Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.34253.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 52x + 48 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.25531\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.25531 | −1.63612 | −0.818061 | − | 0.575131i | \(-0.804951\pi\) | ||||
−0.818061 | + | 0.575131i | \(0.804951\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 53.6607 | 1.67690 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −83.2977 | −0.944616 | ||||||||
\(7\) | 36.4478 | 0.281142 | 0.140571 | − | 0.990071i | \(-0.455106\pi\) | ||||
0.140571 | + | 0.990071i | \(0.455106\pi\) | |||||||
\(8\) | −200.476 | −1.10749 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −231.383 | −0.731696 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 482.946 | 0.968156 | ||||||||
\(13\) | −878.032 | −1.44096 | −0.720480 | − | 0.693476i | \(-0.756079\pi\) | ||||
−0.720480 | + | 0.693476i | \(0.756079\pi\) | |||||||
\(14\) | −337.336 | −0.459983 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 138.327 | 0.135085 | ||||||||
\(17\) | 155.385 | 0.130403 | 0.0652014 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652014 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(18\) | −749.680 | −0.545374 | ||||||||
\(19\) | −1932.65 | −1.22820 | −0.614100 | − | 0.789228i | \(-0.710481\pi\) | ||||
−0.614100 | + | 0.789228i | \(0.710481\pi\) | |||||||
\(20\) | 1341.52 | 0.749931 | ||||||||
\(21\) | 328.030 | 0.162318 | ||||||||
\(22\) | 1119.89 | 0.493309 | ||||||||
\(23\) | 1927.38 | 0.759709 | 0.379855 | − | 0.925046i | \(-0.375974\pi\) | ||||
0.379855 | + | 0.925046i | \(0.375974\pi\) | |||||||
\(24\) | −1804.29 | −0.639407 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 8126.46 | 2.35759 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 1955.81 | 0.471447 | ||||||||
\(29\) | −480.444 | −0.106084 | −0.0530418 | − | 0.998592i | \(-0.516892\pi\) | ||||
−0.0530418 | + | 0.998592i | \(0.516892\pi\) | |||||||
\(30\) | −2082.44 | −0.422445 | ||||||||
\(31\) | 1759.49 | 0.328838 | 0.164419 | − | 0.986391i | \(-0.447425\pi\) | ||||
0.164419 | + | 0.986391i | \(0.447425\pi\) | |||||||
\(32\) | 5134.98 | 0.886470 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −1438.14 | −0.213355 | ||||||||
\(35\) | 911.195 | 0.125731 | ||||||||
\(36\) | 4346.51 | 0.558965 | ||||||||
\(37\) | −1898.87 | −0.228029 | −0.114015 | − | 0.993479i | \(-0.536371\pi\) | ||||
−0.114015 | + | 0.993479i | \(0.536371\pi\) | |||||||
\(38\) | 17887.3 | 2.00949 | ||||||||
\(39\) | −7902.29 | −0.831939 | ||||||||
\(40\) | −5011.91 | −0.495282 | ||||||||
\(41\) | −4500.03 | −0.418076 | −0.209038 | − | 0.977907i | \(-0.567033\pi\) | ||||
−0.209038 | + | 0.977907i | \(0.567033\pi\) | |||||||
\(42\) | −3036.02 | −0.265572 | ||||||||
\(43\) | −4475.49 | −0.369121 | −0.184561 | − | 0.982821i | \(-0.559086\pi\) | ||||
−0.184561 | + | 0.982821i | \(0.559086\pi\) | |||||||
\(44\) | −6492.94 | −0.505603 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | −17838.5 | −1.24298 | ||||||||
\(47\) | −12371.2 | −0.816895 | −0.408448 | − | 0.912782i | \(-0.633930\pi\) | ||||
−0.408448 | + | 0.912782i | \(0.633930\pi\) | |||||||
\(48\) | 1244.94 | 0.0779912 | ||||||||
\(49\) | −15478.6 | −0.920959 | ||||||||
\(50\) | −5784.57 | −0.327224 | ||||||||
\(51\) | 1398.47 | 0.0752881 | ||||||||
\(52\) | −47115.8 | −2.41634 | ||||||||
\(53\) | 2145.12 | 0.104897 | 0.0524483 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524483 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(54\) | −6747.12 | −0.314872 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −7306.92 | −0.311361 | ||||||||
\(57\) | −17393.8 | −0.709102 | ||||||||
\(58\) | 4446.66 | 0.173566 | ||||||||
\(59\) | −15857.9 | −0.593084 | −0.296542 | − | 0.955020i | \(-0.595834\pi\) | ||||
−0.296542 | + | 0.955020i | \(0.595834\pi\) | |||||||
\(60\) | 12073.7 | 0.432973 | ||||||||
\(61\) | −36447.7 | −1.25414 | −0.627070 | − | 0.778963i | \(-0.715746\pi\) | ||||
−0.627070 | + | 0.778963i | \(0.715746\pi\) | |||||||
\(62\) | −16284.6 | −0.538020 | ||||||||
\(63\) | 2952.27 | 0.0937141 | ||||||||
\(64\) | −51952.3 | −1.58546 | ||||||||
\(65\) | −21950.8 | −0.644417 | ||||||||
\(66\) | 10079.0 | 0.284812 | ||||||||
\(67\) | −15668.5 | −0.426424 | −0.213212 | − | 0.977006i | \(-0.568393\pi\) | ||||
−0.213212 | + | 0.977006i | \(0.568393\pi\) | |||||||
\(68\) | 8338.07 | 0.218672 | ||||||||
\(69\) | 17346.4 | 0.438618 | ||||||||
\(70\) | −8433.39 | −0.205711 | ||||||||
\(71\) | 10689.5 | 0.251659 | 0.125830 | − | 0.992052i | \(-0.459841\pi\) | ||||
0.125830 | + | 0.992052i | \(0.459841\pi\) | |||||||
\(72\) | −16238.6 | −0.369162 | ||||||||
\(73\) | 12172.6 | 0.267347 | 0.133674 | − | 0.991025i | \(-0.457323\pi\) | ||||
0.133674 | + | 0.991025i | \(0.457323\pi\) | |||||||
\(74\) | 17574.6 | 0.373084 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | −103707. | −2.05956 | ||||||||
\(77\) | −4410.19 | −0.0847676 | ||||||||
\(78\) | 73138.1 | 1.36115 | ||||||||
\(79\) | −87205.6 | −1.57209 | −0.786043 | − | 0.618171i | \(-0.787874\pi\) | ||||
−0.786043 | + | 0.618171i | \(0.787874\pi\) | |||||||
\(80\) | 3458.17 | 0.0604117 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 41649.2 | 0.684024 | ||||||||
\(83\) | 97230.6 | 1.54920 | 0.774600 | − | 0.632451i | \(-0.217951\pi\) | ||||
0.774600 | + | 0.632451i | \(0.217951\pi\) | |||||||
\(84\) | 17602.3 | 0.272190 | ||||||||
\(85\) | 3884.63 | 0.0583179 | ||||||||
\(86\) | 41422.0 | 0.603928 | ||||||||
\(87\) | −4324.00 | −0.0612473 | ||||||||
\(88\) | 24257.6 | 0.333919 | ||||||||
\(89\) | 38639.2 | 0.517075 | 0.258537 | − | 0.966001i | \(-0.416759\pi\) | ||||
0.258537 | + | 0.966001i | \(0.416759\pi\) | |||||||
\(90\) | −18742.0 | −0.243899 | ||||||||
\(91\) | −32002.4 | −0.405115 | ||||||||
\(92\) | 103424. | 1.27395 | ||||||||
\(93\) | 15835.4 | 0.189855 | ||||||||
\(94\) | 114499. | 1.33654 | ||||||||
\(95\) | −48316.2 | −0.549268 | ||||||||
\(96\) | 46214.8 | 0.511804 | ||||||||
\(97\) | −36754.5 | −0.396626 | −0.198313 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198313 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(98\) | 143259. | 1.50680 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 33537.9 | 0.335379 | ||||||||
\(101\) | −185487. | −1.80929 | −0.904647 | − | 0.426161i | \(-0.859866\pi\) | ||||
−0.904647 | + | 0.426161i | \(0.859866\pi\) | |||||||
\(102\) | −12943.2 | −0.123181 | ||||||||
\(103\) | 36890.7 | 0.342629 | 0.171315 | − | 0.985216i | \(-0.445199\pi\) | ||||
0.171315 | + | 0.985216i | \(0.445199\pi\) | |||||||
\(104\) | 176025. | 1.59584 | ||||||||
\(105\) | 8200.76 | 0.0725907 | ||||||||
\(106\) | −19853.7 | −0.171624 | ||||||||
\(107\) | −124996. | −1.05545 | −0.527725 | − | 0.849415i | \(-0.676955\pi\) | ||||
−0.527725 | + | 0.849415i | \(0.676955\pi\) | |||||||
\(108\) | 39118.6 | 0.322719 | ||||||||
\(109\) | −150975. | −1.21714 | −0.608568 | − | 0.793502i | \(-0.708256\pi\) | ||||
−0.608568 | + | 0.793502i | \(0.708256\pi\) | |||||||
\(110\) | 27997.3 | 0.220615 | ||||||||
\(111\) | −17089.8 | −0.131653 | ||||||||
\(112\) | 5041.71 | 0.0379780 | ||||||||
\(113\) | 157970. | 1.16380 | 0.581899 | − | 0.813261i | \(-0.302310\pi\) | ||||
0.581899 | + | 0.813261i | \(0.302310\pi\) | |||||||
\(114\) | 160985. | 1.16018 | ||||||||
\(115\) | 48184.5 | 0.339752 | ||||||||
\(116\) | −25781.0 | −0.177891 | ||||||||
\(117\) | −71120.6 | −0.480320 | ||||||||
\(118\) | 146770. | 0.970359 | ||||||||
\(119\) | 5663.45 | 0.0366618 | ||||||||
\(120\) | −45107.1 | −0.285951 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 337335. | 2.05193 | ||||||||
\(123\) | −40500.3 | −0.241377 | ||||||||
\(124\) | 94415.4 | 0.551428 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −27324.2 | −0.153328 | ||||||||
\(127\) | 268814. | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235082\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235082\pi\) | |||||||
\(128\) | 316515. | 1.70753 | ||||||||
\(129\) | −40279.4 | −0.213112 | ||||||||
\(130\) | 203161. | 1.05435 | ||||||||
\(131\) | −366914. | −1.86804 | −0.934020 | − | 0.357220i | \(-0.883725\pi\) | ||||
−0.934020 | + | 0.357220i | \(0.883725\pi\) | |||||||
\(132\) | −58436.5 | −0.291910 | ||||||||
\(133\) | −70440.9 | −0.345299 | ||||||||
\(134\) | 145017. | 0.697682 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | −31151.0 | −0.144419 | ||||||||
\(137\) | −182927. | −0.832678 | −0.416339 | − | 0.909209i | \(-0.636687\pi\) | ||||
−0.416339 | + | 0.909209i | \(0.636687\pi\) | |||||||
\(138\) | −160546. | −0.717633 | ||||||||
\(139\) | 8429.85 | 0.0370069 | 0.0185035 | − | 0.999829i | \(-0.494110\pi\) | ||||
0.0185035 | + | 0.999829i | \(0.494110\pi\) | |||||||
\(140\) | 48895.4 | 0.210837 | ||||||||
\(141\) | −111341. | −0.471635 | ||||||||
\(142\) | −98934.8 | −0.411745 | ||||||||
\(143\) | 106242. | 0.434466 | ||||||||
\(144\) | 11204.5 | 0.0450282 | ||||||||
\(145\) | −12011.1 | −0.0474420 | ||||||||
\(146\) | −112661. | −0.437413 | ||||||||
\(147\) | −139307. | −0.531716 | ||||||||
\(148\) | −101895. | −0.382381 | ||||||||
\(149\) | 271810. | 1.00300 | 0.501499 | − | 0.865158i | \(-0.332782\pi\) | ||||
0.501499 | + | 0.865158i | \(0.332782\pi\) | |||||||
\(150\) | −52061.1 | −0.188923 | ||||||||
\(151\) | −236565. | −0.844322 | −0.422161 | − | 0.906521i | \(-0.638728\pi\) | ||||
−0.422161 | + | 0.906521i | \(0.638728\pi\) | |||||||
\(152\) | 387450. | 1.36021 | ||||||||
\(153\) | 12586.2 | 0.0434676 | ||||||||
\(154\) | 40817.6 | 0.138690 | ||||||||
\(155\) | 43987.2 | 0.147061 | ||||||||
\(156\) | −424042. | −1.39508 | ||||||||
\(157\) | 211824. | 0.685846 | 0.342923 | − | 0.939364i | \(-0.388583\pi\) | ||||
0.342923 | + | 0.939364i | \(0.388583\pi\) | |||||||
\(158\) | 807114. | 2.57213 | ||||||||
\(159\) | 19306.1 | 0.0605621 | ||||||||
\(160\) | 128375. | 0.396441 | ||||||||
\(161\) | 70248.7 | 0.213586 | ||||||||
\(162\) | −60724.1 | −0.181791 | ||||||||
\(163\) | −341315. | −1.00620 | −0.503102 | − | 0.864227i | \(-0.667808\pi\) | ||||
−0.503102 | + | 0.864227i | \(0.667808\pi\) | |||||||
\(164\) | −241475. | −0.701071 | ||||||||
\(165\) | −27225.0 | −0.0778499 | ||||||||
\(166\) | −899899. | −2.53468 | ||||||||
\(167\) | −180548. | −0.500958 | −0.250479 | − | 0.968122i | \(-0.580588\pi\) | ||||
−0.250479 | + | 0.968122i | \(0.580588\pi\) | |||||||
\(168\) | −65762.3 | −0.179764 | ||||||||
\(169\) | 399647. | 1.07637 | ||||||||
\(170\) | −35953.4 | −0.0954153 | ||||||||
\(171\) | −156545. | −0.409400 | ||||||||
\(172\) | −240158. | −0.618978 | ||||||||
\(173\) | −643322. | −1.63423 | −0.817114 | − | 0.576476i | \(-0.804428\pi\) | ||||
−0.817114 | + | 0.576476i | \(0.804428\pi\) | |||||||
\(174\) | 40019.9 | 0.100208 | ||||||||
\(175\) | 22779.9 | 0.0562285 | ||||||||
\(176\) | −16737.5 | −0.0407296 | ||||||||
\(177\) | −142721. | −0.342417 | ||||||||
\(178\) | −357618. | −0.845998 | ||||||||
\(179\) | −266922. | −0.622662 | −0.311331 | − | 0.950302i | \(-0.600775\pi\) | ||||
−0.311331 | + | 0.950302i | \(0.600775\pi\) | |||||||
\(180\) | 108663. | 0.249977 | ||||||||
\(181\) | 281529. | 0.638745 | 0.319372 | − | 0.947629i | \(-0.396528\pi\) | ||||
0.319372 | + | 0.947629i | \(0.396528\pi\) | |||||||
\(182\) | 296192. | 0.662818 | ||||||||
\(183\) | −328030. | −0.724078 | ||||||||
\(184\) | −386393. | −0.841366 | ||||||||
\(185\) | −47471.7 | −0.101978 | ||||||||
\(186\) | −146561. | −0.310626 | ||||||||
\(187\) | −18801.6 | −0.0393179 | ||||||||
\(188\) | −663846. | −1.36985 | ||||||||
\(189\) | 26570.5 | 0.0541059 | ||||||||
\(190\) | 447182. | 0.898669 | ||||||||
\(191\) | 933723. | 1.85197 | 0.925987 | − | 0.377556i | \(-0.123235\pi\) | ||||
0.925987 | + | 0.377556i | \(0.123235\pi\) | |||||||
\(192\) | −467571. | −0.915365 | ||||||||
\(193\) | 300124. | 0.579973 | 0.289986 | − | 0.957031i | \(-0.406349\pi\) | ||||
0.289986 | + | 0.957031i | \(0.406349\pi\) | |||||||
\(194\) | 340174. | 0.648929 | ||||||||
\(195\) | −197557. | −0.372054 | ||||||||
\(196\) | −830590. | −1.54435 | ||||||||
\(197\) | −944940. | −1.73476 | −0.867378 | − | 0.497649i | \(-0.834197\pi\) | ||||
−0.867378 | + | 0.497649i | \(0.834197\pi\) | |||||||
\(198\) | 90711.2 | 0.164436 | ||||||||
\(199\) | −1.00821e6 | −1.80475 | −0.902374 | − | 0.430954i | \(-0.858177\pi\) | ||||
−0.902374 | + | 0.430954i | \(0.858177\pi\) | |||||||
\(200\) | −125298. | −0.221497 | ||||||||
\(201\) | −141017. | −0.246196 | ||||||||
\(202\) | 1.71674e6 | 2.96023 | ||||||||
\(203\) | −17511.1 | −0.0298246 | ||||||||
\(204\) | 75042.6 | 0.126250 | ||||||||
\(205\) | −112501. | −0.186969 | ||||||||
\(206\) | −341435. | −0.560583 | ||||||||
\(207\) | 156118. | 0.253236 | ||||||||
\(208\) | −121455. | −0.194652 | ||||||||
\(209\) | 233851. | 0.370316 | ||||||||
\(210\) | −75900.5 | −0.118767 | ||||||||
\(211\) | 497479. | 0.769253 | 0.384626 | − | 0.923072i | \(-0.374330\pi\) | ||||
0.384626 | + | 0.923072i | \(0.374330\pi\) | |||||||
\(212\) | 115108. | 0.175901 | ||||||||
\(213\) | 96205.7 | 0.145295 | ||||||||
\(214\) | 1.15688e6 | 1.72684 | ||||||||
\(215\) | −111887. | −0.165076 | ||||||||
\(216\) | −146147. | −0.213136 | ||||||||
\(217\) | 64129.5 | 0.0924504 | ||||||||
\(218\) | 1.39732e6 | 1.99138 | ||||||||
\(219\) | 109553. | 0.154353 | ||||||||
\(220\) | −162324. | −0.226113 | ||||||||
\(221\) | −136433. | −0.187905 | ||||||||
\(222\) | 158172. | 0.215400 | ||||||||
\(223\) | 1.14136e6 | 1.53695 | 0.768477 | − | 0.639878i | \(-0.221015\pi\) | ||||
0.768477 | + | 0.639878i | \(0.221015\pi\) | |||||||
\(224\) | 187159. | 0.249224 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −1.46206e6 | −1.90411 | ||||||||
\(227\) | 669451. | 0.862292 | 0.431146 | − | 0.902282i | \(-0.358109\pi\) | ||||
0.431146 | + | 0.902282i | \(0.358109\pi\) | |||||||
\(228\) | −933366. | −1.18909 | ||||||||
\(229\) | 588061. | 0.741026 | 0.370513 | − | 0.928827i | \(-0.379182\pi\) | ||||
0.370513 | + | 0.928827i | \(0.379182\pi\) | |||||||
\(230\) | −445962. | −0.555876 | ||||||||
\(231\) | −39691.7 | −0.0489406 | ||||||||
\(232\) | 96317.6 | 0.117486 | ||||||||
\(233\) | 199417. | 0.240642 | 0.120321 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120321 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(234\) | 658243. | 0.785862 | ||||||||
\(235\) | −309279. | −0.365327 | ||||||||
\(236\) | −850947. | −0.994541 | ||||||||
\(237\) | −784850. | −0.907645 | ||||||||
\(238\) | −52416.9 | −0.0599832 | ||||||||
\(239\) | −408055. | −0.462088 | −0.231044 | − | 0.972943i | \(-0.574214\pi\) | ||||
−0.231044 | + | 0.972943i | \(0.574214\pi\) | |||||||
\(240\) | 31123.5 | 0.0348787 | ||||||||
\(241\) | 1.24022e6 | 1.37548 | 0.687742 | − | 0.725956i | \(-0.258602\pi\) | ||||
0.687742 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(242\) | −135507. | −0.148738 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.95581e6 | −2.10306 | ||||||||
\(245\) | −386964. | −0.411865 | ||||||||
\(246\) | 374842. | 0.394922 | ||||||||
\(247\) | 1.69693e6 | 1.76979 | ||||||||
\(248\) | −352736. | −0.364183 | ||||||||
\(249\) | 875075. | 0.894431 | ||||||||
\(250\) | −144614. | −0.146339 | ||||||||
\(251\) | 30660.6 | 0.0307183 | 0.0153591 | − | 0.999882i | \(-0.495111\pi\) | ||||
0.0153591 | + | 0.999882i | \(0.495111\pi\) | |||||||
\(252\) | 158421. | 0.157149 | ||||||||
\(253\) | −233213. | −0.229061 | ||||||||
\(254\) | −2.48796e6 | −2.41968 | ||||||||
\(255\) | 34961.7 | 0.0336699 | ||||||||
\(256\) | −1.26697e6 | −1.20828 | ||||||||
\(257\) | −687971. | −0.649737 | −0.324868 | − | 0.945759i | \(-0.605320\pi\) | ||||
−0.324868 | + | 0.945759i | \(0.605320\pi\) | |||||||
\(258\) | 372798. | 0.348678 | ||||||||
\(259\) | −69209.6 | −0.0641087 | ||||||||
\(260\) | −1.17790e6 | −1.08062 | ||||||||
\(261\) | −38916.0 | −0.0353612 | ||||||||
\(262\) | 3.39590e6 | 3.05634 | ||||||||
\(263\) | 1.70103e6 | 1.51643 | 0.758216 | − | 0.652004i | \(-0.226071\pi\) | ||||
0.758216 | + | 0.652004i | \(0.226071\pi\) | |||||||
\(264\) | 218319. | 0.192788 | ||||||||
\(265\) | 53628.0 | 0.0469112 | ||||||||
\(266\) | 651952. | 0.564952 | ||||||||
\(267\) | 347753. | 0.298533 | ||||||||
\(268\) | −840785. | −0.715069 | ||||||||
\(269\) | −982644. | −0.827972 | −0.413986 | − | 0.910283i | \(-0.635864\pi\) | ||||
−0.413986 | + | 0.910283i | \(0.635864\pi\) | |||||||
\(270\) | −168678. | −0.140815 | ||||||||
\(271\) | −276206. | −0.228459 | −0.114230 | − | 0.993454i | \(-0.536440\pi\) | ||||
−0.114230 | + | 0.993454i | \(0.536440\pi\) | |||||||
\(272\) | 21493.9 | 0.0176154 | ||||||||
\(273\) | −288021. | −0.233893 | ||||||||
\(274\) | 1.69305e6 | 1.36236 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 930820. | 0.735517 | ||||||||
\(277\) | 148776. | 0.116502 | 0.0582509 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582509 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(278\) | −78020.8 | −0.0605478 | ||||||||
\(279\) | 142519. | 0.109613 | ||||||||
\(280\) | −182673. | −0.139245 | ||||||||
\(281\) | 357772. | 0.270297 | 0.135148 | − | 0.990825i | \(-0.456849\pi\) | ||||
0.135148 | + | 0.990825i | \(0.456849\pi\) | |||||||
\(282\) | 1.03049e6 | 0.771652 | ||||||||
\(283\) | −492090. | −0.365240 | −0.182620 | − | 0.983184i | \(-0.558458\pi\) | ||||
−0.182620 | + | 0.983184i | \(0.558458\pi\) | |||||||
\(284\) | 573607. | 0.422006 | ||||||||
\(285\) | −434846. | −0.317120 | ||||||||
\(286\) | −983301. | −0.710839 | ||||||||
\(287\) | −164016. | −0.117539 | ||||||||
\(288\) | 415934. | 0.295490 | ||||||||
\(289\) | −1.39571e6 | −0.982995 | ||||||||
\(290\) | 111166. | 0.0776209 | ||||||||
\(291\) | −330791. | −0.228992 | ||||||||
\(292\) | 653189. | 0.448314 | ||||||||
\(293\) | 498120. | 0.338973 | 0.169487 | − | 0.985532i | \(-0.445789\pi\) | ||||
0.169487 | + | 0.985532i | \(0.445789\pi\) | |||||||
\(294\) | 1.28933e6 | 0.869952 | ||||||||
\(295\) | −396448. | −0.265235 | ||||||||
\(296\) | 380678. | 0.252539 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −2.51568e6 | −1.64103 | ||||||||
\(299\) | −1.69230e6 | −1.09471 | ||||||||
\(300\) | 301841. | 0.193631 | ||||||||
\(301\) | −163122. | −0.103776 | ||||||||
\(302\) | 2.18948e6 | 1.38141 | ||||||||
\(303\) | −1.66938e6 | −1.04460 | ||||||||
\(304\) | −267337. | −0.165911 | ||||||||
\(305\) | −911194. | −0.560869 | ||||||||
\(306\) | −116489. | −0.0711183 | ||||||||
\(307\) | −998760. | −0.604805 | −0.302402 | − | 0.953180i | \(-0.597789\pi\) | ||||
−0.302402 | + | 0.953180i | \(0.597789\pi\) | |||||||
\(308\) | −236654. | −0.142147 | ||||||||
\(309\) | 332017. | 0.197817 | ||||||||
\(310\) | −407115. | −0.240610 | ||||||||
\(311\) | 1.88783e6 | 1.10678 | 0.553389 | − | 0.832923i | \(-0.313334\pi\) | ||||
0.553389 | + | 0.832923i | \(0.313334\pi\) | |||||||
\(312\) | 1.58422e6 | 0.921360 | ||||||||
\(313\) | −2.34787e6 | −1.35461 | −0.677303 | − | 0.735704i | \(-0.736851\pi\) | ||||
−0.677303 | + | 0.735704i | \(0.736851\pi\) | |||||||
\(314\) | −1.96050e6 | −1.12213 | ||||||||
\(315\) | 73806.8 | 0.0419102 | ||||||||
\(316\) | −4.67951e6 | −2.63623 | ||||||||
\(317\) | 562721. | 0.314518 | 0.157259 | − | 0.987557i | \(-0.449734\pi\) | ||||
0.157259 | + | 0.987557i | \(0.449734\pi\) | |||||||
\(318\) | −178684. | −0.0990870 | ||||||||
\(319\) | 58133.7 | 0.0319854 | ||||||||
\(320\) | −1.29881e6 | −0.709038 | ||||||||
\(321\) | −1.12497e6 | −0.609364 | ||||||||
\(322\) | −650173. | −0.349454 | ||||||||
\(323\) | −300305. | −0.160161 | ||||||||
\(324\) | 352068. | 0.186322 | ||||||||
\(325\) | −548770. | −0.288192 | ||||||||
\(326\) | 3.15897e6 | 1.64627 | ||||||||
\(327\) | −1.35878e6 | −0.702713 | ||||||||
\(328\) | 902149. | 0.463013 | ||||||||
\(329\) | −450902. | −0.229664 | ||||||||
\(330\) | 251976. | 0.127372 | ||||||||
\(331\) | −1.00593e6 | −0.504657 | −0.252328 | − | 0.967642i | \(-0.581196\pi\) | ||||
−0.252328 | + | 0.967642i | \(0.581196\pi\) | |||||||
\(332\) | 5.21746e6 | 2.59785 | ||||||||
\(333\) | −153808. | −0.0760098 | ||||||||
\(334\) | 1.67103e6 | 0.819628 | ||||||||
\(335\) | −391714. | −0.190703 | ||||||||
\(336\) | 45375.4 | 0.0219266 | ||||||||
\(337\) | −280192. | −0.134394 | −0.0671971 | − | 0.997740i | \(-0.521406\pi\) | ||||
−0.0671971 | + | 0.997740i | \(0.521406\pi\) | |||||||
\(338\) | −3.69886e6 | −1.76107 | ||||||||
\(339\) | 1.42173e6 | 0.671919 | ||||||||
\(340\) | 208452. | 0.0977931 | ||||||||
\(341\) | −212898. | −0.0991485 | ||||||||
\(342\) | 1.44887e6 | 0.669829 | ||||||||
\(343\) | −1.17674e6 | −0.540063 | ||||||||
\(344\) | 897229. | 0.408796 | ||||||||
\(345\) | 433660. | 0.196156 | ||||||||
\(346\) | 5.95414e6 | 2.67380 | ||||||||
\(347\) | 2.10913e6 | 0.940328 | 0.470164 | − | 0.882579i | \(-0.344195\pi\) | ||||
0.470164 | + | 0.882579i | \(0.344195\pi\) | |||||||
\(348\) | −232029. | −0.102705 | ||||||||
\(349\) | 3.88469e6 | 1.70723 | 0.853617 | − | 0.520901i | \(-0.174404\pi\) | ||||
0.853617 | + | 0.520901i | \(0.174404\pi\) | |||||||
\(350\) | −210835. | −0.0919967 | ||||||||
\(351\) | −640085. | −0.277313 | ||||||||
\(352\) | −621333. | −0.267281 | ||||||||
\(353\) | 1.35663e6 | 0.579463 | 0.289732 | − | 0.957108i | \(-0.406434\pi\) | ||||
0.289732 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(354\) | 1.32093e6 | 0.560237 | ||||||||
\(355\) | 267238. | 0.112545 | ||||||||
\(356\) | 2.07341e6 | 0.867081 | ||||||||
\(357\) | 50971.0 | 0.0211667 | ||||||||
\(358\) | 2.47045e6 | 1.01875 | ||||||||
\(359\) | 3.93436e6 | 1.61116 | 0.805579 | − | 0.592488i | \(-0.201854\pi\) | ||||
0.805579 | + | 0.592488i | \(0.201854\pi\) | |||||||
\(360\) | −405964. | −0.165094 | ||||||||
\(361\) | 1.25904e6 | 0.508476 | ||||||||
\(362\) | −2.60564e6 | −1.04506 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −1.71727e6 | −0.679336 | ||||||||
\(365\) | 304315. | 0.119561 | ||||||||
\(366\) | 3.03602e6 | 1.18468 | ||||||||
\(367\) | −2.82588e6 | −1.09519 | −0.547594 | − | 0.836744i | \(-0.684456\pi\) | ||||
−0.547594 | + | 0.836744i | \(0.684456\pi\) | |||||||
\(368\) | 266608. | 0.102625 | ||||||||
\(369\) | −364502. | −0.139359 | ||||||||
\(370\) | 439365. | 0.166848 | ||||||||
\(371\) | 78184.9 | 0.0294909 | ||||||||
\(372\) | 849738. | 0.318367 | ||||||||
\(373\) | 4.58790e6 | 1.70743 | 0.853713 | − | 0.520744i | \(-0.174345\pi\) | ||||
0.853713 | + | 0.520744i | \(0.174345\pi\) | |||||||
\(374\) | 174015. | 0.0643290 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 2.48013e6 | 0.904699 | ||||||||
\(377\) | 421845. | 0.152862 | ||||||||
\(378\) | −245918. | −0.0885239 | ||||||||
\(379\) | 2.84827e6 | 1.01855 | 0.509277 | − | 0.860603i | \(-0.329913\pi\) | ||||
0.509277 | + | 0.860603i | \(0.329913\pi\) | |||||||
\(380\) | −2.59268e6 | −0.921065 | ||||||||
\(381\) | 2.41933e6 | 0.853852 | ||||||||
\(382\) | −8.64190e6 | −3.03006 | ||||||||
\(383\) | −2.78467e6 | −0.970013 | −0.485006 | − | 0.874511i | \(-0.661183\pi\) | ||||
−0.485006 | + | 0.874511i | \(0.661183\pi\) | |||||||
\(384\) | 2.84863e6 | 0.985845 | ||||||||
\(385\) | −110255. | −0.0379092 | ||||||||
\(386\) | −2.77774e6 | −0.948906 | ||||||||
\(387\) | −362514. | −0.123040 | ||||||||
\(388\) | −1.97227e6 | −0.665101 | ||||||||
\(389\) | 3.95277e6 | 1.32442 | 0.662212 | − | 0.749316i | \(-0.269618\pi\) | ||||
0.662212 | + | 0.749316i | \(0.269618\pi\) | |||||||
\(390\) | 1.82845e6 | 0.608726 | ||||||||
\(391\) | 299486. | 0.0990682 | ||||||||
\(392\) | 3.10308e6 | 1.01995 | ||||||||
\(393\) | −3.30223e6 | −1.07851 | ||||||||
\(394\) | 8.74571e6 | 2.83827 | ||||||||
\(395\) | −2.18014e6 | −0.703059 | ||||||||
\(396\) | −525928. | −0.168534 | ||||||||
\(397\) | −5.55351e6 | −1.76844 | −0.884221 | − | 0.467068i | \(-0.845310\pi\) | ||||
−0.884221 | + | 0.467068i | \(0.845310\pi\) | |||||||
\(398\) | 9.33125e6 | 2.95279 | ||||||||
\(399\) | −633968. | −0.199359 | ||||||||
\(400\) | 86454.2 | 0.0270169 | ||||||||
\(401\) | −279266. | −0.0867277 | −0.0433639 | − | 0.999059i | \(-0.513807\pi\) | ||||
−0.0433639 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(402\) | 1.30515e6 | 0.402807 | ||||||||
\(403\) | −1.54489e6 | −0.473843 | ||||||||
\(404\) | −9.95334e6 | −3.03400 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 162071. | 0.0487967 | ||||||||
\(407\) | 229763. | 0.0687534 | ||||||||
\(408\) | −280359. | −0.0833805 | ||||||||
\(409\) | 5.17128e6 | 1.52859 | 0.764293 | − | 0.644869i | \(-0.223088\pi\) | ||||
0.764293 | + | 0.644869i | \(0.223088\pi\) | |||||||
\(410\) | 1.04123e6 | 0.305905 | ||||||||
\(411\) | −1.64635e6 | −0.480747 | ||||||||
\(412\) | 1.97958e6 | 0.574554 | ||||||||
\(413\) | −577987. | −0.166741 | ||||||||
\(414\) | −1.44492e6 | −0.414326 | ||||||||
\(415\) | 2.43076e6 | 0.692824 | ||||||||
\(416\) | −4.50868e6 | −1.27737 | ||||||||
\(417\) | 75868.7 | 0.0213660 | ||||||||
\(418\) | −2.16436e6 | −0.605883 | ||||||||
\(419\) | −6.04152e6 | −1.68117 | −0.840585 | − | 0.541680i | \(-0.817788\pi\) | ||||
−0.840585 | + | 0.541680i | \(0.817788\pi\) | |||||||
\(420\) | 440058. | 0.121727 | ||||||||
\(421\) | −895386. | −0.246210 | −0.123105 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123105 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(422\) | −4.60432e6 | −1.25859 | ||||||||
\(423\) | −1.00207e6 | −0.272298 | ||||||||
\(424\) | −430045. | −0.116171 | ||||||||
\(425\) | 97115.7 | 0.0260806 | ||||||||
\(426\) | −890413. | −0.237721 | ||||||||
\(427\) | −1.32844e6 | −0.352592 | ||||||||
\(428\) | −6.70738e6 | −1.76988 | ||||||||
\(429\) | 956177. | 0.250839 | ||||||||
\(430\) | 1.03555e6 | 0.270085 | ||||||||
\(431\) | −1.60867e6 | −0.417132 | −0.208566 | − | 0.978008i | \(-0.566880\pi\) | ||||
−0.208566 | + | 0.978008i | \(0.566880\pi\) | |||||||
\(432\) | 100840. | 0.0259971 | ||||||||
\(433\) | 1.86039e6 | 0.476853 | 0.238427 | − | 0.971161i | \(-0.423368\pi\) | ||||
0.238427 | + | 0.971161i | \(0.423368\pi\) | |||||||
\(434\) | −593538. | −0.151260 | ||||||||
\(435\) | −108100. | −0.0273906 | ||||||||
\(436\) | −8.10142e6 | −2.04101 | ||||||||
\(437\) | −3.72495e6 | −0.933075 | ||||||||
\(438\) | −1.01395e6 | −0.252540 | ||||||||
\(439\) | 2.75051e6 | 0.681164 | 0.340582 | − | 0.940215i | \(-0.389376\pi\) | ||||
0.340582 | + | 0.940215i | \(0.389376\pi\) | |||||||
\(440\) | 606441. | 0.149333 | ||||||||
\(441\) | −1.25376e6 | −0.306986 | ||||||||
\(442\) | 1.26273e6 | 0.307436 | ||||||||
\(443\) | 3.15804e6 | 0.764555 | 0.382278 | − | 0.924048i | \(-0.375140\pi\) | ||||
0.382278 | + | 0.924048i | \(0.375140\pi\) | |||||||
\(444\) | −917051. | −0.220768 | ||||||||
\(445\) | 965981. | 0.231243 | ||||||||
\(446\) | −1.05636e7 | −2.51464 | ||||||||
\(447\) | 2.44629e6 | 0.579081 | ||||||||
\(448\) | −1.89355e6 | −0.445740 | ||||||||
\(449\) | −127508. | −0.0298484 | −0.0149242 | − | 0.999889i | \(-0.504751\pi\) | ||||
−0.0149242 | + | 0.999889i | \(0.504751\pi\) | |||||||
\(450\) | −468550. | −0.109075 | ||||||||
\(451\) | 544504. | 0.126055 | ||||||||
\(452\) | 8.47675e6 | 1.95157 | ||||||||
\(453\) | −2.12908e6 | −0.487469 | ||||||||
\(454\) | −6.19598e6 | −1.41082 | ||||||||
\(455\) | −800059. | −0.181173 | ||||||||
\(456\) | 3.48705e6 | 0.785319 | ||||||||
\(457\) | 2.19209e6 | 0.490984 | 0.245492 | − | 0.969399i | \(-0.421050\pi\) | ||||
0.245492 | + | 0.969399i | \(0.421050\pi\) | |||||||
\(458\) | −5.44268e6 | −1.21241 | ||||||||
\(459\) | 113276. | 0.0250960 | ||||||||
\(460\) | 2.58561e6 | 0.569729 | ||||||||
\(461\) | 5.20229e6 | 1.14010 | 0.570050 | − | 0.821610i | \(-0.306924\pi\) | ||||
0.570050 | + | 0.821610i | \(0.306924\pi\) | |||||||
\(462\) | 367359. | 0.0800728 | ||||||||
\(463\) | 2.66624e6 | 0.578025 | 0.289013 | − | 0.957325i | \(-0.406673\pi\) | ||||
0.289013 | + | 0.957325i | \(0.406673\pi\) | |||||||
\(464\) | −66458.3 | −0.0143303 | ||||||||
\(465\) | 395885. | 0.0849057 | ||||||||
\(466\) | −1.84566e6 | −0.393720 | ||||||||
\(467\) | −2.35578e6 | −0.499853 | −0.249926 | − | 0.968265i | \(-0.580406\pi\) | ||||
−0.249926 | + | 0.968265i | \(0.580406\pi\) | |||||||
\(468\) | −3.81638e6 | −0.805447 | ||||||||
\(469\) | −571084. | −0.119886 | ||||||||
\(470\) | 2.86247e6 | 0.597719 | ||||||||
\(471\) | 1.90642e6 | 0.395973 | ||||||||
\(472\) | 3.17914e6 | 0.656832 | ||||||||
\(473\) | 541534. | 0.111294 | ||||||||
\(474\) | 7.26403e6 | 1.48502 | ||||||||
\(475\) | −1.20791e6 | −0.245640 | ||||||||
\(476\) | 303905. | 0.0614780 | ||||||||
\(477\) | 173755. | 0.0349655 | ||||||||
\(478\) | 3.77668e6 | 0.756032 | ||||||||
\(479\) | −4.78329e6 | −0.952551 | −0.476276 | − | 0.879296i | \(-0.658014\pi\) | ||||
−0.476276 | + | 0.879296i | \(0.658014\pi\) | |||||||
\(480\) | 1.15537e6 | 0.228886 | ||||||||
\(481\) | 1.66727e6 | 0.328581 | ||||||||
\(482\) | −1.14786e7 | −2.25046 | ||||||||
\(483\) | 632239. | 0.123314 | ||||||||
\(484\) | 785646. | 0.152445 | ||||||||
\(485\) | −918863. | −0.177377 | ||||||||
\(486\) | −546517. | −0.104957 | ||||||||
\(487\) | −3.31515e6 | −0.633405 | −0.316702 | − | 0.948525i | \(-0.602576\pi\) | ||||
−0.316702 | + | 0.948525i | \(0.602576\pi\) | |||||||
\(488\) | 7.30691e6 | 1.38894 | ||||||||
\(489\) | −3.07183e6 | −0.580932 | ||||||||
\(490\) | 3.58147e6 | 0.673862 | ||||||||
\(491\) | −3.02276e6 | −0.565847 | −0.282924 | − | 0.959142i | \(-0.591304\pi\) | ||||
−0.282924 | + | 0.959142i | \(0.591304\pi\) | |||||||
\(492\) | −2.17327e6 | −0.404763 | ||||||||
\(493\) | −74653.9 | −0.0138336 | ||||||||
\(494\) | −1.57056e7 | −2.89559 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | 243384. | 0.0444210 | ||||||||
\(497\) | 389610. | 0.0707520 | ||||||||
\(498\) | −8.09909e6 | −1.46340 | ||||||||
\(499\) | 4.46530e6 | 0.802785 | 0.401392 | − | 0.915906i | \(-0.368526\pi\) | ||||
0.401392 | + | 0.915906i | \(0.368526\pi\) | |||||||
\(500\) | 838448. | 0.149986 | ||||||||
\(501\) | −1.62493e6 | −0.289228 | ||||||||
\(502\) | −283774. | −0.0502589 | ||||||||
\(503\) | −1.77528e6 | −0.312858 | −0.156429 | − | 0.987689i | \(-0.549998\pi\) | ||||
−0.156429 | + | 0.987689i | \(0.549998\pi\) | |||||||
\(504\) | −591861. | −0.103787 | ||||||||
\(505\) | −4.63717e6 | −0.809141 | ||||||||
\(506\) | 2.15846e6 | 0.374772 | ||||||||
\(507\) | 3.59683e6 | 0.621441 | ||||||||
\(508\) | 1.44248e7 | 2.47999 | ||||||||
\(509\) | −485180. | −0.0830058 | −0.0415029 | − | 0.999138i | \(-0.513215\pi\) | ||||
−0.0415029 | + | 0.999138i | \(0.513215\pi\) | |||||||
\(510\) | −323581. | −0.0550880 | ||||||||
\(511\) | 443664. | 0.0751627 | ||||||||
\(512\) | 1.59770e6 | 0.269353 | ||||||||
\(513\) | −1.40890e6 | −0.236367 | ||||||||
\(514\) | 6.36739e6 | 1.06305 | ||||||||
\(515\) | 922269. | 0.153228 | ||||||||
\(516\) | −2.16142e6 | −0.357367 | ||||||||
\(517\) | 1.49691e6 | 0.246303 | ||||||||
\(518\) | 640556. | 0.104890 | ||||||||
\(519\) | −5.78989e6 | −0.943522 | ||||||||
\(520\) | 4.40061e6 | 0.713682 | ||||||||
\(521\) | 9.92932e6 | 1.60260 | 0.801300 | − | 0.598262i | \(-0.204142\pi\) | ||||
0.801300 | + | 0.598262i | \(0.204142\pi\) | |||||||
\(522\) | 360179. | 0.0578552 | ||||||||
\(523\) | 5.04767e6 | 0.806931 | 0.403466 | − | 0.914995i | \(-0.367805\pi\) | ||||
0.403466 | + | 0.914995i | \(0.367805\pi\) | |||||||
\(524\) | −1.96889e7 | −3.13251 | ||||||||
\(525\) | 205019. | 0.0324635 | ||||||||
\(526\) | −1.57436e7 | −2.48107 | ||||||||
\(527\) | 273398. | 0.0428815 | ||||||||
\(528\) | −150638. | −0.0235152 | ||||||||
\(529\) | −2.72156e6 | −0.422842 | ||||||||
\(530\) | −496343. | −0.0767525 | ||||||||
\(531\) | −1.28449e6 | −0.197695 | ||||||||
\(532\) | −3.77990e6 | −0.579031 | ||||||||
\(533\) | 3.95117e6 | 0.602432 | ||||||||
\(534\) | −3.21856e6 | −0.488437 | ||||||||
\(535\) | −3.12491e6 | −0.472011 | ||||||||
\(536\) | 3.14117e6 | 0.472258 | ||||||||
\(537\) | −2.40230e6 | −0.359494 | ||||||||
\(538\) | 9.09467e6 | 1.35466 | ||||||||
\(539\) | 1.87291e6 | 0.277680 | ||||||||
\(540\) | 977966. | 0.144324 | ||||||||
\(541\) | −4.46393e6 | −0.655729 | −0.327864 | − | 0.944725i | \(-0.606329\pi\) | ||||
−0.327864 | + | 0.944725i | \(0.606329\pi\) | |||||||
\(542\) | 2.55637e6 | 0.373788 | ||||||||
\(543\) | 2.53376e6 | 0.368779 | ||||||||
\(544\) | 797900. | 0.115598 | ||||||||
\(545\) | −3.77438e6 | −0.544319 | ||||||||
\(546\) | 2.66572e6 | 0.382678 | ||||||||
\(547\) | −6.62530e6 | −0.946755 | −0.473377 | − | 0.880860i | \(-0.656965\pi\) | ||||
−0.473377 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(548\) | −9.81601e6 | −1.39632 | ||||||||
\(549\) | −2.95227e6 | −0.418047 | ||||||||
\(550\) | 699932. | 0.0986619 | ||||||||
\(551\) | 928530. | 0.130292 | ||||||||
\(552\) | −3.47754e6 | −0.485763 | ||||||||
\(553\) | −3.17845e6 | −0.441980 | ||||||||
\(554\) | −1.37696e6 | −0.190611 | ||||||||
\(555\) | −427246. | −0.0588769 | ||||||||
\(556\) | 452351. | 0.0620568 | ||||||||
\(557\) | −717580. | −0.0980014 | −0.0490007 | − | 0.998799i | \(-0.515604\pi\) | ||||
−0.0490007 | + | 0.998799i | \(0.515604\pi\) | |||||||
\(558\) | −1.31905e6 | −0.179340 | ||||||||
\(559\) | 3.92962e6 | 0.531889 | ||||||||
\(560\) | 126043. | 0.0169843 | ||||||||
\(561\) | −169214. | −0.0227002 | ||||||||
\(562\) | −3.31129e6 | −0.442238 | ||||||||
\(563\) | 1.35097e7 | 1.79629 | 0.898143 | − | 0.439703i | \(-0.144916\pi\) | ||||
0.898143 | + | 0.439703i | \(0.144916\pi\) | |||||||
\(564\) | −5.97461e6 | −0.790882 | ||||||||
\(565\) | 3.94924e6 | 0.520466 | ||||||||
\(566\) | 4.55444e6 | 0.597577 | ||||||||
\(567\) | 239134. | 0.0312380 | ||||||||
\(568\) | −2.14300e6 | −0.278709 | ||||||||
\(569\) | 1.35535e7 | 1.75498 | 0.877488 | − | 0.479598i | \(-0.159218\pi\) | ||||
0.877488 | + | 0.479598i | \(0.159218\pi\) | |||||||
\(570\) | 4.02463e6 | 0.518847 | ||||||||
\(571\) | 7.82130e6 | 1.00390 | 0.501948 | − | 0.864898i | \(-0.332617\pi\) | ||||
0.501948 | + | 0.864898i | \(0.332617\pi\) | |||||||
\(572\) | 5.70101e6 | 0.728554 | ||||||||
\(573\) | 8.40351e6 | 1.06924 | ||||||||
\(574\) | 1.51802e6 | 0.192308 | ||||||||
\(575\) | 1.20461e6 | 0.151942 | ||||||||
\(576\) | −4.20814e6 | −0.528486 | ||||||||
\(577\) | 218443. | 0.0273149 | 0.0136574 | − | 0.999907i | \(-0.495653\pi\) | ||||
0.0136574 | + | 0.999907i | \(0.495653\pi\) | |||||||
\(578\) | 1.29177e7 | 1.60830 | ||||||||
\(579\) | 2.70112e6 | 0.334847 | ||||||||
\(580\) | −644524. | −0.0795553 | ||||||||
\(581\) | 3.54384e6 | 0.435546 | ||||||||
\(582\) | 3.06157e6 | 0.374659 | ||||||||
\(583\) | −259559. | −0.0316275 | ||||||||
\(584\) | −2.44031e6 | −0.296083 | ||||||||
\(585\) | −1.77802e6 | −0.214806 | ||||||||
\(586\) | −4.61026e6 | −0.554602 | ||||||||
\(587\) | −5.46003e6 | −0.654033 | −0.327017 | − | 0.945019i | \(-0.606043\pi\) | ||||
−0.327017 | + | 0.945019i | \(0.606043\pi\) | |||||||
\(588\) | −7.47531e6 | −0.891632 | ||||||||
\(589\) | −3.40048e6 | −0.403879 | ||||||||
\(590\) | 3.66925e6 | 0.433958 | ||||||||
\(591\) | −8.50446e6 | −1.00156 | ||||||||
\(592\) | −262664. | −0.0308033 | ||||||||
\(593\) | 1.41186e7 | 1.64875 | 0.824375 | − | 0.566044i | \(-0.191527\pi\) | ||||
0.824375 | + | 0.566044i | \(0.191527\pi\) | |||||||
\(594\) | 816401. | 0.0949374 | ||||||||
\(595\) | 141586. | 0.0163956 | ||||||||
\(596\) | 1.45855e7 | 1.68192 | ||||||||
\(597\) | −9.07385e6 | −1.04197 | ||||||||
\(598\) | 1.56628e7 | 1.79108 | ||||||||
\(599\) | 8.02044e6 | 0.913338 | 0.456669 | − | 0.889637i | \(-0.349042\pi\) | ||||
0.456669 | + | 0.889637i | \(0.349042\pi\) | |||||||
\(600\) | −1.12768e6 | −0.127881 | ||||||||
\(601\) | −1.20301e7 | −1.35857 | −0.679286 | − | 0.733874i | \(-0.737710\pi\) | ||||
−0.679286 | + | 0.733874i | \(0.737710\pi\) | |||||||
\(602\) | 1.50974e6 | 0.169790 | ||||||||
\(603\) | −1.26915e6 | −0.142141 | ||||||||
\(604\) | −1.26942e7 | −1.41584 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 1.54506e7 | 1.70909 | ||||||||
\(607\) | −1.58863e7 | −1.75005 | −0.875025 | − | 0.484078i | \(-0.839155\pi\) | ||||
−0.875025 | + | 0.484078i | \(0.839155\pi\) | |||||||
\(608\) | −9.92412e6 | −1.08876 | ||||||||
\(609\) | −157600. | −0.0172192 | ||||||||
\(610\) | 8.43338e6 | 0.917650 | ||||||||
\(611\) | 1.08623e7 | 1.17711 | ||||||||
\(612\) | 675384. | 0.0728907 | ||||||||
\(613\) | 1.27701e7 | 1.37260 | 0.686301 | − | 0.727318i | \(-0.259233\pi\) | ||||
0.686301 | + | 0.727318i | \(0.259233\pi\) | |||||||
\(614\) | 9.24383e6 | 0.989535 | ||||||||
\(615\) | −1.01251e6 | −0.107947 | ||||||||
\(616\) | 884137. | 0.0938789 | ||||||||
\(617\) | 5.32363e6 | 0.562982 | 0.281491 | − | 0.959564i | \(-0.409171\pi\) | ||||
0.281491 | + | 0.959564i | \(0.409171\pi\) | |||||||
\(618\) | −3.07292e6 | −0.323653 | ||||||||
\(619\) | −5.79882e6 | −0.608293 | −0.304147 | − | 0.952625i | \(-0.598371\pi\) | ||||
−0.304147 | + | 0.952625i | \(0.598371\pi\) | |||||||
\(620\) | 2.36038e6 | 0.246606 | ||||||||
\(621\) | 1.40506e6 | 0.146206 | ||||||||
\(622\) | −1.74724e7 | −1.81083 | ||||||||
\(623\) | 1.40832e6 | 0.145372 | ||||||||
\(624\) | −1.09310e6 | −0.112382 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.17302e7 | 2.21630 | ||||||||
\(627\) | 2.10466e6 | 0.213802 | ||||||||
\(628\) | 1.13666e7 | 1.15009 | ||||||||
\(629\) | −295056. | −0.0297357 | ||||||||
\(630\) | −683105. | −0.0685703 | ||||||||
\(631\) | −8.25264e6 | −0.825124 | −0.412562 | − | 0.910929i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910929i | \(0.635366\pi\) | |||||||
\(632\) | 1.74826e7 | 1.74106 | ||||||||
\(633\) | 4.47731e6 | 0.444128 | ||||||||
\(634\) | −5.20816e6 | −0.514590 | ||||||||
\(635\) | 6.72036e6 | 0.661391 | ||||||||
\(636\) | 1.03598e6 | 0.101556 | ||||||||
\(637\) | 1.35907e7 | 1.32707 | ||||||||
\(638\) | −538045. | −0.0523320 | ||||||||
\(639\) | 865852. | 0.0838864 | ||||||||
\(640\) | 7.91287e6 | 0.763632 | ||||||||
\(641\) | 1.14111e7 | 1.09694 | 0.548471 | − | 0.836169i | \(-0.315210\pi\) | ||||
0.548471 | + | 0.836169i | \(0.315210\pi\) | |||||||
\(642\) | 1.04119e7 | 0.996994 | ||||||||
\(643\) | −3.26961e6 | −0.311866 | −0.155933 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155933 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(644\) | 3.76959e6 | 0.358162 | ||||||||
\(645\) | −1.00698e6 | −0.0953067 | ||||||||
\(646\) | 2.77941e6 | 0.262043 | ||||||||
\(647\) | −9.95068e6 | −0.934527 | −0.467264 | − | 0.884118i | \(-0.654760\pi\) | ||||
−0.467264 | + | 0.884118i | \(0.654760\pi\) | |||||||
\(648\) | −1.31532e6 | −0.123054 | ||||||||
\(649\) | 1.91881e6 | 0.178822 | ||||||||
\(650\) | 5.07903e6 | 0.471517 | ||||||||
\(651\) | 577166. | 0.0533763 | ||||||||
\(652\) | −1.83152e7 | −1.68730 | ||||||||
\(653\) | 1.52022e7 | 1.39515 | 0.697577 | − | 0.716509i | \(-0.254261\pi\) | ||||
0.697577 | + | 0.716509i | \(0.254261\pi\) | |||||||
\(654\) | 1.25759e7 | 1.14973 | ||||||||
\(655\) | −9.17285e6 | −0.835413 | ||||||||
\(656\) | −622474. | −0.0564757 | ||||||||
\(657\) | 985979. | 0.0891157 | ||||||||
\(658\) | 4.17324e6 | 0.375758 | ||||||||
\(659\) | −9.63232e6 | −0.864007 | −0.432004 | − | 0.901872i | \(-0.642193\pi\) | ||||
−0.432004 | + | 0.901872i | \(0.642193\pi\) | |||||||
\(660\) | −1.46091e6 | −0.130546 | ||||||||
\(661\) | 2.04631e7 | 1.82166 | 0.910832 | − | 0.412778i | \(-0.135442\pi\) | ||||
0.910832 | + | 0.412778i | \(0.135442\pi\) | |||||||
\(662\) | 9.31016e6 | 0.825681 | ||||||||
\(663\) | −1.22790e6 | −0.108487 | ||||||||
\(664\) | −1.94924e7 | −1.71572 | ||||||||
\(665\) | −1.76102e6 | −0.154422 | ||||||||
\(666\) | 1.42354e6 | 0.124361 | ||||||||
\(667\) | −925997. | −0.0805926 | ||||||||
\(668\) | −9.68832e6 | −0.840054 | ||||||||
\(669\) | 1.02722e7 | 0.887361 | ||||||||
\(670\) | 3.62543e6 | 0.312013 | ||||||||
\(671\) | 4.41018e6 | 0.378137 | ||||||||
\(672\) | 1.68443e6 | 0.143890 | ||||||||
\(673\) | 1.57773e6 | 0.134275 | 0.0671376 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671376 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(674\) | 2.59326e6 | 0.219885 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | 2.14454e7 | 1.80496 | ||||||||
\(677\) | 6.92750e6 | 0.580904 | 0.290452 | − | 0.956890i | \(-0.406194\pi\) | ||||
0.290452 | + | 0.956890i | \(0.406194\pi\) | |||||||
\(678\) | −1.31585e7 | −1.09934 | ||||||||
\(679\) | −1.33962e6 | −0.111509 | ||||||||
\(680\) | −778776. | −0.0645862 | ||||||||
\(681\) | 6.02506e6 | 0.497845 | ||||||||
\(682\) | 1.97044e6 | 0.162219 | ||||||||
\(683\) | −277554. | −0.0227665 | −0.0113833 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113833 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(684\) | −8.40029e6 | −0.686521 | ||||||||
\(685\) | −4.57318e6 | −0.372385 | ||||||||
\(686\) | 1.08911e7 | 0.883609 | ||||||||
\(687\) | 5.29255e6 | 0.427832 | ||||||||
\(688\) | −619080. | −0.0498627 | ||||||||
\(689\) | −1.88348e6 | −0.151152 | ||||||||
\(690\) | −4.01366e6 | −0.320935 | ||||||||
\(691\) | −2.12446e7 | −1.69259 | −0.846297 | − | 0.532712i | \(-0.821173\pi\) | ||||
−0.846297 | + | 0.532712i | \(0.821173\pi\) | |||||||
\(692\) | −3.45211e7 | −2.74043 | ||||||||
\(693\) | −357225. | −0.0282559 | ||||||||
\(694\) | −1.95206e7 | −1.53849 | ||||||||
\(695\) | 210746. | 0.0165500 | ||||||||
\(696\) | 866858. | 0.0678305 | ||||||||
\(697\) | −699238. | −0.0545184 | ||||||||
\(698\) | −3.59540e7 | −2.79324 | ||||||||
\(699\) | 1.79475e6 | 0.138935 | ||||||||
\(700\) | 1.22238e6 | 0.0942893 | ||||||||
\(701\) | −1.06971e7 | −0.822184 | −0.411092 | − | 0.911594i | \(-0.634853\pi\) | ||||
−0.411092 | + | 0.911594i | \(0.634853\pi\) | |||||||
\(702\) | 5.92419e6 | 0.453718 | ||||||||
\(703\) | 3.66985e6 | 0.280066 | ||||||||
\(704\) | 6.28623e6 | 0.478034 | ||||||||
\(705\) | −2.78351e6 | −0.210921 | ||||||||
\(706\) | −1.25561e7 | −0.948072 | ||||||||
\(707\) | −6.76058e6 | −0.508669 | ||||||||
\(708\) | −7.65853e6 | −0.574199 | ||||||||
\(709\) | 6.52521e6 | 0.487505 | 0.243752 | − | 0.969838i | \(-0.421622\pi\) | ||||
0.243752 | + | 0.969838i | \(0.421622\pi\) | |||||||
\(710\) | −2.47337e6 | −0.184138 | ||||||||
\(711\) | −7.06365e6 | −0.524029 | ||||||||
\(712\) | −7.74625e6 | −0.572653 | ||||||||
\(713\) | 3.39120e6 | 0.249821 | ||||||||
\(714\) | −471753. | −0.0346313 | ||||||||
\(715\) | 2.65605e6 | 0.194299 | ||||||||
\(716\) | −1.43232e7 | −1.04414 | ||||||||
\(717\) | −3.67250e6 | −0.266786 | ||||||||
\(718\) | −3.64137e7 | −2.63605 | ||||||||
\(719\) | −2.12413e7 | −1.53235 | −0.766176 | − | 0.642631i | \(-0.777843\pi\) | ||||
−0.766176 | + | 0.642631i | \(0.777843\pi\) | |||||||
\(720\) | 280112. | 0.0201372 | ||||||||
\(721\) | 1.34459e6 | 0.0963276 | ||||||||
\(722\) | −1.16528e7 | −0.831928 | ||||||||
\(723\) | 1.11620e7 | 0.794135 | ||||||||
\(724\) | 1.51071e7 | 1.07111 | ||||||||
\(725\) | −300278. | −0.0212167 | ||||||||
\(726\) | −1.21956e6 | −0.0858742 | ||||||||
\(727\) | −1.06687e7 | −0.748646 | −0.374323 | − | 0.927298i | \(-0.622125\pi\) | ||||
−0.374323 | + | 0.927298i | \(0.622125\pi\) | |||||||
\(728\) | 6.41571e6 | 0.448659 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.81652e6 | −0.195617 | ||||||||
\(731\) | −695424. | −0.0481345 | ||||||||
\(732\) | −1.76023e7 | −1.21420 | ||||||||
\(733\) | −2.30788e7 | −1.58655 | −0.793274 | − | 0.608864i | \(-0.791625\pi\) | ||||
−0.793274 | + | 0.608864i | \(0.791625\pi\) | |||||||
\(734\) | 2.61544e7 | 1.79186 | ||||||||
\(735\) | −3.48268e6 | −0.237791 | ||||||||
\(736\) | 9.89705e6 | 0.673459 | ||||||||
\(737\) | 1.89589e6 | 0.128572 | ||||||||
\(738\) | 3.37358e6 | 0.228008 | ||||||||
\(739\) | −2.27313e7 | −1.53113 | −0.765566 | − | 0.643358i | \(-0.777541\pi\) | ||||
−0.765566 | + | 0.643358i | \(0.777541\pi\) | |||||||
\(740\) | −2.54736e6 | −0.171006 | ||||||||
\(741\) | 1.52724e7 | 1.02179 | ||||||||
\(742\) | −723625. | −0.0482507 | ||||||||
\(743\) | −1.49328e7 | −0.992360 | −0.496180 | − | 0.868220i | \(-0.665264\pi\) | ||||
−0.496180 | + | 0.868220i | \(0.665264\pi\) | |||||||
\(744\) | −3.17462e6 | −0.210261 | ||||||||
\(745\) | 6.79525e6 | 0.448554 | ||||||||
\(746\) | −4.24624e7 | −2.79356 | ||||||||
\(747\) | 7.87568e6 | 0.516400 | ||||||||
\(748\) | −1.00891e6 | −0.0659321 | ||||||||
\(749\) | −4.55584e6 | −0.296732 | ||||||||
\(750\) | −1.30153e6 | −0.0844890 | ||||||||
\(751\) | −1.92964e7 | −1.24846 | −0.624232 | − | 0.781239i | \(-0.714588\pi\) | ||||
−0.624232 | + | 0.781239i | \(0.714588\pi\) | |||||||
\(752\) | −1.71126e6 | −0.110350 | ||||||||
\(753\) | 275946. | 0.0177352 | ||||||||
\(754\) | −3.90431e6 | −0.250101 | ||||||||
\(755\) | −5.91412e6 | −0.377592 | ||||||||
\(756\) | 1.42579e6 | 0.0907300 | ||||||||
\(757\) | 1.35397e7 | 0.858756 | 0.429378 | − | 0.903125i | \(-0.358733\pi\) | ||||
0.429378 | + | 0.903125i | \(0.358733\pi\) | |||||||
\(758\) | −2.63616e7 | −1.66648 | ||||||||
\(759\) | −2.09891e6 | −0.132248 | ||||||||
\(760\) | 9.68626e6 | 0.608306 | ||||||||
\(761\) | 2.60669e7 | 1.63165 | 0.815825 | − | 0.578299i | \(-0.196283\pi\) | ||||
0.815825 | + | 0.578299i | \(0.196283\pi\) | |||||||
\(762\) | −2.23916e7 | −1.39701 | ||||||||
\(763\) | −5.50271e6 | −0.342188 | ||||||||
\(764\) | 5.01042e7 | 3.10557 | ||||||||
\(765\) | 314655. | 0.0194393 | ||||||||
\(766\) | 2.57730e7 | 1.58706 | ||||||||
\(767\) | 1.39238e7 | 0.854611 | ||||||||
\(768\) | −1.14027e7 | −0.697598 | ||||||||
\(769\) | −1.65354e7 | −1.00832 | −0.504162 | − | 0.863609i | \(-0.668199\pi\) | ||||
−0.504162 | + | 0.863609i | \(0.668199\pi\) | |||||||
\(770\) | 1.02044e6 | 0.0620242 | ||||||||
\(771\) | −6.19174e6 | −0.375126 | ||||||||
\(772\) | 1.61049e7 | 0.972554 | ||||||||
\(773\) | 8.95978e6 | 0.539323 | 0.269661 | − | 0.962955i | \(-0.413088\pi\) | ||||
0.269661 | + | 0.962955i | \(0.413088\pi\) | |||||||
\(774\) | 3.35518e6 | 0.201309 | ||||||||
\(775\) | 1.09968e6 | 0.0657677 | ||||||||
\(776\) | 7.36841e6 | 0.439258 | ||||||||
\(777\) | −622887. | −0.0370132 | ||||||||
\(778\) | −3.65841e7 | −2.16692 | ||||||||
\(779\) | 8.69698e6 | 0.513482 | ||||||||
\(780\) | −1.06011e7 | −0.623897 | ||||||||
\(781\) | −1.29343e6 | −0.0758781 | ||||||||
\(782\) | −2.77183e6 | −0.162088 | ||||||||
\(783\) | −350244. | −0.0204158 | ||||||||
\(784\) | −2.14110e6 | −0.124407 | ||||||||
\(785\) | 5.29561e6 | 0.306720 | ||||||||
\(786\) | 3.05631e7 | 1.76458 | ||||||||
\(787\) | −2.31723e7 | −1.33362 | −0.666812 | − | 0.745226i | \(-0.732341\pi\) | ||||
−0.666812 | + | 0.745226i | \(0.732341\pi\) | |||||||
\(788\) | −5.07061e7 | −2.90901 | ||||||||
\(789\) | 1.53093e7 | 0.875512 | ||||||||
\(790\) | 2.01779e7 | 1.15029 | ||||||||
\(791\) | 5.75765e6 | 0.327193 | ||||||||
\(792\) | 1.96487e6 | 0.111306 | ||||||||
\(793\) | 3.20023e7 | 1.80717 | ||||||||
\(794\) | 5.13994e7 | 2.89339 | ||||||||
\(795\) | 482652. | 0.0270842 | ||||||||
\(796\) | −5.41010e7 | −3.02638 | ||||||||
\(797\) | −3.40811e7 | −1.90050 | −0.950250 | − | 0.311489i | \(-0.899172\pi\) | ||||
−0.950250 | + | 0.311489i | \(0.899172\pi\) | |||||||
\(798\) | 5.86757e6 | 0.326175 | ||||||||
\(799\) | −1.92230e6 | −0.106525 | ||||||||
\(800\) | 3.20936e6 | 0.177294 | ||||||||
\(801\) | 3.12978e6 | 0.172358 | ||||||||
\(802\) | 2.58470e6 | 0.141897 | ||||||||
\(803\) | −1.47288e6 | −0.0806082 | ||||||||
\(804\) | −7.56706e6 | −0.412845 | ||||||||
\(805\) | 1.75622e6 | 0.0955188 | ||||||||
\(806\) | 1.42984e7 | 0.775265 | ||||||||
\(807\) | −8.84380e6 | −0.478030 | ||||||||
\(808\) | 3.71857e7 | 2.00377 | ||||||||
\(809\) | 1.77957e6 | 0.0955969 | 0.0477985 | − | 0.998857i | \(-0.484779\pi\) | ||||
0.0477985 | + | 0.998857i | \(0.484779\pi\) | |||||||
\(810\) | −1.51810e6 | −0.0812996 | ||||||||
\(811\) | 1.28099e7 | 0.683900 | 0.341950 | − | 0.939718i | \(-0.388913\pi\) | ||||
0.341950 | + | 0.939718i | \(0.388913\pi\) | |||||||
\(812\) | −939660. | −0.0500127 | ||||||||
\(813\) | −2.48585e6 | −0.131901 | ||||||||
\(814\) | −2.12653e6 | −0.112489 | ||||||||
\(815\) | −8.53287e6 | −0.449988 | ||||||||
\(816\) | 193445. | 0.0101703 | ||||||||
\(817\) | 8.64955e6 | 0.453355 | ||||||||
\(818\) | −4.78618e7 | −2.50095 | ||||||||
\(819\) | −2.59219e6 | −0.135038 | ||||||||
\(820\) | −6.03687e6 | −0.313528 | ||||||||
\(821\) | 1.47980e7 | 0.766205 | 0.383102 | − | 0.923706i | \(-0.374856\pi\) | ||||
0.383102 | + | 0.923706i | \(0.374856\pi\) | |||||||
\(822\) | 1.52374e7 | 0.786561 | ||||||||
\(823\) | −1.17405e7 | −0.604207 | −0.302103 | − | 0.953275i | \(-0.597689\pi\) | ||||
−0.302103 | + | 0.953275i | \(0.597689\pi\) | |||||||
\(824\) | −7.39572e6 | −0.379457 | ||||||||
\(825\) | −680625. | −0.0348155 | ||||||||
\(826\) | 5.34945e6 | 0.272809 | ||||||||
\(827\) | 1.61763e7 | 0.822461 | 0.411231 | − | 0.911531i | \(-0.365099\pi\) | ||||
0.411231 | + | 0.911531i | \(0.365099\pi\) | |||||||
\(828\) | 8.37738e6 | 0.424651 | ||||||||
\(829\) | −1.56514e7 | −0.790984 | −0.395492 | − | 0.918470i | \(-0.629426\pi\) | ||||
−0.395492 | + | 0.918470i | \(0.629426\pi\) | |||||||
\(830\) | −2.24975e7 | −1.13354 | ||||||||
\(831\) | 1.33898e6 | 0.0672623 | ||||||||
\(832\) | 4.56158e7 | 2.28458 | ||||||||
\(833\) | −2.40514e6 | −0.120096 | ||||||||
\(834\) | −702188. | −0.0349573 | ||||||||
\(835\) | −4.51370e6 | −0.224035 | ||||||||
\(836\) | 1.25486e7 | 0.620982 | ||||||||
\(837\) | 1.28267e6 | 0.0632850 | ||||||||
\(838\) | 5.59161e7 | 2.75060 | ||||||||
\(839\) | 2.70692e7 | 1.32761 | 0.663806 | − | 0.747905i | \(-0.268940\pi\) | ||||
0.663806 | + | 0.747905i | \(0.268940\pi\) | |||||||
\(840\) | −1.64406e6 | −0.0803931 | ||||||||
\(841\) | −2.02803e7 | −0.988746 | ||||||||
\(842\) | 8.28707e6 | 0.402829 | ||||||||
\(843\) | 3.21995e6 | 0.156056 | ||||||||
\(844\) | 2.66951e7 | 1.28996 | ||||||||
\(845\) | 9.99119e6 | 0.481366 | ||||||||
\(846\) | 9.27442e6 | 0.445513 | ||||||||
\(847\) | 533632. | 0.0255584 | ||||||||
\(848\) | 296727. | 0.0141699 | ||||||||
\(849\) | −4.42881e6 | −0.210871 | ||||||||
\(850\) | −898836. | −0.0426710 | ||||||||
\(851\) | −3.65984e6 | −0.173236 | ||||||||
\(852\) | 5.16246e6 | 0.243645 | ||||||||
\(853\) | −2.43979e7 | −1.14810 | −0.574050 | − | 0.818820i | \(-0.694629\pi\) | ||||
−0.574050 | + | 0.818820i | \(0.694629\pi\) | |||||||
\(854\) | 1.22951e7 | 0.576884 | ||||||||
\(855\) | −3.91362e6 | −0.183089 | ||||||||
\(856\) | 2.50588e7 | 1.16889 | ||||||||
\(857\) | 1.33841e7 | 0.622496 | 0.311248 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311248 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(858\) | −8.84971e6 | −0.410403 | ||||||||
\(859\) | −2.60324e7 | −1.20374 | −0.601869 | − | 0.798595i | \(-0.705577\pi\) | ||||
−0.601869 | + | 0.798595i | \(0.705577\pi\) | |||||||
\(860\) | −6.00394e6 | −0.276815 | ||||||||
\(861\) | −1.47615e6 | −0.0678612 | ||||||||
\(862\) | 1.48887e7 | 0.682479 | ||||||||
\(863\) | −2.45378e7 | −1.12152 | −0.560762 | − | 0.827977i | \(-0.689492\pi\) | ||||
−0.560762 | + | 0.827977i | \(0.689492\pi\) | |||||||
\(864\) | 3.74340e6 | 0.170601 | ||||||||
\(865\) | −1.60830e7 | −0.730849 | ||||||||
\(866\) | −1.72185e7 | −0.780190 | ||||||||
\(867\) | −1.25614e7 | −0.567532 | ||||||||
\(868\) | 3.44123e6 | 0.155030 | ||||||||
\(869\) | 1.05519e7 | 0.474002 | ||||||||
\(870\) | 1.00050e6 | 0.0448144 | ||||||||
\(871\) | 1.37575e7 | 0.614460 | ||||||||
\(872\) | 3.02669e7 | 1.34796 | ||||||||
\(873\) | −2.97712e6 | −0.132209 | ||||||||
\(874\) | 3.44755e7 | 1.52662 | ||||||||
\(875\) | 569497. | 0.0251461 | ||||||||
\(876\) | 5.87870e6 | 0.258834 | ||||||||
\(877\) | 1.99034e7 | 0.873833 | 0.436917 | − | 0.899502i | \(-0.356070\pi\) | ||||
0.436917 | + | 0.899502i | \(0.356070\pi\) | |||||||
\(878\) | −2.54568e7 | −1.11447 | ||||||||
\(879\) | 4.48308e6 | 0.195706 | ||||||||
\(880\) | −418438. | −0.0182148 | ||||||||
\(881\) | −3.90880e7 | −1.69669 | −0.848346 | − | 0.529442i | \(-0.822401\pi\) | ||||
−0.848346 | + | 0.529442i | \(0.822401\pi\) | |||||||
\(882\) | 1.16040e7 | 0.502267 | ||||||||
\(883\) | 2.14490e7 | 0.925776 | 0.462888 | − | 0.886417i | \(-0.346813\pi\) | ||||
0.462888 | + | 0.886417i | \(0.346813\pi\) | |||||||
\(884\) | −7.32109e6 | −0.315098 | ||||||||
\(885\) | −3.56803e6 | −0.153134 | ||||||||
\(886\) | −2.92287e7 | −1.25091 | ||||||||
\(887\) | 6.08624e6 | 0.259741 | 0.129870 | − | 0.991531i | \(-0.458544\pi\) | ||||
0.129870 | + | 0.991531i | \(0.458544\pi\) | |||||||
\(888\) | 3.42610e6 | 0.145803 | ||||||||
\(889\) | 9.79769e6 | 0.415786 | ||||||||
\(890\) | −8.94045e6 | −0.378342 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 6.12462e7 | 2.57731 | ||||||||
\(893\) | 2.39091e7 | 1.00331 | ||||||||
\(894\) | −2.26412e7 | −0.947447 | ||||||||
\(895\) | −6.67306e6 | −0.278463 | ||||||||
\(896\) | 1.15363e7 | 0.480060 | ||||||||
\(897\) | −1.52307e7 | −0.632031 | ||||||||
\(898\) | 1.18012e6 | 0.0488356 | ||||||||
\(899\) | −845336. | −0.0348843 | ||||||||
\(900\) | 2.71657e6 | 0.111793 | ||||||||
\(901\) | 333319. | 0.0136788 | ||||||||
\(902\) | −5.03955e6 | −0.206241 | ||||||||
\(903\) | −1.46810e6 | −0.0599149 | ||||||||
\(904\) | −3.16691e7 | −1.28889 | ||||||||
\(905\) | 7.03823e6 | 0.285655 | ||||||||
\(906\) | 1.97053e7 | 0.797560 | ||||||||
\(907\) | −2.14459e7 | −0.865618 | −0.432809 | − | 0.901486i | \(-0.642477\pi\) | ||||
−0.432809 | + | 0.901486i | \(0.642477\pi\) | |||||||
\(908\) | 3.59232e7 | 1.44597 | ||||||||
\(909\) | −1.50244e7 | −0.603098 | ||||||||
\(910\) | 7.40479e6 | 0.296421 | ||||||||
\(911\) | 1.03374e7 | 0.412682 | 0.206341 | − | 0.978480i | \(-0.433844\pi\) | ||||
0.206341 | + | 0.978480i | \(0.433844\pi\) | |||||||
\(912\) | −2.40603e6 | −0.0957888 | ||||||||
\(913\) | −1.17649e7 | −0.467102 | ||||||||
\(914\) | −2.02884e7 | −0.803310 | ||||||||
\(915\) | −8.20074e6 | −0.323818 | ||||||||
\(916\) | 3.15557e7 | 1.24262 | ||||||||
\(917\) | −1.33732e7 | −0.525185 | ||||||||
\(918\) | −1.04840e6 | −0.0410602 | ||||||||
\(919\) | −4.75142e7 | −1.85581 | −0.927907 | − | 0.372811i | \(-0.878394\pi\) | ||||
−0.927907 | + | 0.372811i | \(0.878394\pi\) | |||||||
\(920\) | −9.65984e6 | −0.376271 | ||||||||
\(921\) | −8.98884e6 | −0.349184 | ||||||||
\(922\) | −4.81488e7 | −1.86534 | ||||||||
\(923\) | −9.38575e6 | −0.362631 | ||||||||
\(924\) | −2.12988e6 | −0.0820683 | ||||||||
\(925\) | −1.18679e6 | −0.0456059 | ||||||||
\(926\) | −2.46769e7 | −0.945720 | ||||||||
\(927\) | 2.98815e6 | 0.114210 | ||||||||
\(928\) | −2.46707e6 | −0.0940398 | ||||||||
\(929\) | 6.08962e6 | 0.231500 | 0.115750 | − | 0.993278i | \(-0.463073\pi\) | ||||
0.115750 | + | 0.993278i | \(0.463073\pi\) | |||||||
\(930\) | −3.66404e6 | −0.138916 | ||||||||
\(931\) | 2.99146e7 | 1.13112 | ||||||||
\(932\) | 1.07008e7 | 0.403532 | ||||||||
\(933\) | 1.69904e7 | 0.638999 | ||||||||
\(934\) | 2.18034e7 | 0.817820 | ||||||||
\(935\) | −470040. | −0.0175835 | ||||||||
\(936\) | 1.42580e7 | 0.531947 | ||||||||
\(937\) | −2.73781e6 | −0.101872 | −0.0509360 | − | 0.998702i | \(-0.516220\pi\) | ||||
−0.0509360 | + | 0.998702i | \(0.516220\pi\) | |||||||
\(938\) | 5.28556e6 | 0.196148 | ||||||||
\(939\) | −2.11308e7 | −0.782082 | ||||||||
\(940\) | −1.65961e7 | −0.612615 | ||||||||
\(941\) | 3.73849e7 | 1.37633 | 0.688165 | − | 0.725554i | \(-0.258417\pi\) | ||||
0.688165 | + | 0.725554i | \(0.258417\pi\) | |||||||
\(942\) | −1.76445e7 | −0.647861 | ||||||||
\(943\) | −8.67326e6 | −0.317617 | ||||||||
\(944\) | −2.19358e6 | −0.0801166 | ||||||||
\(945\) | 664261. | 0.0241969 | ||||||||
\(946\) | −5.01206e6 | −0.182091 | ||||||||
\(947\) | −4.08261e7 | −1.47932 | −0.739661 | − | 0.672979i | \(-0.765014\pi\) | ||||
−0.739661 | + | 0.672979i | \(0.765014\pi\) | |||||||
\(948\) | −4.21156e7 | −1.52203 | ||||||||
\(949\) | −1.06879e7 | −0.385237 | ||||||||
\(950\) | 1.11795e7 | 0.401897 | ||||||||
\(951\) | 5.06449e6 | 0.181587 | ||||||||
\(952\) | −1.13539e6 | −0.0406024 | ||||||||
\(953\) | −4.60553e7 | −1.64266 | −0.821330 | − | 0.570453i | \(-0.806768\pi\) | ||||
−0.821330 | + | 0.570453i | \(0.806768\pi\) | |||||||
\(954\) | −1.60815e6 | −0.0572079 | ||||||||
\(955\) | 2.33431e7 | 0.828228 | ||||||||
\(956\) | −2.18965e7 | −0.774873 | ||||||||
\(957\) | 523204. | 0.0184668 | ||||||||
\(958\) | 4.42709e7 | 1.55849 | ||||||||
\(959\) | −6.66730e6 | −0.234101 | ||||||||
\(960\) | −1.16893e7 | −0.409363 | ||||||||
\(961\) | −2.55333e7 | −0.891865 | ||||||||
\(962\) | −1.54311e7 | −0.537599 | ||||||||
\(963\) | −1.01247e7 | −0.351817 | ||||||||
\(964\) | 6.65509e7 | 2.30654 | ||||||||
\(965\) | 7.50310e6 | 0.259372 | ||||||||
\(966\) | −5.85156e6 | −0.201757 | ||||||||
\(967\) | 1.48162e7 | 0.509532 | 0.254766 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254766 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(968\) | −2.93517e6 | −0.100680 | ||||||||
\(969\) | −2.70275e6 | −0.0924689 | ||||||||
\(970\) | 8.50436e6 | 0.290210 | ||||||||
\(971\) | −3.27641e7 | −1.11519 | −0.557597 | − | 0.830112i | \(-0.688277\pi\) | ||||
−0.557597 | + | 0.830112i | \(0.688277\pi\) | |||||||
\(972\) | 3.16861e6 | 0.107573 | ||||||||
\(973\) | 307250. | 0.0104042 | ||||||||
\(974\) | 3.06828e7 | 1.03633 | ||||||||
\(975\) | −4.93893e6 | −0.166388 | ||||||||
\(976\) | −5.04170e6 | −0.169415 | ||||||||
\(977\) | −4.06772e6 | −0.136337 | −0.0681686 | − | 0.997674i | \(-0.521716\pi\) | ||||
−0.0681686 | + | 0.997674i | \(0.521716\pi\) | |||||||
\(978\) | 2.84307e7 | 0.950476 | ||||||||
\(979\) | −4.67535e6 | −0.155904 | ||||||||
\(980\) | −2.07647e7 | −0.690655 | ||||||||
\(981\) | −1.22290e7 | −0.405712 | ||||||||
\(982\) | 2.79765e7 | 0.925795 | ||||||||
\(983\) | 3.76095e7 | 1.24141 | 0.620704 | − | 0.784045i | \(-0.286847\pi\) | ||||
0.620704 | + | 0.784045i | \(0.286847\pi\) | |||||||
\(984\) | 8.11934e6 | 0.267321 | ||||||||
\(985\) | −2.36235e7 | −0.775807 | ||||||||
\(986\) | 690944. | 0.0226335 | ||||||||
\(987\) | −4.05812e6 | −0.132596 | ||||||||
\(988\) | 9.10583e7 | 2.96775 | ||||||||
\(989\) | −8.62596e6 | −0.280425 | ||||||||
\(990\) | 2.26778e6 | 0.0735382 | ||||||||
\(991\) | 1.02888e7 | 0.332797 | 0.166399 | − | 0.986059i | \(-0.446786\pi\) | ||||
0.166399 | + | 0.986059i | \(0.446786\pi\) | |||||||
\(992\) | 9.03495e6 | 0.291505 | ||||||||
\(993\) | −9.05334e6 | −0.291364 | ||||||||
\(994\) | −3.60596e6 | −0.115759 | ||||||||
\(995\) | −2.52052e7 | −0.807108 | ||||||||
\(996\) | 4.69571e7 | 1.49987 | ||||||||
\(997\) | 4.37776e7 | 1.39481 | 0.697403 | − | 0.716680i | \(-0.254339\pi\) | ||||
0.697403 | + | 0.716680i | \(0.254339\pi\) | |||||||
\(998\) | −4.13277e7 | −1.31345 | ||||||||
\(999\) | −1.38428e6 | −0.0438843 |
(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 | 165.6.a.a.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.e.1.3 | 3 | |||
5.4 | even | 2 | 825.6.a.j.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.e.1.3 | 3 | 3.2 | odd | 2 | |||
825.6.a.j.1.3 | 3 | 5.4 | even | 2 |