Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,6,Mod(1,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, 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("99.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.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: | \(15.8779981615\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.37228 | −1.65680 | −0.828400 | − | 0.560136i | \(-0.810749\pi\) | ||||
−0.828400 | + | 0.560136i | \(0.810749\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 55.8397 | 1.74499 | ||||||||
\(5\) | −0.277187 | −0.00495847 | −0.00247923 | − | 0.999997i | \(-0.500789\pi\) | ||||
−0.00247923 | + | 0.999997i | \(0.500789\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −105.081 | −0.810552 | −0.405276 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405276 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(8\) | −223.432 | −1.23430 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.59787 | 0.00821519 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 147.549 | 0.242146 | 0.121073 | − | 0.992644i | \(-0.461366\pi\) | ||||
0.121073 | + | 0.992644i | \(0.461366\pi\) | |||||||
\(14\) | 984.853 | 1.34292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 307.198 | 0.299998 | ||||||||
\(17\) | 1432.49 | 1.20218 | 0.601089 | − | 0.799182i | \(-0.294734\pi\) | ||||
0.601089 | + | 0.799182i | \(0.294734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2033.18 | 1.29209 | 0.646045 | − | 0.763300i | \(-0.276422\pi\) | ||||
0.646045 | + | 0.763300i | \(0.276422\pi\) | |||||||
\(20\) | −15.4780 | −0.00865247 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1134.05 | −0.499544 | ||||||||
\(23\) | −828.853 | −0.326707 | −0.163353 | − | 0.986568i | \(-0.552231\pi\) | ||||
−0.163353 | + | 0.986568i | \(0.552231\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3124.92 | −0.999975 | ||||||||
\(26\) | −1382.87 | −0.401188 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5867.71 | −1.41440 | ||||||||
\(29\) | −4633.44 | −1.02308 | −0.511539 | − | 0.859260i | \(-0.670924\pi\) | ||||
−0.511539 | + | 0.859260i | \(0.670924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9835.65 | −1.83823 | −0.919113 | − | 0.393994i | \(-0.871093\pi\) | ||||
−0.919113 | + | 0.393994i | \(0.871093\pi\) | |||||||
\(32\) | 4270.67 | 0.737261 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13425.7 | −1.99177 | ||||||||
\(35\) | 29.1272 | 0.00401910 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7134.34 | 0.856741 | 0.428371 | − | 0.903603i | \(-0.359088\pi\) | ||||
0.428371 | + | 0.903603i | \(0.359088\pi\) | |||||||
\(38\) | −19055.6 | −2.14074 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 61.9324 | 0.00612023 | ||||||||
\(41\) | −18265.0 | −1.69691 | −0.848456 | − | 0.529265i | \(-0.822468\pi\) | ||||
−0.848456 | + | 0.529265i | \(0.822468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13822.5 | 1.14003 | 0.570016 | − | 0.821634i | \(-0.306937\pi\) | ||||
0.570016 | + | 0.821634i | \(0.306937\pi\) | |||||||
\(44\) | 6756.60 | 0.526134 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7768.24 | 0.541288 | ||||||||
\(47\) | −22991.2 | −1.51816 | −0.759079 | − | 0.650999i | \(-0.774350\pi\) | ||||
−0.759079 | + | 0.650999i | \(0.774350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5764.89 | −0.343005 | ||||||||
\(50\) | 29287.7 | 1.65676 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8239.08 | 0.422542 | ||||||||
\(53\) | −14311.9 | −0.699856 | −0.349928 | − | 0.936777i | \(-0.613794\pi\) | ||||
−0.349928 | + | 0.936777i | \(0.613794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33.5396 | −0.00149503 | ||||||||
\(56\) | 23478.6 | 1.00046 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 43425.9 | 1.69504 | ||||||||
\(59\) | 7081.12 | 0.264833 | 0.132416 | − | 0.991194i | \(-0.457726\pi\) | ||||
0.132416 | + | 0.991194i | \(0.457726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18470.2 | −0.635547 | −0.317774 | − | 0.948167i | \(-0.602935\pi\) | ||||
−0.317774 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(62\) | 92182.5 | 3.04557 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −49856.3 | −1.52149 | ||||||||
\(65\) | −40.8986 | −0.00120067 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16229.5 | 0.441690 | 0.220845 | − | 0.975309i | \(-0.429119\pi\) | ||||
0.220845 | + | 0.975309i | \(0.429119\pi\) | |||||||
\(68\) | 79989.7 | 2.09779 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −272.988 | −0.00665884 | ||||||||
\(71\) | −28198.9 | −0.663875 | −0.331938 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331938 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39382.9 | −0.864968 | −0.432484 | − | 0.901642i | \(-0.642363\pi\) | ||||
−0.432484 | + | 0.901642i | \(0.642363\pi\) | |||||||
\(74\) | −66865.1 | −1.41945 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 113532. | 2.25468 | ||||||||
\(77\) | −12714.9 | −0.244391 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −41243.7 | −0.743515 | −0.371758 | − | 0.928330i | \(-0.621245\pi\) | ||||
−0.371758 | + | 0.928330i | \(0.621245\pi\) | |||||||
\(80\) | −85.1513 | −0.00148753 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 171185. | 2.81145 | ||||||||
\(83\) | 23355.3 | 0.372126 | 0.186063 | − | 0.982538i | \(-0.440427\pi\) | ||||
0.186063 | + | 0.982538i | \(0.440427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −397.067 | −0.00596096 | ||||||||
\(86\) | −129549. | −1.88880 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −27035.3 | −0.372155 | ||||||||
\(89\) | 103803. | 1.38911 | 0.694555 | − | 0.719440i | \(-0.255601\pi\) | ||||
0.694555 | + | 0.719440i | \(0.255601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15504.6 | −0.196272 | ||||||||
\(92\) | −46282.9 | −0.570099 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 215480. | 2.51528 | ||||||||
\(95\) | −563.572 | −0.00640678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −149289. | −1.61101 | −0.805503 | − | 0.592592i | \(-0.798105\pi\) | ||||
−0.805503 | + | 0.592592i | \(0.798105\pi\) | |||||||
\(98\) | 54030.2 | 0.568292 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −174495. | −1.74495 | ||||||||
\(101\) | −62410.1 | −0.608768 | −0.304384 | − | 0.952549i | \(-0.598451\pi\) | ||||
−0.304384 | + | 0.952549i | \(0.598451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −90047.2 | −0.836329 | −0.418165 | − | 0.908371i | \(-0.637326\pi\) | ||||
−0.418165 | + | 0.908371i | \(0.637326\pi\) | |||||||
\(104\) | −32967.1 | −0.298881 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 134136. | 1.15952 | ||||||||
\(107\) | −120458. | −1.01713 | −0.508566 | − | 0.861023i | \(-0.669824\pi\) | ||||
−0.508566 | + | 0.861023i | \(0.669824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −91854.0 | −0.740511 | −0.370256 | − | 0.928930i | \(-0.620730\pi\) | ||||
−0.370256 | + | 0.928930i | \(0.620730\pi\) | |||||||
\(110\) | 314.343 | 0.00247697 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32280.8 | −0.243164 | ||||||||
\(113\) | 29619.6 | 0.218214 | 0.109107 | − | 0.994030i | \(-0.465201\pi\) | ||||
0.109107 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 229.747 | 0.00161996 | ||||||||
\(116\) | −258730. | −1.78526 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −66366.2 | −0.438775 | ||||||||
\(119\) | −150528. | −0.974428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 173108. | 1.05298 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −549219. | −3.20768 | ||||||||
\(125\) | 1732.40 | 0.00991681 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 271128. | 1.49165 | 0.745823 | − | 0.666145i | \(-0.232057\pi\) | ||||
0.745823 | + | 0.666145i | \(0.232057\pi\) | |||||||
\(128\) | 330606. | 1.78355 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 383.313 | 0.00198928 | ||||||||
\(131\) | 223990. | 1.14038 | 0.570191 | − | 0.821512i | \(-0.306869\pi\) | ||||
0.570191 | + | 0.821512i | \(0.306869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −213650. | −1.04731 | ||||||||
\(134\) | −152107. | −0.731792 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −320064. | −1.48385 | ||||||||
\(137\) | 348229. | 1.58513 | 0.792563 | − | 0.609789i | \(-0.208746\pi\) | ||||
0.792563 | + | 0.609789i | \(0.208746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 333802. | 1.46538 | 0.732692 | − | 0.680560i | \(-0.238264\pi\) | ||||
0.732692 | + | 0.680560i | \(0.238264\pi\) | |||||||
\(140\) | 1626.45 | 0.00701328 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 264288. | 1.09991 | ||||||||
\(143\) | 17853.4 | 0.0730098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1284.33 | 0.00507290 | ||||||||
\(146\) | 369107. | 1.43308 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 398379. | 1.49500 | ||||||||
\(149\) | −310249. | −1.14484 | −0.572419 | − | 0.819961i | \(-0.693995\pi\) | ||||
−0.572419 | + | 0.819961i | \(0.693995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −54751.5 | −0.195413 | −0.0977066 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977066 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(152\) | −454278. | −1.59482 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 119167. | 0.404907 | ||||||||
\(155\) | 2726.31 | 0.00911478 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 221556. | 0.717354 | 0.358677 | − | 0.933462i | \(-0.383228\pi\) | ||||
0.358677 | + | 0.933462i | \(0.383228\pi\) | |||||||
\(158\) | 386547. | 1.23186 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1183.77 | −0.00365569 | ||||||||
\(161\) | 87097.1 | 0.264813 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −225239. | −0.664010 | −0.332005 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332005 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(164\) | −1.01991e6 | −2.96109 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −218892. | −0.616539 | ||||||||
\(167\) | −186796. | −0.518294 | −0.259147 | − | 0.965838i | \(-0.583441\pi\) | ||||
−0.259147 | + | 0.965838i | \(0.583441\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −349522. | −0.941365 | ||||||||
\(170\) | 3721.42 | 0.00987613 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 771846. | 1.98934 | ||||||||
\(173\) | 713662. | 1.81292 | 0.906458 | − | 0.422296i | \(-0.138776\pi\) | ||||
0.906458 | + | 0.422296i | \(0.138776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 328371. | 0.810532 | ||||||||
\(176\) | 37171.0 | 0.0904529 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −972875. | −2.30148 | ||||||||
\(179\) | −789450. | −1.84159 | −0.920793 | − | 0.390051i | \(-0.872457\pi\) | ||||
−0.920793 | + | 0.390051i | \(0.872457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 40330.7 | 0.0915039 | 0.0457519 | − | 0.998953i | \(-0.485432\pi\) | ||||
0.0457519 | + | 0.998953i | \(0.485432\pi\) | |||||||
\(182\) | 145314. | 0.325184 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 185192. | 0.403254 | ||||||||
\(185\) | −1977.55 | −0.00424812 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 173331. | 0.362470 | ||||||||
\(188\) | −1.28382e6 | −2.64917 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5281.95 | 0.0106148 | ||||||||
\(191\) | −133736. | −0.265256 | −0.132628 | − | 0.991166i | \(-0.542342\pi\) | ||||
−0.132628 | + | 0.991166i | \(0.542342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −462266. | −0.893303 | −0.446652 | − | 0.894708i | \(-0.647384\pi\) | ||||
−0.446652 | + | 0.894708i | \(0.647384\pi\) | |||||||
\(194\) | 1.39917e6 | 2.66912 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −321910. | −0.598541 | ||||||||
\(197\) | −96432.5 | −0.177035 | −0.0885173 | − | 0.996075i | \(-0.528213\pi\) | ||||
−0.0885173 | + | 0.996075i | \(0.528213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.08264e6 | −1.93800 | −0.968999 | − | 0.247066i | \(-0.920533\pi\) | ||||
−0.968999 | + | 0.247066i | \(0.920533\pi\) | |||||||
\(200\) | 698208. | 1.23427 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 584925. | 1.00861 | ||||||||
\(203\) | 486889. | 0.829258 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5062.81 | 0.00841409 | ||||||||
\(206\) | 843948. | 1.38563 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 45326.7 | 0.0726434 | ||||||||
\(209\) | 246015. | 0.389580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 875588. | 1.35392 | 0.676961 | − | 0.736019i | \(-0.263297\pi\) | ||||
0.676961 | + | 0.736019i | \(0.263297\pi\) | |||||||
\(212\) | −799174. | −1.22124 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.12897e6 | 1.68518 | ||||||||
\(215\) | −3831.43 | −0.00565281 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.03354e6 | 1.48998 | ||||||||
\(218\) | 860881. | 1.22688 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1872.84 | −0.00260882 | ||||||||
\(221\) | 211362. | 0.291103 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 988042. | 1.33049 | 0.665247 | − | 0.746623i | \(-0.268326\pi\) | ||||
0.665247 | + | 0.746623i | \(0.268326\pi\) | |||||||
\(224\) | −448769. | −0.597589 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −277603. | −0.361537 | ||||||||
\(227\) | −67066.0 | −0.0863849 | −0.0431925 | − | 0.999067i | \(-0.513753\pi\) | ||||
−0.0431925 | + | 0.999067i | \(0.513753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −662131. | −0.834363 | −0.417182 | − | 0.908823i | \(-0.636982\pi\) | ||||
−0.417182 | + | 0.908823i | \(0.636982\pi\) | |||||||
\(230\) | −2153.25 | −0.00268396 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.03526e6 | 1.26278 | ||||||||
\(233\) | −1.37961e6 | −1.66482 | −0.832411 | − | 0.554159i | \(-0.813040\pi\) | ||||
−0.832411 | + | 0.554159i | \(0.813040\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6372.85 | 0.00752773 | ||||||||
\(236\) | 395407. | 0.462130 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.41079e6 | 1.61443 | ||||||||
\(239\) | −423791. | −0.479907 | −0.239954 | − | 0.970784i | \(-0.577132\pi\) | ||||
−0.239954 | + | 0.970784i | \(0.577132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34802e6 | −1.49504 | −0.747521 | − | 0.664238i | \(-0.768756\pi\) | ||||
−0.747521 | + | 0.664238i | \(0.768756\pi\) | |||||||
\(242\) | −137220. | −0.150618 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.03137e6 | −1.10902 | ||||||||
\(245\) | 1597.95 | 0.00170078 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 299994. | 0.312874 | ||||||||
\(248\) | 2.19760e6 | 2.26892 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16236.5 | −0.0164302 | ||||||||
\(251\) | 1.45914e6 | 1.46188 | 0.730940 | − | 0.682442i | \(-0.239082\pi\) | ||||
0.730940 | + | 0.682442i | \(0.239082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −100291. | −0.0985057 | ||||||||
\(254\) | −2.54109e6 | −2.47136 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.50313e6 | −1.43349 | ||||||||
\(257\) | −548503. | −0.518020 | −0.259010 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259010 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −749687. | −0.694434 | ||||||||
\(260\) | −2283.76 | −0.00209516 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.09930e6 | −1.88939 | ||||||||
\(263\) | −905299. | −0.807054 | −0.403527 | − | 0.914968i | \(-0.632216\pi\) | ||||
−0.403527 | + | 0.914968i | \(0.632216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3967.08 | 0.00347021 | ||||||||
\(266\) | 2.00239e6 | 1.73518 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 906248. | 0.770744 | ||||||||
\(269\) | 164041. | 0.138220 | 0.0691100 | − | 0.997609i | \(-0.477984\pi\) | ||||
0.0691100 | + | 0.997609i | \(0.477984\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 989636. | 0.818563 | 0.409282 | − | 0.912408i | \(-0.365779\pi\) | ||||
0.409282 | + | 0.912408i | \(0.365779\pi\) | |||||||
\(272\) | 440058. | 0.360651 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.26370e6 | −2.62624 | ||||||||
\(275\) | −378116. | −0.301504 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 727149. | 0.569409 | 0.284704 | − | 0.958615i | \(-0.408105\pi\) | ||||
0.284704 | + | 0.958615i | \(0.408105\pi\) | |||||||
\(278\) | −3.12848e6 | −2.42785 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6507.94 | −0.00496077 | ||||||||
\(281\) | 379100. | 0.286410 | 0.143205 | − | 0.989693i | \(-0.454259\pi\) | ||||
0.143205 | + | 0.989693i | \(0.454259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −695371. | −0.516120 | −0.258060 | − | 0.966129i | \(-0.583083\pi\) | ||||
−0.258060 | + | 0.966129i | \(0.583083\pi\) | |||||||
\(284\) | −1.57462e6 | −1.15846 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −167327. | −0.120963 | ||||||||
\(287\) | 1.91931e6 | 1.37544 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 632167. | 0.445233 | ||||||||
\(290\) | −12037.1 | −0.00840479 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.19913e6 | −1.50936 | ||||||||
\(293\) | −268373. | −0.182629 | −0.0913146 | − | 0.995822i | \(-0.529107\pi\) | ||||
−0.0913146 | + | 0.995822i | \(0.529107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1962.79 | −0.00131316 | ||||||||
\(296\) | −1.59404e6 | −1.05747 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.90774e6 | 1.89677 | ||||||||
\(299\) | −122296. | −0.0791107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.45249e6 | −0.924055 | ||||||||
\(302\) | 513147. | 0.323761 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 624591. | 0.387625 | ||||||||
\(305\) | 5119.71 | 0.00315134 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.78841e6 | 1.08298 | 0.541491 | − | 0.840706i | \(-0.317860\pi\) | ||||
0.541491 | + | 0.840706i | \(0.317860\pi\) | |||||||
\(308\) | −709993. | −0.426459 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25551.8 | −0.0151014 | ||||||||
\(311\) | −362727. | −0.212657 | −0.106328 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106328 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.14382e6 | −0.659926 | −0.329963 | − | 0.943994i | \(-0.607036\pi\) | ||||
−0.329963 | + | 0.943994i | \(0.607036\pi\) | |||||||
\(314\) | −2.07648e6 | −1.18851 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.30303e6 | −1.29743 | ||||||||
\(317\) | −3.43750e6 | −1.92130 | −0.960649 | − | 0.277766i | \(-0.910406\pi\) | ||||
−0.960649 | + | 0.277766i | \(0.910406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −560647. | −0.308470 | ||||||||
\(320\) | 13819.5 | 0.00754428 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −816298. | −0.438742 | ||||||||
\(323\) | 2.91251e6 | 1.55332 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −461079. | −0.242140 | ||||||||
\(326\) | 2.11100e6 | 1.10013 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.08098e6 | 2.09450 | ||||||||
\(329\) | 2.41595e6 | 1.23055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.11428e6 | 0.559015 | 0.279507 | − | 0.960144i | \(-0.409829\pi\) | ||||
0.279507 | + | 0.960144i | \(0.409829\pi\) | |||||||
\(332\) | 1.30415e6 | 0.649356 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.75070e6 | 0.858710 | ||||||||
\(335\) | −4498.59 | −0.00219010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.25804e6 | −1.08307 | −0.541535 | − | 0.840678i | \(-0.682157\pi\) | ||||
−0.541535 | + | 0.840678i | \(0.682157\pi\) | |||||||
\(338\) | 3.27582e6 | 1.55965 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22172.1 | −0.0104018 | ||||||||
\(341\) | −1.19011e6 | −0.554246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.37189e6 | 1.08858 | ||||||||
\(344\) | −3.08840e6 | −1.40714 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.68865e6 | −3.00364 | ||||||||
\(347\) | 1.17055e6 | 0.521873 | 0.260937 | − | 0.965356i | \(-0.415969\pi\) | ||||
0.260937 | + | 0.965356i | \(0.415969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.21704e6 | 0.534863 | 0.267432 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267432 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(350\) | −3.07759e6 | −1.34289 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 516752. | 0.222293 | ||||||||
\(353\) | −286188. | −0.122240 | −0.0611201 | − | 0.998130i | \(-0.519467\pi\) | ||||
−0.0611201 | + | 0.998130i | \(0.519467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7816.37 | 0.00329180 | ||||||||
\(356\) | 5.79635e6 | 2.42398 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.39895e6 | 3.05114 | ||||||||
\(359\) | −1.19066e6 | −0.487588 | −0.243794 | − | 0.969827i | \(-0.578392\pi\) | ||||
−0.243794 | + | 0.969827i | \(0.578392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.65774e6 | 0.669495 | ||||||||
\(362\) | −377991. | −0.151604 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −865774. | −0.342492 | ||||||||
\(365\) | 10916.4 | 0.00428892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.11120e6 | 1.20577 | 0.602884 | − | 0.797829i | \(-0.294018\pi\) | ||||
0.602884 | + | 0.797829i | \(0.294018\pi\) | |||||||
\(368\) | −254622. | −0.0980114 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18534.1 | 0.00703830 | ||||||||
\(371\) | 1.50392e6 | 0.567270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.58536e6 | 1.33432 | 0.667160 | − | 0.744914i | \(-0.267510\pi\) | ||||
0.667160 | + | 0.744914i | \(0.267510\pi\) | |||||||
\(374\) | −1.62451e6 | −0.600541 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.13697e6 | 1.87386 | ||||||||
\(377\) | −683659. | −0.247734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.87822e6 | 0.671660 | 0.335830 | − | 0.941923i | \(-0.390983\pi\) | ||||
0.335830 | + | 0.941923i | \(0.390983\pi\) | |||||||
\(380\) | −31469.6 | −0.0111798 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.25341e6 | 0.439476 | ||||||||
\(383\) | 662654. | 0.230829 | 0.115414 | − | 0.993317i | \(-0.463180\pi\) | ||||
0.115414 | + | 0.993317i | \(0.463180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3524.39 | 0.00121180 | ||||||||
\(386\) | 4.33249e6 | 1.48003 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.33622e6 | −2.81119 | ||||||||
\(389\) | 5.08370e6 | 1.70336 | 0.851678 | − | 0.524065i | \(-0.175585\pi\) | ||||
0.851678 | + | 0.524065i | \(0.175585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.18732e6 | −0.392760 | ||||||||
\(392\) | 1.28806e6 | 0.423371 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 903793. | 0.293311 | ||||||||
\(395\) | 11432.2 | 0.00368670 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −518385. | −0.165073 | −0.0825366 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825366 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(398\) | 1.01468e7 | 3.21088 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −959971. | −0.299991 | ||||||||
\(401\) | −1.12538e6 | −0.349493 | −0.174747 | − | 0.984613i | \(-0.555911\pi\) | ||||
−0.174747 | + | 0.984613i | \(0.555911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.45124e6 | −0.445119 | ||||||||
\(404\) | −3.48496e6 | −1.06229 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.56326e6 | −1.37392 | ||||||||
\(407\) | 863256. | 0.258317 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.15394e6 | 0.932279 | 0.466139 | − | 0.884711i | \(-0.345645\pi\) | ||||
0.466139 | + | 0.884711i | \(0.345645\pi\) | |||||||
\(410\) | −47450.1 | −0.0139405 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.02821e6 | −1.45939 | ||||||||
\(413\) | −744094. | −0.214661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6473.78 | −0.00184518 | ||||||||
\(416\) | 630133. | 0.178525 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.30572e6 | −0.645456 | ||||||||
\(419\) | −801315. | −0.222981 | −0.111491 | − | 0.993765i | \(-0.535562\pi\) | ||||
−0.111491 | + | 0.993765i | \(0.535562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.85449e6 | −0.509940 | −0.254970 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254970 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(422\) | −8.20626e6 | −2.24318 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.19775e6 | 0.863832 | ||||||||
\(425\) | −4.47642e6 | −1.20215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.94088e6 | 0.515144 | ||||||||
\(428\) | −6.72635e6 | −1.77488 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35909.2 | 0.00936558 | ||||||||
\(431\) | −2.46004e6 | −0.637895 | −0.318947 | − | 0.947772i | \(-0.603329\pi\) | ||||
−0.318947 | + | 0.947772i | \(0.603329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.12223e6 | 0.800287 | 0.400144 | − | 0.916452i | \(-0.368960\pi\) | ||||
0.400144 | + | 0.916452i | \(0.368960\pi\) | |||||||
\(434\) | −9.68667e6 | −2.46860 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.12910e6 | −1.29218 | ||||||||
\(437\) | −1.68521e6 | −0.422134 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.09275e6 | −1.50887 | −0.754436 | − | 0.656374i | \(-0.772089\pi\) | ||||
−0.754436 | + | 0.656374i | \(0.772089\pi\) | |||||||
\(440\) | 7493.82 | 0.00184532 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.98094e6 | −0.482299 | ||||||||
\(443\) | 7.93457e6 | 1.92094 | 0.960470 | − | 0.278382i | \(-0.0897982\pi\) | ||||
0.960470 | + | 0.278382i | \(0.0897982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28772.9 | −0.00688786 | ||||||||
\(446\) | −9.26021e6 | −2.20436 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.23897e6 | 1.23325 | ||||||||
\(449\) | −4.61011e6 | −1.07918 | −0.539592 | − | 0.841926i | \(-0.681422\pi\) | ||||
−0.539592 | + | 0.841926i | \(0.681422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.21006e6 | −0.511638 | ||||||||
\(452\) | 1.65395e6 | 0.380781 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 628562. | 0.143123 | ||||||||
\(455\) | 4297.68 | 0.000973208 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.05458e6 | −1.80407 | −0.902033 | − | 0.431667i | \(-0.857926\pi\) | ||||
−0.902033 | + | 0.431667i | \(0.857926\pi\) | |||||||
\(458\) | 6.20568e6 | 1.38237 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12829.0 | 0.00282682 | ||||||||
\(461\) | −3.22431e6 | −0.706617 | −0.353309 | − | 0.935507i | \(-0.614943\pi\) | ||||
−0.353309 | + | 0.935507i | \(0.614943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.29607e6 | 0.280979 | 0.140490 | − | 0.990082i | \(-0.455132\pi\) | ||||
0.140490 | + | 0.990082i | \(0.455132\pi\) | |||||||
\(464\) | −1.42339e6 | −0.306922 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.29301e7 | 2.75828 | ||||||||
\(467\) | 2.13902e6 | 0.453860 | 0.226930 | − | 0.973911i | \(-0.427131\pi\) | ||||
0.226930 | + | 0.973911i | \(0.427131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.70542e6 | −0.358012 | ||||||||
\(470\) | −59728.2 | −0.0124720 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.58215e6 | −0.326883 | ||||||||
\(473\) | 1.67253e6 | 0.343732 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.35354e6 | −1.29206 | ||||||||
\(476\) | −8.40543e6 | −1.70037 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.97189e6 | 0.795111 | ||||||||
\(479\) | 4.77343e6 | 0.950586 | 0.475293 | − | 0.879828i | \(-0.342342\pi\) | ||||
0.475293 | + | 0.879828i | \(0.342342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05266e6 | 0.207457 | ||||||||
\(482\) | 1.26340e7 | 2.47699 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 817548. | 0.158635 | ||||||||
\(485\) | 41380.8 | 0.00798812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.98376e6 | 1.52541 | 0.762703 | − | 0.646749i | \(-0.223872\pi\) | ||||
0.762703 | + | 0.646749i | \(0.223872\pi\) | |||||||
\(488\) | 4.12684e6 | 0.784456 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14976.4 | −0.00281786 | ||||||||
\(491\) | 3.70031e6 | 0.692682 | 0.346341 | − | 0.938109i | \(-0.387424\pi\) | ||||
0.346341 | + | 0.938109i | \(0.387424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.63736e6 | −1.22992 | ||||||||
\(494\) | −2.81163e6 | −0.518371 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.02149e6 | −0.551465 | ||||||||
\(497\) | 2.96318e6 | 0.538105 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.05137e6 | −1.26772 | −0.633858 | − | 0.773449i | \(-0.718530\pi\) | ||||
−0.633858 | + | 0.773449i | \(0.718530\pi\) | |||||||
\(500\) | 96736.4 | 0.0173047 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.36754e7 | −2.42204 | ||||||||
\(503\) | 7.77325e6 | 1.36988 | 0.684940 | − | 0.728599i | \(-0.259828\pi\) | ||||
0.684940 | + | 0.728599i | \(0.259828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17299.3 | 0.00301856 | ||||||||
\(506\) | 939957. | 0.163204 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.51397e7 | 2.60290 | ||||||||
\(509\) | −4.11598e6 | −0.704173 | −0.352086 | − | 0.935968i | \(-0.614528\pi\) | ||||
−0.352086 | + | 0.935968i | \(0.614528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.13841e6 | 0.701102 | ||||||||
\(512\) | 3.50836e6 | 0.591465 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.14073e6 | 0.858256 | ||||||||
\(515\) | 24959.9 | 0.00414691 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.78193e6 | −0.457742 | ||||||||
\(518\) | 7.02628e6 | 1.15054 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9138.05 | 0.00148199 | ||||||||
\(521\) | 2.56352e6 | 0.413754 | 0.206877 | − | 0.978367i | \(-0.433670\pi\) | ||||
0.206877 | + | 0.978367i | \(0.433670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.69240e6 | −0.590274 | −0.295137 | − | 0.955455i | \(-0.595365\pi\) | ||||
−0.295137 | + | 0.955455i | \(0.595365\pi\) | |||||||
\(524\) | 1.25075e7 | 1.98996 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.48471e6 | 1.33713 | ||||||||
\(527\) | −1.40895e7 | −2.20988 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.74935e6 | −0.893263 | ||||||||
\(530\) | −37180.6 | −0.00574946 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.19301e7 | −1.82754 | ||||||||
\(533\) | −2.69498e6 | −0.410901 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33389.4 | 0.00504341 | ||||||||
\(536\) | −3.62618e6 | −0.545177 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.53743e6 | −0.229003 | ||||||||
\(539\) | −697552. | −0.103420 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.33636e6 | −1.37146 | −0.685732 | − | 0.727854i | \(-0.740518\pi\) | ||||
−0.685732 | + | 0.727854i | \(0.740518\pi\) | |||||||
\(542\) | −9.27515e6 | −1.35620 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.11769e6 | 0.886320 | ||||||||
\(545\) | 25460.7 | 0.00367180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.30814e6 | 0.186933 | 0.0934664 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934664 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(548\) | 1.94450e7 | 2.76603 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.54381e6 | 0.499532 | ||||||||
\(551\) | −9.42064e6 | −1.32191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.33395e6 | 0.602658 | ||||||||
\(554\) | −6.81505e6 | −0.943397 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.86394e7 | 2.55708 | ||||||||
\(557\) | −6.95945e6 | −0.950467 | −0.475234 | − | 0.879860i | \(-0.657636\pi\) | ||||
−0.475234 | + | 0.879860i | \(0.657636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.03950e6 | 0.276054 | ||||||||
\(560\) | 8947.82 | 0.00120572 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.55303e6 | −0.474524 | ||||||||
\(563\) | −6.90198e6 | −0.917704 | −0.458852 | − | 0.888513i | \(-0.651739\pi\) | ||||
−0.458852 | + | 0.888513i | \(0.651739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8210.15 | −0.00108201 | ||||||||
\(566\) | 6.51721e6 | 0.855107 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.30054e6 | 0.819421 | ||||||||
\(569\) | −3.31261e6 | −0.428933 | −0.214466 | − | 0.976731i | \(-0.568801\pi\) | ||||
−0.214466 | + | 0.976731i | \(0.568801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.43930e7 | 1.84741 | 0.923703 | − | 0.383109i | \(-0.125147\pi\) | ||||
0.923703 | + | 0.383109i | \(0.125147\pi\) | |||||||
\(572\) | 996928. | 0.127401 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.79883e7 | −2.27882 | ||||||||
\(575\) | 2.59010e6 | 0.326699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.31761e6 | 0.414845 | 0.207423 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207423 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(578\) | −5.92484e6 | −0.737662 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 71716.5 | 0.00885216 | ||||||||
\(581\) | −2.45421e6 | −0.301628 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.73174e6 | −0.211015 | ||||||||
\(584\) | 8.79939e6 | 1.06763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.51527e6 | 0.302580 | ||||||||
\(587\) | −2.10735e6 | −0.252431 | −0.126215 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126215 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.99977e7 | −2.37515 | ||||||||
\(590\) | 18395.8 | 0.00217565 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.19166e6 | 0.257021 | ||||||||
\(593\) | −525039. | −0.0613133 | −0.0306566 | − | 0.999530i | \(-0.509760\pi\) | ||||
−0.0306566 | + | 0.999530i | \(0.509760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41724.4 | 0.00483167 | ||||||||
\(596\) | −1.73242e7 | −1.99773 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.14619e6 | 0.131071 | ||||||||
\(599\) | 7.02964e6 | 0.800509 | 0.400254 | − | 0.916404i | \(-0.368922\pi\) | ||||
0.400254 | + | 0.916404i | \(0.368922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.11158e6 | −0.125532 | −0.0627660 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627660 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(602\) | 1.36132e7 | 1.53097 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.05731e6 | −0.340994 | ||||||||
\(605\) | −4058.29 | −0.000450770 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.53428e7 | 1.69018 | 0.845088 | − | 0.534627i | \(-0.179548\pi\) | ||||
0.845088 | + | 0.534627i | \(0.179548\pi\) | |||||||
\(608\) | 8.68307e6 | 0.952608 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −47983.3 | −0.00522115 | ||||||||
\(611\) | −3.39232e6 | −0.367616 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.78522e6 | 0.514341 | 0.257170 | − | 0.966366i | \(-0.417210\pi\) | ||||
0.257170 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(614\) | −1.67615e7 | −1.79429 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.84091e6 | 0.301651 | ||||||||
\(617\) | −1.69116e7 | −1.78843 | −0.894215 | − | 0.447639i | \(-0.852265\pi\) | ||||
−0.894215 | + | 0.447639i | \(0.852265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.65985e6 | −0.908414 | −0.454207 | − | 0.890896i | \(-0.650077\pi\) | ||||
−0.454207 | + | 0.890896i | \(0.650077\pi\) | |||||||
\(620\) | 152236. | 0.0159052 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.39958e6 | 0.352330 | ||||||||
\(623\) | −1.09078e7 | −1.12595 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.76490e6 | 0.999926 | ||||||||
\(626\) | 1.07202e7 | 1.09337 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.23716e7 | 1.25178 | ||||||||
\(629\) | 1.02199e7 | 1.02996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.04083e6 | 0.903930 | 0.451965 | − | 0.892036i | \(-0.350723\pi\) | ||||
0.451965 | + | 0.892036i | \(0.350723\pi\) | |||||||
\(632\) | 9.21516e6 | 0.917720 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.22172e7 | 3.18321 | ||||||||
\(635\) | −75153.2 | −0.00739627 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −850603. | −0.0830574 | ||||||||
\(638\) | 5.25454e6 | 0.511073 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −91639.5 | −0.00884368 | ||||||||
\(641\) | 1.21113e7 | 1.16424 | 0.582122 | − | 0.813101i | \(-0.302222\pi\) | ||||
0.582122 | + | 0.813101i | \(0.302222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.24955e6 | 0.214570 | 0.107285 | − | 0.994228i | \(-0.465784\pi\) | ||||
0.107285 | + | 0.994228i | \(0.465784\pi\) | |||||||
\(644\) | 4.86347e6 | 0.462095 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.72969e7 | −2.57355 | ||||||||
\(647\) | −8.21206e6 | −0.771244 | −0.385622 | − | 0.922657i | \(-0.626013\pi\) | ||||
−0.385622 | + | 0.922657i | \(0.626013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 856815. | 0.0798501 | ||||||||
\(650\) | 4.32136e6 | 0.401178 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.25773e7 | −1.15869 | ||||||||
\(653\) | 1.15110e7 | 1.05641 | 0.528203 | − | 0.849118i | \(-0.322866\pi\) | ||||
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −62087.1 | −0.00565455 | ||||||||
\(656\) | −5.61097e6 | −0.509071 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.26429e7 | −2.03877 | ||||||||
\(659\) | 1.79339e7 | 1.60865 | 0.804323 | − | 0.594192i | \(-0.202528\pi\) | ||||
0.804323 | + | 0.594192i | \(0.202528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.63046e6 | −0.768299 | −0.384150 | − | 0.923271i | \(-0.625505\pi\) | ||||
−0.384150 | + | 0.923271i | \(0.625505\pi\) | |||||||
\(662\) | −1.04433e7 | −0.926176 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.21832e6 | −0.459315 | ||||||||
\(665\) | 59220.9 | 0.00519303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.84044e6 | 0.334246 | ||||||||
\(668\) | −1.04306e7 | −0.904418 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 42162.1 | 0.00362857 | ||||||||
\(671\) | −2.23490e6 | −0.191625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.92878e7 | −1.64152 | −0.820758 | − | 0.571276i | \(-0.806449\pi\) | ||||
−0.820758 | + | 0.571276i | \(0.806449\pi\) | |||||||
\(674\) | 2.11630e7 | 1.79443 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.95172e7 | −1.64267 | ||||||||
\(677\) | −6.67400e6 | −0.559647 | −0.279824 | − | 0.960051i | \(-0.590276\pi\) | ||||
−0.279824 | + | 0.960051i | \(0.590276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.56875e7 | 1.30580 | ||||||||
\(680\) | 88717.4 | 0.00735761 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.11541e7 | 0.918275 | ||||||||
\(683\) | 7.83722e6 | 0.642851 | 0.321426 | − | 0.946935i | \(-0.395838\pi\) | ||||
0.321426 | + | 0.946935i | \(0.395838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −96524.6 | −0.00785980 | ||||||||
\(686\) | −2.22300e7 | −1.80355 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.24626e6 | 0.342007 | ||||||||
\(689\) | −2.11171e6 | −0.169467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.05838e7 | −1.63995 | −0.819974 | − | 0.572400i | \(-0.806012\pi\) | ||||
−0.819974 | + | 0.572400i | \(0.806012\pi\) | |||||||
\(692\) | 3.98507e7 | 3.16352 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.09707e7 | −0.864640 | ||||||||
\(695\) | −92525.4 | −0.00726606 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.61644e7 | −2.03999 | ||||||||
\(698\) | −1.14065e7 | −0.886162 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.83361e7 | 1.41437 | ||||||||
\(701\) | 8.88356e6 | 0.682797 | 0.341399 | − | 0.939919i | \(-0.389099\pi\) | ||||
0.341399 | + | 0.939919i | \(0.389099\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.45054e7 | 1.10699 | ||||||||
\(704\) | −6.03261e6 | −0.458748 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.68223e6 | 0.202528 | ||||||||
\(707\) | 6.55815e6 | 0.493438 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.33167e6 | 0.473045 | 0.236523 | − | 0.971626i | \(-0.423992\pi\) | ||||
0.236523 | + | 0.971626i | \(0.423992\pi\) | |||||||
\(710\) | −73257.2 | −0.00545386 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.31930e7 | −1.71458 | ||||||||
\(713\) | 8.15231e6 | 0.600560 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4948.73 | −0.000362017 0 | ||||||||
\(716\) | −4.40826e7 | −3.21355 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.11592e7 | 0.807836 | ||||||||
\(719\) | −3.88936e6 | −0.280579 | −0.140290 | − | 0.990111i | \(-0.544803\pi\) | ||||
−0.140290 | + | 0.990111i | \(0.544803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.46229e6 | 0.677888 | ||||||||
\(722\) | −1.55368e7 | −1.10922 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.25205e6 | 0.159673 | ||||||||
\(725\) | 1.44792e7 | 1.02305 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.34319e7 | 1.64426 | 0.822131 | − | 0.569299i | \(-0.192785\pi\) | ||||
0.822131 | + | 0.569299i | \(0.192785\pi\) | |||||||
\(728\) | 3.46423e6 | 0.242258 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −102312. | −0.00710588 | ||||||||
\(731\) | 1.98006e7 | 1.37052 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.77978e7 | 1.22351 | 0.611753 | − | 0.791049i | \(-0.290465\pi\) | ||||
0.611753 | + | 0.791049i | \(0.290465\pi\) | |||||||
\(734\) | −2.91591e7 | −1.99772 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.53976e6 | −0.240868 | ||||||||
\(737\) | 1.96376e6 | 0.133174 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.15950e6 | 0.212817 | 0.106409 | − | 0.994322i | \(-0.466065\pi\) | ||||
0.106409 | + | 0.994322i | \(0.466065\pi\) | |||||||
\(740\) | −110425. | −0.00741293 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.40952e7 | −0.939853 | ||||||||
\(743\) | 4.37086e6 | 0.290465 | 0.145233 | − | 0.989398i | \(-0.453607\pi\) | ||||
0.145233 | + | 0.989398i | \(0.453607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 85996.8 | 0.00567664 | ||||||||
\(746\) | −3.36030e7 | −2.21070 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.67875e6 | 0.632507 | ||||||||
\(749\) | 1.26579e7 | 0.824438 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.72544e7 | 1.11635 | 0.558173 | − | 0.829724i | \(-0.311502\pi\) | ||||
0.558173 | + | 0.829724i | \(0.311502\pi\) | |||||||
\(752\) | −7.06285e6 | −0.455445 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.40745e6 | 0.410447 | ||||||||
\(755\) | 15176.4 | 0.000968950 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.57084e7 | −0.996307 | −0.498153 | − | 0.867089i | \(-0.665988\pi\) | ||||
−0.498153 | + | 0.867089i | \(0.665988\pi\) | |||||||
\(758\) | −1.76033e7 | −1.11281 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 125920. | 0.00790789 | ||||||||
\(761\) | −5.01006e6 | −0.313604 | −0.156802 | − | 0.987630i | \(-0.550118\pi\) | ||||
−0.156802 | + | 0.987630i | \(0.550118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.65215e6 | 0.600223 | ||||||||
\(764\) | −7.46778e6 | −0.462869 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.21058e6 | −0.382437 | ||||||||
\(767\) | 1.04481e6 | 0.0641282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.47489e6 | 0.211897 | 0.105949 | − | 0.994372i | \(-0.466212\pi\) | ||||
0.105949 | + | 0.994372i | \(0.466212\pi\) | |||||||
\(770\) | −33031.6 | −0.00200772 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.58128e7 | −1.55880 | ||||||||
\(773\) | −2.29786e7 | −1.38317 | −0.691584 | − | 0.722296i | \(-0.743087\pi\) | ||||
−0.691584 | + | 0.722296i | \(0.743087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.07357e7 | 1.83818 | ||||||||
\(776\) | 3.33558e7 | 1.98846 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.76458e7 | −2.82212 | ||||||||
\(779\) | −3.71361e7 | −2.19256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.41207e6 | −0.200166 | ||||||||
\(782\) | 1.11279e7 | 0.650724 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.77096e6 | −0.102901 | ||||||||
\(785\) | −61412.3 | −0.00355698 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.40930e7 | −0.811087 | −0.405544 | − | 0.914076i | \(-0.632918\pi\) | ||||
−0.405544 | + | 0.914076i | \(0.632918\pi\) | |||||||
\(788\) | −5.38476e6 | −0.308923 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −107146. | −0.00610812 | ||||||||
\(791\) | −3.11247e6 | −0.176874 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.72526e6 | −0.153895 | ||||||||
\(794\) | 4.85845e6 | 0.273493 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.04545e7 | −3.38178 | ||||||||
\(797\) | 1.08281e7 | 0.603819 | 0.301909 | − | 0.953337i | \(-0.402376\pi\) | ||||
0.301909 | + | 0.953337i | \(0.402376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.29346e7 | −1.82510 | ||||||||
\(800\) | −1.33455e7 | −0.737243 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.05474e7 | 0.579041 | ||||||||
\(803\) | −4.76533e6 | −0.260798 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24142.2 | −0.00131307 | ||||||||
\(806\) | 1.36014e7 | 0.737474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.39444e7 | 0.751402 | ||||||||
\(809\) | 2.27494e7 | 1.22208 | 0.611040 | − | 0.791600i | \(-0.290752\pi\) | ||||
0.611040 | + | 0.791600i | \(0.290752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.33958e7 | −0.715179 | −0.357590 | − | 0.933879i | \(-0.616401\pi\) | ||||
−0.357590 | + | 0.933879i | \(0.616401\pi\) | |||||||
\(812\) | 2.71877e7 | 1.44705 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.09067e6 | −0.427980 | ||||||||
\(815\) | 62433.2 | 0.00329247 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.81038e7 | 1.47302 | ||||||||
\(818\) | −2.95596e7 | −1.54460 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 282706. | 0.0146825 | ||||||||
\(821\) | 1.77359e7 | 0.918323 | 0.459161 | − | 0.888353i | \(-0.348150\pi\) | ||||
0.459161 | + | 0.888353i | \(0.348150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.24560e7 | −1.15567 | −0.577834 | − | 0.816154i | \(-0.696102\pi\) | ||||
−0.577834 | + | 0.816154i | \(0.696102\pi\) | |||||||
\(824\) | 2.01194e7 | 1.03228 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.97386e6 | 0.355650 | ||||||||
\(827\) | 1.97457e7 | 1.00394 | 0.501972 | − | 0.864884i | \(-0.332608\pi\) | ||||
0.501972 | + | 0.864884i | \(0.332608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.61754e7 | 1.32284 | 0.661418 | − | 0.750017i | \(-0.269955\pi\) | ||||
0.661418 | + | 0.750017i | \(0.269955\pi\) | |||||||
\(830\) | 60674.1 | 0.00305709 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.35624e6 | −0.368424 | ||||||||
\(833\) | −8.25814e6 | −0.412354 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51777.4 | 0.00256995 | ||||||||
\(836\) | 1.37374e7 | 0.679812 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.51015e6 | 0.369435 | ||||||||
\(839\) | 3.69992e6 | 0.181463 | 0.0907313 | − | 0.995875i | \(-0.471080\pi\) | ||||
0.0907313 | + | 0.995875i | \(0.471080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 957652. | 0.0466893 | ||||||||
\(842\) | 1.73808e7 | 0.844869 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.88925e7 | 2.36258 | ||||||||
\(845\) | 96883.0 | 0.00466773 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.53850e6 | −0.0736866 | ||||||||
\(848\) | −4.39660e6 | −0.209956 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.19542e7 | 1.99172 | ||||||||
\(851\) | −5.91332e6 | −0.279903 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.90121e7 | 1.36523 | 0.682617 | − | 0.730776i | \(-0.260842\pi\) | ||||
0.682617 | + | 0.730776i | \(0.260842\pi\) | |||||||
\(854\) | −1.81905e7 | −0.853492 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.69142e7 | 1.25544 | ||||||||
\(857\) | 3.60120e7 | 1.67493 | 0.837463 | − | 0.546494i | \(-0.184038\pi\) | ||||
0.837463 | + | 0.546494i | \(0.184038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.14715e7 | −0.992841 | −0.496421 | − | 0.868082i | \(-0.665353\pi\) | ||||
−0.496421 | + | 0.868082i | \(0.665353\pi\) | |||||||
\(860\) | −213945. | −0.00986409 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.30562e7 | 1.05686 | ||||||||
\(863\) | −1.43154e7 | −0.654298 | −0.327149 | − | 0.944973i | \(-0.606088\pi\) | ||||
−0.327149 | + | 0.944973i | \(0.606088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −197818. | −0.00898928 | ||||||||
\(866\) | −2.92625e7 | −1.32592 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.77128e7 | 2.60000 | ||||||||
\(869\) | −4.99049e6 | −0.224178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.39464e6 | 0.106953 | ||||||||
\(872\) | 2.05231e7 | 0.914013 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.57943e7 | 0.699392 | ||||||||
\(875\) | −182043. | −0.00803809 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.25088e7 | 0.988221 | 0.494110 | − | 0.869399i | \(-0.335494\pi\) | ||||
0.494110 | + | 0.869399i | \(0.335494\pi\) | |||||||
\(878\) | 5.71030e7 | 2.49990 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10303.3 | −0.000448508 0 | ||||||||
\(881\) | −8.39629e6 | −0.364458 | −0.182229 | − | 0.983256i | \(-0.558331\pi\) | ||||
−0.182229 | + | 0.983256i | \(0.558331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.08666e7 | 0.469021 | 0.234510 | − | 0.972114i | \(-0.424651\pi\) | ||||
0.234510 | + | 0.972114i | \(0.424651\pi\) | |||||||
\(884\) | 1.18024e7 | 0.507971 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.43650e7 | −3.18262 | ||||||||
\(887\) | −1.53488e7 | −0.655038 | −0.327519 | − | 0.944845i | \(-0.606212\pi\) | ||||
−0.327519 | + | 0.944845i | \(0.606212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.84905e7 | −1.20906 | ||||||||
\(890\) | 269668. | 0.0114118 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.51719e7 | 2.32170 | ||||||||
\(893\) | −4.67453e7 | −1.96160 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 218825. | 0.00913145 | ||||||||
\(896\) | −3.47405e7 | −1.44566 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.32073e7 | 1.78799 | ||||||||
\(899\) | 4.55729e7 | 1.88065 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.05017e7 | −0.841352 | ||||||||
\(902\) | 2.07133e7 | 0.847683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.61796e6 | −0.269341 | ||||||||
\(905\) | −11179.1 | −0.000453719 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.93009e6 | 0.320081 | 0.160041 | − | 0.987110i | \(-0.448838\pi\) | ||||
0.160041 | + | 0.987110i | \(0.448838\pi\) | |||||||
\(908\) | −3.74494e6 | −0.150741 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −40279.1 | −0.00161241 | ||||||||
\(911\) | 4.31907e7 | 1.72423 | 0.862114 | − | 0.506715i | \(-0.169140\pi\) | ||||
0.862114 | + | 0.506715i | \(0.169140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.82599e6 | 0.112200 | ||||||||
\(914\) | 7.54898e7 | 2.98898 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.69732e7 | −1.45595 | ||||||||
\(917\) | −2.35372e7 | −0.924340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.17987e7 | −0.851414 | −0.425707 | − | 0.904861i | \(-0.639975\pi\) | ||||
−0.425707 | + | 0.904861i | \(0.639975\pi\) | |||||||
\(920\) | −51332.8 | −0.00199952 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.02191e7 | 1.17072 | ||||||||
\(923\) | −4.16072e6 | −0.160755 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.22943e7 | −0.856720 | ||||||||
\(926\) | −1.21471e7 | −0.465527 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.97879e7 | −0.754276 | ||||||||
\(929\) | 1.33390e7 | 0.507089 | 0.253545 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253545 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17211e7 | −0.443194 | ||||||||
\(932\) | −7.70371e7 | −2.90510 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.00475e7 | −0.751956 | ||||||||
\(935\) | −48045.1 | −0.00179730 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.33697e7 | 0.497476 | 0.248738 | − | 0.968571i | \(-0.419984\pi\) | ||||
0.248738 | + | 0.968571i | \(0.419984\pi\) | |||||||
\(938\) | 1.59836e7 | 0.593155 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 355858. | 0.0131358 | ||||||||
\(941\) | −2.28926e7 | −0.842793 | −0.421397 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.51390e7 | 0.554393 | ||||||||
\(944\) | 2.17531e6 | 0.0794494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.56754e7 | −0.569496 | ||||||||
\(947\) | −3.33079e6 | −0.120690 | −0.0603451 | − | 0.998178i | \(-0.519220\pi\) | ||||
−0.0603451 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.81089e6 | −0.209449 | ||||||||
\(950\) | 5.95472e7 | 2.14068 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.36328e7 | 1.20274 | ||||||||
\(953\) | −4.68461e7 | −1.67087 | −0.835433 | − | 0.549593i | \(-0.814783\pi\) | ||||
−0.835433 | + | 0.549593i | \(0.814783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37069.9 | 0.00131526 | ||||||||
\(956\) | −2.36644e7 | −0.837433 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.47379e7 | −1.57493 | ||||||||
\(959\) | −3.65924e7 | −1.28483 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.81109e7 | 2.37907 | ||||||||
\(962\) | −9.86586e6 | −0.343714 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.52730e7 | −2.60883 | ||||||||
\(965\) | 128134. | 0.00442942 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.65887e7 | −1.25829 | −0.629146 | − | 0.777287i | \(-0.716595\pi\) | ||||
−0.629146 | + | 0.777287i | \(0.716595\pi\) | |||||||
\(968\) | −3.27127e6 | −0.112209 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −387833. | −0.0132347 | ||||||||
\(971\) | −1.62147e7 | −0.551901 | −0.275951 | − | 0.961172i | \(-0.588993\pi\) | ||||
−0.275951 | + | 0.961172i | \(0.588993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.50764e7 | −1.18777 | ||||||||
\(974\) | −7.48261e7 | −2.52729 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.67403e6 | −0.190663 | ||||||||
\(977\) | 1.50181e6 | 0.0503360 | 0.0251680 | − | 0.999683i | \(-0.491988\pi\) | ||||
0.0251680 | + | 0.999683i | \(0.491988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.25602e7 | 0.418832 | ||||||||
\(980\) | 89229.1 | 0.00296784 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.46803e7 | −1.14764 | ||||||||
\(983\) | −3.72690e7 | −1.23017 | −0.615083 | − | 0.788462i | \(-0.710878\pi\) | ||||
−0.615083 | + | 0.788462i | \(0.710878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26729.8 | 0.000877820 0 | ||||||||
\(986\) | 6.22072e7 | 2.03774 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.67516e7 | 0.545962 | ||||||||
\(989\) | −1.14569e7 | −0.372456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.20015e7 | −1.03511 | −0.517554 | − | 0.855651i | \(-0.673157\pi\) | ||||
−0.517554 | + | 0.855651i | \(0.673157\pi\) | |||||||
\(992\) | −4.20049e7 | −1.35525 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.77718e7 | −0.891534 | ||||||||
\(995\) | 300095. | 0.00960950 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.59172e7 | −1.78159 | −0.890795 | − | 0.454406i | \(-0.849852\pi\) | ||||
−0.890795 | + | 0.454406i | \(0.849852\pi\) | |||||||
\(998\) | 6.60874e7 | 2.10035 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 99.6.a.d.1.1 | 2 | ||
3.2 | odd | 2 | 33.6.a.e.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 1089.6.a.p.1.2 | 2 | |||
12.11 | even | 2 | 528.6.a.o.1.1 | 2 | |||
15.14 | odd | 2 | 825.6.a.c.1.1 | 2 | |||
33.32 | even | 2 | 363.6.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.e.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
99.6.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
363.6.a.f.1.1 | 2 | 33.32 | even | 2 | |||
528.6.a.o.1.1 | 2 | 12.11 | even | 2 | |||
825.6.a.c.1.1 | 2 | 15.14 | odd | 2 | |||
1089.6.a.p.1.2 | 2 | 11.10 | odd | 2 |