Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, 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("33.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(5.29266605383\) |
Analytic rank: | \(0\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 | \(-0.189251\pi\) | ||||
0.828400 | + | 0.560136i | \(0.189251\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 55.8397 | 1.74499 | ||||||||
\(5\) | 0.277187 | 0.00495847 | 0.00247923 | − | 0.999997i | \(-0.499211\pi\) | ||||
0.00247923 | + | 0.999997i | \(0.499211\pi\) | |||||||
\(6\) | 84.3505 | 0.956554 | ||||||||
\(7\) | −105.081 | −0.810552 | −0.405276 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405276 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(8\) | 223.432 | 1.23430 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 2.59787 | 0.00821519 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 502.557 | 1.00747 | ||||||||
\(13\) | 147.549 | 0.242146 | 0.121073 | − | 0.992644i | \(-0.461366\pi\) | ||||
0.121073 | + | 0.992644i | \(0.461366\pi\) | |||||||
\(14\) | −984.853 | −1.34292 | ||||||||
\(15\) | 2.49468 | 0.00286277 | ||||||||
\(16\) | 307.198 | 0.299998 | ||||||||
\(17\) | −1432.49 | −1.20218 | −0.601089 | − | 0.799182i | \(-0.705266\pi\) | ||||
−0.601089 | + | 0.799182i | \(0.705266\pi\) | |||||||
\(18\) | 759.155 | 0.552267 | ||||||||
\(19\) | 2033.18 | 1.29209 | 0.646045 | − | 0.763300i | \(-0.276422\pi\) | ||||
0.646045 | + | 0.763300i | \(0.276422\pi\) | |||||||
\(20\) | 15.4780 | 0.00865247 | ||||||||
\(21\) | −945.733 | −0.467972 | ||||||||
\(22\) | −1134.05 | −0.499544 | ||||||||
\(23\) | 828.853 | 0.326707 | 0.163353 | − | 0.986568i | \(-0.447769\pi\) | ||||
0.163353 | + | 0.986568i | \(0.447769\pi\) | |||||||
\(24\) | 2010.89 | 0.712623 | ||||||||
\(25\) | −3124.92 | −0.999975 | ||||||||
\(26\) | 1382.87 | 0.401188 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −5867.71 | −1.41440 | ||||||||
\(29\) | 4633.44 | 1.02308 | 0.511539 | − | 0.859260i | \(-0.329076\pi\) | ||||
0.511539 | + | 0.859260i | \(0.329076\pi\) | |||||||
\(30\) | 23.3809 | 0.00474304 | ||||||||
\(31\) | −9835.65 | −1.83823 | −0.919113 | − | 0.393994i | \(-0.871093\pi\) | ||||
−0.919113 | + | 0.393994i | \(0.871093\pi\) | |||||||
\(32\) | −4270.67 | −0.737261 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −13425.7 | −1.99177 | ||||||||
\(35\) | −29.1272 | −0.00401910 | ||||||||
\(36\) | 4523.01 | 0.581663 | ||||||||
\(37\) | 7134.34 | 0.856741 | 0.428371 | − | 0.903603i | \(-0.359088\pi\) | ||||
0.428371 | + | 0.903603i | \(0.359088\pi\) | |||||||
\(38\) | 19055.6 | 2.14074 | ||||||||
\(39\) | 1327.94 | 0.139803 | ||||||||
\(40\) | 61.9324 | 0.00612023 | ||||||||
\(41\) | 18265.0 | 1.69691 | 0.848456 | − | 0.529265i | \(-0.177532\pi\) | ||||
0.848456 | + | 0.529265i | \(0.177532\pi\) | |||||||
\(42\) | −8863.68 | −0.775337 | ||||||||
\(43\) | 13822.5 | 1.14003 | 0.570016 | − | 0.821634i | \(-0.306937\pi\) | ||||
0.570016 | + | 0.821634i | \(0.306937\pi\) | |||||||
\(44\) | −6756.60 | −0.526134 | ||||||||
\(45\) | 22.4521 | 0.00165282 | ||||||||
\(46\) | 7768.24 | 0.541288 | ||||||||
\(47\) | 22991.2 | 1.51816 | 0.759079 | − | 0.650999i | \(-0.225650\pi\) | ||||
0.759079 | + | 0.650999i | \(0.225650\pi\) | |||||||
\(48\) | 2764.78 | 0.173204 | ||||||||
\(49\) | −5764.89 | −0.343005 | ||||||||
\(50\) | −29287.7 | −1.65676 | ||||||||
\(51\) | −12892.4 | −0.694078 | ||||||||
\(52\) | 8239.08 | 0.422542 | ||||||||
\(53\) | 14311.9 | 0.699856 | 0.349928 | − | 0.936777i | \(-0.386206\pi\) | ||||
0.349928 | + | 0.936777i | \(0.386206\pi\) | |||||||
\(54\) | 6832.39 | 0.318851 | ||||||||
\(55\) | −33.5396 | −0.00149503 | ||||||||
\(56\) | −23478.6 | −1.00046 | ||||||||
\(57\) | 18298.7 | 0.745988 | ||||||||
\(58\) | 43425.9 | 1.69504 | ||||||||
\(59\) | −7081.12 | −0.264833 | −0.132416 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132416 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(60\) | 139.302 | 0.00499551 | ||||||||
\(61\) | −18470.2 | −0.635547 | −0.317774 | − | 0.948167i | \(-0.602935\pi\) | ||||
−0.317774 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(62\) | −92182.5 | −3.04557 | ||||||||
\(63\) | −8511.60 | −0.270184 | ||||||||
\(64\) | −49856.3 | −1.52149 | ||||||||
\(65\) | 40.8986 | 0.00120067 | ||||||||
\(66\) | −10206.4 | −0.288412 | ||||||||
\(67\) | 16229.5 | 0.441690 | 0.220845 | − | 0.975309i | \(-0.429119\pi\) | ||||
0.220845 | + | 0.975309i | \(0.429119\pi\) | |||||||
\(68\) | −79989.7 | −2.09779 | ||||||||
\(69\) | 7459.68 | 0.188624 | ||||||||
\(70\) | −272.988 | −0.00665884 | ||||||||
\(71\) | 28198.9 | 0.663875 | 0.331938 | − | 0.943301i | \(-0.392298\pi\) | ||||
0.331938 | + | 0.943301i | \(0.392298\pi\) | |||||||
\(72\) | 18098.0 | 0.411433 | ||||||||
\(73\) | −39382.9 | −0.864968 | −0.432484 | − | 0.901642i | \(-0.642363\pi\) | ||||
−0.432484 | + | 0.901642i | \(0.642363\pi\) | |||||||
\(74\) | 66865.1 | 1.41945 | ||||||||
\(75\) | −28124.3 | −0.577336 | ||||||||
\(76\) | 113532. | 2.25468 | ||||||||
\(77\) | 12714.9 | 0.244391 | ||||||||
\(78\) | 12445.8 | 0.231626 | ||||||||
\(79\) | −41243.7 | −0.743515 | −0.371758 | − | 0.928330i | \(-0.621245\pi\) | ||||
−0.371758 | + | 0.928330i | \(0.621245\pi\) | |||||||
\(80\) | 85.1513 | 0.00148753 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 171185. | 2.81145 | ||||||||
\(83\) | −23355.3 | −0.372126 | −0.186063 | − | 0.982538i | \(-0.559573\pi\) | ||||
−0.186063 | + | 0.982538i | \(0.559573\pi\) | |||||||
\(84\) | −52809.4 | −0.816607 | ||||||||
\(85\) | −397.067 | −0.00596096 | ||||||||
\(86\) | 129549. | 1.88880 | ||||||||
\(87\) | 41701.0 | 0.590675 | ||||||||
\(88\) | −27035.3 | −0.372155 | ||||||||
\(89\) | −103803. | −1.38911 | −0.694555 | − | 0.719440i | \(-0.744399\pi\) | ||||
−0.694555 | + | 0.719440i | \(0.744399\pi\) | |||||||
\(90\) | 210.428 | 0.00273840 | ||||||||
\(91\) | −15504.6 | −0.196272 | ||||||||
\(92\) | 46282.9 | 0.570099 | ||||||||
\(93\) | −88520.9 | −1.06130 | ||||||||
\(94\) | 215480. | 2.51528 | ||||||||
\(95\) | 563.572 | 0.00640678 | ||||||||
\(96\) | −38436.1 | −0.425658 | ||||||||
\(97\) | −149289. | −1.61101 | −0.805503 | − | 0.592592i | \(-0.798105\pi\) | ||||
−0.805503 | + | 0.592592i | \(0.798105\pi\) | |||||||
\(98\) | −54030.2 | −0.568292 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −174495. | −1.74495 | ||||||||
\(101\) | 62410.1 | 0.608768 | 0.304384 | − | 0.952549i | \(-0.401549\pi\) | ||||
0.304384 | + | 0.952549i | \(0.401549\pi\) | |||||||
\(102\) | −120831. | −1.14995 | ||||||||
\(103\) | −90047.2 | −0.836329 | −0.418165 | − | 0.908371i | \(-0.637326\pi\) | ||||
−0.418165 | + | 0.908371i | \(0.637326\pi\) | |||||||
\(104\) | 32967.1 | 0.298881 | ||||||||
\(105\) | −262.145 | −0.00232043 | ||||||||
\(106\) | 134136. | 1.15952 | ||||||||
\(107\) | 120458. | 1.01713 | 0.508566 | − | 0.861023i | \(-0.330176\pi\) | ||||
0.508566 | + | 0.861023i | \(0.330176\pi\) | |||||||
\(108\) | 40707.1 | 0.335823 | ||||||||
\(109\) | −91854.0 | −0.740511 | −0.370256 | − | 0.928930i | \(-0.620730\pi\) | ||||
−0.370256 | + | 0.928930i | \(0.620730\pi\) | |||||||
\(110\) | −314.343 | −0.00247697 | ||||||||
\(111\) | 64209.1 | 0.494640 | ||||||||
\(112\) | −32280.8 | −0.243164 | ||||||||
\(113\) | −29619.6 | −0.218214 | −0.109107 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109107 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(114\) | 171500. | 1.23595 | ||||||||
\(115\) | 229.747 | 0.00161996 | ||||||||
\(116\) | 258730. | 1.78526 | ||||||||
\(117\) | 11951.5 | 0.0807153 | ||||||||
\(118\) | −66366.2 | −0.438775 | ||||||||
\(119\) | 150528. | 0.974428 | ||||||||
\(120\) | 557.391 | 0.00353352 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −173108. | −1.05298 | ||||||||
\(123\) | 164385. | 0.979713 | ||||||||
\(124\) | −549219. | −3.20768 | ||||||||
\(125\) | −1732.40 | −0.00991681 | ||||||||
\(126\) | −79773.1 | −0.447641 | ||||||||
\(127\) | 271128. | 1.49165 | 0.745823 | − | 0.666145i | \(-0.232057\pi\) | ||||
0.745823 | + | 0.666145i | \(0.232057\pi\) | |||||||
\(128\) | −330606. | −1.78355 | ||||||||
\(129\) | 124403. | 0.658197 | ||||||||
\(130\) | 383.313 | 0.00198928 | ||||||||
\(131\) | −223990. | −1.14038 | −0.570191 | − | 0.821512i | \(-0.693131\pi\) | ||||
−0.570191 | + | 0.821512i | \(0.693131\pi\) | |||||||
\(132\) | −60809.4 | −0.303764 | ||||||||
\(133\) | −213650. | −1.04731 | ||||||||
\(134\) | 152107. | 0.731792 | ||||||||
\(135\) | 202.069 | 0.000954258 0 | ||||||||
\(136\) | −320064. | −1.48385 | ||||||||
\(137\) | −348229. | −1.58513 | −0.792563 | − | 0.609789i | \(-0.791254\pi\) | ||||
−0.792563 | + | 0.609789i | \(0.791254\pi\) | |||||||
\(138\) | 69914.2 | 0.312513 | ||||||||
\(139\) | 333802. | 1.46538 | 0.732692 | − | 0.680560i | \(-0.238264\pi\) | ||||
0.732692 | + | 0.680560i | \(0.238264\pi\) | |||||||
\(140\) | −1626.45 | −0.00701328 | ||||||||
\(141\) | 206921. | 0.876509 | ||||||||
\(142\) | 264288. | 1.09991 | ||||||||
\(143\) | −17853.4 | −0.0730098 | ||||||||
\(144\) | 24883.1 | 0.0999994 | ||||||||
\(145\) | 1284.33 | 0.00507290 | ||||||||
\(146\) | −369107. | −1.43308 | ||||||||
\(147\) | −51884.0 | −0.198034 | ||||||||
\(148\) | 398379. | 1.49500 | ||||||||
\(149\) | 310249. | 1.14484 | 0.572419 | − | 0.819961i | \(-0.306005\pi\) | ||||
0.572419 | + | 0.819961i | \(0.306005\pi\) | |||||||
\(150\) | −263589. | −0.956531 | ||||||||
\(151\) | −54751.5 | −0.195413 | −0.0977066 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977066 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(152\) | 454278. | 1.59482 | ||||||||
\(153\) | −116032. | −0.400726 | ||||||||
\(154\) | 119167. | 0.404907 | ||||||||
\(155\) | −2726.31 | −0.00911478 | ||||||||
\(156\) | 74151.7 | 0.243955 | ||||||||
\(157\) | 221556. | 0.717354 | 0.358677 | − | 0.933462i | \(-0.383228\pi\) | ||||
0.358677 | + | 0.933462i | \(0.383228\pi\) | |||||||
\(158\) | −386547. | −1.23186 | ||||||||
\(159\) | 128807. | 0.404062 | ||||||||
\(160\) | −1183.77 | −0.00365569 | ||||||||
\(161\) | −87097.1 | −0.264813 | ||||||||
\(162\) | 61491.5 | 0.184089 | ||||||||
\(163\) | −225239. | −0.664010 | −0.332005 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332005 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(164\) | 1.01991e6 | 2.96109 | ||||||||
\(165\) | −301.856 | −0.000863158 0 | ||||||||
\(166\) | −218892. | −0.616539 | ||||||||
\(167\) | 186796. | 0.518294 | 0.259147 | − | 0.965838i | \(-0.416559\pi\) | ||||
0.259147 | + | 0.965838i | \(0.416559\pi\) | |||||||
\(168\) | −211307. | −0.577618 | ||||||||
\(169\) | −349522. | −0.941365 | ||||||||
\(170\) | −3721.42 | −0.00987613 | ||||||||
\(171\) | 164688. | 0.430697 | ||||||||
\(172\) | 771846. | 1.98934 | ||||||||
\(173\) | −713662. | −1.81292 | −0.906458 | − | 0.422296i | \(-0.861224\pi\) | ||||
−0.906458 | + | 0.422296i | \(0.861224\pi\) | |||||||
\(174\) | 390833. | 0.978630 | ||||||||
\(175\) | 328371. | 0.810532 | ||||||||
\(176\) | −37171.0 | −0.0904529 | ||||||||
\(177\) | −63730.1 | −0.152901 | ||||||||
\(178\) | −972875. | −2.30148 | ||||||||
\(179\) | 789450. | 1.84159 | 0.920793 | − | 0.390051i | \(-0.127543\pi\) | ||||
0.920793 | + | 0.390051i | \(0.127543\pi\) | |||||||
\(180\) | 1253.72 | 0.00288416 | ||||||||
\(181\) | 40330.7 | 0.0915039 | 0.0457519 | − | 0.998953i | \(-0.485432\pi\) | ||||
0.0457519 | + | 0.998953i | \(0.485432\pi\) | |||||||
\(182\) | −145314. | −0.325184 | ||||||||
\(183\) | −166232. | −0.366934 | ||||||||
\(184\) | 185192. | 0.403254 | ||||||||
\(185\) | 1977.55 | 0.00424812 | ||||||||
\(186\) | −829642. | −1.75836 | ||||||||
\(187\) | 173331. | 0.362470 | ||||||||
\(188\) | 1.28382e6 | 2.64917 | ||||||||
\(189\) | −76604.4 | −0.155991 | ||||||||
\(190\) | 5281.95 | 0.0106148 | ||||||||
\(191\) | 133736. | 0.265256 | 0.132628 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132628 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(192\) | −448707. | −0.878435 | ||||||||
\(193\) | −462266. | −0.893303 | −0.446652 | − | 0.894708i | \(-0.647384\pi\) | ||||
−0.446652 | + | 0.894708i | \(0.647384\pi\) | |||||||
\(194\) | −1.39917e6 | −2.66912 | ||||||||
\(195\) | 368.087 | 0.000693209 0 | ||||||||
\(196\) | −321910. | −0.598541 | ||||||||
\(197\) | 96432.5 | 0.177035 | 0.0885173 | − | 0.996075i | \(-0.471787\pi\) | ||||
0.0885173 | + | 0.996075i | \(0.471787\pi\) | |||||||
\(198\) | −91857.7 | −0.166515 | ||||||||
\(199\) | −1.08264e6 | −1.93800 | −0.968999 | − | 0.247066i | \(-0.920533\pi\) | ||||
−0.968999 | + | 0.247066i | \(0.920533\pi\) | |||||||
\(200\) | −698208. | −1.23427 | ||||||||
\(201\) | 146065. | 0.255010 | ||||||||
\(202\) | 584925. | 1.00861 | ||||||||
\(203\) | −486889. | −0.829258 | ||||||||
\(204\) | −719907. | −1.21116 | ||||||||
\(205\) | 5062.81 | 0.00841409 | ||||||||
\(206\) | −843948. | −1.38563 | ||||||||
\(207\) | 67137.1 | 0.108902 | ||||||||
\(208\) | 45326.7 | 0.0726434 | ||||||||
\(209\) | −246015. | −0.389580 | ||||||||
\(210\) | −2456.89 | −0.00384448 | ||||||||
\(211\) | 875588. | 1.35392 | 0.676961 | − | 0.736019i | \(-0.263297\pi\) | ||||
0.676961 | + | 0.736019i | \(0.263297\pi\) | |||||||
\(212\) | 799174. | 1.22124 | ||||||||
\(213\) | 253790. | 0.383289 | ||||||||
\(214\) | 1.12897e6 | 1.68518 | ||||||||
\(215\) | 3831.43 | 0.00565281 | ||||||||
\(216\) | 162882. | 0.237541 | ||||||||
\(217\) | 1.03354e6 | 1.48998 | ||||||||
\(218\) | −860881. | −1.22688 | ||||||||
\(219\) | −354446. | −0.499390 | ||||||||
\(220\) | −1872.84 | −0.00260882 | ||||||||
\(221\) | −211362. | −0.291103 | ||||||||
\(222\) | 601786. | 0.819520 | ||||||||
\(223\) | 988042. | 1.33049 | 0.665247 | − | 0.746623i | \(-0.268326\pi\) | ||||
0.665247 | + | 0.746623i | \(0.268326\pi\) | |||||||
\(224\) | 448769. | 0.597589 | ||||||||
\(225\) | −253119. | −0.333325 | ||||||||
\(226\) | −277603. | −0.361537 | ||||||||
\(227\) | 67066.0 | 0.0863849 | 0.0431925 | − | 0.999067i | \(-0.486247\pi\) | ||||
0.0431925 | + | 0.999067i | \(0.486247\pi\) | |||||||
\(228\) | 1.02179e6 | 1.30174 | ||||||||
\(229\) | −662131. | −0.834363 | −0.417182 | − | 0.908823i | \(-0.636982\pi\) | ||||
−0.417182 | + | 0.908823i | \(0.636982\pi\) | |||||||
\(230\) | 2153.25 | 0.00268396 | ||||||||
\(231\) | 114434. | 0.141099 | ||||||||
\(232\) | 1.03526e6 | 1.26278 | ||||||||
\(233\) | 1.37961e6 | 1.66482 | 0.832411 | − | 0.554159i | \(-0.186960\pi\) | ||||
0.832411 | + | 0.554159i | \(0.186960\pi\) | |||||||
\(234\) | 112012. | 0.133729 | ||||||||
\(235\) | 6372.85 | 0.00752773 | ||||||||
\(236\) | −395407. | −0.462130 | ||||||||
\(237\) | −371193. | −0.429269 | ||||||||
\(238\) | 1.41079e6 | 1.61443 | ||||||||
\(239\) | 423791. | 0.479907 | 0.239954 | − | 0.970784i | \(-0.422868\pi\) | ||||
0.239954 | + | 0.970784i | \(0.422868\pi\) | |||||||
\(240\) | 766.362 | 0.000858827 0 | ||||||||
\(241\) | −1.34802e6 | −1.49504 | −0.747521 | − | 0.664238i | \(-0.768756\pi\) | ||||
−0.747521 | + | 0.664238i | \(0.768756\pi\) | |||||||
\(242\) | 137220. | 0.150618 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.03137e6 | −1.10902 | ||||||||
\(245\) | −1597.95 | −0.00170078 | ||||||||
\(246\) | 1.54066e6 | 1.62319 | ||||||||
\(247\) | 299994. | 0.312874 | ||||||||
\(248\) | −2.19760e6 | −2.26892 | ||||||||
\(249\) | −210198. | −0.214847 | ||||||||
\(250\) | −16236.5 | −0.0164302 | ||||||||
\(251\) | −1.45914e6 | −1.46188 | −0.730940 | − | 0.682442i | \(-0.760918\pi\) | ||||
−0.730940 | + | 0.682442i | \(0.760918\pi\) | |||||||
\(252\) | −475285. | −0.471468 | ||||||||
\(253\) | −100291. | −0.0985057 | ||||||||
\(254\) | 2.54109e6 | 2.47136 | ||||||||
\(255\) | −3573.60 | −0.00344156 | ||||||||
\(256\) | −1.50313e6 | −1.43349 | ||||||||
\(257\) | 548503. | 0.518020 | 0.259010 | − | 0.965875i | \(-0.416604\pi\) | ||||
0.259010 | + | 0.965875i | \(0.416604\pi\) | |||||||
\(258\) | 1.16594e6 | 1.09050 | ||||||||
\(259\) | −749687. | −0.694434 | ||||||||
\(260\) | 2283.76 | 0.00209516 | ||||||||
\(261\) | 375309. | 0.341026 | ||||||||
\(262\) | −2.09930e6 | −1.88939 | ||||||||
\(263\) | 905299. | 0.807054 | 0.403527 | − | 0.914968i | \(-0.367784\pi\) | ||||
0.403527 | + | 0.914968i | \(0.367784\pi\) | |||||||
\(264\) | −243317. | −0.214864 | ||||||||
\(265\) | 3967.08 | 0.00347021 | ||||||||
\(266\) | −2.00239e6 | −1.73518 | ||||||||
\(267\) | −934231. | −0.802003 | ||||||||
\(268\) | 906248. | 0.770744 | ||||||||
\(269\) | −164041. | −0.138220 | −0.0691100 | − | 0.997609i | \(-0.522016\pi\) | ||||
−0.0691100 | + | 0.997609i | \(0.522016\pi\) | |||||||
\(270\) | 1893.85 | 0.00158101 | ||||||||
\(271\) | 989636. | 0.818563 | 0.409282 | − | 0.912408i | \(-0.365779\pi\) | ||||
0.409282 | + | 0.912408i | \(0.365779\pi\) | |||||||
\(272\) | −440058. | −0.360651 | ||||||||
\(273\) | −139542. | −0.113318 | ||||||||
\(274\) | −3.26370e6 | −2.62624 | ||||||||
\(275\) | 378116. | 0.301504 | ||||||||
\(276\) | 416546. | 0.329147 | ||||||||
\(277\) | 727149. | 0.569409 | 0.284704 | − | 0.958615i | \(-0.408105\pi\) | ||||
0.284704 | + | 0.958615i | \(0.408105\pi\) | |||||||
\(278\) | 3.12848e6 | 2.42785 | ||||||||
\(279\) | −796688. | −0.612742 | ||||||||
\(280\) | −6507.94 | −0.00496077 | ||||||||
\(281\) | −379100. | −0.286410 | −0.143205 | − | 0.989693i | \(-0.545741\pi\) | ||||
−0.143205 | + | 0.989693i | \(0.545741\pi\) | |||||||
\(282\) | 1.93932e6 | 1.45220 | ||||||||
\(283\) | −695371. | −0.516120 | −0.258060 | − | 0.966129i | \(-0.583083\pi\) | ||||
−0.258060 | + | 0.966129i | \(0.583083\pi\) | |||||||
\(284\) | 1.57462e6 | 1.15846 | ||||||||
\(285\) | 5072.14 | 0.00369896 | ||||||||
\(286\) | −167327. | −0.120963 | ||||||||
\(287\) | −1.91931e6 | −1.37544 | ||||||||
\(288\) | −345925. | −0.245754 | ||||||||
\(289\) | 632167. | 0.445233 | ||||||||
\(290\) | 12037.1 | 0.00840479 | ||||||||
\(291\) | −1.34360e6 | −0.930115 | ||||||||
\(292\) | −2.19913e6 | −1.50936 | ||||||||
\(293\) | 268373. | 0.182629 | 0.0913146 | − | 0.995822i | \(-0.470893\pi\) | ||||
0.0913146 | + | 0.995822i | \(0.470893\pi\) | |||||||
\(294\) | −486272. | −0.328103 | ||||||||
\(295\) | −1962.79 | −0.00131316 | ||||||||
\(296\) | 1.59404e6 | 1.05747 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 2.90774e6 | 1.89677 | ||||||||
\(299\) | 122296. | 0.0791107 | ||||||||
\(300\) | −1.57045e6 | −1.00745 | ||||||||
\(301\) | −1.45249e6 | −0.924055 | ||||||||
\(302\) | −513147. | −0.323761 | ||||||||
\(303\) | 561691. | 0.351472 | ||||||||
\(304\) | 624591. | 0.387625 | ||||||||
\(305\) | −5119.71 | −0.00315134 | ||||||||
\(306\) | −1.08748e6 | −0.663923 | ||||||||
\(307\) | 1.78841e6 | 1.08298 | 0.541491 | − | 0.840706i | \(-0.317860\pi\) | ||||
0.541491 | + | 0.840706i | \(0.317860\pi\) | |||||||
\(308\) | 709993. | 0.426459 | ||||||||
\(309\) | −810425. | −0.482855 | ||||||||
\(310\) | −25551.8 | −0.0151014 | ||||||||
\(311\) | 362727. | 0.212657 | 0.106328 | − | 0.994331i | \(-0.466091\pi\) | ||||
0.106328 | + | 0.994331i | \(0.466091\pi\) | |||||||
\(312\) | 296704. | 0.172559 | ||||||||
\(313\) | −1.14382e6 | −0.659926 | −0.329963 | − | 0.943994i | \(-0.607036\pi\) | ||||
−0.329963 | + | 0.943994i | \(0.607036\pi\) | |||||||
\(314\) | 2.07648e6 | 1.18851 | ||||||||
\(315\) | −2359.30 | −0.00133970 | ||||||||
\(316\) | −2.30303e6 | −1.29743 | ||||||||
\(317\) | 3.43750e6 | 1.92130 | 0.960649 | − | 0.277766i | \(-0.0895941\pi\) | ||||
0.960649 | + | 0.277766i | \(0.0895941\pi\) | |||||||
\(318\) | 1.20722e6 | 0.669451 | ||||||||
\(319\) | −560647. | −0.308470 | ||||||||
\(320\) | −13819.5 | −0.00754428 | ||||||||
\(321\) | 1.08412e6 | 0.587241 | ||||||||
\(322\) | −816298. | −0.438742 | ||||||||
\(323\) | −2.91251e6 | −1.55332 | ||||||||
\(324\) | 366364. | 0.193888 | ||||||||
\(325\) | −461079. | −0.242140 | ||||||||
\(326\) | −2.11100e6 | −1.10013 | ||||||||
\(327\) | −826686. | −0.427534 | ||||||||
\(328\) | 4.08098e6 | 2.09450 | ||||||||
\(329\) | −2.41595e6 | −1.23055 | ||||||||
\(330\) | −2829.08 | −0.00143008 | ||||||||
\(331\) | 1.11428e6 | 0.559015 | 0.279507 | − | 0.960144i | \(-0.409829\pi\) | ||||
0.279507 | + | 0.960144i | \(0.409829\pi\) | |||||||
\(332\) | −1.30415e6 | −0.649356 | ||||||||
\(333\) | 577882. | 0.285580 | ||||||||
\(334\) | 1.75070e6 | 0.858710 | ||||||||
\(335\) | 4498.59 | 0.00219010 | ||||||||
\(336\) | −290528. | −0.140391 | ||||||||
\(337\) | −2.25804e6 | −1.08307 | −0.541535 | − | 0.840678i | \(-0.682157\pi\) | ||||
−0.541535 | + | 0.840678i | \(0.682157\pi\) | |||||||
\(338\) | −3.27582e6 | −1.55965 | ||||||||
\(339\) | −266576. | −0.125986 | ||||||||
\(340\) | −22172.1 | −0.0104018 | ||||||||
\(341\) | 1.19011e6 | 0.554246 | ||||||||
\(342\) | 1.54350e6 | 0.713578 | ||||||||
\(343\) | 2.37189e6 | 1.08858 | ||||||||
\(344\) | 3.08840e6 | 1.40714 | ||||||||
\(345\) | 2067.72 | 0.000935287 0 | ||||||||
\(346\) | −6.68865e6 | −3.00364 | ||||||||
\(347\) | −1.17055e6 | −0.521873 | −0.260937 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(348\) | 2.32857e6 | 1.03072 | ||||||||
\(349\) | 1.21704e6 | 0.534863 | 0.267432 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267432 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(350\) | 3.07759e6 | 1.34289 | ||||||||
\(351\) | 107563. | 0.0466010 | ||||||||
\(352\) | 516752. | 0.222293 | ||||||||
\(353\) | 286188. | 0.122240 | 0.0611201 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611201 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(354\) | −597296. | −0.253327 | ||||||||
\(355\) | 7816.37 | 0.00329180 | ||||||||
\(356\) | −5.79635e6 | −2.42398 | ||||||||
\(357\) | 1.35475e6 | 0.562586 | ||||||||
\(358\) | 7.39895e6 | 3.05114 | ||||||||
\(359\) | 1.19066e6 | 0.487588 | 0.243794 | − | 0.969827i | \(-0.421608\pi\) | ||||
0.243794 | + | 0.969827i | \(0.421608\pi\) | |||||||
\(360\) | 5016.52 | 0.00204008 | ||||||||
\(361\) | 1.65774e6 | 0.669495 | ||||||||
\(362\) | 377991. | 0.151604 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −865774. | −0.342492 | ||||||||
\(365\) | −10916.4 | −0.00428892 | ||||||||
\(366\) | −1.55797e6 | −0.607936 | ||||||||
\(367\) | 3.11120e6 | 1.20577 | 0.602884 | − | 0.797829i | \(-0.294018\pi\) | ||||
0.602884 | + | 0.797829i | \(0.294018\pi\) | |||||||
\(368\) | 254622. | 0.0980114 | ||||||||
\(369\) | 1.47946e6 | 0.565638 | ||||||||
\(370\) | 18534.1 | 0.00703830 | ||||||||
\(371\) | −1.50392e6 | −0.567270 | ||||||||
\(372\) | −4.94297e6 | −1.85196 | ||||||||
\(373\) | 3.58536e6 | 1.33432 | 0.667160 | − | 0.744914i | \(-0.267510\pi\) | ||||
0.667160 | + | 0.744914i | \(0.267510\pi\) | |||||||
\(374\) | 1.62451e6 | 0.600541 | ||||||||
\(375\) | −15591.6 | −0.00572547 | ||||||||
\(376\) | 5.13697e6 | 1.87386 | ||||||||
\(377\) | 683659. | 0.247734 | ||||||||
\(378\) | −717958. | −0.258446 | ||||||||
\(379\) | 1.87822e6 | 0.671660 | 0.335830 | − | 0.941923i | \(-0.390983\pi\) | ||||
0.335830 | + | 0.941923i | \(0.390983\pi\) | |||||||
\(380\) | 31469.6 | 0.0111798 | ||||||||
\(381\) | 2.44015e6 | 0.861202 | ||||||||
\(382\) | 1.25341e6 | 0.439476 | ||||||||
\(383\) | −662654. | −0.230829 | −0.115414 | − | 0.993317i | \(-0.536820\pi\) | ||||
−0.115414 | + | 0.993317i | \(0.536820\pi\) | |||||||
\(384\) | −2.97545e6 | −1.02973 | ||||||||
\(385\) | 3524.39 | 0.00121180 | ||||||||
\(386\) | −4.33249e6 | −1.48003 | ||||||||
\(387\) | 1.11963e6 | 0.380010 | ||||||||
\(388\) | −8.33622e6 | −2.81119 | ||||||||
\(389\) | −5.08370e6 | −1.70336 | −0.851678 | − | 0.524065i | \(-0.824415\pi\) | ||||
−0.851678 | + | 0.524065i | \(0.824415\pi\) | |||||||
\(390\) | 3449.82 | 0.00114851 | ||||||||
\(391\) | −1.18732e6 | −0.392760 | ||||||||
\(392\) | −1.28806e6 | −0.423371 | ||||||||
\(393\) | −2.01591e6 | −0.658400 | ||||||||
\(394\) | 903793. | 0.293311 | ||||||||
\(395\) | −11432.2 | −0.00368670 | ||||||||
\(396\) | −547284. | −0.175378 | ||||||||
\(397\) | −518385. | −0.165073 | −0.0825366 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825366 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(398\) | −1.01468e7 | −3.21088 | ||||||||
\(399\) | −1.92285e6 | −0.604662 | ||||||||
\(400\) | −959971. | −0.299991 | ||||||||
\(401\) | 1.12538e6 | 0.349493 | 0.174747 | − | 0.984613i | \(-0.444089\pi\) | ||||
0.174747 | + | 0.984613i | \(0.444089\pi\) | |||||||
\(402\) | 1.36896e6 | 0.422500 | ||||||||
\(403\) | −1.45124e6 | −0.445119 | ||||||||
\(404\) | 3.48496e6 | 1.06229 | ||||||||
\(405\) | 1818.62 | 0.000550941 0 | ||||||||
\(406\) | −4.56326e6 | −1.37392 | ||||||||
\(407\) | −863256. | −0.258317 | ||||||||
\(408\) | −2.88057e6 | −0.856700 | ||||||||
\(409\) | 3.15394e6 | 0.932279 | 0.466139 | − | 0.884711i | \(-0.345645\pi\) | ||||
0.466139 | + | 0.884711i | \(0.345645\pi\) | |||||||
\(410\) | 47450.1 | 0.0139405 | ||||||||
\(411\) | −3.13406e6 | −0.915173 | ||||||||
\(412\) | −5.02821e6 | −1.45939 | ||||||||
\(413\) | 744094. | 0.214661 | ||||||||
\(414\) | 629228. | 0.180429 | ||||||||
\(415\) | −6473.78 | −0.00184518 | ||||||||
\(416\) | −630133. | −0.178525 | ||||||||
\(417\) | 3.00421e6 | 0.846040 | ||||||||
\(418\) | −2.30572e6 | −0.645456 | ||||||||
\(419\) | 801315. | 0.222981 | 0.111491 | − | 0.993765i | \(-0.464438\pi\) | ||||
0.111491 | + | 0.993765i | \(0.464438\pi\) | |||||||
\(420\) | −14638.1 | −0.00404912 | ||||||||
\(421\) | −1.85449e6 | −0.509940 | −0.254970 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254970 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(422\) | 8.20626e6 | 2.24318 | ||||||||
\(423\) | 1.86229e6 | 0.506052 | ||||||||
\(424\) | 3.19775e6 | 0.863832 | ||||||||
\(425\) | 4.47642e6 | 1.20215 | ||||||||
\(426\) | 2.37859e6 | 0.635033 | ||||||||
\(427\) | 1.94088e6 | 0.515144 | ||||||||
\(428\) | 6.72635e6 | 1.77488 | ||||||||
\(429\) | −160681. | −0.0421522 | ||||||||
\(430\) | 35909.2 | 0.00936558 | ||||||||
\(431\) | 2.46004e6 | 0.637895 | 0.318947 | − | 0.947772i | \(-0.396671\pi\) | ||||
0.318947 | + | 0.947772i | \(0.396671\pi\) | |||||||
\(432\) | 223948. | 0.0577347 | ||||||||
\(433\) | 3.12223e6 | 0.800287 | 0.400144 | − | 0.916452i | \(-0.368960\pi\) | ||||
0.400144 | + | 0.916452i | \(0.368960\pi\) | |||||||
\(434\) | 9.68667e6 | 2.46860 | ||||||||
\(435\) | 11559.0 | 0.00292884 | ||||||||
\(436\) | −5.12910e6 | −1.29218 | ||||||||
\(437\) | 1.68521e6 | 0.422134 | ||||||||
\(438\) | −3.32197e6 | −0.827389 | ||||||||
\(439\) | −6.09275e6 | −1.50887 | −0.754436 | − | 0.656374i | \(-0.772089\pi\) | ||||
−0.754436 | + | 0.656374i | \(0.772089\pi\) | |||||||
\(440\) | −7493.82 | −0.00184532 | ||||||||
\(441\) | −466956. | −0.114335 | ||||||||
\(442\) | −1.98094e6 | −0.482299 | ||||||||
\(443\) | −7.93457e6 | −1.92094 | −0.960470 | − | 0.278382i | \(-0.910202\pi\) | ||||
−0.960470 | + | 0.278382i | \(0.910202\pi\) | |||||||
\(444\) | 3.58541e6 | 0.863141 | ||||||||
\(445\) | −28772.9 | −0.00688786 | ||||||||
\(446\) | 9.26021e6 | 2.20436 | ||||||||
\(447\) | 2.79224e6 | 0.660973 | ||||||||
\(448\) | 5.23897e6 | 1.23325 | ||||||||
\(449\) | 4.61011e6 | 1.07918 | 0.539592 | − | 0.841926i | \(-0.318578\pi\) | ||||
0.539592 | + | 0.841926i | \(0.318578\pi\) | |||||||
\(450\) | −2.37230e6 | −0.552253 | ||||||||
\(451\) | −2.21006e6 | −0.511638 | ||||||||
\(452\) | −1.65395e6 | −0.380781 | ||||||||
\(453\) | −492764. | −0.112822 | ||||||||
\(454\) | 628562. | 0.143123 | ||||||||
\(455\) | −4297.68 | −0.000973208 0 | ||||||||
\(456\) | 4.08850e6 | 0.920773 | ||||||||
\(457\) | −8.05458e6 | −1.80407 | −0.902033 | − | 0.431667i | \(-0.857926\pi\) | ||||
−0.902033 | + | 0.431667i | \(0.857926\pi\) | |||||||
\(458\) | −6.20568e6 | −1.38237 | ||||||||
\(459\) | −1.04428e6 | −0.231359 | ||||||||
\(460\) | 12829.0 | 0.00282682 | ||||||||
\(461\) | 3.22431e6 | 0.706617 | 0.353309 | − | 0.935507i | \(-0.385057\pi\) | ||||
0.353309 | + | 0.935507i | \(0.385057\pi\) | |||||||
\(462\) | 1.07250e6 | 0.233773 | ||||||||
\(463\) | 1.29607e6 | 0.280979 | 0.140490 | − | 0.990082i | \(-0.455132\pi\) | ||||
0.140490 | + | 0.990082i | \(0.455132\pi\) | |||||||
\(464\) | 1.42339e6 | 0.306922 | ||||||||
\(465\) | −24536.8 | −0.00526242 | ||||||||
\(466\) | 1.29301e7 | 2.75828 | ||||||||
\(467\) | −2.13902e6 | −0.453860 | −0.226930 | − | 0.973911i | \(-0.572869\pi\) | ||||
−0.226930 | + | 0.973911i | \(0.572869\pi\) | |||||||
\(468\) | 667365. | 0.140847 | ||||||||
\(469\) | −1.70542e6 | −0.358012 | ||||||||
\(470\) | 59728.2 | 0.0124720 | ||||||||
\(471\) | 1.99400e6 | 0.414165 | ||||||||
\(472\) | −1.58215e6 | −0.326883 | ||||||||
\(473\) | −1.67253e6 | −0.343732 | ||||||||
\(474\) | −3.47893e6 | −0.711213 | ||||||||
\(475\) | −6.35354e6 | −1.29206 | ||||||||
\(476\) | 8.40543e6 | 1.70037 | ||||||||
\(477\) | 1.15927e6 | 0.233285 | ||||||||
\(478\) | 3.97189e6 | 0.795111 | ||||||||
\(479\) | −4.77343e6 | −0.950586 | −0.475293 | − | 0.879828i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(480\) | −10654.0 | −0.00211061 | ||||||||
\(481\) | 1.05266e6 | 0.207457 | ||||||||
\(482\) | −1.26340e7 | −2.47699 | ||||||||
\(483\) | −783873. | −0.152890 | ||||||||
\(484\) | 817548. | 0.158635 | ||||||||
\(485\) | −41380.8 | −0.00798812 | ||||||||
\(486\) | 553424. | 0.106284 | ||||||||
\(487\) | 7.98376e6 | 1.52541 | 0.762703 | − | 0.646749i | \(-0.223872\pi\) | ||||
0.762703 | + | 0.646749i | \(0.223872\pi\) | |||||||
\(488\) | −4.12684e6 | −0.784456 | ||||||||
\(489\) | −2.02715e6 | −0.383366 | ||||||||
\(490\) | −14976.4 | −0.00281786 | ||||||||
\(491\) | −3.70031e6 | −0.692682 | −0.346341 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346341 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(492\) | 9.17919e6 | 1.70959 | ||||||||
\(493\) | −6.63736e6 | −1.22992 | ||||||||
\(494\) | 2.81163e6 | 0.518371 | ||||||||
\(495\) | −2716.71 | −0.000498345 0 | ||||||||
\(496\) | −3.02149e6 | −0.551465 | ||||||||
\(497\) | −2.96318e6 | −0.538105 | ||||||||
\(498\) | −1.97003e6 | −0.355959 | ||||||||
\(499\) | −7.05137e6 | −1.26772 | −0.633858 | − | 0.773449i | \(-0.718530\pi\) | ||||
−0.633858 | + | 0.773449i | \(0.718530\pi\) | |||||||
\(500\) | −96736.4 | −0.0173047 | ||||||||
\(501\) | 1.68116e6 | 0.299237 | ||||||||
\(502\) | −1.36754e7 | −2.42204 | ||||||||
\(503\) | −7.77325e6 | −1.36988 | −0.684940 | − | 0.728599i | \(-0.740172\pi\) | ||||
−0.684940 | + | 0.728599i | \(0.740172\pi\) | |||||||
\(504\) | −1.90176e6 | −0.333488 | ||||||||
\(505\) | 17299.3 | 0.00301856 | ||||||||
\(506\) | −939957. | −0.163204 | ||||||||
\(507\) | −3.14570e6 | −0.543498 | ||||||||
\(508\) | 1.51397e7 | 2.60290 | ||||||||
\(509\) | 4.11598e6 | 0.704173 | 0.352086 | − | 0.935968i | \(-0.385472\pi\) | ||||
0.352086 | + | 0.935968i | \(0.385472\pi\) | |||||||
\(510\) | −33492.8 | −0.00570198 | ||||||||
\(511\) | 4.13841e6 | 0.701102 | ||||||||
\(512\) | −3.50836e6 | −0.591465 | ||||||||
\(513\) | 1.48219e6 | 0.248663 | ||||||||
\(514\) | 5.14073e6 | 0.858256 | ||||||||
\(515\) | −24959.9 | −0.00414691 | ||||||||
\(516\) | 6.94661e6 | 1.14855 | ||||||||
\(517\) | −2.78193e6 | −0.457742 | ||||||||
\(518\) | −7.02628e6 | −1.15054 | ||||||||
\(519\) | −6.42296e6 | −1.04669 | ||||||||
\(520\) | 9138.05 | 0.00148199 | ||||||||
\(521\) | −2.56352e6 | −0.413754 | −0.206877 | − | 0.978367i | \(-0.566330\pi\) | ||||
−0.206877 | + | 0.978367i | \(0.566330\pi\) | |||||||
\(522\) | 3.51750e6 | 0.565012 | ||||||||
\(523\) | −3.69240e6 | −0.590274 | −0.295137 | − | 0.955455i | \(-0.595365\pi\) | ||||
−0.295137 | + | 0.955455i | \(0.595365\pi\) | |||||||
\(524\) | −1.25075e7 | −1.98996 | ||||||||
\(525\) | 2.95534e6 | 0.467961 | ||||||||
\(526\) | 8.48471e6 | 1.33713 | ||||||||
\(527\) | 1.40895e7 | 2.20988 | ||||||||
\(528\) | −334539. | −0.0522230 | ||||||||
\(529\) | −5.74935e6 | −0.893263 | ||||||||
\(530\) | 37180.6 | 0.00574946 | ||||||||
\(531\) | −573570. | −0.0882776 | ||||||||
\(532\) | −1.19301e7 | −1.82754 | ||||||||
\(533\) | 2.69498e6 | 0.410901 | ||||||||
\(534\) | −8.75587e6 | −1.32876 | ||||||||
\(535\) | 33389.4 | 0.00504341 | ||||||||
\(536\) | 3.62618e6 | 0.545177 | ||||||||
\(537\) | 7.10505e6 | 1.06324 | ||||||||
\(538\) | −1.53743e6 | −0.229003 | ||||||||
\(539\) | 697552. | 0.103420 | ||||||||
\(540\) | 11283.5 | 0.00166517 | ||||||||
\(541\) | −9.33636e6 | −1.37146 | −0.685732 | − | 0.727854i | \(-0.740518\pi\) | ||||
−0.685732 | + | 0.727854i | \(0.740518\pi\) | |||||||
\(542\) | 9.27515e6 | 1.35620 | ||||||||
\(543\) | 362977. | 0.0528298 | ||||||||
\(544\) | 6.11769e6 | 0.886320 | ||||||||
\(545\) | −25460.7 | −0.00367180 | ||||||||
\(546\) | −1.30782e6 | −0.187745 | ||||||||
\(547\) | 1.30814e6 | 0.186933 | 0.0934664 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934664 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(548\) | −1.94450e7 | −2.76603 | ||||||||
\(549\) | −1.49609e6 | −0.211849 | ||||||||
\(550\) | 3.54381e6 | 0.499532 | ||||||||
\(551\) | 9.42064e6 | 1.32191 | ||||||||
\(552\) | 1.66673e6 | 0.232819 | ||||||||
\(553\) | 4.33395e6 | 0.602658 | ||||||||
\(554\) | 6.81505e6 | 0.943397 | ||||||||
\(555\) | 17797.9 | 0.00245266 | ||||||||
\(556\) | 1.86394e7 | 2.55708 | ||||||||
\(557\) | 6.95945e6 | 0.950467 | 0.475234 | − | 0.879860i | \(-0.342364\pi\) | ||||
0.475234 | + | 0.879860i | \(0.342364\pi\) | |||||||
\(558\) | −7.46678e6 | −1.01519 | ||||||||
\(559\) | 2.03950e6 | 0.276054 | ||||||||
\(560\) | −8947.82 | −0.00120572 | ||||||||
\(561\) | 1.55998e6 | 0.209272 | ||||||||
\(562\) | −3.55303e6 | −0.474524 | ||||||||
\(563\) | 6.90198e6 | 0.917704 | 0.458852 | − | 0.888513i | \(-0.348261\pi\) | ||||
0.458852 | + | 0.888513i | \(0.348261\pi\) | |||||||
\(564\) | 1.15544e7 | 1.52950 | ||||||||
\(565\) | −8210.15 | −0.00108201 | ||||||||
\(566\) | −6.51721e6 | −0.855107 | ||||||||
\(567\) | −689439. | −0.0900613 | ||||||||
\(568\) | 6.30054e6 | 0.819421 | ||||||||
\(569\) | 3.31261e6 | 0.428933 | 0.214466 | − | 0.976731i | \(-0.431199\pi\) | ||||
0.214466 | + | 0.976731i | \(0.431199\pi\) | |||||||
\(570\) | 47537.6 | 0.00612844 | ||||||||
\(571\) | 1.43930e7 | 1.84741 | 0.923703 | − | 0.383109i | \(-0.125147\pi\) | ||||
0.923703 | + | 0.383109i | \(0.125147\pi\) | |||||||
\(572\) | −996928. | −0.127401 | ||||||||
\(573\) | 1.20362e6 | 0.153146 | ||||||||
\(574\) | −1.79883e7 | −2.27882 | ||||||||
\(575\) | −2.59010e6 | −0.326699 | ||||||||
\(576\) | −4.03836e6 | −0.507165 | ||||||||
\(577\) | 3.31761e6 | 0.414845 | 0.207423 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207423 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(578\) | 5.92484e6 | 0.737662 | ||||||||
\(579\) | −4.16040e6 | −0.515749 | ||||||||
\(580\) | 71716.5 | 0.00885216 | ||||||||
\(581\) | 2.45421e6 | 0.301628 | ||||||||
\(582\) | −1.25926e7 | −1.54101 | ||||||||
\(583\) | −1.73174e6 | −0.211015 | ||||||||
\(584\) | −8.79939e6 | −1.06763 | ||||||||
\(585\) | 3312.78 | 0.000400224 0 | ||||||||
\(586\) | 2.51527e6 | 0.302580 | ||||||||
\(587\) | 2.10735e6 | 0.252431 | 0.126215 | − | 0.992003i | \(-0.459717\pi\) | ||||
0.126215 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(588\) | −2.89719e6 | −0.345568 | ||||||||
\(589\) | −1.99977e7 | −2.37515 | ||||||||
\(590\) | −18395.8 | −0.00217565 | ||||||||
\(591\) | 867893. | 0.102211 | ||||||||
\(592\) | 2.19166e6 | 0.257021 | ||||||||
\(593\) | 525039. | 0.0613133 | 0.0306566 | − | 0.999530i | \(-0.490240\pi\) | ||||
0.0306566 | + | 0.999530i | \(0.490240\pi\) | |||||||
\(594\) | −826720. | −0.0961373 | ||||||||
\(595\) | 41724.4 | 0.00483167 | ||||||||
\(596\) | 1.73242e7 | 1.99773 | ||||||||
\(597\) | −9.74380e6 | −1.11890 | ||||||||
\(598\) | 1.14619e6 | 0.131071 | ||||||||
\(599\) | −7.02964e6 | −0.800509 | −0.400254 | − | 0.916404i | \(-0.631078\pi\) | ||||
−0.400254 | + | 0.916404i | \(0.631078\pi\) | |||||||
\(600\) | −6.28387e6 | −0.712605 | ||||||||
\(601\) | −1.11158e6 | −0.125532 | −0.0627660 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627660 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(602\) | −1.36132e7 | −1.53097 | ||||||||
\(603\) | 1.31459e6 | 0.147230 | ||||||||
\(604\) | −3.05731e6 | −0.340994 | ||||||||
\(605\) | 4058.29 | 0.000450770 0 | ||||||||
\(606\) | 5.26433e6 | 0.582320 | ||||||||
\(607\) | 1.53428e7 | 1.69018 | 0.845088 | − | 0.534627i | \(-0.179548\pi\) | ||||
0.845088 | + | 0.534627i | \(0.179548\pi\) | |||||||
\(608\) | −8.68307e6 | −0.952608 | ||||||||
\(609\) | −4.38200e6 | −0.478772 | ||||||||
\(610\) | −47983.3 | −0.00522115 | ||||||||
\(611\) | 3.39232e6 | 0.367616 | ||||||||
\(612\) | −6.47916e6 | −0.699263 | ||||||||
\(613\) | 4.78522e6 | 0.514341 | 0.257170 | − | 0.966366i | \(-0.417210\pi\) | ||||
0.257170 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(614\) | 1.67615e7 | 1.79429 | ||||||||
\(615\) | 45565.3 | 0.00485788 | ||||||||
\(616\) | 2.84091e6 | 0.301651 | ||||||||
\(617\) | 1.69116e7 | 1.78843 | 0.894215 | − | 0.447639i | \(-0.147735\pi\) | ||||
0.894215 | + | 0.447639i | \(0.147735\pi\) | |||||||
\(618\) | −7.59553e6 | −0.799994 | ||||||||
\(619\) | −8.65985e6 | −0.908414 | −0.454207 | − | 0.890896i | \(-0.650077\pi\) | ||||
−0.454207 | + | 0.890896i | \(0.650077\pi\) | |||||||
\(620\) | −152236. | −0.0159052 | ||||||||
\(621\) | 604234. | 0.0628747 | ||||||||
\(622\) | 3.39958e6 | 0.352330 | ||||||||
\(623\) | 1.09078e7 | 1.12595 | ||||||||
\(624\) | 407941. | 0.0419407 | ||||||||
\(625\) | 9.76490e6 | 0.999926 | ||||||||
\(626\) | −1.07202e7 | −1.09337 | ||||||||
\(627\) | −2.21414e6 | −0.224924 | ||||||||
\(628\) | 1.23716e7 | 1.25178 | ||||||||
\(629\) | −1.02199e7 | −1.02996 | ||||||||
\(630\) | −22112.0 | −0.00221961 | ||||||||
\(631\) | 9.04083e6 | 0.903930 | 0.451965 | − | 0.892036i | \(-0.350723\pi\) | ||||
0.451965 | + | 0.892036i | \(0.350723\pi\) | |||||||
\(632\) | −9.21516e6 | −0.917720 | ||||||||
\(633\) | 7.88029e6 | 0.781687 | ||||||||
\(634\) | 3.22172e7 | 3.18321 | ||||||||
\(635\) | 75153.2 | 0.00739627 | ||||||||
\(636\) | 7.19257e6 | 0.705084 | ||||||||
\(637\) | −850603. | −0.0830574 | ||||||||
\(638\) | −5.25454e6 | −0.511073 | ||||||||
\(639\) | 2.28411e6 | 0.221292 | ||||||||
\(640\) | −91639.5 | −0.00884368 | ||||||||
\(641\) | −1.21113e7 | −1.16424 | −0.582122 | − | 0.813101i | \(-0.697778\pi\) | ||||
−0.582122 | + | 0.813101i | \(0.697778\pi\) | |||||||
\(642\) | 1.01607e7 | 0.972942 | ||||||||
\(643\) | 2.24955e6 | 0.214570 | 0.107285 | − | 0.994228i | \(-0.465784\pi\) | ||||
0.107285 | + | 0.994228i | \(0.465784\pi\) | |||||||
\(644\) | −4.86347e6 | −0.462095 | ||||||||
\(645\) | 34482.8 | 0.00326365 | ||||||||
\(646\) | −2.72969e7 | −2.57355 | ||||||||
\(647\) | 8.21206e6 | 0.771244 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) | ||||
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(648\) | 1.46594e6 | 0.137144 | ||||||||
\(649\) | 856815. | 0.0798501 | ||||||||
\(650\) | −4.32136e6 | −0.401178 | ||||||||
\(651\) | 9.30190e6 | 0.860239 | ||||||||
\(652\) | −1.25773e7 | −1.15869 | ||||||||
\(653\) | −1.15110e7 | −1.05641 | −0.528203 | − | 0.849118i | \(-0.677134\pi\) | ||||
−0.528203 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(654\) | −7.74793e6 | −0.708340 | ||||||||
\(655\) | −62087.1 | −0.00565455 | ||||||||
\(656\) | 5.61097e6 | 0.509071 | ||||||||
\(657\) | −3.19001e6 | −0.288323 | ||||||||
\(658\) | −2.26429e7 | −2.03877 | ||||||||
\(659\) | −1.79339e7 | −1.60865 | −0.804323 | − | 0.594192i | \(-0.797472\pi\) | ||||
−0.804323 | + | 0.594192i | \(0.797472\pi\) | |||||||
\(660\) | −16855.6 | −0.00150620 | ||||||||
\(661\) | −8.63046e6 | −0.768299 | −0.384150 | − | 0.923271i | \(-0.625505\pi\) | ||||
−0.384150 | + | 0.923271i | \(0.625505\pi\) | |||||||
\(662\) | 1.04433e7 | 0.926176 | ||||||||
\(663\) | −1.90226e6 | −0.168068 | ||||||||
\(664\) | −5.21832e6 | −0.459315 | ||||||||
\(665\) | −59220.9 | −0.00519303 | ||||||||
\(666\) | 5.41607e6 | 0.473150 | ||||||||
\(667\) | 3.84044e6 | 0.334246 | ||||||||
\(668\) | 1.04306e7 | 0.904418 | ||||||||
\(669\) | 8.89238e6 | 0.768162 | ||||||||
\(670\) | 42162.1 | 0.00362857 | ||||||||
\(671\) | 2.23490e6 | 0.191625 | ||||||||
\(672\) | 4.03892e6 | 0.345018 | ||||||||
\(673\) | −1.92878e7 | −1.64152 | −0.820758 | − | 0.571276i | \(-0.806449\pi\) | ||||
−0.820758 | + | 0.571276i | \(0.806449\pi\) | |||||||
\(674\) | −2.11630e7 | −1.79443 | ||||||||
\(675\) | −2.27807e6 | −0.192445 | ||||||||
\(676\) | −1.95172e7 | −1.64267 | ||||||||
\(677\) | 6.67400e6 | 0.559647 | 0.279824 | − | 0.960051i | \(-0.409724\pi\) | ||||
0.279824 | + | 0.960051i | \(0.409724\pi\) | |||||||
\(678\) | −2.49843e6 | −0.208734 | ||||||||
\(679\) | 1.56875e7 | 1.30580 | ||||||||
\(680\) | −88717.4 | −0.00735761 | ||||||||
\(681\) | 603594. | 0.0498744 | ||||||||
\(682\) | 1.11541e7 | 0.918275 | ||||||||
\(683\) | −7.83722e6 | −0.642851 | −0.321426 | − | 0.946935i | \(-0.604162\pi\) | ||||
−0.321426 | + | 0.946935i | \(0.604162\pi\) | |||||||
\(684\) | 9.19611e6 | 0.751561 | ||||||||
\(685\) | −96524.6 | −0.00785980 | ||||||||
\(686\) | 2.22300e7 | 1.80355 | ||||||||
\(687\) | −5.95918e6 | −0.481720 | ||||||||
\(688\) | 4.24626e6 | 0.342007 | ||||||||
\(689\) | 2.11171e6 | 0.169467 | ||||||||
\(690\) | 19379.3 | 0.00154958 | ||||||||
\(691\) | −2.05838e7 | −1.63995 | −0.819974 | − | 0.572400i | \(-0.806012\pi\) | ||||
−0.819974 | + | 0.572400i | \(0.806012\pi\) | |||||||
\(692\) | −3.98507e7 | −3.16352 | ||||||||
\(693\) | 1.02990e6 | 0.0814635 | ||||||||
\(694\) | −1.09707e7 | −0.864640 | ||||||||
\(695\) | 92525.4 | 0.00726606 | ||||||||
\(696\) | 9.31734e6 | 0.729069 | ||||||||
\(697\) | −2.61644e7 | −2.03999 | ||||||||
\(698\) | 1.14065e7 | 0.886162 | ||||||||
\(699\) | 1.24165e7 | 0.961185 | ||||||||
\(700\) | 1.83361e7 | 1.41437 | ||||||||
\(701\) | −8.88356e6 | −0.682797 | −0.341399 | − | 0.939919i | \(-0.610901\pi\) | ||||
−0.341399 | + | 0.939919i | \(0.610901\pi\) | |||||||
\(702\) | 1.00811e6 | 0.0772086 | ||||||||
\(703\) | 1.45054e7 | 1.10699 | ||||||||
\(704\) | 6.03261e6 | 0.458748 | ||||||||
\(705\) | 57355.7 | 0.00434614 | ||||||||
\(706\) | 2.68223e6 | 0.202528 | ||||||||
\(707\) | −6.55815e6 | −0.493438 | ||||||||
\(708\) | −3.55866e6 | −0.266811 | ||||||||
\(709\) | 6.33167e6 | 0.473045 | 0.236523 | − | 0.971626i | \(-0.423992\pi\) | ||||
0.236523 | + | 0.971626i | \(0.423992\pi\) | |||||||
\(710\) | 73257.2 | 0.00545386 | ||||||||
\(711\) | −3.34074e6 | −0.247838 | ||||||||
\(712\) | −2.31930e7 | −1.71458 | ||||||||
\(713\) | −8.15231e6 | −0.600560 | ||||||||
\(714\) | 1.26971e7 | 0.932094 | ||||||||
\(715\) | −4948.73 | −0.000362017 0 | ||||||||
\(716\) | 4.40826e7 | 3.21355 | ||||||||
\(717\) | 3.81412e6 | 0.277075 | ||||||||
\(718\) | 1.11592e7 | 0.807836 | ||||||||
\(719\) | 3.88936e6 | 0.280579 | 0.140290 | − | 0.990111i | \(-0.455197\pi\) | ||||
0.140290 | + | 0.990111i | \(0.455197\pi\) | |||||||
\(720\) | 6897.26 | 0.000495844 0 | ||||||||
\(721\) | 9.46229e6 | 0.677888 | ||||||||
\(722\) | 1.55368e7 | 1.10922 | ||||||||
\(723\) | −1.21322e7 | −0.863163 | ||||||||
\(724\) | 2.25205e6 | 0.159673 | ||||||||
\(725\) | −1.44792e7 | −1.02305 | ||||||||
\(726\) | 1.23498e6 | 0.0869595 | ||||||||
\(727\) | 2.34319e7 | 1.64426 | 0.822131 | − | 0.569299i | \(-0.192785\pi\) | ||||
0.822131 | + | 0.569299i | \(0.192785\pi\) | |||||||
\(728\) | −3.46423e6 | −0.242258 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −102312. | −0.00710588 | ||||||||
\(731\) | −1.98006e7 | −1.37052 | ||||||||
\(732\) | −9.28235e6 | −0.640295 | ||||||||
\(733\) | 1.77978e7 | 1.22351 | 0.611753 | − | 0.791049i | \(-0.290465\pi\) | ||||
0.611753 | + | 0.791049i | \(0.290465\pi\) | |||||||
\(734\) | 2.91591e7 | 1.99772 | ||||||||
\(735\) | −14381.6 | −0.000981946 0 | ||||||||
\(736\) | −3.53976e6 | −0.240868 | ||||||||
\(737\) | −1.96376e6 | −0.133174 | ||||||||
\(738\) | 1.38659e7 | 0.937149 | ||||||||
\(739\) | 3.15950e6 | 0.212817 | 0.106409 | − | 0.994322i | \(-0.466065\pi\) | ||||
0.106409 | + | 0.994322i | \(0.466065\pi\) | |||||||
\(740\) | 110425. | 0.00741293 | ||||||||
\(741\) | 2.69994e6 | 0.180638 | ||||||||
\(742\) | −1.40952e7 | −0.939853 | ||||||||
\(743\) | −4.37086e6 | −0.290465 | −0.145233 | − | 0.989398i | \(-0.546393\pi\) | ||||
−0.145233 | + | 0.989398i | \(0.546393\pi\) | |||||||
\(744\) | −1.97784e7 | −1.30996 | ||||||||
\(745\) | 85996.8 | 0.00567664 | ||||||||
\(746\) | 3.36030e7 | 2.21070 | ||||||||
\(747\) | −1.89178e6 | −0.124042 | ||||||||
\(748\) | 9.67875e6 | 0.632507 | ||||||||
\(749\) | −1.26579e7 | −0.824438 | ||||||||
\(750\) | −146129. | −0.00948597 | ||||||||
\(751\) | 1.72544e7 | 1.11635 | 0.558173 | − | 0.829724i | \(-0.311502\pi\) | ||||
0.558173 | + | 0.829724i | \(0.311502\pi\) | |||||||
\(752\) | 7.06285e6 | 0.455445 | ||||||||
\(753\) | −1.31322e7 | −0.844017 | ||||||||
\(754\) | 6.40745e6 | 0.410447 | ||||||||
\(755\) | −15176.4 | −0.000968950 0 | ||||||||
\(756\) | −4.27756e6 | −0.272202 | ||||||||
\(757\) | −1.57084e7 | −0.996307 | −0.498153 | − | 0.867089i | \(-0.665988\pi\) | ||||
−0.498153 | + | 0.867089i | \(0.665988\pi\) | |||||||
\(758\) | 1.76033e7 | 1.11281 | ||||||||
\(759\) | −902621. | −0.0568723 | ||||||||
\(760\) | 125920. | 0.00790789 | ||||||||
\(761\) | 5.01006e6 | 0.313604 | 0.156802 | − | 0.987630i | \(-0.449882\pi\) | ||||
0.156802 | + | 0.987630i | \(0.449882\pi\) | |||||||
\(762\) | 2.28698e7 | 1.42684 | ||||||||
\(763\) | 9.65215e6 | 0.600223 | ||||||||
\(764\) | 7.46778e6 | 0.462869 | ||||||||
\(765\) | −32162.4 | −0.00198699 | ||||||||
\(766\) | −6.21058e6 | −0.382437 | ||||||||
\(767\) | −1.04481e6 | −0.0641282 | ||||||||
\(768\) | −1.35282e7 | −0.827629 | ||||||||
\(769\) | 3.47489e6 | 0.211897 | 0.105949 | − | 0.994372i | \(-0.466212\pi\) | ||||
0.105949 | + | 0.994372i | \(0.466212\pi\) | |||||||
\(770\) | 33031.6 | 0.00200772 | ||||||||
\(771\) | 4.93653e6 | 0.299079 | ||||||||
\(772\) | −2.58128e7 | −1.55880 | ||||||||
\(773\) | 2.29786e7 | 1.38317 | 0.691584 | − | 0.722296i | \(-0.256913\pi\) | ||||
0.691584 | + | 0.722296i | \(0.256913\pi\) | |||||||
\(774\) | 1.04934e7 | 0.629602 | ||||||||
\(775\) | 3.07357e7 | 1.83818 | ||||||||
\(776\) | −3.33558e7 | −1.98846 | ||||||||
\(777\) | −6.74718e6 | −0.400931 | ||||||||
\(778\) | −4.76458e7 | −2.82212 | ||||||||
\(779\) | 3.71361e7 | 2.19256 | ||||||||
\(780\) | 20553.9 | 0.00120964 | ||||||||
\(781\) | −3.41207e6 | −0.200166 | ||||||||
\(782\) | −1.11279e7 | −0.650724 | ||||||||
\(783\) | 3.37778e6 | 0.196892 | ||||||||
\(784\) | −1.77096e6 | −0.102901 | ||||||||
\(785\) | 61412.3 | 0.00355698 | ||||||||
\(786\) | −1.88937e7 | −1.09084 | ||||||||
\(787\) | −1.40930e7 | −0.811087 | −0.405544 | − | 0.914076i | \(-0.632918\pi\) | ||||
−0.405544 | + | 0.914076i | \(0.632918\pi\) | |||||||
\(788\) | 5.38476e6 | 0.308923 | ||||||||
\(789\) | 8.14769e6 | 0.465953 | ||||||||
\(790\) | −107146. | −0.00610812 | ||||||||
\(791\) | 3.11247e6 | 0.176874 | ||||||||
\(792\) | −2.18986e6 | −0.124052 | ||||||||
\(793\) | −2.72526e6 | −0.153895 | ||||||||
\(794\) | −4.85845e6 | −0.273493 | ||||||||
\(795\) | 35703.7 | 0.00200353 | ||||||||
\(796\) | −6.04545e7 | −3.38178 | ||||||||
\(797\) | −1.08281e7 | −0.603819 | −0.301909 | − | 0.953337i | \(-0.597624\pi\) | ||||
−0.301909 | + | 0.953337i | \(0.597624\pi\) | |||||||
\(798\) | −1.80215e7 | −1.00181 | ||||||||
\(799\) | −3.29346e7 | −1.82510 | ||||||||
\(800\) | 1.33455e7 | 0.737243 | ||||||||
\(801\) | −8.40808e6 | −0.463037 | ||||||||
\(802\) | 1.05474e7 | 0.579041 | ||||||||
\(803\) | 4.76533e6 | 0.260798 | ||||||||
\(804\) | 8.15623e6 | 0.444989 | ||||||||
\(805\) | −24142.2 | −0.00131307 | ||||||||
\(806\) | −1.36014e7 | −0.737474 | ||||||||
\(807\) | −1.47637e6 | −0.0798013 | ||||||||
\(808\) | 1.39444e7 | 0.751402 | ||||||||
\(809\) | −2.27494e7 | −1.22208 | −0.611040 | − | 0.791600i | \(-0.709248\pi\) | ||||
−0.611040 | + | 0.791600i | \(0.709248\pi\) | |||||||
\(810\) | 17044.6 | 0.000912799 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 | ||||||||
\(813\) | 8.90673e6 | 0.472598 | ||||||||
\(814\) | −8.09067e6 | −0.427980 | ||||||||
\(815\) | −62433.2 | −0.00329247 | ||||||||
\(816\) | −3.96052e6 | −0.208222 | ||||||||
\(817\) | 2.81038e7 | 1.47302 | ||||||||
\(818\) | 2.95596e7 | 1.54460 | ||||||||
\(819\) | −1.25588e6 | −0.0654240 | ||||||||
\(820\) | 282706. | 0.0146825 | ||||||||
\(821\) | −1.77359e7 | −0.918323 | −0.459161 | − | 0.888353i | \(-0.651850\pi\) | ||||
−0.459161 | + | 0.888353i | \(0.651850\pi\) | |||||||
\(822\) | −2.93733e7 | −1.51626 | ||||||||
\(823\) | −2.24560e7 | −1.15567 | −0.577834 | − | 0.816154i | \(-0.696102\pi\) | ||||
−0.577834 | + | 0.816154i | \(0.696102\pi\) | |||||||
\(824\) | −2.01194e7 | −1.03228 | ||||||||
\(825\) | 3.40304e6 | 0.174073 | ||||||||
\(826\) | 6.97386e6 | 0.355650 | ||||||||
\(827\) | −1.97457e7 | −1.00394 | −0.501972 | − | 0.864884i | \(-0.667392\pi\) | ||||
−0.501972 | + | 0.864884i | \(0.667392\pi\) | |||||||
\(828\) | 3.74891e6 | 0.190033 | ||||||||
\(829\) | 2.61754e7 | 1.32284 | 0.661418 | − | 0.750017i | \(-0.269955\pi\) | ||||
0.661418 | + | 0.750017i | \(0.269955\pi\) | |||||||
\(830\) | −60674.1 | −0.00305709 | ||||||||
\(831\) | 6.54434e6 | 0.328748 | ||||||||
\(832\) | −7.35624e6 | −0.368424 | ||||||||
\(833\) | 8.25814e6 | 0.412354 | ||||||||
\(834\) | 2.81563e7 | 1.40172 | ||||||||
\(835\) | 51777.4 | 0.00256995 | ||||||||
\(836\) | −1.37374e7 | −0.679812 | ||||||||
\(837\) | −7.17019e6 | −0.353767 | ||||||||
\(838\) | 7.51015e6 | 0.369435 | ||||||||
\(839\) | −3.69992e6 | −0.181463 | −0.0907313 | − | 0.995875i | \(-0.528920\pi\) | ||||
−0.0907313 | + | 0.995875i | \(0.528920\pi\) | |||||||
\(840\) | −58571.5 | −0.00286410 | ||||||||
\(841\) | 957652. | 0.0466893 | ||||||||
\(842\) | −1.73808e7 | −0.844869 | ||||||||
\(843\) | −3.41190e6 | −0.165359 | ||||||||
\(844\) | 4.88925e7 | 2.36258 | ||||||||
\(845\) | −96883.0 | −0.00466773 | ||||||||
\(846\) | 1.74539e7 | 0.838428 | ||||||||
\(847\) | −1.53850e6 | −0.0736866 | ||||||||
\(848\) | 4.39660e6 | 0.209956 | ||||||||
\(849\) | −6.25834e6 | −0.297982 | ||||||||
\(850\) | 4.19542e7 | 1.99172 | ||||||||
\(851\) | 5.91332e6 | 0.279903 | ||||||||
\(852\) | 1.41716e7 | 0.668834 | ||||||||
\(853\) | 2.90121e7 | 1.36523 | 0.682617 | − | 0.730776i | \(-0.260842\pi\) | ||||
0.682617 | + | 0.730776i | \(0.260842\pi\) | |||||||
\(854\) | 1.81905e7 | 0.853492 | ||||||||
\(855\) | 45649.3 | 0.00213559 | ||||||||
\(856\) | 2.69142e7 | 1.25544 | ||||||||
\(857\) | −3.60120e7 | −1.67493 | −0.837463 | − | 0.546494i | \(-0.815962\pi\) | ||||
−0.837463 | + | 0.546494i | \(0.815962\pi\) | |||||||
\(858\) | −1.50594e6 | −0.0698378 | ||||||||
\(859\) | −2.14715e7 | −0.992841 | −0.496421 | − | 0.868082i | \(-0.665353\pi\) | ||||
−0.496421 | + | 0.868082i | \(0.665353\pi\) | |||||||
\(860\) | 213945. | 0.00986409 | ||||||||
\(861\) | −1.72738e7 | −0.794108 | ||||||||
\(862\) | 2.30562e7 | 1.05686 | ||||||||
\(863\) | 1.43154e7 | 0.654298 | 0.327149 | − | 0.944973i | \(-0.393912\pi\) | ||||
0.327149 | + | 0.944973i | \(0.393912\pi\) | |||||||
\(864\) | −3.11332e6 | −0.141886 | ||||||||
\(865\) | −197818. | −0.00898928 | ||||||||
\(866\) | 2.92625e7 | 1.32592 | ||||||||
\(867\) | 5.68950e6 | 0.257055 | ||||||||
\(868\) | 5.77128e7 | 2.60000 | ||||||||
\(869\) | 4.99049e6 | 0.224178 | ||||||||
\(870\) | 108334. | 0.00485251 | ||||||||
\(871\) | 2.39464e6 | 0.106953 | ||||||||
\(872\) | −2.05231e7 | −0.914013 | ||||||||
\(873\) | −1.20924e7 | −0.537002 | ||||||||
\(874\) | 1.57943e7 | 0.699392 | ||||||||
\(875\) | 182043. | 0.00803809 | ||||||||
\(876\) | −1.97921e7 | −0.871430 | ||||||||
\(877\) | 2.25088e7 | 0.988221 | 0.494110 | − | 0.869399i | \(-0.335494\pi\) | ||||
0.494110 | + | 0.869399i | \(0.335494\pi\) | |||||||
\(878\) | −5.71030e7 | −2.49990 | ||||||||
\(879\) | 2.41536e6 | 0.105441 | ||||||||
\(880\) | −10303.3 | −0.000448508 0 | ||||||||
\(881\) | 8.39629e6 | 0.364458 | 0.182229 | − | 0.983256i | \(-0.441669\pi\) | ||||
0.182229 | + | 0.983256i | \(0.441669\pi\) | |||||||
\(882\) | −4.37644e6 | −0.189431 | ||||||||
\(883\) | 1.08666e7 | 0.469021 | 0.234510 | − | 0.972114i | \(-0.424651\pi\) | ||||
0.234510 | + | 0.972114i | \(0.424651\pi\) | |||||||
\(884\) | −1.18024e7 | −0.507971 | ||||||||
\(885\) | −17665.1 | −0.000758156 0 | ||||||||
\(886\) | −7.43650e7 | −3.18262 | ||||||||
\(887\) | 1.53488e7 | 0.655038 | 0.327519 | − | 0.944845i | \(-0.393788\pi\) | ||||
0.327519 | + | 0.944845i | \(0.393788\pi\) | |||||||
\(888\) | 1.43464e7 | 0.610533 | ||||||||
\(889\) | −2.84905e7 | −1.20906 | ||||||||
\(890\) | −269668. | −0.0114118 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 5.51719e7 | 2.32170 | ||||||||
\(893\) | 4.67453e7 | 1.96160 | ||||||||
\(894\) | 2.61696e7 | 1.09510 | ||||||||
\(895\) | 218825. | 0.00913145 | ||||||||
\(896\) | 3.47405e7 | 1.44566 | ||||||||
\(897\) | 1.10067e6 | 0.0456746 | ||||||||
\(898\) | 4.32073e7 | 1.78799 | ||||||||
\(899\) | −4.55729e7 | −1.88065 | ||||||||
\(900\) | −1.41341e7 | −0.581649 | ||||||||
\(901\) | −2.05017e7 | −0.841352 | ||||||||
\(902\) | −2.07133e7 | −0.847683 | ||||||||
\(903\) | −1.30724e7 | −0.533503 | ||||||||
\(904\) | −6.61796e6 | −0.269341 | ||||||||
\(905\) | 11179.1 | 0.000453719 0 | ||||||||
\(906\) | −4.61832e6 | −0.186923 | ||||||||
\(907\) | 7.93009e6 | 0.320081 | 0.160041 | − | 0.987110i | \(-0.448838\pi\) | ||||
0.160041 | + | 0.987110i | \(0.448838\pi\) | |||||||
\(908\) | 3.74494e6 | 0.150741 | ||||||||
\(909\) | 5.05522e6 | 0.202923 | ||||||||
\(910\) | −40279.1 | −0.00161241 | ||||||||
\(911\) | −4.31907e7 | −1.72423 | −0.862114 | − | 0.506715i | \(-0.830860\pi\) | ||||
−0.862114 | + | 0.506715i | \(0.830860\pi\) | |||||||
\(912\) | 5.62131e6 | 0.223795 | ||||||||
\(913\) | 2.82599e6 | 0.112200 | ||||||||
\(914\) | −7.54898e7 | −2.98898 | ||||||||
\(915\) | −46077.4 | −0.00181943 | ||||||||
\(916\) | −3.69732e7 | −1.45595 | ||||||||
\(917\) | 2.35372e7 | 0.924340 | ||||||||
\(918\) | −9.78733e6 | −0.383316 | ||||||||
\(919\) | −2.17987e7 | −0.851414 | −0.425707 | − | 0.904861i | \(-0.639975\pi\) | ||||
−0.425707 | + | 0.904861i | \(0.639975\pi\) | |||||||
\(920\) | 51332.8 | 0.00199952 | ||||||||
\(921\) | 1.60957e7 | 0.625260 | ||||||||
\(922\) | 3.02191e7 | 1.17072 | ||||||||
\(923\) | 4.16072e6 | 0.160755 | ||||||||
\(924\) | 6.38994e6 | 0.246216 | ||||||||
\(925\) | −2.22943e7 | −0.856720 | ||||||||
\(926\) | 1.21471e7 | 0.465527 | ||||||||
\(927\) | −7.29382e6 | −0.278776 | ||||||||
\(928\) | −1.97879e7 | −0.754276 | ||||||||
\(929\) | −1.33390e7 | −0.507089 | −0.253545 | − | 0.967324i | \(-0.581596\pi\) | ||||
−0.253545 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(930\) | −229966. | −0.00871879 | ||||||||
\(931\) | −1.17211e7 | −0.443194 | ||||||||
\(932\) | 7.70371e7 | 2.90510 | ||||||||
\(933\) | 3.26454e6 | 0.122777 | ||||||||
\(934\) | −2.00475e7 | −0.751956 | ||||||||
\(935\) | 48045.1 | 0.00179730 | ||||||||
\(936\) | 2.67034e6 | 0.0996269 | ||||||||
\(937\) | 1.33697e7 | 0.497476 | 0.248738 | − | 0.968571i | \(-0.419984\pi\) | ||||
0.248738 | + | 0.968571i | \(0.419984\pi\) | |||||||
\(938\) | −1.59836e7 | −0.593155 | ||||||||
\(939\) | −1.02943e7 | −0.381008 | ||||||||
\(940\) | 355858. | 0.0131358 | ||||||||
\(941\) | 2.28926e7 | 0.842793 | 0.421397 | − | 0.906876i | \(-0.361540\pi\) | ||||
0.421397 | + | 0.906876i | \(0.361540\pi\) | |||||||
\(942\) | 1.86883e7 | 0.686189 | ||||||||
\(943\) | 1.51390e7 | 0.554393 | ||||||||
\(944\) | −2.17531e6 | −0.0794494 | ||||||||
\(945\) | −21233.7 | −0.000773475 0 | ||||||||
\(946\) | −1.56754e7 | −0.569496 | ||||||||
\(947\) | 3.33079e6 | 0.120690 | 0.0603451 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603451 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(948\) | −2.07273e7 | −0.749069 | ||||||||
\(949\) | −5.81089e6 | −0.209449 | ||||||||
\(950\) | −5.95472e7 | −2.14068 | ||||||||
\(951\) | 3.09375e7 | 1.10926 | ||||||||
\(952\) | 3.36328e7 | 1.20274 | ||||||||
\(953\) | 4.68461e7 | 1.67087 | 0.835433 | − | 0.549593i | \(-0.185217\pi\) | ||||
0.835433 | + | 0.549593i | \(0.185217\pi\) | |||||||
\(954\) | 1.08650e7 | 0.386508 | ||||||||
\(955\) | 37069.9 | 0.00131526 | ||||||||
\(956\) | 2.36644e7 | 0.837433 | ||||||||
\(957\) | −5.04582e6 | −0.178095 | ||||||||
\(958\) | −4.47379e7 | −1.57493 | ||||||||
\(959\) | 3.65924e7 | 1.28483 | ||||||||
\(960\) | −124376. | −0.00435569 | ||||||||
\(961\) | 6.81109e7 | 2.37907 | ||||||||
\(962\) | 9.86586e6 | 0.343714 | ||||||||
\(963\) | 9.75712e6 | 0.339044 | ||||||||
\(964\) | −7.52730e7 | −2.60883 | ||||||||
\(965\) | −128134. | −0.00442942 | ||||||||
\(966\) | −7.34668e6 | −0.253308 | ||||||||
\(967\) | −3.65887e7 | −1.25829 | −0.629146 | − | 0.777287i | \(-0.716595\pi\) | ||||
−0.629146 | + | 0.777287i | \(0.716595\pi\) | |||||||
\(968\) | 3.27127e6 | 0.112209 | ||||||||
\(969\) | −2.62126e7 | −0.896811 | ||||||||
\(970\) | −387833. | −0.0132347 | ||||||||
\(971\) | 1.62147e7 | 0.551901 | 0.275951 | − | 0.961172i | \(-0.411007\pi\) | ||||
0.275951 | + | 0.961172i | \(0.411007\pi\) | |||||||
\(972\) | 3.29728e6 | 0.111941 | ||||||||
\(973\) | −3.50764e7 | −1.18777 | ||||||||
\(974\) | 7.48261e7 | 2.52729 | ||||||||
\(975\) | −4.14971e6 | −0.139800 | ||||||||
\(976\) | −5.67403e6 | −0.190663 | ||||||||
\(977\) | −1.50181e6 | −0.0503360 | −0.0251680 | − | 0.999683i | \(-0.508012\pi\) | ||||
−0.0251680 | + | 0.999683i | \(0.508012\pi\) | |||||||
\(978\) | −1.89990e7 | −0.635161 | ||||||||
\(979\) | 1.25602e7 | 0.418832 | ||||||||
\(980\) | −89229.1 | −0.00296784 | ||||||||
\(981\) | −7.44017e6 | −0.246837 | ||||||||
\(982\) | −3.46803e7 | −1.14764 | ||||||||
\(983\) | 3.72690e7 | 1.23017 | 0.615083 | − | 0.788462i | \(-0.289122\pi\) | ||||
0.615083 | + | 0.788462i | \(0.289122\pi\) | |||||||
\(984\) | 3.67288e7 | 1.20926 | ||||||||
\(985\) | 26729.8 | 0.000877820 0 | ||||||||
\(986\) | −6.22072e7 | −2.03774 | ||||||||
\(987\) | −2.17435e7 | −0.710456 | ||||||||
\(988\) | 1.67516e7 | 0.545962 | ||||||||
\(989\) | 1.14569e7 | 0.372456 | ||||||||
\(990\) | −25461.7 | −0.000825658 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 | ||||||||
\(993\) | 1.00285e7 | 0.322747 | ||||||||
\(994\) | −2.77718e7 | −0.891534 | ||||||||
\(995\) | −300095. | −0.00960950 | ||||||||
\(996\) | −1.17374e7 | −0.374906 | ||||||||
\(997\) | −5.59172e7 | −1.78159 | −0.890795 | − | 0.454406i | \(-0.849852\pi\) | ||||
−0.890795 | + | 0.454406i | \(0.849852\pi\) | |||||||
\(998\) | −6.60874e7 | −2.10035 | ||||||||
\(999\) | 5.20094e6 | 0.164880 |
(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 | 33.6.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 99.6.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 528.6.a.o.1.1 | 2 | |||
5.4 | even | 2 | 825.6.a.c.1.1 | 2 | |||
11.10 | odd | 2 | 363.6.a.f.1.1 | 2 | |||
33.32 | even | 2 | 1089.6.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.6.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
363.6.a.f.1.1 | 2 | 11.10 | odd | 2 | |||
528.6.a.o.1.1 | 2 | 4.3 | odd | 2 | |||
825.6.a.c.1.1 | 2 | 5.4 | even | 2 | |||
1089.6.a.p.1.2 | 2 | 33.32 | even | 2 |