Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + 7583055 x^{2} + 5935300 x - 22888100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(10.2693\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.26930 | −1.63860 | −0.819298 | − | 0.573368i | \(-0.805637\pi\) | ||||
−0.819298 | + | 0.573368i | \(0.805637\pi\) | |||||||
\(3\) | 1.27429 | 0.0817458 | 0.0408729 | − | 0.999164i | \(-0.486986\pi\) | ||||
0.0408729 | + | 0.999164i | \(0.486986\pi\) | |||||||
\(4\) | 53.9199 | 1.68500 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −11.8118 | −0.133948 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −203.182 | −1.12243 | ||||||||
\(9\) | −241.376 | −0.993318 | ||||||||
\(10\) | −231.732 | −0.732802 | ||||||||
\(11\) | 478.980 | 1.19354 | 0.596768 | − | 0.802414i | \(-0.296451\pi\) | ||||
0.596768 | + | 0.802414i | \(0.296451\pi\) | |||||||
\(12\) | 68.7096 | 0.137741 | ||||||||
\(13\) | −203.039 | −0.333213 | −0.166607 | − | 0.986023i | \(-0.553281\pi\) | ||||
−0.166607 | + | 0.986023i | \(0.553281\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 31.8573 | 0.0365578 | ||||||||
\(16\) | 157.917 | 0.154216 | ||||||||
\(17\) | 854.151 | 0.716824 | 0.358412 | − | 0.933564i | \(-0.383318\pi\) | ||||
0.358412 | + | 0.933564i | \(0.383318\pi\) | |||||||
\(18\) | 2237.39 | 1.62765 | ||||||||
\(19\) | 1385.35 | 0.880389 | 0.440195 | − | 0.897902i | \(-0.354909\pi\) | ||||
0.440195 | + | 0.897902i | \(0.354909\pi\) | |||||||
\(20\) | 1348.00 | 0.753553 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4439.81 | −1.95572 | ||||||||
\(23\) | 2414.39 | 0.951674 | 0.475837 | − | 0.879533i | \(-0.342145\pi\) | ||||
0.475837 | + | 0.879533i | \(0.342145\pi\) | |||||||
\(24\) | −258.913 | −0.0917541 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1882.03 | 0.546002 | ||||||||
\(27\) | −617.236 | −0.162945 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4207.61 | −0.929053 | −0.464526 | − | 0.885559i | \(-0.653775\pi\) | ||||
−0.464526 | + | 0.885559i | \(0.653775\pi\) | |||||||
\(30\) | −295.295 | −0.0599035 | ||||||||
\(31\) | −7478.19 | −1.39763 | −0.698815 | − | 0.715303i | \(-0.746289\pi\) | ||||
−0.698815 | + | 0.715303i | \(0.746289\pi\) | |||||||
\(32\) | 5038.04 | 0.869734 | ||||||||
\(33\) | 610.360 | 0.0975666 | ||||||||
\(34\) | −7917.38 | −1.17458 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13015.0 | −1.67374 | ||||||||
\(37\) | 9593.09 | 1.15200 | 0.576002 | − | 0.817448i | \(-0.304612\pi\) | ||||
0.576002 | + | 0.817448i | \(0.304612\pi\) | |||||||
\(38\) | −12841.2 | −1.44260 | ||||||||
\(39\) | −258.731 | −0.0272388 | ||||||||
\(40\) | −5079.55 | −0.501967 | ||||||||
\(41\) | −5503.30 | −0.511285 | −0.255643 | − | 0.966771i | \(-0.582287\pi\) | ||||
−0.255643 | + | 0.966771i | \(0.582287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5020.82 | −0.414099 | −0.207049 | − | 0.978331i | \(-0.566386\pi\) | ||||
−0.207049 | + | 0.978331i | \(0.566386\pi\) | |||||||
\(44\) | 25826.5 | 2.01110 | ||||||||
\(45\) | −6034.40 | −0.444225 | ||||||||
\(46\) | −22379.7 | −1.55941 | ||||||||
\(47\) | −23703.5 | −1.56520 | −0.782598 | − | 0.622527i | \(-0.786106\pi\) | ||||
−0.782598 | + | 0.622527i | \(0.786106\pi\) | |||||||
\(48\) | 201.232 | 0.0126065 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5793.31 | −0.327719 | ||||||||
\(51\) | 1088.44 | 0.0585973 | ||||||||
\(52\) | −10947.9 | −0.561463 | ||||||||
\(53\) | −10841.4 | −0.530144 | −0.265072 | − | 0.964229i | \(-0.585396\pi\) | ||||
−0.265072 | + | 0.964229i | \(0.585396\pi\) | |||||||
\(54\) | 5721.35 | 0.267002 | ||||||||
\(55\) | 11974.5 | 0.533766 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1765.34 | 0.0719681 | ||||||||
\(58\) | 39001.6 | 1.52234 | ||||||||
\(59\) | 10487.3 | 0.392224 | 0.196112 | − | 0.980582i | \(-0.437168\pi\) | ||||
0.196112 | + | 0.980582i | \(0.437168\pi\) | |||||||
\(60\) | 1717.74 | 0.0615998 | ||||||||
\(61\) | 44185.5 | 1.52039 | 0.760196 | − | 0.649694i | \(-0.225103\pi\) | ||||
0.760196 | + | 0.649694i | \(0.225103\pi\) | |||||||
\(62\) | 69317.5 | 2.29015 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51752.4 | −1.57936 | ||||||||
\(65\) | −5075.99 | −0.149017 | ||||||||
\(66\) | −5657.61 | −0.159872 | ||||||||
\(67\) | 53131.2 | 1.44598 | 0.722991 | − | 0.690857i | \(-0.242767\pi\) | ||||
0.722991 | + | 0.690857i | \(0.242767\pi\) | |||||||
\(68\) | 46055.7 | 1.20785 | ||||||||
\(69\) | 3076.64 | 0.0777954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15897.1 | 0.374258 | 0.187129 | − | 0.982335i | \(-0.440082\pi\) | ||||
0.187129 | + | 0.982335i | \(0.440082\pi\) | |||||||
\(72\) | 49043.3 | 1.11493 | ||||||||
\(73\) | 77627.1 | 1.70493 | 0.852464 | − | 0.522786i | \(-0.175107\pi\) | ||||
0.852464 | + | 0.522786i | \(0.175107\pi\) | |||||||
\(74\) | −88921.2 | −1.88767 | ||||||||
\(75\) | 796.432 | 0.0163492 | ||||||||
\(76\) | 74697.8 | 1.48345 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2398.26 | 0.0446333 | ||||||||
\(79\) | −86136.0 | −1.55280 | −0.776402 | − | 0.630238i | \(-0.782957\pi\) | ||||
−0.776402 | + | 0.630238i | \(0.782957\pi\) | |||||||
\(80\) | 3947.92 | 0.0689674 | ||||||||
\(81\) | 57867.9 | 0.979998 | ||||||||
\(82\) | 51011.7 | 0.837790 | ||||||||
\(83\) | −52126.2 | −0.830541 | −0.415271 | − | 0.909698i | \(-0.636313\pi\) | ||||
−0.415271 | + | 0.909698i | \(0.636313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21353.8 | 0.320573 | ||||||||
\(86\) | 46539.5 | 0.678540 | ||||||||
\(87\) | −5361.72 | −0.0759461 | ||||||||
\(88\) | −97320.0 | −1.33966 | ||||||||
\(89\) | 23299.1 | 0.311791 | 0.155896 | − | 0.987774i | \(-0.450174\pi\) | ||||
0.155896 | + | 0.987774i | \(0.450174\pi\) | |||||||
\(90\) | 55934.7 | 0.727905 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 130184. | 1.60357 | ||||||||
\(93\) | −9529.38 | −0.114250 | ||||||||
\(94\) | 219715. | 2.56472 | ||||||||
\(95\) | 34633.7 | 0.393722 | ||||||||
\(96\) | 6419.93 | 0.0710971 | ||||||||
\(97\) | 180093. | 1.94343 | 0.971714 | − | 0.236161i | \(-0.0758893\pi\) | ||||
0.971714 | + | 0.236161i | \(0.0758893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −115614. | −1.18556 | ||||||||
\(100\) | 33699.9 | 0.336999 | ||||||||
\(101\) | 107548. | 1.04906 | 0.524531 | − | 0.851392i | \(-0.324241\pi\) | ||||
0.524531 | + | 0.851392i | \(0.324241\pi\) | |||||||
\(102\) | −10089.0 | −0.0960173 | ||||||||
\(103\) | 172551. | 1.60259 | 0.801297 | − | 0.598266i | \(-0.204144\pi\) | ||||
0.801297 | + | 0.598266i | \(0.204144\pi\) | |||||||
\(104\) | 41253.9 | 0.374009 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 100492. | 0.868691 | ||||||||
\(107\) | 14341.5 | 0.121098 | 0.0605488 | − | 0.998165i | \(-0.480715\pi\) | ||||
0.0605488 | + | 0.998165i | \(0.480715\pi\) | |||||||
\(108\) | −33281.3 | −0.274562 | ||||||||
\(109\) | −190351. | −1.53458 | −0.767290 | − | 0.641300i | \(-0.778395\pi\) | ||||
−0.767290 | + | 0.641300i | \(0.778395\pi\) | |||||||
\(110\) | −110995. | −0.874626 | ||||||||
\(111\) | 12224.4 | 0.0941715 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 66701.8 | 0.491407 | 0.245704 | − | 0.969345i | \(-0.420981\pi\) | ||||
0.245704 | + | 0.969345i | \(0.420981\pi\) | |||||||
\(114\) | −16363.4 | −0.117927 | ||||||||
\(115\) | 60359.8 | 0.425602 | ||||||||
\(116\) | −226874. | −1.56545 | ||||||||
\(117\) | 49008.9 | 0.330986 | ||||||||
\(118\) | −97209.9 | −0.642696 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6472.82 | −0.0410337 | ||||||||
\(121\) | 68370.8 | 0.424529 | ||||||||
\(122\) | −409569. | −2.49131 | ||||||||
\(123\) | −7012.80 | −0.0417954 | ||||||||
\(124\) | −403223. | −2.35500 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 156626. | 0.861698 | 0.430849 | − | 0.902424i | \(-0.358214\pi\) | ||||
0.430849 | + | 0.902424i | \(0.358214\pi\) | |||||||
\(128\) | 318491. | 1.71820 | ||||||||
\(129\) | −6397.99 | −0.0338508 | ||||||||
\(130\) | 47050.8 | 0.244179 | ||||||||
\(131\) | 71582.9 | 0.364444 | 0.182222 | − | 0.983257i | \(-0.441671\pi\) | ||||
0.182222 | + | 0.983257i | \(0.441671\pi\) | |||||||
\(132\) | 32910.5 | 0.164399 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −492489. | −2.36938 | ||||||||
\(135\) | −15430.9 | −0.0728714 | ||||||||
\(136\) | −173548. | −0.804586 | ||||||||
\(137\) | 299786. | 1.36462 | 0.682308 | − | 0.731065i | \(-0.260976\pi\) | ||||
0.682308 | + | 0.731065i | \(0.260976\pi\) | |||||||
\(138\) | −28518.3 | −0.127475 | ||||||||
\(139\) | 52166.8 | 0.229012 | 0.114506 | − | 0.993423i | \(-0.463472\pi\) | ||||
0.114506 | + | 0.993423i | \(0.463472\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30205.2 | −0.127948 | ||||||||
\(142\) | −147355. | −0.613258 | ||||||||
\(143\) | −97251.8 | −0.397702 | ||||||||
\(144\) | −38117.4 | −0.153185 | ||||||||
\(145\) | −105190. | −0.415485 | ||||||||
\(146\) | −719549. | −2.79369 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 517258. | 1.94112 | ||||||||
\(149\) | −432166. | −1.59472 | −0.797361 | − | 0.603502i | \(-0.793772\pi\) | ||||
−0.797361 | + | 0.603502i | \(0.793772\pi\) | |||||||
\(150\) | −7382.36 | −0.0267897 | ||||||||
\(151\) | 224235. | 0.800315 | 0.400157 | − | 0.916446i | \(-0.368955\pi\) | ||||
0.400157 | + | 0.916446i | \(0.368955\pi\) | |||||||
\(152\) | −281477. | −0.988177 | ||||||||
\(153\) | −206172. | −0.712034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −186955. | −0.625039 | ||||||||
\(156\) | −13950.8 | −0.0458972 | ||||||||
\(157\) | 235433. | 0.762287 | 0.381143 | − | 0.924516i | \(-0.375530\pi\) | ||||
0.381143 | + | 0.924516i | \(0.375530\pi\) | |||||||
\(158\) | 798420. | 2.54442 | ||||||||
\(159\) | −13815.0 | −0.0433370 | ||||||||
\(160\) | 125951. | 0.388957 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −536395. | −1.60582 | ||||||||
\(163\) | 2875.40 | 0.00847675 | 0.00423837 | − | 0.999991i | \(-0.498651\pi\) | ||||
0.00423837 | + | 0.999991i | \(0.498651\pi\) | |||||||
\(164\) | −296737. | −0.861513 | ||||||||
\(165\) | 15259.0 | 0.0436331 | ||||||||
\(166\) | 483174. | 1.36092 | ||||||||
\(167\) | −402505. | −1.11681 | −0.558406 | − | 0.829568i | \(-0.688587\pi\) | ||||
−0.558406 | + | 0.829568i | \(0.688587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −330068. | −0.888969 | ||||||||
\(170\) | −197935. | −0.525290 | ||||||||
\(171\) | −334390. | −0.874506 | ||||||||
\(172\) | −270722. | −0.697755 | ||||||||
\(173\) | 599804. | 1.52368 | 0.761841 | − | 0.647764i | \(-0.224296\pi\) | ||||
0.761841 | + | 0.647764i | \(0.224296\pi\) | |||||||
\(174\) | 49699.3 | 0.124445 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 75639.0 | 0.184062 | ||||||||
\(177\) | 13363.9 | 0.0320626 | ||||||||
\(178\) | −215966. | −0.510900 | ||||||||
\(179\) | 640796. | 1.49481 | 0.747407 | − | 0.664366i | \(-0.231298\pi\) | ||||
0.747407 | + | 0.664366i | \(0.231298\pi\) | |||||||
\(180\) | −325374. | −0.748518 | ||||||||
\(181\) | 640997. | 1.45432 | 0.727160 | − | 0.686468i | \(-0.240840\pi\) | ||||
0.727160 | + | 0.686468i | \(0.240840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 56305.2 | 0.124286 | ||||||||
\(184\) | −490561. | −1.06819 | ||||||||
\(185\) | 239827. | 0.515192 | ||||||||
\(186\) | 88330.7 | 0.187210 | ||||||||
\(187\) | 409121. | 0.855555 | ||||||||
\(188\) | −1.27809e6 | −2.63735 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −321030. | −0.645151 | ||||||||
\(191\) | −795460. | −1.57774 | −0.788870 | − | 0.614561i | \(-0.789333\pi\) | ||||
−0.788870 | + | 0.614561i | \(0.789333\pi\) | |||||||
\(192\) | −65947.7 | −0.129106 | ||||||||
\(193\) | 164019. | 0.316958 | 0.158479 | − | 0.987362i | \(-0.449341\pi\) | ||||
0.158479 | + | 0.987362i | \(0.449341\pi\) | |||||||
\(194\) | −1.66934e6 | −3.18449 | ||||||||
\(195\) | −6468.28 | −0.0121816 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −79137.4 | −0.145283 | −0.0726417 | − | 0.997358i | \(-0.523143\pi\) | ||||
−0.0726417 | + | 0.997358i | \(0.523143\pi\) | |||||||
\(198\) | 1.07166e6 | 1.94265 | ||||||||
\(199\) | 990048. | 1.77224 | 0.886122 | − | 0.463451i | \(-0.153389\pi\) | ||||
0.886122 | + | 0.463451i | \(0.153389\pi\) | |||||||
\(200\) | −126989. | −0.224486 | ||||||||
\(201\) | 67704.6 | 0.118203 | ||||||||
\(202\) | −996899. | −1.71899 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 58688.4 | 0.0987363 | ||||||||
\(205\) | −137582. | −0.228654 | ||||||||
\(206\) | −1.59942e6 | −2.62600 | ||||||||
\(207\) | −582777. | −0.945315 | ||||||||
\(208\) | −32063.4 | −0.0513867 | ||||||||
\(209\) | 663554. | 1.05078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 983192. | 1.52031 | 0.760155 | − | 0.649742i | \(-0.225123\pi\) | ||||
0.760155 | + | 0.649742i | \(0.225123\pi\) | |||||||
\(212\) | −584564. | −0.893290 | ||||||||
\(213\) | 20257.5 | 0.0305940 | ||||||||
\(214\) | −132936. | −0.198430 | ||||||||
\(215\) | −125521. | −0.185191 | ||||||||
\(216\) | 125411. | 0.182895 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.76442e6 | 2.51456 | ||||||||
\(219\) | 98919.5 | 0.139371 | ||||||||
\(220\) | 645663. | 0.899393 | ||||||||
\(221\) | −173426. | −0.238855 | ||||||||
\(222\) | −113311. | −0.154309 | ||||||||
\(223\) | 285245. | 0.384110 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −150860. | −0.198664 | ||||||||
\(226\) | −618279. | −0.805218 | ||||||||
\(227\) | 949950. | 1.22359 | 0.611795 | − | 0.791016i | \(-0.290448\pi\) | ||||
0.611795 | + | 0.791016i | \(0.290448\pi\) | |||||||
\(228\) | 95186.7 | 0.121266 | ||||||||
\(229\) | −1.05143e6 | −1.32493 | −0.662463 | − | 0.749094i | \(-0.730489\pi\) | ||||
−0.662463 | + | 0.749094i | \(0.730489\pi\) | |||||||
\(230\) | −559493. | −0.697389 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 854910. | 1.04280 | ||||||||
\(233\) | −168689. | −0.203562 | −0.101781 | − | 0.994807i | \(-0.532454\pi\) | ||||
−0.101781 | + | 0.994807i | \(0.532454\pi\) | |||||||
\(234\) | −454278. | −0.542353 | ||||||||
\(235\) | −592589. | −0.699977 | ||||||||
\(236\) | 565474. | 0.660895 | ||||||||
\(237\) | −109762. | −0.126935 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 658618. | 0.745829 | 0.372914 | − | 0.927866i | \(-0.378359\pi\) | ||||
0.372914 | + | 0.927866i | \(0.378359\pi\) | |||||||
\(240\) | 5030.80 | 0.00563779 | ||||||||
\(241\) | 314422. | 0.348715 | 0.174358 | − | 0.984682i | \(-0.444215\pi\) | ||||
0.174358 | + | 0.984682i | \(0.444215\pi\) | |||||||
\(242\) | −633749. | −0.695631 | ||||||||
\(243\) | 223729. | 0.243056 | ||||||||
\(244\) | 2.38248e6 | 2.56185 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 65003.7 | 0.0684858 | ||||||||
\(247\) | −281280. | −0.293357 | ||||||||
\(248\) | 1.51943e6 | 1.56874 | ||||||||
\(249\) | −66424.0 | −0.0678932 | ||||||||
\(250\) | −144833. | −0.146560 | ||||||||
\(251\) | −18719.5 | −0.0187547 | −0.00937736 | − | 0.999956i | \(-0.502985\pi\) | ||||
−0.00937736 | + | 0.999956i | \(0.502985\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15645e6 | 1.13586 | ||||||||
\(254\) | −1.45181e6 | −1.41197 | ||||||||
\(255\) | 27210.9 | 0.0262055 | ||||||||
\(256\) | −1.29611e6 | −1.23607 | ||||||||
\(257\) | 638749. | 0.603251 | 0.301625 | − | 0.953427i | \(-0.402471\pi\) | ||||
0.301625 | + | 0.953427i | \(0.402471\pi\) | |||||||
\(258\) | 59304.9 | 0.0554678 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −273697. | −0.251094 | ||||||||
\(261\) | 1.01562e6 | 0.922844 | ||||||||
\(262\) | −663524. | −0.597177 | ||||||||
\(263\) | 32605.9 | 0.0290674 | 0.0145337 | − | 0.999894i | \(-0.495374\pi\) | ||||
0.0145337 | + | 0.999894i | \(0.495374\pi\) | |||||||
\(264\) | −124014. | −0.109512 | ||||||||
\(265\) | −271034. | −0.237088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29689.8 | 0.0254876 | ||||||||
\(268\) | 2.86483e6 | 2.43647 | ||||||||
\(269\) | −137381. | −0.115757 | −0.0578785 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578785 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(270\) | 143034. | 0.119407 | ||||||||
\(271\) | 1.08503e6 | 0.897467 | 0.448733 | − | 0.893666i | \(-0.351875\pi\) | ||||
0.448733 | + | 0.893666i | \(0.351875\pi\) | |||||||
\(272\) | 134885. | 0.110545 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.77881e6 | −2.23605 | ||||||||
\(275\) | 299362. | 0.238707 | ||||||||
\(276\) | 165892. | 0.131085 | ||||||||
\(277\) | −1.19753e6 | −0.937753 | −0.468877 | − | 0.883264i | \(-0.655341\pi\) | ||||
−0.468877 | + | 0.883264i | \(0.655341\pi\) | |||||||
\(278\) | −483550. | −0.375257 | ||||||||
\(279\) | 1.80506e6 | 1.38829 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 864879. | 0.653415 | 0.326708 | − | 0.945125i | \(-0.394061\pi\) | ||||
0.326708 | + | 0.945125i | \(0.394061\pi\) | |||||||
\(282\) | 279981. | 0.209655 | ||||||||
\(283\) | 1.34159e6 | 0.995757 | 0.497879 | − | 0.867247i | \(-0.334112\pi\) | ||||
0.497879 | + | 0.867247i | \(0.334112\pi\) | |||||||
\(284\) | 857168. | 0.630623 | ||||||||
\(285\) | 44133.4 | 0.0321851 | ||||||||
\(286\) | 901456. | 0.651673 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.21606e6 | −0.863923 | ||||||||
\(289\) | −690283. | −0.486164 | ||||||||
\(290\) | 975039. | 0.680812 | ||||||||
\(291\) | 229491. | 0.158867 | ||||||||
\(292\) | 4.18564e6 | 2.87280 | ||||||||
\(293\) | −669371. | −0.455510 | −0.227755 | − | 0.973718i | \(-0.573139\pi\) | ||||
−0.227755 | + | 0.973718i | \(0.573139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 262183. | 0.175408 | ||||||||
\(296\) | −1.94914e6 | −1.29305 | ||||||||
\(297\) | −295644. | −0.194481 | ||||||||
\(298\) | 4.00588e6 | 2.61311 | ||||||||
\(299\) | −490217. | −0.317110 | ||||||||
\(300\) | 42943.5 | 0.0275483 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.07850e6 | −1.31139 | ||||||||
\(303\) | 137048. | 0.0857563 | ||||||||
\(304\) | 218770. | 0.135770 | ||||||||
\(305\) | 1.10464e6 | 0.679940 | ||||||||
\(306\) | 1.91107e6 | 1.16674 | ||||||||
\(307\) | 134224. | 0.0812804 | 0.0406402 | − | 0.999174i | \(-0.487060\pi\) | ||||
0.0406402 | + | 0.999174i | \(0.487060\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 219880. | 0.131005 | ||||||||
\(310\) | 1.73294e6 | 1.02419 | ||||||||
\(311\) | −395022. | −0.231590 | −0.115795 | − | 0.993273i | \(-0.536942\pi\) | ||||
−0.115795 | + | 0.993273i | \(0.536942\pi\) | |||||||
\(312\) | 52569.5 | 0.0305737 | ||||||||
\(313\) | −1.37654e6 | −0.794195 | −0.397098 | − | 0.917776i | \(-0.629983\pi\) | ||||
−0.397098 | + | 0.917776i | \(0.629983\pi\) | |||||||
\(314\) | −2.18230e6 | −1.24908 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.64444e6 | −2.61647 | ||||||||
\(317\) | −1.68888e6 | −0.943951 | −0.471976 | − | 0.881612i | \(-0.656459\pi\) | ||||
−0.471976 | + | 0.881612i | \(0.656459\pi\) | |||||||
\(318\) | 128056. | 0.0710119 | ||||||||
\(319\) | −2.01536e6 | −1.10886 | ||||||||
\(320\) | −1.29381e6 | −0.706311 | ||||||||
\(321\) | 18275.3 | 0.00989922 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.18330e6 | 0.631084 | ||||||||
\(324\) | 3.12023e6 | 1.65129 | ||||||||
\(325\) | −126900. | −0.0666426 | ||||||||
\(326\) | −26652.9 | −0.0138900 | ||||||||
\(327\) | −242563. | −0.125445 | ||||||||
\(328\) | 1.11817e6 | 0.573883 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −141440. | −0.0714970 | ||||||||
\(331\) | 1.59017e6 | 0.797760 | 0.398880 | − | 0.917003i | \(-0.369399\pi\) | ||||
0.398880 | + | 0.917003i | \(0.369399\pi\) | |||||||
\(332\) | −2.81064e6 | −1.39946 | ||||||||
\(333\) | −2.31554e6 | −1.14431 | ||||||||
\(334\) | 3.73094e6 | 1.83000 | ||||||||
\(335\) | 1.32828e6 | 0.646663 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −823436. | −0.394962 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(338\) | 3.05950e6 | 1.45666 | ||||||||
\(339\) | 84997.5 | 0.0401705 | ||||||||
\(340\) | 1.15139e6 | 0.540165 | ||||||||
\(341\) | −3.58190e6 | −1.66812 | ||||||||
\(342\) | 3.09956e6 | 1.43296 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.02014e6 | 0.464797 | ||||||||
\(345\) | 76915.9 | 0.0347911 | ||||||||
\(346\) | −5.55977e6 | −2.49670 | ||||||||
\(347\) | −2.62964e6 | −1.17239 | −0.586195 | − | 0.810170i | \(-0.699375\pi\) | ||||
−0.586195 | + | 0.810170i | \(0.699375\pi\) | |||||||
\(348\) | −289103. | −0.127969 | ||||||||
\(349\) | −3.26813e6 | −1.43627 | −0.718134 | − | 0.695905i | \(-0.755003\pi\) | ||||
−0.718134 | + | 0.695905i | \(0.755003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 125323. | 0.0542955 | ||||||||
\(352\) | 2.41312e6 | 1.03806 | ||||||||
\(353\) | −621440. | −0.265438 | −0.132719 | − | 0.991154i | \(-0.542371\pi\) | ||||
−0.132719 | + | 0.991154i | \(0.542371\pi\) | |||||||
\(354\) | −123874. | −0.0525377 | ||||||||
\(355\) | 397427. | 0.167373 | ||||||||
\(356\) | 1.25628e6 | 0.525367 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.93973e6 | −2.44940 | ||||||||
\(359\) | 1.34486e6 | 0.550734 | 0.275367 | − | 0.961339i | \(-0.411201\pi\) | ||||
0.275367 | + | 0.961339i | \(0.411201\pi\) | |||||||
\(360\) | 1.22608e6 | 0.498612 | ||||||||
\(361\) | −556911. | −0.224915 | ||||||||
\(362\) | −5.94159e6 | −2.38304 | ||||||||
\(363\) | 87124.3 | 0.0347034 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.94068e6 | 0.762467 | ||||||||
\(366\) | −521910. | −0.203654 | ||||||||
\(367\) | −2.75801e6 | −1.06888 | −0.534442 | − | 0.845205i | \(-0.679478\pi\) | ||||
−0.534442 | + | 0.845205i | \(0.679478\pi\) | |||||||
\(368\) | 381273. | 0.146763 | ||||||||
\(369\) | 1.32836e6 | 0.507869 | ||||||||
\(370\) | −2.22303e6 | −0.844192 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −513823. | −0.192511 | ||||||||
\(373\) | 3.29037e6 | 1.22454 | 0.612269 | − | 0.790649i | \(-0.290257\pi\) | ||||
0.612269 | + | 0.790649i | \(0.290257\pi\) | |||||||
\(374\) | −3.79227e6 | −1.40191 | ||||||||
\(375\) | 19910.8 | 0.00731157 | ||||||||
\(376\) | 4.81613e6 | 1.75683 | ||||||||
\(377\) | 854311. | 0.309573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.33527e6 | −0.477496 | −0.238748 | − | 0.971081i | \(-0.576737\pi\) | ||||
−0.238748 | + | 0.971081i | \(0.576737\pi\) | |||||||
\(380\) | 1.86744e6 | 0.663420 | ||||||||
\(381\) | 199587. | 0.0704402 | ||||||||
\(382\) | 7.37336e6 | 2.58528 | ||||||||
\(383\) | −3.37282e6 | −1.17489 | −0.587443 | − | 0.809266i | \(-0.699865\pi\) | ||||
−0.587443 | + | 0.809266i | \(0.699865\pi\) | |||||||
\(384\) | 405851. | 0.140455 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.52034e6 | −0.519366 | ||||||||
\(387\) | 1.21191e6 | 0.411332 | ||||||||
\(388\) | 9.71061e6 | 3.27467 | ||||||||
\(389\) | −3.46519e6 | −1.16105 | −0.580527 | − | 0.814241i | \(-0.697154\pi\) | ||||
−0.580527 | + | 0.814241i | \(0.697154\pi\) | |||||||
\(390\) | 59956.4 | 0.0199606 | ||||||||
\(391\) | 2.06226e6 | 0.682183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 91217.5 | 0.0297918 | ||||||||
\(394\) | 733548. | 0.238061 | ||||||||
\(395\) | −2.15340e6 | −0.694435 | ||||||||
\(396\) | −6.23391e6 | −1.99766 | ||||||||
\(397\) | −1.75508e6 | −0.558882 | −0.279441 | − | 0.960163i | \(-0.590149\pi\) | ||||
−0.279441 | + | 0.960163i | \(0.590149\pi\) | |||||||
\(398\) | −9.17705e6 | −2.90399 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 98698.0 | 0.0308431 | ||||||||
\(401\) | −5.12451e6 | −1.59145 | −0.795723 | − | 0.605661i | \(-0.792909\pi\) | ||||
−0.795723 | + | 0.605661i | \(0.792909\pi\) | |||||||
\(402\) | −627574. | −0.193687 | ||||||||
\(403\) | 1.51837e6 | 0.465708 | ||||||||
\(404\) | 5.79900e6 | 1.76766 | ||||||||
\(405\) | 1.44670e6 | 0.438268 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.59490e6 | 1.37496 | ||||||||
\(408\) | −221151. | −0.0657715 | ||||||||
\(409\) | 879358. | 0.259931 | 0.129965 | − | 0.991519i | \(-0.458513\pi\) | ||||
0.129965 | + | 0.991519i | \(0.458513\pi\) | |||||||
\(410\) | 1.27529e6 | 0.374671 | ||||||||
\(411\) | 382015. | 0.111552 | ||||||||
\(412\) | 9.30391e6 | 2.70037 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.40193e6 | 1.54899 | ||||||||
\(415\) | −1.30316e6 | −0.371429 | ||||||||
\(416\) | −1.02292e6 | −0.289807 | ||||||||
\(417\) | 66475.7 | 0.0187207 | ||||||||
\(418\) | −6.15068e6 | −1.72180 | ||||||||
\(419\) | −5.68610e6 | −1.58227 | −0.791133 | − | 0.611644i | \(-0.790508\pi\) | ||||
−0.791133 | + | 0.611644i | \(0.790508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 627448. | 0.172533 | 0.0862666 | − | 0.996272i | \(-0.472506\pi\) | ||||
0.0862666 | + | 0.996272i | \(0.472506\pi\) | |||||||
\(422\) | −9.11350e6 | −2.49117 | ||||||||
\(423\) | 5.72147e6 | 1.55474 | ||||||||
\(424\) | 2.20277e6 | 0.595050 | ||||||||
\(425\) | 533844. | 0.143365 | ||||||||
\(426\) | −187773. | −0.0501312 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 773292. | 0.204049 | ||||||||
\(429\) | −123927. | −0.0325105 | ||||||||
\(430\) | 1.16349e6 | 0.303452 | ||||||||
\(431\) | −953877. | −0.247343 | −0.123671 | − | 0.992323i | \(-0.539467\pi\) | ||||
−0.123671 | + | 0.992323i | \(0.539467\pi\) | |||||||
\(432\) | −97472.0 | −0.0251287 | ||||||||
\(433\) | 4.52050e6 | 1.15869 | 0.579344 | − | 0.815083i | \(-0.303309\pi\) | ||||
0.579344 | + | 0.815083i | \(0.303309\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −134043. | −0.0339641 | ||||||||
\(436\) | −1.02637e7 | −2.58576 | ||||||||
\(437\) | 3.34477e6 | 0.837844 | ||||||||
\(438\) | −916914. | −0.228372 | ||||||||
\(439\) | 6.99034e6 | 1.73116 | 0.865579 | − | 0.500772i | \(-0.166950\pi\) | ||||
0.865579 | + | 0.500772i | \(0.166950\pi\) | |||||||
\(440\) | −2.43300e6 | −0.599115 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.60754e6 | 0.391387 | ||||||||
\(443\) | −4.66063e6 | −1.12833 | −0.564164 | − | 0.825663i | \(-0.690801\pi\) | ||||
−0.564164 | + | 0.825663i | \(0.690801\pi\) | |||||||
\(444\) | 659137. | 0.158679 | ||||||||
\(445\) | 582478. | 0.139437 | ||||||||
\(446\) | −2.64402e6 | −0.629401 | ||||||||
\(447\) | −550706. | −0.130362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.40084e6 | 1.49838 | 0.749189 | − | 0.662357i | \(-0.230444\pi\) | ||||
0.749189 | + | 0.662357i | \(0.230444\pi\) | |||||||
\(450\) | 1.39837e6 | 0.325529 | ||||||||
\(451\) | −2.63597e6 | −0.610237 | ||||||||
\(452\) | 3.59655e6 | 0.828020 | ||||||||
\(453\) | 285740. | 0.0654224 | ||||||||
\(454\) | −8.80537e6 | −2.00497 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −358684. | −0.0807793 | ||||||||
\(457\) | 4.09410e6 | 0.916997 | 0.458498 | − | 0.888695i | \(-0.348387\pi\) | ||||
0.458498 | + | 0.888695i | \(0.348387\pi\) | |||||||
\(458\) | 9.74602e6 | 2.17102 | ||||||||
\(459\) | −527213. | −0.116803 | ||||||||
\(460\) | 3.25459e6 | 0.717137 | ||||||||
\(461\) | 7.91448e6 | 1.73448 | 0.867242 | − | 0.497887i | \(-0.165891\pi\) | ||||
0.867242 | + | 0.497887i | \(0.165891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.60789e6 | −0.998963 | −0.499482 | − | 0.866324i | \(-0.666476\pi\) | ||||
−0.499482 | + | 0.866324i | \(0.666476\pi\) | |||||||
\(464\) | −664452. | −0.143275 | ||||||||
\(465\) | −238235. | −0.0510943 | ||||||||
\(466\) | 1.56363e6 | 0.333555 | ||||||||
\(467\) | 3.90317e6 | 0.828181 | 0.414090 | − | 0.910236i | \(-0.364100\pi\) | ||||
0.414090 | + | 0.910236i | \(0.364100\pi\) | |||||||
\(468\) | 2.64255e6 | 0.557711 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.49288e6 | 1.14698 | ||||||||
\(471\) | 300010. | 0.0623137 | ||||||||
\(472\) | −2.13083e6 | −0.440244 | ||||||||
\(473\) | −2.40487e6 | −0.494242 | ||||||||
\(474\) | 1.01742e6 | 0.207996 | ||||||||
\(475\) | 865842. | 0.176078 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.61684e6 | 0.526601 | ||||||||
\(478\) | −6.10493e6 | −1.22211 | ||||||||
\(479\) | 4.42629e6 | 0.881457 | 0.440728 | − | 0.897640i | \(-0.354720\pi\) | ||||
0.440728 | + | 0.897640i | \(0.354720\pi\) | |||||||
\(480\) | 160498. | 0.0317956 | ||||||||
\(481\) | −1.94778e6 | −0.383863 | ||||||||
\(482\) | −2.91447e6 | −0.571403 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.68654e6 | 0.715329 | ||||||||
\(485\) | 4.50233e6 | 0.869127 | ||||||||
\(486\) | −2.07381e6 | −0.398271 | ||||||||
\(487\) | −2.22924e6 | −0.425926 | −0.212963 | − | 0.977060i | \(-0.568311\pi\) | ||||
−0.212963 | + | 0.977060i | \(0.568311\pi\) | |||||||
\(488\) | −8.97770e6 | −1.70654 | ||||||||
\(489\) | 3664.10 | 0.000692939 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 627714. | 0.117505 | 0.0587527 | − | 0.998273i | \(-0.481288\pi\) | ||||
0.0587527 | + | 0.998273i | \(0.481288\pi\) | |||||||
\(492\) | −378129. | −0.0704251 | ||||||||
\(493\) | −3.59393e6 | −0.665967 | ||||||||
\(494\) | 2.60727e6 | 0.480694 | ||||||||
\(495\) | −2.89036e6 | −0.530199 | ||||||||
\(496\) | −1.18093e6 | −0.215536 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 615704. | 0.111250 | ||||||||
\(499\) | 1.00327e6 | 0.180370 | 0.0901850 | − | 0.995925i | \(-0.471254\pi\) | ||||
0.0901850 | + | 0.995925i | \(0.471254\pi\) | |||||||
\(500\) | 842498. | 0.150711 | ||||||||
\(501\) | −512908. | −0.0912946 | ||||||||
\(502\) | 173517. | 0.0307314 | ||||||||
\(503\) | −904051. | −0.159321 | −0.0796605 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796605 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.68871e6 | 0.469154 | ||||||||
\(506\) | −1.07194e7 | −1.86121 | ||||||||
\(507\) | −420603. | −0.0726695 | ||||||||
\(508\) | 8.44526e6 | 1.45196 | ||||||||
\(509\) | −3.02145e6 | −0.516917 | −0.258458 | − | 0.966022i | \(-0.583215\pi\) | ||||
−0.258458 | + | 0.966022i | \(0.583215\pi\) | |||||||
\(510\) | −252226. | −0.0429403 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.82234e6 | 0.307223 | ||||||||
\(513\) | −855087. | −0.143455 | ||||||||
\(514\) | −5.92076e6 | −0.988484 | ||||||||
\(515\) | 4.31377e6 | 0.716702 | ||||||||
\(516\) | −344979. | −0.0570385 | ||||||||
\(517\) | −1.13535e7 | −1.86812 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 764325. | 0.124555 | ||||||||
\(520\) | 1.03135e6 | 0.167262 | ||||||||
\(521\) | 8882.28 | 0.00143361 | 0.000716804 | − | 1.00000i | \(-0.499772\pi\) | ||||
0.000716804 | 1.00000i | \(0.499772\pi\) | ||||||||
\(522\) | −9.41405e6 | −1.51217 | ||||||||
\(523\) | −9.60588e6 | −1.53562 | −0.767809 | − | 0.640679i | \(-0.778653\pi\) | ||||
−0.767809 | + | 0.640679i | \(0.778653\pi\) | |||||||
\(524\) | 3.85974e6 | 0.614087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −302234. | −0.0476298 | ||||||||
\(527\) | −6.38750e6 | −1.00185 | ||||||||
\(528\) | 96386.1 | 0.0150463 | ||||||||
\(529\) | −607053. | −0.0943165 | ||||||||
\(530\) | 2.51229e6 | 0.388491 | ||||||||
\(531\) | −2.53138e6 | −0.389603 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.11739e6 | 0.170367 | ||||||||
\(534\) | −275204. | −0.0417639 | ||||||||
\(535\) | 358538. | 0.0541565 | ||||||||
\(536\) | −1.07953e7 | −1.62302 | ||||||||
\(537\) | 816561. | 0.122195 | ||||||||
\(538\) | 1.27343e6 | 0.189679 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −832032. | −0.122788 | ||||||||
\(541\) | 2.47643e6 | 0.363775 | 0.181887 | − | 0.983319i | \(-0.441779\pi\) | ||||
0.181887 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(542\) | −1.00575e7 | −1.47058 | ||||||||
\(543\) | 816817. | 0.118884 | ||||||||
\(544\) | 4.30325e6 | 0.623446 | ||||||||
\(545\) | −4.75878e6 | −0.686285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.10660e7 | −1.58132 | −0.790662 | − | 0.612253i | \(-0.790263\pi\) | ||||
−0.790662 | + | 0.612253i | \(0.790263\pi\) | |||||||
\(548\) | 1.61644e7 | 2.29937 | ||||||||
\(549\) | −1.06653e7 | −1.51023 | ||||||||
\(550\) | −2.77488e6 | −0.391145 | ||||||||
\(551\) | −5.82900e6 | −0.817928 | ||||||||
\(552\) | −625117. | −0.0873200 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.11003e7 | 1.53660 | ||||||||
\(555\) | 305610. | 0.0421148 | ||||||||
\(556\) | 2.81283e6 | 0.385884 | ||||||||
\(557\) | −4.36913e6 | −0.596702 | −0.298351 | − | 0.954456i | \(-0.596437\pi\) | ||||
−0.298351 | + | 0.954456i | \(0.596437\pi\) | |||||||
\(558\) | −1.67316e7 | −2.27485 | ||||||||
\(559\) | 1.01943e6 | 0.137983 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 521339. | 0.0699380 | ||||||||
\(562\) | −8.01682e6 | −1.07068 | ||||||||
\(563\) | −5.02223e6 | −0.667768 | −0.333884 | − | 0.942614i | \(-0.608359\pi\) | ||||
−0.333884 | + | 0.942614i | \(0.608359\pi\) | |||||||
\(564\) | −1.62866e6 | −0.215592 | ||||||||
\(565\) | 1.66755e6 | 0.219764 | ||||||||
\(566\) | −1.24356e7 | −1.63164 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.23000e6 | −0.420079 | ||||||||
\(569\) | −348871. | −0.0451735 | −0.0225868 | − | 0.999745i | \(-0.507190\pi\) | ||||
−0.0225868 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(570\) | −409086. | −0.0527384 | ||||||||
\(571\) | 1.53588e7 | 1.97136 | 0.985680 | − | 0.168627i | \(-0.0539334\pi\) | ||||
0.985680 | + | 0.168627i | \(0.0539334\pi\) | |||||||
\(572\) | −5.24381e6 | −0.670126 | ||||||||
\(573\) | −1.01365e6 | −0.128974 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.50900e6 | 0.190335 | ||||||||
\(576\) | 1.24918e7 | 1.56881 | ||||||||
\(577\) | 1.05696e7 | 1.32166 | 0.660830 | − | 0.750536i | \(-0.270204\pi\) | ||||
0.660830 | + | 0.750536i | \(0.270204\pi\) | |||||||
\(578\) | 6.39844e6 | 0.796626 | ||||||||
\(579\) | 209008. | 0.0259100 | ||||||||
\(580\) | −5.67184e6 | −0.700091 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.12722e6 | −0.260319 | ||||||||
\(583\) | −5.19279e6 | −0.632746 | ||||||||
\(584\) | −1.57724e7 | −1.91367 | ||||||||
\(585\) | 1.22522e6 | 0.148022 | ||||||||
\(586\) | 6.20460e6 | 0.746397 | ||||||||
\(587\) | −4.57417e6 | −0.547920 | −0.273960 | − | 0.961741i | \(-0.588334\pi\) | ||||
−0.273960 | + | 0.961741i | \(0.588334\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03599e7 | −1.23046 | ||||||||
\(590\) | −2.43025e6 | −0.287422 | ||||||||
\(591\) | −100844. | −0.0118763 | ||||||||
\(592\) | 1.51491e6 | 0.177657 | ||||||||
\(593\) | 1.46686e7 | 1.71297 | 0.856487 | − | 0.516169i | \(-0.172642\pi\) | ||||
0.856487 | + | 0.516169i | \(0.172642\pi\) | |||||||
\(594\) | 2.74041e6 | 0.318676 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.33024e7 | −2.68710 | ||||||||
\(597\) | 1.26161e6 | 0.144874 | ||||||||
\(598\) | 4.54397e6 | 0.519616 | ||||||||
\(599\) | 1.42374e7 | 1.62130 | 0.810649 | − | 0.585532i | \(-0.199114\pi\) | ||||
0.810649 | + | 0.585532i | \(0.199114\pi\) | |||||||
\(600\) | −161820. | −0.0183508 | ||||||||
\(601\) | 8.21658e6 | 0.927908 | 0.463954 | − | 0.885859i | \(-0.346430\pi\) | ||||
0.463954 | + | 0.885859i | \(0.346430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.28246e7 | −1.43632 | ||||||||
\(604\) | 1.20907e7 | 1.34853 | ||||||||
\(605\) | 1.70927e6 | 0.189855 | ||||||||
\(606\) | −1.27034e6 | −0.140520 | ||||||||
\(607\) | 1.69772e7 | 1.87023 | 0.935114 | − | 0.354348i | \(-0.115297\pi\) | ||||
0.935114 | + | 0.354348i | \(0.115297\pi\) | |||||||
\(608\) | 6.97944e6 | 0.765705 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.02392e7 | −1.11415 | ||||||||
\(611\) | 4.81276e6 | 0.521544 | ||||||||
\(612\) | −1.11168e7 | −1.19977 | ||||||||
\(613\) | 5.22841e6 | 0.561977 | 0.280988 | − | 0.959711i | \(-0.409338\pi\) | ||||
0.280988 | + | 0.959711i | \(0.409338\pi\) | |||||||
\(614\) | −1.24417e6 | −0.133186 | ||||||||
\(615\) | −175320. | −0.0186915 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.71179e7 | −1.81025 | −0.905123 | − | 0.425150i | \(-0.860221\pi\) | ||||
−0.905123 | + | 0.425150i | \(0.860221\pi\) | |||||||
\(618\) | −2.03813e6 | −0.214665 | ||||||||
\(619\) | 7.20377e6 | 0.755672 | 0.377836 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377836 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(620\) | −1.00806e7 | −1.05319 | ||||||||
\(621\) | −1.49025e6 | −0.155071 | ||||||||
\(622\) | 3.66158e6 | 0.379483 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −40858.0 | −0.00420065 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.27595e7 | 1.30136 | ||||||||
\(627\) | 845560. | 0.0858966 | ||||||||
\(628\) | 1.26945e7 | 1.28445 | ||||||||
\(629\) | 8.19395e6 | 0.825784 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.56923e6 | 0.856779 | 0.428389 | − | 0.903594i | \(-0.359081\pi\) | ||||
0.428389 | + | 0.903594i | \(0.359081\pi\) | |||||||
\(632\) | 1.75013e7 | 1.74292 | ||||||||
\(633\) | 1.25287e6 | 0.124279 | ||||||||
\(634\) | 1.56547e7 | 1.54675 | ||||||||
\(635\) | 3.91565e6 | 0.385363 | ||||||||
\(636\) | −744905. | −0.0730227 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.86810e7 | 1.81697 | ||||||||
\(639\) | −3.83717e6 | −0.371757 | ||||||||
\(640\) | 7.96229e6 | 0.768401 | ||||||||
\(641\) | 9.91653e6 | 0.953267 | 0.476633 | − | 0.879102i | \(-0.341857\pi\) | ||||
0.476633 | + | 0.879102i | \(0.341857\pi\) | |||||||
\(642\) | −169399. | −0.0162208 | ||||||||
\(643\) | 3.70762e6 | 0.353645 | 0.176822 | − | 0.984243i | \(-0.443418\pi\) | ||||
0.176822 | + | 0.984243i | \(0.443418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −159950. | −0.0151385 | ||||||||
\(646\) | −1.09683e7 | −1.03409 | ||||||||
\(647\) | 6.36378e6 | 0.597660 | 0.298830 | − | 0.954306i | \(-0.403404\pi\) | ||||
0.298830 | + | 0.954306i | \(0.403404\pi\) | |||||||
\(648\) | −1.17577e7 | −1.09998 | ||||||||
\(649\) | 5.02321e6 | 0.468133 | ||||||||
\(650\) | 1.17627e6 | 0.109200 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 155041. | 0.0142833 | ||||||||
\(653\) | 7.58179e6 | 0.695807 | 0.347903 | − | 0.937530i | \(-0.386894\pi\) | ||||
0.347903 | + | 0.937530i | \(0.386894\pi\) | |||||||
\(654\) | 2.24839e6 | 0.205554 | ||||||||
\(655\) | 1.78957e6 | 0.162984 | ||||||||
\(656\) | −869063. | −0.0788482 | ||||||||
\(657\) | −1.87373e7 | −1.69354 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.44484e6 | −0.847191 | −0.423595 | − | 0.905851i | \(-0.639232\pi\) | ||||
−0.423595 | + | 0.905851i | \(0.639232\pi\) | |||||||
\(660\) | 822763. | 0.0735216 | ||||||||
\(661\) | −2.23762e7 | −1.99197 | −0.995985 | − | 0.0895192i | \(-0.971467\pi\) | ||||
−0.995985 | + | 0.0895192i | \(0.971467\pi\) | |||||||
\(662\) | −1.47397e7 | −1.30721 | ||||||||
\(663\) | −220996. | −0.0195254 | ||||||||
\(664\) | 1.05911e7 | 0.932226 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.14635e7 | 1.87506 | ||||||||
\(667\) | −1.01588e7 | −0.884155 | ||||||||
\(668\) | −2.17030e7 | −1.88182 | ||||||||
\(669\) | 363485. | 0.0313994 | ||||||||
\(670\) | −1.23122e7 | −1.05962 | ||||||||
\(671\) | 2.11640e7 | 1.81464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 121935. | 0.0103775 | 0.00518875 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00518875 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(674\) | 7.63267e6 | 0.647183 | ||||||||
\(675\) | −385773. | −0.0325891 | ||||||||
\(676\) | −1.77972e7 | −1.49791 | ||||||||
\(677\) | −4.12171e6 | −0.345625 | −0.172813 | − | 0.984955i | \(-0.555286\pi\) | ||||
−0.172813 | + | 0.984955i | \(0.555286\pi\) | |||||||
\(678\) | −787868. | −0.0658232 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.33870e6 | −0.359822 | ||||||||
\(681\) | 1.21051e6 | 0.100023 | ||||||||
\(682\) | 3.32017e7 | 2.73338 | ||||||||
\(683\) | −4.30505e6 | −0.353123 | −0.176562 | − | 0.984290i | \(-0.556497\pi\) | ||||
−0.176562 | + | 0.984290i | \(0.556497\pi\) | |||||||
\(684\) | −1.80303e7 | −1.47354 | ||||||||
\(685\) | 7.49466e6 | 0.610275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.33983e6 | −0.108307 | ||||||||
\(688\) | −792873. | −0.0638605 | ||||||||
\(689\) | 2.20122e6 | 0.176651 | ||||||||
\(690\) | −712957. | −0.0570086 | ||||||||
\(691\) | 1.54709e7 | 1.23260 | 0.616298 | − | 0.787513i | \(-0.288632\pi\) | ||||
0.616298 | + | 0.787513i | \(0.288632\pi\) | |||||||
\(692\) | 3.23414e7 | 2.56740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.43749e7 | 1.92107 | ||||||||
\(695\) | 1.30417e6 | 0.102417 | ||||||||
\(696\) | 1.08940e6 | 0.0852444 | ||||||||
\(697\) | −4.70065e6 | −0.366501 | ||||||||
\(698\) | 3.02932e7 | 2.35346 | ||||||||
\(699\) | −214958. | −0.0166403 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 631976. | 0.0485742 | 0.0242871 | − | 0.999705i | \(-0.492268\pi\) | ||||
0.0242871 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(702\) | −1.16166e6 | −0.0889684 | ||||||||
\(703\) | 1.32898e7 | 1.01421 | ||||||||
\(704\) | −2.47884e7 | −1.88502 | ||||||||
\(705\) | −755130. | −0.0572202 | ||||||||
\(706\) | 5.76032e6 | 0.434945 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 720578. | 0.0540254 | ||||||||
\(709\) | −1.13182e7 | −0.845594 | −0.422797 | − | 0.906224i | \(-0.638952\pi\) | ||||
−0.422797 | + | 0.906224i | \(0.638952\pi\) | |||||||
\(710\) | −3.68387e6 | −0.274257 | ||||||||
\(711\) | 2.07912e7 | 1.54243 | ||||||||
\(712\) | −4.73396e6 | −0.349965 | ||||||||
\(713\) | −1.80553e7 | −1.33009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.43130e6 | −0.177858 | ||||||||
\(716\) | 3.45516e7 | 2.51876 | ||||||||
\(717\) | 839271. | 0.0609684 | ||||||||
\(718\) | −1.24659e7 | −0.902431 | ||||||||
\(719\) | −1.35453e7 | −0.977162 | −0.488581 | − | 0.872519i | \(-0.662485\pi\) | ||||
−0.488581 | + | 0.872519i | \(0.662485\pi\) | |||||||
\(720\) | −952934. | −0.0685065 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.16218e6 | 0.368545 | ||||||||
\(723\) | 400666. | 0.0285060 | ||||||||
\(724\) | 3.45625e7 | 2.45052 | ||||||||
\(725\) | −2.62976e6 | −0.185811 | ||||||||
\(726\) | −807581. | −0.0568649 | ||||||||
\(727\) | −1.41927e7 | −0.995932 | −0.497966 | − | 0.867197i | \(-0.665920\pi\) | ||||
−0.497966 | + | 0.867197i | \(0.665920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.37768e7 | −0.960129 | ||||||||
\(730\) | −1.79887e7 | −1.24938 | ||||||||
\(731\) | −4.28854e6 | −0.296836 | ||||||||
\(732\) | 3.03597e6 | 0.209421 | ||||||||
\(733\) | −1.55238e6 | −0.106718 | −0.0533591 | − | 0.998575i | \(-0.516993\pi\) | ||||
−0.0533591 | + | 0.998575i | \(0.516993\pi\) | |||||||
\(734\) | 2.55648e7 | 1.75147 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.21638e7 | 0.827704 | ||||||||
\(737\) | 2.54488e7 | 1.72583 | ||||||||
\(738\) | −1.23130e7 | −0.832191 | ||||||||
\(739\) | −1.20108e7 | −0.809026 | −0.404513 | − | 0.914532i | \(-0.632559\pi\) | ||||
−0.404513 | + | 0.914532i | \(0.632559\pi\) | |||||||
\(740\) | 1.29315e7 | 0.868097 | ||||||||
\(741\) | −358433. | −0.0239807 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.84220e6 | 0.521154 | 0.260577 | − | 0.965453i | \(-0.416087\pi\) | ||||
0.260577 | + | 0.965453i | \(0.416087\pi\) | |||||||
\(744\) | 1.93620e6 | 0.128238 | ||||||||
\(745\) | −1.08042e7 | −0.713182 | ||||||||
\(746\) | −3.04994e7 | −2.00652 | ||||||||
\(747\) | 1.25820e7 | 0.824991 | ||||||||
\(748\) | 2.20598e7 | 1.44161 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −184559. | −0.0119807 | ||||||||
\(751\) | −3.95564e6 | −0.255927 | −0.127964 | − | 0.991779i | \(-0.540844\pi\) | ||||
−0.127964 | + | 0.991779i | \(0.540844\pi\) | |||||||
\(752\) | −3.74319e6 | −0.241378 | ||||||||
\(753\) | −23854.1 | −0.00153312 | ||||||||
\(754\) | −7.91886e6 | −0.507264 | ||||||||
\(755\) | 5.60587e6 | 0.357912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.28287e7 | 1.44791 | 0.723956 | − | 0.689846i | \(-0.242322\pi\) | ||||
0.723956 | + | 0.689846i | \(0.242322\pi\) | |||||||
\(758\) | 1.23770e7 | 0.782424 | ||||||||
\(759\) | 1.47365e6 | 0.0928516 | ||||||||
\(760\) | −7.03694e6 | −0.441926 | ||||||||
\(761\) | −2.59221e7 | −1.62259 | −0.811295 | − | 0.584638i | \(-0.801237\pi\) | ||||
−0.811295 | + | 0.584638i | \(0.801237\pi\) | |||||||
\(762\) | −1.85003e6 | −0.115423 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.28911e7 | −2.65848 | ||||||||
\(765\) | −5.15429e6 | −0.318431 | ||||||||
\(766\) | 3.12636e7 | 1.92516 | ||||||||
\(767\) | −2.12934e6 | −0.130694 | ||||||||
\(768\) | −1.65163e6 | −0.101044 | ||||||||
\(769\) | −381532. | −0.0232656 | −0.0116328 | − | 0.999932i | \(-0.503703\pi\) | ||||
−0.0116328 | + | 0.999932i | \(0.503703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 813953. | 0.0493132 | ||||||||
\(772\) | 8.84390e6 | 0.534073 | ||||||||
\(773\) | −9.18755e6 | −0.553033 | −0.276516 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276516 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(774\) | −1.12335e7 | −0.674006 | ||||||||
\(775\) | −4.67387e6 | −0.279526 | ||||||||
\(776\) | −3.65917e7 | −2.18136 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.21198e7 | 1.90250 | ||||||||
\(779\) | −7.62398e6 | −0.450130 | ||||||||
\(780\) | −348769. | −0.0205259 | ||||||||
\(781\) | 7.61438e6 | 0.446691 | ||||||||
\(782\) | −1.91157e7 | −1.11782 | ||||||||
\(783\) | 2.59709e6 | 0.151385 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.88583e6 | 0.340905 | ||||||||
\(786\) | −845522. | −0.0488167 | ||||||||
\(787\) | −6.94528e6 | −0.399717 | −0.199859 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199859 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(788\) | −4.26708e6 | −0.244802 | ||||||||
\(789\) | 41549.4 | 0.00237614 | ||||||||
\(790\) | 1.99605e7 | 1.13790 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.34907e7 | 1.33071 | ||||||||
\(793\) | −8.97141e6 | −0.506614 | ||||||||
\(794\) | 1.62683e7 | 0.915782 | ||||||||
\(795\) | −345376. | −0.0193809 | ||||||||
\(796\) | 5.33833e7 | 2.98623 | ||||||||
\(797\) | 5.81421e6 | 0.324224 | 0.162112 | − | 0.986772i | \(-0.448169\pi\) | ||||
0.162112 | + | 0.986772i | \(0.448169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.02464e7 | −1.12197 | ||||||||
\(800\) | 3.14878e6 | 0.173947 | ||||||||
\(801\) | −5.62385e6 | −0.309708 | ||||||||
\(802\) | 4.75007e7 | 2.60774 | ||||||||
\(803\) | 3.71818e7 | 2.03489 | ||||||||
\(804\) | 3.65063e6 | 0.199172 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.40742e7 | −0.763108 | ||||||||
\(807\) | −175064. | −0.00946265 | ||||||||
\(808\) | −2.18519e7 | −1.17750 | ||||||||
\(809\) | −2.76000e7 | −1.48265 | −0.741324 | − | 0.671147i | \(-0.765802\pi\) | ||||
−0.741324 | + | 0.671147i | \(0.765802\pi\) | |||||||
\(810\) | −1.34099e7 | −0.718144 | ||||||||
\(811\) | −5.51268e6 | −0.294314 | −0.147157 | − | 0.989113i | \(-0.547012\pi\) | ||||
−0.147157 | + | 0.989113i | \(0.547012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.38264e6 | 0.0733641 | ||||||||
\(814\) | −4.25915e7 | −2.25300 | ||||||||
\(815\) | 71885.0 | 0.00379092 | ||||||||
\(816\) | 171883. | 0.00903663 | ||||||||
\(817\) | −6.95559e6 | −0.364568 | ||||||||
\(818\) | −8.15103e6 | −0.425921 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.41842e6 | −0.385281 | ||||||||
\(821\) | 4.69730e6 | 0.243215 | 0.121607 | − | 0.992578i | \(-0.461195\pi\) | ||||
0.121607 | + | 0.992578i | \(0.461195\pi\) | |||||||
\(822\) | −3.54101e6 | −0.182788 | ||||||||
\(823\) | 1.68012e7 | 0.864652 | 0.432326 | − | 0.901717i | \(-0.357693\pi\) | ||||
0.432326 | + | 0.901717i | \(0.357693\pi\) | |||||||
\(824\) | −3.50592e7 | −1.79880 | ||||||||
\(825\) | 381475. | 0.0195133 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.91479e6 | 0.0973548 | 0.0486774 | − | 0.998815i | \(-0.484499\pi\) | ||||
0.0486774 | + | 0.998815i | \(0.484499\pi\) | |||||||
\(828\) | −3.14233e7 | −1.59285 | ||||||||
\(829\) | 7.32861e6 | 0.370369 | 0.185185 | − | 0.982704i | \(-0.440712\pi\) | ||||
0.185185 | + | 0.982704i | \(0.440712\pi\) | |||||||
\(830\) | 1.20793e7 | 0.608622 | ||||||||
\(831\) | −1.52601e6 | −0.0766574 | ||||||||
\(832\) | 1.05078e7 | 0.526263 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −616183. | −0.0306757 | ||||||||
\(835\) | −1.00626e7 | −0.499453 | ||||||||
\(836\) | 3.57787e7 | 1.77055 | ||||||||
\(837\) | 4.61581e6 | 0.227737 | ||||||||
\(838\) | 5.27062e7 | 2.59269 | ||||||||
\(839\) | −1.77241e7 | −0.869281 | −0.434641 | − | 0.900604i | \(-0.643125\pi\) | ||||
−0.434641 | + | 0.900604i | \(0.643125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.80718e6 | −0.136861 | ||||||||
\(842\) | −5.81601e6 | −0.282712 | ||||||||
\(843\) | 1.10211e6 | 0.0534140 | ||||||||
\(844\) | 5.30136e7 | 2.56172 | ||||||||
\(845\) | −8.25170e6 | −0.397559 | ||||||||
\(846\) | −5.30340e7 | −2.54759 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.71203e6 | −0.0817565 | ||||||||
\(849\) | 1.70958e6 | 0.0813990 | ||||||||
\(850\) | −4.94836e6 | −0.234917 | ||||||||
\(851\) | 2.31615e7 | 1.09633 | ||||||||
\(852\) | 1.09228e6 | 0.0515508 | ||||||||
\(853\) | −2.61947e7 | −1.23265 | −0.616327 | − | 0.787490i | \(-0.711380\pi\) | ||||
−0.616327 | + | 0.787490i | \(0.711380\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.35975e6 | −0.391091 | ||||||||
\(856\) | −2.91393e6 | −0.135924 | ||||||||
\(857\) | −3.21925e7 | −1.49728 | −0.748639 | − | 0.662977i | \(-0.769293\pi\) | ||||
−0.748639 | + | 0.662977i | \(0.769293\pi\) | |||||||
\(858\) | 1.14872e6 | 0.0532715 | ||||||||
\(859\) | −2.22096e7 | −1.02697 | −0.513485 | − | 0.858098i | \(-0.671646\pi\) | ||||
−0.513485 | + | 0.858098i | \(0.671646\pi\) | |||||||
\(860\) | −6.76805e6 | −0.312045 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.84177e6 | 0.405295 | ||||||||
\(863\) | 2.10546e7 | 0.962322 | 0.481161 | − | 0.876632i | \(-0.340215\pi\) | ||||
0.481161 | + | 0.876632i | \(0.340215\pi\) | |||||||
\(864\) | −3.10966e6 | −0.141719 | ||||||||
\(865\) | 1.49951e7 | 0.681411 | ||||||||
\(866\) | −4.19018e7 | −1.89862 | ||||||||
\(867\) | −879621. | −0.0397418 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.12574e7 | −1.85333 | ||||||||
\(870\) | 1.24248e6 | 0.0556535 | ||||||||
\(871\) | −1.07877e7 | −0.481820 | ||||||||
\(872\) | 3.86759e7 | 1.72246 | ||||||||
\(873\) | −4.34703e7 | −1.93044 | ||||||||
\(874\) | −3.10037e7 | −1.37289 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.33373e6 | 0.234839 | ||||||||
\(877\) | 1.49233e7 | 0.655189 | 0.327594 | − | 0.944818i | \(-0.393762\pi\) | ||||
0.327594 | + | 0.944818i | \(0.393762\pi\) | |||||||
\(878\) | −6.47955e7 | −2.83667 | ||||||||
\(879\) | −852974. | −0.0372360 | ||||||||
\(880\) | 1.89098e6 | 0.0823150 | ||||||||
\(881\) | 3.85987e7 | 1.67546 | 0.837729 | − | 0.546087i | \(-0.183883\pi\) | ||||
0.837729 | + | 0.546087i | \(0.183883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.35117e7 | −1.44642 | −0.723210 | − | 0.690628i | \(-0.757334\pi\) | ||||
−0.723210 | + | 0.690628i | \(0.757334\pi\) | |||||||
\(884\) | −9.35113e6 | −0.402470 | ||||||||
\(885\) | 334097. | 0.0143388 | ||||||||
\(886\) | 4.32008e7 | 1.84887 | ||||||||
\(887\) | 4.18929e7 | 1.78785 | 0.893927 | − | 0.448213i | \(-0.147939\pi\) | ||||
0.893927 | + | 0.448213i | \(0.147939\pi\) | |||||||
\(888\) | −2.48377e6 | −0.105701 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.39916e6 | −0.228482 | ||||||||
\(891\) | 2.77176e7 | 1.16966 | ||||||||
\(892\) | 1.53804e7 | 0.647224 | ||||||||
\(893\) | −3.28377e7 | −1.37798 | ||||||||
\(894\) | 5.10465e6 | 0.213610 | ||||||||
\(895\) | 1.60199e7 | 0.668501 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −624679. | −0.0259224 | ||||||||
\(898\) | −5.93313e7 | −2.45524 | ||||||||
\(899\) | 3.14653e7 | 1.29847 | ||||||||
\(900\) | −8.13436e6 | −0.334747 | ||||||||
\(901\) | −9.26015e6 | −0.380020 | ||||||||
\(902\) | 2.44336e7 | 0.999932 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.35526e7 | −0.551571 | ||||||||
\(905\) | 1.60249e7 | 0.650391 | ||||||||
\(906\) | −2.64861e6 | −0.107201 | ||||||||
\(907\) | 2.30904e6 | 0.0931993 | 0.0465997 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0465997 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(908\) | 5.12212e7 | 2.06175 | ||||||||
\(909\) | −2.59596e7 | −1.04205 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.48503e7 | 0.592843 | 0.296421 | − | 0.955057i | \(-0.404207\pi\) | ||||
0.296421 | + | 0.955057i | \(0.404207\pi\) | |||||||
\(912\) | 278776. | 0.0110986 | ||||||||
\(913\) | −2.49674e7 | −0.991281 | ||||||||
\(914\) | −3.79494e7 | −1.50259 | ||||||||
\(915\) | 1.40763e6 | 0.0555822 | ||||||||
\(916\) | −5.66930e7 | −2.23250 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.88689e6 | 0.191393 | ||||||||
\(919\) | 1.02358e7 | 0.399793 | 0.199896 | − | 0.979817i | \(-0.435939\pi\) | ||||
0.199896 | + | 0.979817i | \(0.435939\pi\) | |||||||
\(920\) | −1.22640e7 | −0.477709 | ||||||||
\(921\) | 171041. | 0.00664433 | ||||||||
\(922\) | −7.33617e7 | −2.84212 | ||||||||
\(923\) | −3.22773e6 | −0.124708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.99568e6 | 0.230401 | ||||||||
\(926\) | 4.27119e7 | 1.63690 | ||||||||
\(927\) | −4.16496e7 | −1.59189 | ||||||||
\(928\) | −2.11981e7 | −0.808029 | ||||||||
\(929\) | −2.00459e7 | −0.762054 | −0.381027 | − | 0.924564i | \(-0.624429\pi\) | ||||
−0.381027 | + | 0.924564i | \(0.624429\pi\) | |||||||
\(930\) | 2.20827e6 | 0.0837229 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.09567e6 | −0.343001 | ||||||||
\(933\) | −503373. | −0.0189315 | ||||||||
\(934\) | −3.61796e7 | −1.35705 | ||||||||
\(935\) | 1.02280e7 | 0.382616 | ||||||||
\(936\) | −9.95772e6 | −0.371510 | ||||||||
\(937\) | −3.63602e7 | −1.35293 | −0.676467 | − | 0.736473i | \(-0.736490\pi\) | ||||
−0.676467 | + | 0.736473i | \(0.736490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.75411e6 | −0.0649221 | ||||||||
\(940\) | −3.19523e7 | −1.17946 | ||||||||
\(941\) | 1.57487e7 | 0.579789 | 0.289895 | − | 0.957059i | \(-0.406380\pi\) | ||||
0.289895 | + | 0.957059i | \(0.406380\pi\) | |||||||
\(942\) | −2.78088e6 | −0.102107 | ||||||||
\(943\) | −1.32871e7 | −0.486577 | ||||||||
\(944\) | 1.65612e6 | 0.0604870 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.22915e7 | 0.809862 | ||||||||
\(947\) | −2.19938e7 | −0.796938 | −0.398469 | − | 0.917182i | \(-0.630458\pi\) | ||||
−0.398469 | + | 0.917182i | \(0.630458\pi\) | |||||||
\(948\) | −5.91837e6 | −0.213885 | ||||||||
\(949\) | −1.57614e7 | −0.568105 | ||||||||
\(950\) | −8.02575e6 | −0.288520 | ||||||||
\(951\) | −2.15212e6 | −0.0771640 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.79156e7 | 1.35234 | 0.676170 | − | 0.736746i | \(-0.263639\pi\) | ||||
0.676170 | + | 0.736746i | \(0.263639\pi\) | |||||||
\(954\) | −2.42563e7 | −0.862887 | ||||||||
\(955\) | −1.98865e7 | −0.705586 | ||||||||
\(956\) | 3.55126e7 | 1.25672 | ||||||||
\(957\) | −2.56815e6 | −0.0906445 | ||||||||
\(958\) | −4.10286e7 | −1.44435 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.64869e6 | −0.0577379 | ||||||||
\(961\) | 2.72941e7 | 0.953368 | ||||||||
\(962\) | 1.80545e7 | 0.628996 | ||||||||
\(963\) | −3.46170e6 | −0.120288 | ||||||||
\(964\) | 1.69536e7 | 0.587584 | ||||||||
\(965\) | 4.10048e6 | 0.141748 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.20041e7 | −0.756724 | −0.378362 | − | 0.925658i | \(-0.623513\pi\) | ||||
−0.378362 | + | 0.925658i | \(0.623513\pi\) | |||||||
\(968\) | −1.38917e7 | −0.476505 | ||||||||
\(969\) | 1.50786e6 | 0.0515885 | ||||||||
\(970\) | −4.17335e7 | −1.42415 | ||||||||
\(971\) | −3.57397e7 | −1.21647 | −0.608237 | − | 0.793755i | \(-0.708123\pi\) | ||||
−0.608237 | + | 0.793755i | \(0.708123\pi\) | |||||||
\(972\) | 1.20634e7 | 0.409548 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.06635e7 | 0.697921 | ||||||||
\(975\) | −161707. | −0.00544775 | ||||||||
\(976\) | 6.97764e6 | 0.234468 | ||||||||
\(977\) | −5.52739e7 | −1.85261 | −0.926305 | − | 0.376774i | \(-0.877033\pi\) | ||||
−0.926305 | + | 0.376774i | \(0.877033\pi\) | |||||||
\(978\) | −33963.6 | −0.00113545 | ||||||||
\(979\) | 1.11598e7 | 0.372134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.59463e7 | 1.52433 | ||||||||
\(982\) | −5.81847e6 | −0.192544 | ||||||||
\(983\) | −22923.2 | −0.000756644 0 | −0.000378322 | − | 1.00000i | \(-0.500120\pi\) | ||||
−0.000378322 | 1.00000i | \(0.500120\pi\) | ||||||||
\(984\) | 1.42487e6 | 0.0469125 | ||||||||
\(985\) | −1.97843e6 | −0.0649727 | ||||||||
\(986\) | 3.33132e7 | 1.09125 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.51666e7 | −0.494306 | ||||||||
\(989\) | −1.21222e7 | −0.394087 | ||||||||
\(990\) | 2.67916e7 | 0.868782 | ||||||||
\(991\) | −8.30772e6 | −0.268719 | −0.134359 | − | 0.990933i | \(-0.542898\pi\) | ||||
−0.134359 | + | 0.990933i | \(0.542898\pi\) | |||||||
\(992\) | −3.76754e7 | −1.21557 | ||||||||
\(993\) | 2.02633e6 | 0.0652136 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.47512e7 | 0.792572 | ||||||||
\(996\) | −3.58157e6 | −0.114400 | ||||||||
\(997\) | 3.35426e7 | 1.06871 | 0.534353 | − | 0.845261i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845261i | \(0.320555\pi\) | |||||||
\(998\) | −9.29956e6 | −0.295554 | ||||||||
\(999\) | −5.92120e6 | −0.187714 |
(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 | 245.6.a.m.1.2 | yes | 10 | |
7.6 | odd | 2 | 245.6.a.l.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.6.a.l.1.2 | ✓ | 10 | 7.6 | odd | 2 | ||
245.6.a.m.1.2 | yes | 10 | 1.1 | even | 1 | trivial |