Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,7,Mod(449,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.449");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.b (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: | \(103.524337629\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.449 |
Dual form | 450.7.b.a.449.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 32.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 484.000i | − 1.41108i | −0.708671 | − | 0.705539i | \(-0.750705\pi\) | ||||
0.708671 | − | 0.705539i | \(-0.249295\pi\) | |||||||
\(8\) | −181.019 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1340.67i | 1.00727i | 0.863917 | + | 0.503634i | \(0.168004\pi\) | ||||
−0.863917 | + | 0.503634i | \(0.831996\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3368.00i | − 1.53300i | −0.642245 | − | 0.766500i | \(-0.721997\pi\) | ||||
0.642245 | − | 0.766500i | \(-0.278003\pi\) | |||||||
\(14\) | 2737.92i | 0.997783i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | −12.7279 | −0.00259066 | −0.00129533 | − | 0.999999i | \(-0.500412\pi\) | ||||
−0.00129533 | + | 0.999999i | \(0.500412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5744.00 | −0.837440 | −0.418720 | − | 0.908115i | \(-0.637521\pi\) | ||||
−0.418720 | + | 0.908115i | \(0.637521\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 7584.00i | − 0.712246i | ||||||||
\(23\) | −3377.14 | −0.277566 | −0.138783 | − | 0.990323i | \(-0.544319\pi\) | ||||
−0.138783 | + | 0.990323i | \(0.544319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 19052.3i | 1.08399i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 15488.0i | − 0.705539i | ||||||||
\(29\) | − 29354.8i | − 1.20361i | −0.798643 | − | 0.601805i | \(-0.794449\pi\) | ||||
0.798643 | − | 0.601805i | \(-0.205551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39796.0 | −1.33584 | −0.667920 | − | 0.744233i | \(-0.732815\pi\) | ||||
−0.667920 | + | 0.744233i | \(0.732815\pi\) | |||||||
\(32\) | −5792.62 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 72.0000 | 0.00183187 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52526.0i | 1.03698i | 0.855085 | + | 0.518489i | \(0.173505\pi\) | ||||
−0.855085 | + | 0.518489i | \(0.826495\pi\) | |||||||
\(38\) | 32493.0 | 0.592159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 37042.5i | − 0.537463i | −0.963215 | − | 0.268732i | \(-0.913396\pi\) | ||||
0.963215 | − | 0.268732i | \(-0.0866045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3800.00i | − 0.0477945i | −0.999714 | − | 0.0238973i | \(-0.992393\pi\) | ||||
0.999714 | − | 0.0238973i | \(-0.00760746\pi\) | |||||||
\(44\) | 42901.6i | 0.503634i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19104.0 | 0.196269 | ||||||||
\(47\) | −76791.8 | −0.739641 | −0.369821 | − | 0.929103i | \(-0.620581\pi\) | ||||
−0.369821 | + | 0.929103i | \(0.620581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −116607. | −0.991143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 107776.i | − 0.766500i | ||||||||
\(53\) | 238738. | 1.60359 | 0.801795 | − | 0.597599i | \(-0.203879\pi\) | ||||
0.801795 | + | 0.597599i | \(0.203879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 87613.4i | 0.498892i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 166056.i | 0.851080i | ||||||||
\(59\) | 249841.i | 1.21649i | 0.793751 | + | 0.608243i | \(0.208125\pi\) | ||||
−0.793751 | + | 0.608243i | \(0.791875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13250.0 | 0.0583749 | 0.0291875 | − | 0.999574i | \(-0.490708\pi\) | ||||
0.0291875 | + | 0.999574i | \(0.490708\pi\) | |||||||
\(62\) | 225120. | 0.944581 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32768.0 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 168968.i | 0.561798i | 0.959737 | + | 0.280899i | \(0.0906326\pi\) | ||||
−0.959737 | + | 0.280899i | \(0.909367\pi\) | |||||||
\(68\) | −407.294 | −0.00129533 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 531467.i | − 1.48491i | −0.669894 | − | 0.742457i | \(-0.733660\pi\) | ||||
0.669894 | − | 0.742457i | \(-0.266340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 236144.i | − 0.607027i | −0.952827 | − | 0.303514i | \(-0.901840\pi\) | ||||
0.952827 | − | 0.303514i | \(-0.0981598\pi\) | |||||||
\(74\) | − 297132.i | − 0.733254i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −183808. | −0.418720 | ||||||||
\(77\) | 648886. | 1.42134 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35116.0 | 0.0712236 | 0.0356118 | − | 0.999366i | \(-0.488662\pi\) | ||||
0.0356118 | + | 0.999366i | \(0.488662\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 209544.i | 0.380044i | ||||||||
\(83\) | −10980.0 | −0.0192029 | −0.00960144 | − | 0.999954i | \(-0.503056\pi\) | ||||
−0.00960144 | + | 0.999954i | \(0.503056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21496.0i | 0.0337958i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 242688.i | − 0.356123i | ||||||||
\(89\) | 129328.i | 0.183453i | 0.995784 | + | 0.0917263i | \(0.0292385\pi\) | ||||
−0.995784 | + | 0.0917263i | \(0.970762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.63011e6 | −2.16318 | ||||||||
\(92\) | −108069. | −0.138783 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 434400. | 0.523005 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 321424.i | − 0.352179i | −0.984374 | − | 0.176089i | \(-0.943655\pi\) | ||||
0.984374 | − | 0.176089i | \(-0.0563448\pi\) | |||||||
\(98\) | 659629. | 0.700844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 668780.i | 0.649111i | 0.945867 | + | 0.324556i | \(0.105215\pi\) | ||||
−0.945867 | + | 0.324556i | \(0.894785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.99341e6i | − 1.82425i | −0.409907 | − | 0.912127i | \(-0.634439\pi\) | ||||
0.409907 | − | 0.912127i | \(-0.365561\pi\) | |||||||
\(104\) | 609673.i | 0.541997i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.35050e6 | −1.13391 | ||||||||
\(107\) | 260668. | 0.212783 | 0.106391 | − | 0.994324i | \(-0.466070\pi\) | ||||
0.106391 | + | 0.994324i | \(0.466070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −194456. | −0.150156 | −0.0750779 | − | 0.997178i | \(-0.523921\pi\) | ||||
−0.0750779 | + | 0.997178i | \(0.523921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 495616.i | − 0.352770i | ||||||||
\(113\) | −821897. | −0.569616 | −0.284808 | − | 0.958585i | \(-0.591930\pi\) | ||||
−0.284808 | + | 0.958585i | \(0.591930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 939355.i | − 0.601805i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1.41331e6i | − 0.860185i | ||||||||
\(119\) | 6160.31i | 0.00365563i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25847.0 | −0.0145900 | ||||||||
\(122\) | −74953.3 | −0.0412773 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.27347e6 | −0.667920 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05721e6i | 1.49250i | 0.665666 | + | 0.746250i | \(0.268148\pi\) | ||||
−0.665666 | + | 0.746250i | \(0.731852\pi\) | |||||||
\(128\) | −185364. | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.07388e6i | 1.36733i | 0.729797 | + | 0.683664i | \(0.239615\pi\) | ||||
−0.729797 | + | 0.683664i | \(0.760385\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.78010e6i | 1.18169i | ||||||||
\(134\) | − 955827.i | − 0.397251i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2304.00 | 0.000915937 0 | ||||||||
\(137\) | 4.48412e6 | 1.74388 | 0.871938 | − | 0.489617i | \(-0.162863\pi\) | ||||
0.871938 | + | 0.489617i | \(0.162863\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.09233e6 | 0.406732 | 0.203366 | − | 0.979103i | \(-0.434812\pi\) | ||||
0.203366 | + | 0.979103i | \(0.434812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00643e6i | 1.04999i | ||||||||
\(143\) | 4.51539e6 | 1.54414 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.33583e6i | 0.429233i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.68083e6i | 0.518489i | ||||||||
\(149\) | 2.22087e6i | 0.671375i | 0.941973 | + | 0.335687i | \(0.108969\pi\) | ||||
−0.941973 | + | 0.335687i | \(0.891031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.07871e6 | −1.18465 | −0.592327 | − | 0.805697i | \(-0.701791\pi\) | ||||
−0.592327 | + | 0.805697i | \(0.701791\pi\) | |||||||
\(152\) | 1.03978e6 | 0.296080 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.67066e6 | −1.00504 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.15568e6i | 1.59066i | 0.606178 | + | 0.795329i | \(0.292702\pi\) | ||||
−0.606178 | + | 0.795329i | \(0.707298\pi\) | |||||||
\(158\) | −198646. | −0.0503627 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.63454e6i | 0.391667i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 800696.i | − 0.184886i | −0.995718 | − | 0.0924432i | \(-0.970532\pi\) | ||||
0.995718 | − | 0.0924432i | \(-0.0294676\pi\) | |||||||
\(164\) | − 1.18536e6i | − 0.268732i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62112.0 | 0.0135785 | ||||||||
\(167\) | −4.80467e6 | −1.03161 | −0.515804 | − | 0.856707i | \(-0.672507\pi\) | ||||
−0.515804 | + | 0.856707i | \(0.672507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.51661e6 | −1.35009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 121600.i | − 0.0238973i | ||||||||
\(173\) | −3.56992e6 | −0.689478 | −0.344739 | − | 0.938699i | \(-0.612033\pi\) | ||||
−0.344739 | + | 0.938699i | \(0.612033\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.37285e6i | 0.251817i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 731592.i | − 0.129721i | ||||||||
\(179\) | 7.43698e6i | 1.29669i | 0.761345 | + | 0.648347i | \(0.224539\pi\) | ||||
−0.761345 | + | 0.648347i | \(0.775461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03812e7 | −1.75070 | −0.875350 | − | 0.483491i | \(-0.839369\pi\) | ||||
−0.875350 | + | 0.483491i | \(0.839369\pi\) | |||||||
\(182\) | 9.22131e6 | 1.52960 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 611328. | 0.0981343 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17064.0i | − 0.00260949i | ||||||||
\(188\) | −2.45734e6 | −0.369821 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.29941e7i | 1.86485i | 0.361360 | + | 0.932426i | \(0.382313\pi\) | ||||
−0.361360 | + | 0.932426i | \(0.617687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.93195e6i | 0.546936i | 0.961881 | + | 0.273468i | \(0.0881708\pi\) | ||||
−0.961881 | + | 0.273468i | \(0.911829\pi\) | |||||||
\(194\) | 1.81825e6i | 0.249028i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.73142e6 | −0.495572 | ||||||||
\(197\) | −5.37967e6 | −0.703651 | −0.351825 | − | 0.936066i | \(-0.614439\pi\) | ||||
−0.351825 | + | 0.936066i | \(0.614439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 565900. | 0.0718093 | 0.0359046 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359046 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 3.78319e6i | − 0.458991i | ||||||||
\(203\) | −1.42077e7 | −1.69839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.12764e7i | 1.28994i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 3.44883e6i | − 0.383250i | ||||||||
\(209\) | − 7.70083e6i | − 0.843527i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.35165e7 | −1.43885 | −0.719427 | − | 0.694568i | \(-0.755596\pi\) | ||||
−0.719427 | + | 0.694568i | \(0.755596\pi\) | |||||||
\(212\) | 7.63960e6 | 0.801795 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.47456e6 | −0.150460 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.92613e7i | 1.88497i | ||||||||
\(218\) | 1.10001e6 | 0.106176 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42867.6i | 0.00397148i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.35484e6i | 0.482872i | 0.970417 | + | 0.241436i | \(0.0776183\pi\) | ||||
−0.970417 | + | 0.241436i | \(0.922382\pi\) | |||||||
\(224\) | 2.80363e6i | 0.249446i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.64935e6 | 0.402779 | ||||||||
\(227\) | 1.36063e7 | 1.16322 | 0.581612 | − | 0.813466i | \(-0.302422\pi\) | ||||
0.581612 | + | 0.813466i | \(0.302422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.34641e6 | −0.361930 | −0.180965 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180965 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.31379e6i | 0.425540i | ||||||||
\(233\) | −2.02333e7 | −1.59956 | −0.799778 | − | 0.600297i | \(-0.795049\pi\) | ||||
−0.799778 | + | 0.600297i | \(0.795049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.99490e6i | 0.608243i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 34848.0i | − 0.00258492i | ||||||||
\(239\) | 2.03947e7i | 1.49391i | 0.664877 | + | 0.746953i | \(0.268484\pi\) | ||||
−0.664877 | + | 0.746953i | \(0.731516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.12093e6 | −0.222963 | −0.111481 | − | 0.993767i | \(-0.535560\pi\) | ||||
−0.111481 | + | 0.993767i | \(0.535560\pi\) | |||||||
\(242\) | 146213. | 0.0103167 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 424000. | 0.0291875 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.93458e7i | 1.28379i | ||||||||
\(248\) | 7.20385e6 | 0.472291 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.09519e6i | 0.322210i | 0.986937 | + | 0.161105i | \(0.0515058\pi\) | ||||
−0.986937 | + | 0.161105i | \(0.948494\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.52765e6i | − 0.279583i | ||||||||
\(254\) | − 1.72942e7i | − 1.05536i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | −1.44374e7 | −0.850529 | −0.425264 | − | 0.905069i | \(-0.639819\pi\) | ||||
−0.425264 | + | 0.905069i | \(0.639819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.54226e7 | 1.46326 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 1.73885e7i | − 0.966847i | ||||||||
\(263\) | 3.12567e7 | 1.71821 | 0.859104 | − | 0.511801i | \(-0.171022\pi\) | ||||
0.859104 | + | 0.511801i | \(0.171022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 1.57266e7i | − 0.835584i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.40698e6i | 0.280899i | ||||||||
\(269\) | − 251338.i | − 0.0129122i | −0.999979 | − | 0.00645612i | \(-0.997945\pi\) | ||||
0.999979 | − | 0.00645612i | \(-0.00205506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.96399e7 | 1.48925 | 0.744627 | − | 0.667481i | \(-0.232627\pi\) | ||||
0.744627 | + | 0.667481i | \(0.232627\pi\) | |||||||
\(272\) | −13033.4 | −0.000647665 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.53660e7 | −1.23311 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.32213e7i | 0.622062i | 0.950400 | + | 0.311031i | \(0.100674\pi\) | ||||
−0.950400 | + | 0.311031i | \(0.899326\pi\) | |||||||
\(278\) | −6.17914e6 | −0.287603 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 6.12360e6i | − 0.275987i | −0.990433 | − | 0.137993i | \(-0.955935\pi\) | ||||
0.990433 | − | 0.137993i | \(-0.0440652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.74325e6i | 0.297516i | 0.988874 | + | 0.148758i | \(0.0475275\pi\) | ||||
−0.988874 | + | 0.148758i | \(0.952473\pi\) | |||||||
\(284\) | − 1.70069e7i | − 0.742457i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.55429e7 | −1.09187 | ||||||||
\(287\) | −1.79286e7 | −0.758403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.41374e7 | −0.999993 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 7.55661e6i | − 0.303514i | ||||||||
\(293\) | −1.00239e7 | −0.398505 | −0.199253 | − | 0.979948i | \(-0.563851\pi\) | ||||
−0.199253 | + | 0.979948i | \(0.563851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 9.50822e6i | − 0.366627i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.25632e7i | − 0.474734i | ||||||||
\(299\) | 1.13742e7i | 0.425508i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.83920e6 | −0.0674418 | ||||||||
\(302\) | 2.30727e7 | 0.837677 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.88186e6 | −0.209360 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.23060e6i | − 0.180774i | −0.995907 | − | 0.0903871i | \(-0.971190\pi\) | ||||
0.995907 | − | 0.0903871i | \(-0.0288104\pi\) | |||||||
\(308\) | 2.07644e7 | 0.710668 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.12221e7i | 1.03796i | 0.854786 | + | 0.518981i | \(0.173688\pi\) | ||||
−0.854786 | + | 0.518981i | \(0.826312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2.24778e7i | − 0.733029i | −0.930412 | − | 0.366515i | \(-0.880551\pi\) | ||||
0.930412 | − | 0.366515i | \(-0.119449\pi\) | |||||||
\(314\) | − 3.48218e7i | − 1.12477i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.12371e6 | 0.0356118 | ||||||||
\(317\) | 2.76211e7 | 0.867088 | 0.433544 | − | 0.901132i | \(-0.357263\pi\) | ||||
0.433544 | + | 0.901132i | \(0.357263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.93553e7 | 1.21236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 9.24634e6i | − 0.276950i | ||||||||
\(323\) | 73109.2 | 0.00216952 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.52942e6i | 0.130734i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.70541e6i | 0.190022i | ||||||||
\(329\) | 3.71672e7i | 1.04369i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.76138e6 | −0.158870 | −0.0794352 | − | 0.996840i | \(-0.525312\pi\) | ||||
−0.0794352 | + | 0.996840i | \(0.525312\pi\) | |||||||
\(332\) | −351359. | −0.00960144 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.71793e7 | 0.729456 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.01052e7i | − 1.04788i | −0.851756 | − | 0.523939i | \(-0.824462\pi\) | ||||
0.851756 | − | 0.523939i | \(-0.175538\pi\) | |||||||
\(338\) | 3.68635e7 | 0.954656 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5.33535e7i | − 1.34555i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 504328.i | − 0.0124977i | ||||||||
\(344\) | 687873.i | 0.0168979i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.01945e7 | 0.487535 | ||||||||
\(347\) | −6.78127e7 | −1.62302 | −0.811508 | − | 0.584341i | \(-0.801353\pi\) | ||||
−0.811508 | + | 0.584341i | \(0.801353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.20638e7 | 0.989538 | 0.494769 | − | 0.869024i | \(-0.335253\pi\) | ||||
0.494769 | + | 0.869024i | \(0.335253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 7.76602e6i | − 0.178062i | ||||||||
\(353\) | −1.75976e7 | −0.400063 | −0.200032 | − | 0.979789i | \(-0.564104\pi\) | ||||
−0.200032 | + | 0.979789i | \(0.564104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.13851e6i | 0.0917263i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 4.20699e7i | − 0.916901i | ||||||||
\(359\) | 1.39920e7i | 0.302410i | 0.988502 | + | 0.151205i | \(0.0483154\pi\) | ||||
−0.988502 | + | 0.151205i | \(0.951685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.40523e7 | −0.298694 | ||||||||
\(362\) | 5.87249e7 | 1.23793 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.21636e7 | −1.08159 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.65855e7i | − 0.537832i | −0.963164 | − | 0.268916i | \(-0.913335\pi\) | ||||
0.963164 | − | 0.268916i | \(-0.0866653\pi\) | |||||||
\(368\) | −3.45819e6 | −0.0693914 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.15549e8i | − 2.26279i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.78829e7i | − 0.344598i | −0.985045 | − | 0.172299i | \(-0.944881\pi\) | ||||
0.985045 | − | 0.172299i | \(-0.0551195\pi\) | |||||||
\(374\) | 96528.6i | 0.00184519i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.39008e7 | 0.261503 | ||||||||
\(377\) | −9.88671e7 | −1.84513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.20978e7 | −1.32435 | −0.662177 | − | 0.749347i | \(-0.730367\pi\) | ||||
−0.662177 | + | 0.749347i | \(0.730367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 7.35055e7i | − 1.31865i | ||||||||
\(383\) | 8.68648e6 | 0.154614 | 0.0773068 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773068 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 2.22425e7i | − 0.386742i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 1.02856e7i | − 0.176089i | ||||||||
\(389\) | 4.94411e7i | 0.839923i | 0.907542 | + | 0.419962i | \(0.137956\pi\) | ||||
−0.907542 | + | 0.419962i | \(0.862044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42984.0 | 0.000719079 0 | ||||||||
\(392\) | 2.11081e7 | 0.350422 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.04320e7 | 0.497556 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.56911e7i | 0.250774i | 0.992108 | + | 0.125387i | \(0.0400172\pi\) | ||||
−0.992108 | + | 0.125387i | \(0.959983\pi\) | |||||||
\(398\) | −3.20121e6 | −0.0507768 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 4.74514e7i | − 0.735895i | −0.929847 | − | 0.367947i | \(-0.880061\pi\) | ||||
0.929847 | − | 0.367947i | \(-0.119939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.34033e8i | 2.04784i | ||||||||
\(404\) | 2.14010e7i | 0.324556i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.03711e7 | 1.20094 | ||||||||
\(407\) | −7.04203e7 | −1.04451 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.15512e8 | 1.68832 | 0.844162 | − | 0.536088i | \(-0.180099\pi\) | ||||
0.844162 | + | 0.536088i | \(0.180099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 6.37892e7i | − 0.912127i | ||||||||
\(413\) | 1.20923e8 | 1.71656 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.95095e7i | 0.270999i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.35625e7i | 0.596464i | ||||||||
\(419\) | − 1.46693e8i | − 1.99420i | −0.0761306 | − | 0.997098i | \(-0.524257\pi\) | ||||
0.0761306 | − | 0.997098i | \(-0.475743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.39239e8 | 1.86601 | 0.933005 | − | 0.359863i | \(-0.117176\pi\) | ||||
0.933005 | + | 0.359863i | \(0.117176\pi\) | |||||||
\(422\) | 7.64609e7 | 1.01742 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.32161e7 | −0.566955 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.41300e6i | − 0.0823716i | ||||||||
\(428\) | 8.34137e6 | 0.106391 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.00392e8i | − 1.25391i | −0.779056 | − | 0.626954i | \(-0.784301\pi\) | ||||
0.779056 | − | 0.626954i | \(-0.215699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00631e7i | 0.493493i | 0.969080 | + | 0.246747i | \(0.0793616\pi\) | ||||
−0.969080 | + | 0.246747i | \(0.920638\pi\) | |||||||
\(434\) | − 1.08958e8i | − 1.33288i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.22259e6 | −0.0750779 | ||||||||
\(437\) | 1.93983e7 | 0.232445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.38592e8 | 1.63811 | 0.819057 | − | 0.573712i | \(-0.194497\pi\) | ||||
0.819057 | + | 0.573712i | \(0.194497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 242496.i | − 0.00280826i | ||||||||
\(443\) | −1.11443e8 | −1.28186 | −0.640929 | − | 0.767600i | \(-0.721451\pi\) | ||||
−0.640929 | + | 0.767600i | \(0.721451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 3.02915e7i | − 0.341442i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1.58597e7i | − 0.176385i | ||||||||
\(449\) | 6.11166e7i | 0.675181i | 0.941293 | + | 0.337591i | \(0.109612\pi\) | ||||
−0.941293 | + | 0.337591i | \(0.890388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.96619e7 | 0.541370 | ||||||||
\(452\) | −2.63007e7 | −0.284808 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.69691e7 | −0.822524 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.56665e7i | 0.373690i | 0.982389 | + | 0.186845i | \(0.0598262\pi\) | ||||
−0.982389 | + | 0.186845i | \(0.940174\pi\) | |||||||
\(458\) | 2.45870e7 | 0.255923 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.51983e8i | 1.55128i | 0.631173 | + | 0.775642i | \(0.282574\pi\) | ||||
−0.631173 | + | 0.775642i | \(0.717426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.14978e8i | − 1.15844i | −0.815173 | − | 0.579218i | \(-0.803358\pi\) | ||||
0.815173 | − | 0.579218i | \(-0.196642\pi\) | |||||||
\(464\) | − 3.00593e7i | − 0.300902i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.14457e8 | 1.13106 | ||||||||
\(467\) | −8.81705e7 | −0.865711 | −0.432855 | − | 0.901463i | \(-0.642494\pi\) | ||||
−0.432855 | + | 0.901463i | \(0.642494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.17805e7 | 0.792741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 4.52260e7i | − 0.430093i | ||||||||
\(473\) | 5.09456e6 | 0.0481419 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 197130.i | 0.00182781i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 1.15370e8i | − 1.05635i | ||||||||
\(479\) | 8.94388e7i | 0.813803i | 0.913472 | + | 0.406902i | \(0.133391\pi\) | ||||
−0.913472 | + | 0.406902i | \(0.866609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.76908e8 | 1.58969 | ||||||||
\(482\) | 1.76546e7 | 0.157659 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −827104. | −0.00729498 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7.51688e7i | − 0.650805i | −0.945576 | − | 0.325403i | \(-0.894500\pi\) | ||||
0.945576 | − | 0.325403i | \(-0.105500\pi\) | |||||||
\(488\) | −2.39851e6 | −0.0206387 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50822e7i | 0.380856i | 0.981701 | + | 0.190428i | \(0.0609876\pi\) | ||||
−0.981701 | + | 0.190428i | \(0.939012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 373626.i | 0.00311815i | ||||||||
\(494\) | − 1.09436e8i | − 0.907780i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.07511e7 | −0.333960 | ||||||||
\(497\) | −2.57230e8 | −2.09533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.15458e7 | −0.736778 | −0.368389 | − | 0.929672i | \(-0.620091\pi\) | ||||
−0.368389 | + | 0.929672i | \(0.620091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2.88228e7i | − 0.227837i | ||||||||
\(503\) | −1.61043e8 | −1.26543 | −0.632713 | − | 0.774386i | \(-0.718059\pi\) | ||||
−0.632713 | + | 0.774386i | \(0.718059\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.56122e7i | 0.197695i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.78308e7i | 0.746250i | ||||||||
\(509\) | − 2.39995e7i | − 0.181990i | −0.995851 | − | 0.0909951i | \(-0.970995\pi\) | ||||
0.995851 | − | 0.0909951i | \(-0.0290048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.14294e8 | −0.856564 | ||||||||
\(512\) | −5.93164e6 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.16702e7 | 0.601415 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.02953e8i | − 0.745018i | ||||||||
\(518\) | −1.43812e8 | −1.03468 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 9.00897e7i | − 0.637033i | −0.947917 | − | 0.318517i | \(-0.896815\pi\) | ||||
0.947917 | − | 0.318517i | \(-0.103185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.77691e7i | 0.264016i | 0.991249 | + | 0.132008i | \(0.0421425\pi\) | ||||
−0.991249 | + | 0.132008i | \(0.957857\pi\) | |||||||
\(524\) | 9.83641e7i | 0.683664i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.76815e8 | −1.21496 | ||||||||
\(527\) | 506520. | 0.00346071 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.36631e8 | −0.922957 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.89631e7i | 0.590847i | ||||||||
\(533\) | −1.24759e8 | −0.823931 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 3.05865e7i | − 0.198626i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.42178e6i | 0.00913034i | ||||||||
\(539\) | − 1.56332e8i | − 0.998347i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.54800e7 | 0.160919 | 0.0804595 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804595 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(542\) | −1.67669e8 | −1.05306 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 73728.0 | 0.000457969 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.05216e8i | 1.25386i | 0.779076 | + | 0.626930i | \(0.215689\pi\) | ||||
−0.779076 | + | 0.626930i | \(0.784311\pi\) | |||||||
\(548\) | 1.43492e8 | 0.871938 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.68614e8i | 1.00795i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.69961e7i | − 0.100502i | ||||||||
\(554\) | − 7.47908e7i | − 0.439865i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.49545e7 | 0.203366 | ||||||||
\(557\) | 2.41143e8 | 1.39543 | 0.697715 | − | 0.716375i | \(-0.254200\pi\) | ||||
0.697715 | + | 0.716375i | \(0.254200\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.27984e7 | −0.0732690 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.46403e7i | 0.195152i | ||||||||
\(563\) | −1.68877e8 | −0.946337 | −0.473168 | − | 0.880972i | \(-0.656890\pi\) | ||||
−0.473168 | + | 0.880972i | \(0.656890\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 3.81456e7i | − 0.210375i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.62058e7i | 0.524996i | ||||||||
\(569\) | 2.43995e8i | 1.32448i | 0.749293 | + | 0.662238i | \(0.230393\pi\) | ||||
−0.749293 | + | 0.662238i | \(0.769607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.41502e8 | 1.29722 | 0.648608 | − | 0.761123i | \(-0.275352\pi\) | ||||
0.648608 | + | 0.761123i | \(0.275352\pi\) | |||||||
\(572\) | 1.44493e8 | 0.772071 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.01419e8 | 0.536272 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 4.93979e7i | − 0.257147i | −0.991700 | − | 0.128573i | \(-0.958960\pi\) | ||||
0.991700 | − | 0.128573i | \(-0.0410398\pi\) | |||||||
\(578\) | 1.36542e8 | 0.707102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.31430e6i | 0.0270968i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.20069e8i | 1.61525i | ||||||||
\(584\) | 4.27466e7i | 0.214617i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.67038e7 | 0.281786 | ||||||||
\(587\) | 1.72052e8 | 0.850639 | 0.425320 | − | 0.905043i | \(-0.360162\pi\) | ||||
0.425320 | + | 0.905043i | \(0.360162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.28588e8 | 1.11869 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.37866e7i | 0.259244i | ||||||||
\(593\) | 2.70643e8 | 1.29788 | 0.648938 | − | 0.760841i | \(-0.275213\pi\) | ||||
0.648938 | + | 0.760841i | \(0.275213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.10680e7i | 0.335687i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 6.43423e7i | − 0.300880i | ||||||||
\(599\) | 1.73299e8i | 0.806337i | 0.915126 | + | 0.403169i | \(0.132091\pi\) | ||||
−0.915126 | + | 0.403169i | \(0.867909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.31090e8 | −1.98584 | −0.992921 | − | 0.118775i | \(-0.962103\pi\) | ||||
−0.992921 | + | 0.118775i | \(0.962103\pi\) | |||||||
\(602\) | 1.04041e7 | 0.0476886 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.30519e8 | −0.592327 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.66991e7i | 0.0746665i | 0.999303 | + | 0.0373332i | \(0.0118863\pi\) | ||||
−0.999303 | + | 0.0373332i | \(0.988114\pi\) | |||||||
\(608\) | 3.32728e7 | 0.148040 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.58635e8i | 1.13387i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.92321e8i | 0.834920i | 0.908695 | + | 0.417460i | \(0.137080\pi\) | ||||
−0.908695 | + | 0.417460i | \(0.862920\pi\) | |||||||
\(614\) | 2.95887e7i | 0.127827i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.17461e8 | −0.502518 | ||||||||
\(617\) | 1.87023e8 | 0.796233 | 0.398117 | − | 0.917335i | \(-0.369664\pi\) | ||||
0.398117 | + | 0.917335i | \(0.369664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.54873e8 | −1.07461 | −0.537307 | − | 0.843387i | \(-0.680558\pi\) | ||||
−0.537307 | + | 0.843387i | \(0.680558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 1.76619e8i | − 0.733950i | ||||||||
\(623\) | 6.25950e7 | 0.258866 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.27154e8i | 0.518330i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.96982e8i | 0.795329i | ||||||||
\(629\) | − 668547.i | − 0.00268646i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.23602e7 | 0.367618 | 0.183809 | − | 0.982962i | \(-0.441157\pi\) | ||||
0.183809 | + | 0.982962i | \(0.441157\pi\) | |||||||
\(632\) | −6.35668e6 | −0.0251813 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.56249e8 | −0.613124 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.92732e8i | 1.51942i | ||||||||
\(638\) | −2.22627e8 | −0.857267 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 4.24666e8i | − 1.61240i | −0.591643 | − | 0.806200i | \(-0.701520\pi\) | ||||
0.591643 | − | 0.806200i | \(-0.298480\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.75946e8i | − 1.41414i | −0.707143 | − | 0.707071i | \(-0.750016\pi\) | ||||
0.707143 | − | 0.707071i | \(-0.249984\pi\) | |||||||
\(644\) | 5.23052e7i | 0.195834i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −413568. | −0.00153408 | ||||||||
\(647\) | −2.63747e7 | −0.0973813 | −0.0486906 | − | 0.998814i | \(-0.515505\pi\) | ||||
−0.0486906 | + | 0.998814i | \(0.515505\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.34955e8 | −1.22533 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 2.56223e7i | − 0.0924432i | ||||||||
\(653\) | 2.58756e8 | 0.929291 | 0.464645 | − | 0.885497i | \(-0.346182\pi\) | ||||
0.464645 | + | 0.885497i | \(0.346182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 3.79315e7i | − 0.134366i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 2.10250e8i | − 0.738002i | ||||||||
\(659\) | 1.39345e8i | 0.486895i | 0.969914 | + | 0.243447i | \(0.0782783\pi\) | ||||
−0.969914 | + | 0.243447i | \(0.921722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.72545e8 | −1.63621 | −0.818104 | − | 0.575070i | \(-0.804975\pi\) | ||||
−0.818104 | + | 0.575070i | \(0.804975\pi\) | |||||||
\(662\) | 3.25913e7 | 0.112338 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.98758e6 | 0.00678924 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.91354e7i | 0.334081i | ||||||||
\(668\) | −1.53749e8 | −0.515804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.77639e7i | 0.0587992i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 5.48833e8i | − 1.80051i | −0.435364 | − | 0.900254i | \(-0.643380\pi\) | ||||
0.435364 | − | 0.900254i | \(-0.356620\pi\) | |||||||
\(674\) | 2.26869e8i | 0.740961i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.08532e8 | −0.675044 | ||||||||
\(677\) | 1.00760e8 | 0.324731 | 0.162365 | − | 0.986731i | \(-0.448088\pi\) | ||||
0.162365 | + | 0.986731i | \(0.448088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.55569e8 | −0.496952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.01813e8i | 0.951447i | ||||||||
\(683\) | −313056. | −0.000982562 0 | −0.000491281 | − | 1.00000i | \(-0.500156\pi\) | ||||
−0.000491281 | 1.00000i | \(0.500156\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.85291e6i | 0.00883722i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 3.89120e6i | − 0.0119486i | ||||||||
\(689\) | − 8.04068e8i | − 2.45830i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.72812e8 | −1.12994 | −0.564971 | − | 0.825111i | \(-0.691113\pi\) | ||||
−0.564971 | + | 0.825111i | \(0.691113\pi\) | |||||||
\(692\) | −1.14238e8 | −0.344739 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.83607e8 | 1.14765 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 471474.i | 0.00139239i | ||||||||
\(698\) | −2.37949e8 | −0.699709 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.21170e8i | 1.80325i | 0.432517 | + | 0.901626i | \(0.357626\pi\) | ||||
−0.432517 | + | 0.901626i | \(0.642374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.01709e8i | − 0.868406i | ||||||||
\(704\) | 4.39312e7i | 0.125909i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.95469e7 | 0.282887 | ||||||||
\(707\) | 3.23690e8 | 0.915947 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.46510e8 | 0.691666 | 0.345833 | − | 0.938296i | \(-0.387596\pi\) | ||||
0.345833 | + | 0.938296i | \(0.387596\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 2.34109e7i | − 0.0648603i | ||||||||
\(713\) | 1.34397e8 | 0.370783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.37983e8i | 0.648347i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 7.91508e7i | − 0.213836i | ||||||||
\(719\) | 9.60389e7i | 0.258381i | 0.991620 | + | 0.129191i | \(0.0412379\pi\) | ||||
−0.991620 | + | 0.129191i | \(0.958762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.64811e8 | −2.57417 | ||||||||
\(722\) | 7.94921e7 | 0.211209 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.32198e8 | −0.875350 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.91371e8i | 1.01856i | 0.860602 | + | 0.509278i | \(0.170088\pi\) | ||||
−0.860602 | + | 0.509278i | \(0.829912\pi\) | |||||||
\(728\) | 2.95082e8 | 0.764801 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48366.1i | 0 0.000123819i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 3.49078e7i | − 0.0886361i | −0.999017 | − | 0.0443181i | \(-0.985889\pi\) | ||||
0.999017 | − | 0.0443181i | \(-0.0141115\pi\) | |||||||
\(734\) | 1.50390e8i | 0.380304i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.95625e7 | 0.0490671 | ||||||||
\(737\) | −2.26531e8 | −0.565881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.02999e8 | 0.750773 | 0.375386 | − | 0.926868i | \(-0.377510\pi\) | ||||
0.375386 | + | 0.926868i | \(0.377510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.53644e8i | 1.60004i | ||||||||
\(743\) | 2.45628e8 | 0.598842 | 0.299421 | − | 0.954121i | \(-0.403207\pi\) | ||||
0.299421 | + | 0.954121i | \(0.403207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.01161e8i | 0.243667i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 546048.i | − 0.00130475i | ||||||||
\(749\) | − 1.26163e8i | − 0.300253i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.23270e7 | −0.194367 | −0.0971835 | − | 0.995266i | \(-0.530983\pi\) | ||||
−0.0971835 | + | 0.995266i | \(0.530983\pi\) | |||||||
\(752\) | −7.86348e7 | −0.184910 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.59277e8 | 1.30471 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6.03579e8i | − 1.39138i | −0.718341 | − | 0.695691i | \(-0.755098\pi\) | ||||
0.718341 | − | 0.695691i | \(-0.244902\pi\) | |||||||
\(758\) | 4.07847e8 | 0.936460 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 2.32982e8i | − 0.528651i | −0.964434 | − | 0.264325i | \(-0.914851\pi\) | ||||
0.964434 | − | 0.264325i | \(-0.0851493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.41167e7i | 0.211882i | ||||||||
\(764\) | 4.15810e8i | 0.932426i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.91382e7 | −0.109328 | ||||||||
\(767\) | 8.41463e8 | 1.86487 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.15796e8 | −1.79392 | −0.896958 | − | 0.442115i | \(-0.854228\pi\) | ||||
−0.896958 | + | 0.442115i | \(0.854228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.25823e8i | 0.273468i | ||||||||
\(773\) | −3.66587e8 | −0.793667 | −0.396833 | − | 0.917891i | \(-0.629891\pi\) | ||||
−0.396833 | + | 0.917891i | \(0.629891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.81840e7i | 0.124514i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 2.79681e8i | − 0.593915i | ||||||||
\(779\) | 2.12772e8i | 0.450093i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.12524e8 | 1.49571 | ||||||||
\(782\) | −243154. | −0.000508466 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.19406e8 | −0.247786 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.02462e8i | − 0.825659i | −0.910808 | − | 0.412830i | \(-0.864540\pi\) | ||||
0.910808 | − | 0.412830i | \(-0.135460\pi\) | |||||||
\(788\) | −1.72150e8 | −0.351825 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.97798e8i | 0.803773i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.46260e7i | − 0.0894887i | ||||||||
\(794\) | − 8.87623e7i | − 0.177324i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.81088e7 | 0.0359046 | ||||||||
\(797\) | 5.18940e8 | 1.02504 | 0.512521 | − | 0.858675i | \(-0.328712\pi\) | ||||
0.512521 | + | 0.858675i | \(0.328712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 977400. | 0.00191616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.68426e8i | 0.520356i | ||||||||
\(803\) | 3.16592e8 | 0.611440 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 7.58205e8i | − 1.44804i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1.21062e8i | − 0.229496i | ||||||||
\(809\) | 3.04036e6i | 0.00574221i | 0.999996 | + | 0.00287110i | \(0.000913902\pi\) | ||||
−0.999996 | + | 0.00287110i | \(0.999086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.25521e8 | 0.422790 | 0.211395 | − | 0.977401i | \(-0.432199\pi\) | ||||
0.211395 | + | 0.977401i | \(0.432199\pi\) | |||||||
\(812\) | −4.54648e8 | −0.849194 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.98357e8 | 0.738583 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.18272e7i | 0.0400250i | ||||||||
\(818\) | −6.53432e8 | −1.19383 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.77035e8i | 0.500617i | 0.968166 | + | 0.250309i | \(0.0805321\pi\) | ||||
−0.968166 | + | 0.250309i | \(0.919468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.07336e8i | 1.26890i | 0.772965 | + | 0.634448i | \(0.218773\pi\) | ||||
−0.772965 | + | 0.634448i | \(0.781227\pi\) | |||||||
\(824\) | 3.60846e8i | 0.644971i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.84043e8 | −1.21379 | ||||||||
\(827\) | 2.66346e8 | 0.470900 | 0.235450 | − | 0.971886i | \(-0.424344\pi\) | ||||
0.235450 | + | 0.971886i | \(0.424344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.03826e8 | −0.884336 | −0.442168 | − | 0.896932i | \(-0.645791\pi\) | ||||
−0.442168 | + | 0.896932i | \(0.645791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1.10363e8i | − 0.191625i | ||||||||
\(833\) | 1.48416e6 | 0.00256772 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 2.46427e8i | − 0.421763i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.29822e8i | 1.41011i | ||||||||
\(839\) | − 7.63364e8i | − 1.29255i | −0.763106 | − | 0.646273i | \(-0.776327\pi\) | ||||
0.763106 | − | 0.646273i | \(-0.223673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.66883e8 | −0.448676 | ||||||||
\(842\) | −7.87654e8 | −1.31947 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.32528e8 | −0.719427 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.25099e7i | 0.0205876i | ||||||||
\(848\) | 2.44467e8 | 0.400897 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.77388e8i | − 0.287829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.87985e7i | 0.0302884i | 0.999885 | + | 0.0151442i | \(0.00482073\pi\) | ||||
−0.999885 | + | 0.0151442i | \(0.995179\pi\) | |||||||
\(854\) | 3.62774e7i | 0.0582455i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.71859e7 | −0.0752300 | ||||||||
\(857\) | 6.86427e8 | 1.09057 | 0.545283 | − | 0.838252i | \(-0.316422\pi\) | ||||
0.545283 | + | 0.838252i | \(0.316422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.51932e8 | −0.870775 | −0.435387 | − | 0.900243i | \(-0.643389\pi\) | ||||
−0.435387 | + | 0.900243i | \(0.643389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.67901e8i | 0.886647i | ||||||||
\(863\) | 3.65665e8 | 0.568920 | 0.284460 | − | 0.958688i | \(-0.408186\pi\) | ||||
0.284460 | + | 0.958688i | \(0.408186\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 2.26631e8i | − 0.348952i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.16360e8i | 0.942487i | ||||||||
\(869\) | 4.70791e7i | 0.0717413i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.69084e8 | 0.861236 | ||||||||
\(872\) | 3.52003e7 | 0.0530881 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.09733e8 | −0.164363 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5.85387e8i | − 0.867849i | −0.900949 | − | 0.433925i | \(-0.857128\pi\) | ||||
0.900949 | − | 0.433925i | \(-0.142872\pi\) | |||||||
\(878\) | −7.83994e8 | −1.15832 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 4.29761e8i | − 0.628491i | −0.949342 | − | 0.314246i | \(-0.898248\pi\) | ||||
0.949342 | − | 0.314246i | \(-0.101752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.20085e8i | − 0.319675i | −0.987143 | − | 0.159837i | \(-0.948903\pi\) | ||||
0.987143 | − | 0.159837i | \(-0.0510970\pi\) | |||||||
\(884\) | 1.37176e6i | 0.00198574i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.30415e8 | 0.906411 | ||||||||
\(887\) | −1.17196e9 | −1.67936 | −0.839678 | − | 0.543084i | \(-0.817256\pi\) | ||||
−0.839678 | + | 0.543084i | \(0.817256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.47969e9 | 2.10604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.71355e8i | 0.241436i | ||||||||
\(893\) | 4.41092e8 | 0.619405 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.97161e7i | 0.124723i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 3.45728e8i | − 0.477425i | ||||||||
\(899\) | 1.16820e9i | 1.60783i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.03863e6 | −0.00415436 | ||||||||
\(902\) | −2.80930e8 | −0.382806 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.48779e8 | 0.201390 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.31614e8i | 0.980529i | 0.871574 | + | 0.490264i | \(0.163100\pi\) | ||||
−0.871574 | + | 0.490264i | \(0.836900\pi\) | |||||||
\(908\) | 4.35403e8 | 0.581612 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.18595e8i | 1.21498i | 0.794327 | + | 0.607490i | \(0.207823\pi\) | ||||
−0.794327 | + | 0.607490i | \(0.792177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.47205e7i | − 0.0193425i | ||||||||
\(914\) | − 2.01760e8i | − 0.264239i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.39085e8 | −0.180965 | ||||||||
\(917\) | 1.48776e9 | 1.92941 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.15987e8 | 0.278279 | 0.139139 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139139 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 8.59744e8i | − 1.09692i | ||||||||
\(923\) | −1.78998e9 | −2.27637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.50414e8i | 0.819138i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.70041e8i | 0.212770i | ||||||||
\(929\) | − 3.10124e8i | − 0.386802i | −0.981120 | − | 0.193401i | \(-0.938048\pi\) | ||||
0.981120 | − | 0.193401i | \(-0.0619518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.69791e8 | 0.830023 | ||||||||
\(932\) | −6.47466e8 | −0.799778 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.98768e8 | 0.612150 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 7.42448e8i | − 0.902501i | −0.892397 | − | 0.451250i | \(-0.850978\pi\) | ||||
0.892397 | − | 0.451250i | \(-0.149022\pi\) | |||||||
\(938\) | −4.62620e8 | −0.560553 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.81766e8i | 0.218144i | 0.994034 | + | 0.109072i | \(0.0347879\pi\) | ||||
−0.994034 | + | 0.109072i | \(0.965212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.25098e8i | 0.149181i | ||||||||
\(944\) | 2.55837e8i | 0.304121i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.88192e7 | −0.0340415 | ||||||||
\(947\) | −8.59189e8 | −1.01167 | −0.505835 | − | 0.862630i | \(-0.668816\pi\) | ||||
−0.505835 | + | 0.862630i | \(0.668816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.95333e8 | −0.930573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 1.11514e6i | − 0.00129246i | ||||||||
\(953\) | 6.86819e8 | 0.793530 | 0.396765 | − | 0.917920i | \(-0.370133\pi\) | ||||
0.396765 | + | 0.917920i | \(0.370133\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.52630e8i | 0.746953i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 5.05942e8i | − 0.575446i | ||||||||
\(959\) | − 2.17031e9i | − 2.46075i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.96218e8 | 0.784468 | ||||||||
\(962\) | −1.00074e9 | −1.12408 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.98697e7 | −0.111481 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.09411e9i | − 1.20999i | −0.796230 | − | 0.604995i | \(-0.793175\pi\) | ||||
0.796230 | − | 0.604995i | \(-0.206825\pi\) | |||||||
\(968\) | 4.67881e6 | 0.00515833 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.43115e8i | 0.484014i | 0.970274 | + | 0.242007i | \(0.0778058\pi\) | ||||
−0.970274 | + | 0.242007i | \(0.922194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5.28687e8i | − 0.573931i | ||||||||
\(974\) | 4.25219e8i | 0.460189i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.35680e7 | 0.0145937 | ||||||||
\(977\) | −1.19004e9 | −1.27608 | −0.638042 | − | 0.770001i | \(-0.720256\pi\) | ||||
−0.638042 | + | 0.770001i | \(0.720256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.73387e8 | −0.184786 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 2.55024e8i | − 0.269306i | ||||||||
\(983\) | −1.18187e9 | −1.24425 | −0.622125 | − | 0.782918i | \(-0.713730\pi\) | ||||
−0.622125 | + | 0.782918i | \(0.713730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 2.11355e6i | − 0.00220486i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.19065e8i | 0.641897i | ||||||||
\(989\) | 1.28331e7i | 0.0132661i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.09602e8 | 0.523613 | 0.261806 | − | 0.965120i | \(-0.415682\pi\) | ||||
0.261806 | + | 0.965120i | \(0.415682\pi\) | |||||||
\(992\) | 2.30523e8 | 0.236145 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.45511e9 | 1.48162 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 9.90780e8i | − 0.999751i | −0.866097 | − | 0.499875i | \(-0.833379\pi\) | ||||
0.866097 | − | 0.499875i | \(-0.166621\pi\) | |||||||
\(998\) | 5.17861e8 | 0.520981 | ||||||||
\(999\) | 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 | 450.7.b.a.449.1 | 4 | ||
3.2 | odd | 2 | inner | 450.7.b.a.449.3 | 4 | ||
5.2 | odd | 4 | 450.7.d.a.251.1 | 2 | |||
5.3 | odd | 4 | 18.7.b.a.17.2 | yes | 2 | ||
5.4 | even | 2 | inner | 450.7.b.a.449.4 | 4 | ||
15.2 | even | 4 | 450.7.d.a.251.2 | 2 | |||
15.8 | even | 4 | 18.7.b.a.17.1 | ✓ | 2 | ||
15.14 | odd | 2 | inner | 450.7.b.a.449.2 | 4 | ||
20.3 | even | 4 | 144.7.e.d.17.2 | 2 | |||
40.3 | even | 4 | 576.7.e.k.449.1 | 2 | |||
40.13 | odd | 4 | 576.7.e.b.449.1 | 2 | |||
45.13 | odd | 12 | 162.7.d.d.107.1 | 4 | |||
45.23 | even | 12 | 162.7.d.d.107.2 | 4 | |||
45.38 | even | 12 | 162.7.d.d.53.1 | 4 | |||
45.43 | odd | 12 | 162.7.d.d.53.2 | 4 | |||
60.23 | odd | 4 | 144.7.e.d.17.1 | 2 | |||
120.53 | even | 4 | 576.7.e.b.449.2 | 2 | |||
120.83 | odd | 4 | 576.7.e.k.449.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.7.b.a.17.1 | ✓ | 2 | 15.8 | even | 4 | ||
18.7.b.a.17.2 | yes | 2 | 5.3 | odd | 4 | ||
144.7.e.d.17.1 | 2 | 60.23 | odd | 4 | |||
144.7.e.d.17.2 | 2 | 20.3 | even | 4 | |||
162.7.d.d.53.1 | 4 | 45.38 | even | 12 | |||
162.7.d.d.53.2 | 4 | 45.43 | odd | 12 | |||
162.7.d.d.107.1 | 4 | 45.13 | odd | 12 | |||
162.7.d.d.107.2 | 4 | 45.23 | even | 12 | |||
450.7.b.a.449.1 | 4 | 1.1 | even | 1 | trivial | ||
450.7.b.a.449.2 | 4 | 15.14 | odd | 2 | inner | ||
450.7.b.a.449.3 | 4 | 3.2 | odd | 2 | inner | ||
450.7.b.a.449.4 | 4 | 5.4 | even | 2 | inner | ||
450.7.d.a.251.1 | 2 | 5.2 | odd | 4 | |||
450.7.d.a.251.2 | 2 | 15.2 | even | 4 | |||
576.7.e.b.449.1 | 2 | 40.13 | odd | 4 | |||
576.7.e.b.449.2 | 2 | 120.53 | even | 4 | |||
576.7.e.k.449.1 | 2 | 40.3 | even | 4 | |||
576.7.e.k.449.2 | 2 | 120.83 | odd | 4 |