Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,6,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, 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("722.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.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: | \(115.797117905\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 19^{6} \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.51331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 1.16601 | 0.0747996 | 0.0373998 | − | 0.999300i | \(-0.488092\pi\) | ||||
0.0373998 | + | 0.999300i | \(0.488092\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −65.1319 | −1.16511 | −0.582557 | − | 0.812790i | \(-0.697948\pi\) | ||||
−0.582557 | + | 0.812790i | \(0.697948\pi\) | |||||||
\(6\) | 4.66404 | 0.0528913 | ||||||||
\(7\) | 94.5243 | 0.729119 | 0.364559 | − | 0.931180i | \(-0.381220\pi\) | ||||
0.364559 | + | 0.931180i | \(0.381220\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −241.640 | −0.994405 | ||||||||
\(10\) | −260.528 | −0.823860 | ||||||||
\(11\) | −458.262 | −1.14191 | −0.570955 | − | 0.820981i | \(-0.693427\pi\) | ||||
−0.570955 | + | 0.820981i | \(0.693427\pi\) | |||||||
\(12\) | 18.6562 | 0.0373998 | ||||||||
\(13\) | −984.374 | −1.61548 | −0.807740 | − | 0.589538i | \(-0.799310\pi\) | ||||
−0.807740 | + | 0.589538i | \(0.799310\pi\) | |||||||
\(14\) | 378.097 | 0.515565 | ||||||||
\(15\) | −75.9445 | −0.0871501 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 2124.68 | 1.78308 | 0.891539 | − | 0.452944i | \(-0.149626\pi\) | ||||
0.891539 | + | 0.452944i | \(0.149626\pi\) | |||||||
\(18\) | −966.562 | −0.703151 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1042.11 | −0.582557 | ||||||||
\(21\) | 110.216 | 0.0545378 | ||||||||
\(22\) | −1833.05 | −0.807453 | ||||||||
\(23\) | −3844.87 | −1.51552 | −0.757761 | − | 0.652532i | \(-0.773707\pi\) | ||||
−0.757761 | + | 0.652532i | \(0.773707\pi\) | |||||||
\(24\) | 74.6247 | 0.0264457 | ||||||||
\(25\) | 1117.16 | 0.357492 | ||||||||
\(26\) | −3937.50 | −1.14232 | ||||||||
\(27\) | −565.096 | −0.149181 | ||||||||
\(28\) | 1512.39 | 0.364559 | ||||||||
\(29\) | 7336.37 | 1.61989 | 0.809947 | − | 0.586503i | \(-0.199496\pi\) | ||||
0.809947 | + | 0.586503i | \(0.199496\pi\) | |||||||
\(30\) | −303.778 | −0.0616244 | ||||||||
\(31\) | −1177.06 | −0.219985 | −0.109993 | − | 0.993932i | \(-0.535083\pi\) | ||||
−0.109993 | + | 0.993932i | \(0.535083\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −534.338 | −0.0854145 | ||||||||
\(34\) | 8498.70 | 1.26083 | ||||||||
\(35\) | −6156.55 | −0.849507 | ||||||||
\(36\) | −3866.25 | −0.497203 | ||||||||
\(37\) | 1760.46 | 0.211409 | 0.105704 | − | 0.994398i | \(-0.466290\pi\) | ||||
0.105704 | + | 0.994398i | \(0.466290\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1147.79 | −0.120837 | ||||||||
\(40\) | −4168.44 | −0.411930 | ||||||||
\(41\) | 2450.34 | 0.227649 | 0.113825 | − | 0.993501i | \(-0.463690\pi\) | ||||
0.113825 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(42\) | 440.865 | 0.0385641 | ||||||||
\(43\) | 2125.30 | 0.175287 | 0.0876434 | − | 0.996152i | \(-0.472066\pi\) | ||||
0.0876434 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(44\) | −7332.19 | −0.570955 | ||||||||
\(45\) | 15738.5 | 1.15860 | ||||||||
\(46\) | −15379.5 | −1.07164 | ||||||||
\(47\) | 12732.9 | 0.840784 | 0.420392 | − | 0.907343i | \(-0.361893\pi\) | ||||
0.420392 | + | 0.907343i | \(0.361893\pi\) | |||||||
\(48\) | 298.499 | 0.0186999 | ||||||||
\(49\) | −7872.16 | −0.468386 | ||||||||
\(50\) | 4468.65 | 0.252785 | ||||||||
\(51\) | 2477.39 | 0.133374 | ||||||||
\(52\) | −15750.0 | −0.807740 | ||||||||
\(53\) | 33120.3 | 1.61959 | 0.809793 | − | 0.586715i | \(-0.199579\pi\) | ||||
0.809793 | + | 0.586715i | \(0.199579\pi\) | |||||||
\(54\) | −2260.38 | −0.105487 | ||||||||
\(55\) | 29847.5 | 1.33046 | ||||||||
\(56\) | 6049.55 | 0.257782 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 29345.5 | 1.14544 | ||||||||
\(59\) | 9236.15 | 0.345431 | 0.172715 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172715 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(60\) | −1215.11 | −0.0435751 | ||||||||
\(61\) | 10296.4 | 0.354293 | 0.177146 | − | 0.984185i | \(-0.443313\pi\) | ||||
0.177146 | + | 0.984185i | \(0.443313\pi\) | |||||||
\(62\) | −4708.23 | −0.155553 | ||||||||
\(63\) | −22840.9 | −0.725039 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 64114.1 | 1.88222 | ||||||||
\(66\) | −2137.35 | −0.0603972 | ||||||||
\(67\) | 28631.3 | 0.779209 | 0.389605 | − | 0.920982i | \(-0.372612\pi\) | ||||
0.389605 | + | 0.920982i | \(0.372612\pi\) | |||||||
\(68\) | 33994.8 | 0.891539 | ||||||||
\(69\) | −4483.16 | −0.113360 | ||||||||
\(70\) | −24626.2 | −0.600692 | ||||||||
\(71\) | −68701.6 | −1.61741 | −0.808707 | − | 0.588212i | \(-0.799832\pi\) | ||||
−0.808707 | + | 0.588212i | \(0.799832\pi\) | |||||||
\(72\) | −15465.0 | −0.351575 | ||||||||
\(73\) | 36251.3 | 0.796189 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(74\) | 7041.85 | 0.149488 | ||||||||
\(75\) | 1302.62 | 0.0267403 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −43316.9 | −0.832589 | ||||||||
\(78\) | −4591.16 | −0.0854449 | ||||||||
\(79\) | 21981.5 | 0.396269 | 0.198134 | − | 0.980175i | \(-0.436512\pi\) | ||||
0.198134 | + | 0.980175i | \(0.436512\pi\) | |||||||
\(80\) | −16673.8 | −0.291279 | ||||||||
\(81\) | 58059.7 | 0.983246 | ||||||||
\(82\) | 9801.34 | 0.160972 | ||||||||
\(83\) | −102618. | −1.63505 | −0.817524 | − | 0.575895i | \(-0.804654\pi\) | ||||
−0.817524 | + | 0.575895i | \(0.804654\pi\) | |||||||
\(84\) | 1763.46 | 0.0272689 | ||||||||
\(85\) | −138384. | −2.07749 | ||||||||
\(86\) | 8501.20 | 0.123946 | ||||||||
\(87\) | 8554.29 | 0.121167 | ||||||||
\(88\) | −29328.8 | −0.403726 | ||||||||
\(89\) | 28261.5 | 0.378199 | 0.189100 | − | 0.981958i | \(-0.439443\pi\) | ||||
0.189100 | + | 0.981958i | \(0.439443\pi\) | |||||||
\(90\) | 62954.0 | 0.819251 | ||||||||
\(91\) | −93047.3 | −1.17788 | ||||||||
\(92\) | −61517.9 | −0.757761 | ||||||||
\(93\) | −1372.46 | −0.0164548 | ||||||||
\(94\) | 50931.8 | 0.594524 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1193.99 | 0.0132228 | ||||||||
\(97\) | 80776.2 | 0.871674 | 0.435837 | − | 0.900026i | \(-0.356452\pi\) | ||||
0.435837 | + | 0.900026i | \(0.356452\pi\) | |||||||
\(98\) | −31488.6 | −0.331199 | ||||||||
\(99\) | 110735. | 1.13552 | ||||||||
\(100\) | 17874.6 | 0.178746 | ||||||||
\(101\) | 6404.65 | 0.0624730 | 0.0312365 | − | 0.999512i | \(-0.490055\pi\) | ||||
0.0312365 | + | 0.999512i | \(0.490055\pi\) | |||||||
\(102\) | 9909.58 | 0.0943094 | ||||||||
\(103\) | −146931. | −1.36465 | −0.682325 | − | 0.731049i | \(-0.739031\pi\) | ||||
−0.682325 | + | 0.731049i | \(0.739031\pi\) | |||||||
\(104\) | −62999.9 | −0.571159 | ||||||||
\(105\) | −7178.60 | −0.0635428 | ||||||||
\(106\) | 132481. | 1.14522 | ||||||||
\(107\) | 143484. | 1.21156 | 0.605779 | − | 0.795633i | \(-0.292862\pi\) | ||||
0.605779 | + | 0.795633i | \(0.292862\pi\) | |||||||
\(108\) | −9041.53 | −0.0745904 | ||||||||
\(109\) | 100557. | 0.810671 | 0.405335 | − | 0.914168i | \(-0.367155\pi\) | ||||
0.405335 | + | 0.914168i | \(0.367155\pi\) | |||||||
\(110\) | 119390. | 0.940775 | ||||||||
\(111\) | 2052.72 | 0.0158133 | ||||||||
\(112\) | 24198.2 | 0.182280 | ||||||||
\(113\) | −116363. | −0.857272 | −0.428636 | − | 0.903477i | \(-0.641006\pi\) | ||||
−0.428636 | + | 0.903477i | \(0.641006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 250424. | 1.76576 | ||||||||
\(116\) | 117382. | 0.809947 | ||||||||
\(117\) | 237865. | 1.60644 | ||||||||
\(118\) | 36944.6 | 0.244257 | ||||||||
\(119\) | 200833. | 1.30008 | ||||||||
\(120\) | −4860.45 | −0.0308122 | ||||||||
\(121\) | 48953.1 | 0.303960 | ||||||||
\(122\) | 41185.7 | 0.250523 | ||||||||
\(123\) | 2857.12 | 0.0170281 | ||||||||
\(124\) | −18832.9 | −0.109993 | ||||||||
\(125\) | 130774. | 0.748595 | ||||||||
\(126\) | −91363.6 | −0.512680 | ||||||||
\(127\) | 482.007 | 0.00265182 | 0.00132591 | − | 0.999999i | \(-0.499578\pi\) | ||||
0.00132591 | + | 0.999999i | \(0.499578\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 2478.12 | 0.0131114 | ||||||||
\(130\) | 256457. | 1.33093 | ||||||||
\(131\) | 91708.9 | 0.466910 | 0.233455 | − | 0.972368i | \(-0.424997\pi\) | ||||
0.233455 | + | 0.972368i | \(0.424997\pi\) | |||||||
\(132\) | −8549.41 | −0.0427072 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 114525. | 0.550984 | ||||||||
\(135\) | 36805.8 | 0.173813 | ||||||||
\(136\) | 135979. | 0.630413 | ||||||||
\(137\) | 235112. | 1.07022 | 0.535110 | − | 0.844783i | \(-0.320270\pi\) | ||||
0.535110 | + | 0.844783i | \(0.320270\pi\) | |||||||
\(138\) | −17932.6 | −0.0801579 | ||||||||
\(139\) | 75845.7 | 0.332962 | 0.166481 | − | 0.986045i | \(-0.446760\pi\) | ||||
0.166481 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(140\) | −98504.7 | −0.424754 | ||||||||
\(141\) | 14846.8 | 0.0628903 | ||||||||
\(142\) | −274806. | −1.14368 | ||||||||
\(143\) | 451101. | 1.84474 | ||||||||
\(144\) | −61859.9 | −0.248601 | ||||||||
\(145\) | −477832. | −1.88736 | ||||||||
\(146\) | 145005. | 0.562990 | ||||||||
\(147\) | −9179.02 | −0.0350351 | ||||||||
\(148\) | 28167.4 | 0.105704 | ||||||||
\(149\) | 137287. | 0.506599 | 0.253299 | − | 0.967388i | \(-0.418484\pi\) | ||||
0.253299 | + | 0.967388i | \(0.418484\pi\) | |||||||
\(150\) | 5210.49 | 0.0189082 | ||||||||
\(151\) | −85090.8 | −0.303697 | −0.151848 | − | 0.988404i | \(-0.548523\pi\) | ||||
−0.151848 | + | 0.988404i | \(0.548523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −513408. | −1.77310 | ||||||||
\(154\) | −173268. | −0.588729 | ||||||||
\(155\) | 76664.0 | 0.256308 | ||||||||
\(156\) | −18364.7 | −0.0604187 | ||||||||
\(157\) | −81098.1 | −0.262580 | −0.131290 | − | 0.991344i | \(-0.541912\pi\) | ||||
−0.131290 | + | 0.991344i | \(0.541912\pi\) | |||||||
\(158\) | 87926.0 | 0.280204 | ||||||||
\(159\) | 38618.6 | 0.121144 | ||||||||
\(160\) | −66695.1 | −0.205965 | ||||||||
\(161\) | −363434. | −1.10500 | ||||||||
\(162\) | 232239. | 0.695260 | ||||||||
\(163\) | 485148. | 1.43023 | 0.715113 | − | 0.699009i | \(-0.246375\pi\) | ||||
0.715113 | + | 0.699009i | \(0.246375\pi\) | |||||||
\(164\) | 39205.4 | 0.113825 | ||||||||
\(165\) | 34802.5 | 0.0995177 | ||||||||
\(166\) | −410474. | −1.15615 | ||||||||
\(167\) | 336511. | 0.933700 | 0.466850 | − | 0.884336i | \(-0.345389\pi\) | ||||
0.466850 | + | 0.884336i | \(0.345389\pi\) | |||||||
\(168\) | 7053.84 | 0.0192820 | ||||||||
\(169\) | 597700. | 1.60978 | ||||||||
\(170\) | −553537. | −1.46901 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34004.8 | 0.0876434 | ||||||||
\(173\) | −107309. | −0.272598 | −0.136299 | − | 0.990668i | \(-0.543521\pi\) | ||||
−0.136299 | + | 0.990668i | \(0.543521\pi\) | |||||||
\(174\) | 34217.2 | 0.0856783 | ||||||||
\(175\) | 105599. | 0.260654 | ||||||||
\(176\) | −117315. | −0.285478 | ||||||||
\(177\) | 10769.5 | 0.0258381 | ||||||||
\(178\) | 113046. | 0.267427 | ||||||||
\(179\) | 266250. | 0.621095 | 0.310547 | − | 0.950558i | \(-0.399488\pi\) | ||||
0.310547 | + | 0.950558i | \(0.399488\pi\) | |||||||
\(180\) | 251816. | 0.579298 | ||||||||
\(181\) | −42455.8 | −0.0963253 | −0.0481626 | − | 0.998840i | \(-0.515337\pi\) | ||||
−0.0481626 | + | 0.998840i | \(0.515337\pi\) | |||||||
\(182\) | −372189. | −0.832885 | ||||||||
\(183\) | 12005.7 | 0.0265009 | ||||||||
\(184\) | −246072. | −0.535818 | ||||||||
\(185\) | −114662. | −0.246315 | ||||||||
\(186\) | −5489.85 | −0.0116353 | ||||||||
\(187\) | −973658. | −2.03612 | ||||||||
\(188\) | 203727. | 0.420392 | ||||||||
\(189\) | −53415.3 | −0.108770 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 950028. | 1.88431 | 0.942157 | − | 0.335172i | \(-0.108795\pi\) | ||||
0.942157 | + | 0.335172i | \(0.108795\pi\) | |||||||
\(192\) | 4775.98 | 0.00934995 | ||||||||
\(193\) | −127823. | −0.247010 | −0.123505 | − | 0.992344i | \(-0.539413\pi\) | ||||
−0.123505 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(194\) | 323105. | 0.616367 | ||||||||
\(195\) | 74757.8 | 0.140789 | ||||||||
\(196\) | −125955. | −0.234193 | ||||||||
\(197\) | −725481. | −1.33187 | −0.665933 | − | 0.746012i | \(-0.731966\pi\) | ||||
−0.665933 | + | 0.746012i | \(0.731966\pi\) | |||||||
\(198\) | 442939. | 0.802935 | ||||||||
\(199\) | −134661. | −0.241052 | −0.120526 | − | 0.992710i | \(-0.538458\pi\) | ||||
−0.120526 | + | 0.992710i | \(0.538458\pi\) | |||||||
\(200\) | 71498.4 | 0.126393 | ||||||||
\(201\) | 33384.4 | 0.0582846 | ||||||||
\(202\) | 25618.6 | 0.0441751 | ||||||||
\(203\) | 693466. | 1.18110 | ||||||||
\(204\) | 39638.3 | 0.0666868 | ||||||||
\(205\) | −159595. | −0.265237 | ||||||||
\(206\) | −587725. | −0.964954 | ||||||||
\(207\) | 929076. | 1.50704 | ||||||||
\(208\) | −252000. | −0.403870 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −28714.4 | −0.0449315 | ||||||||
\(211\) | −968337. | −1.49734 | −0.748670 | − | 0.662943i | \(-0.769307\pi\) | ||||
−0.748670 | + | 0.662943i | \(0.769307\pi\) | |||||||
\(212\) | 529924. | 0.809793 | ||||||||
\(213\) | −80106.8 | −0.120982 | ||||||||
\(214\) | 573936. | 0.856701 | ||||||||
\(215\) | −138425. | −0.204229 | ||||||||
\(216\) | −36166.1 | −0.0527434 | ||||||||
\(217\) | −111261. | −0.160395 | ||||||||
\(218\) | 402227. | 0.573231 | ||||||||
\(219\) | 42269.3 | 0.0595546 | ||||||||
\(220\) | 477560. | 0.665228 | ||||||||
\(221\) | −2.09148e6 | −2.88053 | ||||||||
\(222\) | 8210.87 | 0.0111817 | ||||||||
\(223\) | 843800. | 1.13626 | 0.568130 | − | 0.822939i | \(-0.307667\pi\) | ||||
0.568130 | + | 0.822939i | \(0.307667\pi\) | |||||||
\(224\) | 96792.9 | 0.128891 | ||||||||
\(225\) | −269952. | −0.355492 | ||||||||
\(226\) | −465452. | −0.606183 | ||||||||
\(227\) | −1.22573e6 | −1.57881 | −0.789406 | − | 0.613872i | \(-0.789611\pi\) | ||||
−0.789406 | + | 0.613872i | \(0.789611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 887407. | 1.11824 | 0.559119 | − | 0.829087i | \(-0.311140\pi\) | ||||
0.559119 | + | 0.829087i | \(0.311140\pi\) | |||||||
\(230\) | 1.00169e6 | 1.24858 | ||||||||
\(231\) | −50508.0 | −0.0622773 | ||||||||
\(232\) | 469528. | 0.572719 | ||||||||
\(233\) | 453440. | 0.547180 | 0.273590 | − | 0.961846i | \(-0.411789\pi\) | ||||
0.273590 | + | 0.961846i | \(0.411789\pi\) | |||||||
\(234\) | 951458. | 1.13593 | ||||||||
\(235\) | −829321. | −0.979610 | ||||||||
\(236\) | 147778. | 0.172715 | ||||||||
\(237\) | 25630.7 | 0.0296407 | ||||||||
\(238\) | 803334. | 0.919293 | ||||||||
\(239\) | −170897. | −0.193526 | −0.0967629 | − | 0.995307i | \(-0.530849\pi\) | ||||
−0.0967629 | + | 0.995307i | \(0.530849\pi\) | |||||||
\(240\) | −19441.8 | −0.0217875 | ||||||||
\(241\) | 184308. | 0.204409 | 0.102205 | − | 0.994763i | \(-0.467410\pi\) | ||||
0.102205 | + | 0.994763i | \(0.467410\pi\) | |||||||
\(242\) | 195812. | 0.214932 | ||||||||
\(243\) | 205017. | 0.222727 | ||||||||
\(244\) | 164743. | 0.177146 | ||||||||
\(245\) | 512728. | 0.545723 | ||||||||
\(246\) | 11428.5 | 0.0120407 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −75331.7 | −0.0777765 | ||||||||
\(249\) | −119654. | −0.122301 | ||||||||
\(250\) | 523097. | 0.529337 | ||||||||
\(251\) | −403050. | −0.403808 | −0.201904 | − | 0.979405i | \(-0.564713\pi\) | ||||
−0.201904 | + | 0.979405i | \(0.564713\pi\) | |||||||
\(252\) | −365454. | −0.362520 | ||||||||
\(253\) | 1.76196e6 | 1.73059 | ||||||||
\(254\) | 1928.03 | 0.00187512 | ||||||||
\(255\) | −161357. | −0.155395 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −123088. | −0.116247 | −0.0581236 | − | 0.998309i | \(-0.518512\pi\) | ||||
−0.0581236 | + | 0.998309i | \(0.518512\pi\) | |||||||
\(258\) | 9912.49 | 0.00927115 | ||||||||
\(259\) | 166406. | 0.154142 | ||||||||
\(260\) | 1.02583e6 | 0.941110 | ||||||||
\(261\) | −1.77276e6 | −1.61083 | ||||||||
\(262\) | 366836. | 0.330155 | ||||||||
\(263\) | 816728. | 0.728095 | 0.364047 | − | 0.931380i | \(-0.381395\pi\) | ||||
0.364047 | + | 0.931380i | \(0.381395\pi\) | |||||||
\(264\) | −34197.7 | −0.0301986 | ||||||||
\(265\) | −2.15719e6 | −1.88700 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32953.2 | 0.0282892 | ||||||||
\(268\) | 458101. | 0.389605 | ||||||||
\(269\) | −1.26180e6 | −1.06319 | −0.531595 | − | 0.846999i | \(-0.678407\pi\) | ||||
−0.531595 | + | 0.846999i | \(0.678407\pi\) | |||||||
\(270\) | 147223. | 0.122904 | ||||||||
\(271\) | 1.16608e6 | 0.964502 | 0.482251 | − | 0.876033i | \(-0.339819\pi\) | ||||
0.482251 | + | 0.876033i | \(0.339819\pi\) | |||||||
\(272\) | 543917. | 0.445770 | ||||||||
\(273\) | −108494. | −0.0881048 | ||||||||
\(274\) | 940447. | 0.756759 | ||||||||
\(275\) | −511953. | −0.408224 | ||||||||
\(276\) | −71730.6 | −0.0566802 | ||||||||
\(277\) | 1.67477e6 | 1.31146 | 0.655730 | − | 0.754996i | \(-0.272361\pi\) | ||||
0.655730 | + | 0.754996i | \(0.272361\pi\) | |||||||
\(278\) | 303383. | 0.235439 | ||||||||
\(279\) | 284425. | 0.218754 | ||||||||
\(280\) | −394019. | −0.300346 | ||||||||
\(281\) | −1.61515e6 | −1.22025 | −0.610124 | − | 0.792306i | \(-0.708880\pi\) | ||||
−0.610124 | + | 0.792306i | \(0.708880\pi\) | |||||||
\(282\) | 59387.0 | 0.0444702 | ||||||||
\(283\) | 2.34442e6 | 1.74008 | 0.870039 | − | 0.492983i | \(-0.164093\pi\) | ||||
0.870039 | + | 0.492983i | \(0.164093\pi\) | |||||||
\(284\) | −1.09923e6 | −0.808707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.80441e6 | 1.30442 | ||||||||
\(287\) | 231616. | 0.165983 | ||||||||
\(288\) | −247440. | −0.175788 | ||||||||
\(289\) | 3.09439e6 | 2.17937 | ||||||||
\(290\) | −1.91133e6 | −1.33457 | ||||||||
\(291\) | 94185.9 | 0.0652009 | ||||||||
\(292\) | 580020. | 0.398094 | ||||||||
\(293\) | −41797.8 | −0.0284436 | −0.0142218 | − | 0.999899i | \(-0.504527\pi\) | ||||
−0.0142218 | + | 0.999899i | \(0.504527\pi\) | |||||||
\(294\) | −36716.1 | −0.0247735 | ||||||||
\(295\) | −601568. | −0.402467 | ||||||||
\(296\) | 112670. | 0.0747442 | ||||||||
\(297\) | 258962. | 0.170351 | ||||||||
\(298\) | 549148. | 0.358219 | ||||||||
\(299\) | 3.78479e6 | 2.44830 | ||||||||
\(300\) | 20842.0 | 0.0133701 | ||||||||
\(301\) | 200893. | 0.127805 | ||||||||
\(302\) | −340363. | −0.214746 | ||||||||
\(303\) | 7467.89 | 0.00467295 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −670626. | −0.412791 | ||||||||
\(306\) | −2.05363e6 | −1.25377 | ||||||||
\(307\) | 1.43037e6 | 0.866166 | 0.433083 | − | 0.901354i | \(-0.357426\pi\) | ||||
0.433083 | + | 0.901354i | \(0.357426\pi\) | |||||||
\(308\) | −693070. | −0.416294 | ||||||||
\(309\) | −171324. | −0.102075 | ||||||||
\(310\) | 306656. | 0.181237 | ||||||||
\(311\) | −914782. | −0.536311 | −0.268155 | − | 0.963376i | \(-0.586414\pi\) | ||||
−0.268155 | + | 0.963376i | \(0.586414\pi\) | |||||||
\(312\) | −73458.6 | −0.0427225 | ||||||||
\(313\) | 1.81979e6 | 1.04993 | 0.524965 | − | 0.851124i | \(-0.324078\pi\) | ||||
0.524965 | + | 0.851124i | \(0.324078\pi\) | |||||||
\(314\) | −324392. | −0.185672 | ||||||||
\(315\) | 1.48767e6 | 0.844754 | ||||||||
\(316\) | 351704. | 0.198134 | ||||||||
\(317\) | −606362. | −0.338910 | −0.169455 | − | 0.985538i | \(-0.554201\pi\) | ||||
−0.169455 | + | 0.985538i | \(0.554201\pi\) | |||||||
\(318\) | 154474. | 0.0856621 | ||||||||
\(319\) | −3.36198e6 | −1.84977 | ||||||||
\(320\) | −266780. | −0.145639 | ||||||||
\(321\) | 167304. | 0.0906241 | ||||||||
\(322\) | −1.45373e6 | −0.781350 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 928955. | 0.491623 | ||||||||
\(325\) | −1.09971e6 | −0.577522 | ||||||||
\(326\) | 1.94059e6 | 1.01132 | ||||||||
\(327\) | 117250. | 0.0606379 | ||||||||
\(328\) | 156822. | 0.0804861 | ||||||||
\(329\) | 1.20357e6 | 0.613031 | ||||||||
\(330\) | 139210. | 0.0703696 | ||||||||
\(331\) | −579109. | −0.290529 | −0.145265 | − | 0.989393i | \(-0.546403\pi\) | ||||
−0.145265 | + | 0.989393i | \(0.546403\pi\) | |||||||
\(332\) | −1.64190e6 | −0.817524 | ||||||||
\(333\) | −425399. | −0.210226 | ||||||||
\(334\) | 1.34604e6 | 0.660226 | ||||||||
\(335\) | −1.86481e6 | −0.907868 | ||||||||
\(336\) | 28215.4 | 0.0136345 | ||||||||
\(337\) | −846958. | −0.406244 | −0.203122 | − | 0.979153i | \(-0.565109\pi\) | ||||
−0.203122 | + | 0.979153i | \(0.565109\pi\) | |||||||
\(338\) | 2.39080e6 | 1.13829 | ||||||||
\(339\) | −135681. | −0.0641236 | ||||||||
\(340\) | −2.21415e6 | −1.03875 | ||||||||
\(341\) | 539401. | 0.251204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.33278e6 | −1.07063 | ||||||||
\(344\) | 136019. | 0.0619732 | ||||||||
\(345\) | 291997. | 0.132078 | ||||||||
\(346\) | −429238. | −0.192756 | ||||||||
\(347\) | 359108. | 0.160104 | 0.0800519 | − | 0.996791i | \(-0.474491\pi\) | ||||
0.0800519 | + | 0.996791i | \(0.474491\pi\) | |||||||
\(348\) | 136869. | 0.0605837 | ||||||||
\(349\) | 400158. | 0.175860 | 0.0879301 | − | 0.996127i | \(-0.471975\pi\) | ||||
0.0879301 | + | 0.996127i | \(0.471975\pi\) | |||||||
\(350\) | 422396. | 0.184310 | ||||||||
\(351\) | 556266. | 0.240999 | ||||||||
\(352\) | −469260. | −0.201863 | ||||||||
\(353\) | −2.22449e6 | −0.950152 | −0.475076 | − | 0.879945i | \(-0.657579\pi\) | ||||
−0.475076 | + | 0.879945i | \(0.657579\pi\) | |||||||
\(354\) | 43077.8 | 0.0182703 | ||||||||
\(355\) | 4.47466e6 | 1.88447 | ||||||||
\(356\) | 452184. | 0.189100 | ||||||||
\(357\) | 234174. | 0.0972452 | ||||||||
\(358\) | 1.06500e6 | 0.439180 | ||||||||
\(359\) | 475655. | 0.194785 | 0.0973927 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973927 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(360\) | 1.00726e6 | 0.409625 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −169823. | −0.0681123 | ||||||||
\(363\) | 57079.8 | 0.0227361 | ||||||||
\(364\) | −1.48876e6 | −0.588939 | ||||||||
\(365\) | −2.36111e6 | −0.927651 | ||||||||
\(366\) | 48023.0 | 0.0187390 | ||||||||
\(367\) | −3.55083e6 | −1.37615 | −0.688073 | − | 0.725642i | \(-0.741543\pi\) | ||||
−0.688073 | + | 0.725642i | \(0.741543\pi\) | |||||||
\(368\) | −984287. | −0.378880 | ||||||||
\(369\) | −592100. | −0.226375 | ||||||||
\(370\) | −458649. | −0.174171 | ||||||||
\(371\) | 3.13067e6 | 1.18087 | ||||||||
\(372\) | −21959.4 | −0.00822741 | ||||||||
\(373\) | −1.93944e6 | −0.721778 | −0.360889 | − | 0.932609i | \(-0.617527\pi\) | ||||
−0.360889 | + | 0.932609i | \(0.617527\pi\) | |||||||
\(374\) | −3.89463e6 | −1.43975 | ||||||||
\(375\) | 152484. | 0.0559946 | ||||||||
\(376\) | 814909. | 0.297262 | ||||||||
\(377\) | −7.22174e6 | −2.61691 | ||||||||
\(378\) | −213661. | −0.0769123 | ||||||||
\(379\) | 2.12461e6 | 0.759768 | 0.379884 | − | 0.925034i | \(-0.375964\pi\) | ||||
0.379884 | + | 0.925034i | \(0.375964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 562.025 | 0.000198355 0 | ||||||||
\(382\) | 3.80011e6 | 1.33241 | ||||||||
\(383\) | −4.63648e6 | −1.61507 | −0.807535 | − | 0.589820i | \(-0.799199\pi\) | ||||
−0.807535 | + | 0.589820i | \(0.799199\pi\) | |||||||
\(384\) | 19103.9 | 0.00661141 | ||||||||
\(385\) | 2.82131e6 | 0.970061 | ||||||||
\(386\) | −511290. | −0.174662 | ||||||||
\(387\) | −513558. | −0.174306 | ||||||||
\(388\) | 1.29242e6 | 0.435837 | ||||||||
\(389\) | −3.29250e6 | −1.10319 | −0.551597 | − | 0.834111i | \(-0.685981\pi\) | ||||
−0.551597 | + | 0.834111i | \(0.685981\pi\) | |||||||
\(390\) | 299031. | 0.0995531 | ||||||||
\(391\) | −8.16910e6 | −2.70229 | ||||||||
\(392\) | −503818. | −0.165599 | ||||||||
\(393\) | 106934. | 0.0349247 | ||||||||
\(394\) | −2.90192e6 | −0.941771 | ||||||||
\(395\) | −1.43170e6 | −0.461698 | ||||||||
\(396\) | 1.77175e6 | 0.567761 | ||||||||
\(397\) | 1.60659e6 | 0.511598 | 0.255799 | − | 0.966730i | \(-0.417661\pi\) | ||||
0.255799 | + | 0.966730i | \(0.417661\pi\) | |||||||
\(398\) | −538646. | −0.170449 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 285994. | 0.0893730 | ||||||||
\(401\) | −1.18032e6 | −0.366556 | −0.183278 | − | 0.983061i | \(-0.558671\pi\) | ||||
−0.183278 | + | 0.983061i | \(0.558671\pi\) | |||||||
\(402\) | 133538. | 0.0412134 | ||||||||
\(403\) | 1.15867e6 | 0.355382 | ||||||||
\(404\) | 102474. | 0.0312365 | ||||||||
\(405\) | −3.78154e6 | −1.14559 | ||||||||
\(406\) | 2.77386e6 | 0.835160 | ||||||||
\(407\) | −806753. | −0.241410 | ||||||||
\(408\) | 158553. | 0.0471547 | ||||||||
\(409\) | −1.68903e6 | −0.499264 | −0.249632 | − | 0.968341i | \(-0.580310\pi\) | ||||
−0.249632 | + | 0.968341i | \(0.580310\pi\) | |||||||
\(410\) | −638380. | −0.187551 | ||||||||
\(411\) | 274143. | 0.0800520 | ||||||||
\(412\) | −2.35090e6 | −0.682325 | ||||||||
\(413\) | 873041. | 0.251860 | ||||||||
\(414\) | 3.71630e6 | 1.06564 | ||||||||
\(415\) | 6.68374e6 | 1.90502 | ||||||||
\(416\) | −1.00800e6 | −0.285579 | ||||||||
\(417\) | 88436.9 | 0.0249054 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.08104e6 | 0.300821 | 0.150411 | − | 0.988624i | \(-0.451940\pi\) | ||||
0.150411 | + | 0.988624i | \(0.451940\pi\) | |||||||
\(420\) | −114858. | −0.0317714 | ||||||||
\(421\) | 5.58922e6 | 1.53690 | 0.768451 | − | 0.639909i | \(-0.221028\pi\) | ||||
0.768451 | + | 0.639909i | \(0.221028\pi\) | |||||||
\(422\) | −3.87335e6 | −1.05878 | ||||||||
\(423\) | −3.07680e6 | −0.836080 | ||||||||
\(424\) | 2.11970e6 | 0.572610 | ||||||||
\(425\) | 2.37361e6 | 0.637436 | ||||||||
\(426\) | −320427. | −0.0855471 | ||||||||
\(427\) | 973263. | 0.258321 | ||||||||
\(428\) | 2.29574e6 | 0.605779 | ||||||||
\(429\) | 525989. | 0.137985 | ||||||||
\(430\) | −553699. | −0.144412 | ||||||||
\(431\) | −5.95712e6 | −1.54470 | −0.772348 | − | 0.635200i | \(-0.780918\pi\) | ||||
−0.772348 | + | 0.635200i | \(0.780918\pi\) | |||||||
\(432\) | −144665. | −0.0372952 | ||||||||
\(433\) | 5.19586e6 | 1.33180 | 0.665898 | − | 0.746043i | \(-0.268048\pi\) | ||||
0.665898 | + | 0.746043i | \(0.268048\pi\) | |||||||
\(434\) | −445042. | −0.113417 | ||||||||
\(435\) | −557157. | −0.141174 | ||||||||
\(436\) | 1.60891e6 | 0.405335 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 169077. | 0.0421115 | ||||||||
\(439\) | 251173. | 0.0622031 | 0.0311016 | − | 0.999516i | \(-0.490098\pi\) | ||||
0.0311016 | + | 0.999516i | \(0.490098\pi\) | |||||||
\(440\) | 1.91024e6 | 0.470388 | ||||||||
\(441\) | 1.90223e6 | 0.465765 | ||||||||
\(442\) | −8.36591e6 | −2.03684 | ||||||||
\(443\) | −2.98401e6 | −0.722422 | −0.361211 | − | 0.932484i | \(-0.617637\pi\) | ||||
−0.361211 | + | 0.932484i | \(0.617637\pi\) | |||||||
\(444\) | 32843.5 | 0.00790664 | ||||||||
\(445\) | −1.84073e6 | −0.440645 | ||||||||
\(446\) | 3.37520e6 | 0.803457 | ||||||||
\(447\) | 160078. | 0.0378934 | ||||||||
\(448\) | 387172. | 0.0911399 | ||||||||
\(449\) | 5.01310e6 | 1.17352 | 0.586760 | − | 0.809761i | \(-0.300403\pi\) | ||||
0.586760 | + | 0.809761i | \(0.300403\pi\) | |||||||
\(450\) | −1.07981e6 | −0.251371 | ||||||||
\(451\) | −1.12290e6 | −0.259955 | ||||||||
\(452\) | −1.86181e6 | −0.428636 | ||||||||
\(453\) | −99216.8 | −0.0227164 | ||||||||
\(454\) | −4.90292e6 | −1.11639 | ||||||||
\(455\) | 6.06034e6 | 1.37236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.93647e6 | −1.55363 | −0.776816 | − | 0.629728i | \(-0.783166\pi\) | ||||
−0.776816 | + | 0.629728i | \(0.783166\pi\) | |||||||
\(458\) | 3.54963e6 | 0.790714 | ||||||||
\(459\) | −1.20065e6 | −0.266001 | ||||||||
\(460\) | 4.00678e6 | 0.882878 | ||||||||
\(461\) | 4.99252e6 | 1.09413 | 0.547063 | − | 0.837091i | \(-0.315746\pi\) | ||||
0.547063 | + | 0.837091i | \(0.315746\pi\) | |||||||
\(462\) | −202032. | −0.0440367 | ||||||||
\(463\) | −2.65065e6 | −0.574645 | −0.287323 | − | 0.957834i | \(-0.592765\pi\) | ||||
−0.287323 | + | 0.957834i | \(0.592765\pi\) | |||||||
\(464\) | 1.87811e6 | 0.404973 | ||||||||
\(465\) | 89391.0 | 0.0191717 | ||||||||
\(466\) | 1.81376e6 | 0.386915 | ||||||||
\(467\) | 7.68506e6 | 1.63063 | 0.815314 | − | 0.579019i | \(-0.196564\pi\) | ||||
0.815314 | + | 0.579019i | \(0.196564\pi\) | |||||||
\(468\) | 3.80583e6 | 0.803221 | ||||||||
\(469\) | 2.70635e6 | 0.568136 | ||||||||
\(470\) | −3.31728e6 | −0.692689 | ||||||||
\(471\) | −94561.2 | −0.0196409 | ||||||||
\(472\) | 591114. | 0.122128 | ||||||||
\(473\) | −973944. | −0.200162 | ||||||||
\(474\) | 102523. | 0.0209592 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.21334e6 | 0.650038 | ||||||||
\(477\) | −8.00320e6 | −1.61053 | ||||||||
\(478\) | −683587. | −0.136843 | ||||||||
\(479\) | −6.72219e6 | −1.33867 | −0.669333 | − | 0.742963i | \(-0.733420\pi\) | ||||
−0.669333 | + | 0.742963i | \(0.733420\pi\) | |||||||
\(480\) | −77767.1 | −0.0154061 | ||||||||
\(481\) | −1.73295e6 | −0.341526 | ||||||||
\(482\) | 737230. | 0.144539 | ||||||||
\(483\) | −423768. | −0.0826532 | ||||||||
\(484\) | 783249. | 0.151980 | ||||||||
\(485\) | −5.26111e6 | −1.01560 | ||||||||
\(486\) | 820066. | 0.157492 | ||||||||
\(487\) | 7.70276e6 | 1.47172 | 0.735858 | − | 0.677136i | \(-0.236779\pi\) | ||||
0.735858 | + | 0.677136i | \(0.236779\pi\) | |||||||
\(488\) | 658972. | 0.125261 | ||||||||
\(489\) | 565687. | 0.106980 | ||||||||
\(490\) | 2.05091e6 | 0.385884 | ||||||||
\(491\) | −2.05199e6 | −0.384124 | −0.192062 | − | 0.981383i | \(-0.561517\pi\) | ||||
−0.192062 | + | 0.981383i | \(0.561517\pi\) | |||||||
\(492\) | 45713.9 | 0.00851403 | ||||||||
\(493\) | 1.55874e7 | 2.88840 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.21236e6 | −1.32301 | ||||||||
\(496\) | −301327. | −0.0549963 | ||||||||
\(497\) | −6.49397e6 | −1.17929 | ||||||||
\(498\) | −478617. | −0.0864798 | ||||||||
\(499\) | 6.20643e6 | 1.11581 | 0.557906 | − | 0.829904i | \(-0.311605\pi\) | ||||
0.557906 | + | 0.829904i | \(0.311605\pi\) | |||||||
\(500\) | 2.09239e6 | 0.374298 | ||||||||
\(501\) | 392375. | 0.0698404 | ||||||||
\(502\) | −1.61220e6 | −0.285535 | ||||||||
\(503\) | 2.83149e6 | 0.498994 | 0.249497 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249497 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(504\) | −1.46182e6 | −0.256340 | ||||||||
\(505\) | −417147. | −0.0727882 | ||||||||
\(506\) | 7.04783e6 | 1.22371 | ||||||||
\(507\) | 696924. | 0.120411 | ||||||||
\(508\) | 7712.11 | 0.00132591 | ||||||||
\(509\) | −6.63957e6 | −1.13591 | −0.567957 | − | 0.823058i | \(-0.692266\pi\) | ||||
−0.567957 | + | 0.823058i | \(0.692266\pi\) | |||||||
\(510\) | −645430. | −0.109881 | ||||||||
\(511\) | 3.42662e6 | 0.580516 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −492351. | −0.0821991 | ||||||||
\(515\) | 9.56992e6 | 1.58997 | ||||||||
\(516\) | 39650.0 | 0.00655569 | ||||||||
\(517\) | −5.83503e6 | −0.960100 | ||||||||
\(518\) | 665626. | 0.108995 | ||||||||
\(519\) | −125124. | −0.0203902 | ||||||||
\(520\) | 4.10331e6 | 0.665465 | ||||||||
\(521\) | −9.81565e6 | −1.58425 | −0.792127 | − | 0.610357i | \(-0.791026\pi\) | ||||
−0.792127 | + | 0.610357i | \(0.791026\pi\) | |||||||
\(522\) | −7.09106e6 | −1.13903 | ||||||||
\(523\) | −8.32979e6 | −1.33162 | −0.665809 | − | 0.746122i | \(-0.731914\pi\) | ||||
−0.665809 | + | 0.746122i | \(0.731914\pi\) | |||||||
\(524\) | 1.46734e6 | 0.233455 | ||||||||
\(525\) | 123130. | 0.0194968 | ||||||||
\(526\) | 3.26691e6 | 0.514841 | ||||||||
\(527\) | −2.50087e6 | −0.392251 | ||||||||
\(528\) | −136791. | −0.0213536 | ||||||||
\(529\) | 8.34669e6 | 1.29681 | ||||||||
\(530\) | −8.62874e6 | −1.33431 | ||||||||
\(531\) | −2.23183e6 | −0.343498 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.41205e6 | −0.367763 | ||||||||
\(534\) | 131813. | 0.0200035 | ||||||||
\(535\) | −9.34539e6 | −1.41160 | ||||||||
\(536\) | 1.83240e6 | 0.275492 | ||||||||
\(537\) | 310451. | 0.0464576 | ||||||||
\(538\) | −5.04721e6 | −0.751788 | ||||||||
\(539\) | 3.60751e6 | 0.534855 | ||||||||
\(540\) | 588892. | 0.0869063 | ||||||||
\(541\) | −1.31845e6 | −0.193673 | −0.0968365 | − | 0.995300i | \(-0.530872\pi\) | ||||
−0.0968365 | + | 0.995300i | \(0.530872\pi\) | |||||||
\(542\) | 4.66430e6 | 0.682006 | ||||||||
\(543\) | −49503.9 | −0.00720509 | ||||||||
\(544\) | 2.17567e6 | 0.315207 | ||||||||
\(545\) | −6.54944e6 | −0.944524 | ||||||||
\(546\) | −433976. | −0.0622995 | ||||||||
\(547\) | −3.41377e6 | −0.487827 | −0.243913 | − | 0.969797i | \(-0.578431\pi\) | ||||
−0.243913 | + | 0.969797i | \(0.578431\pi\) | |||||||
\(548\) | 3.76179e6 | 0.535110 | ||||||||
\(549\) | −2.48803e6 | −0.352310 | ||||||||
\(550\) | −2.04781e6 | −0.288658 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −286922. | −0.0400790 | ||||||||
\(553\) | 2.07779e6 | 0.288927 | ||||||||
\(554\) | 6.69907e6 | 0.927342 | ||||||||
\(555\) | −133697. | −0.0184243 | ||||||||
\(556\) | 1.21353e6 | 0.166481 | ||||||||
\(557\) | 2.46992e6 | 0.337322 | 0.168661 | − | 0.985674i | \(-0.446056\pi\) | ||||
0.168661 | + | 0.985674i | \(0.446056\pi\) | |||||||
\(558\) | 1.13770e6 | 0.154683 | ||||||||
\(559\) | −2.09209e6 | −0.283172 | ||||||||
\(560\) | −1.57608e6 | −0.212377 | ||||||||
\(561\) | −1.13530e6 | −0.152301 | ||||||||
\(562\) | −6.46061e6 | −0.862845 | ||||||||
\(563\) | −8.34626e6 | −1.10974 | −0.554870 | − | 0.831937i | \(-0.687232\pi\) | ||||
−0.554870 | + | 0.831937i | \(0.687232\pi\) | |||||||
\(564\) | 237548. | 0.0314452 | ||||||||
\(565\) | 7.57894e6 | 0.998821 | ||||||||
\(566\) | 9.37767e6 | 1.23042 | ||||||||
\(567\) | 5.48805e6 | 0.716903 | ||||||||
\(568\) | −4.39690e6 | −0.571842 | ||||||||
\(569\) | 6.16363e6 | 0.798097 | 0.399048 | − | 0.916930i | \(-0.369341\pi\) | ||||
0.399048 | + | 0.916930i | \(0.369341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.79609e6 | 1.12901 | 0.564507 | − | 0.825428i | \(-0.309066\pi\) | ||||
0.564507 | + | 0.825428i | \(0.309066\pi\) | |||||||
\(572\) | 7.21762e6 | 0.922368 | ||||||||
\(573\) | 1.10774e6 | 0.140946 | ||||||||
\(574\) | 926465. | 0.117368 | ||||||||
\(575\) | −4.29535e6 | −0.541787 | ||||||||
\(576\) | −989759. | −0.124301 | ||||||||
\(577\) | −2.25027e6 | −0.281381 | −0.140691 | − | 0.990054i | \(-0.544932\pi\) | ||||
−0.140691 | + | 0.990054i | \(0.544932\pi\) | |||||||
\(578\) | 1.23776e7 | 1.54105 | ||||||||
\(579\) | −149043. | −0.0184762 | ||||||||
\(580\) | −7.64531e6 | −0.943681 | ||||||||
\(581\) | −9.69994e6 | −1.19214 | ||||||||
\(582\) | 376744. | 0.0461040 | ||||||||
\(583\) | −1.51778e7 | −1.84942 | ||||||||
\(584\) | 2.32008e6 | 0.281495 | ||||||||
\(585\) | −1.54926e7 | −1.87169 | ||||||||
\(586\) | −167191. | −0.0201126 | ||||||||
\(587\) | −3.10442e6 | −0.371865 | −0.185933 | − | 0.982563i | \(-0.559531\pi\) | ||||
−0.185933 | + | 0.982563i | \(0.559531\pi\) | |||||||
\(588\) | −146864. | −0.0175175 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.40627e6 | −0.284587 | ||||||||
\(591\) | −845919. | −0.0996231 | ||||||||
\(592\) | 450678. | 0.0528521 | ||||||||
\(593\) | 5.98086e6 | 0.698436 | 0.349218 | − | 0.937041i | \(-0.386447\pi\) | ||||
0.349218 | + | 0.937041i | \(0.386447\pi\) | |||||||
\(594\) | 1.03585e6 | 0.120456 | ||||||||
\(595\) | −1.30807e7 | −1.51474 | ||||||||
\(596\) | 2.19659e6 | 0.253299 | ||||||||
\(597\) | −157017. | −0.0180306 | ||||||||
\(598\) | 1.51392e7 | 1.73121 | ||||||||
\(599\) | −6.92305e6 | −0.788370 | −0.394185 | − | 0.919031i | \(-0.628973\pi\) | ||||
−0.394185 | + | 0.919031i | \(0.628973\pi\) | |||||||
\(600\) | 83367.9 | 0.00945411 | ||||||||
\(601\) | −4.63926e6 | −0.523917 | −0.261959 | − | 0.965079i | \(-0.584368\pi\) | ||||
−0.261959 | + | 0.965079i | \(0.584368\pi\) | |||||||
\(602\) | 803570. | 0.0903717 | ||||||||
\(603\) | −6.91848e6 | −0.774850 | ||||||||
\(604\) | −1.36145e6 | −0.151848 | ||||||||
\(605\) | −3.18841e6 | −0.354148 | ||||||||
\(606\) | 29871.6 | 0.00330428 | ||||||||
\(607\) | 8.70257e6 | 0.958685 | 0.479343 | − | 0.877628i | \(-0.340875\pi\) | ||||
0.479343 | + | 0.877628i | \(0.340875\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 808588. | 0.0883454 | ||||||||
\(610\) | −2.68250e6 | −0.291888 | ||||||||
\(611\) | −1.25340e7 | −1.35827 | ||||||||
\(612\) | −8.21452e6 | −0.886551 | ||||||||
\(613\) | −5.42194e6 | −0.582778 | −0.291389 | − | 0.956605i | \(-0.594117\pi\) | ||||
−0.291389 | + | 0.956605i | \(0.594117\pi\) | |||||||
\(614\) | 5.72146e6 | 0.612472 | ||||||||
\(615\) | −186089. | −0.0198396 | ||||||||
\(616\) | −2.77228e6 | −0.294365 | ||||||||
\(617\) | 4.64831e6 | 0.491566 | 0.245783 | − | 0.969325i | \(-0.420955\pi\) | ||||
0.245783 | + | 0.969325i | \(0.420955\pi\) | |||||||
\(618\) | −685294. | −0.0721782 | ||||||||
\(619\) | 3.56785e6 | 0.374266 | 0.187133 | − | 0.982335i | \(-0.440080\pi\) | ||||
0.187133 | + | 0.982335i | \(0.440080\pi\) | |||||||
\(620\) | 1.22662e6 | 0.128154 | ||||||||
\(621\) | 2.17272e6 | 0.226087 | ||||||||
\(622\) | −3.65913e6 | −0.379229 | ||||||||
\(623\) | 2.67140e6 | 0.275752 | ||||||||
\(624\) | −293834. | −0.0302093 | ||||||||
\(625\) | −1.20087e7 | −1.22969 | ||||||||
\(626\) | 7.27916e6 | 0.742413 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.29757e6 | −0.131290 | ||||||||
\(629\) | 3.74041e6 | 0.376958 | ||||||||
\(630\) | 5.95068e6 | 0.597331 | ||||||||
\(631\) | −1.08645e7 | −1.08627 | −0.543134 | − | 0.839646i | \(-0.682762\pi\) | ||||
−0.543134 | + | 0.839646i | \(0.682762\pi\) | |||||||
\(632\) | 1.40682e6 | 0.140102 | ||||||||
\(633\) | −1.12909e6 | −0.112000 | ||||||||
\(634\) | −2.42545e6 | −0.239645 | ||||||||
\(635\) | −31394.0 | −0.00308967 | ||||||||
\(636\) | 617897. | 0.0605722 | ||||||||
\(637\) | 7.74915e6 | 0.756668 | ||||||||
\(638\) | −1.34479e7 | −1.30799 | ||||||||
\(639\) | 1.66011e7 | 1.60836 | ||||||||
\(640\) | −1.06712e6 | −0.102983 | ||||||||
\(641\) | 7.19318e6 | 0.691474 | 0.345737 | − | 0.938331i | \(-0.387629\pi\) | ||||
0.345737 | + | 0.938331i | \(0.387629\pi\) | |||||||
\(642\) | 669216. | 0.0640809 | ||||||||
\(643\) | −1.59363e7 | −1.52006 | −0.760030 | − | 0.649888i | \(-0.774816\pi\) | ||||
−0.760030 | + | 0.649888i | \(0.774816\pi\) | |||||||
\(644\) | −5.81494e6 | −0.552498 | ||||||||
\(645\) | −161405. | −0.0152763 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.77399e6 | −0.917934 | −0.458967 | − | 0.888453i | \(-0.651780\pi\) | ||||
−0.458967 | + | 0.888453i | \(0.651780\pi\) | |||||||
\(648\) | 3.71582e6 | 0.347630 | ||||||||
\(649\) | −4.23258e6 | −0.394451 | ||||||||
\(650\) | −4.39882e6 | −0.408369 | ||||||||
\(651\) | −129731. | −0.0119975 | ||||||||
\(652\) | 7.76236e6 | 0.715113 | ||||||||
\(653\) | −5.52435e6 | −0.506989 | −0.253494 | − | 0.967337i | \(-0.581580\pi\) | ||||
−0.253494 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(654\) | 469000. | 0.0428774 | ||||||||
\(655\) | −5.97317e6 | −0.544004 | ||||||||
\(656\) | 627286. | 0.0569123 | ||||||||
\(657\) | −8.75977e6 | −0.791734 | ||||||||
\(658\) | 4.81429e6 | 0.433479 | ||||||||
\(659\) | 1.22620e7 | 1.09989 | 0.549943 | − | 0.835202i | \(-0.314650\pi\) | ||||
0.549943 | + | 0.835202i | \(0.314650\pi\) | |||||||
\(660\) | 556839. | 0.0497588 | ||||||||
\(661\) | 1.65710e7 | 1.47518 | 0.737589 | − | 0.675250i | \(-0.235964\pi\) | ||||
0.737589 | + | 0.675250i | \(0.235964\pi\) | |||||||
\(662\) | −2.31644e6 | −0.205435 | ||||||||
\(663\) | −2.43868e6 | −0.215462 | ||||||||
\(664\) | −6.56758e6 | −0.578077 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70160e6 | −0.148652 | ||||||||
\(667\) | −2.82074e7 | −2.45498 | ||||||||
\(668\) | 5.38417e6 | 0.466850 | ||||||||
\(669\) | 983880. | 0.0849918 | ||||||||
\(670\) | −7.45924e6 | −0.641960 | ||||||||
\(671\) | −4.71846e6 | −0.404571 | ||||||||
\(672\) | 112862. | 0.00964101 | ||||||||
\(673\) | 644074. | 0.0548148 | 0.0274074 | − | 0.999624i | \(-0.491275\pi\) | ||||
0.0274074 | + | 0.999624i | \(0.491275\pi\) | |||||||
\(674\) | −3.38783e6 | −0.287258 | ||||||||
\(675\) | −631304. | −0.0533309 | ||||||||
\(676\) | 9.56319e6 | 0.804889 | ||||||||
\(677\) | 9.78531e6 | 0.820546 | 0.410273 | − | 0.911963i | \(-0.365433\pi\) | ||||
0.410273 | + | 0.911963i | \(0.365433\pi\) | |||||||
\(678\) | −542722. | −0.0453423 | ||||||||
\(679\) | 7.63531e6 | 0.635554 | ||||||||
\(680\) | −8.85659e6 | −0.734504 | ||||||||
\(681\) | −1.42921e6 | −0.118094 | ||||||||
\(682\) | 2.15760e6 | 0.177628 | ||||||||
\(683\) | −3.75534e6 | −0.308033 | −0.154017 | − | 0.988068i | \(-0.549221\pi\) | ||||
−0.154017 | + | 0.988068i | \(0.549221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.53133e7 | −1.24693 | ||||||||
\(686\) | −9.33112e6 | −0.757048 | ||||||||
\(687\) | 1.03473e6 | 0.0836438 | ||||||||
\(688\) | 544077. | 0.0438217 | ||||||||
\(689\) | −3.26027e7 | −2.61641 | ||||||||
\(690\) | 1.16799e6 | 0.0933932 | ||||||||
\(691\) | 2.10376e7 | 1.67610 | 0.838051 | − | 0.545593i | \(-0.183695\pi\) | ||||
0.838051 | + | 0.545593i | \(0.183695\pi\) | |||||||
\(692\) | −1.71695e6 | −0.136299 | ||||||||
\(693\) | 1.04671e7 | 0.827930 | ||||||||
\(694\) | 1.43643e6 | 0.113211 | ||||||||
\(695\) | −4.93997e6 | −0.387938 | ||||||||
\(696\) | 547475. | 0.0428392 | ||||||||
\(697\) | 5.20617e6 | 0.405916 | ||||||||
\(698\) | 1.60063e6 | 0.124352 | ||||||||
\(699\) | 528716. | 0.0409289 | ||||||||
\(700\) | 1.68958e6 | 0.130327 | ||||||||
\(701\) | 9.56329e6 | 0.735043 | 0.367521 | − | 0.930015i | \(-0.380207\pi\) | ||||
0.367521 | + | 0.930015i | \(0.380207\pi\) | |||||||
\(702\) | 2.22506e6 | 0.170412 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.87704e6 | −0.142739 | ||||||||
\(705\) | −966997. | −0.0732744 | ||||||||
\(706\) | −8.89794e6 | −0.671859 | ||||||||
\(707\) | 605395. | 0.0455502 | ||||||||
\(708\) | 172311. | 0.0129190 | ||||||||
\(709\) | −5.73053e6 | −0.428133 | −0.214067 | − | 0.976819i | \(-0.568671\pi\) | ||||
−0.214067 | + | 0.976819i | \(0.568671\pi\) | |||||||
\(710\) | 1.78987e7 | 1.33252 | ||||||||
\(711\) | −5.31162e6 | −0.394051 | ||||||||
\(712\) | 1.80874e6 | 0.133714 | ||||||||
\(713\) | 4.52564e6 | 0.333392 | ||||||||
\(714\) | 936696. | 0.0687627 | ||||||||
\(715\) | −2.93811e7 | −2.14933 | ||||||||
\(716\) | 4.26001e6 | 0.310547 | ||||||||
\(717\) | −199267. | −0.0144757 | ||||||||
\(718\) | 1.90262e6 | 0.137734 | ||||||||
\(719\) | 858188. | 0.0619099 | 0.0309550 | − | 0.999521i | \(-0.490145\pi\) | ||||
0.0309550 | + | 0.999521i | \(0.490145\pi\) | |||||||
\(720\) | 4.02906e6 | 0.289649 | ||||||||
\(721\) | −1.38886e7 | −0.994992 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 214905. | 0.0152897 | ||||||||
\(724\) | −679292. | −0.0481626 | ||||||||
\(725\) | 8.19592e6 | 0.579099 | ||||||||
\(726\) | 228319. | 0.0160768 | ||||||||
\(727\) | 1.15990e7 | 0.813923 | 0.406962 | − | 0.913445i | \(-0.366588\pi\) | ||||
0.406962 | + | 0.913445i | \(0.366588\pi\) | |||||||
\(728\) | −5.95503e6 | −0.416443 | ||||||||
\(729\) | −1.38695e7 | −0.966586 | ||||||||
\(730\) | −9.44445e6 | −0.655948 | ||||||||
\(731\) | 4.51557e6 | 0.312550 | ||||||||
\(732\) | 192092. | 0.0132505 | ||||||||
\(733\) | −1.13392e7 | −0.779511 | −0.389756 | − | 0.920918i | \(-0.627441\pi\) | ||||
−0.389756 | + | 0.920918i | \(0.627441\pi\) | |||||||
\(734\) | −1.42033e7 | −0.973082 | ||||||||
\(735\) | 597847. | 0.0408199 | ||||||||
\(736\) | −3.93715e6 | −0.267909 | ||||||||
\(737\) | −1.31206e7 | −0.889787 | ||||||||
\(738\) | −2.36840e6 | −0.160072 | ||||||||
\(739\) | 2.06956e7 | 1.39402 | 0.697008 | − | 0.717063i | \(-0.254514\pi\) | ||||
0.697008 | + | 0.717063i | \(0.254514\pi\) | |||||||
\(740\) | −1.83460e6 | −0.123158 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.25227e7 | 0.835002 | ||||||||
\(743\) | −1.77897e7 | −1.18221 | −0.591107 | − | 0.806593i | \(-0.701309\pi\) | ||||
−0.591107 | + | 0.806593i | \(0.701309\pi\) | |||||||
\(744\) | −87837.6 | −0.00581765 | ||||||||
\(745\) | −8.94177e6 | −0.590245 | ||||||||
\(746\) | −7.75775e6 | −0.510374 | ||||||||
\(747\) | 2.47968e7 | 1.62590 | ||||||||
\(748\) | −1.55785e7 | −1.01806 | ||||||||
\(749\) | 1.35627e7 | 0.883370 | ||||||||
\(750\) | 609937. | 0.0395942 | ||||||||
\(751\) | −2.41833e7 | −1.56465 | −0.782324 | − | 0.622872i | \(-0.785966\pi\) | ||||
−0.782324 | + | 0.622872i | \(0.785966\pi\) | |||||||
\(752\) | 3.25964e6 | 0.210196 | ||||||||
\(753\) | −469960. | −0.0302047 | ||||||||
\(754\) | −2.88870e7 | −1.85043 | ||||||||
\(755\) | 5.54213e6 | 0.353842 | ||||||||
\(756\) | −854645. | −0.0543852 | ||||||||
\(757\) | 1.89248e7 | 1.20030 | 0.600151 | − | 0.799887i | \(-0.295107\pi\) | ||||
0.600151 | + | 0.799887i | \(0.295107\pi\) | |||||||
\(758\) | 8.49843e6 | 0.537237 | ||||||||
\(759\) | 2.05446e6 | 0.129447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.72399e6 | −0.107913 | −0.0539565 | − | 0.998543i | \(-0.517183\pi\) | ||||
−0.0539565 | + | 0.998543i | \(0.517183\pi\) | |||||||
\(762\) | 2248.10 | 0.000140258 0 | ||||||||
\(763\) | 9.50504e6 | 0.591075 | ||||||||
\(764\) | 1.52005e7 | 0.942157 | ||||||||
\(765\) | 3.34392e7 | 2.06587 | ||||||||
\(766\) | −1.85459e7 | −1.14203 | ||||||||
\(767\) | −9.09183e6 | −0.558037 | ||||||||
\(768\) | 76415.7 | 0.00467498 | ||||||||
\(769\) | 3.08370e7 | 1.88043 | 0.940214 | − | 0.340585i | \(-0.110625\pi\) | ||||
0.940214 | + | 0.340585i | \(0.110625\pi\) | |||||||
\(770\) | 1.12852e7 | 0.685937 | ||||||||
\(771\) | −143522. | −0.00869524 | ||||||||
\(772\) | −2.04516e6 | −0.123505 | ||||||||
\(773\) | 1.21764e7 | 0.732942 | 0.366471 | − | 0.930429i | \(-0.380566\pi\) | ||||
0.366471 | + | 0.930429i | \(0.380566\pi\) | |||||||
\(774\) | −2.05423e6 | −0.123253 | ||||||||
\(775\) | −1.31497e6 | −0.0786430 | ||||||||
\(776\) | 5.16968e6 | 0.308183 | ||||||||
\(777\) | 194032. | 0.0115298 | ||||||||
\(778\) | −1.31700e7 | −0.780076 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.19612e6 | 0.0703947 | ||||||||
\(781\) | 3.14833e7 | 1.84694 | ||||||||
\(782\) | −3.26764e7 | −1.91081 | ||||||||
\(783\) | −4.14575e6 | −0.241657 | ||||||||
\(784\) | −2.01527e6 | −0.117096 | ||||||||
\(785\) | 5.28207e6 | 0.305936 | ||||||||
\(786\) | 427734. | 0.0246955 | ||||||||
\(787\) | 7.35704e6 | 0.423415 | 0.211708 | − | 0.977333i | \(-0.432098\pi\) | ||||
0.211708 | + | 0.977333i | \(0.432098\pi\) | |||||||
\(788\) | −1.16077e7 | −0.665933 | ||||||||
\(789\) | 952313. | 0.0544612 | ||||||||
\(790\) | −5.72679e6 | −0.326470 | ||||||||
\(791\) | −1.09991e7 | −0.625054 | ||||||||
\(792\) | 7.08702e6 | 0.401468 | ||||||||
\(793\) | −1.01355e7 | −0.572353 | ||||||||
\(794\) | 6.42636e6 | 0.361754 | ||||||||
\(795\) | −2.51530e6 | −0.141147 | ||||||||
\(796\) | −2.15458e6 | −0.120526 | ||||||||
\(797\) | −1.72232e7 | −0.960434 | −0.480217 | − | 0.877150i | \(-0.659442\pi\) | ||||
−0.480217 | + | 0.877150i | \(0.659442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.70534e7 | 1.49918 | ||||||||
\(800\) | 1.14397e6 | 0.0631963 | ||||||||
\(801\) | −6.82913e6 | −0.376083 | ||||||||
\(802\) | −4.72130e6 | −0.259194 | ||||||||
\(803\) | −1.66126e7 | −0.909176 | ||||||||
\(804\) | 534150. | 0.0291423 | ||||||||
\(805\) | 2.36711e7 | 1.28745 | ||||||||
\(806\) | 4.63466e6 | 0.251293 | ||||||||
\(807\) | −1.47127e6 | −0.0795261 | ||||||||
\(808\) | 409898. | 0.0220875 | ||||||||
\(809\) | 2.01553e7 | 1.08272 | 0.541361 | − | 0.840790i | \(-0.317909\pi\) | ||||
0.541361 | + | 0.840790i | \(0.317909\pi\) | |||||||
\(810\) | −1.51262e7 | −0.810058 | ||||||||
\(811\) | 4.12961e6 | 0.220474 | 0.110237 | − | 0.993905i | \(-0.464839\pi\) | ||||
0.110237 | + | 0.993905i | \(0.464839\pi\) | |||||||
\(812\) | 1.10954e7 | 0.590548 | ||||||||
\(813\) | 1.35966e6 | 0.0721444 | ||||||||
\(814\) | −3.22701e6 | −0.170702 | ||||||||
\(815\) | −3.15986e7 | −1.66638 | ||||||||
\(816\) | 634213. | 0.0333434 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.75613e6 | −0.353033 | ||||||||
\(819\) | 2.24840e7 | 1.17129 | ||||||||
\(820\) | −2.55352e6 | −0.132619 | ||||||||
\(821\) | 1.43194e7 | 0.741425 | 0.370712 | − | 0.928748i | \(-0.379114\pi\) | ||||
0.370712 | + | 0.928748i | \(0.379114\pi\) | |||||||
\(822\) | 1.09657e6 | 0.0566053 | ||||||||
\(823\) | 3.02457e7 | 1.55655 | 0.778276 | − | 0.627922i | \(-0.216094\pi\) | ||||
0.778276 | + | 0.627922i | \(0.216094\pi\) | |||||||
\(824\) | −9.40361e6 | −0.482477 | ||||||||
\(825\) | −596943. | −0.0305350 | ||||||||
\(826\) | 3.49216e6 | 0.178092 | ||||||||
\(827\) | 2.66650e7 | 1.35575 | 0.677873 | − | 0.735179i | \(-0.262902\pi\) | ||||
0.677873 | + | 0.735179i | \(0.262902\pi\) | |||||||
\(828\) | 1.48652e7 | 0.753521 | ||||||||
\(829\) | 2.83495e7 | 1.43271 | 0.716356 | − | 0.697735i | \(-0.245809\pi\) | ||||
0.716356 | + | 0.697735i | \(0.245809\pi\) | |||||||
\(830\) | 2.67349e7 | 1.34705 | ||||||||
\(831\) | 1.95280e6 | 0.0980966 | ||||||||
\(832\) | −4.03200e6 | −0.201935 | ||||||||
\(833\) | −1.67258e7 | −0.835168 | ||||||||
\(834\) | 353748. | 0.0176108 | ||||||||
\(835\) | −2.19176e7 | −1.08787 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 665151. | 0.0328176 | ||||||||
\(838\) | 4.32418e6 | 0.212713 | ||||||||
\(839\) | 3.44319e7 | 1.68871 | 0.844356 | − | 0.535782i | \(-0.179983\pi\) | ||||
0.844356 | + | 0.535782i | \(0.179983\pi\) | |||||||
\(840\) | −459430. | −0.0224658 | ||||||||
\(841\) | 3.33112e7 | 1.62406 | ||||||||
\(842\) | 2.23569e7 | 1.08675 | ||||||||
\(843\) | −1.88329e6 | −0.0912740 | ||||||||
\(844\) | −1.54934e7 | −0.748670 | ||||||||
\(845\) | −3.89293e7 | −1.87558 | ||||||||
\(846\) | −1.23072e7 | −0.591198 | ||||||||
\(847\) | 4.62726e6 | 0.221623 | ||||||||
\(848\) | 8.47879e6 | 0.404897 | ||||||||
\(849\) | 2.73361e6 | 0.130157 | ||||||||
\(850\) | 9.49443e6 | 0.450736 | ||||||||
\(851\) | −6.76875e6 | −0.320394 | ||||||||
\(852\) | −1.28171e6 | −0.0604909 | ||||||||
\(853\) | 2.18193e7 | 1.02676 | 0.513378 | − | 0.858162i | \(-0.328394\pi\) | ||||
0.513378 | + | 0.858162i | \(0.328394\pi\) | |||||||
\(854\) | 3.89305e6 | 0.182661 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.18298e6 | 0.428350 | ||||||||
\(857\) | −2.97380e6 | −0.138312 | −0.0691560 | − | 0.997606i | \(-0.522031\pi\) | ||||
−0.0691560 | + | 0.997606i | \(0.522031\pi\) | |||||||
\(858\) | 2.10396e6 | 0.0975705 | ||||||||
\(859\) | 1.61719e7 | 0.747786 | 0.373893 | − | 0.927472i | \(-0.378023\pi\) | ||||
0.373893 | + | 0.927472i | \(0.378023\pi\) | |||||||
\(860\) | −2.21480e6 | −0.102115 | ||||||||
\(861\) | 270067. | 0.0124155 | ||||||||
\(862\) | −2.38285e7 | −1.09226 | ||||||||
\(863\) | −2.36695e7 | −1.08184 | −0.540918 | − | 0.841075i | \(-0.681923\pi\) | ||||
−0.540918 | + | 0.841075i | \(0.681923\pi\) | |||||||
\(864\) | −578658. | −0.0263717 | ||||||||
\(865\) | 6.98927e6 | 0.317608 | ||||||||
\(866\) | 2.07834e7 | 0.941722 | ||||||||
\(867\) | 3.60809e6 | 0.163016 | ||||||||
\(868\) | −1.78017e6 | −0.0801977 | ||||||||
\(869\) | −1.00733e7 | −0.452503 | ||||||||
\(870\) | −2.22863e6 | −0.0998250 | ||||||||
\(871\) | −2.81839e7 | −1.25880 | ||||||||
\(872\) | 6.43562e6 | 0.286615 | ||||||||
\(873\) | −1.95188e7 | −0.866797 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.23613e7 | 0.545815 | ||||||||
\(876\) | 676310. | 0.0297773 | ||||||||
\(877\) | 2.13817e7 | 0.938736 | 0.469368 | − | 0.883003i | \(-0.344482\pi\) | ||||
0.469368 | + | 0.883003i | \(0.344482\pi\) | |||||||
\(878\) | 1.00469e6 | 0.0439843 | ||||||||
\(879\) | −48736.6 | −0.00212757 | ||||||||
\(880\) | 7.64095e6 | 0.332614 | ||||||||
\(881\) | −1.89553e7 | −0.822794 | −0.411397 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411397 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(882\) | 7.60893e6 | 0.329346 | ||||||||
\(883\) | −2.85853e7 | −1.23379 | −0.616895 | − | 0.787045i | \(-0.711610\pi\) | ||||
−0.616895 | + | 0.787045i | \(0.711610\pi\) | |||||||
\(884\) | −3.34636e7 | −1.44026 | ||||||||
\(885\) | −701435. | −0.0301043 | ||||||||
\(886\) | −1.19360e7 | −0.510830 | ||||||||
\(887\) | −473148. | −0.0201924 | −0.0100962 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100962 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(888\) | 131374. | 0.00559084 | ||||||||
\(889\) | 45561.3 | 0.00193349 | ||||||||
\(890\) | −7.36291e6 | −0.311583 | ||||||||
\(891\) | −2.66066e7 | −1.12278 | ||||||||
\(892\) | 1.35008e7 | 0.568130 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 640313. | 0.0267947 | ||||||||
\(895\) | −1.73414e7 | −0.723646 | ||||||||
\(896\) | 1.54869e6 | 0.0644456 | ||||||||
\(897\) | 4.41311e6 | 0.183132 | ||||||||
\(898\) | 2.00524e7 | 0.829803 | ||||||||
\(899\) | −8.63534e6 | −0.356353 | ||||||||
\(900\) | −4.31923e6 | −0.177746 | ||||||||
\(901\) | 7.03698e7 | 2.88785 | ||||||||
\(902\) | −4.49158e6 | −0.183816 | ||||||||
\(903\) | 234243. | 0.00955976 | ||||||||
\(904\) | −7.44723e6 | −0.303092 | ||||||||
\(905\) | 2.76522e6 | 0.112230 | ||||||||
\(906\) | −396867. | −0.0160629 | ||||||||
\(907\) | −1.53315e7 | −0.618824 | −0.309412 | − | 0.950928i | \(-0.600132\pi\) | ||||
−0.309412 | + | 0.950928i | \(0.600132\pi\) | |||||||
\(908\) | −1.96117e7 | −0.789406 | ||||||||
\(909\) | −1.54762e6 | −0.0621234 | ||||||||
\(910\) | 2.42414e7 | 0.970407 | ||||||||
\(911\) | 1.73110e7 | 0.691076 | 0.345538 | − | 0.938405i | \(-0.387696\pi\) | ||||
0.345538 | + | 0.938405i | \(0.387696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.70262e7 | 1.86708 | ||||||||
\(914\) | −2.77459e7 | −1.09858 | ||||||||
\(915\) | −781957. | −0.0308766 | ||||||||
\(916\) | 1.41985e7 | 0.559119 | ||||||||
\(917\) | 8.66872e6 | 0.340433 | ||||||||
\(918\) | −4.80258e6 | −0.188091 | ||||||||
\(919\) | −2.77310e7 | −1.08312 | −0.541560 | − | 0.840662i | \(-0.682166\pi\) | ||||
−0.541560 | + | 0.840662i | \(0.682166\pi\) | |||||||
\(920\) | 1.60271e7 | 0.624289 | ||||||||
\(921\) | 1.66782e6 | 0.0647889 | ||||||||
\(922\) | 1.99701e7 | 0.773664 | ||||||||
\(923\) | 6.76281e7 | 2.61290 | ||||||||
\(924\) | −808127. | −0.0311387 | ||||||||
\(925\) | 1.96672e6 | 0.0755769 | ||||||||
\(926\) | −1.06026e7 | −0.406336 | ||||||||
\(927\) | 3.55046e7 | 1.35702 | ||||||||
\(928\) | 7.51245e6 | 0.286359 | ||||||||
\(929\) | 5.06392e7 | 1.92508 | 0.962538 | − | 0.271148i | \(-0.0874032\pi\) | ||||
0.962538 | + | 0.271148i | \(0.0874032\pi\) | |||||||
\(930\) | 357564. | 0.0135565 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.25505e6 | 0.273590 | ||||||||
\(933\) | −1.06665e6 | −0.0401158 | ||||||||
\(934\) | 3.07402e7 | 1.15303 | ||||||||
\(935\) | 6.34162e7 | 2.37231 | ||||||||
\(936\) | 1.52233e7 | 0.567963 | ||||||||
\(937\) | 7.26908e6 | 0.270477 | 0.135239 | − | 0.990813i | \(-0.456820\pi\) | ||||
0.135239 | + | 0.990813i | \(0.456820\pi\) | |||||||
\(938\) | 1.08254e7 | 0.401733 | ||||||||
\(939\) | 2.12189e6 | 0.0785343 | ||||||||
\(940\) | −1.32691e7 | −0.489805 | ||||||||
\(941\) | 4.59306e7 | 1.69094 | 0.845469 | − | 0.534025i | \(-0.179321\pi\) | ||||
0.845469 | + | 0.534025i | \(0.179321\pi\) | |||||||
\(942\) | −378245. | −0.0138882 | ||||||||
\(943\) | −9.42123e6 | −0.345007 | ||||||||
\(944\) | 2.36446e6 | 0.0863577 | ||||||||
\(945\) | 3.47904e6 | 0.126730 | ||||||||
\(946\) | −3.89578e6 | −0.141536 | ||||||||
\(947\) | 3.02687e7 | 1.09678 | 0.548388 | − | 0.836224i | \(-0.315242\pi\) | ||||
0.548388 | + | 0.836224i | \(0.315242\pi\) | |||||||
\(948\) | 410091. | 0.0148204 | ||||||||
\(949\) | −3.56848e7 | −1.28623 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −707025. | −0.0253503 | ||||||||
\(952\) | 1.28533e7 | 0.459646 | ||||||||
\(953\) | −2.24045e7 | −0.799104 | −0.399552 | − | 0.916710i | \(-0.630834\pi\) | ||||
−0.399552 | + | 0.916710i | \(0.630834\pi\) | |||||||
\(954\) | −3.20128e7 | −1.13881 | ||||||||
\(955\) | −6.18771e7 | −2.19544 | ||||||||
\(956\) | −2.73435e6 | −0.0967629 | ||||||||
\(957\) | −3.92011e6 | −0.138362 | ||||||||
\(958\) | −2.68888e7 | −0.946580 | ||||||||
\(959\) | 2.22238e7 | 0.780317 | ||||||||
\(960\) | −311069. | −0.0108938 | ||||||||
\(961\) | −2.72437e7 | −0.951606 | ||||||||
\(962\) | −6.93182e6 | −0.241496 | ||||||||
\(963\) | −3.46715e7 | −1.20478 | ||||||||
\(964\) | 2.94892e6 | 0.102205 | ||||||||
\(965\) | 8.32533e6 | 0.287795 | ||||||||
\(966\) | −1.69507e6 | −0.0584447 | ||||||||
\(967\) | 1.23627e7 | 0.425153 | 0.212577 | − | 0.977144i | \(-0.431814\pi\) | ||||
0.212577 | + | 0.977144i | \(0.431814\pi\) | |||||||
\(968\) | 3.13300e6 | 0.107466 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.10444e7 | −0.718138 | ||||||||
\(971\) | 4.47561e7 | 1.52337 | 0.761683 | − | 0.647950i | \(-0.224373\pi\) | ||||
0.761683 | + | 0.647950i | \(0.224373\pi\) | |||||||
\(972\) | 3.28026e6 | 0.111364 | ||||||||
\(973\) | 7.16926e6 | 0.242769 | ||||||||
\(974\) | 3.08110e7 | 1.04066 | ||||||||
\(975\) | −1.28227e6 | −0.0431984 | ||||||||
\(976\) | 2.63589e6 | 0.0885731 | ||||||||
\(977\) | 1.47843e7 | 0.495524 | 0.247762 | − | 0.968821i | \(-0.420305\pi\) | ||||
0.247762 | + | 0.968821i | \(0.420305\pi\) | |||||||
\(978\) | 2.26275e6 | 0.0756466 | ||||||||
\(979\) | −1.29512e7 | −0.431870 | ||||||||
\(980\) | 8.20366e6 | 0.272861 | ||||||||
\(981\) | −2.42985e7 | −0.806135 | ||||||||
\(982\) | −8.20795e6 | −0.271616 | ||||||||
\(983\) | −1.47485e7 | −0.486814 | −0.243407 | − | 0.969924i | \(-0.578265\pi\) | ||||
−0.243407 | + | 0.969924i | \(0.578265\pi\) | |||||||
\(984\) | 182856. | 0.00602033 | ||||||||
\(985\) | 4.72520e7 | 1.55178 | ||||||||
\(986\) | 6.23497e7 | 2.04241 | ||||||||
\(987\) | 1.40338e6 | 0.0458545 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.17150e6 | −0.265651 | ||||||||
\(990\) | −2.88494e7 | −0.935511 | ||||||||
\(991\) | 2.53843e7 | 0.821072 | 0.410536 | − | 0.911844i | \(-0.365342\pi\) | ||||
0.410536 | + | 0.911844i | \(0.365342\pi\) | |||||||
\(992\) | −1.20531e6 | −0.0388883 | ||||||||
\(993\) | −675247. | −0.0217315 | ||||||||
\(994\) | −2.59759e7 | −0.833881 | ||||||||
\(995\) | 8.77076e6 | 0.280853 | ||||||||
\(996\) | −1.91447e6 | −0.0611505 | ||||||||
\(997\) | −2.62082e7 | −0.835024 | −0.417512 | − | 0.908671i | \(-0.637098\pi\) | ||||
−0.417512 | + | 0.908671i | \(0.637098\pi\) | |||||||
\(998\) | 2.48257e7 | 0.788998 | ||||||||
\(999\) | −994830. | −0.0315381 |
(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 | 722.6.a.r.1.8 | 15 | ||
19.6 | even | 9 | 38.6.e.b.17.3 | yes | 30 | ||
19.16 | even | 9 | 38.6.e.b.9.3 | ✓ | 30 | ||
19.18 | odd | 2 | 722.6.a.q.1.8 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.9.3 | ✓ | 30 | 19.16 | even | 9 | ||
38.6.e.b.17.3 | yes | 30 | 19.6 | even | 9 | ||
722.6.a.q.1.8 | 15 | 19.18 | odd | 2 | |||
722.6.a.r.1.8 | 15 | 1.1 | even | 1 | trivial |