Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
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, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.a (trivial) |
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: | yes |
Analytic conductor: | \(24.0575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 47.0000 | 0.362537 | 0.181269 | − | 0.983434i | \(-0.441980\pi\) | ||||
0.181269 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 222.000 | 0.553186 | 0.276593 | − | 0.960987i | \(-0.410795\pi\) | ||||
0.276593 | + | 0.960987i | \(0.410795\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 101.000 | 0.165754 | 0.0828768 | − | 0.996560i | \(-0.473589\pi\) | ||||
0.0828768 | + | 0.996560i | \(0.473589\pi\) | |||||||
\(14\) | 188.000 | 0.256353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 162.000 | 0.135954 | 0.0679771 | − | 0.997687i | \(-0.478346\pi\) | ||||
0.0679771 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 1685.00 | 1.07082 | 0.535409 | − | 0.844593i | \(-0.320157\pi\) | ||||
0.535409 | + | 0.844593i | \(0.320157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 423.000 | 0.209311 | ||||||||
\(22\) | 888.000 | 0.391162 | ||||||||
\(23\) | 306.000 | 0.120615 | 0.0603076 | − | 0.998180i | \(-0.480792\pi\) | ||||
0.0603076 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 404.000 | 0.117206 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 752.000 | 0.181269 | ||||||||
\(29\) | 7890.00 | 1.74214 | 0.871068 | − | 0.491163i | \(-0.163428\pi\) | ||||
0.871068 | + | 0.491163i | \(0.163428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8593.00 | −1.60598 | −0.802991 | − | 0.595991i | \(-0.796759\pi\) | ||||
−0.802991 | + | 0.595991i | \(0.796759\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 1998.00 | 0.319382 | ||||||||
\(34\) | 648.000 | 0.0961342 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 8642.00 | 1.03779 | 0.518896 | − | 0.854838i | \(-0.326343\pi\) | ||||
0.518896 | + | 0.854838i | \(0.326343\pi\) | |||||||
\(38\) | 6740.00 | 0.757183 | ||||||||
\(39\) | 909.000 | 0.0956979 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18168.0 | −1.68790 | −0.843951 | − | 0.536420i | \(-0.819777\pi\) | ||||
−0.843951 | + | 0.536420i | \(0.819777\pi\) | |||||||
\(42\) | 1692.00 | 0.148005 | ||||||||
\(43\) | 14351.0 | 1.18362 | 0.591808 | − | 0.806079i | \(-0.298414\pi\) | ||||
0.591808 | + | 0.806079i | \(0.298414\pi\) | |||||||
\(44\) | 3552.00 | 0.276593 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1224.00 | 0.0852878 | ||||||||
\(47\) | −1098.00 | −0.0725033 | −0.0362516 | − | 0.999343i | \(-0.511542\pi\) | ||||
−0.0362516 | + | 0.999343i | \(0.511542\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | −14598.0 | −0.868567 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1458.00 | 0.0784932 | ||||||||
\(52\) | 1616.00 | 0.0828768 | ||||||||
\(53\) | 17916.0 | 0.876095 | 0.438048 | − | 0.898952i | \(-0.355670\pi\) | ||||
0.438048 | + | 0.898952i | \(0.355670\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3008.00 | 0.128176 | ||||||||
\(57\) | 15165.0 | 0.618237 | ||||||||
\(58\) | 31560.0 | 1.23188 | ||||||||
\(59\) | 17610.0 | 0.658612 | 0.329306 | − | 0.944223i | \(-0.393185\pi\) | ||||
0.329306 | + | 0.944223i | \(0.393185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21853.0 | −0.751946 | −0.375973 | − | 0.926631i | \(-0.622691\pi\) | ||||
−0.375973 | + | 0.926631i | \(0.622691\pi\) | |||||||
\(62\) | −34372.0 | −1.13560 | ||||||||
\(63\) | 3807.00 | 0.120846 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7992.00 | 0.225837 | ||||||||
\(67\) | 107.000 | 0.00291204 | 0.00145602 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145602 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(68\) | 2592.00 | 0.0679771 | ||||||||
\(69\) | 2754.00 | 0.0696372 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −40728.0 | −0.958842 | −0.479421 | − | 0.877585i | \(-0.659153\pi\) | ||||
−0.479421 | + | 0.877585i | \(0.659153\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 34706.0 | 0.762250 | 0.381125 | − | 0.924524i | \(-0.375537\pi\) | ||||
0.381125 | + | 0.924524i | \(0.375537\pi\) | |||||||
\(74\) | 34568.0 | 0.733829 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26960.0 | 0.535409 | ||||||||
\(77\) | 10434.0 | 0.200551 | ||||||||
\(78\) | 3636.00 | 0.0676686 | ||||||||
\(79\) | −69160.0 | −1.24677 | −0.623386 | − | 0.781914i | \(-0.714244\pi\) | ||||
−0.623386 | + | 0.781914i | \(0.714244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −72672.0 | −1.19353 | ||||||||
\(83\) | −108534. | −1.72930 | −0.864650 | − | 0.502374i | \(-0.832460\pi\) | ||||
−0.864650 | + | 0.502374i | \(0.832460\pi\) | |||||||
\(84\) | 6768.00 | 0.104656 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57404.0 | 0.836943 | ||||||||
\(87\) | 71010.0 | 1.00582 | ||||||||
\(88\) | 14208.0 | 0.195581 | ||||||||
\(89\) | 35040.0 | 0.468910 | 0.234455 | − | 0.972127i | \(-0.424670\pi\) | ||||
0.234455 | + | 0.972127i | \(0.424670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4747.00 | 0.0600919 | ||||||||
\(92\) | 4896.00 | 0.0603076 | ||||||||
\(93\) | −77337.0 | −0.927214 | ||||||||
\(94\) | −4392.00 | −0.0512676 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −823.000 | −0.00888118 | −0.00444059 | − | 0.999990i | \(-0.501413\pi\) | ||||
−0.00444059 | + | 0.999990i | \(0.501413\pi\) | |||||||
\(98\) | −58392.0 | −0.614169 | ||||||||
\(99\) | 17982.0 | 0.184395 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33828.0 | −0.329969 | −0.164984 | − | 0.986296i | \(-0.552757\pi\) | ||||
−0.164984 | + | 0.986296i | \(0.552757\pi\) | |||||||
\(102\) | 5832.00 | 0.0555031 | ||||||||
\(103\) | −133444. | −1.23938 | −0.619692 | − | 0.784845i | \(-0.712743\pi\) | ||||
−0.619692 | + | 0.784845i | \(0.712743\pi\) | |||||||
\(104\) | 6464.00 | 0.0586028 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 71664.0 | 0.619493 | ||||||||
\(107\) | 81252.0 | 0.686080 | 0.343040 | − | 0.939321i | \(-0.388543\pi\) | ||||
0.343040 | + | 0.939321i | \(0.388543\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −217015. | −1.74954 | −0.874769 | − | 0.484540i | \(-0.838987\pi\) | ||||
−0.874769 | + | 0.484540i | \(0.838987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 77778.0 | 0.599169 | ||||||||
\(112\) | 12032.0 | 0.0906343 | ||||||||
\(113\) | −138324. | −1.01906 | −0.509532 | − | 0.860452i | \(-0.670181\pi\) | ||||
−0.509532 | + | 0.860452i | \(0.670181\pi\) | |||||||
\(114\) | 60660.0 | 0.437160 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 126240. | 0.871068 | ||||||||
\(117\) | 8181.00 | 0.0552512 | ||||||||
\(118\) | 70440.0 | 0.465709 | ||||||||
\(119\) | 7614.00 | 0.0492885 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −111767. | −0.693985 | ||||||||
\(122\) | −87412.0 | −0.531706 | ||||||||
\(123\) | −163512. | −0.974511 | ||||||||
\(124\) | −137488. | −0.802991 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15228.0 | 0.0854509 | ||||||||
\(127\) | −256048. | −1.40868 | −0.704340 | − | 0.709863i | \(-0.748757\pi\) | ||||
−0.704340 | + | 0.709863i | \(0.748757\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 129159. | 0.683361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118452. | 0.603065 | 0.301533 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301533 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(132\) | 31968.0 | 0.159691 | ||||||||
\(133\) | 79195.0 | 0.388212 | ||||||||
\(134\) | 428.000 | 0.00205912 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10368.0 | 0.0480671 | ||||||||
\(137\) | −13218.0 | −0.0601678 | −0.0300839 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300839 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(138\) | 11016.0 | 0.0492409 | ||||||||
\(139\) | −350740. | −1.53974 | −0.769872 | − | 0.638199i | \(-0.779680\pi\) | ||||
−0.769872 | + | 0.638199i | \(0.779680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9882.00 | −0.0418598 | ||||||||
\(142\) | −162912. | −0.678004 | ||||||||
\(143\) | 22422.0 | 0.0916926 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 138824. | 0.538992 | ||||||||
\(147\) | −131382. | −0.501467 | ||||||||
\(148\) | 138272. | 0.518896 | ||||||||
\(149\) | 109890. | 0.405502 | 0.202751 | − | 0.979230i | \(-0.435012\pi\) | ||||
0.202751 | + | 0.979230i | \(0.435012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −172603. | −0.616036 | −0.308018 | − | 0.951381i | \(-0.599666\pi\) | ||||
−0.308018 | + | 0.951381i | \(0.599666\pi\) | |||||||
\(152\) | 107840. | 0.378592 | ||||||||
\(153\) | 13122.0 | 0.0453181 | ||||||||
\(154\) | 41736.0 | 0.141811 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14544.0 | 0.0478489 | ||||||||
\(157\) | −349993. | −1.13321 | −0.566605 | − | 0.823990i | \(-0.691743\pi\) | ||||
−0.566605 | + | 0.823990i | \(0.691743\pi\) | |||||||
\(158\) | −276640. | −0.881601 | ||||||||
\(159\) | 161244. | 0.505814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14382.0 | 0.0437275 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | 192581. | 0.567733 | 0.283867 | − | 0.958864i | \(-0.408383\pi\) | ||||
0.283867 | + | 0.958864i | \(0.408383\pi\) | |||||||
\(164\) | −290688. | −0.843951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −434136. | −1.22280 | ||||||||
\(167\) | 580692. | 1.61122 | 0.805610 | − | 0.592447i | \(-0.201838\pi\) | ||||
0.805610 | + | 0.592447i | \(0.201838\pi\) | |||||||
\(168\) | 27072.0 | 0.0740026 | ||||||||
\(169\) | −361092. | −0.972526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136485. | 0.356940 | ||||||||
\(172\) | 229616. | 0.591808 | ||||||||
\(173\) | 738126. | 1.87506 | 0.937530 | − | 0.347904i | \(-0.113106\pi\) | ||||
0.937530 | + | 0.347904i | \(0.113106\pi\) | |||||||
\(174\) | 284040. | 0.711224 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 56832.0 | 0.138297 | ||||||||
\(177\) | 158490. | 0.380250 | ||||||||
\(178\) | 140160. | 0.331569 | ||||||||
\(179\) | 497370. | 1.16024 | 0.580119 | − | 0.814532i | \(-0.303006\pi\) | ||||
0.580119 | + | 0.814532i | \(0.303006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −333163. | −0.755893 | −0.377947 | − | 0.925827i | \(-0.623370\pi\) | ||||
−0.377947 | + | 0.925827i | \(0.623370\pi\) | |||||||
\(182\) | 18988.0 | 0.0424914 | ||||||||
\(183\) | −196677. | −0.434136 | ||||||||
\(184\) | 19584.0 | 0.0426439 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −309348. | −0.655639 | ||||||||
\(187\) | 35964.0 | 0.0752080 | ||||||||
\(188\) | −17568.0 | −0.0362516 | ||||||||
\(189\) | 34263.0 | 0.0697703 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −40638.0 | −0.0806026 | −0.0403013 | − | 0.999188i | \(-0.512832\pi\) | ||||
−0.0403013 | + | 0.999188i | \(0.512832\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 494651. | 0.955885 | 0.477942 | − | 0.878391i | \(-0.341383\pi\) | ||||
0.477942 | + | 0.878391i | \(0.341383\pi\) | |||||||
\(194\) | −3292.00 | −0.00627994 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −233568. | −0.434283 | ||||||||
\(197\) | 552342. | 1.01401 | 0.507005 | − | 0.861943i | \(-0.330752\pi\) | ||||
0.507005 | + | 0.861943i | \(0.330752\pi\) | |||||||
\(198\) | 71928.0 | 0.130387 | ||||||||
\(199\) | 685625. | 1.22731 | 0.613655 | − | 0.789575i | \(-0.289699\pi\) | ||||
0.613655 | + | 0.789575i | \(0.289699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 963.000 | 0.00168126 | ||||||||
\(202\) | −135312. | −0.233323 | ||||||||
\(203\) | 370830. | 0.631589 | ||||||||
\(204\) | 23328.0 | 0.0392466 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −533776. | −0.876377 | ||||||||
\(207\) | 24786.0 | 0.0402050 | ||||||||
\(208\) | 25856.0 | 0.0414384 | ||||||||
\(209\) | 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. | 0.438048 | ||||||||
\(213\) | −366552. | −0.553588 | ||||||||
\(214\) | 325008. | 0.485132 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −403871. | −0.582228 | ||||||||
\(218\) | −868060. | −1.23711 | ||||||||
\(219\) | 312354. | 0.440085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16362.0 | 0.0225349 | ||||||||
\(222\) | 311112. | 0.423676 | ||||||||
\(223\) | 169271. | 0.227940 | 0.113970 | − | 0.993484i | \(-0.463643\pi\) | ||||
0.113970 | + | 0.993484i | \(0.463643\pi\) | |||||||
\(224\) | 48128.0 | 0.0640882 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −553296. | −0.720587 | ||||||||
\(227\) | −46488.0 | −0.0598792 | −0.0299396 | − | 0.999552i | \(-0.509532\pi\) | ||||
−0.0299396 | + | 0.999552i | \(0.509532\pi\) | |||||||
\(228\) | 242640. | 0.309119 | ||||||||
\(229\) | −90115.0 | −0.113556 | −0.0567778 | − | 0.998387i | \(-0.518083\pi\) | ||||
−0.0567778 | + | 0.998387i | \(0.518083\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 93906.0 | 0.115788 | ||||||||
\(232\) | 504960. | 0.615938 | ||||||||
\(233\) | 1.06414e6 | 1.28413 | 0.642063 | − | 0.766652i | \(-0.278079\pi\) | ||||
0.642063 | + | 0.766652i | \(0.278079\pi\) | |||||||
\(234\) | 32724.0 | 0.0390685 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 281760. | 0.329306 | ||||||||
\(237\) | −622440. | −0.719825 | ||||||||
\(238\) | 30456.0 | 0.0348522 | ||||||||
\(239\) | 1.15158e6 | 1.30407 | 0.652033 | − | 0.758191i | \(-0.273916\pi\) | ||||
0.652033 | + | 0.758191i | \(0.273916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 856217. | 0.949601 | 0.474801 | − | 0.880093i | \(-0.342520\pi\) | ||||
0.474801 | + | 0.880093i | \(0.342520\pi\) | |||||||
\(242\) | −447068. | −0.490722 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −349648. | −0.375973 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −654048. | −0.689084 | ||||||||
\(247\) | 170185. | 0.177492 | ||||||||
\(248\) | −549952. | −0.567800 | ||||||||
\(249\) | −976806. | −0.998412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −207708. | −0.208098 | −0.104049 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104049 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(252\) | 60912.0 | 0.0604229 | ||||||||
\(253\) | 67932.0 | 0.0667226 | ||||||||
\(254\) | −1.02419e6 | −0.996087 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.45319e6 | −1.37243 | −0.686213 | − | 0.727401i | \(-0.740728\pi\) | ||||
−0.686213 | + | 0.727401i | \(0.740728\pi\) | |||||||
\(258\) | 516636. | 0.483209 | ||||||||
\(259\) | 406174. | 0.376238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 639090. | 0.580712 | ||||||||
\(262\) | 473808. | 0.426431 | ||||||||
\(263\) | 169296. | 0.150924 | 0.0754618 | − | 0.997149i | \(-0.475957\pi\) | ||||
0.0754618 | + | 0.997149i | \(0.475957\pi\) | |||||||
\(264\) | 127872. | 0.112919 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 316780. | 0.274507 | ||||||||
\(267\) | 315360. | 0.270725 | ||||||||
\(268\) | 1712.00 | 0.00145602 | ||||||||
\(269\) | −1.58109e6 | −1.33222 | −0.666110 | − | 0.745854i | \(-0.732042\pi\) | ||||
−0.666110 | + | 0.745854i | \(0.732042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 822512. | 0.680329 | 0.340165 | − | 0.940366i | \(-0.389517\pi\) | ||||
0.340165 | + | 0.940366i | \(0.389517\pi\) | |||||||
\(272\) | 41472.0 | 0.0339886 | ||||||||
\(273\) | 42723.0 | 0.0346941 | ||||||||
\(274\) | −52872.0 | −0.0425451 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 44064.0 | 0.0348186 | ||||||||
\(277\) | −546823. | −0.428201 | −0.214100 | − | 0.976812i | \(-0.568682\pi\) | ||||
−0.214100 | + | 0.976812i | \(0.568682\pi\) | |||||||
\(278\) | −1.40296e6 | −1.08876 | ||||||||
\(279\) | −696033. | −0.535327 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09250e6 | −0.825382 | −0.412691 | − | 0.910871i | \(-0.635411\pi\) | ||||
−0.412691 | + | 0.910871i | \(0.635411\pi\) | |||||||
\(282\) | −39528.0 | −0.0295993 | ||||||||
\(283\) | −2.48480e6 | −1.84427 | −0.922136 | − | 0.386865i | \(-0.873558\pi\) | ||||
−0.922136 | + | 0.386865i | \(0.873558\pi\) | |||||||
\(284\) | −651648. | −0.479421 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 89688.0 | 0.0648365 | ||||||||
\(287\) | −853896. | −0.611928 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −1.39361e6 | −0.981516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7407.00 | −0.00512755 | ||||||||
\(292\) | 555296. | 0.381125 | ||||||||
\(293\) | −341394. | −0.232320 | −0.116160 | − | 0.993231i | \(-0.537059\pi\) | ||||
−0.116160 | + | 0.993231i | \(0.537059\pi\) | |||||||
\(294\) | −525528. | −0.354591 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 553088. | 0.366915 | ||||||||
\(297\) | 161838. | 0.106461 | ||||||||
\(298\) | 439560. | 0.286733 | ||||||||
\(299\) | 30906.0 | 0.0199924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 674497. | 0.429105 | ||||||||
\(302\) | −690412. | −0.435603 | ||||||||
\(303\) | −304452. | −0.190508 | ||||||||
\(304\) | 431360. | 0.267705 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 52488.0 | 0.0320447 | ||||||||
\(307\) | 2.02898e6 | 1.22866 | 0.614329 | − | 0.789050i | \(-0.289427\pi\) | ||||
0.614329 | + | 0.789050i | \(0.289427\pi\) | |||||||
\(308\) | 166944. | 0.100275 | ||||||||
\(309\) | −1.20100e6 | −0.715559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −206598. | −0.121123 | −0.0605613 | − | 0.998164i | \(-0.519289\pi\) | ||||
−0.0605613 | + | 0.998164i | \(0.519289\pi\) | |||||||
\(312\) | 58176.0 | 0.0338343 | ||||||||
\(313\) | −3.34223e6 | −1.92830 | −0.964152 | − | 0.265352i | \(-0.914512\pi\) | ||||
−0.964152 | + | 0.265352i | \(0.914512\pi\) | |||||||
\(314\) | −1.39997e6 | −0.801300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10656e6 | −0.623386 | ||||||||
\(317\) | −2.53289e6 | −1.41569 | −0.707844 | − | 0.706368i | \(-0.750332\pi\) | ||||
−0.707844 | + | 0.706368i | \(0.750332\pi\) | |||||||
\(318\) | 644976. | 0.357664 | ||||||||
\(319\) | 1.75158e6 | 0.963725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 731268. | 0.396108 | ||||||||
\(322\) | 57528.0 | 0.0309200 | ||||||||
\(323\) | 272970. | 0.145582 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 770324. | 0.401448 | ||||||||
\(327\) | −1.95314e6 | −1.01010 | ||||||||
\(328\) | −1.16275e6 | −0.596764 | ||||||||
\(329\) | −51606.0 | −0.0262851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 602132. | 0.302080 | 0.151040 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151040 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(332\) | −1.73654e6 | −0.864650 | ||||||||
\(333\) | 700002. | 0.345930 | ||||||||
\(334\) | 2.32277e6 | 1.13930 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 108288. | 0.0523278 | ||||||||
\(337\) | 209777. | 0.100620 | 0.0503099 | − | 0.998734i | \(-0.483979\pi\) | ||||
0.0503099 | + | 0.998734i | \(0.483979\pi\) | |||||||
\(338\) | −1.44437e6 | −0.687680 | ||||||||
\(339\) | −1.24492e6 | −0.588357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90765e6 | −0.888407 | ||||||||
\(342\) | 545940. | 0.252394 | ||||||||
\(343\) | −1.47603e6 | −0.677425 | ||||||||
\(344\) | 918464. | 0.418472 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.95250e6 | 1.32587 | ||||||||
\(347\) | 4.02166e6 | 1.79301 | 0.896503 | − | 0.443037i | \(-0.146099\pi\) | ||||
0.896503 | + | 0.443037i | \(0.146099\pi\) | |||||||
\(348\) | 1.13616e6 | 0.502911 | ||||||||
\(349\) | 8330.00 | 0.00366085 | 0.00183042 | − | 0.999998i | \(-0.499417\pi\) | ||||
0.00183042 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 73629.0 | 0.0318993 | ||||||||
\(352\) | 227328. | 0.0977904 | ||||||||
\(353\) | 1.95001e6 | 0.832912 | 0.416456 | − | 0.909156i | \(-0.363272\pi\) | ||||
0.416456 | + | 0.909156i | \(0.363272\pi\) | |||||||
\(354\) | 633960. | 0.268877 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 560640. | 0.234455 | ||||||||
\(357\) | 68526.0 | 0.0284567 | ||||||||
\(358\) | 1.98948e6 | 0.820412 | ||||||||
\(359\) | 2.27088e6 | 0.929947 | 0.464973 | − | 0.885325i | \(-0.346064\pi\) | ||||
0.464973 | + | 0.885325i | \(0.346064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 363126. | 0.146652 | ||||||||
\(362\) | −1.33265e6 | −0.534497 | ||||||||
\(363\) | −1.00590e6 | −0.400673 | ||||||||
\(364\) | 75952.0 | 0.0300459 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −786708. | −0.306981 | ||||||||
\(367\) | 2.86154e6 | 1.10901 | 0.554503 | − | 0.832181i | \(-0.312908\pi\) | ||||
0.554503 | + | 0.832181i | \(0.312908\pi\) | |||||||
\(368\) | 78336.0 | 0.0301538 | ||||||||
\(369\) | −1.47161e6 | −0.562634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 842052. | 0.317617 | ||||||||
\(372\) | −1.23739e6 | −0.463607 | ||||||||
\(373\) | 615311. | 0.228993 | 0.114497 | − | 0.993424i | \(-0.463474\pi\) | ||||
0.114497 | + | 0.993424i | \(0.463474\pi\) | |||||||
\(374\) | 143856. | 0.0531801 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −70272.0 | −0.0256338 | ||||||||
\(377\) | 796890. | 0.288765 | ||||||||
\(378\) | 137052. | 0.0493351 | ||||||||
\(379\) | 5.39878e6 | 1.93062 | 0.965311 | − | 0.261103i | \(-0.0840863\pi\) | ||||
0.965311 | + | 0.261103i | \(0.0840863\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.30443e6 | −0.813301 | ||||||||
\(382\) | −162552. | −0.0569946 | ||||||||
\(383\) | 1.08688e6 | 0.378602 | 0.189301 | − | 0.981919i | \(-0.439378\pi\) | ||||
0.189301 | + | 0.981919i | \(0.439378\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.97860e6 | 0.675913 | ||||||||
\(387\) | 1.16243e6 | 0.394539 | ||||||||
\(388\) | −13168.0 | −0.00444059 | ||||||||
\(389\) | −3.48432e6 | −1.16747 | −0.583733 | − | 0.811946i | \(-0.698408\pi\) | ||||
−0.583733 | + | 0.811946i | \(0.698408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49572.0 | 0.0163981 | ||||||||
\(392\) | −934272. | −0.307085 | ||||||||
\(393\) | 1.06607e6 | 0.348180 | ||||||||
\(394\) | 2.20937e6 | 0.717014 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 287712. | 0.0921977 | ||||||||
\(397\) | 3.26591e6 | 1.03999 | 0.519993 | − | 0.854170i | \(-0.325935\pi\) | ||||
0.519993 | + | 0.854170i | \(0.325935\pi\) | |||||||
\(398\) | 2.74250e6 | 0.867839 | ||||||||
\(399\) | 712755. | 0.224134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.27319e6 | −1.32706 | −0.663531 | − | 0.748149i | \(-0.730943\pi\) | ||||
−0.663531 | + | 0.748149i | \(0.730943\pi\) | |||||||
\(402\) | 3852.00 | 0.00118883 | ||||||||
\(403\) | −867893. | −0.266197 | ||||||||
\(404\) | −541248. | −0.164984 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.48332e6 | 0.446601 | ||||||||
\(407\) | 1.91852e6 | 0.574092 | ||||||||
\(408\) | 93312.0 | 0.0277515 | ||||||||
\(409\) | −1.45188e6 | −0.429162 | −0.214581 | − | 0.976706i | \(-0.568839\pi\) | ||||
−0.214581 | + | 0.976706i | \(0.568839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −118962. | −0.0347379 | ||||||||
\(412\) | −2.13510e6 | −0.619692 | ||||||||
\(413\) | 827670. | 0.238771 | ||||||||
\(414\) | 99144.0 | 0.0284293 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 103424. | 0.0293014 | ||||||||
\(417\) | −3.15666e6 | −0.888971 | ||||||||
\(418\) | 1.49628e6 | 0.418863 | ||||||||
\(419\) | 559380. | 0.155658 | 0.0778291 | − | 0.996967i | \(-0.475201\pi\) | ||||
0.0778291 | + | 0.996967i | \(0.475201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.91470e6 | −1.07645 | −0.538224 | − | 0.842802i | \(-0.680905\pi\) | ||||
−0.538224 | + | 0.842802i | \(0.680905\pi\) | |||||||
\(422\) | 2.99791e6 | 0.819478 | ||||||||
\(423\) | −88938.0 | −0.0241678 | ||||||||
\(424\) | 1.14662e6 | 0.309746 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.46621e6 | −0.391446 | ||||||||
\(427\) | −1.02709e6 | −0.272608 | ||||||||
\(428\) | 1.30003e6 | 0.343040 | ||||||||
\(429\) | 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. | 0.0481125 | ||||||||
\(433\) | 7.15969e6 | 1.83516 | 0.917581 | − | 0.397548i | \(-0.130139\pi\) | ||||
0.917581 | + | 0.397548i | \(0.130139\pi\) | |||||||
\(434\) | −1.61548e6 | −0.411698 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.47224e6 | −0.874769 | ||||||||
\(437\) | 515610. | 0.129157 | ||||||||
\(438\) | 1.24942e6 | 0.311187 | ||||||||
\(439\) | 1.71790e6 | 0.425437 | 0.212719 | − | 0.977114i | \(-0.431768\pi\) | ||||
0.212719 | + | 0.977114i | \(0.431768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18244e6 | −0.289522 | ||||||||
\(442\) | 65448.0 | 0.0159346 | ||||||||
\(443\) | 3.39670e6 | 0.822332 | 0.411166 | − | 0.911560i | \(-0.365122\pi\) | ||||
0.411166 | + | 0.911560i | \(0.365122\pi\) | |||||||
\(444\) | 1.24445e6 | 0.299584 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 677084. | 0.161178 | ||||||||
\(447\) | 989010. | 0.234116 | ||||||||
\(448\) | 192512. | 0.0453172 | ||||||||
\(449\) | −3.39606e6 | −0.794986 | −0.397493 | − | 0.917605i | \(-0.630120\pi\) | ||||
−0.397493 | + | 0.917605i | \(0.630120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.03330e6 | −0.933724 | ||||||||
\(452\) | −2.21318e6 | −0.509532 | ||||||||
\(453\) | −1.55343e6 | −0.355668 | ||||||||
\(454\) | −185952. | −0.0423410 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 970560. | 0.218580 | ||||||||
\(457\) | −4.52814e6 | −1.01421 | −0.507106 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507106 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(458\) | −360460. | −0.0802959 | ||||||||
\(459\) | 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. | 0.0818744 | ||||||||
\(463\) | −7.19862e6 | −1.56062 | −0.780310 | − | 0.625393i | \(-0.784939\pi\) | ||||
−0.780310 | + | 0.625393i | \(0.784939\pi\) | |||||||
\(464\) | 2.01984e6 | 0.435534 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.25654e6 | 0.908014 | ||||||||
\(467\) | 4.83034e6 | 1.02491 | 0.512455 | − | 0.858714i | \(-0.328736\pi\) | ||||
0.512455 | + | 0.858714i | \(0.328736\pi\) | |||||||
\(468\) | 130896. | 0.0276256 | ||||||||
\(469\) | 5029.00 | 0.00105572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.14994e6 | −0.654259 | ||||||||
\(472\) | 1.12704e6 | 0.232854 | ||||||||
\(473\) | 3.18592e6 | 0.654760 | ||||||||
\(474\) | −2.48976e6 | −0.508993 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 121824. | 0.0246442 | ||||||||
\(477\) | 1.45120e6 | 0.292032 | ||||||||
\(478\) | 4.60632e6 | 0.922113 | ||||||||
\(479\) | 748650. | 0.149087 | 0.0745435 | − | 0.997218i | \(-0.476250\pi\) | ||||
0.0745435 | + | 0.997218i | \(0.476250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 872842. | 0.172018 | ||||||||
\(482\) | 3.42487e6 | 0.671469 | ||||||||
\(483\) | 129438. | 0.0252461 | ||||||||
\(484\) | −1.78827e6 | −0.346993 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −5.16394e6 | −0.986641 | −0.493320 | − | 0.869848i | \(-0.664217\pi\) | ||||
−0.493320 | + | 0.869848i | \(0.664217\pi\) | |||||||
\(488\) | −1.39859e6 | −0.265853 | ||||||||
\(489\) | 1.73323e6 | 0.327781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.54287e6 | 1.59919 | 0.799595 | − | 0.600539i | \(-0.205047\pi\) | ||||
0.799595 | + | 0.600539i | \(0.205047\pi\) | |||||||
\(492\) | −2.61619e6 | −0.487256 | ||||||||
\(493\) | 1.27818e6 | 0.236851 | ||||||||
\(494\) | 680740. | 0.125506 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.19981e6 | −0.401495 | ||||||||
\(497\) | −1.91422e6 | −0.347616 | ||||||||
\(498\) | −3.90722e6 | −0.705984 | ||||||||
\(499\) | −4.20588e6 | −0.756145 | −0.378072 | − | 0.925776i | \(-0.623413\pi\) | ||||
−0.378072 | + | 0.925776i | \(0.623413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.22623e6 | 0.930238 | ||||||||
\(502\) | −830832. | −0.147148 | ||||||||
\(503\) | −8.18342e6 | −1.44217 | −0.721083 | − | 0.692849i | \(-0.756355\pi\) | ||||
−0.721083 | + | 0.692849i | \(0.756355\pi\) | |||||||
\(504\) | 243648. | 0.0427254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 271728. | 0.0471800 | ||||||||
\(507\) | −3.24983e6 | −0.561488 | ||||||||
\(508\) | −4.09677e6 | −0.704340 | ||||||||
\(509\) | 3.85923e6 | 0.660247 | 0.330123 | − | 0.943938i | \(-0.392910\pi\) | ||||
0.330123 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63118e6 | 0.276344 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 1.22837e6 | 0.206079 | ||||||||
\(514\) | −5.81275e6 | −0.970452 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.06654e6 | 0.341681 | ||||||||
\(517\) | −243756. | −0.0401078 | ||||||||
\(518\) | 1.62470e6 | 0.266040 | ||||||||
\(519\) | 6.64313e6 | 1.08257 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.55410e6 | 0.735036 | 0.367518 | − | 0.930016i | \(-0.380208\pi\) | ||||
0.367518 | + | 0.930016i | \(0.380208\pi\) | |||||||
\(522\) | 2.55636e6 | 0.410625 | ||||||||
\(523\) | 4.82224e6 | 0.770894 | 0.385447 | − | 0.922730i | \(-0.374047\pi\) | ||||
0.385447 | + | 0.922730i | \(0.374047\pi\) | |||||||
\(524\) | 1.89523e6 | 0.301533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 677184. | 0.106719 | ||||||||
\(527\) | −1.39207e6 | −0.218340 | ||||||||
\(528\) | 511488. | 0.0798455 | ||||||||
\(529\) | −6.34271e6 | −0.985452 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.42641e6 | 0.219537 | ||||||||
\(532\) | 1.26712e6 | 0.194106 | ||||||||
\(533\) | −1.83497e6 | −0.279776 | ||||||||
\(534\) | 1.26144e6 | 0.191432 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6848.00 | 0.00102956 | ||||||||
\(537\) | 4.47633e6 | 0.669864 | ||||||||
\(538\) | −6.32436e6 | −0.942022 | ||||||||
\(539\) | −3.24076e6 | −0.480479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 362537. | 0.0532549 | 0.0266274 | − | 0.999645i | \(-0.491523\pi\) | ||||
0.0266274 | + | 0.999645i | \(0.491523\pi\) | |||||||
\(542\) | 3.29005e6 | 0.481065 | ||||||||
\(543\) | −2.99847e6 | −0.436415 | ||||||||
\(544\) | 165888. | 0.0240335 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 170892. | 0.0245324 | ||||||||
\(547\) | 3.11439e6 | 0.445046 | 0.222523 | − | 0.974927i | \(-0.428571\pi\) | ||||
0.222523 | + | 0.974927i | \(0.428571\pi\) | |||||||
\(548\) | −211488. | −0.0300839 | ||||||||
\(549\) | −1.77009e6 | −0.250649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.32947e7 | 1.86551 | ||||||||
\(552\) | 176256. | 0.0246205 | ||||||||
\(553\) | −3.25052e6 | −0.452002 | ||||||||
\(554\) | −2.18729e6 | −0.302784 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.61184e6 | −0.769872 | ||||||||
\(557\) | −7.99304e6 | −1.09163 | −0.545813 | − | 0.837907i | \(-0.683779\pi\) | ||||
−0.545813 | + | 0.837907i | \(0.683779\pi\) | |||||||
\(558\) | −2.78413e6 | −0.378534 | ||||||||
\(559\) | 1.44945e6 | 0.196189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 323676. | 0.0434214 | ||||||||
\(562\) | −4.36999e6 | −0.583633 | ||||||||
\(563\) | −1.23236e7 | −1.63857 | −0.819286 | − | 0.573385i | \(-0.805630\pi\) | ||||
−0.819286 | + | 0.573385i | \(0.805630\pi\) | |||||||
\(564\) | −158112. | −0.0209299 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.93920e6 | −1.30410 | ||||||||
\(567\) | 308367. | 0.0402819 | ||||||||
\(568\) | −2.60659e6 | −0.339002 | ||||||||
\(569\) | 1.01364e7 | 1.31252 | 0.656258 | − | 0.754537i | \(-0.272138\pi\) | ||||
0.656258 | + | 0.754537i | \(0.272138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.53084e6 | 0.838260 | 0.419130 | − | 0.907926i | \(-0.362335\pi\) | ||||
0.419130 | + | 0.907926i | \(0.362335\pi\) | |||||||
\(572\) | 358752. | 0.0458463 | ||||||||
\(573\) | −365742. | −0.0465359 | ||||||||
\(574\) | −3.41558e6 | −0.432698 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.24453e6 | −0.155621 | −0.0778103 | − | 0.996968i | \(-0.524793\pi\) | ||||
−0.0778103 | + | 0.996968i | \(0.524793\pi\) | |||||||
\(578\) | −5.57445e6 | −0.694037 | ||||||||
\(579\) | 4.45186e6 | 0.551880 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.10110e6 | −0.626936 | ||||||||
\(582\) | −29628.0 | −0.00362573 | ||||||||
\(583\) | 3.97735e6 | 0.484644 | ||||||||
\(584\) | 2.22118e6 | 0.269496 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.36558e6 | −0.164275 | ||||||||
\(587\) | −1.33403e6 | −0.159797 | −0.0798987 | − | 0.996803i | \(-0.525460\pi\) | ||||
−0.0798987 | + | 0.996803i | \(0.525460\pi\) | |||||||
\(588\) | −2.10211e6 | −0.250734 | ||||||||
\(589\) | −1.44792e7 | −1.71972 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.97108e6 | 0.585439 | ||||||||
\(592\) | 2.21235e6 | 0.259448 | ||||||||
\(593\) | −1.19401e7 | −1.39435 | −0.697177 | − | 0.716899i | \(-0.745561\pi\) | ||||
−0.697177 | + | 0.716899i | \(0.745561\pi\) | |||||||
\(594\) | 647352. | 0.0752791 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.75824e6 | 0.202751 | ||||||||
\(597\) | 6.17062e6 | 0.708587 | ||||||||
\(598\) | 123624. | 0.0141368 | ||||||||
\(599\) | −7.16430e6 | −0.815843 | −0.407922 | − | 0.913017i | \(-0.633746\pi\) | ||||
−0.407922 | + | 0.913017i | \(0.633746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.15163e6 | 0.130055 | 0.0650273 | − | 0.997883i | \(-0.479287\pi\) | ||||
0.0650273 | + | 0.997883i | \(0.479287\pi\) | |||||||
\(602\) | 2.69799e6 | 0.303423 | ||||||||
\(603\) | 8667.00 | 0.000970679 0 | ||||||||
\(604\) | −2.76165e6 | −0.308018 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.21781e6 | −0.134709 | ||||||||
\(607\) | −1.34268e7 | −1.47911 | −0.739554 | − | 0.673097i | \(-0.764963\pi\) | ||||
−0.739554 | + | 0.673097i | \(0.764963\pi\) | |||||||
\(608\) | 1.72544e6 | 0.189296 | ||||||||
\(609\) | 3.33747e6 | 0.364648 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −110898. | −0.0120177 | ||||||||
\(612\) | 209952. | 0.0226590 | ||||||||
\(613\) | 1.20184e7 | 1.29180 | 0.645900 | − | 0.763422i | \(-0.276482\pi\) | ||||
0.645900 | + | 0.763422i | \(0.276482\pi\) | |||||||
\(614\) | 8.11591e6 | 0.868793 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 667776. | 0.0709054 | ||||||||
\(617\) | −6.98519e6 | −0.738695 | −0.369348 | − | 0.929291i | \(-0.620419\pi\) | ||||
−0.369348 | + | 0.929291i | \(0.620419\pi\) | |||||||
\(618\) | −4.80398e6 | −0.505977 | ||||||||
\(619\) | −8.20625e6 | −0.860832 | −0.430416 | − | 0.902631i | \(-0.641633\pi\) | ||||
−0.430416 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 223074. | 0.0232124 | ||||||||
\(622\) | −826392. | −0.0856466 | ||||||||
\(623\) | 1.64688e6 | 0.169997 | ||||||||
\(624\) | 232704. | 0.0239245 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.33689e7 | −1.36352 | ||||||||
\(627\) | 3.36663e6 | 0.342000 | ||||||||
\(628\) | −5.59989e6 | −0.566605 | ||||||||
\(629\) | 1.40000e6 | 0.141092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.07686e7 | −1.07668 | −0.538338 | − | 0.842729i | \(-0.680947\pi\) | ||||
−0.538338 | + | 0.842729i | \(0.680947\pi\) | |||||||
\(632\) | −4.42624e6 | −0.440801 | ||||||||
\(633\) | 6.74529e6 | 0.669101 | ||||||||
\(634\) | −1.01316e7 | −1.00104 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.57990e6 | 0.252907 | ||||||||
\(637\) | −1.47440e6 | −0.143968 | ||||||||
\(638\) | 7.00632e6 | 0.681457 | ||||||||
\(639\) | −3.29897e6 | −0.319614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.92571e7 | 1.85117 | 0.925585 | − | 0.378539i | \(-0.123573\pi\) | ||||
0.925585 | + | 0.378539i | \(0.123573\pi\) | |||||||
\(642\) | 2.92507e6 | 0.280091 | ||||||||
\(643\) | 1.00999e7 | 0.963364 | 0.481682 | − | 0.876346i | \(-0.340026\pi\) | ||||
0.481682 | + | 0.876346i | \(0.340026\pi\) | |||||||
\(644\) | 230112. | 0.0218637 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.09188e6 | 0.102942 | ||||||||
\(647\) | 7.52113e6 | 0.706354 | 0.353177 | − | 0.935556i | \(-0.385101\pi\) | ||||
0.353177 | + | 0.935556i | \(0.385101\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 3.90942e6 | 0.364335 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.63484e6 | −0.336150 | ||||||||
\(652\) | 3.08130e6 | 0.283867 | ||||||||
\(653\) | −2.67197e6 | −0.245216 | −0.122608 | − | 0.992455i | \(-0.539126\pi\) | ||||
−0.122608 | + | 0.992455i | \(0.539126\pi\) | |||||||
\(654\) | −7.81254e6 | −0.714246 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.65101e6 | −0.421976 | ||||||||
\(657\) | 2.81119e6 | 0.254083 | ||||||||
\(658\) | −206424. | −0.0185864 | ||||||||
\(659\) | 6.99948e6 | 0.627845 | 0.313922 | − | 0.949449i | \(-0.398357\pi\) | ||||
0.313922 | + | 0.949449i | \(0.398357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 408122. | 0.0363318 | 0.0181659 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181659 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(662\) | 2.40853e6 | 0.213603 | ||||||||
\(663\) | 147258. | 0.0130105 | ||||||||
\(664\) | −6.94618e6 | −0.611400 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.80001e6 | 0.244610 | ||||||||
\(667\) | 2.41434e6 | 0.210128 | ||||||||
\(668\) | 9.29107e6 | 0.805610 | ||||||||
\(669\) | 1.52344e6 | 0.131601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.85137e6 | −0.415966 | ||||||||
\(672\) | 433152. | 0.0370013 | ||||||||
\(673\) | 1.74939e7 | 1.48885 | 0.744423 | − | 0.667709i | \(-0.232725\pi\) | ||||
0.744423 | + | 0.667709i | \(0.232725\pi\) | |||||||
\(674\) | 839108. | 0.0711489 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.77747e6 | −0.486263 | ||||||||
\(677\) | −8.67440e6 | −0.727391 | −0.363695 | − | 0.931518i | \(-0.618485\pi\) | ||||
−0.363695 | + | 0.931518i | \(0.618485\pi\) | |||||||
\(678\) | −4.97966e6 | −0.416031 | ||||||||
\(679\) | −38681.0 | −0.00321976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −418392. | −0.0345713 | ||||||||
\(682\) | −7.63058e6 | −0.628198 | ||||||||
\(683\) | 1.18478e7 | 0.971822 | 0.485911 | − | 0.874008i | \(-0.338488\pi\) | ||||
0.485911 | + | 0.874008i | \(0.338488\pi\) | |||||||
\(684\) | 2.18376e6 | 0.178470 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.90414e6 | −0.479012 | ||||||||
\(687\) | −811035. | −0.0655613 | ||||||||
\(688\) | 3.67386e6 | 0.295904 | ||||||||
\(689\) | 1.80952e6 | 0.145216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.47775e6 | 0.755110 | 0.377555 | − | 0.925987i | \(-0.376765\pi\) | ||||
0.377555 | + | 0.925987i | \(0.376765\pi\) | |||||||
\(692\) | 1.18100e7 | 0.937530 | ||||||||
\(693\) | 845154. | 0.0668502 | ||||||||
\(694\) | 1.60866e7 | 1.26785 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.54464e6 | 0.355612 | ||||||||
\(697\) | −2.94322e6 | −0.229478 | ||||||||
\(698\) | 33320.0 | 0.00258861 | ||||||||
\(699\) | 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. | 0.0225562 | ||||||||
\(703\) | 1.45618e7 | 1.11129 | ||||||||
\(704\) | 909312. | 0.0691483 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.80002e6 | 0.588958 | ||||||||
\(707\) | −1.58992e6 | −0.119626 | ||||||||
\(708\) | 2.53584e6 | 0.190125 | ||||||||
\(709\) | 1.27436e7 | 0.952090 | 0.476045 | − | 0.879421i | \(-0.342070\pi\) | ||||
0.476045 | + | 0.879421i | \(0.342070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.60196e6 | −0.415591 | ||||||||
\(712\) | 2.24256e6 | 0.165785 | ||||||||
\(713\) | −2.62946e6 | −0.193706 | ||||||||
\(714\) | 274104. | 0.0201219 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.95792e6 | 0.580119 | ||||||||
\(717\) | 1.03642e7 | 0.752902 | ||||||||
\(718\) | 9.08352e6 | 0.657572 | ||||||||
\(719\) | 2.44929e6 | 0.176692 | 0.0883462 | − | 0.996090i | \(-0.471842\pi\) | ||||
0.0883462 | + | 0.996090i | \(0.471842\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.27187e6 | −0.449323 | ||||||||
\(722\) | 1.45250e6 | 0.103699 | ||||||||
\(723\) | 7.70595e6 | 0.548252 | ||||||||
\(724\) | −5.33061e6 | −0.377947 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.02361e6 | −0.283318 | ||||||||
\(727\) | −415033. | −0.0291237 | −0.0145619 | − | 0.999894i | \(-0.504635\pi\) | ||||
−0.0145619 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(728\) | 303808. | 0.0212457 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32486e6 | 0.160918 | ||||||||
\(732\) | −3.14683e6 | −0.217068 | ||||||||
\(733\) | −1.72877e7 | −1.18844 | −0.594221 | − | 0.804302i | \(-0.702539\pi\) | ||||
−0.594221 | + | 0.804302i | \(0.702539\pi\) | |||||||
\(734\) | 1.14461e7 | 0.784186 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 313344. | 0.0213219 | ||||||||
\(737\) | 23754.0 | 0.00161090 | ||||||||
\(738\) | −5.88643e6 | −0.397843 | ||||||||
\(739\) | 5.18834e6 | 0.349476 | 0.174738 | − | 0.984615i | \(-0.444092\pi\) | ||||
0.174738 | + | 0.984615i | \(0.444092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.53166e6 | 0.102475 | ||||||||
\(742\) | 3.36821e6 | 0.224589 | ||||||||
\(743\) | 4.79572e6 | 0.318700 | 0.159350 | − | 0.987222i | \(-0.449060\pi\) | ||||
0.159350 | + | 0.987222i | \(0.449060\pi\) | |||||||
\(744\) | −4.94957e6 | −0.327820 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.46124e6 | 0.161923 | ||||||||
\(747\) | −8.79125e6 | −0.576434 | ||||||||
\(748\) | 575424. | 0.0376040 | ||||||||
\(749\) | 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. | −0.0181258 | ||||||||
\(753\) | −1.86937e6 | −0.120146 | ||||||||
\(754\) | 3.18756e6 | 0.204188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 548208. | 0.0348852 | ||||||||
\(757\) | 2.82068e7 | 1.78902 | 0.894508 | − | 0.447053i | \(-0.147526\pi\) | ||||
0.894508 | + | 0.447053i | \(0.147526\pi\) | |||||||
\(758\) | 2.15951e7 | 1.36516 | ||||||||
\(759\) | 611388. | 0.0385223 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.56161e6 | 0.410723 | 0.205361 | − | 0.978686i | \(-0.434163\pi\) | ||||
0.205361 | + | 0.978686i | \(0.434163\pi\) | |||||||
\(762\) | −9.21773e6 | −0.575091 | ||||||||
\(763\) | −1.01997e7 | −0.634273 | ||||||||
\(764\) | −650208. | −0.0403013 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.34750e6 | 0.267712 | ||||||||
\(767\) | 1.77861e6 | 0.109167 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 2.20930e7 | 1.34722 | 0.673610 | − | 0.739087i | \(-0.264743\pi\) | ||||
0.673610 | + | 0.739087i | \(0.264743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.30787e7 | −0.792371 | ||||||||
\(772\) | 7.91442e6 | 0.477942 | ||||||||
\(773\) | −3.00787e7 | −1.81055 | −0.905276 | − | 0.424824i | \(-0.860336\pi\) | ||||
−0.905276 | + | 0.424824i | \(0.860336\pi\) | |||||||
\(774\) | 4.64972e6 | 0.278981 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −52672.0 | −0.00313997 | ||||||||
\(777\) | 3.65557e6 | 0.217221 | ||||||||
\(778\) | −1.39373e7 | −0.825523 | ||||||||
\(779\) | −3.06131e7 | −1.80744 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.04162e6 | −0.530418 | ||||||||
\(782\) | 198288. | 0.0115952 | ||||||||
\(783\) | 5.75181e6 | 0.335274 | ||||||||
\(784\) | −3.73709e6 | −0.217142 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.26427e6 | 0.246200 | ||||||||
\(787\) | −3.28954e6 | −0.189321 | −0.0946605 | − | 0.995510i | \(-0.530177\pi\) | ||||
−0.0946605 | + | 0.995510i | \(0.530177\pi\) | |||||||
\(788\) | 8.83747e6 | 0.507005 | ||||||||
\(789\) | 1.52366e6 | 0.0871358 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.50123e6 | −0.369449 | ||||||||
\(792\) | 1.15085e6 | 0.0651936 | ||||||||
\(793\) | −2.20715e6 | −0.124638 | ||||||||
\(794\) | 1.30636e7 | 0.735381 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.09700e7 | 0.613655 | ||||||||
\(797\) | 6.71053e6 | 0.374206 | 0.187103 | − | 0.982340i | \(-0.440090\pi\) | ||||
0.187103 | + | 0.982340i | \(0.440090\pi\) | |||||||
\(798\) | 2.85102e6 | 0.158487 | ||||||||
\(799\) | −177876. | −0.00985713 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.83824e6 | 0.156303 | ||||||||
\(802\) | −1.70928e7 | −0.938374 | ||||||||
\(803\) | 7.70473e6 | 0.421666 | ||||||||
\(804\) | 15408.0 | 0.000840632 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.47157e6 | −0.188230 | ||||||||
\(807\) | −1.42298e7 | −0.769157 | ||||||||
\(808\) | −2.16499e6 | −0.116662 | ||||||||
\(809\) | 8.74254e6 | 0.469641 | 0.234821 | − | 0.972039i | \(-0.424550\pi\) | ||||
0.234821 | + | 0.972039i | \(0.424550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.48410e7 | −1.32622 | −0.663112 | − | 0.748520i | \(-0.730765\pi\) | ||||
−0.663112 | + | 0.748520i | \(0.730765\pi\) | |||||||
\(812\) | 5.93328e6 | 0.315795 | ||||||||
\(813\) | 7.40261e6 | 0.392788 | ||||||||
\(814\) | 7.67410e6 | 0.405944 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 373248. | 0.0196233 | ||||||||
\(817\) | 2.41814e7 | 1.26744 | ||||||||
\(818\) | −5.80750e6 | −0.303463 | ||||||||
\(819\) | 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. | −0.0245634 | ||||||||
\(823\) | −8.70659e6 | −0.448073 | −0.224036 | − | 0.974581i | \(-0.571923\pi\) | ||||
−0.224036 | + | 0.974581i | \(0.571923\pi\) | |||||||
\(824\) | −8.54042e6 | −0.438189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.31068e6 | 0.168837 | ||||||||
\(827\) | 3.71184e7 | 1.88723 | 0.943617 | − | 0.331040i | \(-0.107400\pi\) | ||||
0.943617 | + | 0.331040i | \(0.107400\pi\) | |||||||
\(828\) | 396576. | 0.0201025 | ||||||||
\(829\) | 1.01765e6 | 0.0514295 | 0.0257147 | − | 0.999669i | \(-0.491814\pi\) | ||||
0.0257147 | + | 0.999669i | \(0.491814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.92141e6 | −0.247222 | ||||||||
\(832\) | 413696. | 0.0207192 | ||||||||
\(833\) | −2.36488e6 | −0.118085 | ||||||||
\(834\) | −1.26266e7 | −0.628598 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.98512e6 | 0.296181 | ||||||||
\(837\) | −6.26430e6 | −0.309071 | ||||||||
\(838\) | 2.23752e6 | 0.110067 | ||||||||
\(839\) | −3.36194e7 | −1.64887 | −0.824433 | − | 0.565960i | \(-0.808506\pi\) | ||||
−0.824433 | + | 0.565960i | \(0.808506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.17410e7 | 2.03504 | ||||||||
\(842\) | −1.56588e7 | −0.761164 | ||||||||
\(843\) | −9.83248e6 | −0.476534 | ||||||||
\(844\) | 1.19916e7 | 0.579458 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −355752. | −0.0170892 | ||||||||
\(847\) | −5.25305e6 | −0.251596 | ||||||||
\(848\) | 4.58650e6 | 0.219024 | ||||||||
\(849\) | −2.23632e7 | −1.06479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.64445e6 | 0.125173 | ||||||||
\(852\) | −5.86483e6 | −0.276794 | ||||||||
\(853\) | −3.52574e7 | −1.65912 | −0.829559 | − | 0.558419i | \(-0.811408\pi\) | ||||
−0.829559 | + | 0.558419i | \(0.811408\pi\) | |||||||
\(854\) | −4.10836e6 | −0.192763 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.20013e6 | 0.242566 | ||||||||
\(857\) | −3.14941e7 | −1.46480 | −0.732398 | − | 0.680877i | \(-0.761599\pi\) | ||||
−0.732398 | + | 0.680877i | \(0.761599\pi\) | |||||||
\(858\) | 807192. | 0.0374333 | ||||||||
\(859\) | 1.19344e7 | 0.551848 | 0.275924 | − | 0.961180i | \(-0.411016\pi\) | ||||
0.275924 | + | 0.961180i | \(0.411016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.68506e6 | −0.353297 | ||||||||
\(862\) | −1.43000e7 | −0.655492 | ||||||||
\(863\) | 8.70442e6 | 0.397844 | 0.198922 | − | 0.980015i | \(-0.436256\pi\) | ||||
0.198922 | + | 0.980015i | \(0.436256\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.86388e7 | 1.29766 | ||||||||
\(867\) | −1.25425e7 | −0.566679 | ||||||||
\(868\) | −6.46194e6 | −0.291114 | ||||||||
\(869\) | −1.53535e7 | −0.689697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10807.0 | 0.000482681 0 | ||||||||
\(872\) | −1.38890e7 | −0.618555 | ||||||||
\(873\) | −66663.0 | −0.00296039 | ||||||||
\(874\) | 2.06244e6 | 0.0913277 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.99766e6 | 0.220043 | ||||||||
\(877\) | 1.17999e7 | 0.518059 | 0.259029 | − | 0.965869i | \(-0.416597\pi\) | ||||
0.259029 | + | 0.965869i | \(0.416597\pi\) | |||||||
\(878\) | 6.87158e6 | 0.300829 | ||||||||
\(879\) | −3.07255e6 | −0.134130 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.73840e7 | −1.18866 | −0.594330 | − | 0.804221i | \(-0.702583\pi\) | ||||
−0.594330 | + | 0.804221i | \(0.702583\pi\) | |||||||
\(882\) | −4.72975e6 | −0.204723 | ||||||||
\(883\) | −8.80577e6 | −0.380072 | −0.190036 | − | 0.981777i | \(-0.560860\pi\) | ||||
−0.190036 | + | 0.981777i | \(0.560860\pi\) | |||||||
\(884\) | 261792. | 0.0112675 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.35868e7 | 0.581477 | ||||||||
\(887\) | 250122. | 0.0106744 | 0.00533719 | − | 0.999986i | \(-0.498301\pi\) | ||||
0.00533719 | + | 0.999986i | \(0.498301\pi\) | |||||||
\(888\) | 4.97779e6 | 0.211838 | ||||||||
\(889\) | −1.20343e7 | −0.510699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45654e6 | 0.0614651 | ||||||||
\(892\) | 2.70834e6 | 0.113970 | ||||||||
\(893\) | −1.85013e6 | −0.0776379 | ||||||||
\(894\) | 3.95604e6 | 0.165545 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 770048. | 0.0320441 | ||||||||
\(897\) | 278154. | 0.0115426 | ||||||||
\(898\) | −1.35842e7 | −0.562140 | ||||||||
\(899\) | −6.77988e7 | −2.79784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.90239e6 | 0.119109 | ||||||||
\(902\) | −1.61332e7 | −0.660243 | ||||||||
\(903\) | 6.07047e6 | 0.247744 | ||||||||
\(904\) | −8.85274e6 | −0.360294 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.21371e6 | −0.251496 | ||||||||
\(907\) | −3.24955e7 | −1.31161 | −0.655806 | − | 0.754929i | \(-0.727671\pi\) | ||||
−0.655806 | + | 0.754929i | \(0.727671\pi\) | |||||||
\(908\) | −743808. | −0.0299396 | ||||||||
\(909\) | −2.74007e6 | −0.109990 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24595e7 | 1.69504 | 0.847518 | − | 0.530766i | \(-0.178096\pi\) | ||||
0.847518 | + | 0.530766i | \(0.178096\pi\) | |||||||
\(912\) | 3.88224e6 | 0.154559 | ||||||||
\(913\) | −2.40945e7 | −0.956625 | ||||||||
\(914\) | −1.81126e7 | −0.717157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.44184e6 | −0.0567778 | ||||||||
\(917\) | 5.56724e6 | 0.218634 | ||||||||
\(918\) | 472392. | 0.0185010 | ||||||||
\(919\) | 1.41629e7 | 0.553176 | 0.276588 | − | 0.960989i | \(-0.410796\pi\) | ||||
0.276588 | + | 0.960989i | \(0.410796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.82608e7 | 0.709366 | ||||||||
\(922\) | −5.11579e6 | −0.198192 | ||||||||
\(923\) | −4.11353e6 | −0.158932 | ||||||||
\(924\) | 1.50250e6 | 0.0578940 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.87945e7 | −1.10352 | ||||||||
\(927\) | −1.08090e7 | −0.413128 | ||||||||
\(928\) | 8.07936e6 | 0.307969 | ||||||||
\(929\) | 4.37292e7 | 1.66239 | 0.831194 | − | 0.555982i | \(-0.187658\pi\) | ||||
0.831194 | + | 0.555982i | \(0.187658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.45976e7 | −0.930077 | ||||||||
\(932\) | 1.70262e7 | 0.642063 | ||||||||
\(933\) | −1.85938e6 | −0.0699302 | ||||||||
\(934\) | 1.93214e7 | 0.724721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 523584. | 0.0195343 | ||||||||
\(937\) | 5.73509e6 | 0.213398 | 0.106699 | − | 0.994291i | \(-0.465972\pi\) | ||||
0.106699 | + | 0.994291i | \(0.465972\pi\) | |||||||
\(938\) | 20116.0 | 0.000746508 0 | ||||||||
\(939\) | −3.00801e7 | −1.11331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.37395e7 | −1.24212 | −0.621061 | − | 0.783762i | \(-0.713298\pi\) | ||||
−0.621061 | + | 0.783762i | \(0.713298\pi\) | |||||||
\(942\) | −1.25997e7 | −0.462631 | ||||||||
\(943\) | −5.55941e6 | −0.203587 | ||||||||
\(944\) | 4.50816e6 | 0.164653 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.27437e7 | 0.462985 | ||||||||
\(947\) | −3.07342e7 | −1.11365 | −0.556823 | − | 0.830631i | \(-0.687980\pi\) | ||||
−0.556823 | + | 0.830631i | \(0.687980\pi\) | |||||||
\(948\) | −9.95904e6 | −0.359912 | ||||||||
\(949\) | 3.50531e6 | 0.126346 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.27960e7 | −0.817348 | ||||||||
\(952\) | 487296. | 0.0174261 | ||||||||
\(953\) | −2.51847e7 | −0.898264 | −0.449132 | − | 0.893465i | \(-0.648267\pi\) | ||||
−0.449132 | + | 0.893465i | \(0.648267\pi\) | |||||||
\(954\) | 5.80478e6 | 0.206498 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.84253e7 | 0.652033 | ||||||||
\(957\) | 1.57642e7 | 0.556407 | ||||||||
\(958\) | 2.99460e6 | 0.105420 | ||||||||
\(959\) | −621246. | −0.0218131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.52105e7 | 1.57918 | ||||||||
\(962\) | 3.49137e6 | 0.121635 | ||||||||
\(963\) | 6.58141e6 | 0.228693 | ||||||||
\(964\) | 1.36995e7 | 0.474801 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 517752. | 0.0178517 | ||||||||
\(967\) | 1.44556e7 | 0.497130 | 0.248565 | − | 0.968615i | \(-0.420041\pi\) | ||||
0.248565 | + | 0.968615i | \(0.420041\pi\) | |||||||
\(968\) | −7.15309e6 | −0.245361 | ||||||||
\(969\) | 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. | 0.0320750 | ||||||||
\(973\) | −1.64848e7 | −0.558214 | ||||||||
\(974\) | −2.06558e7 | −0.697660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.59437e6 | −0.187986 | ||||||||
\(977\) | −8.41568e6 | −0.282067 | −0.141034 | − | 0.990005i | \(-0.545043\pi\) | ||||
−0.141034 | + | 0.990005i | \(0.545043\pi\) | |||||||
\(978\) | 6.93292e6 | 0.231776 | ||||||||
\(979\) | 7.77888e6 | 0.259394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75782e7 | −0.583180 | ||||||||
\(982\) | 3.41715e7 | 1.13080 | ||||||||
\(983\) | 3.89409e7 | 1.28535 | 0.642676 | − | 0.766138i | \(-0.277824\pi\) | ||||
0.642676 | + | 0.766138i | \(0.277824\pi\) | |||||||
\(984\) | −1.04648e7 | −0.344542 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.11272e6 | 0.167479 | ||||||||
\(987\) | −464454. | −0.0151757 | ||||||||
\(988\) | 2.72296e6 | 0.0887460 | ||||||||
\(989\) | 4.39141e6 | 0.142762 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.84592e7 | 1.56745 | 0.783723 | − | 0.621111i | \(-0.213318\pi\) | ||||
0.783723 | + | 0.621111i | \(0.213318\pi\) | |||||||
\(992\) | −8.79923e6 | −0.283900 | ||||||||
\(993\) | 5.41919e6 | 0.174406 | ||||||||
\(994\) | −7.65686e6 | −0.245802 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.56289e7 | −0.499206 | ||||||||
\(997\) | 3.84733e7 | 1.22581 | 0.612903 | − | 0.790158i | \(-0.290002\pi\) | ||||
0.612903 | + | 0.790158i | \(0.290002\pi\) | |||||||
\(998\) | −1.68235e7 | −0.534675 | ||||||||
\(999\) | 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.a.m.1.1 | yes | 1 | |
3.2 | odd | 2 | 450.6.a.i.1.1 | 1 | |||
5.2 | odd | 4 | 150.6.c.g.49.2 | 2 | |||
5.3 | odd | 4 | 150.6.c.g.49.1 | 2 | |||
5.4 | even | 2 | 150.6.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.e.199.1 | 2 | |||
15.8 | even | 4 | 450.6.c.e.199.2 | 2 | |||
15.14 | odd | 2 | 450.6.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
150.6.a.m.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
150.6.c.g.49.1 | 2 | 5.3 | odd | 4 | |||
150.6.c.g.49.2 | 2 | 5.2 | odd | 4 | |||
450.6.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.a.p.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.c.e.199.1 | 2 | 15.2 | even | 4 | |||
450.6.c.e.199.2 | 2 | 15.8 | even | 4 |