Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.46823\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −8.46823 | −0.543237 | −0.271619 | − | 0.962405i | \(-0.587559\pi\) | ||||
−0.271619 | + | 0.962405i | \(0.587559\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 33.8729 | 0.384127 | ||||||||
\(7\) | −118.977 | −0.917737 | −0.458869 | − | 0.888504i | \(-0.651745\pi\) | ||||
−0.458869 | + | 0.888504i | \(0.651745\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −171.289 | −0.704894 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 358.711 | 0.893846 | 0.446923 | − | 0.894573i | \(-0.352520\pi\) | ||||
0.446923 | + | 0.894573i | \(0.352520\pi\) | |||||||
\(12\) | −135.492 | −0.271619 | ||||||||
\(13\) | −515.740 | −0.846393 | −0.423197 | − | 0.906038i | \(-0.639092\pi\) | ||||
−0.423197 | + | 0.906038i | \(0.639092\pi\) | |||||||
\(14\) | 475.909 | 0.648938 | ||||||||
\(15\) | −211.706 | −0.242943 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 2092.78 | 1.75631 | 0.878155 | − | 0.478376i | \(-0.158774\pi\) | ||||
0.878155 | + | 0.478376i | \(0.158774\pi\) | |||||||
\(18\) | 685.157 | 0.498435 | ||||||||
\(19\) | −2775.19 | −1.76364 | −0.881818 | − | 0.471589i | \(-0.843680\pi\) | ||||
−0.881818 | + | 0.471589i | \(0.843680\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 1007.53 | 0.498549 | ||||||||
\(22\) | −1434.84 | −0.632044 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 541.967 | 0.192063 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2062.96 | 0.598490 | ||||||||
\(27\) | 3508.29 | 0.926161 | ||||||||
\(28\) | −1903.63 | −0.458869 | ||||||||
\(29\) | −2344.09 | −0.517583 | −0.258791 | − | 0.965933i | \(-0.583324\pi\) | ||||
−0.258791 | + | 0.965933i | \(0.583324\pi\) | |||||||
\(30\) | 846.823 | 0.171787 | ||||||||
\(31\) | −9787.95 | −1.82931 | −0.914655 | − | 0.404235i | \(-0.867538\pi\) | ||||
−0.914655 | + | 0.404235i | \(0.867538\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −3037.64 | −0.485570 | ||||||||
\(34\) | −8371.12 | −1.24190 | ||||||||
\(35\) | −2974.43 | −0.410425 | ||||||||
\(36\) | −2740.63 | −0.352447 | ||||||||
\(37\) | 4816.40 | 0.578387 | 0.289193 | − | 0.957271i | \(-0.406613\pi\) | ||||
0.289193 | + | 0.957271i | \(0.406613\pi\) | |||||||
\(38\) | 11100.8 | 1.24708 | ||||||||
\(39\) | 4367.40 | 0.459792 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −24.0689 | −0.00223613 | −0.00111806 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111806 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(42\) | −4030.10 | −0.352527 | ||||||||
\(43\) | −1068.84 | −0.0881541 | −0.0440770 | − | 0.999028i | \(-0.514035\pi\) | ||||
−0.0440770 | + | 0.999028i | \(0.514035\pi\) | |||||||
\(44\) | 5739.37 | 0.446923 | ||||||||
\(45\) | −4282.23 | −0.315238 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | 17918.2 | 1.18317 | 0.591587 | − | 0.806241i | \(-0.298501\pi\) | ||||
0.591587 | + | 0.806241i | \(0.298501\pi\) | |||||||
\(48\) | −2167.87 | −0.135809 | ||||||||
\(49\) | −2651.44 | −0.157758 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −17722.1 | −0.954093 | ||||||||
\(52\) | −8251.83 | −0.423197 | ||||||||
\(53\) | 15651.6 | 0.765365 | 0.382682 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382682 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(54\) | −14033.2 | −0.654895 | ||||||||
\(55\) | 8967.76 | 0.399740 | ||||||||
\(56\) | 7614.54 | 0.324469 | ||||||||
\(57\) | 23501.0 | 0.958073 | ||||||||
\(58\) | 9376.37 | 0.365986 | ||||||||
\(59\) | 45399.8 | 1.69795 | 0.848973 | − | 0.528436i | \(-0.177221\pi\) | ||||
0.848973 | + | 0.528436i | \(0.177221\pi\) | |||||||
\(60\) | −3387.29 | −0.121471 | ||||||||
\(61\) | 18440.5 | 0.634525 | 0.317263 | − | 0.948338i | \(-0.397236\pi\) | ||||
0.317263 | + | 0.948338i | \(0.397236\pi\) | |||||||
\(62\) | 39151.8 | 1.29352 | ||||||||
\(63\) | 20379.5 | 0.646907 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −12893.5 | −0.378519 | ||||||||
\(66\) | 12150.6 | 0.343350 | ||||||||
\(67\) | 48487.9 | 1.31961 | 0.659806 | − | 0.751436i | \(-0.270639\pi\) | ||||
0.659806 | + | 0.751436i | \(0.270639\pi\) | |||||||
\(68\) | 33484.5 | 0.878155 | ||||||||
\(69\) | 4479.69 | 0.113273 | ||||||||
\(70\) | 11897.7 | 0.290214 | ||||||||
\(71\) | 3989.29 | 0.0939182 | 0.0469591 | − | 0.998897i | \(-0.485047\pi\) | ||||
0.0469591 | + | 0.998897i | \(0.485047\pi\) | |||||||
\(72\) | 10962.5 | 0.249218 | ||||||||
\(73\) | 5579.98 | 0.122553 | 0.0612767 | − | 0.998121i | \(-0.480483\pi\) | ||||
0.0612767 | + | 0.998121i | \(0.480483\pi\) | |||||||
\(74\) | −19265.6 | −0.408981 | ||||||||
\(75\) | −5292.64 | −0.108647 | ||||||||
\(76\) | −44403.1 | −0.881818 | ||||||||
\(77\) | −42678.4 | −0.820316 | ||||||||
\(78\) | −17469.6 | −0.325122 | ||||||||
\(79\) | 38453.9 | 0.693222 | 0.346611 | − | 0.938009i | \(-0.387332\pi\) | ||||
0.346611 | + | 0.938009i | \(0.387332\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 11914.2 | 0.201768 | ||||||||
\(82\) | 96.2757 | 0.00158118 | ||||||||
\(83\) | −29897.7 | −0.476368 | −0.238184 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238184 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(84\) | 16120.4 | 0.249274 | ||||||||
\(85\) | 52319.5 | 0.785446 | ||||||||
\(86\) | 4275.37 | 0.0623343 | ||||||||
\(87\) | 19850.3 | 0.281170 | ||||||||
\(88\) | −22957.5 | −0.316022 | ||||||||
\(89\) | 50329.9 | 0.673521 | 0.336760 | − | 0.941590i | \(-0.390669\pi\) | ||||
0.336760 | + | 0.941590i | \(0.390669\pi\) | |||||||
\(90\) | 17128.9 | 0.222907 | ||||||||
\(91\) | 61361.2 | 0.776767 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | 82886.6 | 0.993749 | ||||||||
\(94\) | −71672.7 | −0.836631 | ||||||||
\(95\) | −69379.8 | −0.788722 | ||||||||
\(96\) | 8671.46 | 0.0960316 | ||||||||
\(97\) | −71867.5 | −0.775538 | −0.387769 | − | 0.921757i | \(-0.626754\pi\) | ||||
−0.387769 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(98\) | 10605.8 | 0.111552 | ||||||||
\(99\) | −61443.2 | −0.630066 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 61080.4 | 0.595798 | 0.297899 | − | 0.954597i | \(-0.403714\pi\) | ||||
0.297899 | + | 0.954597i | \(0.403714\pi\) | |||||||
\(102\) | 70888.5 | 0.674645 | ||||||||
\(103\) | 181954. | 1.68993 | 0.844964 | − | 0.534823i | \(-0.179622\pi\) | ||||
0.844964 | + | 0.534823i | \(0.179622\pi\) | |||||||
\(104\) | 33007.3 | 0.299245 | ||||||||
\(105\) | 25188.1 | 0.222958 | ||||||||
\(106\) | −62606.3 | −0.541195 | ||||||||
\(107\) | −99429.8 | −0.839571 | −0.419785 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419785 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(108\) | 56132.7 | 0.463081 | ||||||||
\(109\) | 157698. | 1.27134 | 0.635668 | − | 0.771963i | \(-0.280725\pi\) | ||||
0.635668 | + | 0.771963i | \(0.280725\pi\) | |||||||
\(110\) | −35871.1 | −0.282659 | ||||||||
\(111\) | −40786.4 | −0.314201 | ||||||||
\(112\) | −30458.2 | −0.229434 | ||||||||
\(113\) | 178966. | 1.31848 | 0.659242 | − | 0.751931i | \(-0.270877\pi\) | ||||
0.659242 | + | 0.751931i | \(0.270877\pi\) | |||||||
\(114\) | −94003.8 | −0.677460 | ||||||||
\(115\) | −13225.0 | −0.0932505 | ||||||||
\(116\) | −37505.5 | −0.258791 | ||||||||
\(117\) | 88340.6 | 0.596617 | ||||||||
\(118\) | −181599. | −1.20063 | ||||||||
\(119\) | −248993. | −1.61183 | ||||||||
\(120\) | 13549.2 | 0.0858933 | ||||||||
\(121\) | −32377.7 | −0.201040 | ||||||||
\(122\) | −73762.2 | −0.448677 | ||||||||
\(123\) | 203.821 | 0.00121475 | ||||||||
\(124\) | −156607. | −0.914655 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −81518.0 | −0.457432 | ||||||||
\(127\) | 161206. | 0.886896 | 0.443448 | − | 0.896300i | \(-0.353755\pi\) | ||||
0.443448 | + | 0.896300i | \(0.353755\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 9051.19 | 0.0478885 | ||||||||
\(130\) | 51574.0 | 0.267653 | ||||||||
\(131\) | −137424. | −0.699654 | −0.349827 | − | 0.936814i | \(-0.613760\pi\) | ||||
−0.349827 | + | 0.936814i | \(0.613760\pi\) | |||||||
\(132\) | −48602.3 | −0.242785 | ||||||||
\(133\) | 330184. | 1.61856 | ||||||||
\(134\) | −193951. | −0.933106 | ||||||||
\(135\) | 87707.4 | 0.414192 | ||||||||
\(136\) | −133938. | −0.620949 | ||||||||
\(137\) | 305275. | 1.38960 | 0.694800 | − | 0.719203i | \(-0.255493\pi\) | ||||
0.694800 | + | 0.719203i | \(0.255493\pi\) | |||||||
\(138\) | −17918.8 | −0.0800959 | ||||||||
\(139\) | −143928. | −0.631840 | −0.315920 | − | 0.948786i | \(-0.602313\pi\) | ||||
−0.315920 | + | 0.948786i | \(0.602313\pi\) | |||||||
\(140\) | −47590.9 | −0.205212 | ||||||||
\(141\) | −151735. | −0.642744 | ||||||||
\(142\) | −15957.2 | −0.0664102 | ||||||||
\(143\) | −185001. | −0.756545 | ||||||||
\(144\) | −43850.0 | −0.176223 | ||||||||
\(145\) | −58602.3 | −0.231470 | ||||||||
\(146\) | −22319.9 | −0.0866583 | ||||||||
\(147\) | 22453.0 | 0.0856999 | ||||||||
\(148\) | 77062.4 | 0.289193 | ||||||||
\(149\) | 355454. | 1.31165 | 0.655824 | − | 0.754913i | \(-0.272321\pi\) | ||||
0.655824 | + | 0.754913i | \(0.272321\pi\) | |||||||
\(150\) | 21170.6 | 0.0768253 | ||||||||
\(151\) | −225364. | −0.804344 | −0.402172 | − | 0.915564i | \(-0.631745\pi\) | ||||
−0.402172 | + | 0.915564i | \(0.631745\pi\) | |||||||
\(152\) | 177612. | 0.623540 | ||||||||
\(153\) | −358470. | −1.23801 | ||||||||
\(154\) | 170713. | 0.580051 | ||||||||
\(155\) | −244699. | −0.818092 | ||||||||
\(156\) | 69878.4 | 0.229896 | ||||||||
\(157\) | 279940. | 0.906391 | 0.453195 | − | 0.891411i | \(-0.350284\pi\) | ||||
0.453195 | + | 0.891411i | \(0.350284\pi\) | |||||||
\(158\) | −153816. | −0.490182 | ||||||||
\(159\) | −132541. | −0.415775 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 62938.9 | 0.191361 | ||||||||
\(162\) | −47656.9 | −0.142672 | ||||||||
\(163\) | −642292. | −1.89349 | −0.946747 | − | 0.321980i | \(-0.895652\pi\) | ||||
−0.946747 | + | 0.321980i | \(0.895652\pi\) | |||||||
\(164\) | −385.103 | −0.00111806 | ||||||||
\(165\) | −75941.1 | −0.217153 | ||||||||
\(166\) | 119591. | 0.336843 | ||||||||
\(167\) | −61147.1 | −0.169662 | −0.0848310 | − | 0.996395i | \(-0.527035\pi\) | ||||
−0.0848310 | + | 0.996395i | \(0.527035\pi\) | |||||||
\(168\) | −64481.6 | −0.176264 | ||||||||
\(169\) | −105306. | −0.283619 | ||||||||
\(170\) | −209278. | −0.555394 | ||||||||
\(171\) | 475360. | 1.24318 | ||||||||
\(172\) | −17101.5 | −0.0440770 | ||||||||
\(173\) | −270177. | −0.686331 | −0.343165 | − | 0.939275i | \(-0.611499\pi\) | ||||
−0.343165 | + | 0.939275i | \(0.611499\pi\) | |||||||
\(174\) | −79401.2 | −0.198817 | ||||||||
\(175\) | −74360.7 | −0.183547 | ||||||||
\(176\) | 91829.9 | 0.223461 | ||||||||
\(177\) | −384456. | −0.922387 | ||||||||
\(178\) | −201320. | −0.476251 | ||||||||
\(179\) | −222698. | −0.519499 | −0.259749 | − | 0.965676i | \(-0.583640\pi\) | ||||
−0.259749 | + | 0.965676i | \(0.583640\pi\) | |||||||
\(180\) | −68515.7 | −0.157619 | ||||||||
\(181\) | −277646. | −0.629934 | −0.314967 | − | 0.949103i | \(-0.601994\pi\) | ||||
−0.314967 | + | 0.949103i | \(0.601994\pi\) | |||||||
\(182\) | −245445. | −0.549257 | ||||||||
\(183\) | −156159. | −0.344698 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | 120410. | 0.258662 | ||||||||
\(186\) | −331546. | −0.702687 | ||||||||
\(187\) | 750702. | 1.56987 | ||||||||
\(188\) | 286691. | 0.591587 | ||||||||
\(189\) | −417407. | −0.849973 | ||||||||
\(190\) | 277519. | 0.557711 | ||||||||
\(191\) | 541372. | 1.07377 | 0.536886 | − | 0.843655i | \(-0.319600\pi\) | ||||
0.536886 | + | 0.843655i | \(0.319600\pi\) | |||||||
\(192\) | −34685.9 | −0.0679046 | ||||||||
\(193\) | −33487.9 | −0.0647136 | −0.0323568 | − | 0.999476i | \(-0.510301\pi\) | ||||
−0.0323568 | + | 0.999476i | \(0.510301\pi\) | |||||||
\(194\) | 287470. | 0.548388 | ||||||||
\(195\) | 109185. | 0.205625 | ||||||||
\(196\) | −42423.0 | −0.0788790 | ||||||||
\(197\) | −149329. | −0.274144 | −0.137072 | − | 0.990561i | \(-0.543769\pi\) | ||||
−0.137072 | + | 0.990561i | \(0.543769\pi\) | |||||||
\(198\) | 245773. | 0.445524 | ||||||||
\(199\) | 274716. | 0.491759 | 0.245879 | − | 0.969300i | \(-0.420923\pi\) | ||||
0.245879 | + | 0.969300i | \(0.420923\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −410606. | −0.716862 | ||||||||
\(202\) | −244322. | −0.421292 | ||||||||
\(203\) | 278893. | 0.475005 | ||||||||
\(204\) | −283554. | −0.477046 | ||||||||
\(205\) | −601.723 | −0.00100003 | ||||||||
\(206\) | −727816. | −1.19496 | ||||||||
\(207\) | 90611.9 | 0.146980 | ||||||||
\(208\) | −132029. | −0.211598 | ||||||||
\(209\) | −995491. | −1.57642 | ||||||||
\(210\) | −100753. | −0.157655 | ||||||||
\(211\) | 353497. | 0.546612 | 0.273306 | − | 0.961927i | \(-0.411883\pi\) | ||||
0.273306 | + | 0.961927i | \(0.411883\pi\) | |||||||
\(212\) | 250425. | 0.382682 | ||||||||
\(213\) | −33782.2 | −0.0510198 | ||||||||
\(214\) | 397719. | 0.593666 | ||||||||
\(215\) | −26721.0 | −0.0394237 | ||||||||
\(216\) | −224531. | −0.327447 | ||||||||
\(217\) | 1.16454e6 | 1.67883 | ||||||||
\(218\) | −630792. | −0.898970 | ||||||||
\(219\) | −47252.5 | −0.0665755 | ||||||||
\(220\) | 143484. | 0.199870 | ||||||||
\(221\) | −1.07933e6 | −1.48653 | ||||||||
\(222\) | 163146. | 0.222174 | ||||||||
\(223\) | −602989. | −0.811984 | −0.405992 | − | 0.913877i | \(-0.633074\pi\) | ||||
−0.405992 | + | 0.913877i | \(0.633074\pi\) | |||||||
\(224\) | 121833. | 0.162235 | ||||||||
\(225\) | −107056. | −0.140979 | ||||||||
\(226\) | −715865. | −0.932309 | ||||||||
\(227\) | 543612. | 0.700204 | 0.350102 | − | 0.936712i | \(-0.386147\pi\) | ||||
0.350102 | + | 0.936712i | \(0.386147\pi\) | |||||||
\(228\) | 376015. | 0.479036 | ||||||||
\(229\) | 890736. | 1.12243 | 0.561216 | − | 0.827669i | \(-0.310334\pi\) | ||||
0.561216 | + | 0.827669i | \(0.310334\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | 361410. | 0.445626 | ||||||||
\(232\) | 150022. | 0.182993 | ||||||||
\(233\) | 1.05640e6 | 1.27478 | 0.637392 | − | 0.770539i | \(-0.280013\pi\) | ||||
0.637392 | + | 0.770539i | \(0.280013\pi\) | |||||||
\(234\) | −353362. | −0.421872 | ||||||||
\(235\) | 447954. | 0.529132 | ||||||||
\(236\) | 726397. | 0.848973 | ||||||||
\(237\) | −325636. | −0.376584 | ||||||||
\(238\) | 995972. | 1.13974 | ||||||||
\(239\) | −805507. | −0.912167 | −0.456084 | − | 0.889937i | \(-0.650748\pi\) | ||||
−0.456084 | + | 0.889937i | \(0.650748\pi\) | |||||||
\(240\) | −54196.7 | −0.0607357 | ||||||||
\(241\) | −848758. | −0.941328 | −0.470664 | − | 0.882312i | \(-0.655986\pi\) | ||||
−0.470664 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(242\) | 129511. | 0.142157 | ||||||||
\(243\) | −953408. | −1.03577 | ||||||||
\(244\) | 295049. | 0.317263 | ||||||||
\(245\) | −66285.9 | −0.0705515 | ||||||||
\(246\) | −815.284 | −0.000858957 0 | ||||||||
\(247\) | 1.43128e6 | 1.49273 | ||||||||
\(248\) | 626429. | 0.646759 | ||||||||
\(249\) | 253180. | 0.258781 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −1.61847e6 | −1.62151 | −0.810755 | − | 0.585386i | \(-0.800943\pi\) | ||||
−0.810755 | + | 0.585386i | \(0.800943\pi\) | |||||||
\(252\) | 326072. | 0.323454 | ||||||||
\(253\) | −189758. | −0.186380 | ||||||||
\(254\) | −644825. | −0.627130 | ||||||||
\(255\) | −443053. | −0.426683 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.31624e6 | 1.24309 | 0.621544 | − | 0.783379i | \(-0.286506\pi\) | ||||
0.621544 | + | 0.783379i | \(0.286506\pi\) | |||||||
\(258\) | −36204.8 | −0.0338623 | ||||||||
\(259\) | −573042. | −0.530807 | ||||||||
\(260\) | −206296. | −0.189259 | ||||||||
\(261\) | 401518. | 0.364841 | ||||||||
\(262\) | 549695. | 0.494730 | ||||||||
\(263\) | −605771. | −0.540032 | −0.270016 | − | 0.962856i | \(-0.587029\pi\) | ||||
−0.270016 | + | 0.962856i | \(0.587029\pi\) | |||||||
\(264\) | 194409. | 0.171675 | ||||||||
\(265\) | 391290. | 0.342282 | ||||||||
\(266\) | −1.32074e6 | −1.14449 | ||||||||
\(267\) | −426205. | −0.365881 | ||||||||
\(268\) | 775806. | 0.659806 | ||||||||
\(269\) | 11040.1 | 0.00930233 | 0.00465116 | − | 0.999989i | \(-0.498519\pi\) | ||||
0.00465116 | + | 0.999989i | \(0.498519\pi\) | |||||||
\(270\) | −350829. | −0.292878 | ||||||||
\(271\) | 1.30158e6 | 1.07658 | 0.538291 | − | 0.842759i | \(-0.319070\pi\) | ||||
0.538291 | + | 0.842759i | \(0.319070\pi\) | |||||||
\(272\) | 535752. | 0.439078 | ||||||||
\(273\) | −519621. | −0.421968 | ||||||||
\(274\) | −1.22110e6 | −0.982596 | ||||||||
\(275\) | 224194. | 0.178769 | ||||||||
\(276\) | 71675.1 | 0.0566364 | ||||||||
\(277\) | 2.07170e6 | 1.62229 | 0.811143 | − | 0.584848i | \(-0.198846\pi\) | ||||
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(278\) | 575710. | 0.446778 | ||||||||
\(279\) | 1.67657e6 | 1.28947 | ||||||||
\(280\) | 190363. | 0.145107 | ||||||||
\(281\) | 705629. | 0.533102 | 0.266551 | − | 0.963821i | \(-0.414116\pi\) | ||||
0.266551 | + | 0.963821i | \(0.414116\pi\) | |||||||
\(282\) | 606940. | 0.454489 | ||||||||
\(283\) | −1.85265e6 | −1.37508 | −0.687538 | − | 0.726148i | \(-0.741309\pi\) | ||||
−0.687538 | + | 0.726148i | \(0.741309\pi\) | |||||||
\(284\) | 63828.6 | 0.0469591 | ||||||||
\(285\) | 587524. | 0.428463 | ||||||||
\(286\) | 740005. | 0.534958 | ||||||||
\(287\) | 2863.65 | 0.00205218 | ||||||||
\(288\) | 175400. | 0.124609 | ||||||||
\(289\) | 2.95987e6 | 2.08462 | ||||||||
\(290\) | 234409. | 0.163674 | ||||||||
\(291\) | 608590. | 0.421301 | ||||||||
\(292\) | 89279.6 | 0.0612767 | ||||||||
\(293\) | 1.06802e6 | 0.726790 | 0.363395 | − | 0.931635i | \(-0.381618\pi\) | ||||
0.363395 | + | 0.931635i | \(0.381618\pi\) | |||||||
\(294\) | −89811.9 | −0.0605990 | ||||||||
\(295\) | 1.13500e6 | 0.759345 | ||||||||
\(296\) | −308250. | −0.204491 | ||||||||
\(297\) | 1.25846e6 | 0.827845 | ||||||||
\(298\) | −1.42182e6 | −0.927476 | ||||||||
\(299\) | 272826. | 0.176485 | ||||||||
\(300\) | −84682.3 | −0.0543237 | ||||||||
\(301\) | 127168. | 0.0809023 | ||||||||
\(302\) | 901455. | 0.568757 | ||||||||
\(303\) | −517243. | −0.323659 | ||||||||
\(304\) | −710449. | −0.440909 | ||||||||
\(305\) | 461013. | 0.283768 | ||||||||
\(306\) | 1.43388e6 | 0.875406 | ||||||||
\(307\) | −34869.7 | −0.0211156 | −0.0105578 | − | 0.999944i | \(-0.503361\pi\) | ||||
−0.0105578 | + | 0.999944i | \(0.503361\pi\) | |||||||
\(308\) | −682854. | −0.410158 | ||||||||
\(309\) | −1.54083e6 | −0.918032 | ||||||||
\(310\) | 978795. | 0.578479 | ||||||||
\(311\) | 2.27802e6 | 1.33554 | 0.667770 | − | 0.744368i | \(-0.267249\pi\) | ||||
0.667770 | + | 0.744368i | \(0.267249\pi\) | |||||||
\(312\) | −279514. | −0.162561 | ||||||||
\(313\) | −1.31658e6 | −0.759600 | −0.379800 | − | 0.925069i | \(-0.624007\pi\) | ||||
−0.379800 | + | 0.925069i | \(0.624007\pi\) | |||||||
\(314\) | −1.11976e6 | −0.640915 | ||||||||
\(315\) | 509487. | 0.289306 | ||||||||
\(316\) | 615262. | 0.346611 | ||||||||
\(317\) | −1.15067e6 | −0.643135 | −0.321568 | − | 0.946887i | \(-0.604210\pi\) | ||||
−0.321568 | + | 0.946887i | \(0.604210\pi\) | |||||||
\(318\) | 530165. | 0.293997 | ||||||||
\(319\) | −840851. | −0.462639 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 841995. | 0.456086 | ||||||||
\(322\) | −251756. | −0.135313 | ||||||||
\(323\) | −5.80787e6 | −3.09749 | ||||||||
\(324\) | 190628. | 0.100884 | ||||||||
\(325\) | −322337. | −0.169279 | ||||||||
\(326\) | 2.56917e6 | 1.33890 | ||||||||
\(327\) | −1.33542e6 | −0.690637 | ||||||||
\(328\) | 1540.41 | 0.000790591 0 | ||||||||
\(329\) | −2.13185e6 | −1.08584 | ||||||||
\(330\) | 303764. | 0.153551 | ||||||||
\(331\) | −3.62446e6 | −1.81833 | −0.909166 | − | 0.416434i | \(-0.863280\pi\) | ||||
−0.909166 | + | 0.416434i | \(0.863280\pi\) | |||||||
\(332\) | −478363. | −0.238184 | ||||||||
\(333\) | −824997. | −0.407701 | ||||||||
\(334\) | 244588. | 0.119969 | ||||||||
\(335\) | 1.21220e6 | 0.590148 | ||||||||
\(336\) | 257927. | 0.124637 | ||||||||
\(337\) | 308341. | 0.147896 | 0.0739481 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739481 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(338\) | 421222. | 0.200549 | ||||||||
\(339\) | −1.51553e6 | −0.716249 | ||||||||
\(340\) | 837112. | 0.392723 | ||||||||
\(341\) | −3.51104e6 | −1.63512 | ||||||||
\(342\) | −1.90144e6 | −0.879058 | ||||||||
\(343\) | 2.31511e6 | 1.06252 | ||||||||
\(344\) | 68405.9 | 0.0311672 | ||||||||
\(345\) | 111992. | 0.0506571 | ||||||||
\(346\) | 1.08071e6 | 0.485309 | ||||||||
\(347\) | −850011. | −0.378967 | −0.189483 | − | 0.981884i | \(-0.560681\pi\) | ||||
−0.189483 | + | 0.981884i | \(0.560681\pi\) | |||||||
\(348\) | 317605. | 0.140585 | ||||||||
\(349\) | −2.96385e6 | −1.30255 | −0.651273 | − | 0.758844i | \(-0.725765\pi\) | ||||
−0.651273 | + | 0.758844i | \(0.725765\pi\) | |||||||
\(350\) | 297443. | 0.129788 | ||||||||
\(351\) | −1.80937e6 | −0.783897 | ||||||||
\(352\) | −367320. | −0.158011 | ||||||||
\(353\) | 2.14490e6 | 0.916157 | 0.458078 | − | 0.888912i | \(-0.348538\pi\) | ||||
0.458078 | + | 0.888912i | \(0.348538\pi\) | |||||||
\(354\) | 1.53782e6 | 0.652226 | ||||||||
\(355\) | 99732.2 | 0.0420015 | ||||||||
\(356\) | 805278. | 0.336760 | ||||||||
\(357\) | 2.10853e6 | 0.875607 | ||||||||
\(358\) | 890793. | 0.367341 | ||||||||
\(359\) | −438888. | −0.179729 | −0.0898643 | − | 0.995954i | \(-0.528643\pi\) | ||||
−0.0898643 | + | 0.995954i | \(0.528643\pi\) | |||||||
\(360\) | 274063. | 0.111453 | ||||||||
\(361\) | 5.22559e6 | 2.11041 | ||||||||
\(362\) | 1.11058e6 | 0.445431 | ||||||||
\(363\) | 274182. | 0.109212 | ||||||||
\(364\) | 981780. | 0.388383 | ||||||||
\(365\) | 139499. | 0.0548075 | ||||||||
\(366\) | 624635. | 0.243738 | ||||||||
\(367\) | 1.38893e6 | 0.538289 | 0.269144 | − | 0.963100i | \(-0.413259\pi\) | ||||
0.269144 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | 4122.74 | 0.00157623 | ||||||||
\(370\) | −481640. | −0.182902 | ||||||||
\(371\) | −1.86218e6 | −0.702404 | ||||||||
\(372\) | 1.32618e6 | 0.496875 | ||||||||
\(373\) | 2.14429e6 | 0.798017 | 0.399009 | − | 0.916947i | \(-0.369354\pi\) | ||||
0.399009 | + | 0.916947i | \(0.369354\pi\) | |||||||
\(374\) | −3.00281e6 | −1.11007 | ||||||||
\(375\) | −132316. | −0.0485886 | ||||||||
\(376\) | −1.14676e6 | −0.418316 | ||||||||
\(377\) | 1.20894e6 | 0.438078 | ||||||||
\(378\) | 1.66963e6 | 0.601022 | ||||||||
\(379\) | 2.55976e6 | 0.915378 | 0.457689 | − | 0.889112i | \(-0.348677\pi\) | ||||
0.457689 | + | 0.889112i | \(0.348677\pi\) | |||||||
\(380\) | −1.11008e6 | −0.394361 | ||||||||
\(381\) | −1.36513e6 | −0.481795 | ||||||||
\(382\) | −2.16549e6 | −0.759272 | ||||||||
\(383\) | −2.89975e6 | −1.01010 | −0.505049 | − | 0.863091i | \(-0.668526\pi\) | ||||
−0.505049 | + | 0.863091i | \(0.668526\pi\) | |||||||
\(384\) | 138743. | 0.0480158 | ||||||||
\(385\) | −1.06696e6 | −0.366856 | ||||||||
\(386\) | 133952. | 0.0457594 | ||||||||
\(387\) | 183081. | 0.0621392 | ||||||||
\(388\) | −1.14988e6 | −0.387769 | ||||||||
\(389\) | 1.47101e6 | 0.492882 | 0.246441 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246441 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(390\) | −436740. | −0.145399 | ||||||||
\(391\) | −1.10708e6 | −0.366216 | ||||||||
\(392\) | 169692. | 0.0557759 | ||||||||
\(393\) | 1.16374e6 | 0.380078 | ||||||||
\(394\) | 597316. | 0.193849 | ||||||||
\(395\) | 961347. | 0.310018 | ||||||||
\(396\) | −983092. | −0.315033 | ||||||||
\(397\) | −4.88528e6 | −1.55565 | −0.777827 | − | 0.628479i | \(-0.783678\pi\) | ||||
−0.777827 | + | 0.628479i | \(0.783678\pi\) | |||||||
\(398\) | −1.09887e6 | −0.347726 | ||||||||
\(399\) | −2.79608e6 | −0.879259 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −4.03714e6 | −1.25376 | −0.626878 | − | 0.779117i | \(-0.715668\pi\) | ||||
−0.626878 | + | 0.779117i | \(0.715668\pi\) | |||||||
\(402\) | 1.64243e6 | 0.506898 | ||||||||
\(403\) | 5.04803e6 | 1.54832 | ||||||||
\(404\) | 977287. | 0.297899 | ||||||||
\(405\) | 297856. | 0.0902336 | ||||||||
\(406\) | −1.11557e6 | −0.335879 | ||||||||
\(407\) | 1.72769e6 | 0.516989 | ||||||||
\(408\) | 1.13422e6 | 0.337323 | ||||||||
\(409\) | −4.13883e6 | −1.22340 | −0.611702 | − | 0.791088i | \(-0.709515\pi\) | ||||
−0.611702 | + | 0.791088i | \(0.709515\pi\) | |||||||
\(410\) | 2406.89 | 0.000707126 0 | ||||||||
\(411\) | −2.58514e6 | −0.754882 | ||||||||
\(412\) | 2.91126e6 | 0.844964 | ||||||||
\(413\) | −5.40154e6 | −1.55827 | ||||||||
\(414\) | −362448. | −0.103931 | ||||||||
\(415\) | −747442. | −0.213038 | ||||||||
\(416\) | 528117. | 0.149623 | ||||||||
\(417\) | 1.21881e6 | 0.343239 | ||||||||
\(418\) | 3.98196e6 | 1.11470 | ||||||||
\(419\) | 536280. | 0.149230 | 0.0746150 | − | 0.997212i | \(-0.476227\pi\) | ||||
0.0746150 | + | 0.997212i | \(0.476227\pi\) | |||||||
\(420\) | 403010. | 0.111479 | ||||||||
\(421\) | 6.59556e6 | 1.81362 | 0.906810 | − | 0.421539i | \(-0.138510\pi\) | ||||
0.906810 | + | 0.421539i | \(0.138510\pi\) | |||||||
\(422\) | −1.41399e6 | −0.386513 | ||||||||
\(423\) | −3.06919e6 | −0.834012 | ||||||||
\(424\) | −1.00170e6 | −0.270597 | ||||||||
\(425\) | 1.30799e6 | 0.351262 | ||||||||
\(426\) | 135129. | 0.0360765 | ||||||||
\(427\) | −2.19400e6 | −0.582328 | ||||||||
\(428\) | −1.59088e6 | −0.419785 | ||||||||
\(429\) | 1.56663e6 | 0.410983 | ||||||||
\(430\) | 106884. | 0.0278768 | ||||||||
\(431\) | 3.65012e6 | 0.946486 | 0.473243 | − | 0.880932i | \(-0.343083\pi\) | ||||
0.473243 | + | 0.880932i | \(0.343083\pi\) | |||||||
\(432\) | 898123. | 0.231540 | ||||||||
\(433\) | 5.50340e6 | 1.41062 | 0.705311 | − | 0.708898i | \(-0.250807\pi\) | ||||
0.705311 | + | 0.708898i | \(0.250807\pi\) | |||||||
\(434\) | −4.65817e6 | −1.18711 | ||||||||
\(435\) | 496258. | 0.125743 | ||||||||
\(436\) | 2.52317e6 | 0.635668 | ||||||||
\(437\) | 1.46808e6 | 0.367744 | ||||||||
\(438\) | 189010. | 0.0470760 | ||||||||
\(439\) | −4.23173e6 | −1.04799 | −0.523994 | − | 0.851722i | \(-0.675559\pi\) | ||||
−0.523994 | + | 0.851722i | \(0.675559\pi\) | |||||||
\(440\) | −573937. | −0.141329 | ||||||||
\(441\) | 454162. | 0.111203 | ||||||||
\(442\) | 4.31732e6 | 1.05113 | ||||||||
\(443\) | −4.22418e6 | −1.02266 | −0.511332 | − | 0.859383i | \(-0.670848\pi\) | ||||
−0.511332 | + | 0.859383i | \(0.670848\pi\) | |||||||
\(444\) | −652582. | −0.157101 | ||||||||
\(445\) | 1.25825e6 | 0.301208 | ||||||||
\(446\) | 2.41196e6 | 0.574159 | ||||||||
\(447\) | −3.01006e6 | −0.712536 | ||||||||
\(448\) | −487330. | −0.114717 | ||||||||
\(449\) | −6.45197e6 | −1.51035 | −0.755173 | − | 0.655526i | \(-0.772447\pi\) | ||||
−0.755173 | + | 0.655526i | \(0.772447\pi\) | |||||||
\(450\) | 428223. | 0.0996870 | ||||||||
\(451\) | −8633.78 | −0.00199875 | ||||||||
\(452\) | 2.86346e6 | 0.659242 | ||||||||
\(453\) | 1.90843e6 | 0.436949 | ||||||||
\(454\) | −2.17445e6 | −0.495119 | ||||||||
\(455\) | 1.53403e6 | 0.347381 | ||||||||
\(456\) | −1.50406e6 | −0.338730 | ||||||||
\(457\) | 1.98425e6 | 0.444432 | 0.222216 | − | 0.974997i | \(-0.428671\pi\) | ||||
0.222216 | + | 0.974997i | \(0.428671\pi\) | |||||||
\(458\) | −3.56294e6 | −0.793679 | ||||||||
\(459\) | 7.34209e6 | 1.62663 | ||||||||
\(460\) | −211600. | −0.0466252 | ||||||||
\(461\) | 5.78438e6 | 1.26767 | 0.633833 | − | 0.773470i | \(-0.281481\pi\) | ||||
0.633833 | + | 0.773470i | \(0.281481\pi\) | |||||||
\(462\) | −1.44564e6 | −0.315105 | ||||||||
\(463\) | −7.76227e6 | −1.68281 | −0.841407 | − | 0.540402i | \(-0.818272\pi\) | ||||
−0.841407 | + | 0.540402i | \(0.818272\pi\) | |||||||
\(464\) | −600088. | −0.129396 | ||||||||
\(465\) | 2.07216e6 | 0.444418 | ||||||||
\(466\) | −4.22558e6 | −0.901409 | ||||||||
\(467\) | 7.51036e6 | 1.59356 | 0.796780 | − | 0.604269i | \(-0.206535\pi\) | ||||
0.796780 | + | 0.604269i | \(0.206535\pi\) | |||||||
\(468\) | 1.41345e6 | 0.298309 | ||||||||
\(469\) | −5.76895e6 | −1.21106 | ||||||||
\(470\) | −1.79182e6 | −0.374153 | ||||||||
\(471\) | −2.37059e6 | −0.492385 | ||||||||
\(472\) | −2.90559e6 | −0.600315 | ||||||||
\(473\) | −383405. | −0.0787961 | ||||||||
\(474\) | 1.30255e6 | 0.266285 | ||||||||
\(475\) | −1.73450e6 | −0.352727 | ||||||||
\(476\) | −3.98389e6 | −0.805916 | ||||||||
\(477\) | −2.68095e6 | −0.539501 | ||||||||
\(478\) | 3.22203e6 | 0.645000 | ||||||||
\(479\) | −7.38377e6 | −1.47041 | −0.735207 | − | 0.677843i | \(-0.762915\pi\) | ||||
−0.735207 | + | 0.677843i | \(0.762915\pi\) | |||||||
\(480\) | 216787. | 0.0429467 | ||||||||
\(481\) | −2.48401e6 | −0.489543 | ||||||||
\(482\) | 3.39503e6 | 0.665620 | ||||||||
\(483\) | −532981. | −0.103955 | ||||||||
\(484\) | −518043. | −0.100520 | ||||||||
\(485\) | −1.79669e6 | −0.346831 | ||||||||
\(486\) | 3.81363e6 | 0.732400 | ||||||||
\(487\) | −9.26947e6 | −1.77106 | −0.885528 | − | 0.464586i | \(-0.846203\pi\) | ||||
−0.885528 | + | 0.464586i | \(0.846203\pi\) | |||||||
\(488\) | −1.18019e6 | −0.224339 | ||||||||
\(489\) | 5.43908e6 | 1.02862 | ||||||||
\(490\) | 265144. | 0.0498874 | ||||||||
\(491\) | −3.61323e6 | −0.676381 | −0.338190 | − | 0.941078i | \(-0.609815\pi\) | ||||
−0.338190 | + | 0.941078i | \(0.609815\pi\) | |||||||
\(492\) | 3261.14 | 0.000607374 0 | ||||||||
\(493\) | −4.90567e6 | −0.909036 | ||||||||
\(494\) | −5.72511e6 | −1.05552 | ||||||||
\(495\) | −1.53608e6 | −0.281774 | ||||||||
\(496\) | −2.50571e6 | −0.457328 | ||||||||
\(497\) | −474634. | −0.0861922 | ||||||||
\(498\) | −1.01272e6 | −0.182986 | ||||||||
\(499\) | 6.40637e6 | 1.15176 | 0.575878 | − | 0.817535i | \(-0.304660\pi\) | ||||
0.575878 | + | 0.817535i | \(0.304660\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 517808. | 0.0921667 | ||||||||
\(502\) | 6.47387e6 | 1.14658 | ||||||||
\(503\) | 1.04304e7 | 1.83815 | 0.919074 | − | 0.394086i | \(-0.128939\pi\) | ||||
0.919074 | + | 0.394086i | \(0.128939\pi\) | |||||||
\(504\) | −1.30429e6 | −0.228716 | ||||||||
\(505\) | 1.52701e6 | 0.266449 | ||||||||
\(506\) | 759032. | 0.131790 | ||||||||
\(507\) | 891752. | 0.154072 | ||||||||
\(508\) | 2.57930e6 | 0.443448 | ||||||||
\(509\) | 44659.2 | 0.00764040 | 0.00382020 | − | 0.999993i | \(-0.498784\pi\) | ||||
0.00382020 | + | 0.999993i | \(0.498784\pi\) | |||||||
\(510\) | 1.77221e6 | 0.301711 | ||||||||
\(511\) | −663890. | −0.112472 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −9.73619e6 | −1.63341 | ||||||||
\(514\) | −5.26496e6 | −0.878997 | ||||||||
\(515\) | 4.54885e6 | 0.755759 | ||||||||
\(516\) | 144819. | 0.0239443 | ||||||||
\(517\) | 6.42744e6 | 1.05758 | ||||||||
\(518\) | 2.29217e6 | 0.375337 | ||||||||
\(519\) | 2.28792e6 | 0.372840 | ||||||||
\(520\) | 825183. | 0.133827 | ||||||||
\(521\) | 6.03155e6 | 0.973497 | 0.486749 | − | 0.873542i | \(-0.338183\pi\) | ||||
0.486749 | + | 0.873542i | \(0.338183\pi\) | |||||||
\(522\) | −1.60607e6 | −0.257981 | ||||||||
\(523\) | 1.12464e6 | 0.179788 | 0.0898939 | − | 0.995951i | \(-0.471347\pi\) | ||||
0.0898939 | + | 0.995951i | \(0.471347\pi\) | |||||||
\(524\) | −2.19878e6 | −0.349827 | ||||||||
\(525\) | 629703. | 0.0997098 | ||||||||
\(526\) | 2.42309e6 | 0.381860 | ||||||||
\(527\) | −2.04840e7 | −3.21284 | ||||||||
\(528\) | −777637. | −0.121392 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −1.56516e6 | −0.242030 | ||||||||
\(531\) | −7.77649e6 | −1.19687 | ||||||||
\(532\) | 5.28295e6 | 0.809278 | ||||||||
\(533\) | 12413.3 | 0.00189264 | ||||||||
\(534\) | 1.70482e6 | 0.258717 | ||||||||
\(535\) | −2.48575e6 | −0.375467 | ||||||||
\(536\) | −3.10322e6 | −0.466553 | ||||||||
\(537\) | 1.88586e6 | 0.282211 | ||||||||
\(538\) | −44160.3 | −0.00657774 | ||||||||
\(539\) | −951099. | −0.141011 | ||||||||
\(540\) | 1.40332e6 | 0.207096 | ||||||||
\(541\) | −8.07492e6 | −1.18617 | −0.593083 | − | 0.805142i | \(-0.702089\pi\) | ||||
−0.593083 | + | 0.805142i | \(0.702089\pi\) | |||||||
\(542\) | −5.20631e6 | −0.761258 | ||||||||
\(543\) | 2.35117e6 | 0.342204 | ||||||||
\(544\) | −2.14301e6 | −0.310475 | ||||||||
\(545\) | 3.94245e6 | 0.568559 | ||||||||
\(546\) | 2.07848e6 | 0.298377 | ||||||||
\(547\) | 5.64519e6 | 0.806697 | 0.403348 | − | 0.915047i | \(-0.367846\pi\) | ||||
0.403348 | + | 0.915047i | \(0.367846\pi\) | |||||||
\(548\) | 4.88440e6 | 0.694800 | ||||||||
\(549\) | −3.15866e6 | −0.447273 | ||||||||
\(550\) | −896776. | −0.126409 | ||||||||
\(551\) | 6.50531e6 | 0.912828 | ||||||||
\(552\) | −286700. | −0.0400480 | ||||||||
\(553\) | −4.57513e6 | −0.636196 | ||||||||
\(554\) | −8.28680e6 | −1.14713 | ||||||||
\(555\) | −1.01966e6 | −0.140515 | ||||||||
\(556\) | −2.30284e6 | −0.315920 | ||||||||
\(557\) | 1.00532e7 | 1.37299 | 0.686496 | − | 0.727134i | \(-0.259148\pi\) | ||||
0.686496 | + | 0.727134i | \(0.259148\pi\) | |||||||
\(558\) | −6.70628e6 | −0.911792 | ||||||||
\(559\) | 551244. | 0.0746130 | ||||||||
\(560\) | −761454. | −0.102606 | ||||||||
\(561\) | −6.35712e6 | −0.852811 | ||||||||
\(562\) | −2.82251e6 | −0.376960 | ||||||||
\(563\) | −7.02958e6 | −0.934670 | −0.467335 | − | 0.884080i | \(-0.654786\pi\) | ||||
−0.467335 | + | 0.884080i | \(0.654786\pi\) | |||||||
\(564\) | −2.42776e6 | −0.321372 | ||||||||
\(565\) | 4.47415e6 | 0.589644 | ||||||||
\(566\) | 7.41059e6 | 0.972326 | ||||||||
\(567\) | −1.41752e6 | −0.185170 | ||||||||
\(568\) | −255315. | −0.0332051 | ||||||||
\(569\) | −6.22757e6 | −0.806377 | −0.403188 | − | 0.915117i | \(-0.632098\pi\) | ||||
−0.403188 | + | 0.915117i | \(0.632098\pi\) | |||||||
\(570\) | −2.35010e6 | −0.302969 | ||||||||
\(571\) | 1.08461e7 | 1.39215 | 0.696074 | − | 0.717970i | \(-0.254929\pi\) | ||||
0.696074 | + | 0.717970i | \(0.254929\pi\) | |||||||
\(572\) | −2.96002e6 | −0.378272 | ||||||||
\(573\) | −4.58446e6 | −0.583313 | ||||||||
\(574\) | −11454.6 | −0.00145111 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | −701600. | −0.0881117 | ||||||||
\(577\) | 1.08904e6 | 0.136178 | 0.0680889 | − | 0.997679i | \(-0.478310\pi\) | ||||
0.0680889 | + | 0.997679i | \(0.478310\pi\) | |||||||
\(578\) | −1.18395e7 | −1.47405 | ||||||||
\(579\) | 283584. | 0.0351548 | ||||||||
\(580\) | −937637. | −0.115735 | ||||||||
\(581\) | 3.55714e6 | 0.437181 | ||||||||
\(582\) | −2.43436e6 | −0.297905 | ||||||||
\(583\) | 5.61439e6 | 0.684118 | ||||||||
\(584\) | −357118. | −0.0433292 | ||||||||
\(585\) | 2.20851e6 | 0.266815 | ||||||||
\(586\) | −4.27207e6 | −0.513918 | ||||||||
\(587\) | 1.40443e7 | 1.68230 | 0.841150 | − | 0.540801i | \(-0.181879\pi\) | ||||
0.841150 | + | 0.540801i | \(0.181879\pi\) | |||||||
\(588\) | 359248. | 0.0428500 | ||||||||
\(589\) | 2.71634e7 | 3.22624 | ||||||||
\(590\) | −4.53998e6 | −0.536938 | ||||||||
\(591\) | 1.26455e6 | 0.148925 | ||||||||
\(592\) | 1.23300e6 | 0.144597 | ||||||||
\(593\) | 1.43036e7 | 1.67036 | 0.835180 | − | 0.549977i | \(-0.185363\pi\) | ||||
0.835180 | + | 0.549977i | \(0.185363\pi\) | |||||||
\(594\) | −5.03385e6 | −0.585375 | ||||||||
\(595\) | −6.22482e6 | −0.720833 | ||||||||
\(596\) | 5.68726e6 | 0.655824 | ||||||||
\(597\) | −2.32636e6 | −0.267141 | ||||||||
\(598\) | −1.09131e6 | −0.124794 | ||||||||
\(599\) | −4.51234e6 | −0.513848 | −0.256924 | − | 0.966432i | \(-0.582709\pi\) | ||||
−0.256924 | + | 0.966432i | \(0.582709\pi\) | |||||||
\(600\) | 338729. | 0.0384127 | ||||||||
\(601\) | 1.00918e7 | 1.13968 | 0.569838 | − | 0.821757i | \(-0.307006\pi\) | ||||
0.569838 | + | 0.821757i | \(0.307006\pi\) | |||||||
\(602\) | −508671. | −0.0572065 | ||||||||
\(603\) | −8.30544e6 | −0.930186 | ||||||||
\(604\) | −3.60582e6 | −0.402172 | ||||||||
\(605\) | −809443. | −0.0899079 | ||||||||
\(606\) | 2.06897e6 | 0.228862 | ||||||||
\(607\) | 8.46363e6 | 0.932363 | 0.466182 | − | 0.884689i | \(-0.345629\pi\) | ||||
0.466182 | + | 0.884689i | \(0.345629\pi\) | |||||||
\(608\) | 2.84180e6 | 0.311770 | ||||||||
\(609\) | −2.36173e6 | −0.258040 | ||||||||
\(610\) | −1.84405e6 | −0.200655 | ||||||||
\(611\) | −9.24111e6 | −1.00143 | ||||||||
\(612\) | −5.73553e6 | −0.619006 | ||||||||
\(613\) | 453516. | 0.0487463 | 0.0243732 | − | 0.999703i | \(-0.492241\pi\) | ||||
0.0243732 | + | 0.999703i | \(0.492241\pi\) | |||||||
\(614\) | 139479. | 0.0149310 | ||||||||
\(615\) | 5095.53 | 0.000543252 0 | ||||||||
\(616\) | 2.73142e6 | 0.290025 | ||||||||
\(617\) | 6.89013e6 | 0.728643 | 0.364321 | − | 0.931273i | \(-0.381301\pi\) | ||||
0.364321 | + | 0.931273i | \(0.381301\pi\) | |||||||
\(618\) | 6.16331e6 | 0.649147 | ||||||||
\(619\) | 2.03233e6 | 0.213190 | 0.106595 | − | 0.994303i | \(-0.466005\pi\) | ||||
0.106595 | + | 0.994303i | \(0.466005\pi\) | |||||||
\(620\) | −3.91518e6 | −0.409046 | ||||||||
\(621\) | −1.85589e6 | −0.193118 | ||||||||
\(622\) | −9.11208e6 | −0.944369 | ||||||||
\(623\) | −5.98811e6 | −0.618115 | ||||||||
\(624\) | 1.11805e6 | 0.114948 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 5.26630e6 | 0.537118 | ||||||||
\(627\) | 8.43004e6 | 0.856369 | ||||||||
\(628\) | 4.47904e6 | 0.453195 | ||||||||
\(629\) | 1.00797e7 | 1.01583 | ||||||||
\(630\) | −2.03795e6 | −0.204570 | ||||||||
\(631\) | 1.36301e7 | 1.36278 | 0.681392 | − | 0.731919i | \(-0.261375\pi\) | ||||
0.681392 | + | 0.731919i | \(0.261375\pi\) | |||||||
\(632\) | −2.46105e6 | −0.245091 | ||||||||
\(633\) | −2.99349e6 | −0.296940 | ||||||||
\(634\) | 4.60268e6 | 0.454765 | ||||||||
\(635\) | 4.03016e6 | 0.396632 | ||||||||
\(636\) | −2.12066e6 | −0.207887 | ||||||||
\(637\) | 1.36745e6 | 0.133525 | ||||||||
\(638\) | 3.36340e6 | 0.327135 | ||||||||
\(639\) | −683322. | −0.0662023 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −1.27425e7 | −1.22492 | −0.612462 | − | 0.790500i | \(-0.709821\pi\) | ||||
−0.612462 | + | 0.790500i | \(0.709821\pi\) | |||||||
\(642\) | −3.36798e6 | −0.322501 | ||||||||
\(643\) | 1.23274e7 | 1.17583 | 0.587913 | − | 0.808924i | \(-0.299950\pi\) | ||||
0.587913 | + | 0.808924i | \(0.299950\pi\) | |||||||
\(644\) | 1.00702e6 | 0.0956807 | ||||||||
\(645\) | 226280. | 0.0214164 | ||||||||
\(646\) | 2.32315e7 | 2.19026 | ||||||||
\(647\) | −1.16678e7 | −1.09579 | −0.547894 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547894 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(648\) | −762510. | −0.0713359 | ||||||||
\(649\) | 1.62854e7 | 1.51770 | ||||||||
\(650\) | 1.28935e6 | 0.119698 | ||||||||
\(651\) | −9.86161e6 | −0.912001 | ||||||||
\(652\) | −1.02767e7 | −0.946747 | ||||||||
\(653\) | 1.07123e7 | 0.983108 | 0.491554 | − | 0.870847i | \(-0.336429\pi\) | ||||
0.491554 | + | 0.870847i | \(0.336429\pi\) | |||||||
\(654\) | 5.34169e6 | 0.488354 | ||||||||
\(655\) | −3.43559e6 | −0.312895 | ||||||||
\(656\) | −6161.64 | −0.000559032 0 | ||||||||
\(657\) | −955789. | −0.0863871 | ||||||||
\(658\) | 8.52741e6 | 0.767808 | ||||||||
\(659\) | 1.03868e7 | 0.931686 | 0.465843 | − | 0.884867i | \(-0.345751\pi\) | ||||
0.465843 | + | 0.884867i | \(0.345751\pi\) | |||||||
\(660\) | −1.21506e6 | −0.108577 | ||||||||
\(661\) | 1.32825e7 | 1.18243 | 0.591215 | − | 0.806514i | \(-0.298649\pi\) | ||||
0.591215 | + | 0.806514i | \(0.298649\pi\) | |||||||
\(662\) | 1.44978e7 | 1.28576 | ||||||||
\(663\) | 9.14001e6 | 0.807538 | ||||||||
\(664\) | 1.91345e6 | 0.168421 | ||||||||
\(665\) | 8.25461e6 | 0.723840 | ||||||||
\(666\) | 3.29999e6 | 0.288288 | ||||||||
\(667\) | 1.24002e6 | 0.107923 | ||||||||
\(668\) | −978354. | −0.0848310 | ||||||||
\(669\) | 5.10625e6 | 0.441100 | ||||||||
\(670\) | −4.84879e6 | −0.417298 | ||||||||
\(671\) | 6.61482e6 | 0.567168 | ||||||||
\(672\) | −1.03171e6 | −0.0881318 | ||||||||
\(673\) | −1.21571e7 | −1.03465 | −0.517323 | − | 0.855790i | \(-0.673071\pi\) | ||||
−0.517323 | + | 0.855790i | \(0.673071\pi\) | |||||||
\(674\) | −1.23336e6 | −0.104578 | ||||||||
\(675\) | 2.19268e6 | 0.185232 | ||||||||
\(676\) | −1.68489e6 | −0.141809 | ||||||||
\(677\) | −1.63957e7 | −1.37486 | −0.687431 | − | 0.726250i | \(-0.741262\pi\) | ||||
−0.687431 | + | 0.726250i | \(0.741262\pi\) | |||||||
\(678\) | 6.06210e6 | 0.506465 | ||||||||
\(679\) | 8.55059e6 | 0.711740 | ||||||||
\(680\) | −3.34845e6 | −0.277697 | ||||||||
\(681\) | −4.60343e6 | −0.380377 | ||||||||
\(682\) | 1.40442e7 | 1.15621 | ||||||||
\(683\) | −5.50399e6 | −0.451467 | −0.225733 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225733 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(684\) | 7.60576e6 | 0.621588 | ||||||||
\(685\) | 7.63188e6 | 0.621448 | ||||||||
\(686\) | −9.26044e6 | −0.751314 | ||||||||
\(687\) | −7.54295e6 | −0.609747 | ||||||||
\(688\) | −273623. | −0.0220385 | ||||||||
\(689\) | −8.07214e6 | −0.647800 | ||||||||
\(690\) | −447969. | −0.0358200 | ||||||||
\(691\) | 8.81682e6 | 0.702452 | 0.351226 | − | 0.936291i | \(-0.385765\pi\) | ||||
0.351226 | + | 0.936291i | \(0.385765\pi\) | |||||||
\(692\) | −4.32284e6 | −0.343165 | ||||||||
\(693\) | 7.31034e6 | 0.578235 | ||||||||
\(694\) | 3.40004e6 | 0.267970 | ||||||||
\(695\) | −3.59819e6 | −0.282567 | ||||||||
\(696\) | −1.27042e6 | −0.0994086 | ||||||||
\(697\) | −50370.9 | −0.00392734 | ||||||||
\(698\) | 1.18554e7 | 0.921039 | ||||||||
\(699\) | −8.94580e6 | −0.692510 | ||||||||
\(700\) | −1.18977e6 | −0.0917737 | ||||||||
\(701\) | 9.94017e6 | 0.764010 | 0.382005 | − | 0.924160i | \(-0.375234\pi\) | ||||
0.382005 | + | 0.924160i | \(0.375234\pi\) | |||||||
\(702\) | 7.23747e6 | 0.554299 | ||||||||
\(703\) | −1.33664e7 | −1.02006 | ||||||||
\(704\) | 1.46928e6 | 0.111731 | ||||||||
\(705\) | −3.79338e6 | −0.287444 | ||||||||
\(706\) | −8.57959e6 | −0.647821 | ||||||||
\(707\) | −7.26718e6 | −0.546786 | ||||||||
\(708\) | −6.15129e6 | −0.461194 | ||||||||
\(709\) | 2.13658e7 | 1.59626 | 0.798128 | − | 0.602488i | \(-0.205824\pi\) | ||||
0.798128 | + | 0.602488i | \(0.205824\pi\) | |||||||
\(710\) | −398929. | −0.0296995 | ||||||||
\(711\) | −6.58673e6 | −0.488648 | ||||||||
\(712\) | −3.22111e6 | −0.238126 | ||||||||
\(713\) | 5.17782e6 | 0.381438 | ||||||||
\(714\) | −8.43412e6 | −0.619147 | ||||||||
\(715\) | −4.62503e6 | −0.338337 | ||||||||
\(716\) | −3.56317e6 | −0.259749 | ||||||||
\(717\) | 6.82121e6 | 0.495523 | ||||||||
\(718\) | 1.75555e6 | 0.127087 | ||||||||
\(719\) | 2.21914e6 | 0.160089 | 0.0800445 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800445 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(720\) | −1.09625e6 | −0.0788095 | ||||||||
\(721\) | −2.16484e7 | −1.55091 | ||||||||
\(722\) | −2.09024e7 | −1.49229 | ||||||||
\(723\) | 7.18747e6 | 0.511364 | ||||||||
\(724\) | −4.44234e6 | −0.314967 | ||||||||
\(725\) | −1.46506e6 | −0.103517 | ||||||||
\(726\) | −1.09673e6 | −0.0772249 | ||||||||
\(727\) | 1.66600e7 | 1.16906 | 0.584532 | − | 0.811371i | \(-0.301278\pi\) | ||||
0.584532 | + | 0.811371i | \(0.301278\pi\) | |||||||
\(728\) | −3.92712e6 | −0.274629 | ||||||||
\(729\) | 5.17852e6 | 0.360900 | ||||||||
\(730\) | −557998. | −0.0387548 | ||||||||
\(731\) | −2.23685e6 | −0.154826 | ||||||||
\(732\) | −2.49854e6 | −0.172349 | ||||||||
\(733\) | 6.84915e6 | 0.470844 | 0.235422 | − | 0.971893i | \(-0.424353\pi\) | ||||
0.235422 | + | 0.971893i | \(0.424353\pi\) | |||||||
\(734\) | −5.55572e6 | −0.380627 | ||||||||
\(735\) | 561324. | 0.0383262 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | 1.73931e7 | 1.17953 | ||||||||
\(738\) | −16491.0 | −0.00111457 | ||||||||
\(739\) | 4.66486e6 | 0.314216 | 0.157108 | − | 0.987581i | \(-0.449783\pi\) | ||||
0.157108 | + | 0.987581i | \(0.449783\pi\) | |||||||
\(740\) | 1.92656e6 | 0.129331 | ||||||||
\(741\) | −1.21204e7 | −0.810906 | ||||||||
\(742\) | 7.44872e6 | 0.496675 | ||||||||
\(743\) | −7.85896e6 | −0.522268 | −0.261134 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261134 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(744\) | −5.30474e6 | −0.351343 | ||||||||
\(745\) | 8.88635e6 | 0.586587 | ||||||||
\(746\) | −8.57718e6 | −0.564284 | ||||||||
\(747\) | 5.12115e6 | 0.335789 | ||||||||
\(748\) | 1.20112e7 | 0.784935 | ||||||||
\(749\) | 1.18299e7 | 0.770506 | ||||||||
\(750\) | 529264. | 0.0343573 | ||||||||
\(751\) | −1.85421e7 | −1.19966 | −0.599830 | − | 0.800128i | \(-0.704765\pi\) | ||||
−0.599830 | + | 0.800128i | \(0.704765\pi\) | |||||||
\(752\) | 4.58705e6 | 0.295794 | ||||||||
\(753\) | 1.37055e7 | 0.880864 | ||||||||
\(754\) | −4.83577e6 | −0.309768 | ||||||||
\(755\) | −5.63409e6 | −0.359714 | ||||||||
\(756\) | −6.67851e6 | −0.424986 | ||||||||
\(757\) | −1.07470e7 | −0.681629 | −0.340815 | − | 0.940130i | \(-0.610703\pi\) | ||||
−0.340815 | + | 0.940130i | \(0.610703\pi\) | |||||||
\(758\) | −1.02390e7 | −0.647270 | ||||||||
\(759\) | 1.60691e6 | 0.101248 | ||||||||
\(760\) | 4.44031e6 | 0.278855 | ||||||||
\(761\) | −6.27486e6 | −0.392774 | −0.196387 | − | 0.980526i | \(-0.562921\pi\) | ||||
−0.196387 | + | 0.980526i | \(0.562921\pi\) | |||||||
\(762\) | 5.46053e6 | 0.340680 | ||||||||
\(763\) | −1.87625e7 | −1.16675 | ||||||||
\(764\) | 8.66195e6 | 0.536886 | ||||||||
\(765\) | −8.96176e6 | −0.553656 | ||||||||
\(766\) | 1.15990e7 | 0.714247 | ||||||||
\(767\) | −2.34145e7 | −1.43713 | ||||||||
\(768\) | −554974. | −0.0339523 | ||||||||
\(769\) | −3.06263e7 | −1.86758 | −0.933788 | − | 0.357827i | \(-0.883518\pi\) | ||||
−0.933788 | + | 0.357827i | \(0.883518\pi\) | |||||||
\(770\) | 4.26784e6 | 0.259407 | ||||||||
\(771\) | −1.11462e7 | −0.675292 | ||||||||
\(772\) | −535807. | −0.0323568 | ||||||||
\(773\) | 2.73276e7 | 1.64495 | 0.822474 | − | 0.568803i | \(-0.192593\pi\) | ||||
0.822474 | + | 0.568803i | \(0.192593\pi\) | |||||||
\(774\) | −732324. | −0.0439391 | ||||||||
\(775\) | −6.11747e6 | −0.365862 | ||||||||
\(776\) | 4.59952e6 | 0.274194 | ||||||||
\(777\) | 4.85265e6 | 0.288354 | ||||||||
\(778\) | −5.88406e6 | −0.348520 | ||||||||
\(779\) | 66795.9 | 0.00394372 | ||||||||
\(780\) | 1.74696e6 | 0.102813 | ||||||||
\(781\) | 1.43100e6 | 0.0839483 | ||||||||
\(782\) | 4.42832e6 | 0.258954 | ||||||||
\(783\) | −8.22377e6 | −0.479365 | ||||||||
\(784\) | −678768. | −0.0394395 | ||||||||
\(785\) | 6.99850e6 | 0.405350 | ||||||||
\(786\) | −4.65494e6 | −0.268756 | ||||||||
\(787\) | −1.25785e7 | −0.723925 | −0.361963 | − | 0.932193i | \(-0.617893\pi\) | ||||
−0.361963 | + | 0.932193i | \(0.617893\pi\) | |||||||
\(788\) | −2.38927e6 | −0.137072 | ||||||||
\(789\) | 5.12981e6 | 0.293365 | ||||||||
\(790\) | −3.84539e6 | −0.219216 | ||||||||
\(791\) | −2.12929e7 | −1.21002 | ||||||||
\(792\) | 3.93237e6 | 0.222762 | ||||||||
\(793\) | −9.51052e6 | −0.537058 | ||||||||
\(794\) | 1.95411e7 | 1.10001 | ||||||||
\(795\) | −3.31353e6 | −0.185940 | ||||||||
\(796\) | 4.39546e6 | 0.245879 | ||||||||
\(797\) | −2.82459e7 | −1.57511 | −0.787554 | − | 0.616246i | \(-0.788653\pi\) | ||||
−0.787554 | + | 0.616246i | \(0.788653\pi\) | |||||||
\(798\) | 1.11843e7 | 0.621730 | ||||||||
\(799\) | 3.74988e7 | 2.07802 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −8.62096e6 | −0.474760 | ||||||||
\(802\) | 1.61486e7 | 0.886540 | ||||||||
\(803\) | 2.00160e6 | 0.109544 | ||||||||
\(804\) | −6.56970e6 | −0.358431 | ||||||||
\(805\) | 1.57347e6 | 0.0855795 | ||||||||
\(806\) | −2.01921e7 | −1.09482 | ||||||||
\(807\) | −93489.9 | −0.00505337 | ||||||||
\(808\) | −3.90915e6 | −0.210646 | ||||||||
\(809\) | 3.02669e7 | 1.62591 | 0.812956 | − | 0.582325i | \(-0.197857\pi\) | ||||
0.812956 | + | 0.582325i | \(0.197857\pi\) | |||||||
\(810\) | −1.19142e6 | −0.0638048 | ||||||||
\(811\) | −2.24011e7 | −1.19596 | −0.597981 | − | 0.801510i | \(-0.704030\pi\) | ||||
−0.597981 | + | 0.801510i | \(0.704030\pi\) | |||||||
\(812\) | 4.46229e6 | 0.237503 | ||||||||
\(813\) | −1.10221e7 | −0.584839 | ||||||||
\(814\) | −6.91078e6 | −0.365566 | ||||||||
\(815\) | −1.60573e7 | −0.846796 | ||||||||
\(816\) | −4.53687e6 | −0.238523 | ||||||||
\(817\) | 2.96624e6 | 0.155472 | ||||||||
\(818\) | 1.65553e7 | 0.865077 | ||||||||
\(819\) | −1.05105e7 | −0.547538 | ||||||||
\(820\) | −9627.57 | −0.000500014 0 | ||||||||
\(821\) | 2.07746e7 | 1.07566 | 0.537830 | − | 0.843053i | \(-0.319244\pi\) | ||||
0.537830 | + | 0.843053i | \(0.319244\pi\) | |||||||
\(822\) | 1.03406e7 | 0.533782 | ||||||||
\(823\) | −1.77559e7 | −0.913784 | −0.456892 | − | 0.889522i | \(-0.651037\pi\) | ||||
−0.456892 | + | 0.889522i | \(0.651037\pi\) | |||||||
\(824\) | −1.16451e7 | −0.597480 | ||||||||
\(825\) | −1.89853e6 | −0.0971140 | ||||||||
\(826\) | 2.16062e7 | 1.10186 | ||||||||
\(827\) | −7.87984e6 | −0.400639 | −0.200320 | − | 0.979731i | \(-0.564198\pi\) | ||||
−0.200320 | + | 0.979731i | \(0.564198\pi\) | |||||||
\(828\) | 1.44979e6 | 0.0734902 | ||||||||
\(829\) | 2.16609e7 | 1.09469 | 0.547345 | − | 0.836907i | \(-0.315639\pi\) | ||||
0.547345 | + | 0.836907i | \(0.315639\pi\) | |||||||
\(830\) | 2.98977e6 | 0.150641 | ||||||||
\(831\) | −1.75436e7 | −0.881286 | ||||||||
\(832\) | −2.11247e6 | −0.105799 | ||||||||
\(833\) | −5.54887e6 | −0.277072 | ||||||||
\(834\) | −4.87525e6 | −0.242707 | ||||||||
\(835\) | −1.52868e6 | −0.0758752 | ||||||||
\(836\) | −1.59279e7 | −0.788209 | ||||||||
\(837\) | −3.43390e7 | −1.69424 | ||||||||
\(838\) | −2.14512e6 | −0.105522 | ||||||||
\(839\) | 2.69565e7 | 1.32208 | 0.661041 | − | 0.750350i | \(-0.270115\pi\) | ||||
0.661041 | + | 0.750350i | \(0.270115\pi\) | |||||||
\(840\) | −1.61204e6 | −0.0788275 | ||||||||
\(841\) | −1.50164e7 | −0.732108 | ||||||||
\(842\) | −2.63822e7 | −1.28242 | ||||||||
\(843\) | −5.97542e6 | −0.289601 | ||||||||
\(844\) | 5.65594e6 | 0.273306 | ||||||||
\(845\) | −2.63264e6 | −0.126838 | ||||||||
\(846\) | 1.22767e7 | 0.589736 | ||||||||
\(847\) | 3.85221e6 | 0.184502 | ||||||||
\(848\) | 4.00680e6 | 0.191341 | ||||||||
\(849\) | 1.56886e7 | 0.746993 | ||||||||
\(850\) | −5.23195e6 | −0.248380 | ||||||||
\(851\) | −2.54788e6 | −0.120602 | ||||||||
\(852\) | −540515. | −0.0255099 | ||||||||
\(853\) | −3.01511e7 | −1.41883 | −0.709415 | − | 0.704791i | \(-0.751041\pi\) | ||||
−0.709415 | + | 0.704791i | \(0.751041\pi\) | |||||||
\(854\) | 8.77601e6 | 0.411768 | ||||||||
\(855\) | 1.18840e7 | 0.555965 | ||||||||
\(856\) | 6.36351e6 | 0.296833 | ||||||||
\(857\) | 9.17229e6 | 0.426605 | 0.213302 | − | 0.976986i | \(-0.431578\pi\) | ||||
0.213302 | + | 0.976986i | \(0.431578\pi\) | |||||||
\(858\) | −6.26653e6 | −0.290609 | ||||||||
\(859\) | −9.12169e6 | −0.421786 | −0.210893 | − | 0.977509i | \(-0.567637\pi\) | ||||
−0.210893 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(860\) | −427537. | −0.0197118 | ||||||||
\(861\) | −24250.1 | −0.00111482 | ||||||||
\(862\) | −1.46005e7 | −0.669267 | ||||||||
\(863\) | 1.54060e7 | 0.704145 | 0.352072 | − | 0.935973i | \(-0.385477\pi\) | ||||
0.352072 | + | 0.935973i | \(0.385477\pi\) | |||||||
\(864\) | −3.59249e6 | −0.163724 | ||||||||
\(865\) | −6.75443e6 | −0.306937 | ||||||||
\(866\) | −2.20136e7 | −0.997461 | ||||||||
\(867\) | −2.50648e7 | −1.13245 | ||||||||
\(868\) | 1.86327e7 | 0.839413 | ||||||||
\(869\) | 1.37938e7 | 0.619634 | ||||||||
\(870\) | −1.98503e6 | −0.0889138 | ||||||||
\(871\) | −2.50071e7 | −1.11691 | ||||||||
\(872\) | −1.00927e7 | −0.449485 | ||||||||
\(873\) | 1.23101e7 | 0.546672 | ||||||||
\(874\) | −5.87231e6 | −0.260034 | ||||||||
\(875\) | −1.85902e6 | −0.0820849 | ||||||||
\(876\) | −756040. | −0.0332878 | ||||||||
\(877\) | −1.74936e7 | −0.768032 | −0.384016 | − | 0.923326i | \(-0.625459\pi\) | ||||
−0.384016 | + | 0.923326i | \(0.625459\pi\) | |||||||
\(878\) | 1.69269e7 | 0.741040 | ||||||||
\(879\) | −9.04421e6 | −0.394819 | ||||||||
\(880\) | 2.29575e6 | 0.0999350 | ||||||||
\(881\) | −1.82811e7 | −0.793527 | −0.396763 | − | 0.917921i | \(-0.629867\pi\) | ||||
−0.396763 | + | 0.917921i | \(0.629867\pi\) | |||||||
\(882\) | −1.81665e6 | −0.0786321 | ||||||||
\(883\) | 1.89568e7 | 0.818206 | 0.409103 | − | 0.912488i | \(-0.365842\pi\) | ||||
0.409103 | + | 0.912488i | \(0.365842\pi\) | |||||||
\(884\) | −1.72693e7 | −0.743264 | ||||||||
\(885\) | −9.61140e6 | −0.412504 | ||||||||
\(886\) | 1.68967e7 | 0.723133 | ||||||||
\(887\) | 4.61134e6 | 0.196797 | 0.0983985 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983985 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(888\) | 2.61033e6 | 0.111087 | ||||||||
\(889\) | −1.91799e7 | −0.813938 | ||||||||
\(890\) | −5.03299e6 | −0.212986 | ||||||||
\(891\) | 4.27376e6 | 0.180350 | ||||||||
\(892\) | −9.64782e6 | −0.405992 | ||||||||
\(893\) | −4.97264e7 | −2.08669 | ||||||||
\(894\) | 1.20403e7 | 0.503839 | ||||||||
\(895\) | −5.56746e6 | −0.232327 | ||||||||
\(896\) | 1.94932e6 | 0.0811173 | ||||||||
\(897\) | −2.31035e6 | −0.0958733 | ||||||||
\(898\) | 2.58079e7 | 1.06798 | ||||||||
\(899\) | 2.29439e7 | 0.946819 | ||||||||
\(900\) | −1.71289e6 | −0.0704894 | ||||||||
\(901\) | 3.27553e7 | 1.34422 | ||||||||
\(902\) | 34535.1 | 0.00141333 | ||||||||
\(903\) | −1.07689e6 | −0.0439491 | ||||||||
\(904\) | −1.14538e7 | −0.466154 | ||||||||
\(905\) | −6.94116e6 | −0.281715 | ||||||||
\(906\) | −7.63373e6 | −0.308970 | ||||||||
\(907\) | −1.05722e7 | −0.426726 | −0.213363 | − | 0.976973i | \(-0.568442\pi\) | ||||
−0.213363 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(908\) | 8.69780e6 | 0.350102 | ||||||||
\(909\) | −1.04624e7 | −0.419974 | ||||||||
\(910\) | −6.13612e6 | −0.245635 | ||||||||
\(911\) | 1.06672e7 | 0.425849 | 0.212925 | − | 0.977069i | \(-0.431701\pi\) | ||||
0.212925 | + | 0.977069i | \(0.431701\pi\) | |||||||
\(912\) | 6.01625e6 | 0.239518 | ||||||||
\(913\) | −1.07246e7 | −0.425799 | ||||||||
\(914\) | −7.93699e6 | −0.314261 | ||||||||
\(915\) | −3.90397e6 | −0.154153 | ||||||||
\(916\) | 1.42518e7 | 0.561216 | ||||||||
\(917\) | 1.63503e7 | 0.642099 | ||||||||
\(918\) | −2.93683e7 | −1.15020 | ||||||||
\(919\) | 6018.39 | 0.000235067 0 | 0.000117534 | − | 1.00000i | \(-0.499963\pi\) | ||||
0.000117534 | 1.00000i | \(0.499963\pi\) | ||||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | 295285. | 0.0114708 | ||||||||
\(922\) | −2.31375e7 | −0.896375 | ||||||||
\(923\) | −2.05743e6 | −0.0794917 | ||||||||
\(924\) | 5.78256e6 | 0.222813 | ||||||||
\(925\) | 3.01025e6 | 0.115677 | ||||||||
\(926\) | 3.10491e7 | 1.18993 | ||||||||
\(927\) | −3.11667e7 | −1.19122 | ||||||||
\(928\) | 2.40035e6 | 0.0914966 | ||||||||
\(929\) | −4.69368e7 | −1.78432 | −0.892162 | − | 0.451715i | \(-0.850812\pi\) | ||||
−0.892162 | + | 0.451715i | \(0.850812\pi\) | |||||||
\(930\) | −8.28866e6 | −0.314251 | ||||||||
\(931\) | 7.35825e6 | 0.278228 | ||||||||
\(932\) | 1.69023e7 | 0.637392 | ||||||||
\(933\) | −1.92908e7 | −0.725514 | ||||||||
\(934\) | −3.00414e7 | −1.12682 | ||||||||
\(935\) | 1.87676e7 | 0.702067 | ||||||||
\(936\) | −5.65380e6 | −0.210936 | ||||||||
\(937\) | −4.09932e7 | −1.52533 | −0.762664 | − | 0.646795i | \(-0.776109\pi\) | ||||
−0.762664 | + | 0.646795i | \(0.776109\pi\) | |||||||
\(938\) | 2.30758e7 | 0.856347 | ||||||||
\(939\) | 1.11491e7 | 0.412643 | ||||||||
\(940\) | 7.16727e6 | 0.264566 | ||||||||
\(941\) | 2.29251e7 | 0.843988 | 0.421994 | − | 0.906599i | \(-0.361330\pi\) | ||||
0.421994 | + | 0.906599i | \(0.361330\pi\) | |||||||
\(942\) | 9.48238e6 | 0.348169 | ||||||||
\(943\) | 12732.5 | 0.000466265 0 | ||||||||
\(944\) | 1.16223e7 | 0.424487 | ||||||||
\(945\) | −1.04352e7 | −0.380119 | ||||||||
\(946\) | 1.53362e6 | 0.0557173 | ||||||||
\(947\) | −1.17141e6 | −0.0424456 | −0.0212228 | − | 0.999775i | \(-0.506756\pi\) | ||||
−0.0212228 | + | 0.999775i | \(0.506756\pi\) | |||||||
\(948\) | −5.21018e6 | −0.188292 | ||||||||
\(949\) | −2.87781e6 | −0.103728 | ||||||||
\(950\) | 6.93798e6 | 0.249416 | ||||||||
\(951\) | 9.74413e6 | 0.349375 | ||||||||
\(952\) | 1.59355e7 | 0.569869 | ||||||||
\(953\) | −1.77064e7 | −0.631537 | −0.315768 | − | 0.948836i | \(-0.602262\pi\) | ||||
−0.315768 | + | 0.948836i | \(0.602262\pi\) | |||||||
\(954\) | 1.07238e7 | 0.381485 | ||||||||
\(955\) | 1.35343e7 | 0.480206 | ||||||||
\(956\) | −1.28881e7 | −0.456084 | ||||||||
\(957\) | 7.12052e6 | 0.251323 | ||||||||
\(958\) | 2.95351e7 | 1.03974 | ||||||||
\(959\) | −3.63208e7 | −1.27529 | ||||||||
\(960\) | −867146. | −0.0303679 | ||||||||
\(961\) | 6.71748e7 | 2.34638 | ||||||||
\(962\) | 9.93604e6 | 0.346159 | ||||||||
\(963\) | 1.70313e7 | 0.591808 | ||||||||
\(964\) | −1.35801e7 | −0.470664 | ||||||||
\(965\) | −837199. | −0.0289408 | ||||||||
\(966\) | 2.13192e6 | 0.0735070 | ||||||||
\(967\) | −2.36387e7 | −0.812937 | −0.406468 | − | 0.913665i | \(-0.633240\pi\) | ||||
−0.406468 | + | 0.913665i | \(0.633240\pi\) | |||||||
\(968\) | 2.07217e6 | 0.0710784 | ||||||||
\(969\) | 4.91823e7 | 1.68267 | ||||||||
\(970\) | 7.18675e6 | 0.245247 | ||||||||
\(971\) | 2.33077e7 | 0.793324 | 0.396662 | − | 0.917965i | \(-0.370168\pi\) | ||||
0.396662 | + | 0.917965i | \(0.370168\pi\) | |||||||
\(972\) | −1.52545e7 | −0.517885 | ||||||||
\(973\) | 1.71241e7 | 0.579863 | ||||||||
\(974\) | 3.70779e7 | 1.25233 | ||||||||
\(975\) | 2.72963e6 | 0.0919584 | ||||||||
\(976\) | 4.72078e6 | 0.158631 | ||||||||
\(977\) | 2.37183e7 | 0.794964 | 0.397482 | − | 0.917610i | \(-0.369884\pi\) | ||||
0.397482 | + | 0.917610i | \(0.369884\pi\) | |||||||
\(978\) | −2.17563e7 | −0.727341 | ||||||||
\(979\) | 1.80539e7 | 0.602024 | ||||||||
\(980\) | −1.06058e6 | −0.0352757 | ||||||||
\(981\) | −2.70120e7 | −0.896156 | ||||||||
\(982\) | 1.44529e7 | 0.478274 | ||||||||
\(983\) | −2.54913e7 | −0.841413 | −0.420706 | − | 0.907197i | \(-0.638218\pi\) | ||||
−0.420706 | + | 0.907197i | \(0.638218\pi\) | |||||||
\(984\) | −13044.5 | −0.000429478 0 | ||||||||
\(985\) | −3.73323e6 | −0.122601 | ||||||||
\(986\) | 1.96227e7 | 0.642785 | ||||||||
\(987\) | 1.80530e7 | 0.589871 | ||||||||
\(988\) | 2.29004e7 | 0.746365 | ||||||||
\(989\) | 565417. | 0.0183814 | ||||||||
\(990\) | 6.14432e6 | 0.199244 | ||||||||
\(991\) | −3.42847e7 | −1.10896 | −0.554481 | − | 0.832197i | \(-0.687083\pi\) | ||||
−0.554481 | + | 0.832197i | \(0.687083\pi\) | |||||||
\(992\) | 1.00229e7 | 0.323379 | ||||||||
\(993\) | 3.06927e7 | 0.987785 | ||||||||
\(994\) | 1.89854e6 | 0.0609471 | ||||||||
\(995\) | 6.86791e6 | 0.219921 | ||||||||
\(996\) | 4.05089e6 | 0.129390 | ||||||||
\(997\) | −2.64620e6 | −0.0843111 | −0.0421555 | − | 0.999111i | \(-0.513423\pi\) | ||||
−0.0421555 | + | 0.999111i | \(0.513423\pi\) | |||||||
\(998\) | −2.56255e7 | −0.814415 | ||||||||
\(999\) | 1.68974e7 | 0.535680 |
(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 | 230.6.a.f.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.f.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial |