Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{241})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 121x^{2} + 3600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(-8.26209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.6.c.o.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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 11.5242i | 0.739276i | 0.929176 | + | 0.369638i | \(0.120518\pi\) | ||||
−0.929176 | + | 0.369638i | \(0.879482\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.0483i | 0.208639i | 0.994544 | + | 0.104320i | \(0.0332665\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966734\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 110.193 | 0.453471 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −226.008 | −0.563173 | −0.281586 | − | 0.959536i | \(-0.590861\pi\) | ||||
−0.281586 | + | 0.959536i | \(0.590861\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 511.257i | 0.839037i | 0.907747 | + | 0.419518i | \(0.137801\pi\) | ||||
−0.907747 | + | 0.419518i | \(0.862199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 387.387i | − 0.325104i | −0.986700 | − | 0.162552i | \(-0.948027\pi\) | ||||
0.986700 | − | 0.162552i | \(-0.0519725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1335.93 | −0.848982 | −0.424491 | − | 0.905432i | \(-0.639547\pi\) | ||||
−0.424491 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −311.710 | −0.154242 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 545.369i | − 0.214967i | −0.994207 | − | 0.107483i | \(-0.965721\pi\) | ||||
0.994207 | − | 0.107483i | \(-0.0342792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4070.26i | 1.07452i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4637.58 | 1.02399 | 0.511996 | − | 0.858988i | \(-0.328906\pi\) | ||||
0.511996 | + | 0.858988i | \(0.328906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2991.56 | −0.559105 | −0.279552 | − | 0.960130i | \(-0.590186\pi\) | ||||
−0.279552 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2604.55i | − 0.416340i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1263.70i | 0.151754i | 0.997117 | + | 0.0758770i | \(0.0241756\pi\) | ||||
−0.997117 | + | 0.0758770i | \(0.975824\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5891.82 | −0.620280 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17197.6 | −1.59775 | −0.798875 | − | 0.601497i | \(-0.794571\pi\) | ||||
−0.798875 | + | 0.601497i | \(0.794571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16592.0i | 1.36845i | 0.729272 | + | 0.684223i | \(0.239859\pi\) | ||||
−0.729272 | + | 0.684223i | \(0.760141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13036.0i | 0.860795i | 0.902639 | + | 0.430397i | \(0.141627\pi\) | ||||
−0.902639 | + | 0.430397i | \(0.858373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16075.4 | 0.956470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4464.31 | 0.240342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 28994.7i | − 1.41785i | −0.705286 | − | 0.708923i | \(-0.749181\pi\) | ||||
0.705286 | − | 0.708923i | \(-0.250819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 15395.4i | − 0.627632i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34429.9 | −1.28768 | −0.643838 | − | 0.765162i | \(-0.722659\pi\) | ||||
−0.643838 | + | 0.765162i | \(0.722659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24149.1 | −0.830952 | −0.415476 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415476 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2980.55i | 0.0946117i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 29389.7i | 0.799849i | 0.916548 | + | 0.399925i | \(0.130964\pi\) | ||||
−0.916548 | + | 0.399925i | \(0.869036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6284.93 | 0.158920 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9064.32 | −0.213397 | −0.106699 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106699 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 55528.7i | − 1.21958i | −0.792563 | − | 0.609791i | \(-0.791254\pi\) | ||||
0.792563 | − | 0.609791i | \(-0.208746\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6113.13i | − 0.117500i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −101587. | −1.83135 | −0.915673 | − | 0.401924i | \(-0.868342\pi\) | ||||
−0.915673 | + | 0.401924i | \(0.868342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −20129.4 | −0.340893 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 73240.4i | − 1.16696i | −0.812128 | − | 0.583479i | \(-0.801691\pi\) | ||||
0.812128 | − | 0.583479i | \(-0.198309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 53444.3i | 0.757012i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 42498.5 | 0.568719 | 0.284360 | − | 0.958718i | \(-0.408219\pi\) | ||||
0.284360 | + | 0.958718i | \(0.408219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13828.7 | −0.175056 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 34475.2i | − 0.413333i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10565.9i | − 0.114019i | −0.998374 | − | 0.0570093i | \(-0.981844\pi\) | ||||
0.998374 | − | 0.0570093i | \(-0.0181565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −24904.6 | −0.255382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46486.0 | 0.453439 | 0.226719 | − | 0.973960i | \(-0.427200\pi\) | ||||
0.226719 | + | 0.973960i | \(0.427200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 119526.i | − 1.11012i | −0.831811 | − | 0.555059i | \(-0.812696\pi\) | ||||
0.831811 | − | 0.555059i | \(-0.187304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 22922.4i | − 0.193553i | −0.995306 | − | 0.0967765i | \(-0.969147\pi\) | ||||
0.995306 | − | 0.0967765i | \(-0.0308532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −210121. | −1.69396 | −0.846980 | − | 0.531624i | \(-0.821582\pi\) | ||||
−0.846980 | + | 0.531624i | \(0.821582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14563.1 | −0.112188 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 203886.i | − 1.50208i | −0.660258 | − | 0.751039i | \(-0.729553\pi\) | ||||
0.660258 | − | 0.751039i | \(-0.270447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 56337.2i | 0.380479i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10478.2 | 0.0678294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109972. | −0.682837 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 198188.i | − 1.18118i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 175022.i | − 0.962905i | −0.876472 | − | 0.481453i | \(-0.840109\pi\) | ||||
0.876472 | − | 0.481453i | \(-0.159891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −191209. | −1.01166 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149218. | −0.759701 | −0.379850 | − | 0.925048i | \(-0.624025\pi\) | ||||
−0.379850 | + | 0.925048i | \(0.624025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 36134.6i | − 0.177131i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 212180.i | 0.965836i | 0.875666 | + | 0.482918i | \(0.160423\pi\) | ||||
−0.875666 | + | 0.482918i | \(0.839577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 77082.5 | 0.338391 | 0.169195 | − | 0.985583i | \(-0.445883\pi\) | ||||
0.169195 | + | 0.985583i | \(0.445883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −150229. | −0.636365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 115548.i | − 0.472522i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 185256.i | 0.707095i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −470139. | −1.73485 | −0.867423 | − | 0.497571i | \(-0.834225\pi\) | ||||
−0.867423 | + | 0.497571i | \(0.834225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −311118. | −1.11041 | −0.555205 | − | 0.831714i | \(-0.687360\pi\) | ||||
−0.555205 | + | 0.831714i | \(0.687360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 42687.5i | − 0.147425i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 543649.i | 1.76023i | 0.474760 | + | 0.880115i | \(0.342535\pi\) | ||||
−0.474760 | + | 0.880115i | \(0.657465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 334140. | 1.04818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14751.3 | 0.0448504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 298673.i | − 0.880495i | −0.897876 | − | 0.440248i | \(-0.854891\pi\) | ||||
0.897876 | − | 0.440248i | \(-0.145109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 65486.6i | − 0.181703i | −0.995864 | − | 0.0908513i | \(-0.971041\pi\) | ||||
0.995864 | − | 0.0908513i | \(-0.0289588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 109909. | 0.296017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −147210. | −0.384989 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 355092.i | 0.902040i | 0.892514 | + | 0.451020i | \(0.148940\pi\) | ||||
−0.892514 | + | 0.451020i | \(0.851060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 396777.i | − 0.951947i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −39265.7 | −0.0915970 | −0.0457985 | − | 0.998951i | \(-0.514583\pi\) | ||||
−0.0457985 | + | 0.998951i | \(0.514583\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 99638.2 | 0.226063 | 0.113031 | − | 0.993591i | \(-0.463944\pi\) | ||||
0.113031 | + | 0.993591i | \(0.463944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 278298.i | − 0.614303i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 87552.4i | 0.183090i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −110094. | −0.224186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −380336. | −0.754369 | −0.377185 | − | 0.926138i | \(-0.623108\pi\) | ||||
−0.377185 | + | 0.926138i | \(0.623108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 126401.i | 0.244262i | 0.992514 | + | 0.122131i | \(0.0389728\pi\) | ||||
−0.992514 | + | 0.122131i | \(0.961027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 326136.i | 0.598733i | 0.954138 | + | 0.299366i | \(0.0967753\pi\) | ||||
−0.954138 | + | 0.299366i | \(0.903225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −498559. | −0.892451 | −0.446225 | − | 0.894921i | \(-0.647232\pi\) | ||||
−0.446225 | + | 0.894921i | \(0.647232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −338692. | −0.591309 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 125439.i | 0.213645i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 60096.1i | − 0.0974811i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 301930. | 0.478123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 310763. | 0.480532 | 0.240266 | − | 0.970707i | \(-0.422765\pi\) | ||||
0.240266 | + | 0.970707i | \(0.422765\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 104459.i | − 0.157760i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 80916.7i | − 0.116651i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 639923. | 0.901607 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 198054. | 0.272774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 627285.i | 0.844700i | 0.906433 | + | 0.422350i | \(0.138795\pi\) | ||||
−0.906433 | + | 0.422350i | \(0.861205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 450131.i | 0.579794i | 0.957058 | + | 0.289897i | \(0.0936211\pi\) | ||||
−0.957058 | + | 0.289897i | \(0.906379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 461485. | 0.581526 | 0.290763 | − | 0.956795i | \(-0.406091\pi\) | ||||
0.290763 | + | 0.956795i | \(0.406091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 70448.8 | 0.0868648 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 675812.i | − 0.815523i | −0.913089 | − | 0.407761i | \(-0.866310\pi\) | ||||
0.913089 | − | 0.407761i | \(-0.133690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.17071e6i | − 1.35387i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.00730e6 | −1.14068 | −0.570338 | − | 0.821410i | \(-0.693188\pi\) | ||||
−0.570338 | + | 0.821410i | \(0.693188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −232091. | −0.257404 | −0.128702 | − | 0.991683i | \(-0.541081\pi\) | ||||
−0.128702 | + | 0.991683i | \(0.541081\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 757099.i | 0.822502i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 683002.i | − 0.712327i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 844035. | 0.862704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.77096e6 | 1.77429 | 0.887143 | − | 0.461494i | \(-0.152686\pi\) | ||||
0.887143 | + | 0.461494i | \(0.152686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 123258.i | 0.121063i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 528458.i | − 0.499088i | −0.968363 | − | 0.249544i | \(-0.919719\pi\) | ||||
0.968363 | − | 0.249544i | \(-0.0802808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34181.0 | −0.0316618 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 511030. | 0.464350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.69907e6i | 1.51469i | 0.653016 | + | 0.757344i | \(0.273503\pi\) | ||||
−0.653016 | + | 0.757344i | \(0.726497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 489760.i | 0.420441i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 648393. | 0.546333 | 0.273167 | − | 0.961967i | \(-0.411929\pi\) | ||||
0.273167 | + | 0.961967i | \(0.411929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.94947e6 | 1.61248 | 0.806239 | − | 0.591590i | \(-0.201500\pi\) | ||||
0.806239 | + | 0.591590i | \(0.201500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 159364.i | − 0.129415i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 313195.i | − 0.245254i | −0.992453 | − | 0.122627i | \(-0.960868\pi\) | ||||
0.992453 | − | 0.122627i | \(-0.0391319\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −329650. | −0.253538 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.72743e6 | 1.30507 | 0.652537 | − | 0.757757i | \(-0.273705\pi\) | ||||
0.652537 | + | 0.757757i | \(0.273705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 205142.i | 0.152261i | 0.997098 | + | 0.0761306i | \(0.0242566\pi\) | ||||
−0.997098 | + | 0.0761306i | \(0.975743\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 465167.i | − 0.333353i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26979e6 | 0.894307 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 121763. | 0.0842912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 390309.i | 0.265607i | 0.991142 | + | 0.132804i | \(0.0423979\pi\) | ||||
−0.991142 | + | 0.132804i | \(0.957602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 919911.i | − 0.605138i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 278824. | 0.180365 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −448787. | −0.285511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 535713.i | 0.335217i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.10708e6i | 0.670401i | 0.942147 | + | 0.335201i | \(0.108804\pi\) | ||||
−0.942147 | + | 0.335201i | \(0.891196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.37744e6 | 0.820684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.19106e6 | −1.28455 | −0.642277 | − | 0.766472i | \(-0.722010\pi\) | ||||
−0.642277 | + | 0.766472i | \(0.722010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.89050e6i | 1.66768i | 0.552006 | + | 0.833840i | \(0.313862\pi\) | ||||
−0.552006 | + | 0.833840i | \(0.686138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.46652e6i | − 0.819671i | −0.912160 | − | 0.409835i | \(-0.865586\pi\) | ||||
0.912160 | − | 0.409835i | \(-0.134414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.04813e6 | −0.576684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 264161. | 0.143089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 517520.i | 0.276008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.42147e6i | − 1.25230i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −352602. | −0.179595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.23500e6 | 1.12126 | 0.560632 | − | 0.828065i | \(-0.310558\pi\) | ||||
0.560632 | + | 0.828065i | \(0.310558\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 139251.i | 0.0688160i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.48851e6i | 0.713966i | 0.934111 | + | 0.356983i | \(0.116195\pi\) | ||||
−0.934111 | + | 0.356983i | \(0.883805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.34962e6 | 1.11045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 676115. | 0.314872 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 889414.i | 0.408196i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.34245e6i | 1.04435i | 0.852837 | + | 0.522177i | \(0.174880\pi\) | ||||
−0.852837 | + | 0.522177i | \(0.825120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 119901. | 0.0526940 | 0.0263470 | − | 0.999653i | \(-0.491613\pi\) | ||||
0.0263470 | + | 0.999653i | \(0.491613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.08095e6 | −0.901559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.49528e6i | 1.06582i | 0.846173 | + | 0.532909i | \(0.178901\pi\) | ||||
−0.846173 | + | 0.532909i | \(0.821099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 120752.i | 0.0501447i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.43398e6 | 1.40625 | 0.703124 | − | 0.711068i | \(-0.251788\pi\) | ||||
0.703124 | + | 0.711068i | \(0.251788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −691400. | −0.279230 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.26733e6i | − 0.504805i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.67310e6i | − 1.81109i | −0.424249 | − | 0.905545i | \(-0.639462\pi\) | ||||
0.424249 | − | 0.905545i | \(-0.360538\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.89507e6 | −0.724533 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 784259. | 0.295818 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.03766e6i | 0.758333i | 0.925328 | + | 0.379167i | \(0.123789\pi\) | ||||
−0.925328 | + | 0.379167i | \(0.876211\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.37099e6i | 0.859166i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.78978e6 | 0.640032 | 0.320016 | − | 0.947412i | \(-0.396312\pi\) | ||||
0.320016 | + | 0.947412i | \(0.396312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.01698e6 | 0.711853 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.04521e6i | 0.712429i | 0.934404 | + | 0.356214i | \(0.115933\pi\) | ||||
−0.934404 | + | 0.356214i | \(0.884067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.82833e6i | 0.620551i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −234191. | −0.0784687 | −0.0392344 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392344 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −211269. | −0.0698865 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.71961e6i | − 0.561629i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.81706e6i | 0.897058i | 0.893768 | + | 0.448529i | \(0.148052\pi\) | ||||
−0.893768 | + | 0.448529i | \(0.851948\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 416421. | 0.130949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 735044. | 0.228272 | 0.114136 | − | 0.993465i | \(-0.463590\pi\) | ||||
0.114136 | + | 0.993465i | \(0.463590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.52946e6i | − 0.469109i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 285606.i | − 0.0854636i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.08894e6 | −1.79984 | −0.899918 | − | 0.436058i | \(-0.856374\pi\) | ||||
−0.899918 | + | 0.436058i | \(0.856374\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.44520e6 | −0.714020 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 931273.i | − 0.268659i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 888312.i | 0.250164i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.65964e6 | 1.57490 | 0.787452 | − | 0.616376i | \(-0.211400\pi\) | ||||
0.787452 | + | 0.616376i | \(0.211400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.34902e6 | −1.74583 | −0.872914 | − | 0.487873i | \(-0.837773\pi\) | ||||
−0.872914 | + | 0.487873i | \(0.837773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.43648e6i | 0.390345i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 653192.i | − 0.173369i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.33160e6 | 0.349325 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.03516e6 | −0.787024 | −0.393512 | − | 0.919320i | \(-0.628740\pi\) | ||||
−0.393512 | + | 0.919320i | \(0.628740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.50633e6i | 0.898739i | 0.893346 | + | 0.449369i | \(0.148351\pi\) | ||||
−0.893346 | + | 0.449369i | \(0.851649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 728573.i | 0.182503i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.08849e6 | −1.50782 | −0.753908 | − | 0.656980i | \(-0.771834\pi\) | ||||
−0.753908 | + | 0.656980i | \(0.771834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.77140e6 | 0.433731 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.03357e6i | − 1.46071i | −0.683066 | − | 0.730357i | \(-0.739354\pi\) | ||||
0.683066 | − | 0.730357i | \(-0.260646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.41797e6i | − 1.28253i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.97943e6 | −0.931548 | −0.465774 | − | 0.884904i | \(-0.654224\pi\) | ||||
−0.465774 | + | 0.884904i | \(0.654224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.88680e6 | 0.899809 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.58538e6i | − 0.820899i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 430533.i | − 0.0964308i | −0.998837 | − | 0.0482154i | \(-0.984647\pi\) | ||||
0.998837 | − | 0.0482154i | \(-0.0153534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57677e6 | 0.349330 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.80383e6 | 0.833622 | 0.416811 | − | 0.908993i | \(-0.363148\pi\) | ||||
0.416811 | + | 0.908993i | \(0.363148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.62853e6i | − 1.65382i | −0.562333 | − | 0.826911i | \(-0.690096\pi\) | ||||
0.562333 | − | 0.826911i | \(-0.309904\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.05102e6i | 1.92046i | 0.279209 | + | 0.960230i | \(0.409928\pi\) | ||||
−0.279209 | + | 0.960230i | \(0.590072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −794943. | −0.166880 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.26511e6 | −1.30130 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.74992e6i | − 0.770672i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.19502e6i | − 0.642952i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.51621e6 | −1.69593 | −0.847964 | − | 0.530054i | \(-0.822172\pi\) | ||||
−0.847964 | + | 0.530054i | \(0.822172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −646076. | −0.127327 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 169997.i | 0.0331569i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.65770e6i | − 0.507789i | −0.967232 | − | 0.253895i | \(-0.918288\pi\) | ||||
0.967232 | − | 0.253895i | \(-0.0817117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44196e6 | 0.650929 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.05116e6 | 0.945557 | 0.472779 | − | 0.881181i | \(-0.343251\pi\) | ||||
0.472779 | + | 0.881181i | \(0.343251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.79654e6i | − 0.332904i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 245175.i | − 0.0445230i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.15003e6 | −0.386538 | −0.193269 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193269 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 754679. | 0.134328 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.79475e6i | 0.316289i | 0.987416 | + | 0.158144i | \(0.0505511\pi\) | ||||
−0.987416 | + | 0.158144i | \(0.949449\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.26661e6i | 0.218839i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −697940. | −0.119405 | −0.0597027 | − | 0.998216i | \(-0.519015\pi\) | ||||
−0.0597027 | + | 0.998216i | \(0.519015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50196e6 | 0.254452 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 5.43757e6i | − 0.912245i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.94624e6i | − 0.484776i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.09214e6 | −0.666857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.14928e6 | −0.185495 | −0.0927475 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927475 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.22071e6i | − 1.15432i | −0.816632 | − | 0.577159i | \(-0.804161\pi\) | ||||
0.816632 | − | 0.577159i | \(-0.195839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15889e6i | 0.181767i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.13892e6 | 0.953789 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.79395e6 | −0.583923 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.79241e6i | − 1.34057i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 452505.i | − 0.0677155i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.63316e6 | −0.538657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24720e7 | −1.83207 | −0.916035 | − | 0.401099i | \(-0.868628\pi\) | ||||
−0.916035 | + | 0.401099i | \(0.868628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.14825e6i | 0.167123i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.58966e6i | 1.22746i | 0.789516 | + | 0.613730i | \(0.210332\pi\) | ||||
−0.789516 | + | 0.613730i | \(0.789668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.66107e6 | −0.376812 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.19546e6 | −0.869350 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2.74776e6i | − 0.382090i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.38207e6i | 0.461896i | 0.972966 | + | 0.230948i | \(0.0741827\pi\) | ||||
−0.972966 | + | 0.230948i | \(0.925817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.48278e6 | −1.14818 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00897e6 | −0.135354 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.50247e6i | 0.199772i | 0.994999 | + | 0.0998859i | \(0.0318478\pi\) | ||||
−0.994999 | + | 0.0998859i | \(0.968152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 544468.i | − 0.0711237i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.87838e6 | −0.243222 | −0.121611 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121611 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.49628e7 | 1.92053 | 0.960267 | − | 0.279082i | \(-0.0900301\pi\) | ||||
0.960267 | + | 0.279082i | \(0.0900301\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.38306e6i | − 0.557687i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.03660e6i | 0.504750i | 0.967630 | + | 0.252375i | \(0.0812117\pi\) | ||||
−0.967630 | + | 0.252375i | \(0.918788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.45666e6 | −0.180577 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.98103e6 | 0.243473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.55303e6i | 0.798492i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.57983e7i | 1.89241i | 0.323574 | + | 0.946203i | \(0.395115\pi\) | ||||
−0.323574 | + | 0.946203i | \(0.604885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.99650e6 | 0.474670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.75845e6 | −0.442629 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.37947e7i | − 1.61092i | −0.592647 | − | 0.805462i | \(-0.701917\pi\) | ||||
0.592647 | − | 0.805462i | \(-0.298083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.74549e6i | − 0.659768i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −814106. | −0.0927073 | −0.0463537 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463537 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.55613e7 | −1.75736 | −0.878679 | − | 0.477413i | \(-0.841574\pi\) | ||||
−0.878679 | + | 0.477413i | \(0.841574\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.23855e6i | 0.362708i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.63191e7i | − 1.79773i | −0.438226 | − | 0.898865i | \(-0.644393\pi\) | ||||
0.438226 | − | 0.898865i | \(-0.355607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.44558e6 | −0.157942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.66475e6 | −0.722239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.38233e6i | 0.578520i | 0.957250 | + | 0.289260i | \(0.0934093\pi\) | ||||
−0.957250 | + | 0.289260i | \(0.906591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 5.83565e6i | − 0.617130i | −0.951203 | − | 0.308565i | \(-0.900151\pi\) | ||||
0.951203 | − | 0.308565i | \(-0.0998487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36289e6 | −0.352765 | −0.176383 | − | 0.984322i | \(-0.556440\pi\) | ||||
−0.176383 | + | 0.984322i | \(0.556440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.21980e6 | 0.230985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.14951e6i | 0.118657i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.47949e6i | 0.353465i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 489541. | 0.0493358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10425e6 | −0.810288 | −0.405144 | − | 0.914253i | \(-0.632779\pi\) | ||||
−0.405144 | + | 0.914253i | \(0.632779\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.58128e6i | 0.355246i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.21866e6i | 0.802513i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −998828. | −0.0967695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.08523e6 | 0.681097 | 0.340548 | − | 0.940227i | \(-0.389387\pi\) | ||||
0.340548 | + | 0.940227i | \(0.389387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.72946e6i | − 0.546495i | −0.961944 | − | 0.273247i | \(-0.911902\pi\) | ||||
0.961944 | − | 0.273247i | \(-0.0880978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.17751e6i | 0.204503i | 0.994759 | + | 0.102251i | \(0.0326046\pi\) | ||||
−0.994759 | + | 0.102251i | \(0.967395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.78143e6 | 0.725183 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 932498. | 0.0862374 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.42048e7i | 1.30363i | 0.758379 | + | 0.651813i | \(0.225991\pi\) | ||||
−0.758379 | + | 0.651813i | \(0.774009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 6.11890e6i | − 0.553044i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.54033e7 | 1.38166 | 0.690829 | − | 0.723018i | \(-0.257246\pi\) | ||||
0.690829 | + | 0.723018i | \(0.257246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −544048. | −0.0484322 | −0.0242161 | − | 0.999707i | \(-0.507709\pi\) | ||||
−0.0242161 | + | 0.999707i | \(0.507709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.28241e6i | 0.201656i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.52919e6i | − 0.220124i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.22894e6 | −0.624467 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.45787e6 | 0.467969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37093e7i | 1.16675i | 0.812203 | + | 0.583374i | \(0.198268\pi\) | ||||
−0.812203 | + | 0.583374i | \(0.801732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.49910e7i | 1.25707i | 0.777781 | + | 0.628536i | \(0.216345\pi\) | ||||
−0.777781 | + | 0.628536i | \(0.783655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 285789. | 0.0237887 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.18738e6 | −0.428628 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3.47996e6i | − 0.285445i | −0.989763 | − | 0.142723i | \(-0.954414\pi\) | ||||
0.989763 | − | 0.142723i | \(-0.0455857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.31824e6i | 0.429908i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.48237e7 | 1.18962 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.09436e6 | −0.405877 | −0.202939 | − | 0.979191i | \(-0.565049\pi\) | ||||
−0.202939 | + | 0.979191i | \(0.565049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 673627.i | − 0.0532827i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.66213e6i | 0.519435i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.78817e6 | 0.602896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.75839e7 | 1.35151 | 0.675755 | − | 0.737126i | \(-0.263818\pi\) | ||||
0.675755 | + | 0.737126i | \(0.263818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.68821e6i | − 0.128836i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.25737e6i | 0.0946051i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.35383e7 | −1.01146 | −0.505730 | − | 0.862692i | \(-0.668777\pi\) | ||||
−0.505730 | + | 0.862692i | \(0.668777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.11942e7 | −0.830462 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.63150e6i | 0.120189i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.16083e7i | − 0.843275i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.27911e7 | 0.922756 | 0.461378 | − | 0.887204i | \(-0.347355\pi\) | ||||
0.461378 | + | 0.887204i | \(0.347355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.23298e6 | 0.231614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.67466e6i | − 0.190293i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.11509e7i | − 1.48420i | −0.670289 | − | 0.742100i | \(-0.733830\pi\) | ||||
0.670289 | − | 0.742100i | \(-0.266170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.36164e7 | −0.948949 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.42753e6 | 0.444888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.23015e7i | 0.845667i | 0.906207 | + | 0.422833i | \(0.138964\pi\) | ||||
−0.906207 | + | 0.422833i | \(0.861036\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 6.64230e6i | − 0.450453i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.04425e7 | 0.703383 | 0.351691 | − | 0.936116i | \(-0.385607\pi\) | ||||
0.351691 | + | 0.936116i | \(0.385607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.87103e6 | 0.526606 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.63296e6i | 0.241429i | 0.992687 | + | 0.120714i | \(0.0385185\pi\) | ||||
−0.992687 | + | 0.120714i | \(0.961481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.07060e6i | − 0.529181i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 620012. | 0.0403827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.77346e7 | 1.14741 | 0.573707 | − | 0.819060i | \(-0.305505\pi\) | ||||
0.573707 | + | 0.819060i | \(0.305505\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04088e7i | 1.31169i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.89094e6i | 0.500483i | 0.968183 | + | 0.250241i | \(0.0805100\pi\) | ||||
−0.968183 | + | 0.250241i | \(0.919490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.42044e6 | −0.0894992 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.98455e7 | 1.24223 | 0.621114 | − | 0.783721i | \(-0.286681\pi\) | ||||
0.621114 | + | 0.783721i | \(0.286681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.68343e6i | − 0.353426i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.76026e7i | − 1.08041i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.89976e6 | −0.237806 | −0.118903 | − | 0.992906i | \(-0.537938\pi\) | ||||
−0.118903 | + | 0.992906i | \(0.537938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.09004e6 | 0.368964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2.33736e6i | − 0.140695i | −0.997523 | − | 0.0703474i | \(-0.977589\pi\) | ||||
0.997523 | − | 0.0703474i | \(-0.0224108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 393908.i | − 0.0234068i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.29748e7 | 1.35646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04860e6 | 0.120180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.88762e7i | 1.10030i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.52903e7i | − 0.879993i | −0.897999 | − | 0.439997i | \(-0.854980\pi\) | ||||
0.897999 | − | 0.439997i | \(-0.145020\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.95804e7 | −1.11977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.51479e6 | 0.313392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.23464e7i | − 0.697199i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.25972e7i | 0.702468i | 0.936288 | + | 0.351234i | \(0.114238\pi\) | ||||
−0.936288 | + | 0.351234i | \(0.885762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.04997e6 | 0.279848 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.68305e6 | 0.257898 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.25499e7i | 0.686835i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.47219e6i | 0.403891i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.13476e7 | 0.609584 | 0.304792 | − | 0.952419i | \(-0.401413\pi\) | ||||
0.304792 | + | 0.952419i | \(0.401413\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.91000e7 | 1.01972 | 0.509860 | − | 0.860257i | \(-0.329697\pi\) | ||||
0.509860 | + | 0.860257i | \(0.329697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.24661e7i | 1.19207i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 2.21657e7i | − 1.16179i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52383e6 | −0.0793827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.25668e6 | 0.0650678 | 0.0325339 | − | 0.999471i | \(-0.489642\pi\) | ||||
0.0325339 | + | 0.999471i | \(0.489642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.95590e6i | 0.357976i | 0.983851 | + | 0.178988i | \(0.0572823\pi\) | ||||
−0.983851 | + | 0.178988i | \(0.942718\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.04638e6i | − 0.459950i | −0.973197 | − | 0.229975i | \(-0.926136\pi\) | ||||
0.973197 | − | 0.229975i | \(-0.0738645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.54026e7 | 0.778407 | 0.389203 | − | 0.921152i | \(-0.372750\pi\) | ||||
0.389203 | + | 0.921152i | \(0.372750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.60932e6 | 0.181310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.22739e6i | − 0.310952i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.21764e7i | − 0.600767i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.75941e7 | 0.862903 | 0.431451 | − | 0.902136i | \(-0.358002\pi\) | ||||
0.431451 | + | 0.902136i | \(0.358002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 995979. | 0.0485580 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.99072e7i | 0.964809i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.97455e6i | − 0.142466i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.36410e6 | −0.112563 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 689183. | 0.0326220 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.06755e7i | 0.972934i | 0.873699 | + | 0.486467i | \(0.161715\pi\) | ||||
−0.873699 | + | 0.486467i | \(0.838285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.16205e7i | 1.00557i | 0.864411 | + | 0.502786i | \(0.167692\pi\) | ||||
−0.864411 | + | 0.502786i | \(0.832308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.70061e7 | −0.786362 | −0.393181 | − | 0.919461i | \(-0.628625\pi\) | ||||
−0.393181 | + | 0.919461i | \(0.628625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.36067e6 | 0.246440 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2.96043e7i | − 1.35309i | −0.736399 | − | 0.676547i | \(-0.763475\pi\) | ||||
0.736399 | − | 0.676547i | \(-0.236525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.46333e7i | 0.661140i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.29594e7 | 1.03136 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50257e7 | −0.671103 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.16429e6i | − 0.0517041i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.77691e7i | − 1.21917i | −0.792722 | − | 0.609583i | \(-0.791337\pi\) | ||||
0.792722 | − | 0.609583i | \(-0.208663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.49799e6 | −0.196357 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16824e7 | 0.507099 | 0.253550 | − | 0.967322i | \(-0.418402\pi\) | ||||
0.253550 | + | 0.967322i | \(0.418402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.66919e7i | 1.15207i | 0.817426 | + | 0.576034i | \(0.195400\pi\) | ||||
−0.817426 | + | 0.576034i | \(0.804600\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.95714e7i | 1.68878i | 0.535733 | + | 0.844388i | \(0.320036\pi\) | ||||
−0.535733 | + | 0.844388i | \(0.679964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.73406e6 | 0.200900 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.54940e6 | 0.191982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.74151e7i | − 0.730799i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.21321e6i | 0.133339i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38736e7 | −0.572518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12322e7 | −0.460948 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.17189e6i | − 0.211072i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.79635e7i | − 1.12869i | −0.825541 | − | 0.564343i | \(-0.809130\pi\) | ||||
0.825541 | − | 0.564343i | \(-0.190870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.12245e6 | 0.205621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.87296e7 | 0.747710 | 0.373855 | − | 0.927487i | \(-0.378036\pi\) | ||||
0.373855 | + | 0.927487i | \(0.378036\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65529e7i | 0.657199i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.03610e6i | − 0.158503i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.77613e6 | −0.303721 | −0.151861 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151861 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.27582e7 | −0.495612 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.63420e6i | − 0.179048i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.31710e7i | − 0.503406i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.88269e7 | 1.47602 | 0.738011 | − | 0.674788i | \(-0.235765\pi\) | ||||
0.738011 | + | 0.674788i | \(0.235765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.14755e7 | −0.812026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.52501e7i | − 0.949640i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.75302e7i | − 0.652288i | −0.945320 | − | 0.326144i | \(-0.894251\pi\) | ||||
0.945320 | − | 0.326144i | \(-0.105749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.33107e7 | −1.23288 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.29638e6 | −0.158172 | −0.0790859 | − | 0.996868i | \(-0.525200\pi\) | ||||
−0.0790859 | + | 0.996868i | \(0.525200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.37905e6i | 0.343463i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.43637e7i | 1.60751i | 0.594962 | + | 0.803754i | \(0.297167\pi\) | ||||
−0.594962 | + | 0.803754i | \(0.702833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.83895e7 | 1.02327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.69004e7 | 0.605963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5.71990e6i | − 0.204012i | −0.994784 | − | 0.102006i | \(-0.967474\pi\) | ||||
0.994784 | − | 0.102006i | \(-0.0325261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.20788e7i | − 0.426329i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.73912e6 | −0.201511 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96797e7 | −0.687402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2.52589e6i | − 0.0877706i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.00548e7i | 1.03359i | 0.856110 | + | 0.516794i | \(0.172875\pi\) | ||||
−0.856110 | + | 0.516794i | \(0.827125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.96399e6 | −0.204046 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.89662e7 | −0.645552 | −0.322776 | − | 0.946475i | \(-0.604616\pi\) | ||||
−0.322776 | + | 0.946475i | \(0.604616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.08495e6i | 0.0706015i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.45541e7i | 0.822975i | 0.911415 | + | 0.411488i | \(0.134991\pi\) | ||||
−0.911415 | + | 0.411488i | \(0.865009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.60498e6 | −0.320287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.31540e7 | −0.768162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.35539e7i | 1.10754i | 0.832670 | + | 0.553769i | \(0.186811\pi\) | ||||
−0.832670 | + | 0.553769i | \(0.813189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.06345e6i | − 0.132771i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.04877e6 | 0.294170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.05230e7 | −0.663830 | −0.331915 | − | 0.943309i | \(-0.607695\pi\) | ||||
−0.331915 | + | 0.943309i | \(0.607695\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.57565e7i | 0.828924i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.25729e7i | 0.400589i | 0.979736 | + | 0.200294i | \(0.0641898\pi\) | ||||
−0.979736 | + | 0.200294i | \(0.935810\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.14359e6 | −0.163062 |
(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 | 400.6.c.o.49.3 | 4 | ||
4.3 | odd | 2 | 200.6.c.f.49.2 | 4 | |||
5.2 | odd | 4 | 400.6.a.r.1.2 | 2 | |||
5.3 | odd | 4 | 400.6.a.u.1.1 | 2 | |||
5.4 | even | 2 | inner | 400.6.c.o.49.2 | 4 | ||
20.3 | even | 4 | 200.6.a.e.1.2 | ✓ | 2 | ||
20.7 | even | 4 | 200.6.a.f.1.1 | yes | 2 | ||
20.19 | odd | 2 | 200.6.c.f.49.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.e.1.2 | ✓ | 2 | 20.3 | even | 4 | ||
200.6.a.f.1.1 | yes | 2 | 20.7 | even | 4 | ||
200.6.c.f.49.2 | 4 | 4.3 | odd | 2 | |||
200.6.c.f.49.3 | 4 | 20.19 | odd | 2 | |||
400.6.a.r.1.2 | 2 | 5.2 | odd | 4 | |||
400.6.a.u.1.1 | 2 | 5.3 | odd | 4 | |||
400.6.c.o.49.2 | 4 | 5.4 | even | 2 | inner | ||
400.6.c.o.49.3 | 4 | 1.1 | even | 1 | trivial |