Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(49,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("150.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.49 |
Dual form | 150.6.c.g.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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | − 47.0000i | − 0.362537i | −0.983434 | − | 0.181269i | \(-0.941980\pi\) | ||||
0.983434 | − | 0.181269i | \(-0.0580204\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 222.000 | 0.553186 | 0.276593 | − | 0.960987i | \(-0.410795\pi\) | ||||
0.276593 | + | 0.960987i | \(0.410795\pi\) | |||||||
\(12\) | − 144.000i | − 0.288675i | ||||||||
\(13\) | 101.000i | 0.165754i | 0.996560 | + | 0.0828768i | \(0.0264108\pi\) | ||||
−0.996560 | + | 0.0828768i | \(0.973589\pi\) | |||||||
\(14\) | −188.000 | −0.256353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 162.000i | − 0.135954i | −0.997687 | − | 0.0679771i | \(-0.978346\pi\) | ||||
0.997687 | − | 0.0679771i | \(-0.0216545\pi\) | |||||||
\(18\) | 324.000i | 0.235702i | ||||||||
\(19\) | −1685.00 | −1.07082 | −0.535409 | − | 0.844593i | \(-0.679843\pi\) | ||||
−0.535409 | + | 0.844593i | \(0.679843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 423.000 | 0.209311 | ||||||||
\(22\) | − 888.000i | − 0.391162i | ||||||||
\(23\) | 306.000i | 0.120615i | 0.998180 | + | 0.0603076i | \(0.0192082\pi\) | ||||
−0.998180 | + | 0.0603076i | \(0.980792\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 404.000 | 0.117206 | ||||||||
\(27\) | − 729.000i | − 0.192450i | ||||||||
\(28\) | 752.000i | 0.181269i | ||||||||
\(29\) | −7890.00 | −1.74214 | −0.871068 | − | 0.491163i | \(-0.836572\pi\) | ||||
−0.871068 | + | 0.491163i | \(0.836572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8593.00 | −1.60598 | −0.802991 | − | 0.595991i | \(-0.796759\pi\) | ||||
−0.802991 | + | 0.595991i | \(0.796759\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 1998.00i | 0.319382i | ||||||||
\(34\) | −648.000 | −0.0961342 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | − 8642.00i | − 1.03779i | −0.854838 | − | 0.518896i | \(-0.826343\pi\) | ||||
0.854838 | − | 0.518896i | \(-0.173657\pi\) | |||||||
\(38\) | 6740.00i | 0.757183i | ||||||||
\(39\) | −909.000 | −0.0956979 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18168.0 | −1.68790 | −0.843951 | − | 0.536420i | \(-0.819777\pi\) | ||||
−0.843951 | + | 0.536420i | \(0.819777\pi\) | |||||||
\(42\) | − 1692.00i | − 0.148005i | ||||||||
\(43\) | 14351.0i | 1.18362i | 0.806079 | + | 0.591808i | \(0.201586\pi\) | ||||
−0.806079 | + | 0.591808i | \(0.798414\pi\) | |||||||
\(44\) | −3552.00 | −0.276593 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1224.00 | 0.0852878 | ||||||||
\(47\) | 1098.00i | 0.0725033i | 0.999343 | + | 0.0362516i | \(0.0115418\pi\) | ||||
−0.999343 | + | 0.0362516i | \(0.988458\pi\) | |||||||
\(48\) | 2304.00i | 0.144338i | ||||||||
\(49\) | 14598.0 | 0.868567 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1458.00 | 0.0784932 | ||||||||
\(52\) | − 1616.00i | − 0.0828768i | ||||||||
\(53\) | 17916.0i | 0.876095i | 0.898952 | + | 0.438048i | \(0.144330\pi\) | ||||
−0.898952 | + | 0.438048i | \(0.855670\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3008.00 | 0.128176 | ||||||||
\(57\) | − 15165.0i | − 0.618237i | ||||||||
\(58\) | 31560.0i | 1.23188i | ||||||||
\(59\) | −17610.0 | −0.658612 | −0.329306 | − | 0.944223i | \(-0.606815\pi\) | ||||
−0.329306 | + | 0.944223i | \(0.606815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21853.0 | −0.751946 | −0.375973 | − | 0.926631i | \(-0.622691\pi\) | ||||
−0.375973 | + | 0.926631i | \(0.622691\pi\) | |||||||
\(62\) | 34372.0i | 1.13560i | ||||||||
\(63\) | 3807.00i | 0.120846i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7992.00 | 0.225837 | ||||||||
\(67\) | − 107.000i | − 0.00291204i | −0.999999 | − | 0.00145602i | \(-0.999537\pi\) | ||||
0.999999 | − | 0.00145602i | \(-0.000463465\pi\) | |||||||
\(68\) | 2592.00i | 0.0679771i | ||||||||
\(69\) | −2754.00 | −0.0696372 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −40728.0 | −0.958842 | −0.479421 | − | 0.877585i | \(-0.659153\pi\) | ||||
−0.479421 | + | 0.877585i | \(0.659153\pi\) | |||||||
\(72\) | − 5184.00i | − 0.117851i | ||||||||
\(73\) | 34706.0i | 0.762250i | 0.924524 | + | 0.381125i | \(0.124463\pi\) | ||||
−0.924524 | + | 0.381125i | \(0.875537\pi\) | |||||||
\(74\) | −34568.0 | −0.733829 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26960.0 | 0.535409 | ||||||||
\(77\) | − 10434.0i | − 0.200551i | ||||||||
\(78\) | 3636.00i | 0.0676686i | ||||||||
\(79\) | 69160.0 | 1.24677 | 0.623386 | − | 0.781914i | \(-0.285756\pi\) | ||||
0.623386 | + | 0.781914i | \(0.285756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 72672.0i | 1.19353i | ||||||||
\(83\) | − 108534.i | − 1.72930i | −0.502374 | − | 0.864650i | \(-0.667540\pi\) | ||||
0.502374 | − | 0.864650i | \(-0.332460\pi\) | |||||||
\(84\) | −6768.00 | −0.104656 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57404.0 | 0.836943 | ||||||||
\(87\) | − 71010.0i | − 1.00582i | ||||||||
\(88\) | 14208.0i | 0.195581i | ||||||||
\(89\) | −35040.0 | −0.468910 | −0.234455 | − | 0.972127i | \(-0.575330\pi\) | ||||
−0.234455 | + | 0.972127i | \(0.575330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4747.00 | 0.0600919 | ||||||||
\(92\) | − 4896.00i | − 0.0603076i | ||||||||
\(93\) | − 77337.0i | − 0.927214i | ||||||||
\(94\) | 4392.00 | 0.0512676 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 823.000i | 0.00888118i | 0.999990 | + | 0.00444059i | \(0.00141349\pi\) | ||||
−0.999990 | + | 0.00444059i | \(0.998587\pi\) | |||||||
\(98\) | − 58392.0i | − 0.614169i | ||||||||
\(99\) | −17982.0 | −0.184395 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33828.0 | −0.329969 | −0.164984 | − | 0.986296i | \(-0.552757\pi\) | ||||
−0.164984 | + | 0.986296i | \(0.552757\pi\) | |||||||
\(102\) | − 5832.00i | − 0.0555031i | ||||||||
\(103\) | − 133444.i | − 1.23938i | −0.784845 | − | 0.619692i | \(-0.787257\pi\) | ||||
0.784845 | − | 0.619692i | \(-0.212743\pi\) | |||||||
\(104\) | −6464.00 | −0.0586028 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 71664.0 | 0.619493 | ||||||||
\(107\) | − 81252.0i | − 0.686080i | −0.939321 | − | 0.343040i | \(-0.888543\pi\) | ||||
0.939321 | − | 0.343040i | \(-0.111457\pi\) | |||||||
\(108\) | 11664.0i | 0.0962250i | ||||||||
\(109\) | 217015. | 1.74954 | 0.874769 | − | 0.484540i | \(-0.161013\pi\) | ||||
0.874769 | + | 0.484540i | \(0.161013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 77778.0 | 0.599169 | ||||||||
\(112\) | − 12032.0i | − 0.0906343i | ||||||||
\(113\) | − 138324.i | − 1.01906i | −0.860452 | − | 0.509532i | \(-0.829819\pi\) | ||||
0.860452 | − | 0.509532i | \(-0.170181\pi\) | |||||||
\(114\) | −60660.0 | −0.437160 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 126240. | 0.871068 | ||||||||
\(117\) | − 8181.00i | − 0.0552512i | ||||||||
\(118\) | 70440.0i | 0.465709i | ||||||||
\(119\) | −7614.00 | −0.0492885 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −111767. | −0.693985 | ||||||||
\(122\) | 87412.0i | 0.531706i | ||||||||
\(123\) | − 163512.i | − 0.974511i | ||||||||
\(124\) | 137488. | 0.802991 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15228.0 | 0.0854509 | ||||||||
\(127\) | 256048.i | 1.40868i | 0.709863 | + | 0.704340i | \(0.248757\pi\) | ||||
−0.709863 | + | 0.704340i | \(0.751243\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −129159. | −0.683361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118452. | 0.603065 | 0.301533 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301533 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(132\) | − 31968.0i | − 0.159691i | ||||||||
\(133\) | 79195.0i | 0.388212i | ||||||||
\(134\) | −428.000 | −0.00205912 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10368.0 | 0.0480671 | ||||||||
\(137\) | 13218.0i | 0.0601678i | 0.999547 | + | 0.0300839i | \(0.00957745\pi\) | ||||
−0.999547 | + | 0.0300839i | \(0.990423\pi\) | |||||||
\(138\) | 11016.0i | 0.0492409i | ||||||||
\(139\) | 350740. | 1.53974 | 0.769872 | − | 0.638199i | \(-0.220320\pi\) | ||||
0.769872 | + | 0.638199i | \(0.220320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9882.00 | −0.0418598 | ||||||||
\(142\) | 162912.i | 0.678004i | ||||||||
\(143\) | 22422.0i | 0.0916926i | ||||||||
\(144\) | −20736.0 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 138824. | 0.538992 | ||||||||
\(147\) | 131382.i | 0.501467i | ||||||||
\(148\) | 138272.i | 0.518896i | ||||||||
\(149\) | −109890. | −0.405502 | −0.202751 | − | 0.979230i | \(-0.564988\pi\) | ||||
−0.202751 | + | 0.979230i | \(0.564988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −172603. | −0.616036 | −0.308018 | − | 0.951381i | \(-0.599666\pi\) | ||||
−0.308018 | + | 0.951381i | \(0.599666\pi\) | |||||||
\(152\) | − 107840.i | − 0.378592i | ||||||||
\(153\) | 13122.0i | 0.0453181i | ||||||||
\(154\) | −41736.0 | −0.141811 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14544.0 | 0.0478489 | ||||||||
\(157\) | 349993.i | 1.13321i | 0.823990 | + | 0.566605i | \(0.191743\pi\) | ||||
−0.823990 | + | 0.566605i | \(0.808257\pi\) | |||||||
\(158\) | − 276640.i | − 0.881601i | ||||||||
\(159\) | −161244. | −0.505814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14382.0 | 0.0437275 | ||||||||
\(162\) | − 26244.0i | − 0.0785674i | ||||||||
\(163\) | 192581.i | 0.567733i | 0.958864 | + | 0.283867i | \(0.0916173\pi\) | ||||
−0.958864 | + | 0.283867i | \(0.908383\pi\) | |||||||
\(164\) | 290688. | 0.843951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −434136. | −1.22280 | ||||||||
\(167\) | − 580692.i | − 1.61122i | −0.592447 | − | 0.805610i | \(-0.701838\pi\) | ||||
0.592447 | − | 0.805610i | \(-0.298162\pi\) | |||||||
\(168\) | 27072.0i | 0.0740026i | ||||||||
\(169\) | 361092. | 0.972526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136485. | 0.356940 | ||||||||
\(172\) | − 229616.i | − 0.591808i | ||||||||
\(173\) | 738126.i | 1.87506i | 0.347904 | + | 0.937530i | \(0.386894\pi\) | ||||
−0.347904 | + | 0.937530i | \(0.613106\pi\) | |||||||
\(174\) | −284040. | −0.711224 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 56832.0 | 0.138297 | ||||||||
\(177\) | − 158490.i | − 0.380250i | ||||||||
\(178\) | 140160.i | 0.331569i | ||||||||
\(179\) | −497370. | −1.16024 | −0.580119 | − | 0.814532i | \(-0.696994\pi\) | ||||
−0.580119 | + | 0.814532i | \(0.696994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −333163. | −0.755893 | −0.377947 | − | 0.925827i | \(-0.623370\pi\) | ||||
−0.377947 | + | 0.925827i | \(0.623370\pi\) | |||||||
\(182\) | − 18988.0i | − 0.0424914i | ||||||||
\(183\) | − 196677.i | − 0.434136i | ||||||||
\(184\) | −19584.0 | −0.0426439 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −309348. | −0.655639 | ||||||||
\(187\) | − 35964.0i | − 0.0752080i | ||||||||
\(188\) | − 17568.0i | − 0.0362516i | ||||||||
\(189\) | −34263.0 | −0.0697703 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −40638.0 | −0.0806026 | −0.0403013 | − | 0.999188i | \(-0.512832\pi\) | ||||
−0.0403013 | + | 0.999188i | \(0.512832\pi\) | |||||||
\(192\) | − 36864.0i | − 0.0721688i | ||||||||
\(193\) | 494651.i | 0.955885i | 0.878391 | + | 0.477942i | \(0.158617\pi\) | ||||
−0.878391 | + | 0.477942i | \(0.841383\pi\) | |||||||
\(194\) | 3292.00 | 0.00627994 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −233568. | −0.434283 | ||||||||
\(197\) | − 552342.i | − 1.01401i | −0.861943 | − | 0.507005i | \(-0.830752\pi\) | ||||
0.861943 | − | 0.507005i | \(-0.169248\pi\) | |||||||
\(198\) | 71928.0i | 0.130387i | ||||||||
\(199\) | −685625. | −1.22731 | −0.613655 | − | 0.789575i | \(-0.710301\pi\) | ||||
−0.613655 | + | 0.789575i | \(0.710301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 963.000 | 0.00168126 | ||||||||
\(202\) | 135312.i | 0.233323i | ||||||||
\(203\) | 370830.i | 0.631589i | ||||||||
\(204\) | −23328.0 | −0.0392466 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −533776. | −0.876377 | ||||||||
\(207\) | − 24786.0i | − 0.0402050i | ||||||||
\(208\) | 25856.0i | 0.0414384i | ||||||||
\(209\) | −374070. | −0.592362 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 749477. | 1.15892 | 0.579458 | − | 0.815002i | \(-0.303264\pi\) | ||||
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(212\) | − 286656.i | − 0.438048i | ||||||||
\(213\) | − 366552.i | − 0.553588i | ||||||||
\(214\) | −325008. | −0.485132 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 403871.i | 0.582228i | ||||||||
\(218\) | − 868060.i | − 1.23711i | ||||||||
\(219\) | −312354. | −0.440085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16362.0 | 0.0225349 | ||||||||
\(222\) | − 311112.i | − 0.423676i | ||||||||
\(223\) | 169271.i | 0.227940i | 0.993484 | + | 0.113970i | \(0.0363568\pi\) | ||||
−0.993484 | + | 0.113970i | \(0.963643\pi\) | |||||||
\(224\) | −48128.0 | −0.0640882 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −553296. | −0.720587 | ||||||||
\(227\) | 46488.0i | 0.0598792i | 0.999552 | + | 0.0299396i | \(0.00953150\pi\) | ||||
−0.999552 | + | 0.0299396i | \(0.990468\pi\) | |||||||
\(228\) | 242640.i | 0.309119i | ||||||||
\(229\) | 90115.0 | 0.113556 | 0.0567778 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567778 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 93906.0 | 0.115788 | ||||||||
\(232\) | − 504960.i | − 0.615938i | ||||||||
\(233\) | 1.06414e6i | 1.28413i | 0.766652 | + | 0.642063i | \(0.221921\pi\) | ||||
−0.766652 | + | 0.642063i | \(0.778079\pi\) | |||||||
\(234\) | −32724.0 | −0.0390685 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 281760. | 0.329306 | ||||||||
\(237\) | 622440.i | 0.719825i | ||||||||
\(238\) | 30456.0i | 0.0348522i | ||||||||
\(239\) | −1.15158e6 | −1.30407 | −0.652033 | − | 0.758191i | \(-0.726084\pi\) | ||||
−0.652033 | + | 0.758191i | \(0.726084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 856217. | 0.949601 | 0.474801 | − | 0.880093i | \(-0.342520\pi\) | ||||
0.474801 | + | 0.880093i | \(0.342520\pi\) | |||||||
\(242\) | 447068.i | 0.490722i | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 349648. | 0.375973 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −654048. | −0.689084 | ||||||||
\(247\) | − 170185.i | − 0.177492i | ||||||||
\(248\) | − 549952.i | − 0.567800i | ||||||||
\(249\) | 976806. | 0.998412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −207708. | −0.208098 | −0.104049 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104049 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(252\) | − 60912.0i | − 0.0604229i | ||||||||
\(253\) | 67932.0i | 0.0667226i | ||||||||
\(254\) | 1.02419e6 | 0.996087 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.45319e6i | 1.37243i | 0.727401 | + | 0.686213i | \(0.240728\pi\) | ||||
−0.727401 | + | 0.686213i | \(0.759272\pi\) | |||||||
\(258\) | 516636.i | 0.483209i | ||||||||
\(259\) | −406174. | −0.376238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 639090. | 0.580712 | ||||||||
\(262\) | − 473808.i | − 0.426431i | ||||||||
\(263\) | 169296.i | 0.150924i | 0.997149 | + | 0.0754618i | \(0.0240431\pi\) | ||||
−0.997149 | + | 0.0754618i | \(0.975957\pi\) | |||||||
\(264\) | −127872. | −0.112919 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 316780. | 0.274507 | ||||||||
\(267\) | − 315360.i | − 0.270725i | ||||||||
\(268\) | 1712.00i | 0.00145602i | ||||||||
\(269\) | 1.58109e6 | 1.33222 | 0.666110 | − | 0.745854i | \(-0.267958\pi\) | ||||
0.666110 | + | 0.745854i | \(0.267958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 822512. | 0.680329 | 0.340165 | − | 0.940366i | \(-0.389517\pi\) | ||||
0.340165 | + | 0.940366i | \(0.389517\pi\) | |||||||
\(272\) | − 41472.0i | − 0.0339886i | ||||||||
\(273\) | 42723.0i | 0.0346941i | ||||||||
\(274\) | 52872.0 | 0.0425451 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 44064.0 | 0.0348186 | ||||||||
\(277\) | 546823.i | 0.428201i | 0.976812 | + | 0.214100i | \(0.0686820\pi\) | ||||
−0.976812 | + | 0.214100i | \(0.931318\pi\) | |||||||
\(278\) | − 1.40296e6i | − 1.08876i | ||||||||
\(279\) | 696033. | 0.535327 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09250e6 | −0.825382 | −0.412691 | − | 0.910871i | \(-0.635411\pi\) | ||||
−0.412691 | + | 0.910871i | \(0.635411\pi\) | |||||||
\(282\) | 39528.0i | 0.0295993i | ||||||||
\(283\) | − 2.48480e6i | − 1.84427i | −0.386865 | − | 0.922136i | \(-0.626442\pi\) | ||||
0.386865 | − | 0.922136i | \(-0.373558\pi\) | |||||||
\(284\) | 651648. | 0.479421 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 89688.0 | 0.0648365 | ||||||||
\(287\) | 853896.i | 0.611928i | ||||||||
\(288\) | 82944.0i | 0.0589256i | ||||||||
\(289\) | 1.39361e6 | 0.981516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7407.00 | −0.00512755 | ||||||||
\(292\) | − 555296.i | − 0.381125i | ||||||||
\(293\) | − 341394.i | − 0.232320i | −0.993231 | − | 0.116160i | \(-0.962941\pi\) | ||||
0.993231 | − | 0.116160i | \(-0.0370586\pi\) | |||||||
\(294\) | 525528. | 0.354591 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 553088. | 0.366915 | ||||||||
\(297\) | − 161838.i | − 0.106461i | ||||||||
\(298\) | 439560.i | 0.286733i | ||||||||
\(299\) | −30906.0 | −0.0199924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 674497. | 0.429105 | ||||||||
\(302\) | 690412.i | 0.435603i | ||||||||
\(303\) | − 304452.i | − 0.190508i | ||||||||
\(304\) | −431360. | −0.267705 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 52488.0 | 0.0320447 | ||||||||
\(307\) | − 2.02898e6i | − 1.22866i | −0.789050 | − | 0.614329i | \(-0.789427\pi\) | ||||
0.789050 | − | 0.614329i | \(-0.210573\pi\) | |||||||
\(308\) | 166944.i | 0.100275i | ||||||||
\(309\) | 1.20100e6 | 0.715559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −206598. | −0.121123 | −0.0605613 | − | 0.998164i | \(-0.519289\pi\) | ||||
−0.0605613 | + | 0.998164i | \(0.519289\pi\) | |||||||
\(312\) | − 58176.0i | − 0.0338343i | ||||||||
\(313\) | − 3.34223e6i | − 1.92830i | −0.265352 | − | 0.964152i | \(-0.585488\pi\) | ||||
0.265352 | − | 0.964152i | \(-0.414512\pi\) | |||||||
\(314\) | 1.39997e6 | 0.801300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10656e6 | −0.623386 | ||||||||
\(317\) | 2.53289e6i | 1.41569i | 0.706368 | + | 0.707844i | \(0.250332\pi\) | ||||
−0.706368 | + | 0.707844i | \(0.749668\pi\) | |||||||
\(318\) | 644976.i | 0.357664i | ||||||||
\(319\) | −1.75158e6 | −0.963725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 731268. | 0.396108 | ||||||||
\(322\) | − 57528.0i | − 0.0309200i | ||||||||
\(323\) | 272970.i | 0.145582i | ||||||||
\(324\) | −104976. | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 770324. | 0.401448 | ||||||||
\(327\) | 1.95314e6i | 1.01010i | ||||||||
\(328\) | − 1.16275e6i | − 0.596764i | ||||||||
\(329\) | 51606.0 | 0.0262851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 602132. | 0.302080 | 0.151040 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151040 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(332\) | 1.73654e6i | 0.864650i | ||||||||
\(333\) | 700002.i | 0.345930i | ||||||||
\(334\) | −2.32277e6 | −1.13930 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 108288. | 0.0523278 | ||||||||
\(337\) | − 209777.i | − 0.100620i | −0.998734 | − | 0.0503099i | \(-0.983979\pi\) | ||||
0.998734 | − | 0.0503099i | \(-0.0160209\pi\) | |||||||
\(338\) | − 1.44437e6i | − 0.687680i | ||||||||
\(339\) | 1.24492e6 | 0.588357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90765e6 | −0.888407 | ||||||||
\(342\) | − 545940.i | − 0.252394i | ||||||||
\(343\) | − 1.47603e6i | − 0.677425i | ||||||||
\(344\) | −918464. | −0.418472 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.95250e6 | 1.32587 | ||||||||
\(347\) | − 4.02166e6i | − 1.79301i | −0.443037 | − | 0.896503i | \(-0.646099\pi\) | ||||
0.443037 | − | 0.896503i | \(-0.353901\pi\) | |||||||
\(348\) | 1.13616e6i | 0.502911i | ||||||||
\(349\) | −8330.00 | −0.00366085 | −0.00183042 | − | 0.999998i | \(-0.500583\pi\) | ||||
−0.00183042 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 73629.0 | 0.0318993 | ||||||||
\(352\) | − 227328.i | − 0.0977904i | ||||||||
\(353\) | 1.95001e6i | 0.832912i | 0.909156 | + | 0.416456i | \(0.136728\pi\) | ||||
−0.909156 | + | 0.416456i | \(0.863272\pi\) | |||||||
\(354\) | −633960. | −0.268877 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 560640. | 0.234455 | ||||||||
\(357\) | − 68526.0i | − 0.0284567i | ||||||||
\(358\) | 1.98948e6i | 0.820412i | ||||||||
\(359\) | −2.27088e6 | −0.929947 | −0.464973 | − | 0.885325i | \(-0.653936\pi\) | ||||
−0.464973 | + | 0.885325i | \(0.653936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 363126. | 0.146652 | ||||||||
\(362\) | 1.33265e6i | 0.534497i | ||||||||
\(363\) | − 1.00590e6i | − 0.400673i | ||||||||
\(364\) | −75952.0 | −0.0300459 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −786708. | −0.306981 | ||||||||
\(367\) | − 2.86154e6i | − 1.10901i | −0.832181 | − | 0.554503i | \(-0.812908\pi\) | ||||
0.832181 | − | 0.554503i | \(-0.187092\pi\) | |||||||
\(368\) | 78336.0i | 0.0301538i | ||||||||
\(369\) | 1.47161e6 | 0.562634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 842052. | 0.317617 | ||||||||
\(372\) | 1.23739e6i | 0.463607i | ||||||||
\(373\) | 615311.i | 0.228993i | 0.993424 | + | 0.114497i | \(0.0365255\pi\) | ||||
−0.993424 | + | 0.114497i | \(0.963474\pi\) | |||||||
\(374\) | −143856. | −0.0531801 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −70272.0 | −0.0256338 | ||||||||
\(377\) | − 796890.i | − 0.288765i | ||||||||
\(378\) | 137052.i | 0.0493351i | ||||||||
\(379\) | −5.39878e6 | −1.93062 | −0.965311 | − | 0.261103i | \(-0.915914\pi\) | ||||
−0.965311 | + | 0.261103i | \(0.915914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.30443e6 | −0.813301 | ||||||||
\(382\) | 162552.i | 0.0569946i | ||||||||
\(383\) | 1.08688e6i | 0.378602i | 0.981919 | + | 0.189301i | \(0.0606222\pi\) | ||||
−0.981919 | + | 0.189301i | \(0.939378\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.97860e6 | 0.675913 | ||||||||
\(387\) | − 1.16243e6i | − 0.394539i | ||||||||
\(388\) | − 13168.0i | − 0.00444059i | ||||||||
\(389\) | 3.48432e6 | 1.16747 | 0.583733 | − | 0.811946i | \(-0.301592\pi\) | ||||
0.583733 | + | 0.811946i | \(0.301592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49572.0 | 0.0163981 | ||||||||
\(392\) | 934272.i | 0.307085i | ||||||||
\(393\) | 1.06607e6i | 0.348180i | ||||||||
\(394\) | −2.20937e6 | −0.717014 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 287712. | 0.0921977 | ||||||||
\(397\) | − 3.26591e6i | − 1.03999i | −0.854170 | − | 0.519993i | \(-0.825935\pi\) | ||||
0.854170 | − | 0.519993i | \(-0.174065\pi\) | |||||||
\(398\) | 2.74250e6i | 0.867839i | ||||||||
\(399\) | −712755. | −0.224134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.27319e6 | −1.32706 | −0.663531 | − | 0.748149i | \(-0.730943\pi\) | ||||
−0.663531 | + | 0.748149i | \(0.730943\pi\) | |||||||
\(402\) | − 3852.00i | − 0.00118883i | ||||||||
\(403\) | − 867893.i | − 0.266197i | ||||||||
\(404\) | 541248. | 0.164984 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.48332e6 | 0.446601 | ||||||||
\(407\) | − 1.91852e6i | − 0.574092i | ||||||||
\(408\) | 93312.0i | 0.0277515i | ||||||||
\(409\) | 1.45188e6 | 0.429162 | 0.214581 | − | 0.976706i | \(-0.431161\pi\) | ||||
0.214581 | + | 0.976706i | \(0.431161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −118962. | −0.0347379 | ||||||||
\(412\) | 2.13510e6i | 0.619692i | ||||||||
\(413\) | 827670.i | 0.238771i | ||||||||
\(414\) | −99144.0 | −0.0284293 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 103424. | 0.0293014 | ||||||||
\(417\) | 3.15666e6i | 0.888971i | ||||||||
\(418\) | 1.49628e6i | 0.418863i | ||||||||
\(419\) | −559380. | −0.155658 | −0.0778291 | − | 0.996967i | \(-0.524799\pi\) | ||||
−0.0778291 | + | 0.996967i | \(0.524799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.91470e6 | −1.07645 | −0.538224 | − | 0.842802i | \(-0.680905\pi\) | ||||
−0.538224 | + | 0.842802i | \(0.680905\pi\) | |||||||
\(422\) | − 2.99791e6i | − 0.819478i | ||||||||
\(423\) | − 88938.0i | − 0.0241678i | ||||||||
\(424\) | −1.14662e6 | −0.309746 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.46621e6 | −0.391446 | ||||||||
\(427\) | 1.02709e6i | 0.272608i | ||||||||
\(428\) | 1.30003e6i | 0.343040i | ||||||||
\(429\) | −201798. | −0.0529387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.57500e6 | −0.927006 | −0.463503 | − | 0.886095i | \(-0.653408\pi\) | ||||
−0.463503 | + | 0.886095i | \(0.653408\pi\) | |||||||
\(432\) | − 186624.i | − 0.0481125i | ||||||||
\(433\) | 7.15969e6i | 1.83516i | 0.397548 | + | 0.917581i | \(0.369861\pi\) | ||||
−0.397548 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(434\) | 1.61548e6 | 0.411698 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.47224e6 | −0.874769 | ||||||||
\(437\) | − 515610.i | − 0.129157i | ||||||||
\(438\) | 1.24942e6i | 0.311187i | ||||||||
\(439\) | −1.71790e6 | −0.425437 | −0.212719 | − | 0.977114i | \(-0.568232\pi\) | ||||
−0.212719 | + | 0.977114i | \(0.568232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18244e6 | −0.289522 | ||||||||
\(442\) | − 65448.0i | − 0.0159346i | ||||||||
\(443\) | 3.39670e6i | 0.822332i | 0.911560 | + | 0.411166i | \(0.134878\pi\) | ||||
−0.911560 | + | 0.411166i | \(0.865122\pi\) | |||||||
\(444\) | −1.24445e6 | −0.299584 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 677084. | 0.161178 | ||||||||
\(447\) | − 989010.i | − 0.234116i | ||||||||
\(448\) | 192512.i | 0.0453172i | ||||||||
\(449\) | 3.39606e6 | 0.794986 | 0.397493 | − | 0.917605i | \(-0.369880\pi\) | ||||
0.397493 | + | 0.917605i | \(0.369880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.03330e6 | −0.933724 | ||||||||
\(452\) | 2.21318e6i | 0.509532i | ||||||||
\(453\) | − 1.55343e6i | − 0.355668i | ||||||||
\(454\) | 185952. | 0.0423410 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 970560. | 0.218580 | ||||||||
\(457\) | 4.52814e6i | 1.01421i | 0.861883 | + | 0.507106i | \(0.169285\pi\) | ||||
−0.861883 | + | 0.507106i | \(0.830715\pi\) | |||||||
\(458\) | − 360460.i | − 0.0802959i | ||||||||
\(459\) | −118098. | −0.0261644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.27895e6 | −0.280285 | −0.140143 | − | 0.990131i | \(-0.544756\pi\) | ||||
−0.140143 | + | 0.990131i | \(0.544756\pi\) | |||||||
\(462\) | − 375624.i | − 0.0818744i | ||||||||
\(463\) | − 7.19862e6i | − 1.56062i | −0.625393 | − | 0.780310i | \(-0.715061\pi\) | ||||
0.625393 | − | 0.780310i | \(-0.284939\pi\) | |||||||
\(464\) | −2.01984e6 | −0.435534 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.25654e6 | 0.908014 | ||||||||
\(467\) | − 4.83034e6i | − 1.02491i | −0.858714 | − | 0.512455i | \(-0.828736\pi\) | ||||
0.858714 | − | 0.512455i | \(-0.171264\pi\) | |||||||
\(468\) | 130896.i | 0.0276256i | ||||||||
\(469\) | −5029.00 | −0.00105572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.14994e6 | −0.654259 | ||||||||
\(472\) | − 1.12704e6i | − 0.232854i | ||||||||
\(473\) | 3.18592e6i | 0.654760i | ||||||||
\(474\) | 2.48976e6 | 0.508993 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 121824. | 0.0246442 | ||||||||
\(477\) | − 1.45120e6i | − 0.292032i | ||||||||
\(478\) | 4.60632e6i | 0.922113i | ||||||||
\(479\) | −748650. | −0.149087 | −0.0745435 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745435 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 872842. | 0.172018 | ||||||||
\(482\) | − 3.42487e6i | − 0.671469i | ||||||||
\(483\) | 129438.i | 0.0252461i | ||||||||
\(484\) | 1.78827e6 | 0.346993 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 5.16394e6i | 0.986641i | 0.869848 | + | 0.493320i | \(0.164217\pi\) | ||||
−0.869848 | + | 0.493320i | \(0.835783\pi\) | |||||||
\(488\) | − 1.39859e6i | − 0.265853i | ||||||||
\(489\) | −1.73323e6 | −0.327781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.54287e6 | 1.59919 | 0.799595 | − | 0.600539i | \(-0.205047\pi\) | ||||
0.799595 | + | 0.600539i | \(0.205047\pi\) | |||||||
\(492\) | 2.61619e6i | 0.487256i | ||||||||
\(493\) | 1.27818e6i | 0.236851i | ||||||||
\(494\) | −680740. | −0.125506 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.19981e6 | −0.401495 | ||||||||
\(497\) | 1.91422e6i | 0.347616i | ||||||||
\(498\) | − 3.90722e6i | − 0.705984i | ||||||||
\(499\) | 4.20588e6 | 0.756145 | 0.378072 | − | 0.925776i | \(-0.376587\pi\) | ||||
0.378072 | + | 0.925776i | \(0.376587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.22623e6 | 0.930238 | ||||||||
\(502\) | 830832.i | 0.147148i | ||||||||
\(503\) | − 8.18342e6i | − 1.44217i | −0.692849 | − | 0.721083i | \(-0.743645\pi\) | ||||
0.692849 | − | 0.721083i | \(-0.256355\pi\) | |||||||
\(504\) | −243648. | −0.0427254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 271728. | 0.0471800 | ||||||||
\(507\) | 3.24983e6i | 0.561488i | ||||||||
\(508\) | − 4.09677e6i | − 0.704340i | ||||||||
\(509\) | −3.85923e6 | −0.660247 | −0.330123 | − | 0.943938i | \(-0.607090\pi\) | ||||
−0.330123 | + | 0.943938i | \(0.607090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63118e6 | 0.276344 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 1.22837e6i | 0.206079i | ||||||||
\(514\) | 5.81275e6 | 0.970452 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.06654e6 | 0.341681 | ||||||||
\(517\) | 243756.i | 0.0401078i | ||||||||
\(518\) | 1.62470e6i | 0.266040i | ||||||||
\(519\) | −6.64313e6 | −1.08257 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.55410e6 | 0.735036 | 0.367518 | − | 0.930016i | \(-0.380208\pi\) | ||||
0.367518 | + | 0.930016i | \(0.380208\pi\) | |||||||
\(522\) | − 2.55636e6i | − 0.410625i | ||||||||
\(523\) | 4.82224e6i | 0.770894i | 0.922730 | + | 0.385447i | \(0.125953\pi\) | ||||
−0.922730 | + | 0.385447i | \(0.874047\pi\) | |||||||
\(524\) | −1.89523e6 | −0.301533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 677184. | 0.106719 | ||||||||
\(527\) | 1.39207e6i | 0.218340i | ||||||||
\(528\) | 511488.i | 0.0798455i | ||||||||
\(529\) | 6.34271e6 | 0.985452 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.42641e6 | 0.219537 | ||||||||
\(532\) | − 1.26712e6i | − 0.194106i | ||||||||
\(533\) | − 1.83497e6i | − 0.279776i | ||||||||
\(534\) | −1.26144e6 | −0.191432 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6848.00 | 0.00102956 | ||||||||
\(537\) | − 4.47633e6i | − 0.669864i | ||||||||
\(538\) | − 6.32436e6i | − 0.942022i | ||||||||
\(539\) | 3.24076e6 | 0.480479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 362537. | 0.0532549 | 0.0266274 | − | 0.999645i | \(-0.491523\pi\) | ||||
0.0266274 | + | 0.999645i | \(0.491523\pi\) | |||||||
\(542\) | − 3.29005e6i | − 0.481065i | ||||||||
\(543\) | − 2.99847e6i | − 0.436415i | ||||||||
\(544\) | −165888. | −0.0240335 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 170892. | 0.0245324 | ||||||||
\(547\) | − 3.11439e6i | − 0.445046i | −0.974927 | − | 0.222523i | \(-0.928571\pi\) | ||||
0.974927 | − | 0.222523i | \(-0.0714293\pi\) | |||||||
\(548\) | − 211488.i | − 0.0300839i | ||||||||
\(549\) | 1.77009e6 | 0.250649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.32947e7 | 1.86551 | ||||||||
\(552\) | − 176256.i | − 0.0246205i | ||||||||
\(553\) | − 3.25052e6i | − 0.452002i | ||||||||
\(554\) | 2.18729e6 | 0.302784 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.61184e6 | −0.769872 | ||||||||
\(557\) | 7.99304e6i | 1.09163i | 0.837907 | + | 0.545813i | \(0.183779\pi\) | ||||
−0.837907 | + | 0.545813i | \(0.816221\pi\) | |||||||
\(558\) | − 2.78413e6i | − 0.378534i | ||||||||
\(559\) | −1.44945e6 | −0.196189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 323676. | 0.0434214 | ||||||||
\(562\) | 4.36999e6i | 0.583633i | ||||||||
\(563\) | − 1.23236e7i | − 1.63857i | −0.573385 | − | 0.819286i | \(-0.694370\pi\) | ||||
0.573385 | − | 0.819286i | \(-0.305630\pi\) | |||||||
\(564\) | 158112. | 0.0209299 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.93920e6 | −1.30410 | ||||||||
\(567\) | − 308367.i | − 0.0402819i | ||||||||
\(568\) | − 2.60659e6i | − 0.339002i | ||||||||
\(569\) | −1.01364e7 | −1.31252 | −0.656258 | − | 0.754537i | \(-0.727862\pi\) | ||||
−0.656258 | + | 0.754537i | \(0.727862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.53084e6 | 0.838260 | 0.419130 | − | 0.907926i | \(-0.362335\pi\) | ||||
0.419130 | + | 0.907926i | \(0.362335\pi\) | |||||||
\(572\) | − 358752.i | − 0.0458463i | ||||||||
\(573\) | − 365742.i | − 0.0465359i | ||||||||
\(574\) | 3.41558e6 | 0.432698 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 1.24453e6i | 0.155621i | 0.996968 | + | 0.0778103i | \(0.0247928\pi\) | ||||
−0.996968 | + | 0.0778103i | \(0.975207\pi\) | |||||||
\(578\) | − 5.57445e6i | − 0.694037i | ||||||||
\(579\) | −4.45186e6 | −0.551880 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.10110e6 | −0.626936 | ||||||||
\(582\) | 29628.0i | 0.00362573i | ||||||||
\(583\) | 3.97735e6i | 0.484644i | ||||||||
\(584\) | −2.22118e6 | −0.269496 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.36558e6 | −0.164275 | ||||||||
\(587\) | 1.33403e6i | 0.159797i | 0.996803 | + | 0.0798987i | \(0.0254597\pi\) | ||||
−0.996803 | + | 0.0798987i | \(0.974540\pi\) | |||||||
\(588\) | − 2.10211e6i | − 0.250734i | ||||||||
\(589\) | 1.44792e7 | 1.71972 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.97108e6 | 0.585439 | ||||||||
\(592\) | − 2.21235e6i | − 0.259448i | ||||||||
\(593\) | − 1.19401e7i | − 1.39435i | −0.716899 | − | 0.697177i | \(-0.754439\pi\) | ||||
0.716899 | − | 0.697177i | \(-0.245561\pi\) | |||||||
\(594\) | −647352. | −0.0752791 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.75824e6 | 0.202751 | ||||||||
\(597\) | − 6.17062e6i | − 0.708587i | ||||||||
\(598\) | 123624.i | 0.0141368i | ||||||||
\(599\) | 7.16430e6 | 0.815843 | 0.407922 | − | 0.913017i | \(-0.366254\pi\) | ||||
0.407922 | + | 0.913017i | \(0.366254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.15163e6 | 0.130055 | 0.0650273 | − | 0.997883i | \(-0.479287\pi\) | ||||
0.0650273 | + | 0.997883i | \(0.479287\pi\) | |||||||
\(602\) | − 2.69799e6i | − 0.303423i | ||||||||
\(603\) | 8667.00i | 0 0.000970679i | ||||||||
\(604\) | 2.76165e6 | 0.308018 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.21781e6 | −0.134709 | ||||||||
\(607\) | 1.34268e7i | 1.47911i | 0.673097 | + | 0.739554i | \(0.264963\pi\) | ||||
−0.673097 | + | 0.739554i | \(0.735037\pi\) | |||||||
\(608\) | 1.72544e6i | 0.189296i | ||||||||
\(609\) | −3.33747e6 | −0.364648 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −110898. | −0.0120177 | ||||||||
\(612\) | − 209952.i | − 0.0226590i | ||||||||
\(613\) | 1.20184e7i | 1.29180i | 0.763422 | + | 0.645900i | \(0.223518\pi\) | ||||
−0.763422 | + | 0.645900i | \(0.776482\pi\) | |||||||
\(614\) | −8.11591e6 | −0.868793 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 667776. | 0.0709054 | ||||||||
\(617\) | 6.98519e6i | 0.738695i | 0.929291 | + | 0.369348i | \(0.120419\pi\) | ||||
−0.929291 | + | 0.369348i | \(0.879581\pi\) | |||||||
\(618\) | − 4.80398e6i | − 0.505977i | ||||||||
\(619\) | 8.20625e6 | 0.860832 | 0.430416 | − | 0.902631i | \(-0.358367\pi\) | ||||
0.430416 | + | 0.902631i | \(0.358367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 223074. | 0.0232124 | ||||||||
\(622\) | 826392.i | 0.0856466i | ||||||||
\(623\) | 1.64688e6i | 0.169997i | ||||||||
\(624\) | −232704. | −0.0239245 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.33689e7 | −1.36352 | ||||||||
\(627\) | − 3.36663e6i | − 0.342000i | ||||||||
\(628\) | − 5.59989e6i | − 0.566605i | ||||||||
\(629\) | −1.40000e6 | −0.141092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.07686e7 | −1.07668 | −0.538338 | − | 0.842729i | \(-0.680947\pi\) | ||||
−0.538338 | + | 0.842729i | \(0.680947\pi\) | |||||||
\(632\) | 4.42624e6i | 0.440801i | ||||||||
\(633\) | 6.74529e6i | 0.669101i | ||||||||
\(634\) | 1.01316e7 | 1.00104 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.57990e6 | 0.252907 | ||||||||
\(637\) | 1.47440e6i | 0.143968i | ||||||||
\(638\) | 7.00632e6i | 0.681457i | ||||||||
\(639\) | 3.29897e6 | 0.319614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.92571e7 | 1.85117 | 0.925585 | − | 0.378539i | \(-0.123573\pi\) | ||||
0.925585 | + | 0.378539i | \(0.123573\pi\) | |||||||
\(642\) | − 2.92507e6i | − 0.280091i | ||||||||
\(643\) | 1.00999e7i | 0.963364i | 0.876346 | + | 0.481682i | \(0.159974\pi\) | ||||
−0.876346 | + | 0.481682i | \(0.840026\pi\) | |||||||
\(644\) | −230112. | −0.0218637 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.09188e6 | 0.102942 | ||||||||
\(647\) | − 7.52113e6i | − 0.706354i | −0.935556 | − | 0.353177i | \(-0.885101\pi\) | ||||
0.935556 | − | 0.353177i | \(-0.114899\pi\) | |||||||
\(648\) | 419904.i | 0.0392837i | ||||||||
\(649\) | −3.90942e6 | −0.364335 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.63484e6 | −0.336150 | ||||||||
\(652\) | − 3.08130e6i | − 0.283867i | ||||||||
\(653\) | − 2.67197e6i | − 0.245216i | −0.992455 | − | 0.122608i | \(-0.960874\pi\) | ||||
0.992455 | − | 0.122608i | \(-0.0391258\pi\) | |||||||
\(654\) | 7.81254e6 | 0.714246 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.65101e6 | −0.421976 | ||||||||
\(657\) | − 2.81119e6i | − 0.254083i | ||||||||
\(658\) | − 206424.i | − 0.0185864i | ||||||||
\(659\) | −6.99948e6 | −0.627845 | −0.313922 | − | 0.949449i | \(-0.601643\pi\) | ||||
−0.313922 | + | 0.949449i | \(0.601643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 408122. | 0.0363318 | 0.0181659 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181659 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(662\) | − 2.40853e6i | − 0.213603i | ||||||||
\(663\) | 147258.i | 0.0130105i | ||||||||
\(664\) | 6.94618e6 | 0.611400 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.80001e6 | 0.244610 | ||||||||
\(667\) | − 2.41434e6i | − 0.210128i | ||||||||
\(668\) | 9.29107e6i | 0.805610i | ||||||||
\(669\) | −1.52344e6 | −0.131601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.85137e6 | −0.415966 | ||||||||
\(672\) | − 433152.i | − 0.0370013i | ||||||||
\(673\) | 1.74939e7i | 1.48885i | 0.667709 | + | 0.744423i | \(0.267275\pi\) | ||||
−0.667709 | + | 0.744423i | \(0.732725\pi\) | |||||||
\(674\) | −839108. | −0.0711489 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.77747e6 | −0.486263 | ||||||||
\(677\) | 8.67440e6i | 0.727391i | 0.931518 | + | 0.363695i | \(0.118485\pi\) | ||||
−0.931518 | + | 0.363695i | \(0.881515\pi\) | |||||||
\(678\) | − 4.97966e6i | − 0.416031i | ||||||||
\(679\) | 38681.0 | 0.00321976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −418392. | −0.0345713 | ||||||||
\(682\) | 7.63058e6i | 0.628198i | ||||||||
\(683\) | 1.18478e7i | 0.971822i | 0.874008 | + | 0.485911i | \(0.161512\pi\) | ||||
−0.874008 | + | 0.485911i | \(0.838488\pi\) | |||||||
\(684\) | −2.18376e6 | −0.178470 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.90414e6 | −0.479012 | ||||||||
\(687\) | 811035.i | 0.0655613i | ||||||||
\(688\) | 3.67386e6i | 0.295904i | ||||||||
\(689\) | −1.80952e6 | −0.145216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.47775e6 | 0.755110 | 0.377555 | − | 0.925987i | \(-0.376765\pi\) | ||||
0.377555 | + | 0.925987i | \(0.376765\pi\) | |||||||
\(692\) | − 1.18100e7i | − 0.937530i | ||||||||
\(693\) | 845154.i | 0.0668502i | ||||||||
\(694\) | −1.60866e7 | −1.26785 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.54464e6 | 0.355612 | ||||||||
\(697\) | 2.94322e6i | 0.229478i | ||||||||
\(698\) | 33320.0i | 0.00258861i | ||||||||
\(699\) | −9.57722e6 | −0.741390 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.28147e7 | −1.75355 | −0.876777 | − | 0.480898i | \(-0.840311\pi\) | ||||
−0.876777 | + | 0.480898i | \(0.840311\pi\) | |||||||
\(702\) | − 294516.i | − 0.0225562i | ||||||||
\(703\) | 1.45618e7i | 1.11129i | ||||||||
\(704\) | −909312. | −0.0691483 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.80002e6 | 0.588958 | ||||||||
\(707\) | 1.58992e6i | 0.119626i | ||||||||
\(708\) | 2.53584e6i | 0.190125i | ||||||||
\(709\) | −1.27436e7 | −0.952090 | −0.476045 | − | 0.879421i | \(-0.657930\pi\) | ||||
−0.476045 | + | 0.879421i | \(0.657930\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.60196e6 | −0.415591 | ||||||||
\(712\) | − 2.24256e6i | − 0.165785i | ||||||||
\(713\) | − 2.62946e6i | − 0.193706i | ||||||||
\(714\) | −274104. | −0.0201219 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.95792e6 | 0.580119 | ||||||||
\(717\) | − 1.03642e7i | − 0.752902i | ||||||||
\(718\) | 9.08352e6i | 0.657572i | ||||||||
\(719\) | −2.44929e6 | −0.176692 | −0.0883462 | − | 0.996090i | \(-0.528158\pi\) | ||||
−0.0883462 | + | 0.996090i | \(0.528158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.27187e6 | −0.449323 | ||||||||
\(722\) | − 1.45250e6i | − 0.103699i | ||||||||
\(723\) | 7.70595e6i | 0.548252i | ||||||||
\(724\) | 5.33061e6 | 0.377947 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.02361e6 | −0.283318 | ||||||||
\(727\) | 415033.i | 0.0291237i | 0.999894 | + | 0.0145619i | \(0.00463535\pi\) | ||||
−0.999894 | + | 0.0145619i | \(0.995365\pi\) | |||||||
\(728\) | 303808.i | 0.0212457i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32486e6 | 0.160918 | ||||||||
\(732\) | 3.14683e6i | 0.217068i | ||||||||
\(733\) | − 1.72877e7i | − 1.18844i | −0.804302 | − | 0.594221i | \(-0.797461\pi\) | ||||
0.804302 | − | 0.594221i | \(-0.202539\pi\) | |||||||
\(734\) | −1.14461e7 | −0.784186 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 313344. | 0.0213219 | ||||||||
\(737\) | − 23754.0i | − 0.00161090i | ||||||||
\(738\) | − 5.88643e6i | − 0.397843i | ||||||||
\(739\) | −5.18834e6 | −0.349476 | −0.174738 | − | 0.984615i | \(-0.555908\pi\) | ||||
−0.174738 | + | 0.984615i | \(0.555908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.53166e6 | 0.102475 | ||||||||
\(742\) | − 3.36821e6i | − 0.224589i | ||||||||
\(743\) | 4.79572e6i | 0.318700i | 0.987222 | + | 0.159350i | \(0.0509398\pi\) | ||||
−0.987222 | + | 0.159350i | \(0.949060\pi\) | |||||||
\(744\) | 4.94957e6 | 0.327820 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.46124e6 | 0.161923 | ||||||||
\(747\) | 8.79125e6i | 0.576434i | ||||||||
\(748\) | 575424.i | 0.0376040i | ||||||||
\(749\) | −3.81884e6 | −0.248730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.85654e7 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705066\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705066\pi\) | |||||||
\(752\) | 281088.i | 0.0181258i | ||||||||
\(753\) | − 1.86937e6i | − 0.120146i | ||||||||
\(754\) | −3.18756e6 | −0.204188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 548208. | 0.0348852 | ||||||||
\(757\) | − 2.82068e7i | − 1.78902i | −0.447053 | − | 0.894508i | \(-0.647526\pi\) | ||||
0.447053 | − | 0.894508i | \(-0.352474\pi\) | |||||||
\(758\) | 2.15951e7i | 1.36516i | ||||||||
\(759\) | −611388. | −0.0385223 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.56161e6 | 0.410723 | 0.205361 | − | 0.978686i | \(-0.434163\pi\) | ||||
0.205361 | + | 0.978686i | \(0.434163\pi\) | |||||||
\(762\) | 9.21773e6i | 0.575091i | ||||||||
\(763\) | − 1.01997e7i | − 0.634273i | ||||||||
\(764\) | 650208. | 0.0403013 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.34750e6 | 0.267712 | ||||||||
\(767\) | − 1.77861e6i | − 0.109167i | ||||||||
\(768\) | 589824.i | 0.0360844i | ||||||||
\(769\) | −2.20930e7 | −1.34722 | −0.673610 | − | 0.739087i | \(-0.735257\pi\) | ||||
−0.673610 | + | 0.739087i | \(0.735257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.30787e7 | −0.792371 | ||||||||
\(772\) | − 7.91442e6i | − 0.477942i | ||||||||
\(773\) | − 3.00787e7i | − 1.81055i | −0.424824 | − | 0.905276i | \(-0.639664\pi\) | ||||
0.424824 | − | 0.905276i | \(-0.360336\pi\) | |||||||
\(774\) | −4.64972e6 | −0.278981 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −52672.0 | −0.00313997 | ||||||||
\(777\) | − 3.65557e6i | − 0.217221i | ||||||||
\(778\) | − 1.39373e7i | − 0.825523i | ||||||||
\(779\) | 3.06131e7 | 1.80744 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.04162e6 | −0.530418 | ||||||||
\(782\) | − 198288.i | − 0.0115952i | ||||||||
\(783\) | 5.75181e6i | 0.335274i | ||||||||
\(784\) | 3.73709e6 | 0.217142 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.26427e6 | 0.246200 | ||||||||
\(787\) | 3.28954e6i | 0.189321i | 0.995510 | + | 0.0946605i | \(0.0301766\pi\) | ||||
−0.995510 | + | 0.0946605i | \(0.969823\pi\) | |||||||
\(788\) | 8.83747e6i | 0.507005i | ||||||||
\(789\) | −1.52366e6 | −0.0871358 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.50123e6 | −0.369449 | ||||||||
\(792\) | − 1.15085e6i | − 0.0651936i | ||||||||
\(793\) | − 2.20715e6i | − 0.124638i | ||||||||
\(794\) | −1.30636e7 | −0.735381 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.09700e7 | 0.613655 | ||||||||
\(797\) | − 6.71053e6i | − 0.374206i | −0.982340 | − | 0.187103i | \(-0.940090\pi\) | ||||
0.982340 | − | 0.187103i | \(-0.0599099\pi\) | |||||||
\(798\) | 2.85102e6i | 0.158487i | ||||||||
\(799\) | 177876. | 0.00985713 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.83824e6 | 0.156303 | ||||||||
\(802\) | 1.70928e7i | 0.938374i | ||||||||
\(803\) | 7.70473e6i | 0.421666i | ||||||||
\(804\) | −15408.0 | −0.000840632 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.47157e6 | −0.188230 | ||||||||
\(807\) | 1.42298e7i | 0.769157i | ||||||||
\(808\) | − 2.16499e6i | − 0.116662i | ||||||||
\(809\) | −8.74254e6 | −0.469641 | −0.234821 | − | 0.972039i | \(-0.575450\pi\) | ||||
−0.234821 | + | 0.972039i | \(0.575450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.48410e7 | −1.32622 | −0.663112 | − | 0.748520i | \(-0.730765\pi\) | ||||
−0.663112 | + | 0.748520i | \(0.730765\pi\) | |||||||
\(812\) | − 5.93328e6i | − 0.315795i | ||||||||
\(813\) | 7.40261e6i | 0.392788i | ||||||||
\(814\) | −7.67410e6 | −0.405944 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 373248. | 0.0196233 | ||||||||
\(817\) | − 2.41814e7i | − 1.26744i | ||||||||
\(818\) | − 5.80750e6i | − 0.303463i | ||||||||
\(819\) | −384507. | −0.0200306 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.12219e7 | 1.09882 | 0.549409 | − | 0.835554i | \(-0.314853\pi\) | ||||
0.549409 | + | 0.835554i | \(0.314853\pi\) | |||||||
\(822\) | 475848.i | 0.0245634i | ||||||||
\(823\) | − 8.70659e6i | − 0.448073i | −0.974581 | − | 0.224036i | \(-0.928077\pi\) | ||||
0.974581 | − | 0.224036i | \(-0.0719234\pi\) | |||||||
\(824\) | 8.54042e6 | 0.438189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.31068e6 | 0.168837 | ||||||||
\(827\) | − 3.71184e7i | − 1.88723i | −0.331040 | − | 0.943617i | \(-0.607400\pi\) | ||||
0.331040 | − | 0.943617i | \(-0.392600\pi\) | |||||||
\(828\) | 396576.i | 0.0201025i | ||||||||
\(829\) | −1.01765e6 | −0.0514295 | −0.0257147 | − | 0.999669i | \(-0.508186\pi\) | ||||
−0.0257147 | + | 0.999669i | \(0.508186\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.92141e6 | −0.247222 | ||||||||
\(832\) | − 413696.i | − 0.0207192i | ||||||||
\(833\) | − 2.36488e6i | − 0.118085i | ||||||||
\(834\) | 1.26266e7 | 0.628598 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.98512e6 | 0.296181 | ||||||||
\(837\) | 6.26430e6i | 0.309071i | ||||||||
\(838\) | 2.23752e6i | 0.110067i | ||||||||
\(839\) | 3.36194e7 | 1.64887 | 0.824433 | − | 0.565960i | \(-0.191494\pi\) | ||||
0.824433 | + | 0.565960i | \(0.191494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.17410e7 | 2.03504 | ||||||||
\(842\) | 1.56588e7i | 0.761164i | ||||||||
\(843\) | − 9.83248e6i | − 0.476534i | ||||||||
\(844\) | −1.19916e7 | −0.579458 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −355752. | −0.0170892 | ||||||||
\(847\) | 5.25305e6i | 0.251596i | ||||||||
\(848\) | 4.58650e6i | 0.219024i | ||||||||
\(849\) | 2.23632e7 | 1.06479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.64445e6 | 0.125173 | ||||||||
\(852\) | 5.86483e6i | 0.276794i | ||||||||
\(853\) | − 3.52574e7i | − 1.65912i | −0.558419 | − | 0.829559i | \(-0.688592\pi\) | ||||
0.558419 | − | 0.829559i | \(-0.311408\pi\) | |||||||
\(854\) | 4.10836e6 | 0.192763 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.20013e6 | 0.242566 | ||||||||
\(857\) | 3.14941e7i | 1.46480i | 0.680877 | + | 0.732398i | \(0.261599\pi\) | ||||
−0.680877 | + | 0.732398i | \(0.738401\pi\) | |||||||
\(858\) | 807192.i | 0.0374333i | ||||||||
\(859\) | −1.19344e7 | −0.551848 | −0.275924 | − | 0.961180i | \(-0.588984\pi\) | ||||
−0.275924 | + | 0.961180i | \(0.588984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.68506e6 | −0.353297 | ||||||||
\(862\) | 1.43000e7i | 0.655492i | ||||||||
\(863\) | 8.70442e6i | 0.397844i | 0.980015 | + | 0.198922i | \(0.0637440\pi\) | ||||
−0.980015 | + | 0.198922i | \(0.936256\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.86388e7 | 1.29766 | ||||||||
\(867\) | 1.25425e7i | 0.566679i | ||||||||
\(868\) | − 6.46194e6i | − 0.291114i | ||||||||
\(869\) | 1.53535e7 | 0.689697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10807.0 | 0.000482681 0 | ||||||||
\(872\) | 1.38890e7i | 0.618555i | ||||||||
\(873\) | − 66663.0i | − 0.00296039i | ||||||||
\(874\) | −2.06244e6 | −0.0913277 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.99766e6 | 0.220043 | ||||||||
\(877\) | − 1.17999e7i | − 0.518059i | −0.965869 | − | 0.259029i | \(-0.916597\pi\) | ||||
0.965869 | − | 0.259029i | \(-0.0834026\pi\) | |||||||
\(878\) | 6.87158e6i | 0.300829i | ||||||||
\(879\) | 3.07255e6 | 0.134130 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.73840e7 | −1.18866 | −0.594330 | − | 0.804221i | \(-0.702583\pi\) | ||||
−0.594330 | + | 0.804221i | \(0.702583\pi\) | |||||||
\(882\) | 4.72975e6i | 0.204723i | ||||||||
\(883\) | − 8.80577e6i | − 0.380072i | −0.981777 | − | 0.190036i | \(-0.939140\pi\) | ||||
0.981777 | − | 0.190036i | \(-0.0608604\pi\) | |||||||
\(884\) | −261792. | −0.0112675 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.35868e7 | 0.581477 | ||||||||
\(887\) | − 250122.i | − 0.0106744i | −0.999986 | − | 0.00533719i | \(-0.998301\pi\) | ||||
0.999986 | − | 0.00533719i | \(-0.00169889\pi\) | |||||||
\(888\) | 4.97779e6i | 0.211838i | ||||||||
\(889\) | 1.20343e7 | 0.510699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45654e6 | 0.0614651 | ||||||||
\(892\) | − 2.70834e6i | − 0.113970i | ||||||||
\(893\) | − 1.85013e6i | − 0.0776379i | ||||||||
\(894\) | −3.95604e6 | −0.165545 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 770048. | 0.0320441 | ||||||||
\(897\) | − 278154.i | − 0.0115426i | ||||||||
\(898\) | − 1.35842e7i | − 0.562140i | ||||||||
\(899\) | 6.77988e7 | 2.79784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.90239e6 | 0.119109 | ||||||||
\(902\) | 1.61332e7i | 0.660243i | ||||||||
\(903\) | 6.07047e6i | 0.247744i | ||||||||
\(904\) | 8.85274e6 | 0.360294 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.21371e6 | −0.251496 | ||||||||
\(907\) | 3.24955e7i | 1.31161i | 0.754929 | + | 0.655806i | \(0.227671\pi\) | ||||
−0.754929 | + | 0.655806i | \(0.772329\pi\) | |||||||
\(908\) | − 743808.i | − 0.0299396i | ||||||||
\(909\) | 2.74007e6 | 0.109990 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24595e7 | 1.69504 | 0.847518 | − | 0.530766i | \(-0.178096\pi\) | ||||
0.847518 | + | 0.530766i | \(0.178096\pi\) | |||||||
\(912\) | − 3.88224e6i | − 0.154559i | ||||||||
\(913\) | − 2.40945e7i | − 0.956625i | ||||||||
\(914\) | 1.81126e7 | 0.717157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.44184e6 | −0.0567778 | ||||||||
\(917\) | − 5.56724e6i | − 0.218634i | ||||||||
\(918\) | 472392.i | 0.0185010i | ||||||||
\(919\) | −1.41629e7 | −0.553176 | −0.276588 | − | 0.960989i | \(-0.589204\pi\) | ||||
−0.276588 | + | 0.960989i | \(0.589204\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.82608e7 | 0.709366 | ||||||||
\(922\) | 5.11579e6i | 0.198192i | ||||||||
\(923\) | − 4.11353e6i | − 0.158932i | ||||||||
\(924\) | −1.50250e6 | −0.0578940 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.87945e7 | −1.10352 | ||||||||
\(927\) | 1.08090e7i | 0.413128i | ||||||||
\(928\) | 8.07936e6i | 0.307969i | ||||||||
\(929\) | −4.37292e7 | −1.66239 | −0.831194 | − | 0.555982i | \(-0.812342\pi\) | ||||
−0.831194 | + | 0.555982i | \(0.812342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.45976e7 | −0.930077 | ||||||||
\(932\) | − 1.70262e7i | − 0.642063i | ||||||||
\(933\) | − 1.85938e6i | − 0.0699302i | ||||||||
\(934\) | −1.93214e7 | −0.724721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 523584. | 0.0195343 | ||||||||
\(937\) | − 5.73509e6i | − 0.213398i | −0.994291 | − | 0.106699i | \(-0.965972\pi\) | ||||
0.994291 | − | 0.106699i | \(-0.0340282\pi\) | |||||||
\(938\) | 20116.0i | 0 0.000746508i | ||||||||
\(939\) | 3.00801e7 | 1.11331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.37395e7 | −1.24212 | −0.621061 | − | 0.783762i | \(-0.713298\pi\) | ||||
−0.621061 | + | 0.783762i | \(0.713298\pi\) | |||||||
\(942\) | 1.25997e7i | 0.462631i | ||||||||
\(943\) | − 5.55941e6i | − 0.203587i | ||||||||
\(944\) | −4.50816e6 | −0.164653 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.27437e7 | 0.462985 | ||||||||
\(947\) | 3.07342e7i | 1.11365i | 0.830631 | + | 0.556823i | \(0.187980\pi\) | ||||
−0.830631 | + | 0.556823i | \(0.812020\pi\) | |||||||
\(948\) | − 9.95904e6i | − 0.359912i | ||||||||
\(949\) | −3.50531e6 | −0.126346 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.27960e7 | −0.817348 | ||||||||
\(952\) | − 487296.i | − 0.0174261i | ||||||||
\(953\) | − 2.51847e7i | − 0.898264i | −0.893465 | − | 0.449132i | \(-0.851733\pi\) | ||||
0.893465 | − | 0.449132i | \(-0.148267\pi\) | |||||||
\(954\) | −5.80478e6 | −0.206498 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.84253e7 | 0.652033 | ||||||||
\(957\) | − 1.57642e7i | − 0.556407i | ||||||||
\(958\) | 2.99460e6i | 0.105420i | ||||||||
\(959\) | 621246. | 0.0218131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.52105e7 | 1.57918 | ||||||||
\(962\) | − 3.49137e6i | − 0.121635i | ||||||||
\(963\) | 6.58141e6i | 0.228693i | ||||||||
\(964\) | −1.36995e7 | −0.474801 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 517752. | 0.0178517 | ||||||||
\(967\) | − 1.44556e7i | − 0.497130i | −0.968615 | − | 0.248565i | \(-0.920041\pi\) | ||||
0.968615 | − | 0.248565i | \(-0.0799589\pi\) | |||||||
\(968\) | − 7.15309e6i | − 0.245361i | ||||||||
\(969\) | −2.45673e6 | −0.0840520 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.06974e7 | −0.364109 | −0.182054 | − | 0.983288i | \(-0.558275\pi\) | ||||
−0.182054 | + | 0.983288i | \(0.558275\pi\) | |||||||
\(972\) | − 944784.i | − 0.0320750i | ||||||||
\(973\) | − 1.64848e7i | − 0.558214i | ||||||||
\(974\) | 2.06558e7 | 0.697660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.59437e6 | −0.187986 | ||||||||
\(977\) | 8.41568e6i | 0.282067i | 0.990005 | + | 0.141034i | \(0.0450426\pi\) | ||||
−0.990005 | + | 0.141034i | \(0.954957\pi\) | |||||||
\(978\) | 6.93292e6i | 0.231776i | ||||||||
\(979\) | −7.77888e6 | −0.259394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75782e7 | −0.583180 | ||||||||
\(982\) | − 3.41715e7i | − 1.13080i | ||||||||
\(983\) | 3.89409e7i | 1.28535i | 0.766138 | + | 0.642676i | \(0.222176\pi\) | ||||
−0.766138 | + | 0.642676i | \(0.777824\pi\) | |||||||
\(984\) | 1.04648e7 | 0.344542 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.11272e6 | 0.167479 | ||||||||
\(987\) | 464454.i | 0.0151757i | ||||||||
\(988\) | 2.72296e6i | 0.0887460i | ||||||||
\(989\) | −4.39141e6 | −0.142762 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.84592e7 | 1.56745 | 0.783723 | − | 0.621111i | \(-0.213318\pi\) | ||||
0.783723 | + | 0.621111i | \(0.213318\pi\) | |||||||
\(992\) | 8.79923e6i | 0.283900i | ||||||||
\(993\) | 5.41919e6i | 0.174406i | ||||||||
\(994\) | 7.65686e6 | 0.245802 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.56289e7 | −0.499206 | ||||||||
\(997\) | − 3.84733e7i | − 1.22581i | −0.790158 | − | 0.612903i | \(-0.790002\pi\) | ||||
0.790158 | − | 0.612903i | \(-0.209998\pi\) | |||||||
\(998\) | − 1.68235e7i | − 0.534675i | ||||||||
\(999\) | −6.30002e6 | −0.199723 |
(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 | 150.6.c.g.49.1 | 2 | ||
3.2 | odd | 2 | 450.6.c.e.199.2 | 2 | |||
5.2 | odd | 4 | 150.6.a.m.1.1 | yes | 1 | ||
5.3 | odd | 4 | 150.6.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 150.6.c.g.49.2 | 2 | ||
15.2 | even | 4 | 450.6.a.i.1.1 | 1 | |||
15.8 | even | 4 | 450.6.a.p.1.1 | 1 | |||
15.14 | odd | 2 | 450.6.c.e.199.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
150.6.a.m.1.1 | yes | 1 | 5.2 | odd | 4 | ||
150.6.c.g.49.1 | 2 | 1.1 | even | 1 | trivial | ||
150.6.c.g.49.2 | 2 | 5.4 | even | 2 | inner | ||
450.6.a.i.1.1 | 1 | 15.2 | even | 4 | |||
450.6.a.p.1.1 | 1 | 15.8 | even | 4 | |||
450.6.c.e.199.1 | 2 | 15.14 | odd | 2 | |||
450.6.c.e.199.2 | 2 | 3.2 | odd | 2 |