Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,6,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(87.7299494377\) |
Analytic rank: | \(1\) |
Dimension: | \(111\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.25035 | −1.45847 | −0.729235 | − | 0.684263i | \(-0.760124\pi\) | ||||
−0.729235 | + | 0.684263i | \(0.760124\pi\) | |||||||
\(3\) | −30.3390 | −1.94625 | −0.973125 | − | 0.230276i | \(-0.926037\pi\) | ||||
−0.973125 | + | 0.230276i | \(0.926037\pi\) | |||||||
\(4\) | 36.0683 | 1.12713 | ||||||||
\(5\) | −26.4241 | −0.472688 | −0.236344 | − | 0.971669i | \(-0.575949\pi\) | ||||
−0.236344 | + | 0.971669i | \(0.575949\pi\) | |||||||
\(6\) | 250.308 | 2.83855 | ||||||||
\(7\) | −114.994 | −0.887013 | −0.443506 | − | 0.896271i | \(-0.646266\pi\) | ||||
−0.443506 | + | 0.896271i | \(0.646266\pi\) | |||||||
\(8\) | −33.5649 | −0.185422 | ||||||||
\(9\) | 677.458 | 2.78789 | ||||||||
\(10\) | 218.008 | 0.689401 | ||||||||
\(11\) | 428.707 | 1.06827 | 0.534133 | − | 0.845401i | \(-0.320638\pi\) | ||||
0.534133 | + | 0.845401i | \(0.320638\pi\) | |||||||
\(12\) | −1094.28 | −2.19369 | ||||||||
\(13\) | −862.728 | −1.41584 | −0.707922 | − | 0.706290i | \(-0.750367\pi\) | ||||
−0.707922 | + | 0.706290i | \(0.750367\pi\) | |||||||
\(14\) | 948.740 | 1.29368 | ||||||||
\(15\) | 801.681 | 0.919969 | ||||||||
\(16\) | −877.263 | −0.856702 | ||||||||
\(17\) | −1332.74 | −1.11847 | −0.559234 | − | 0.829010i | \(-0.688905\pi\) | ||||
−0.559234 | + | 0.829010i | \(0.688905\pi\) | |||||||
\(18\) | −5589.26 | −4.06606 | ||||||||
\(19\) | −1168.30 | −0.742455 | −0.371227 | − | 0.928542i | \(-0.621063\pi\) | ||||
−0.371227 | + | 0.928542i | \(0.621063\pi\) | |||||||
\(20\) | −953.071 | −0.532783 | ||||||||
\(21\) | 3488.81 | 1.72635 | ||||||||
\(22\) | −3536.99 | −1.55803 | ||||||||
\(23\) | 1386.99 | 0.546705 | 0.273352 | − | 0.961914i | \(-0.411867\pi\) | ||||
0.273352 | + | 0.961914i | \(0.411867\pi\) | |||||||
\(24\) | 1018.33 | 0.360877 | ||||||||
\(25\) | −2426.77 | −0.776566 | ||||||||
\(26\) | 7117.81 | 2.06497 | ||||||||
\(27\) | −13181.0 | −3.47968 | ||||||||
\(28\) | −4147.64 | −0.999782 | ||||||||
\(29\) | 3554.81 | 0.784912 | 0.392456 | − | 0.919771i | \(-0.371626\pi\) | ||||
0.392456 | + | 0.919771i | \(0.371626\pi\) | |||||||
\(30\) | −6614.15 | −1.34175 | ||||||||
\(31\) | −4864.80 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650218\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650218\pi\) | |||||||
\(32\) | 8311.81 | 1.43490 | ||||||||
\(33\) | −13006.6 | −2.07911 | ||||||||
\(34\) | 10995.6 | 1.63125 | ||||||||
\(35\) | 3038.61 | 0.419280 | ||||||||
\(36\) | 24434.7 | 3.14233 | ||||||||
\(37\) | 11319.1 | 1.35928 | 0.679640 | − | 0.733546i | \(-0.262136\pi\) | ||||
0.679640 | + | 0.733546i | \(0.262136\pi\) | |||||||
\(38\) | 9638.88 | 1.08285 | ||||||||
\(39\) | 26174.4 | 2.75559 | ||||||||
\(40\) | 886.921 | 0.0876466 | ||||||||
\(41\) | −16580.8 | −1.54044 | −0.770222 | − | 0.637775i | \(-0.779855\pi\) | ||||
−0.770222 | + | 0.637775i | \(0.779855\pi\) | |||||||
\(42\) | −28783.9 | −2.51783 | ||||||||
\(43\) | −15275.3 | −1.25985 | −0.629924 | − | 0.776657i | \(-0.716914\pi\) | ||||
−0.629924 | + | 0.776657i | \(0.716914\pi\) | |||||||
\(44\) | 15462.7 | 1.20408 | ||||||||
\(45\) | −17901.2 | −1.31780 | ||||||||
\(46\) | −11443.1 | −0.797353 | ||||||||
\(47\) | 20901.7 | 1.38018 | 0.690092 | − | 0.723722i | \(-0.257570\pi\) | ||||
0.690092 | + | 0.723722i | \(0.257570\pi\) | |||||||
\(48\) | 26615.3 | 1.66736 | ||||||||
\(49\) | −3583.40 | −0.213209 | ||||||||
\(50\) | 20021.7 | 1.13260 | ||||||||
\(51\) | 40434.1 | 2.17682 | ||||||||
\(52\) | −31117.1 | −1.59585 | ||||||||
\(53\) | 10132.7 | 0.495491 | 0.247745 | − | 0.968825i | \(-0.420310\pi\) | ||||
0.247745 | + | 0.968825i | \(0.420310\pi\) | |||||||
\(54\) | 108748. | 5.07501 | ||||||||
\(55\) | −11328.2 | −0.504956 | ||||||||
\(56\) | 3859.76 | 0.164471 | ||||||||
\(57\) | 35445.1 | 1.44500 | ||||||||
\(58\) | −29328.4 | −1.14477 | ||||||||
\(59\) | −9394.76 | −0.351363 | −0.175681 | − | 0.984447i | \(-0.556213\pi\) | ||||
−0.175681 | + | 0.984447i | \(0.556213\pi\) | |||||||
\(60\) | 28915.3 | 1.03693 | ||||||||
\(61\) | 19966.7 | 0.687039 | 0.343519 | − | 0.939146i | \(-0.388381\pi\) | ||||
0.343519 | + | 0.939146i | \(0.388381\pi\) | |||||||
\(62\) | 40136.3 | 1.32605 | ||||||||
\(63\) | −77903.5 | −2.47289 | ||||||||
\(64\) | −40502.9 | −1.23605 | ||||||||
\(65\) | 22796.8 | 0.669253 | ||||||||
\(66\) | 107309. | 3.03232 | ||||||||
\(67\) | −24684.5 | −0.671796 | −0.335898 | − | 0.941898i | \(-0.609040\pi\) | ||||
−0.335898 | + | 0.941898i | \(0.609040\pi\) | |||||||
\(68\) | −48069.7 | −1.26066 | ||||||||
\(69\) | −42079.9 | −1.06402 | ||||||||
\(70\) | −25069.6 | −0.611508 | ||||||||
\(71\) | 48422.0 | 1.13998 | 0.569989 | − | 0.821652i | \(-0.306947\pi\) | ||||
0.569989 | + | 0.821652i | \(0.306947\pi\) | |||||||
\(72\) | −22738.8 | −0.516935 | ||||||||
\(73\) | 19511.6 | 0.428534 | 0.214267 | − | 0.976775i | \(-0.431264\pi\) | ||||
0.214267 | + | 0.976775i | \(0.431264\pi\) | |||||||
\(74\) | −93386.8 | −1.98247 | ||||||||
\(75\) | 73625.8 | 1.51139 | ||||||||
\(76\) | −42138.6 | −0.836846 | ||||||||
\(77\) | −49298.7 | −0.947565 | ||||||||
\(78\) | −215948. | −4.01894 | ||||||||
\(79\) | 68131.6 | 1.22823 | 0.614117 | − | 0.789215i | \(-0.289512\pi\) | ||||
0.614117 | + | 0.789215i | \(0.289512\pi\) | |||||||
\(80\) | 23180.9 | 0.404953 | ||||||||
\(81\) | 235278. | 3.98445 | ||||||||
\(82\) | 136798. | 2.24669 | ||||||||
\(83\) | −60589.1 | −0.965381 | −0.482691 | − | 0.875791i | \(-0.660340\pi\) | ||||
−0.482691 | + | 0.875791i | \(0.660340\pi\) | |||||||
\(84\) | 125835. | 1.94583 | ||||||||
\(85\) | 35216.4 | 0.528686 | ||||||||
\(86\) | 126026. | 1.83745 | ||||||||
\(87\) | −107849. | −1.52764 | ||||||||
\(88\) | −14389.5 | −0.198080 | ||||||||
\(89\) | 61096.0 | 0.817594 | 0.408797 | − | 0.912625i | \(-0.365948\pi\) | ||||
0.408797 | + | 0.912625i | \(0.365948\pi\) | |||||||
\(90\) | 147691. | 1.92198 | ||||||||
\(91\) | 99208.5 | 1.25587 | ||||||||
\(92\) | 50026.3 | 0.616210 | ||||||||
\(93\) | 147594. | 1.76954 | ||||||||
\(94\) | −172446. | −2.01296 | ||||||||
\(95\) | 30871.2 | 0.350949 | ||||||||
\(96\) | −252172. | −2.79267 | ||||||||
\(97\) | 97304.7 | 1.05004 | 0.525018 | − | 0.851091i | \(-0.324058\pi\) | ||||
0.525018 | + | 0.851091i | \(0.324058\pi\) | |||||||
\(98\) | 29564.3 | 0.310958 | ||||||||
\(99\) | 290431. | 2.97821 | ||||||||
\(100\) | −87529.4 | −0.875294 | ||||||||
\(101\) | 127737. | 1.24599 | 0.622995 | − | 0.782226i | \(-0.285916\pi\) | ||||
0.622995 | + | 0.782226i | \(0.285916\pi\) | |||||||
\(102\) | −333595. | −3.17482 | ||||||||
\(103\) | −57338.3 | −0.532540 | −0.266270 | − | 0.963899i | \(-0.585791\pi\) | ||||
−0.266270 | + | 0.963899i | \(0.585791\pi\) | |||||||
\(104\) | 28957.4 | 0.262528 | ||||||||
\(105\) | −92188.4 | −0.816024 | ||||||||
\(106\) | −83598.3 | −0.722658 | ||||||||
\(107\) | 79789.8 | 0.673734 | 0.336867 | − | 0.941552i | \(-0.390633\pi\) | ||||
0.336867 | + | 0.941552i | \(0.390633\pi\) | |||||||
\(108\) | −475417. | −3.92207 | ||||||||
\(109\) | 91310.2 | 0.736128 | 0.368064 | − | 0.929801i | \(-0.380021\pi\) | ||||
0.368064 | + | 0.929801i | \(0.380021\pi\) | |||||||
\(110\) | 93461.5 | 0.736463 | ||||||||
\(111\) | −343411. | −2.64550 | ||||||||
\(112\) | 100880. | 0.759906 | ||||||||
\(113\) | −158647. | −1.16879 | −0.584393 | − | 0.811471i | \(-0.698667\pi\) | ||||
−0.584393 | + | 0.811471i | \(0.698667\pi\) | |||||||
\(114\) | −292434. | −2.10749 | ||||||||
\(115\) | −36649.9 | −0.258421 | ||||||||
\(116\) | 128216. | 0.884701 | ||||||||
\(117\) | −584462. | −3.94722 | ||||||||
\(118\) | 77510.0 | 0.512452 | ||||||||
\(119\) | 153257. | 0.992095 | ||||||||
\(120\) | −26908.3 | −0.170582 | ||||||||
\(121\) | 22738.9 | 0.141191 | ||||||||
\(122\) | −164732. | −1.00203 | ||||||||
\(123\) | 503046. | 2.99809 | ||||||||
\(124\) | −175465. | −1.02479 | ||||||||
\(125\) | 146700. | 0.839761 | ||||||||
\(126\) | 642731. | 3.60664 | ||||||||
\(127\) | −213325. | −1.17363 | −0.586815 | − | 0.809721i | \(-0.699619\pi\) | ||||
−0.586815 | + | 0.809721i | \(0.699619\pi\) | |||||||
\(128\) | 68185.4 | 0.367846 | ||||||||
\(129\) | 463437. | 2.45198 | ||||||||
\(130\) | −188082. | −0.976085 | ||||||||
\(131\) | 303669. | 1.54604 | 0.773022 | − | 0.634379i | \(-0.218744\pi\) | ||||
0.773022 | + | 0.634379i | \(0.218744\pi\) | |||||||
\(132\) | −469125. | −2.34344 | ||||||||
\(133\) | 134347. | 0.658567 | ||||||||
\(134\) | 203656. | 0.979794 | ||||||||
\(135\) | 348296. | 1.64480 | ||||||||
\(136\) | 44733.3 | 0.207388 | ||||||||
\(137\) | −318846. | −1.45138 | −0.725688 | − | 0.688024i | \(-0.758478\pi\) | ||||
−0.725688 | + | 0.688024i | \(0.758478\pi\) | |||||||
\(138\) | 347174. | 1.55185 | ||||||||
\(139\) | 42137.1 | 0.184981 | 0.0924907 | − | 0.995714i | \(-0.470517\pi\) | ||||
0.0924907 | + | 0.995714i | \(0.470517\pi\) | |||||||
\(140\) | 109597. | 0.472585 | ||||||||
\(141\) | −634137. | −2.68618 | ||||||||
\(142\) | −399498. | −1.66262 | ||||||||
\(143\) | −369858. | −1.51250 | ||||||||
\(144\) | −594309. | −2.38839 | ||||||||
\(145\) | −93932.4 | −0.371018 | ||||||||
\(146\) | −160977. | −0.625004 | ||||||||
\(147\) | 108717. | 0.414958 | ||||||||
\(148\) | 408262. | 1.53209 | ||||||||
\(149\) | −351854. | −1.29836 | −0.649182 | − | 0.760633i | \(-0.724889\pi\) | ||||
−0.649182 | + | 0.760633i | \(0.724889\pi\) | |||||||
\(150\) | −607439. | −2.20432 | ||||||||
\(151\) | 64284.8 | 0.229438 | 0.114719 | − | 0.993398i | \(-0.463403\pi\) | ||||
0.114719 | + | 0.993398i | \(0.463403\pi\) | |||||||
\(152\) | 39213.8 | 0.137667 | ||||||||
\(153\) | −902875. | −3.11817 | ||||||||
\(154\) | 406732. | 1.38199 | ||||||||
\(155\) | 128548. | 0.429770 | ||||||||
\(156\) | 944064. | 3.10592 | ||||||||
\(157\) | −167134. | −0.541147 | −0.270573 | − | 0.962699i | \(-0.587213\pi\) | ||||
−0.270573 | + | 0.962699i | \(0.587213\pi\) | |||||||
\(158\) | −562110. | −1.79134 | ||||||||
\(159\) | −307416. | −0.964349 | ||||||||
\(160\) | −219632. | −0.678258 | ||||||||
\(161\) | −159495. | −0.484934 | ||||||||
\(162\) | −1.94112e6 | −5.81119 | ||||||||
\(163\) | −28356.0 | −0.0835943 | −0.0417972 | − | 0.999126i | \(-0.513308\pi\) | ||||
−0.0417972 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(164\) | −598042. | −1.73629 | ||||||||
\(165\) | 343686. | 0.982771 | ||||||||
\(166\) | 499881. | 1.40798 | ||||||||
\(167\) | 579045. | 1.60665 | 0.803325 | − | 0.595541i | \(-0.203062\pi\) | ||||
0.803325 | + | 0.595541i | \(0.203062\pi\) | |||||||
\(168\) | −117101. | −0.320102 | ||||||||
\(169\) | 373007. | 1.00462 | ||||||||
\(170\) | −290548. | −0.771073 | ||||||||
\(171\) | −791473. | −2.06988 | ||||||||
\(172\) | −550953. | −1.42002 | ||||||||
\(173\) | −425916. | −1.08195 | −0.540977 | − | 0.841037i | \(-0.681945\pi\) | ||||
−0.540977 | + | 0.841037i | \(0.681945\pi\) | |||||||
\(174\) | 889796. | 2.22801 | ||||||||
\(175\) | 279064. | 0.688824 | ||||||||
\(176\) | −376089. | −0.915186 | ||||||||
\(177\) | 285028. | 0.683840 | ||||||||
\(178\) | −504063. | −1.19244 | ||||||||
\(179\) | −266030. | −0.620581 | −0.310291 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310291 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(180\) | −645665. | −1.48534 | ||||||||
\(181\) | 618211. | 1.40262 | 0.701310 | − | 0.712857i | \(-0.252599\pi\) | ||||
0.701310 | + | 0.712857i | \(0.252599\pi\) | |||||||
\(182\) | −818505. | −1.83165 | ||||||||
\(183\) | −605770. | −1.33715 | ||||||||
\(184\) | −46554.1 | −0.101371 | ||||||||
\(185\) | −299097. | −0.642515 | ||||||||
\(186\) | −1.21770e6 | −2.58082 | ||||||||
\(187\) | −571356. | −1.19482 | ||||||||
\(188\) | 753889. | 1.55565 | ||||||||
\(189\) | 1.51574e6 | 3.08652 | ||||||||
\(190\) | −254698. | −0.511849 | ||||||||
\(191\) | 783722. | 1.55446 | 0.777228 | − | 0.629219i | \(-0.216625\pi\) | ||||
0.777228 | + | 0.629219i | \(0.216625\pi\) | |||||||
\(192\) | 1.22882e6 | 2.40566 | ||||||||
\(193\) | 196320. | 0.379376 | 0.189688 | − | 0.981844i | \(-0.439252\pi\) | ||||
0.189688 | + | 0.981844i | \(0.439252\pi\) | |||||||
\(194\) | −802798. | −1.53145 | ||||||||
\(195\) | −691633. | −1.30253 | ||||||||
\(196\) | −129247. | −0.240315 | ||||||||
\(197\) | 329724. | 0.605320 | 0.302660 | − | 0.953099i | \(-0.402125\pi\) | ||||
0.302660 | + | 0.953099i | \(0.402125\pi\) | |||||||
\(198\) | −2.39616e6 | −4.34363 | ||||||||
\(199\) | 635923. | 1.13834 | 0.569169 | − | 0.822220i | \(-0.307265\pi\) | ||||
0.569169 | + | 0.822220i | \(0.307265\pi\) | |||||||
\(200\) | 81454.3 | 0.143992 | ||||||||
\(201\) | 748904. | 1.30748 | ||||||||
\(202\) | −1.05388e6 | −1.81724 | ||||||||
\(203\) | −408781. | −0.696227 | ||||||||
\(204\) | 1.45839e6 | 2.45357 | ||||||||
\(205\) | 438132. | 0.728150 | ||||||||
\(206\) | 473061. | 0.776693 | ||||||||
\(207\) | 939625. | 1.52415 | ||||||||
\(208\) | 756840. | 1.21296 | ||||||||
\(209\) | −500858. | −0.793139 | ||||||||
\(210\) | 760587. | 1.19015 | ||||||||
\(211\) | 488148. | 0.754824 | 0.377412 | − | 0.926045i | \(-0.376814\pi\) | ||||
0.377412 | + | 0.926045i | \(0.376814\pi\) | |||||||
\(212\) | 365469. | 0.558484 | ||||||||
\(213\) | −1.46908e6 | −2.21868 | ||||||||
\(214\) | −658294. | −0.982620 | ||||||||
\(215\) | 403635. | 0.595515 | ||||||||
\(216\) | 442420. | 0.645209 | ||||||||
\(217\) | 559423. | 0.806475 | ||||||||
\(218\) | −753341. | −1.07362 | ||||||||
\(219\) | −591963. | −0.834035 | ||||||||
\(220\) | −408588. | −0.569153 | ||||||||
\(221\) | 1.14979e6 | 1.58358 | ||||||||
\(222\) | 2.83327e6 | 3.85838 | ||||||||
\(223\) | 1.00289e6 | 1.35049 | 0.675243 | − | 0.737596i | \(-0.264039\pi\) | ||||
0.675243 | + | 0.737596i | \(0.264039\pi\) | |||||||
\(224\) | −955807. | −1.27277 | ||||||||
\(225\) | −1.64403e6 | −2.16498 | ||||||||
\(226\) | 1.30889e6 | 1.70464 | ||||||||
\(227\) | −252146. | −0.324779 | −0.162390 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162390 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(228\) | 1.27844e6 | 1.62871 | ||||||||
\(229\) | −64290.8 | −0.0810140 | −0.0405070 | − | 0.999179i | \(-0.512897\pi\) | ||||
−0.0405070 | + | 0.999179i | \(0.512897\pi\) | |||||||
\(230\) | 302374. | 0.376899 | ||||||||
\(231\) | 1.49568e6 | 1.84420 | ||||||||
\(232\) | −119317. | −0.145540 | ||||||||
\(233\) | 1.06891e6 | 1.28989 | 0.644945 | − | 0.764229i | \(-0.276880\pi\) | ||||
0.644945 | + | 0.764229i | \(0.276880\pi\) | |||||||
\(234\) | 4.82202e6 | 5.75690 | ||||||||
\(235\) | −552308. | −0.652396 | ||||||||
\(236\) | −338853. | −0.396033 | ||||||||
\(237\) | −2.06705e6 | −2.39045 | ||||||||
\(238\) | −1.26442e6 | −1.44694 | ||||||||
\(239\) | 1.65221e6 | 1.87099 | 0.935493 | − | 0.353345i | \(-0.114956\pi\) | ||||
0.935493 | + | 0.353345i | \(0.114956\pi\) | |||||||
\(240\) | −703285. | −0.788140 | ||||||||
\(241\) | −551406. | −0.611546 | −0.305773 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305773 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(242\) | −187604. | −0.205922 | ||||||||
\(243\) | −3.93511e6 | −4.27505 | ||||||||
\(244\) | 720164. | 0.774385 | ||||||||
\(245\) | 94687.9 | 0.100781 | ||||||||
\(246\) | −4.15031e6 | −4.37263 | ||||||||
\(247\) | 1.00792e6 | 1.05120 | ||||||||
\(248\) | 163287. | 0.168586 | ||||||||
\(249\) | 1.83821e6 | 1.87887 | ||||||||
\(250\) | −1.21033e6 | −1.22477 | ||||||||
\(251\) | 79390.5 | 0.0795397 | 0.0397699 | − | 0.999209i | \(-0.487338\pi\) | ||||
0.0397699 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(252\) | −2.80985e6 | −2.78728 | ||||||||
\(253\) | 594612. | 0.584026 | ||||||||
\(254\) | 1.76000e6 | 1.71171 | ||||||||
\(255\) | −1.06843e6 | −1.02896 | ||||||||
\(256\) | 733540. | 0.699558 | ||||||||
\(257\) | −1.82046e6 | −1.71929 | −0.859645 | − | 0.510892i | \(-0.829315\pi\) | ||||
−0.859645 | + | 0.510892i | \(0.829315\pi\) | |||||||
\(258\) | −3.82352e6 | −3.57614 | ||||||||
\(259\) | −1.30163e6 | −1.20570 | ||||||||
\(260\) | 822241. | 0.754338 | ||||||||
\(261\) | 2.40823e6 | 2.18825 | ||||||||
\(262\) | −2.50537e6 | −2.25486 | ||||||||
\(263\) | −211531. | −0.188576 | −0.0942878 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942878 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(264\) | 436564. | 0.385512 | ||||||||
\(265\) | −267747. | −0.234212 | ||||||||
\(266\) | −1.10841e6 | −0.960500 | ||||||||
\(267\) | −1.85359e6 | −1.59124 | ||||||||
\(268\) | −890328. | −0.757204 | ||||||||
\(269\) | 1.16045e6 | 0.977792 | 0.488896 | − | 0.872342i | \(-0.337400\pi\) | ||||
0.488896 | + | 0.872342i | \(0.337400\pi\) | |||||||
\(270\) | −2.87357e6 | −2.39890 | ||||||||
\(271\) | −1.25402e6 | −1.03724 | −0.518621 | − | 0.855004i | \(-0.673554\pi\) | ||||
−0.518621 | + | 0.855004i | \(0.673554\pi\) | |||||||
\(272\) | 1.16916e6 | 0.958194 | ||||||||
\(273\) | −3.00989e6 | −2.44424 | ||||||||
\(274\) | 2.63059e6 | 2.11679 | ||||||||
\(275\) | −1.04037e6 | −0.829579 | ||||||||
\(276\) | −1.51775e6 | −1.19930 | ||||||||
\(277\) | 1.14668e6 | 0.897932 | 0.448966 | − | 0.893549i | \(-0.351792\pi\) | ||||
0.448966 | + | 0.893549i | \(0.351792\pi\) | |||||||
\(278\) | −347646. | −0.269790 | ||||||||
\(279\) | −3.29570e6 | −2.53476 | ||||||||
\(280\) | −101991. | −0.0777436 | ||||||||
\(281\) | 228129. | 0.172351 | 0.0861755 | − | 0.996280i | \(-0.472535\pi\) | ||||
0.0861755 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(282\) | 5.23186e6 | 3.91772 | ||||||||
\(283\) | −280999. | −0.208564 | −0.104282 | − | 0.994548i | \(-0.533254\pi\) | ||||
−0.104282 | + | 0.994548i | \(0.533254\pi\) | |||||||
\(284\) | 1.74650e6 | 1.28491 | ||||||||
\(285\) | −936603. | −0.683036 | ||||||||
\(286\) | 3.05146e6 | 2.20593 | ||||||||
\(287\) | 1.90669e6 | 1.36639 | ||||||||
\(288\) | 5.63090e6 | 4.00033 | ||||||||
\(289\) | 356341. | 0.250970 | ||||||||
\(290\) | 774975. | 0.541119 | ||||||||
\(291\) | −2.95213e6 | −2.04363 | ||||||||
\(292\) | 703750. | 0.483016 | ||||||||
\(293\) | −1.84060e6 | −1.25253 | −0.626267 | − | 0.779608i | \(-0.715418\pi\) | ||||
−0.626267 | + | 0.779608i | \(0.715418\pi\) | |||||||
\(294\) | −896952. | −0.605203 | ||||||||
\(295\) | 248248. | 0.166085 | ||||||||
\(296\) | −379925. | −0.252040 | ||||||||
\(297\) | −5.65080e6 | −3.71723 | ||||||||
\(298\) | 2.90292e6 | 1.89363 | ||||||||
\(299\) | −1.19659e6 | −0.774049 | ||||||||
\(300\) | 2.65556e6 | 1.70354 | ||||||||
\(301\) | 1.75656e6 | 1.11750 | ||||||||
\(302\) | −530372. | −0.334629 | ||||||||
\(303\) | −3.87543e6 | −2.42501 | ||||||||
\(304\) | 1.02491e6 | 0.636063 | ||||||||
\(305\) | −527601. | −0.324755 | ||||||||
\(306\) | 7.44904e6 | 4.54775 | ||||||||
\(307\) | 1.36190e6 | 0.824709 | 0.412354 | − | 0.911024i | \(-0.364707\pi\) | ||||
0.412354 | + | 0.911024i | \(0.364707\pi\) | |||||||
\(308\) | −1.77812e6 | −1.06803 | ||||||||
\(309\) | 1.73959e6 | 1.03646 | ||||||||
\(310\) | −1.06057e6 | −0.626806 | ||||||||
\(311\) | −1.43376e6 | −0.840574 | −0.420287 | − | 0.907391i | \(-0.638071\pi\) | ||||
−0.420287 | + | 0.907391i | \(0.638071\pi\) | |||||||
\(312\) | −878540. | −0.510946 | ||||||||
\(313\) | 2.05782e6 | 1.18726 | 0.593630 | − | 0.804738i | \(-0.297694\pi\) | ||||
0.593630 | + | 0.804738i | \(0.297694\pi\) | |||||||
\(314\) | 1.37891e6 | 0.789246 | ||||||||
\(315\) | 2.05853e6 | 1.16891 | ||||||||
\(316\) | 2.45739e6 | 1.38438 | ||||||||
\(317\) | −694380. | −0.388105 | −0.194052 | − | 0.980991i | \(-0.562163\pi\) | ||||
−0.194052 | + | 0.980991i | \(0.562163\pi\) | |||||||
\(318\) | 2.53629e6 | 1.40647 | ||||||||
\(319\) | 1.52397e6 | 0.838494 | ||||||||
\(320\) | 1.07025e6 | 0.584266 | ||||||||
\(321\) | −2.42075e6 | −1.31125 | ||||||||
\(322\) | 1.31589e6 | 0.707262 | ||||||||
\(323\) | 1.55704e6 | 0.830412 | ||||||||
\(324\) | 8.48606e6 | 4.49101 | ||||||||
\(325\) | 2.09364e6 | 1.09950 | ||||||||
\(326\) | 233947. | 0.121920 | ||||||||
\(327\) | −2.77026e6 | −1.43269 | ||||||||
\(328\) | 556533. | 0.285632 | ||||||||
\(329\) | −2.40357e6 | −1.22424 | ||||||||
\(330\) | −2.83553e6 | −1.43334 | ||||||||
\(331\) | 1.40117e6 | 0.702943 | 0.351472 | − | 0.936199i | \(-0.385681\pi\) | ||||
0.351472 | + | 0.936199i | \(0.385681\pi\) | |||||||
\(332\) | −2.18534e6 | −1.08811 | ||||||||
\(333\) | 7.66823e6 | 3.78952 | ||||||||
\(334\) | −4.77733e6 | −2.34325 | ||||||||
\(335\) | 652265. | 0.317550 | ||||||||
\(336\) | −3.06060e6 | −1.47897 | ||||||||
\(337\) | −3.16105e6 | −1.51620 | −0.758101 | − | 0.652138i | \(-0.773872\pi\) | ||||
−0.758101 | + | 0.652138i | \(0.773872\pi\) | |||||||
\(338\) | −3.07744e6 | −1.46520 | ||||||||
\(339\) | 4.81319e6 | 2.27475 | ||||||||
\(340\) | 1.27020e6 | 0.595900 | ||||||||
\(341\) | −2.08558e6 | −0.971271 | ||||||||
\(342\) | 6.52993e6 | 3.01886 | ||||||||
\(343\) | 2.34477e6 | 1.07613 | ||||||||
\(344\) | 512713. | 0.233603 | ||||||||
\(345\) | 1.11192e6 | 0.502952 | ||||||||
\(346\) | 3.51396e6 | 1.57800 | ||||||||
\(347\) | 2.41305e6 | 1.07583 | 0.537914 | − | 0.842999i | \(-0.319212\pi\) | ||||
0.537914 | + | 0.842999i | \(0.319212\pi\) | |||||||
\(348\) | −3.88994e6 | −1.72185 | ||||||||
\(349\) | −3.04701e6 | −1.33909 | −0.669546 | − | 0.742771i | \(-0.733511\pi\) | ||||
−0.669546 | + | 0.742771i | \(0.733511\pi\) | |||||||
\(350\) | −2.30237e6 | −1.00463 | ||||||||
\(351\) | 1.13716e7 | 4.92669 | ||||||||
\(352\) | 3.56333e6 | 1.53285 | ||||||||
\(353\) | 4.05547e6 | 1.73222 | 0.866112 | − | 0.499849i | \(-0.166611\pi\) | ||||
0.866112 | + | 0.499849i | \(0.166611\pi\) | |||||||
\(354\) | −2.35158e6 | −0.997359 | ||||||||
\(355\) | −1.27951e6 | −0.538854 | ||||||||
\(356\) | 2.20363e6 | 0.921538 | ||||||||
\(357\) | −4.64967e6 | −1.93087 | ||||||||
\(358\) | 2.19484e6 | 0.905099 | ||||||||
\(359\) | −3.26666e6 | −1.33773 | −0.668865 | − | 0.743384i | \(-0.733219\pi\) | ||||
−0.668865 | + | 0.743384i | \(0.733219\pi\) | |||||||
\(360\) | 600851. | 0.244349 | ||||||||
\(361\) | −1.11118e6 | −0.448761 | ||||||||
\(362\) | −5.10045e6 | −2.04568 | ||||||||
\(363\) | −689877. | −0.274792 | ||||||||
\(364\) | 3.57828e6 | 1.41554 | ||||||||
\(365\) | −515576. | −0.202563 | ||||||||
\(366\) | 4.99781e6 | 1.95019 | ||||||||
\(367\) | 2.35078e6 | 0.911058 | 0.455529 | − | 0.890221i | \(-0.349450\pi\) | ||||
0.455529 | + | 0.890221i | \(0.349450\pi\) | |||||||
\(368\) | −1.21675e6 | −0.468363 | ||||||||
\(369\) | −1.12328e7 | −4.29459 | ||||||||
\(370\) | 2.46766e6 | 0.937089 | ||||||||
\(371\) | −1.16520e6 | −0.439506 | ||||||||
\(372\) | 5.32345e6 | 1.99451 | ||||||||
\(373\) | 226137. | 0.0841589 | 0.0420794 | − | 0.999114i | \(-0.486602\pi\) | ||||
0.0420794 | + | 0.999114i | \(0.486602\pi\) | |||||||
\(374\) | 4.71389e6 | 1.74261 | ||||||||
\(375\) | −4.45075e6 | −1.63439 | ||||||||
\(376\) | −701563. | −0.255916 | ||||||||
\(377\) | −3.06683e6 | −1.11131 | ||||||||
\(378\) | −1.25054e7 | −4.50160 | ||||||||
\(379\) | 373040. | 0.133400 | 0.0667002 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0667002 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(380\) | 1.11347e6 | 0.395567 | ||||||||
\(381\) | 6.47206e6 | 2.28418 | ||||||||
\(382\) | −6.46598e6 | −2.26713 | ||||||||
\(383\) | 5.27984e6 | 1.83918 | 0.919589 | − | 0.392882i | \(-0.128522\pi\) | ||||
0.919589 | + | 0.392882i | \(0.128522\pi\) | |||||||
\(384\) | −2.06868e6 | −0.715921 | ||||||||
\(385\) | 1.30267e6 | 0.447902 | ||||||||
\(386\) | −1.61970e6 | −0.553309 | ||||||||
\(387\) | −1.03484e7 | −3.51232 | ||||||||
\(388\) | 3.50961e6 | 1.18353 | ||||||||
\(389\) | −4.31256e6 | −1.44498 | −0.722488 | − | 0.691383i | \(-0.757002\pi\) | ||||
−0.722488 | + | 0.691383i | \(0.757002\pi\) | |||||||
\(390\) | 5.70621e6 | 1.89971 | ||||||||
\(391\) | −1.84850e6 | −0.611472 | ||||||||
\(392\) | 120276. | 0.0395335 | ||||||||
\(393\) | −9.21302e6 | −3.00899 | ||||||||
\(394\) | −2.72034e6 | −0.882842 | ||||||||
\(395\) | −1.80031e6 | −0.580571 | ||||||||
\(396\) | 1.04754e7 | 3.35684 | ||||||||
\(397\) | −4.90018e6 | −1.56040 | −0.780199 | − | 0.625531i | \(-0.784882\pi\) | ||||
−0.780199 | + | 0.625531i | \(0.784882\pi\) | |||||||
\(398\) | −5.24658e6 | −1.66023 | ||||||||
\(399\) | −4.07597e6 | −1.28174 | ||||||||
\(400\) | 2.12892e6 | 0.665286 | ||||||||
\(401\) | −1.85639e6 | −0.576511 | −0.288255 | − | 0.957554i | \(-0.593075\pi\) | ||||
−0.288255 | + | 0.957554i | \(0.593075\pi\) | |||||||
\(402\) | −6.17872e6 | −1.90692 | ||||||||
\(403\) | 4.19700e6 | 1.28729 | ||||||||
\(404\) | 4.60727e6 | 1.40440 | ||||||||
\(405\) | −6.21699e6 | −1.88340 | ||||||||
\(406\) | 3.37259e6 | 1.01543 | ||||||||
\(407\) | 4.85259e6 | 1.45207 | ||||||||
\(408\) | −1.35717e6 | −0.403629 | ||||||||
\(409\) | 6.10123e6 | 1.80347 | 0.901736 | − | 0.432288i | \(-0.142294\pi\) | ||||
0.901736 | + | 0.432288i | \(0.142294\pi\) | |||||||
\(410\) | −3.61475e6 | −1.06198 | ||||||||
\(411\) | 9.67349e6 | 2.82474 | ||||||||
\(412\) | −2.06810e6 | −0.600244 | ||||||||
\(413\) | 1.08034e6 | 0.311663 | ||||||||
\(414\) | −7.75224e6 | −2.22293 | ||||||||
\(415\) | 1.60101e6 | 0.456324 | ||||||||
\(416\) | −7.17083e6 | −2.03159 | ||||||||
\(417\) | −1.27840e6 | −0.360020 | ||||||||
\(418\) | 4.13226e6 | 1.15677 | ||||||||
\(419\) | −4.65495e6 | −1.29533 | −0.647665 | − | 0.761925i | \(-0.724254\pi\) | ||||
−0.647665 | + | 0.761925i | \(0.724254\pi\) | |||||||
\(420\) | −3.32508e6 | −0.919769 | ||||||||
\(421\) | −1.22677e6 | −0.337331 | −0.168665 | − | 0.985673i | \(-0.553946\pi\) | ||||
−0.168665 | + | 0.985673i | \(0.553946\pi\) | |||||||
\(422\) | −4.02740e6 | −1.10089 | ||||||||
\(423\) | 1.41600e7 | 3.84780 | ||||||||
\(424\) | −340103. | −0.0918747 | ||||||||
\(425\) | 3.23425e6 | 0.868564 | ||||||||
\(426\) | 1.21204e7 | 3.23588 | ||||||||
\(427\) | −2.29605e6 | −0.609412 | ||||||||
\(428\) | 2.87788e6 | 0.759388 | ||||||||
\(429\) | 1.12211e7 | 2.94370 | ||||||||
\(430\) | −3.33013e6 | −0.868541 | ||||||||
\(431\) | 174437. | 0.0452320 | 0.0226160 | − | 0.999744i | \(-0.492800\pi\) | ||||
0.0226160 | + | 0.999744i | \(0.492800\pi\) | |||||||
\(432\) | 1.15632e7 | 2.98105 | ||||||||
\(433\) | −5.91829e6 | −1.51697 | −0.758485 | − | 0.651691i | \(-0.774060\pi\) | ||||
−0.758485 | + | 0.651691i | \(0.774060\pi\) | |||||||
\(434\) | −4.61544e6 | −1.17622 | ||||||||
\(435\) | 2.84982e6 | 0.722095 | ||||||||
\(436\) | 3.29340e6 | 0.829715 | ||||||||
\(437\) | −1.62042e6 | −0.405904 | ||||||||
\(438\) | 4.88390e6 | 1.21641 | ||||||||
\(439\) | 4.22650e6 | 1.04669 | 0.523346 | − | 0.852120i | \(-0.324683\pi\) | ||||
0.523346 | + | 0.852120i | \(0.324683\pi\) | |||||||
\(440\) | 380230. | 0.0936298 | ||||||||
\(441\) | −2.42760e6 | −0.594403 | ||||||||
\(442\) | −9.48620e6 | −2.30960 | ||||||||
\(443\) | 2.13728e6 | 0.517431 | 0.258715 | − | 0.965954i | \(-0.416701\pi\) | ||||
0.258715 | + | 0.965954i | \(0.416701\pi\) | |||||||
\(444\) | −1.23863e7 | −2.98183 | ||||||||
\(445\) | −1.61440e6 | −0.386467 | ||||||||
\(446\) | −8.27417e6 | −1.96964 | ||||||||
\(447\) | 1.06749e7 | 2.52694 | ||||||||
\(448\) | 4.65759e6 | 1.09639 | ||||||||
\(449\) | −2.81178e6 | −0.658210 | −0.329105 | − | 0.944293i | \(-0.606747\pi\) | ||||
−0.329105 | + | 0.944293i | \(0.606747\pi\) | |||||||
\(450\) | 1.35638e7 | 3.15756 | ||||||||
\(451\) | −7.10831e6 | −1.64560 | ||||||||
\(452\) | −5.72212e6 | −1.31738 | ||||||||
\(453\) | −1.95034e6 | −0.446544 | ||||||||
\(454\) | 2.08030e6 | 0.473680 | ||||||||
\(455\) | −2.62149e6 | −0.593636 | ||||||||
\(456\) | −1.18971e6 | −0.267935 | ||||||||
\(457\) | 2.30364e6 | 0.515970 | 0.257985 | − | 0.966149i | \(-0.416941\pi\) | ||||
0.257985 | + | 0.966149i | \(0.416941\pi\) | |||||||
\(458\) | 530422. | 0.118157 | ||||||||
\(459\) | 1.75669e7 | 3.89191 | ||||||||
\(460\) | −1.32190e6 | −0.291275 | ||||||||
\(461\) | −8.76118e6 | −1.92004 | −0.960020 | − | 0.279930i | \(-0.909689\pi\) | ||||
−0.960020 | + | 0.279930i | \(0.909689\pi\) | |||||||
\(462\) | −1.23399e7 | −2.68971 | ||||||||
\(463\) | 4.29017e6 | 0.930083 | 0.465042 | − | 0.885289i | \(-0.346039\pi\) | ||||
0.465042 | + | 0.885289i | \(0.346039\pi\) | |||||||
\(464\) | −3.11850e6 | −0.672436 | ||||||||
\(465\) | −3.90002e6 | −0.836439 | ||||||||
\(466\) | −8.81891e6 | −1.88127 | ||||||||
\(467\) | 940648. | 0.199588 | 0.0997941 | − | 0.995008i | \(-0.468182\pi\) | ||||
0.0997941 | + | 0.995008i | \(0.468182\pi\) | |||||||
\(468\) | −2.10805e7 | −4.44905 | ||||||||
\(469\) | 2.83857e6 | 0.595891 | ||||||||
\(470\) | 4.55673e6 | 0.951500 | ||||||||
\(471\) | 5.07068e6 | 1.05321 | ||||||||
\(472\) | 315334. | 0.0651502 | ||||||||
\(473\) | −6.54862e6 | −1.34585 | ||||||||
\(474\) | 1.70539e7 | 3.48640 | ||||||||
\(475\) | 2.83519e6 | 0.576565 | ||||||||
\(476\) | 5.52772e6 | 1.11822 | ||||||||
\(477\) | 6.86447e6 | 1.38137 | ||||||||
\(478\) | −1.36313e7 | −2.72878 | ||||||||
\(479\) | −301446. | −0.0600303 | −0.0300152 | − | 0.999549i | \(-0.509556\pi\) | ||||
−0.0300152 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(480\) | 6.66342e6 | 1.32006 | ||||||||
\(481\) | −9.76533e6 | −1.92453 | ||||||||
\(482\) | 4.54929e6 | 0.891921 | ||||||||
\(483\) | 4.83893e6 | 0.943803 | ||||||||
\(484\) | 820154. | 0.159141 | ||||||||
\(485\) | −2.57119e6 | −0.496340 | ||||||||
\(486\) | 3.24660e7 | 6.23502 | ||||||||
\(487\) | −1.90919e6 | −0.364777 | −0.182389 | − | 0.983227i | \(-0.558383\pi\) | ||||
−0.182389 | + | 0.983227i | \(0.558383\pi\) | |||||||
\(488\) | −670179. | −0.127392 | ||||||||
\(489\) | 860295. | 0.162695 | ||||||||
\(490\) | −781209. | −0.146986 | ||||||||
\(491\) | 8.26815e6 | 1.54776 | 0.773881 | − | 0.633331i | \(-0.218313\pi\) | ||||
0.773881 | + | 0.633331i | \(0.218313\pi\) | |||||||
\(492\) | 1.81440e7 | 3.37925 | ||||||||
\(493\) | −4.73764e6 | −0.877899 | ||||||||
\(494\) | −8.31573e6 | −1.53314 | ||||||||
\(495\) | −7.67437e6 | −1.40776 | ||||||||
\(496\) | 4.26771e6 | 0.778917 | ||||||||
\(497\) | −5.56823e6 | −1.01118 | ||||||||
\(498\) | −1.51659e7 | −2.74028 | ||||||||
\(499\) | −7.84281e6 | −1.41000 | −0.705002 | − | 0.709206i | \(-0.749054\pi\) | ||||
−0.705002 | + | 0.709206i | \(0.749054\pi\) | |||||||
\(500\) | 5.29123e6 | 0.946524 | ||||||||
\(501\) | −1.75677e7 | −3.12694 | ||||||||
\(502\) | −654999. | −0.116006 | ||||||||
\(503\) | 9.28502e6 | 1.63630 | 0.818150 | − | 0.575005i | \(-0.195000\pi\) | ||||
0.818150 | + | 0.575005i | \(0.195000\pi\) | |||||||
\(504\) | 2.61482e6 | 0.458528 | ||||||||
\(505\) | −3.37534e6 | −0.588965 | ||||||||
\(506\) | −4.90576e6 | −0.851784 | ||||||||
\(507\) | −1.13167e7 | −1.95524 | ||||||||
\(508\) | −7.69425e6 | −1.32284 | ||||||||
\(509\) | −44924.0 | −0.00768570 | −0.00384285 | − | 0.999993i | \(-0.501223\pi\) | ||||
−0.00384285 | + | 0.999993i | \(0.501223\pi\) | |||||||
\(510\) | 8.81495e6 | 1.50070 | ||||||||
\(511\) | −2.24371e6 | −0.380115 | ||||||||
\(512\) | −8.23389e6 | −1.38813 | ||||||||
\(513\) | 1.53994e7 | 2.58351 | ||||||||
\(514\) | 1.50195e7 | 2.50753 | ||||||||
\(515\) | 1.51511e6 | 0.251725 | ||||||||
\(516\) | 1.67154e7 | 2.76371 | ||||||||
\(517\) | 8.96071e6 | 1.47440 | ||||||||
\(518\) | 1.07389e7 | 1.75847 | ||||||||
\(519\) | 1.29219e7 | 2.10575 | ||||||||
\(520\) | −765172. | −0.124094 | ||||||||
\(521\) | −6.43306e6 | −1.03830 | −0.519150 | − | 0.854683i | \(-0.673751\pi\) | ||||
−0.519150 | + | 0.854683i | \(0.673751\pi\) | |||||||
\(522\) | −1.98687e7 | −3.19150 | ||||||||
\(523\) | −6.75944e6 | −1.08058 | −0.540290 | − | 0.841479i | \(-0.681685\pi\) | ||||
−0.540290 | + | 0.841479i | \(0.681685\pi\) | |||||||
\(524\) | 1.09528e7 | 1.74260 | ||||||||
\(525\) | −8.46652e6 | −1.34062 | ||||||||
\(526\) | 1.74521e6 | 0.275032 | ||||||||
\(527\) | 6.48352e6 | 1.01691 | ||||||||
\(528\) | 1.14102e7 | 1.78118 | ||||||||
\(529\) | −4.51261e6 | −0.701114 | ||||||||
\(530\) | 2.20901e6 | 0.341592 | ||||||||
\(531\) | −6.36455e6 | −0.979561 | ||||||||
\(532\) | 4.84568e6 | 0.742293 | ||||||||
\(533\) | 1.43047e7 | 2.18103 | ||||||||
\(534\) | 1.52928e7 | 2.32078 | ||||||||
\(535\) | −2.10837e6 | −0.318466 | ||||||||
\(536\) | 828533. | 0.124565 | ||||||||
\(537\) | 8.07111e6 | 1.20781 | ||||||||
\(538\) | −9.57413e6 | −1.42608 | ||||||||
\(539\) | −1.53623e6 | −0.227763 | ||||||||
\(540\) | 1.25625e7 | 1.85392 | ||||||||
\(541\) | 7.73077e6 | 1.13561 | 0.567806 | − | 0.823163i | \(-0.307793\pi\) | ||||
0.567806 | + | 0.823163i | \(0.307793\pi\) | |||||||
\(542\) | 1.03461e7 | 1.51279 | ||||||||
\(543\) | −1.87559e7 | −2.72985 | ||||||||
\(544\) | −1.10775e7 | −1.60489 | ||||||||
\(545\) | −2.41279e6 | −0.347959 | ||||||||
\(546\) | 2.48327e7 | 3.56485 | ||||||||
\(547\) | −299209. | −0.0427569 | ||||||||
\(548\) | −1.15002e7 | −1.63590 | ||||||||
\(549\) | 1.35266e7 | 1.91539 | ||||||||
\(550\) | 8.58345e6 | 1.20992 | ||||||||
\(551\) | −4.15308e6 | −0.582762 | ||||||||
\(552\) | 1.41241e6 | 0.197293 | ||||||||
\(553\) | −7.83472e6 | −1.08946 | ||||||||
\(554\) | −9.46052e6 | −1.30961 | ||||||||
\(555\) | 9.07433e6 | 1.25050 | ||||||||
\(556\) | 1.51981e6 | 0.208499 | ||||||||
\(557\) | −40290.3 | −0.00550253 | −0.00275127 | − | 0.999996i | \(-0.500876\pi\) | ||||
−0.00275127 | + | 0.999996i | \(0.500876\pi\) | |||||||
\(558\) | 2.71907e7 | 3.69687 | ||||||||
\(559\) | 1.31784e7 | 1.78375 | ||||||||
\(560\) | −2.66566e6 | −0.359198 | ||||||||
\(561\) | 1.73344e7 | 2.32542 | ||||||||
\(562\) | −1.88214e6 | −0.251369 | ||||||||
\(563\) | 1.65062e6 | 0.219470 | 0.109735 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109735 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(564\) | −2.28723e7 | −3.02769 | ||||||||
\(565\) | 4.19209e6 | 0.552471 | ||||||||
\(566\) | 2.31834e6 | 0.304184 | ||||||||
\(567\) | −2.70555e7 | −3.53425 | ||||||||
\(568\) | −1.62528e6 | −0.211377 | ||||||||
\(569\) | 3.75963e6 | 0.486816 | 0.243408 | − | 0.969924i | \(-0.421735\pi\) | ||||
0.243408 | + | 0.969924i | \(0.421735\pi\) | |||||||
\(570\) | 7.72730e6 | 0.996187 | ||||||||
\(571\) | −3.48656e6 | −0.447514 | −0.223757 | − | 0.974645i | \(-0.571832\pi\) | ||||
−0.223757 | + | 0.974645i | \(0.571832\pi\) | |||||||
\(572\) | −1.33401e7 | −1.70479 | ||||||||
\(573\) | −2.37774e7 | −3.02536 | ||||||||
\(574\) | −1.57309e7 | −1.99284 | ||||||||
\(575\) | −3.36590e6 | −0.424553 | ||||||||
\(576\) | −2.74390e7 | −3.44597 | ||||||||
\(577\) | −7.35700e6 | −0.919944 | −0.459972 | − | 0.887933i | \(-0.652141\pi\) | ||||
−0.459972 | + | 0.887933i | \(0.652141\pi\) | |||||||
\(578\) | −2.93994e6 | −0.366032 | ||||||||
\(579\) | −5.95615e6 | −0.738361 | ||||||||
\(580\) | −3.38798e6 | −0.418188 | ||||||||
\(581\) | 6.96737e6 | 0.856306 | ||||||||
\(582\) | 2.43561e7 | 2.98058 | ||||||||
\(583\) | 4.34396e6 | 0.529315 | ||||||||
\(584\) | −654905. | −0.0794595 | ||||||||
\(585\) | 1.54439e7 | 1.86580 | ||||||||
\(586\) | 1.51856e7 | 1.82678 | ||||||||
\(587\) | 4.49819e6 | 0.538819 | 0.269410 | − | 0.963026i | \(-0.413171\pi\) | ||||
0.269410 | + | 0.963026i | \(0.413171\pi\) | |||||||
\(588\) | 3.92123e6 | 0.467713 | ||||||||
\(589\) | 5.68355e6 | 0.675043 | ||||||||
\(590\) | −2.04813e6 | −0.242230 | ||||||||
\(591\) | −1.00035e7 | −1.17811 | ||||||||
\(592\) | −9.92986e6 | −1.16450 | ||||||||
\(593\) | −1.40730e7 | −1.64343 | −0.821715 | − | 0.569899i | \(-0.806982\pi\) | ||||
−0.821715 | + | 0.569899i | \(0.806982\pi\) | |||||||
\(594\) | 4.66211e7 | 5.42146 | ||||||||
\(595\) | −4.04968e6 | −0.468951 | ||||||||
\(596\) | −1.26908e7 | −1.46343 | ||||||||
\(597\) | −1.92933e7 | −2.21549 | ||||||||
\(598\) | 9.87232e6 | 1.12893 | ||||||||
\(599\) | 282573. | 0.0321784 | 0.0160892 | − | 0.999871i | \(-0.494878\pi\) | ||||
0.0160892 | + | 0.999871i | \(0.494878\pi\) | |||||||
\(600\) | −2.47124e6 | −0.280245 | ||||||||
\(601\) | −2.47863e6 | −0.279915 | −0.139958 | − | 0.990158i | \(-0.544697\pi\) | ||||
−0.139958 | + | 0.990158i | \(0.544697\pi\) | |||||||
\(602\) | −1.44923e7 | −1.62984 | ||||||||
\(603\) | −1.67227e7 | −1.87289 | ||||||||
\(604\) | 2.31864e6 | 0.258608 | ||||||||
\(605\) | −600854. | −0.0667392 | ||||||||
\(606\) | 3.19737e7 | 3.53680 | ||||||||
\(607\) | 5.36046e6 | 0.590515 | 0.295257 | − | 0.955418i | \(-0.404595\pi\) | ||||
0.295257 | + | 0.955418i | \(0.404595\pi\) | |||||||
\(608\) | −9.71068e6 | −1.06535 | ||||||||
\(609\) | 1.24020e7 | 1.35503 | ||||||||
\(610\) | 4.35289e6 | 0.473645 | ||||||||
\(611\) | −1.80325e7 | −1.95413 | ||||||||
\(612\) | −3.25652e7 | −3.51459 | ||||||||
\(613\) | 8.50924e6 | 0.914617 | 0.457309 | − | 0.889308i | \(-0.348813\pi\) | ||||
0.457309 | + | 0.889308i | \(0.348813\pi\) | |||||||
\(614\) | −1.12362e7 | −1.20281 | ||||||||
\(615\) | −1.32925e7 | −1.41716 | ||||||||
\(616\) | 1.65471e6 | 0.175699 | ||||||||
\(617\) | −1.27611e7 | −1.34951 | −0.674754 | − | 0.738042i | \(-0.735750\pi\) | ||||
−0.674754 | + | 0.738042i | \(0.735750\pi\) | |||||||
\(618\) | −1.43522e7 | −1.51164 | ||||||||
\(619\) | −1.47029e7 | −1.54232 | −0.771161 | − | 0.636640i | \(-0.780324\pi\) | ||||
−0.771161 | + | 0.636640i | \(0.780324\pi\) | |||||||
\(620\) | 4.63650e6 | 0.484408 | ||||||||
\(621\) | −1.82819e7 | −1.90236 | ||||||||
\(622\) | 1.18290e7 | 1.22595 | ||||||||
\(623\) | −7.02567e6 | −0.725216 | ||||||||
\(624\) | −2.29618e7 | −2.36072 | ||||||||
\(625\) | 3.70723e6 | 0.379621 | ||||||||
\(626\) | −1.69777e7 | −1.73158 | ||||||||
\(627\) | 1.51956e7 | 1.54365 | ||||||||
\(628\) | −6.02823e6 | −0.609945 | ||||||||
\(629\) | −1.50855e7 | −1.52031 | ||||||||
\(630\) | −1.69836e7 | −1.70482 | ||||||||
\(631\) | 8.23332e6 | 0.823193 | 0.411596 | − | 0.911366i | \(-0.364971\pi\) | ||||
0.411596 | + | 0.911366i | \(0.364971\pi\) | |||||||
\(632\) | −2.28683e6 | −0.227741 | ||||||||
\(633\) | −1.48100e7 | −1.46908 | ||||||||
\(634\) | 5.72888e6 | 0.566039 | ||||||||
\(635\) | 5.63690e6 | 0.554761 | ||||||||
\(636\) | −1.10880e7 | −1.08695 | ||||||||
\(637\) | 3.09150e6 | 0.301870 | ||||||||
\(638\) | −1.25733e7 | −1.22292 | ||||||||
\(639\) | 3.28038e7 | 3.17814 | ||||||||
\(640\) | −1.80173e6 | −0.173877 | ||||||||
\(641\) | 7.54288e6 | 0.725090 | 0.362545 | − | 0.931966i | \(-0.381908\pi\) | ||||
0.362545 | + | 0.931966i | \(0.381908\pi\) | |||||||
\(642\) | 1.99720e7 | 1.91242 | ||||||||
\(643\) | −4.00008e6 | −0.381541 | −0.190771 | − | 0.981635i | \(-0.561099\pi\) | ||||
−0.190771 | + | 0.981635i | \(0.561099\pi\) | |||||||
\(644\) | −5.75272e6 | −0.546586 | ||||||||
\(645\) | −1.22459e7 | −1.15902 | ||||||||
\(646\) | −1.28461e7 | −1.21113 | ||||||||
\(647\) | −8.82323e6 | −0.828642 | −0.414321 | − | 0.910131i | \(-0.635981\pi\) | ||||
−0.414321 | + | 0.910131i | \(0.635981\pi\) | |||||||
\(648\) | −7.89707e6 | −0.738802 | ||||||||
\(649\) | −4.02760e6 | −0.375348 | ||||||||
\(650\) | −1.72733e7 | −1.60358 | ||||||||
\(651\) | −1.69724e7 | −1.56960 | ||||||||
\(652\) | −1.02275e6 | −0.0942220 | ||||||||
\(653\) | −1.36679e7 | −1.25435 | −0.627174 | − | 0.778879i | \(-0.715789\pi\) | ||||
−0.627174 | + | 0.778879i | \(0.715789\pi\) | |||||||
\(654\) | 2.28557e7 | 2.08953 | ||||||||
\(655\) | −8.02416e6 | −0.730797 | ||||||||
\(656\) | 1.45457e7 | 1.31970 | ||||||||
\(657\) | 1.32183e7 | 1.19471 | ||||||||
\(658\) | 1.98303e7 | 1.78552 | ||||||||
\(659\) | −1.19060e6 | −0.106796 | −0.0533979 | − | 0.998573i | \(-0.517005\pi\) | ||||
−0.0533979 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(660\) | 1.23962e7 | 1.10772 | ||||||||
\(661\) | 3.25548e6 | 0.289809 | 0.144905 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144905 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(662\) | −1.15601e7 | −1.02522 | ||||||||
\(663\) | −3.48836e7 | −3.08204 | ||||||||
\(664\) | 2.03367e6 | 0.179003 | ||||||||
\(665\) | −3.55000e6 | −0.311297 | ||||||||
\(666\) | −6.32656e7 | −5.52690 | ||||||||
\(667\) | 4.93047e6 | 0.429115 | ||||||||
\(668\) | 2.08852e7 | 1.81091 | ||||||||
\(669\) | −3.04266e7 | −2.62838 | ||||||||
\(670\) | −5.38141e6 | −0.463137 | ||||||||
\(671\) | 8.55986e6 | 0.733939 | ||||||||
\(672\) | 2.89983e7 | 2.47713 | ||||||||
\(673\) | −3.53355e6 | −0.300728 | −0.150364 | − | 0.988631i | \(-0.548045\pi\) | ||||
−0.150364 | + | 0.988631i | \(0.548045\pi\) | |||||||
\(674\) | 2.60798e7 | 2.21133 | ||||||||
\(675\) | 3.19873e7 | 2.70220 | ||||||||
\(676\) | 1.34537e7 | 1.13234 | ||||||||
\(677\) | 1.94898e7 | 1.63431 | 0.817157 | − | 0.576416i | \(-0.195549\pi\) | ||||
0.817157 | + | 0.576416i | \(0.195549\pi\) | |||||||
\(678\) | −3.97105e7 | −3.31765 | ||||||||
\(679\) | −1.11894e7 | −0.931396 | ||||||||
\(680\) | −1.18204e6 | −0.0980299 | ||||||||
\(681\) | 7.64988e6 | 0.632101 | ||||||||
\(682\) | 1.72067e7 | 1.41657 | ||||||||
\(683\) | −9.28219e6 | −0.761375 | −0.380688 | − | 0.924704i | \(-0.624313\pi\) | ||||
−0.380688 | + | 0.924704i | \(0.624313\pi\) | |||||||
\(684\) | −2.85471e7 | −2.33304 | ||||||||
\(685\) | 8.42521e6 | 0.686048 | ||||||||
\(686\) | −1.93452e7 | −1.56951 | ||||||||
\(687\) | 1.95052e6 | 0.157674 | ||||||||
\(688\) | 1.34004e7 | 1.07931 | ||||||||
\(689\) | −8.74176e6 | −0.701538 | ||||||||
\(690\) | −9.17374e6 | −0.733540 | ||||||||
\(691\) | −1.78949e7 | −1.42572 | −0.712862 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712862 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(692\) | −1.53621e7 | −1.21951 | ||||||||
\(693\) | −3.33978e7 | −2.64171 | ||||||||
\(694\) | −1.99085e7 | −1.56906 | ||||||||
\(695\) | −1.11343e6 | −0.0874385 | ||||||||
\(696\) | 3.61995e6 | 0.283257 | ||||||||
\(697\) | 2.20979e7 | 1.72294 | ||||||||
\(698\) | 2.51389e7 | 1.95303 | ||||||||
\(699\) | −3.24298e7 | −2.51045 | ||||||||
\(700\) | 1.00654e7 | 0.776397 | ||||||||
\(701\) | −1.18883e7 | −0.913743 | −0.456871 | − | 0.889533i | \(-0.651030\pi\) | ||||
−0.456871 | + | 0.889533i | \(0.651030\pi\) | |||||||
\(702\) | −9.38201e7 | −7.18543 | ||||||||
\(703\) | −1.32241e7 | −1.00920 | ||||||||
\(704\) | −1.73639e7 | −1.32043 | ||||||||
\(705\) | 1.67565e7 | 1.26973 | ||||||||
\(706\) | −3.34590e7 | −2.52640 | ||||||||
\(707\) | −1.46890e7 | −1.10521 | ||||||||
\(708\) | 1.02805e7 | 0.770779 | ||||||||
\(709\) | −1.49479e7 | −1.11677 | −0.558387 | − | 0.829580i | \(-0.688580\pi\) | ||||
−0.558387 | + | 0.829580i | \(0.688580\pi\) | |||||||
\(710\) | 1.05564e7 | 0.785903 | ||||||||
\(711\) | 4.61563e7 | 3.42418 | ||||||||
\(712\) | −2.05068e6 | −0.151600 | ||||||||
\(713\) | −6.74742e6 | −0.497066 | ||||||||
\(714\) | 3.83614e7 | 2.81611 | ||||||||
\(715\) | 9.77315e6 | 0.714940 | ||||||||
\(716\) | −9.59526e6 | −0.699479 | ||||||||
\(717\) | −5.01265e7 | −3.64141 | ||||||||
\(718\) | 2.69511e7 | 1.95104 | ||||||||
\(719\) | 1.60953e7 | 1.16112 | 0.580560 | − | 0.814218i | \(-0.302834\pi\) | ||||
0.580560 | + | 0.814218i | \(0.302834\pi\) | |||||||
\(720\) | 1.57040e7 | 1.12896 | ||||||||
\(721\) | 6.59356e6 | 0.472369 | ||||||||
\(722\) | 9.16760e6 | 0.654504 | ||||||||
\(723\) | 1.67291e7 | 1.19022 | ||||||||
\(724\) | 2.22978e7 | 1.58094 | ||||||||
\(725\) | −8.62669e6 | −0.609536 | ||||||||
\(726\) | 5.69172e6 | 0.400777 | ||||||||
\(727\) | −1.92489e7 | −1.35073 | −0.675366 | − | 0.737483i | \(-0.736014\pi\) | ||||
−0.675366 | + | 0.737483i | \(0.736014\pi\) | |||||||
\(728\) | −3.32992e6 | −0.232866 | ||||||||
\(729\) | 6.22149e7 | 4.33586 | ||||||||
\(730\) | 4.25368e6 | 0.295432 | ||||||||
\(731\) | 2.03580e7 | 1.40910 | ||||||||
\(732\) | −2.18491e7 | −1.50715 | ||||||||
\(733\) | 1.17391e7 | 0.807003 | 0.403502 | − | 0.914979i | \(-0.367793\pi\) | ||||
0.403502 | + | 0.914979i | \(0.367793\pi\) | |||||||
\(734\) | −1.93947e7 | −1.32875 | ||||||||
\(735\) | −2.87274e6 | −0.196145 | ||||||||
\(736\) | 1.15284e7 | 0.784465 | ||||||||
\(737\) | −1.05824e7 | −0.717656 | ||||||||
\(738\) | 9.26745e7 | 6.26353 | ||||||||
\(739\) | 2.06300e7 | 1.38960 | 0.694799 | − | 0.719204i | \(-0.255493\pi\) | ||||
0.694799 | + | 0.719204i | \(0.255493\pi\) | |||||||
\(740\) | −1.07879e7 | −0.724201 | ||||||||
\(741\) | −3.05795e7 | −2.04590 | ||||||||
\(742\) | 9.61330e6 | 0.641007 | ||||||||
\(743\) | 9.09475e6 | 0.604392 | 0.302196 | − | 0.953246i | \(-0.402280\pi\) | ||||
0.302196 | + | 0.953246i | \(0.402280\pi\) | |||||||
\(744\) | −4.95396e6 | −0.328111 | ||||||||
\(745\) | 9.29741e6 | 0.613721 | ||||||||
\(746\) | −1.86571e6 | −0.122743 | ||||||||
\(747\) | −4.10465e7 | −2.69138 | ||||||||
\(748\) | −2.06078e7 | −1.34672 | ||||||||
\(749\) | −9.17535e6 | −0.597610 | ||||||||
\(750\) | 3.67202e7 | 2.38370 | ||||||||
\(751\) | −1.71018e7 | −1.10647 | −0.553237 | − | 0.833024i | \(-0.686608\pi\) | ||||
−0.553237 | + | 0.833024i | \(0.686608\pi\) | |||||||
\(752\) | −1.83363e7 | −1.18241 | ||||||||
\(753\) | −2.40863e6 | −0.154804 | ||||||||
\(754\) | 2.53024e7 | 1.62082 | ||||||||
\(755\) | −1.69867e6 | −0.108453 | ||||||||
\(756\) | 5.46701e7 | 3.47893 | ||||||||
\(757\) | −693046. | −0.0439564 | −0.0219782 | − | 0.999758i | \(-0.506996\pi\) | ||||
−0.0219782 | + | 0.999758i | \(0.506996\pi\) | |||||||
\(758\) | −3.07771e6 | −0.194560 | ||||||||
\(759\) | −1.80399e7 | −1.13666 | ||||||||
\(760\) | −1.03619e6 | −0.0650736 | ||||||||
\(761\) | −1.87009e7 | −1.17058 | −0.585291 | − | 0.810824i | \(-0.699020\pi\) | ||||
−0.585291 | + | 0.810824i | \(0.699020\pi\) | |||||||
\(762\) | −5.33968e7 | −3.33141 | ||||||||
\(763\) | −1.05001e7 | −0.652955 | ||||||||
\(764\) | 2.82675e7 | 1.75208 | ||||||||
\(765\) | 2.38576e7 | 1.47392 | ||||||||
\(766\) | −4.35605e7 | −2.68239 | ||||||||
\(767\) | 8.10512e6 | 0.497475 | ||||||||
\(768\) | −2.22549e7 | −1.36152 | ||||||||
\(769\) | −3.10535e7 | −1.89363 | −0.946814 | − | 0.321781i | \(-0.895719\pi\) | ||||
−0.946814 | + | 0.321781i | \(0.895719\pi\) | |||||||
\(770\) | −1.07475e7 | −0.653252 | ||||||||
\(771\) | 5.52311e7 | 3.34617 | ||||||||
\(772\) | 7.08091e6 | 0.427608 | ||||||||
\(773\) | −1.86406e7 | −1.12205 | −0.561023 | − | 0.827800i | \(-0.689592\pi\) | ||||
−0.561023 | + | 0.827800i | \(0.689592\pi\) | |||||||
\(774\) | 8.53776e7 | 5.12261 | ||||||||
\(775\) | 1.18058e7 | 0.706057 | ||||||||
\(776\) | −3.26602e6 | −0.194700 | ||||||||
\(777\) | 3.94902e7 | 2.34659 | ||||||||
\(778\) | 3.55801e7 | 2.10745 | ||||||||
\(779\) | 1.93713e7 | 1.14371 | ||||||||
\(780\) | −2.49460e7 | −1.46813 | ||||||||
\(781\) | 2.07589e7 | 1.21780 | ||||||||
\(782\) | 1.52507e7 | 0.891813 | ||||||||
\(783\) | −4.68560e7 | −2.73125 | ||||||||
\(784\) | 3.14358e6 | 0.182656 | ||||||||
\(785\) | 4.41635e6 | 0.255793 | ||||||||
\(786\) | 7.60107e7 | 4.38852 | ||||||||
\(787\) | 2.07834e7 | 1.19613 | 0.598067 | − | 0.801446i | \(-0.295936\pi\) | ||||
0.598067 | + | 0.801446i | \(0.295936\pi\) | |||||||
\(788\) | 1.18926e7 | 0.682277 | ||||||||
\(789\) | 6.41766e6 | 0.367015 | ||||||||
\(790\) | 1.48532e7 | 0.846746 | ||||||||
\(791\) | 1.82434e7 | 1.03673 | ||||||||
\(792\) | −9.74829e6 | −0.552224 | ||||||||
\(793\) | −1.72258e7 | −0.972740 | ||||||||
\(794\) | 4.04282e7 | 2.27579 | ||||||||
\(795\) | 8.12319e6 | 0.455836 | ||||||||
\(796\) | 2.29366e7 | 1.28306 | ||||||||
\(797\) | 1.28133e7 | 0.714522 | 0.357261 | − | 0.934005i | \(-0.383711\pi\) | ||||
0.357261 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(798\) | 3.36282e7 | 1.86937 | ||||||||
\(799\) | −2.78565e7 | −1.54369 | ||||||||
\(800\) | −2.01708e7 | −1.11429 | ||||||||
\(801\) | 4.13899e7 | 2.27936 | ||||||||
\(802\) | 1.53158e7 | 0.840823 | ||||||||
\(803\) | 8.36476e6 | 0.457788 | ||||||||
\(804\) | 2.70117e7 | 1.47371 | ||||||||
\(805\) | 4.21451e6 | 0.229223 | ||||||||
\(806\) | −3.46268e7 | −1.87748 | ||||||||
\(807\) | −3.52070e7 | −1.90303 | ||||||||
\(808\) | −4.28749e6 | −0.231034 | ||||||||
\(809\) | 1.35114e7 | 0.725821 | 0.362910 | − | 0.931824i | \(-0.381783\pi\) | ||||
0.362910 | + | 0.931824i | \(0.381783\pi\) | |||||||
\(810\) | 5.12923e7 | 2.74688 | ||||||||
\(811\) | −8.79590e6 | −0.469600 | −0.234800 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234800 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(812\) | −1.47440e7 | −0.784741 | ||||||||
\(813\) | 3.80457e7 | 2.01873 | ||||||||
\(814\) | −4.00356e7 | −2.11780 | ||||||||
\(815\) | 749282. | 0.0395140 | ||||||||
\(816\) | −3.54713e7 | −1.86489 | ||||||||
\(817\) | 1.78461e7 | 0.935380 | ||||||||
\(818\) | −5.03373e7 | −2.63031 | ||||||||
\(819\) | 6.72095e7 | 3.50123 | ||||||||
\(820\) | 1.58027e7 | 0.820723 | ||||||||
\(821\) | −6.26640e6 | −0.324459 | −0.162230 | − | 0.986753i | \(-0.551869\pi\) | ||||
−0.162230 | + | 0.986753i | \(0.551869\pi\) | |||||||
\(822\) | −7.98097e7 | −4.11980 | ||||||||
\(823\) | −669279. | −0.0344435 | −0.0172218 | − | 0.999852i | \(-0.505482\pi\) | ||||
−0.0172218 | + | 0.999852i | \(0.505482\pi\) | |||||||
\(824\) | 1.92456e6 | 0.0987444 | ||||||||
\(825\) | 3.15639e7 | 1.61457 | ||||||||
\(826\) | −8.91318e6 | −0.454551 | ||||||||
\(827\) | 1.63500e7 | 0.831294 | 0.415647 | − | 0.909526i | \(-0.363555\pi\) | ||||
0.415647 | + | 0.909526i | \(0.363555\pi\) | |||||||
\(828\) | 3.38907e7 | 1.71793 | ||||||||
\(829\) | −1.20501e6 | −0.0608982 | −0.0304491 | − | 0.999536i | \(-0.509694\pi\) | ||||
−0.0304491 | + | 0.999536i | \(0.509694\pi\) | |||||||
\(830\) | −1.32089e7 | −0.665535 | ||||||||
\(831\) | −3.47892e7 | −1.74760 | ||||||||
\(832\) | 3.49430e7 | 1.75006 | ||||||||
\(833\) | 4.77574e6 | 0.238467 | ||||||||
\(834\) | 1.05473e7 | 0.525078 | ||||||||
\(835\) | −1.53007e7 | −0.759444 | ||||||||
\(836\) | −1.80651e7 | −0.893974 | ||||||||
\(837\) | 6.41231e7 | 3.16374 | ||||||||
\(838\) | 3.84050e7 | 1.88920 | ||||||||
\(839\) | 9.09313e6 | 0.445973 | 0.222987 | − | 0.974822i | \(-0.428419\pi\) | ||||
0.222987 | + | 0.974822i | \(0.428419\pi\) | |||||||
\(840\) | 3.09430e6 | 0.151309 | ||||||||
\(841\) | −7.87450e6 | −0.383913 | ||||||||
\(842\) | 1.01212e7 | 0.491987 | ||||||||
\(843\) | −6.92120e6 | −0.335438 | ||||||||
\(844\) | 1.76067e7 | 0.850788 | ||||||||
\(845\) | −9.85636e6 | −0.474870 | ||||||||
\(846\) | −1.16825e8 | −5.61190 | ||||||||
\(847\) | −2.61484e6 | −0.125238 | ||||||||
\(848\) | −8.88904e6 | −0.424488 | ||||||||
\(849\) | 8.52525e6 | 0.405918 | ||||||||
\(850\) | −2.66837e7 | −1.26677 | ||||||||
\(851\) | 1.56995e7 | 0.743125 | ||||||||
\(852\) | −5.29871e7 | −2.50076 | ||||||||
\(853\) | −1.35894e7 | −0.639482 | −0.319741 | − | 0.947505i | \(-0.603596\pi\) | ||||
−0.319741 | + | 0.947505i | \(0.603596\pi\) | |||||||
\(854\) | 1.89432e7 | 0.888809 | ||||||||
\(855\) | 2.09139e7 | 0.978409 | ||||||||
\(856\) | −2.67814e6 | −0.124925 | ||||||||
\(857\) | 4.02924e7 | 1.87401 | 0.937003 | − | 0.349322i | \(-0.113588\pi\) | ||||
0.937003 | + | 0.349322i | \(0.113588\pi\) | |||||||
\(858\) | −9.25783e7 | −4.29330 | ||||||||
\(859\) | −2.40344e7 | −1.11135 | −0.555675 | − | 0.831400i | \(-0.687540\pi\) | ||||
−0.555675 | + | 0.831400i | \(0.687540\pi\) | |||||||
\(860\) | 1.45584e7 | 0.671225 | ||||||||
\(861\) | −5.78472e7 | −2.65935 | ||||||||
\(862\) | −1.43917e6 | −0.0659694 | ||||||||
\(863\) | −3.82161e7 | −1.74670 | −0.873352 | − | 0.487089i | \(-0.838059\pi\) | ||||
−0.873352 | + | 0.487089i | \(0.838059\pi\) | |||||||
\(864\) | −1.09558e8 | −4.99299 | ||||||||
\(865\) | 1.12544e7 | 0.511427 | ||||||||
\(866\) | 4.88280e7 | 2.21245 | ||||||||
\(867\) | −1.08111e7 | −0.488450 | ||||||||
\(868\) | 2.01774e7 | 0.909006 | ||||||||
\(869\) | 2.92085e7 | 1.31208 | ||||||||
\(870\) | −2.35120e7 | −1.05315 | ||||||||
\(871\) | 2.12960e7 | 0.951158 | ||||||||
\(872\) | −3.06482e6 | −0.136494 | ||||||||
\(873\) | 6.59198e7 | 2.92739 | ||||||||
\(874\) | 1.33690e7 | 0.591998 | ||||||||
\(875\) | −1.68696e7 | −0.744879 | ||||||||
\(876\) | −2.13511e7 | −0.940070 | ||||||||
\(877\) | −2.00451e7 | −0.880055 | −0.440028 | − | 0.897984i | \(-0.645031\pi\) | ||||
−0.440028 | + | 0.897984i | \(0.645031\pi\) | |||||||
\(878\) | −3.48701e7 | −1.52657 | ||||||||
\(879\) | 5.58420e7 | 2.43775 | ||||||||
\(880\) | 9.93780e6 | 0.432597 | ||||||||
\(881\) | −4.25741e7 | −1.84802 | −0.924009 | − | 0.382372i | \(-0.875107\pi\) | ||||
−0.924009 | + | 0.382372i | \(0.875107\pi\) | |||||||
\(882\) | 2.00286e7 | 0.866918 | ||||||||
\(883\) | 976214. | 0.0421350 | 0.0210675 | − | 0.999778i | \(-0.493294\pi\) | ||||
0.0210675 | + | 0.999778i | \(0.493294\pi\) | |||||||
\(884\) | 4.14711e7 | 1.78490 | ||||||||
\(885\) | −7.53160e6 | −0.323243 | ||||||||
\(886\) | −1.76333e7 | −0.754657 | ||||||||
\(887\) | 4.23359e7 | 1.80676 | 0.903379 | − | 0.428843i | \(-0.141078\pi\) | ||||
0.903379 | + | 0.428843i | \(0.141078\pi\) | |||||||
\(888\) | 1.15266e7 | 0.490533 | ||||||||
\(889\) | 2.45310e7 | 1.04103 | ||||||||
\(890\) | 1.33194e7 | 0.563650 | ||||||||
\(891\) | 1.00865e8 | 4.25644 | ||||||||
\(892\) | 3.61724e7 | 1.52218 | ||||||||
\(893\) | −2.44194e7 | −1.02472 | ||||||||
\(894\) | −8.80717e7 | −3.68547 | ||||||||
\(895\) | 7.02960e6 | 0.293341 | ||||||||
\(896\) | −7.84090e6 | −0.326284 | ||||||||
\(897\) | 3.63035e7 | 1.50649 | ||||||||
\(898\) | 2.31981e7 | 0.959980 | ||||||||
\(899\) | −1.72934e7 | −0.713645 | ||||||||
\(900\) | −5.92975e7 | −2.44023 | ||||||||
\(901\) | −1.35043e7 | −0.554190 | ||||||||
\(902\) | 5.86461e7 | 2.40006 | ||||||||
\(903\) | −5.32925e7 | −2.17494 | ||||||||
\(904\) | 5.32496e6 | 0.216718 | ||||||||
\(905\) | −1.63356e7 | −0.663002 | ||||||||
\(906\) | 1.60910e7 | 0.651272 | ||||||||
\(907\) | 4.23365e6 | 0.170882 | 0.0854411 | − | 0.996343i | \(-0.472770\pi\) | ||||
0.0854411 | + | 0.996343i | \(0.472770\pi\) | |||||||
\(908\) | −9.09449e6 | −0.366070 | ||||||||
\(909\) | 8.65367e7 | 3.47369 | ||||||||
\(910\) | 2.16282e7 | 0.865800 | ||||||||
\(911\) | −2.27781e6 | −0.0909330 | −0.0454665 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454665 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(912\) | −3.10947e7 | −1.23794 | ||||||||
\(913\) | −2.59750e7 | −1.03128 | ||||||||
\(914\) | −1.90059e7 | −0.752527 | ||||||||
\(915\) | 1.60069e7 | 0.632054 | ||||||||
\(916\) | −2.31886e6 | −0.0913137 | ||||||||
\(917\) | −3.49201e7 | −1.37136 | ||||||||
\(918\) | −1.44933e8 | −5.67624 | ||||||||
\(919\) | 1.14014e6 | 0.0445318 | 0.0222659 | − | 0.999752i | \(-0.492912\pi\) | ||||
0.0222659 | + | 0.999752i | \(0.492912\pi\) | |||||||
\(920\) | 1.23015e6 | 0.0479168 | ||||||||
\(921\) | −4.13189e7 | −1.60509 | ||||||||
\(922\) | 7.22828e7 | 2.80032 | ||||||||
\(923\) | −4.17750e7 | −1.61403 | ||||||||
\(924\) | 5.39465e7 | 2.07866 | ||||||||
\(925\) | −2.74689e7 | −1.05557 | ||||||||
\(926\) | −3.53954e7 | −1.35650 | ||||||||
\(927\) | −3.88443e7 | −1.48466 | ||||||||
\(928\) | 2.95469e7 | 1.12627 | ||||||||
\(929\) | −1.88340e6 | −0.0715985 | −0.0357993 | − | 0.999359i | \(-0.511398\pi\) | ||||
−0.0357993 | + | 0.999359i | \(0.511398\pi\) | |||||||
\(930\) | 3.21765e7 | 1.21992 | ||||||||
\(931\) | 4.18648e6 | 0.158298 | ||||||||
\(932\) | 3.85539e7 | 1.45388 | ||||||||
\(933\) | 4.34989e7 | 1.63597 | ||||||||
\(934\) | −7.76068e6 | −0.291093 | ||||||||
\(935\) | 1.50975e7 | 0.564777 | ||||||||
\(936\) | 1.96174e7 | 0.731900 | ||||||||
\(937\) | 3.16256e7 | 1.17676 | 0.588382 | − | 0.808583i | \(-0.299765\pi\) | ||||
0.588382 | + | 0.808583i | \(0.299765\pi\) | |||||||
\(938\) | −2.34192e7 | −0.869089 | ||||||||
\(939\) | −6.24322e7 | −2.31071 | ||||||||
\(940\) | −1.99208e7 | −0.735338 | ||||||||
\(941\) | 4.16449e7 | 1.53316 | 0.766581 | − | 0.642148i | \(-0.221956\pi\) | ||||
0.766581 | + | 0.642148i | \(0.221956\pi\) | |||||||
\(942\) | −4.18349e7 | −1.53607 | ||||||||
\(943\) | −2.29974e7 | −0.842169 | ||||||||
\(944\) | 8.24168e6 | 0.301013 | ||||||||
\(945\) | −4.00520e7 | −1.45896 | ||||||||
\(946\) | 5.40284e7 | 1.96288 | ||||||||
\(947\) | 9.04562e6 | 0.327766 | 0.163883 | − | 0.986480i | \(-0.447598\pi\) | ||||
0.163883 | + | 0.986480i | \(0.447598\pi\) | |||||||
\(948\) | −7.45549e7 | −2.69436 | ||||||||
\(949\) | −1.68332e7 | −0.606738 | ||||||||
\(950\) | −2.33913e7 | −0.840903 | ||||||||
\(951\) | 2.10668e7 | 0.755349 | ||||||||
\(952\) | −5.14406e6 | −0.183956 | ||||||||
\(953\) | 3.55147e7 | 1.26671 | 0.633353 | − | 0.773863i | \(-0.281678\pi\) | ||||
0.633353 | + | 0.773863i | \(0.281678\pi\) | |||||||
\(954\) | −5.66343e7 | −2.01469 | ||||||||
\(955\) | −2.07091e7 | −0.734773 | ||||||||
\(956\) | 5.95924e7 | 2.10885 | ||||||||
\(957\) | −4.62358e7 | −1.63192 | ||||||||
\(958\) | 2.48704e6 | 0.0875524 | ||||||||
\(959\) | 3.66654e7 | 1.28739 | ||||||||
\(960\) | −3.24704e7 | −1.13713 | ||||||||
\(961\) | −4.96283e6 | −0.173349 | ||||||||
\(962\) | 8.05674e7 | 2.80687 | ||||||||
\(963\) | 5.40542e7 | 1.87830 | ||||||||
\(964\) | −1.98883e7 | −0.689294 | ||||||||
\(965\) | −5.18756e6 | −0.179327 | ||||||||
\(966\) | −3.99229e7 | −1.37651 | ||||||||
\(967\) | 4.89615e7 | 1.68379 | 0.841896 | − | 0.539640i | \(-0.181440\pi\) | ||||
0.841896 | + | 0.539640i | \(0.181440\pi\) | |||||||
\(968\) | −763229. | −0.0261798 | ||||||||
\(969\) | −4.72391e7 | −1.61619 | ||||||||
\(970\) | 2.12132e7 | 0.723896 | ||||||||
\(971\) | 1.50444e7 | 0.512067 | 0.256034 | − | 0.966668i | \(-0.417584\pi\) | ||||
0.256034 | + | 0.966668i | \(0.417584\pi\) | |||||||
\(972\) | −1.41933e8 | −4.81855 | ||||||||
\(973\) | −4.84551e6 | −0.164081 | ||||||||
\(974\) | 1.57515e7 | 0.532016 | ||||||||
\(975\) | −6.35191e7 | −2.13990 | ||||||||
\(976\) | −1.75160e7 | −0.588588 | ||||||||
\(977\) | 1.54848e7 | 0.519002 | 0.259501 | − | 0.965743i | \(-0.416442\pi\) | ||||
0.259501 | + | 0.965743i | \(0.416442\pi\) | |||||||
\(978\) | −7.09774e6 | −0.237286 | ||||||||
\(979\) | 2.61923e7 | 0.873407 | ||||||||
\(980\) | 3.41523e6 | 0.113594 | ||||||||
\(981\) | 6.18588e7 | 2.05224 | ||||||||
\(982\) | −6.82151e7 | −2.25737 | ||||||||
\(983\) | −3.31785e7 | −1.09515 | −0.547574 | − | 0.836757i | \(-0.684448\pi\) | ||||
−0.547574 | + | 0.836757i | \(0.684448\pi\) | |||||||
\(984\) | −1.68847e7 | −0.555911 | ||||||||
\(985\) | −8.71265e6 | −0.286128 | ||||||||
\(986\) | 3.90872e7 | 1.28039 | ||||||||
\(987\) | 7.29219e7 | 2.38268 | ||||||||
\(988\) | 3.63541e7 | 1.18484 | ||||||||
\(989\) | −2.11866e7 | −0.688765 | ||||||||
\(990\) | 6.33162e7 | 2.05318 | ||||||||
\(991\) | 4.10318e7 | 1.32720 | 0.663600 | − | 0.748088i | \(-0.269028\pi\) | ||||
0.663600 | + | 0.748088i | \(0.269028\pi\) | |||||||
\(992\) | −4.04353e7 | −1.30461 | ||||||||
\(993\) | −4.25101e7 | −1.36810 | ||||||||
\(994\) | 4.59399e7 | 1.47477 | ||||||||
\(995\) | −1.68037e7 | −0.538079 | ||||||||
\(996\) | 6.63013e7 | 2.11774 | ||||||||
\(997\) | −1.82199e6 | −0.0580507 | −0.0290254 | − | 0.999579i | \(-0.509240\pi\) | ||||
−0.0290254 | + | 0.999579i | \(0.509240\pi\) | |||||||
\(998\) | 6.47059e7 | 2.05645 | ||||||||
\(999\) | −1.49198e8 | −4.72986 |
(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 | 547.6.a.a.1.18 | ✓ | 111 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.6.a.a.1.18 | ✓ | 111 | 1.1 | even | 1 | trivial |