 603532.i | 1.07009i | 0.844824 | + | 0.535045i | \(0.179705\pi\) | ||||
−0.844824 | + | 0.535045i | \(0.820295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.34324e6 | 2.35645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 784192.i | 1.36846i | 0.729268 | + | 0.684228i | \(0.239861\pi\) | ||||
−0.729268 | + | 0.684228i | \(0.760139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 568076. | 0.980927 | 0.490464 | − | 0.871462i | \(-0.336827\pi\) | ||||
0.490464 | + | 0.871462i | \(0.336827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 611731. | 1.05078 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 240278.i | − 0.408435i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −531757. | −0.899209 | −0.449605 | − | 0.893228i | \(-0.648435\pi\) | ||||
−0.449605 | + | 0.893228i | \(0.648435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 260161.i | 0.435394i | 0.976016 | + | 0.217697i | \(0.0698545\pi\) | ||||
−0.976016 | + | 0.217697i | \(0.930145\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 373662.i | − 0.622122i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.44404e6 | −2.37960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 393556.i | 0.645216i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.14433e6 | 1.85700 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −724342. | −1.16948 | −0.584742 | − | 0.811219i | \(-0.698804\pi\) | ||||
−0.584742 | + | 0.811219i | \(0.698804\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 539332.i | − 0.861993i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −147150. | −0.233998 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.04249e6i | − 1.64117i | −0.571524 | − | 0.820586i | \(-0.693647\pi\) | ||||
0.571524 | − | 0.820586i | \(-0.306353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 880309.i | − 1.37893i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 416584. | 0.646057 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.61506e6i | 2.49227i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 647222. | 0.988909 | 0.494455 | − | 0.869204i | \(-0.335368\pi\) | ||||
0.494455 | + | 0.869204i | \(0.335368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.24087e6 | −1.88662 | −0.943309 | − | 0.331916i | \(-0.892305\pi\) | ||||
−0.943309 | + | 0.331916i | \(0.892305\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 532993.i | 0.802428i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −340418. | −0.509997 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 819276.i | − 1.21547i | −0.794141 | − | 0.607734i | \(-0.792079\pi\) | ||||
0.794141 | − | 0.607734i | \(-0.207921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 515929.i | − 0.761710i | −0.924635 | − | 0.380855i | \(-0.875630\pi\) | ||||
0.924635 | − | 0.380855i | \(-0.124370\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −140674. | −0.205685 | −0.102842 | − | 0.994698i | \(-0.532794\pi\) | ||||
−0.102842 | + | 0.994698i | \(0.532794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 137443.i | 0.199993i | 0.994988 | + | 0.0999964i | \(0.0318831\pi\) | ||||
−0.994988 | + | 0.0999964i | \(0.968117\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −120279. | −0.173341 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 524955. | 0.752920 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 591422.i | − 0.840182i | −0.907482 | − | 0.420091i | \(-0.861998\pi\) | ||||
0.907482 | − | 0.420091i | \(-0.138002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55633.2 | 0.0786579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 203138.i | − 0.284498i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 839029.i | − 1.16953i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 412093. | 0.569031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 169773.i | − 0.233331i | −0.993171 | − | 0.116665i | \(-0.962780\pi\) | ||||
0.993171 | − | 0.116665i | \(-0.0372205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.05083e6 | −1.43077 | −0.715384 | − | 0.698732i | \(-0.753748\pi\) | ||||
−0.715384 | + | 0.698732i | \(0.753748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.05896e6 | −1.43514 | −0.717569 | − | 0.696487i | \(-0.754745\pi\) | ||||
−0.717569 | + | 0.696487i | \(0.754745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.22011e6i | 1.63824i | 0.573621 | + | 0.819121i | \(0.305538\pi\) | ||||
−0.573621 | + | 0.819121i | \(0.694462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14506.6 | −0.0193881 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.94069e6i | 2.56991i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 92815.8i | − 0.122345i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −603927. | −0.788802 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 707060.i | − 0.919299i | −0.888100 | − | 0.459650i | \(-0.847975\pi\) | ||||
0.888100 | − | 0.459650i | \(-0.152025\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −430965. | −0.555252 | −0.277626 | − | 0.960689i | \(-0.589548\pi\) | ||||
−0.277626 | + | 0.960689i | \(0.589548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.08382e6 | −1.39007 | −0.695037 | − | 0.718974i | \(-0.744612\pi\) | ||||
−0.695037 | + | 0.718974i | \(0.744612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 620229.i | − 0.788324i | −0.919041 | − | 0.394162i | \(-0.871035\pi\) | ||||
0.919041 | − | 0.394162i | \(-0.128965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −259709. | −0.328612 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.37511e6i | 1.72439i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 571272.i | 0.713176i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 315856. | 0.390814 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 322589.i | 0.397374i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −161005. | −0.196581 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 155091. | 0.188526 | 0.0942629 | − | 0.995547i | \(-0.469951\pi\) | ||||
0.0942629 | + | 0.995547i | \(0.469951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 670134.i | 0.807467i | 0.914877 | + | 0.403734i | \(0.132288\pi\) | ||||
−0.914877 | + | 0.403734i | \(0.867712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 539828. | 0.647611 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.46981e6i | − 1.74793i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 631844.i | 0.748134i | 0.927402 | + | 0.374067i | \(0.122037\pi\) | ||||
−0.927402 | + | 0.374067i | \(0.877963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 398364. | 0.467602 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 445959.i | 0.521208i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.16204e6 | −1.34645 | −0.673225 | − | 0.739437i | \(-0.735092\pi\) | ||||
−0.673225 | + | 0.739437i | \(0.735092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 187886. | 0.216768 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.08404e6i | 3.52774i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.18305e6 | −1.34748 | −0.673741 | − | 0.738967i | \(-0.735314\pi\) | ||||
−0.673741 | + | 0.738967i | \(0.735314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 159241.i | 0.179836i | 0.995949 | + | 0.0899179i | \(0.0286605\pi\) | ||||
−0.995949 | + | 0.0899179i | \(0.971340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.90606e6i | − 2.14345i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 940316. | 1.04851 | 0.524257 | − | 0.851560i | \(-0.324343\pi\) | ||||
0.524257 | + | 0.851560i | \(0.324343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 421673.i | − 0.468213i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −577950. | −0.636362 | −0.318181 | − | 0.948030i | \(-0.603072\pi\) | ||||
−0.318181 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.98272e6 | 2.17397 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 484170.i | − 0.526454i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 770424. | 0.834225 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.92487e6i | − 2.06703i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 785047.i | − 0.839542i | −0.907630 | − | 0.419771i | \(-0.862110\pi\) | ||||
0.907630 | − | 0.419771i | \(-0.137890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.05236e6 | −1.11616 | −0.558082 | − | 0.829786i | \(-0.688462\pi\) | ||||
−0.558082 | + | 0.829786i | \(0.688462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 689996.i | − 0.728821i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20197.7 | −0.0211598 | −0.0105799 | − | 0.999944i | \(-0.503368\pi\) | ||||
−0.0105799 | + | 0.999944i | \(0.503368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.17724e6 | −1.22829 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.43076e6i | 1.48068i | 0.672234 | + | 0.740338i | \(0.265335\pi\) | ||||
−0.672234 | + | 0.740338i | \(0.734665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 220875. | 0.227653 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 449334.i | − 0.459385i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 787866.i | 0.802241i | 0.916025 | + | 0.401120i | \(0.131379\pi\) | ||||
−0.916025 | + | 0.401120i | \(0.868621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.40858e6 | −2.43285 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 453709.i | − 0.456444i | −0.973609 | − | 0.228222i | \(-0.926709\pi\) | ||||
0.973609 | − | 0.228222i | \(-0.0732912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.5.b.k.703.7 | 8 | ||
3.2 | odd | 2 | 384.5.b.c.319.1 | ✓ | 8 | ||
4.3 | odd | 2 | inner | 1152.5.b.k.703.8 | 8 | ||
8.3 | odd | 2 | inner | 1152.5.b.k.703.2 | 8 | ||
8.5 | even | 2 | inner | 1152.5.b.k.703.1 | 8 | ||
12.11 | even | 2 | 384.5.b.c.319.5 | yes | 8 | ||
24.5 | odd | 2 | 384.5.b.c.319.8 | yes | 8 | ||
24.11 | even | 2 | 384.5.b.c.319.4 | yes | 8 | ||
48.5 | odd | 4 | 768.5.g.g.511.4 | 4 | |||
48.11 | even | 4 | 768.5.g.g.511.2 | 4 | |||
48.29 | odd | 4 | 768.5.g.c.511.1 | 4 | |||
48.35 | even | 4 | 768.5.g.c.511.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.c.319.1 | ✓ | 8 | 3.2 | odd | 2 | ||
384.5.b.c.319.4 | yes | 8 | 24.11 | even | 2 | ||
384.5.b.c.319.5 | yes | 8 | 12.11 | even | 2 | ||
384.5.b.c.319.8 | yes | 8 | 24.5 | odd | 2 | ||
768.5.g.c.511.1 | 4 | 48.29 | odd | 4 | |||
768.5.g.c.511.3 | 4 | 48.35 | even | 4 | |||
768.5.g.g.511.2 | 4 | 48.11 | even | 4 | |||
768.5.g.g.511.4 | 4 | 48.5 | odd | 4 | |||
1152.5.b.k.703.1 | 8 | 8.5 | even | 2 | inner | ||
1152.5.b.k.703.2 | 8 | 8.3 | odd | 2 | inner | ||
1152.5.b.k.703.7 | 8 | 1.1 | even | 1 | trivial | ||
1152.5.b.k.703.8 | 8 | 4.3 | odd | 2 | inner |