Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 152x^{5} + 358x^{4} + 5771x^{3} - 13444x^{2} - 51316x + 92576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.33680\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.33680 | −0.943423 | −0.471711 | − | 0.881753i | \(-0.656364\pi\) | ||||
−0.471711 | + | 0.881753i | \(0.656364\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −3.51852 | −0.109954 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 48.0312 | 0.544685 | ||||||||
\(7\) | −73.9998 | −0.570802 | −0.285401 | − | 0.958408i | \(-0.592127\pi\) | ||||
−0.285401 | + | 0.958408i | \(0.592127\pi\) | |||||||
\(8\) | 189.555 | 1.04716 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 31.6667 | 0.0634819 | ||||||||
\(13\) | 66.6080 | 0.109312 | 0.0546560 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546560 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(14\) | 394.923 | 0.538508 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −899.027 | −0.877956 | ||||||||
\(17\) | 808.876 | 0.678828 | 0.339414 | − | 0.940637i | \(-0.389771\pi\) | ||||
0.339414 | + | 0.940637i | \(0.389771\pi\) | |||||||
\(18\) | −432.281 | −0.314474 | ||||||||
\(19\) | −900.233 | −0.572099 | −0.286049 | − | 0.958215i | \(-0.592342\pi\) | ||||
−0.286049 | + | 0.958215i | \(0.592342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 665.998 | 0.329553 | ||||||||
\(22\) | −645.753 | −0.284453 | ||||||||
\(23\) | −3372.25 | −1.32923 | −0.664615 | − | 0.747186i | \(-0.731405\pi\) | ||||
−0.664615 | + | 0.747186i | \(0.731405\pi\) | |||||||
\(24\) | −1706.00 | −0.604576 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −355.474 | −0.103127 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 260.370 | 0.0627619 | ||||||||
\(29\) | −5030.88 | −1.11083 | −0.555417 | − | 0.831572i | \(-0.687441\pi\) | ||||
−0.555417 | + | 0.831572i | \(0.687441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2599.04 | 0.485745 | 0.242872 | − | 0.970058i | \(-0.421910\pi\) | ||||
0.242872 | + | 0.970058i | \(0.421910\pi\) | |||||||
\(32\) | −1267.84 | −0.218872 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −4316.81 | −0.640422 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −285.000 | −0.0366513 | ||||||||
\(37\) | 6950.65 | 0.834682 | 0.417341 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417341 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(38\) | 4804.37 | 0.539731 | ||||||||
\(39\) | −599.472 | −0.0631113 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 197.788 | 0.0183756 | 0.00918778 | − | 0.999958i | \(-0.497075\pi\) | ||||
0.00918778 | + | 0.999958i | \(0.497075\pi\) | |||||||
\(42\) | −3554.30 | −0.310908 | ||||||||
\(43\) | 13340.3 | 1.10025 | 0.550127 | − | 0.835081i | \(-0.314579\pi\) | ||||
0.550127 | + | 0.835081i | \(0.314579\pi\) | |||||||
\(44\) | −425.741 | −0.0331523 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17997.0 | 1.25403 | ||||||||
\(47\) | 3822.58 | 0.252413 | 0.126207 | − | 0.992004i | \(-0.459720\pi\) | ||||
0.126207 | + | 0.992004i | \(0.459720\pi\) | |||||||
\(48\) | 8091.25 | 0.506888 | ||||||||
\(49\) | −11331.0 | −0.674185 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7279.88 | −0.391921 | ||||||||
\(52\) | −234.362 | −0.0120193 | ||||||||
\(53\) | −4858.62 | −0.237588 | −0.118794 | − | 0.992919i | \(-0.537903\pi\) | ||||
−0.118794 | + | 0.992919i | \(0.537903\pi\) | |||||||
\(54\) | 3890.53 | 0.181562 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14027.1 | −0.597719 | ||||||||
\(57\) | 8102.10 | 0.330301 | ||||||||
\(58\) | 26848.8 | 1.04799 | ||||||||
\(59\) | −6936.31 | −0.259417 | −0.129708 | − | 0.991552i | \(-0.541404\pi\) | ||||
−0.129708 | + | 0.991552i | \(0.541404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10538.4 | −0.362619 | −0.181309 | − | 0.983426i | \(-0.558033\pi\) | ||||
−0.181309 | + | 0.983426i | \(0.558033\pi\) | |||||||
\(62\) | −13870.5 | −0.458263 | ||||||||
\(63\) | −5993.99 | −0.190267 | ||||||||
\(64\) | 35535.1 | 1.08444 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5811.78 | 0.164229 | ||||||||
\(67\) | 30768.1 | 0.837362 | 0.418681 | − | 0.908133i | \(-0.362493\pi\) | ||||
0.418681 | + | 0.908133i | \(0.362493\pi\) | |||||||
\(68\) | −2846.05 | −0.0746397 | ||||||||
\(69\) | 30350.3 | 0.767432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13974.9 | 0.329006 | 0.164503 | − | 0.986377i | \(-0.447398\pi\) | ||||
0.164503 | + | 0.986377i | \(0.447398\pi\) | |||||||
\(72\) | 15354.0 | 0.349052 | ||||||||
\(73\) | 13733.4 | 0.301627 | 0.150813 | − | 0.988562i | \(-0.451811\pi\) | ||||
0.150813 | + | 0.988562i | \(0.451811\pi\) | |||||||
\(74\) | −37094.3 | −0.787458 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3167.49 | 0.0629045 | ||||||||
\(77\) | −8953.98 | −0.172103 | ||||||||
\(78\) | 3199.26 | 0.0595407 | ||||||||
\(79\) | 28954.9 | 0.521980 | 0.260990 | − | 0.965342i | \(-0.415951\pi\) | ||||
0.260990 | + | 0.965342i | \(0.415951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −1055.56 | −0.0173359 | ||||||||
\(83\) | 103828. | 1.65432 | 0.827161 | − | 0.561965i | \(-0.189954\pi\) | ||||
0.827161 | + | 0.561965i | \(0.189954\pi\) | |||||||
\(84\) | −2343.33 | −0.0362356 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −71194.4 | −1.03801 | ||||||||
\(87\) | 45277.9 | 0.641340 | ||||||||
\(88\) | 22936.2 | 0.315729 | ||||||||
\(89\) | −63069.9 | −0.844010 | −0.422005 | − | 0.906594i | \(-0.638673\pi\) | ||||
−0.422005 | + | 0.906594i | \(0.638673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4928.98 | −0.0623955 | ||||||||
\(92\) | 11865.3 | 0.146154 | ||||||||
\(93\) | −23391.3 | −0.280445 | ||||||||
\(94\) | −20400.4 | −0.238132 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 11410.6 | 0.126366 | ||||||||
\(97\) | 62964.9 | 0.679468 | 0.339734 | − | 0.940522i | \(-0.389663\pi\) | ||||
0.339734 | + | 0.940522i | \(0.389663\pi\) | |||||||
\(98\) | 60471.5 | 0.636041 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 32233.2 | 0.314413 | 0.157206 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157206 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(102\) | 38851.3 | 0.369748 | ||||||||
\(103\) | −45990.8 | −0.427148 | −0.213574 | − | 0.976927i | \(-0.568510\pi\) | ||||
−0.213574 | + | 0.976927i | \(0.568510\pi\) | |||||||
\(104\) | 12625.9 | 0.114467 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25929.5 | 0.224145 | ||||||||
\(107\) | −40102.2 | −0.338617 | −0.169309 | − | 0.985563i | \(-0.554153\pi\) | ||||
−0.169309 | + | 0.985563i | \(0.554153\pi\) | |||||||
\(108\) | 2565.00 | 0.0211606 | ||||||||
\(109\) | −44635.8 | −0.359847 | −0.179923 | − | 0.983681i | \(-0.557585\pi\) | ||||
−0.179923 | + | 0.983681i | \(0.557585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −62555.8 | −0.481904 | ||||||||
\(112\) | 66527.9 | 0.501139 | ||||||||
\(113\) | 251257. | 1.85106 | 0.925532 | − | 0.378669i | \(-0.123618\pi\) | ||||
0.925532 | + | 0.378669i | \(0.123618\pi\) | |||||||
\(114\) | −43239.3 | −0.311614 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 17701.3 | 0.122140 | ||||||||
\(117\) | 5395.25 | 0.0364373 | ||||||||
\(118\) | 37017.7 | 0.244740 | ||||||||
\(119\) | −59856.7 | −0.387476 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 56241.4 | 0.342103 | ||||||||
\(123\) | −1780.09 | −0.0106091 | ||||||||
\(124\) | −9144.77 | −0.0534095 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 31988.7 | 0.179503 | ||||||||
\(127\) | −214460. | −1.17988 | −0.589939 | − | 0.807448i | \(-0.700848\pi\) | ||||
−0.589939 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(128\) | −149073. | −0.804218 | ||||||||
\(129\) | −120062. | −0.635232 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 157394. | 0.801325 | 0.400662 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400662 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(132\) | 3831.67 | 0.0191405 | ||||||||
\(133\) | 66617.1 | 0.326555 | ||||||||
\(134\) | −164203. | −0.789986 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 153327. | 0.710838 | ||||||||
\(137\) | 385559. | 1.75505 | 0.877525 | − | 0.479532i | \(-0.159193\pi\) | ||||
0.877525 | + | 0.479532i | \(0.159193\pi\) | |||||||
\(138\) | −161973. | −0.724012 | ||||||||
\(139\) | −181540. | −0.796959 | −0.398480 | − | 0.917177i | \(-0.630462\pi\) | ||||
−0.398480 | + | 0.917177i | \(0.630462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34403.2 | −0.145731 | ||||||||
\(142\) | −74581.5 | −0.310392 | ||||||||
\(143\) | 8059.57 | 0.0329588 | ||||||||
\(144\) | −72821.2 | −0.292652 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −73292.3 | −0.284561 | ||||||||
\(147\) | 101979. | 0.389241 | ||||||||
\(148\) | −24456.0 | −0.0917765 | ||||||||
\(149\) | −189099. | −0.697790 | −0.348895 | − | 0.937162i | \(-0.613443\pi\) | ||||
−0.348895 | + | 0.937162i | \(0.613443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 182551. | 0.651541 | 0.325770 | − | 0.945449i | \(-0.394376\pi\) | ||||
0.325770 | + | 0.945449i | \(0.394376\pi\) | |||||||
\(152\) | −170644. | −0.599076 | ||||||||
\(153\) | 65519.0 | 0.226276 | ||||||||
\(154\) | 47785.6 | 0.162366 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2109.26 | 0.00693933 | ||||||||
\(157\) | 299449. | 0.969559 | 0.484779 | − | 0.874636i | \(-0.338900\pi\) | ||||
0.484779 | + | 0.874636i | \(0.338900\pi\) | |||||||
\(158\) | −154526. | −0.492447 | ||||||||
\(159\) | 43727.6 | 0.137171 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 249546. | 0.758728 | ||||||||
\(162\) | −35014.8 | −0.104825 | ||||||||
\(163\) | 105810. | 0.311930 | 0.155965 | − | 0.987763i | \(-0.450151\pi\) | ||||
0.155965 | + | 0.987763i | \(0.450151\pi\) | |||||||
\(164\) | −695.922 | −0.00202046 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −554111. | −1.56072 | ||||||||
\(167\) | −44979.5 | −0.124802 | −0.0624012 | − | 0.998051i | \(-0.519876\pi\) | ||||
−0.0624012 | + | 0.998051i | \(0.519876\pi\) | |||||||
\(168\) | 126244. | 0.345093 | ||||||||
\(169\) | −366856. | −0.988051 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −72918.9 | −0.190700 | ||||||||
\(172\) | −46938.0 | −0.120977 | ||||||||
\(173\) | 445425. | 1.13151 | 0.565756 | − | 0.824573i | \(-0.308585\pi\) | ||||
0.565756 | + | 0.824573i | \(0.308585\pi\) | |||||||
\(174\) | −241639. | −0.605055 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −108782. | −0.264714 | ||||||||
\(177\) | 62426.8 | 0.149774 | ||||||||
\(178\) | 336592. | 0.796258 | ||||||||
\(179\) | −552254. | −1.28827 | −0.644134 | − | 0.764913i | \(-0.722782\pi\) | ||||
−0.644134 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 52408.5 | 0.118906 | 0.0594532 | − | 0.998231i | \(-0.481064\pi\) | ||||
0.0594532 | + | 0.998231i | \(0.481064\pi\) | |||||||
\(182\) | 26305.0 | 0.0588654 | ||||||||
\(183\) | 94845.6 | 0.209358 | ||||||||
\(184\) | −639228. | −1.39191 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 124835. | 0.264578 | ||||||||
\(187\) | 97874.0 | 0.204674 | ||||||||
\(188\) | −13449.8 | −0.0277538 | ||||||||
\(189\) | 53945.9 | 0.109851 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 135687. | 0.269125 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(192\) | −319816. | −0.626105 | ||||||||
\(193\) | 561304. | 1.08469 | 0.542344 | − | 0.840157i | \(-0.317537\pi\) | ||||
0.542344 | + | 0.840157i | \(0.317537\pi\) | |||||||
\(194\) | −336031. | −0.641026 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 39868.5 | 0.0741292 | ||||||||
\(197\) | −774322. | −1.42153 | −0.710765 | − | 0.703429i | \(-0.751651\pi\) | ||||
−0.710765 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(198\) | −52306.0 | −0.0948175 | ||||||||
\(199\) | −494275. | −0.884780 | −0.442390 | − | 0.896823i | \(-0.645869\pi\) | ||||
−0.442390 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −276913. | −0.483451 | ||||||||
\(202\) | −172022. | −0.296624 | ||||||||
\(203\) | 372284. | 0.634066 | ||||||||
\(204\) | 25614.4 | 0.0430933 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 245444. | 0.402981 | ||||||||
\(207\) | −273152. | −0.443077 | ||||||||
\(208\) | −59882.4 | −0.0959712 | ||||||||
\(209\) | −108928. | −0.172494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −30102.4 | −0.0465474 | −0.0232737 | − | 0.999729i | \(-0.507409\pi\) | ||||
−0.0232737 | + | 0.999729i | \(0.507409\pi\) | |||||||
\(212\) | 17095.2 | 0.0261237 | ||||||||
\(213\) | −125774. | −0.189952 | ||||||||
\(214\) | 214018. | 0.319459 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −138186. | −0.201525 | ||||||||
\(217\) | −192328. | −0.277264 | ||||||||
\(218\) | 238213. | 0.339487 | ||||||||
\(219\) | −123600. | −0.174144 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53877.6 | 0.0742041 | ||||||||
\(222\) | 333848. | 0.454639 | ||||||||
\(223\) | −539464. | −0.726441 | −0.363221 | − | 0.931703i | \(-0.618323\pi\) | ||||
−0.363221 | + | 0.931703i | \(0.618323\pi\) | |||||||
\(224\) | 93820.0 | 0.124932 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.34091e6 | −1.74634 | ||||||||
\(227\) | −972036. | −1.25204 | −0.626019 | − | 0.779808i | \(-0.715317\pi\) | ||||
−0.626019 | + | 0.779808i | \(0.715317\pi\) | |||||||
\(228\) | −28507.4 | −0.0363179 | ||||||||
\(229\) | 172701. | 0.217624 | 0.108812 | − | 0.994062i | \(-0.465295\pi\) | ||||
0.108812 | + | 0.994062i | \(0.465295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 80585.8 | 0.0993639 | ||||||||
\(232\) | −953631. | −1.16322 | ||||||||
\(233\) | −18356.9 | −0.0221519 | −0.0110759 | − | 0.999939i | \(-0.503526\pi\) | ||||
−0.0110759 | + | 0.999939i | \(0.503526\pi\) | |||||||
\(234\) | −28793.4 | −0.0343758 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 24405.6 | 0.0285239 | ||||||||
\(237\) | −260594. | −0.301365 | ||||||||
\(238\) | 319443. | 0.365554 | ||||||||
\(239\) | −50802.6 | −0.0575296 | −0.0287648 | − | 0.999586i | \(-0.509157\pi\) | ||||
−0.0287648 | + | 0.999586i | \(0.509157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 57284.6 | 0.0635324 | 0.0317662 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317662 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(242\) | −78136.1 | −0.0857657 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 37079.6 | 0.0398713 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9500.01 | 0.0100089 | ||||||||
\(247\) | −59962.7 | −0.0625373 | ||||||||
\(248\) | 492661. | 0.508650 | ||||||||
\(249\) | −934454. | −0.955123 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 275746. | 0.276265 | 0.138132 | − | 0.990414i | \(-0.455890\pi\) | ||||
0.138132 | + | 0.990414i | \(0.455890\pi\) | |||||||
\(252\) | 21090.0 | 0.0209206 | ||||||||
\(253\) | −408042. | −0.400778 | ||||||||
\(254\) | 1.14453e6 | 1.11312 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −341550. | −0.325727 | ||||||||
\(257\) | 55323.5 | 0.0522489 | 0.0261244 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261244 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(258\) | 640749. | 0.599293 | ||||||||
\(259\) | −514347. | −0.476438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −407501. | −0.370278 | ||||||||
\(262\) | −839978. | −0.755988 | ||||||||
\(263\) | −1.50652e6 | −1.34303 | −0.671515 | − | 0.740991i | \(-0.734356\pi\) | ||||
−0.671515 | + | 0.740991i | \(0.734356\pi\) | |||||||
\(264\) | −206426. | −0.182286 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −355522. | −0.308080 | ||||||||
\(267\) | 567630. | 0.487289 | ||||||||
\(268\) | −108258. | −0.0920711 | ||||||||
\(269\) | 300252. | 0.252991 | 0.126496 | − | 0.991967i | \(-0.459627\pi\) | ||||
0.126496 | + | 0.991967i | \(0.459627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.88992e6 | −1.56322 | −0.781608 | − | 0.623770i | \(-0.785600\pi\) | ||||
−0.781608 | + | 0.623770i | \(0.785600\pi\) | |||||||
\(272\) | −727202. | −0.595981 | ||||||||
\(273\) | 44360.8 | 0.0360241 | ||||||||
\(274\) | −2.05765e6 | −1.65575 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −106788. | −0.0843821 | ||||||||
\(277\) | −493383. | −0.386354 | −0.193177 | − | 0.981164i | \(-0.561879\pi\) | ||||
−0.193177 | + | 0.981164i | \(0.561879\pi\) | |||||||
\(278\) | 968845. | 0.751869 | ||||||||
\(279\) | 210522. | 0.161915 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.39118e6 | 1.05104 | 0.525518 | − | 0.850783i | \(-0.323872\pi\) | ||||
0.525518 | + | 0.850783i | \(0.323872\pi\) | |||||||
\(282\) | 183603. | 0.137486 | ||||||||
\(283\) | −1.92592e6 | −1.42946 | −0.714730 | − | 0.699400i | \(-0.753451\pi\) | ||||
−0.714730 | + | 0.699400i | \(0.753451\pi\) | |||||||
\(284\) | −49171.1 | −0.0361755 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −43012.3 | −0.0310941 | ||||||||
\(287\) | −14636.3 | −0.0104888 | ||||||||
\(288\) | −102695. | −0.0729572 | ||||||||
\(289\) | −765577. | −0.539193 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −566684. | −0.392291 | ||||||||
\(292\) | −48321.1 | −0.0331650 | ||||||||
\(293\) | 1.53666e6 | 1.04571 | 0.522853 | − | 0.852423i | \(-0.324868\pi\) | ||||
0.522853 | + | 0.852423i | \(0.324868\pi\) | |||||||
\(294\) | −544243. | −0.367219 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.31753e6 | 0.874042 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 1.00919e6 | 0.658311 | ||||||||
\(299\) | −224619. | −0.145301 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −987177. | −0.628028 | ||||||||
\(302\) | −974238. | −0.614678 | ||||||||
\(303\) | −290099. | −0.181526 | ||||||||
\(304\) | 809334. | 0.502278 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −349662. | −0.213474 | ||||||||
\(307\) | −2.17758e6 | −1.31865 | −0.659324 | − | 0.751859i | \(-0.729158\pi\) | ||||
−0.659324 | + | 0.751859i | \(0.729158\pi\) | |||||||
\(308\) | 31504.8 | 0.0189234 | ||||||||
\(309\) | 413917. | 0.246614 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 624920. | 0.366373 | 0.183186 | − | 0.983078i | \(-0.441359\pi\) | ||||
0.183186 | + | 0.983078i | \(0.441359\pi\) | |||||||
\(312\) | −113633. | −0.0660874 | ||||||||
\(313\) | −757413. | −0.436990 | −0.218495 | − | 0.975838i | \(-0.570115\pi\) | ||||
−0.218495 | + | 0.975838i | \(0.570115\pi\) | |||||||
\(314\) | −1.59810e6 | −0.914704 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −101878. | −0.0573937 | ||||||||
\(317\) | −3.10220e6 | −1.73389 | −0.866944 | − | 0.498406i | \(-0.833919\pi\) | ||||
−0.866944 | + | 0.498406i | \(0.833919\pi\) | |||||||
\(318\) | −233366. | −0.129410 | ||||||||
\(319\) | −608737. | −0.334929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 360920. | 0.195501 | ||||||||
\(322\) | −1.33178e6 | −0.715801 | ||||||||
\(323\) | −728177. | −0.388357 | ||||||||
\(324\) | −23085.0 | −0.0122171 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −564687. | −0.294282 | ||||||||
\(327\) | 401723. | 0.207758 | ||||||||
\(328\) | 37491.8 | 0.0192421 | ||||||||
\(329\) | −282870. | −0.144078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59132e6 | −0.798339 | −0.399169 | − | 0.916877i | \(-0.630701\pi\) | ||||
−0.399169 | + | 0.916877i | \(0.630701\pi\) | |||||||
\(332\) | −365322. | −0.181899 | ||||||||
\(333\) | 563003. | 0.278227 | ||||||||
\(334\) | 240047. | 0.117741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −598751. | −0.289333 | ||||||||
\(337\) | 2.25270e6 | 1.08051 | 0.540254 | − | 0.841502i | \(-0.318328\pi\) | ||||
0.540254 | + | 0.841502i | \(0.318328\pi\) | |||||||
\(338\) | 1.95784e6 | 0.932150 | ||||||||
\(339\) | −2.26131e6 | −1.06871 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 314483. | 0.146458 | ||||||||
\(342\) | 389154. | 0.179910 | ||||||||
\(343\) | 2.08221e6 | 0.955628 | ||||||||
\(344\) | 2.52872e6 | 1.15214 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.37714e6 | −1.06749 | ||||||||
\(347\) | −171210. | −0.0763318 | −0.0381659 | − | 0.999271i | \(-0.512152\pi\) | ||||
−0.0381659 | + | 0.999271i | \(0.512152\pi\) | |||||||
\(348\) | −159311. | −0.0705178 | ||||||||
\(349\) | 3.09886e6 | 1.36188 | 0.680940 | − | 0.732339i | \(-0.261571\pi\) | ||||
0.680940 | + | 0.732339i | \(0.261571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −48557.2 | −0.0210371 | ||||||||
\(352\) | −153409. | −0.0659923 | ||||||||
\(353\) | 2.33605e6 | 0.997805 | 0.498903 | − | 0.866658i | \(-0.333737\pi\) | ||||
0.498903 | + | 0.866658i | \(0.333737\pi\) | |||||||
\(354\) | −333159. | −0.141301 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 221913. | 0.0928021 | ||||||||
\(357\) | 538710. | 0.223710 | ||||||||
\(358\) | 2.94727e6 | 1.21538 | ||||||||
\(359\) | 161176. | 0.0660029 | 0.0330015 | − | 0.999455i | \(-0.489493\pi\) | ||||
0.0330015 | + | 0.999455i | \(0.489493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66568e6 | −0.672703 | ||||||||
\(362\) | −279694. | −0.112179 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 17342.7 | 0.00686063 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −506172. | −0.197513 | ||||||||
\(367\) | −2.18840e6 | −0.848129 | −0.424064 | − | 0.905632i | \(-0.639397\pi\) | ||||
−0.424064 | + | 0.905632i | \(0.639397\pi\) | |||||||
\(368\) | 3.03175e6 | 1.16701 | ||||||||
\(369\) | 16020.8 | 0.00612519 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 359537. | 0.135615 | ||||||||
\(372\) | 82302.9 | 0.0308360 | ||||||||
\(373\) | −3.63629e6 | −1.35328 | −0.676639 | − | 0.736315i | \(-0.736564\pi\) | ||||
−0.676639 | + | 0.736315i | \(0.736564\pi\) | |||||||
\(374\) | −522334. | −0.193094 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 724591. | 0.264316 | ||||||||
\(377\) | −335097. | −0.121428 | ||||||||
\(378\) | −287899. | −0.103636 | ||||||||
\(379\) | 1.67725e6 | 0.599791 | 0.299895 | − | 0.953972i | \(-0.403048\pi\) | ||||
0.299895 | + | 0.953972i | \(0.403048\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.93014e6 | 0.681203 | ||||||||
\(382\) | −724134. | −0.253899 | ||||||||
\(383\) | 2.08391e6 | 0.725908 | 0.362954 | − | 0.931807i | \(-0.381768\pi\) | ||||
0.362954 | + | 0.931807i | \(0.381768\pi\) | |||||||
\(384\) | 1.34166e6 | 0.464315 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.99557e6 | −1.02332 | ||||||||
\(387\) | 1.08056e6 | 0.366752 | ||||||||
\(388\) | −221543. | −0.0747101 | ||||||||
\(389\) | −5.80280e6 | −1.94430 | −0.972151 | − | 0.234356i | \(-0.924702\pi\) | ||||
−0.972151 | + | 0.234356i | \(0.924702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.72773e6 | −0.902319 | ||||||||
\(392\) | −2.14786e6 | −0.705976 | ||||||||
\(393\) | −1.41654e6 | −0.462645 | ||||||||
\(394\) | 4.13241e6 | 1.34110 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −34485.0 | −0.0110508 | ||||||||
\(397\) | −1.25839e6 | −0.400718 | −0.200359 | − | 0.979723i | \(-0.564211\pi\) | ||||
−0.200359 | + | 0.979723i | \(0.564211\pi\) | |||||||
\(398\) | 2.63785e6 | 0.834722 | ||||||||
\(399\) | −599554. | −0.188537 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.29837e6 | −0.403216 | −0.201608 | − | 0.979466i | \(-0.564617\pi\) | ||||
−0.201608 | + | 0.979466i | \(0.564617\pi\) | |||||||
\(402\) | 1.47783e6 | 0.456099 | ||||||||
\(403\) | 173117. | 0.0530977 | ||||||||
\(404\) | −113413. | −0.0345709 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.98681e6 | −0.598193 | ||||||||
\(407\) | 841029. | 0.251666 | ||||||||
\(408\) | −1.37994e6 | −0.410403 | ||||||||
\(409\) | −4.45805e6 | −1.31776 | −0.658880 | − | 0.752248i | \(-0.728970\pi\) | ||||
−0.658880 | + | 0.752248i | \(0.728970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.47003e6 | −1.01328 | ||||||||
\(412\) | 161820. | 0.0469665 | ||||||||
\(413\) | 513286. | 0.148076 | ||||||||
\(414\) | 1.45776e6 | 0.418009 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −84448.3 | −0.0239253 | ||||||||
\(417\) | 1.63386e6 | 0.460125 | ||||||||
\(418\) | 581329. | 0.162735 | ||||||||
\(419\) | 2.33339e6 | 0.649312 | 0.324656 | − | 0.945832i | \(-0.394752\pi\) | ||||
0.324656 | + | 0.945832i | \(0.394752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.04741e6 | 1.11294 | 0.556470 | − | 0.830868i | \(-0.312156\pi\) | ||||
0.556470 | + | 0.830868i | \(0.312156\pi\) | |||||||
\(422\) | 160651. | 0.0439139 | ||||||||
\(423\) | 309629. | 0.0841377 | ||||||||
\(424\) | −920978. | −0.248791 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 671234. | 0.179205 | ||||||||
\(427\) | 779840. | 0.206983 | ||||||||
\(428\) | 141101. | 0.0372322 | ||||||||
\(429\) | −72536.1 | −0.0190288 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.38060e6 | 0.617295 | 0.308647 | − | 0.951177i | \(-0.400124\pi\) | ||||
0.308647 | + | 0.951177i | \(0.400124\pi\) | |||||||
\(432\) | 655391. | 0.168963 | ||||||||
\(433\) | −5.02364e6 | −1.28765 | −0.643826 | − | 0.765172i | \(-0.722654\pi\) | ||||
−0.643826 | + | 0.765172i | \(0.722654\pi\) | |||||||
\(434\) | 1.02642e6 | 0.261577 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 157052. | 0.0395665 | ||||||||
\(437\) | 3.03581e6 | 0.760451 | ||||||||
\(438\) | 659630. | 0.164292 | ||||||||
\(439\) | −2.27414e6 | −0.563192 | −0.281596 | − | 0.959533i | \(-0.590864\pi\) | ||||
−0.281596 | + | 0.959533i | \(0.590864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −917813. | −0.224728 | ||||||||
\(442\) | −287534. | −0.0700058 | ||||||||
\(443\) | 93691.6 | 0.0226825 | 0.0113413 | − | 0.999936i | \(-0.496390\pi\) | ||||
0.0113413 | + | 0.999936i | \(0.496390\pi\) | |||||||
\(444\) | 220104. | 0.0529872 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.87901e6 | 0.685341 | ||||||||
\(447\) | 1.70190e6 | 0.402869 | ||||||||
\(448\) | −2.62959e6 | −0.619003 | ||||||||
\(449\) | −5.96118e6 | −1.39546 | −0.697728 | − | 0.716363i | \(-0.745806\pi\) | ||||
−0.697728 | + | 0.716363i | \(0.745806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23932.4 | 0.00554044 | ||||||||
\(452\) | −884052. | −0.203532 | ||||||||
\(453\) | −1.64296e6 | −0.376167 | ||||||||
\(454\) | 5.18756e6 | 1.18120 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.53580e6 | 0.345877 | ||||||||
\(457\) | −878215. | −0.196703 | −0.0983514 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983514 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(458\) | −921673. | −0.205311 | ||||||||
\(459\) | −589671. | −0.130640 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2960.95 | −0.000648901 0 | −0.000324450 | − | 1.00000i | \(-0.500103\pi\) | ||||
−0.000324450 | 1.00000i | \(0.500103\pi\) | ||||||||
\(462\) | −430071. | −0.0937421 | ||||||||
\(463\) | 1.73957e6 | 0.377129 | 0.188564 | − | 0.982061i | \(-0.439617\pi\) | ||||
0.188564 | + | 0.982061i | \(0.439617\pi\) | |||||||
\(464\) | 4.52290e6 | 0.975264 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 97967.3 | 0.0208986 | ||||||||
\(467\) | −236495. | −0.0501800 | −0.0250900 | − | 0.999685i | \(-0.507987\pi\) | ||||
−0.0250900 | + | 0.999685i | \(0.507987\pi\) | |||||||
\(468\) | −18983.3 | −0.00400643 | ||||||||
\(469\) | −2.27683e6 | −0.477968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.69504e6 | −0.559775 | ||||||||
\(472\) | −1.31481e6 | −0.271650 | ||||||||
\(473\) | 1.61417e6 | 0.331739 | ||||||||
\(474\) | 1.39074e6 | 0.284315 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 210607. | 0.0426045 | ||||||||
\(477\) | −393549. | −0.0791958 | ||||||||
\(478\) | 271124. | 0.0542747 | ||||||||
\(479\) | −1.23533e6 | −0.246006 | −0.123003 | − | 0.992406i | \(-0.539252\pi\) | ||||
−0.123003 | + | 0.992406i | \(0.539252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 462969. | 0.0912408 | ||||||||
\(482\) | −305717. | −0.0599379 | ||||||||
\(483\) | −2.24591e6 | −0.438052 | ||||||||
\(484\) | −51514.7 | −0.00999580 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 315133. | 0.0605206 | ||||||||
\(487\) | 4.77244e6 | 0.911839 | 0.455920 | − | 0.890021i | \(-0.349310\pi\) | ||||
0.455920 | + | 0.890021i | \(0.349310\pi\) | |||||||
\(488\) | −1.99761e6 | −0.379718 | ||||||||
\(489\) | −952289. | −0.180093 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.12682e6 | 1.70850 | 0.854251 | − | 0.519860i | \(-0.174016\pi\) | ||||
0.854251 | + | 0.519860i | \(0.174016\pi\) | |||||||
\(492\) | 6263.30 | 0.00116652 | ||||||||
\(493\) | −4.06936e6 | −0.754065 | ||||||||
\(494\) | 320009. | 0.0589991 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.33660e6 | −0.426463 | ||||||||
\(497\) | −1.03414e6 | −0.187797 | ||||||||
\(498\) | 4.98700e6 | 0.901085 | ||||||||
\(499\) | 8.42908e6 | 1.51541 | 0.757703 | − | 0.652600i | \(-0.226322\pi\) | ||||
0.757703 | + | 0.652600i | \(0.226322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 404815. | 0.0720547 | ||||||||
\(502\) | −1.47160e6 | −0.260634 | ||||||||
\(503\) | −9.13714e6 | −1.61024 | −0.805120 | − | 0.593113i | \(-0.797899\pi\) | ||||
−0.805120 | + | 0.593113i | \(0.797899\pi\) | |||||||
\(504\) | −1.13619e6 | −0.199240 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.17764e6 | 0.378103 | ||||||||
\(507\) | 3.30171e6 | 0.570451 | ||||||||
\(508\) | 754583. | 0.129732 | ||||||||
\(509\) | 3.02787e6 | 0.518015 | 0.259008 | − | 0.965875i | \(-0.416605\pi\) | ||||
0.259008 | + | 0.965875i | \(0.416605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.01627e6 | −0.172169 | ||||||||
\(512\) | 6.59312e6 | 1.11152 | ||||||||
\(513\) | 656270. | 0.110100 | ||||||||
\(514\) | −295251. | −0.0492928 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 422442. | 0.0698462 | ||||||||
\(517\) | 462532. | 0.0761054 | ||||||||
\(518\) | 2.74497e6 | 0.449483 | ||||||||
\(519\) | −4.00882e6 | −0.653278 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.19443e7 | 1.92782 | 0.963912 | − | 0.266221i | \(-0.0857751\pi\) | ||||
0.963912 | + | 0.266221i | \(0.0857751\pi\) | |||||||
\(522\) | 2.17476e6 | 0.349329 | ||||||||
\(523\) | −8.53138e6 | −1.36384 | −0.681922 | − | 0.731425i | \(-0.738856\pi\) | ||||
−0.681922 | + | 0.731425i | \(0.738856\pi\) | |||||||
\(524\) | −553793. | −0.0881087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.04000e6 | 1.26704 | ||||||||
\(527\) | 2.10230e6 | 0.329737 | ||||||||
\(528\) | 979041. | 0.152833 | ||||||||
\(529\) | 4.93574e6 | 0.766854 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −561841. | −0.0864723 | ||||||||
\(532\) | −234394. | −0.0359060 | ||||||||
\(533\) | 13174.3 | 0.00200867 | ||||||||
\(534\) | −3.02933e6 | −0.459720 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.83225e6 | 0.876848 | ||||||||
\(537\) | 4.97029e6 | 0.743782 | ||||||||
\(538\) | −1.60239e6 | −0.238678 | ||||||||
\(539\) | −1.37105e6 | −0.203274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.84250e6 | −0.417548 | −0.208774 | − | 0.977964i | \(-0.566947\pi\) | ||||
−0.208774 | + | 0.977964i | \(0.566947\pi\) | |||||||
\(542\) | 1.00861e7 | 1.47477 | ||||||||
\(543\) | −471677. | −0.0686507 | ||||||||
\(544\) | −1.02553e6 | −0.148576 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −236745. | −0.0339859 | ||||||||
\(547\) | −1.40460e6 | −0.200717 | −0.100358 | − | 0.994951i | \(-0.531999\pi\) | ||||
−0.100358 | + | 0.994951i | \(0.531999\pi\) | |||||||
\(548\) | −1.35660e6 | −0.192974 | ||||||||
\(549\) | −853610. | −0.120873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.52897e6 | 0.635507 | ||||||||
\(552\) | 5.75306e6 | 0.803620 | ||||||||
\(553\) | −2.14265e6 | −0.297947 | ||||||||
\(554\) | 2.63309e6 | 0.364495 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 638754. | 0.0876287 | ||||||||
\(557\) | 4.17495e6 | 0.570182 | 0.285091 | − | 0.958500i | \(-0.407976\pi\) | ||||
0.285091 | + | 0.958500i | \(0.407976\pi\) | |||||||
\(558\) | −1.12351e6 | −0.152754 | ||||||||
\(559\) | 888568. | 0.120271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −880866. | −0.118169 | ||||||||
\(562\) | −7.42445e6 | −0.991570 | ||||||||
\(563\) | −7.54584e6 | −1.00331 | −0.501657 | − | 0.865067i | \(-0.667276\pi\) | ||||
−0.501657 | + | 0.865067i | \(0.667276\pi\) | |||||||
\(564\) | 121049. | 0.0160237 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.02783e7 | 1.34859 | ||||||||
\(567\) | −485513. | −0.0634225 | ||||||||
\(568\) | 2.64903e6 | 0.344521 | ||||||||
\(569\) | 1.62724e6 | 0.210703 | 0.105351 | − | 0.994435i | \(-0.466403\pi\) | ||||
0.105351 | + | 0.994435i | \(0.466403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.56277e6 | 0.328942 | 0.164471 | − | 0.986382i | \(-0.447408\pi\) | ||||
0.164471 | + | 0.986382i | \(0.447408\pi\) | |||||||
\(572\) | −28357.8 | −0.00362395 | ||||||||
\(573\) | −1.22118e6 | −0.155379 | ||||||||
\(574\) | 78111.0 | 0.00989538 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.87834e6 | 0.361482 | ||||||||
\(577\) | 6.16261e6 | 0.770594 | 0.385297 | − | 0.922793i | \(-0.374099\pi\) | ||||
0.385297 | + | 0.922793i | \(0.374099\pi\) | |||||||
\(578\) | 4.08573e6 | 0.508687 | ||||||||
\(579\) | −5.05173e6 | −0.626245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.68327e6 | −0.944290 | ||||||||
\(582\) | 3.02428e6 | 0.370096 | ||||||||
\(583\) | −587893. | −0.0716353 | ||||||||
\(584\) | 2.60323e6 | 0.315850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.20086e6 | −0.986542 | ||||||||
\(587\) | 9.16105e6 | 1.09736 | 0.548681 | − | 0.836032i | \(-0.315130\pi\) | ||||
0.548681 | + | 0.836032i | \(0.315130\pi\) | |||||||
\(588\) | −358816. | −0.0427985 | ||||||||
\(589\) | −2.33974e6 | −0.277894 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.96890e6 | 0.820721 | ||||||||
\(592\) | −6.24882e6 | −0.732814 | ||||||||
\(593\) | 6.23563e6 | 0.728188 | 0.364094 | − | 0.931362i | \(-0.381379\pi\) | ||||
0.364094 | + | 0.931362i | \(0.381379\pi\) | |||||||
\(594\) | 470754. | 0.0547429 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 665351. | 0.0767247 | ||||||||
\(597\) | 4.44847e6 | 0.510828 | ||||||||
\(598\) | 1.19875e6 | 0.137080 | ||||||||
\(599\) | −1.48855e6 | −0.169510 | −0.0847552 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847552 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.40965e6 | −0.385055 | −0.192528 | − | 0.981292i | \(-0.561668\pi\) | ||||
−0.192528 | + | 0.981292i | \(0.561668\pi\) | |||||||
\(602\) | 5.26837e6 | 0.592496 | ||||||||
\(603\) | 2.49221e6 | 0.279121 | ||||||||
\(604\) | −642309. | −0.0716394 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.54820e6 | 0.171256 | ||||||||
\(607\) | −4.05477e6 | −0.446678 | −0.223339 | − | 0.974741i | \(-0.571696\pi\) | ||||
−0.223339 | + | 0.974741i | \(0.571696\pi\) | |||||||
\(608\) | 1.14135e6 | 0.125216 | ||||||||
\(609\) | −3.35056e6 | −0.366078 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 254614. | 0.0275918 | ||||||||
\(612\) | −230530. | −0.0248799 | ||||||||
\(613\) | 1.60665e6 | 0.172691 | 0.0863456 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863456 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(614\) | 1.16213e7 | 1.24404 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.69728e6 | −0.180219 | ||||||||
\(617\) | 1.01598e7 | 1.07441 | 0.537207 | − | 0.843451i | \(-0.319480\pi\) | ||||
0.537207 | + | 0.843451i | \(0.319480\pi\) | |||||||
\(618\) | −2.20900e6 | −0.232661 | ||||||||
\(619\) | 3.04114e6 | 0.319014 | 0.159507 | − | 0.987197i | \(-0.449009\pi\) | ||||
0.159507 | + | 0.987197i | \(0.449009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.45837e6 | 0.255811 | ||||||||
\(622\) | −3.33508e6 | −0.345645 | ||||||||
\(623\) | 4.66717e6 | 0.481763 | ||||||||
\(624\) | 538942. | 0.0554090 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.04216e6 | 0.412267 | ||||||||
\(627\) | 980354. | 0.0995896 | ||||||||
\(628\) | −1.05362e6 | −0.106607 | ||||||||
\(629\) | 5.62221e6 | 0.566605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.07109e6 | −0.107091 | −0.0535455 | − | 0.998565i | \(-0.517052\pi\) | ||||
−0.0535455 | + | 0.998565i | \(0.517052\pi\) | |||||||
\(632\) | 5.48855e6 | 0.546594 | ||||||||
\(633\) | 270922. | 0.0268742 | ||||||||
\(634\) | 1.65558e7 | 1.63579 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −153857. | −0.0150825 | ||||||||
\(637\) | −754737. | −0.0736965 | ||||||||
\(638\) | 3.24871e6 | 0.315980 | ||||||||
\(639\) | 1.13197e6 | 0.109669 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −902752. | −0.0867807 | −0.0433904 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433904 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(642\) | −1.92616e6 | −0.184440 | ||||||||
\(643\) | −1.24048e7 | −1.18321 | −0.591607 | − | 0.806227i | \(-0.701506\pi\) | ||||
−0.591607 | + | 0.806227i | \(0.701506\pi\) | |||||||
\(644\) | −878033. | −0.0834250 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.88614e6 | 0.366384 | ||||||||
\(647\) | −1.32160e7 | −1.24119 | −0.620594 | − | 0.784132i | \(-0.713109\pi\) | ||||
−0.620594 | + | 0.784132i | \(0.713109\pi\) | |||||||
\(648\) | 1.24367e6 | 0.116351 | ||||||||
\(649\) | −839293. | −0.0782172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.73095e6 | 0.160079 | ||||||||
\(652\) | −372294. | −0.0342979 | ||||||||
\(653\) | −1.61119e6 | −0.147864 | −0.0739321 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739321 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(654\) | −2.14391e6 | −0.196003 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −177817. | −0.0161329 | ||||||||
\(657\) | 1.11240e6 | 0.100542 | ||||||||
\(658\) | 1.50962e6 | 0.135926 | ||||||||
\(659\) | 2.72261e6 | 0.244215 | 0.122108 | − | 0.992517i | \(-0.461035\pi\) | ||||
0.122108 | + | 0.992517i | \(0.461035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.62010e6 | −0.589333 | −0.294666 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294666 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(662\) | 8.49256e6 | 0.753171 | ||||||||
\(663\) | −484898. | −0.0428417 | ||||||||
\(664\) | 1.96812e7 | 1.73233 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.00463e6 | −0.262486 | ||||||||
\(667\) | 1.69654e7 | 1.47655 | ||||||||
\(668\) | 158261. | 0.0137225 | ||||||||
\(669\) | 4.85518e6 | 0.419411 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.27515e6 | −0.109334 | ||||||||
\(672\) | −844380. | −0.0721298 | ||||||||
\(673\) | −4.49731e6 | −0.382750 | −0.191375 | − | 0.981517i | \(-0.561295\pi\) | ||||
−0.191375 | + | 0.981517i | \(0.561295\pi\) | |||||||
\(674\) | −1.20222e7 | −1.01938 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.29079e6 | 0.108640 | ||||||||
\(677\) | −1.05097e6 | −0.0881288 | −0.0440644 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440644 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(678\) | 1.20682e7 | 1.00825 | ||||||||
\(679\) | −4.65939e6 | −0.387842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.74832e6 | 0.722865 | ||||||||
\(682\) | −1.67834e6 | −0.138171 | ||||||||
\(683\) | −158619. | −0.0130108 | −0.00650540 | − | 0.999979i | \(-0.502071\pi\) | ||||
−0.00650540 | + | 0.999979i | \(0.502071\pi\) | |||||||
\(684\) | 256567. | 0.0209682 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.11123e7 | −0.901561 | ||||||||
\(687\) | −1.55431e6 | −0.125645 | ||||||||
\(688\) | −1.19933e7 | −0.965976 | ||||||||
\(689\) | −323623. | −0.0259712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.14939e7 | −0.915741 | −0.457870 | − | 0.889019i | \(-0.651388\pi\) | ||||
−0.457870 | + | 0.889019i | \(0.651388\pi\) | |||||||
\(692\) | −1.56724e6 | −0.124414 | ||||||||
\(693\) | −725272. | −0.0573678 | ||||||||
\(694\) | 913714. | 0.0720131 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.58268e6 | 0.671583 | ||||||||
\(697\) | 159986. | 0.0124738 | ||||||||
\(698\) | −1.65380e7 | −1.28483 | ||||||||
\(699\) | 165212. | 0.0127894 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.15908e7 | −0.890879 | −0.445440 | − | 0.895312i | \(-0.646953\pi\) | ||||
−0.445440 | + | 0.895312i | \(0.646953\pi\) | |||||||
\(702\) | 259140. | 0.0198469 | ||||||||
\(703\) | −6.25721e6 | −0.477521 | ||||||||
\(704\) | 4.29975e6 | 0.326972 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.24671e7 | −0.941352 | ||||||||
\(707\) | −2.38525e6 | −0.179467 | ||||||||
\(708\) | −219650. | −0.0164683 | ||||||||
\(709\) | 8.43220e6 | 0.629978 | 0.314989 | − | 0.949095i | \(-0.397999\pi\) | ||||
0.314989 | + | 0.949095i | \(0.397999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34534e6 | 0.173993 | ||||||||
\(712\) | −1.19552e7 | −0.883809 | ||||||||
\(713\) | −8.76461e6 | −0.645667 | ||||||||
\(714\) | −2.87499e6 | −0.211053 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.94312e6 | 0.141650 | ||||||||
\(717\) | 457223. | 0.0332147 | ||||||||
\(718\) | −860163. | −0.0622687 | ||||||||
\(719\) | 2.06959e6 | 0.149301 | 0.0746505 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746505 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.40331e6 | 0.243817 | ||||||||
\(722\) | 8.88940e6 | 0.634643 | ||||||||
\(723\) | −515562. | −0.0366805 | ||||||||
\(724\) | −184401. | −0.0130742 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 703225. | 0.0495168 | ||||||||
\(727\) | −1.69013e7 | −1.18600 | −0.593001 | − | 0.805202i | \(-0.702057\pi\) | ||||
−0.593001 | + | 0.805202i | \(0.702057\pi\) | |||||||
\(728\) | −934315. | −0.0653378 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.07906e7 | 0.746884 | ||||||||
\(732\) | −333716. | −0.0230197 | ||||||||
\(733\) | −9.45646e6 | −0.650083 | −0.325041 | − | 0.945700i | \(-0.605378\pi\) | ||||
−0.325041 | + | 0.945700i | \(0.605378\pi\) | |||||||
\(734\) | 1.16791e7 | 0.800144 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.27548e6 | 0.290931 | ||||||||
\(737\) | 3.72294e6 | 0.252474 | ||||||||
\(738\) | −85500.1 | −0.00577864 | ||||||||
\(739\) | 1.41110e7 | 0.950486 | 0.475243 | − | 0.879855i | \(-0.342360\pi\) | ||||
0.475243 | + | 0.879855i | \(0.342360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 539665. | 0.0361059 | ||||||||
\(742\) | −1.91878e6 | −0.127943 | ||||||||
\(743\) | −3.86361e6 | −0.256757 | −0.128378 | − | 0.991725i | \(-0.540977\pi\) | ||||
−0.128378 | + | 0.991725i | \(0.540977\pi\) | |||||||
\(744\) | −4.43395e6 | −0.293669 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.94062e7 | 1.27671 | ||||||||
\(747\) | 8.41008e6 | 0.551441 | ||||||||
\(748\) | −344372. | −0.0225047 | ||||||||
\(749\) | 2.96756e6 | 0.193283 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.68914e6 | 0.368084 | 0.184042 | − | 0.982918i | \(-0.441082\pi\) | ||||
0.184042 | + | 0.982918i | \(0.441082\pi\) | |||||||
\(752\) | −3.43660e6 | −0.221608 | ||||||||
\(753\) | −2.48172e6 | −0.159502 | ||||||||
\(754\) | 1.78835e6 | 0.114557 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −189810. | −0.0120785 | ||||||||
\(757\) | −2.31729e7 | −1.46974 | −0.734870 | − | 0.678208i | \(-0.762757\pi\) | ||||
−0.734870 | + | 0.678208i | \(0.762757\pi\) | |||||||
\(758\) | −8.95116e6 | −0.565856 | ||||||||
\(759\) | 3.67238e6 | 0.231389 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.16856e7 | −0.731455 | −0.365728 | − | 0.930722i | \(-0.619180\pi\) | ||||
−0.365728 | + | 0.930722i | \(0.619180\pi\) | |||||||
\(762\) | −1.03008e7 | −0.642662 | ||||||||
\(763\) | 3.30304e6 | 0.205401 | ||||||||
\(764\) | −477417. | −0.0295913 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.11214e7 | −0.684838 | ||||||||
\(767\) | −462014. | −0.0283574 | ||||||||
\(768\) | 3.07395e6 | 0.188059 | ||||||||
\(769\) | 7.02112e6 | 0.428145 | 0.214072 | − | 0.976818i | \(-0.431327\pi\) | ||||
0.214072 | + | 0.976818i | \(0.431327\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −497912. | −0.0301659 | ||||||||
\(772\) | −1.97496e6 | −0.119266 | ||||||||
\(773\) | −4.45003e6 | −0.267864 | −0.133932 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133932 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(774\) | −5.76674e6 | −0.346002 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.19353e7 | 0.711509 | ||||||||
\(777\) | 4.62912e6 | 0.275072 | ||||||||
\(778\) | 3.09684e7 | 1.83430 | ||||||||
\(779\) | −178056. | −0.0105126 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.69097e6 | 0.0991991 | ||||||||
\(782\) | 1.45574e7 | 0.851268 | ||||||||
\(783\) | 3.66751e6 | 0.213780 | ||||||||
\(784\) | 1.01869e7 | 0.591905 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.55980e6 | 0.436470 | ||||||||
\(787\) | −1.96811e7 | −1.13269 | −0.566347 | − | 0.824167i | \(-0.691644\pi\) | ||||
−0.566347 | + | 0.824167i | \(0.691644\pi\) | |||||||
\(788\) | 2.72447e6 | 0.156303 | ||||||||
\(789\) | 1.35587e7 | 0.775398 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85929e7 | −1.05659 | ||||||||
\(792\) | 1.85783e6 | 0.105243 | ||||||||
\(793\) | −701941. | −0.0396386 | ||||||||
\(794\) | 6.71578e6 | 0.378047 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.73912e6 | 0.0972850 | ||||||||
\(797\) | 3.00192e7 | 1.67399 | 0.836996 | − | 0.547208i | \(-0.184310\pi\) | ||||
0.836996 | + | 0.547208i | \(0.184310\pi\) | |||||||
\(798\) | 3.19970e6 | 0.177870 | ||||||||
\(799\) | 3.09199e6 | 0.171345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.10867e6 | −0.281337 | ||||||||
\(802\) | 6.92915e6 | 0.380403 | ||||||||
\(803\) | 1.66174e6 | 0.0909439 | ||||||||
\(804\) | 974323. | 0.0531573 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −923889. | −0.0500936 | ||||||||
\(807\) | −2.70227e6 | −0.146065 | ||||||||
\(808\) | 6.10998e6 | 0.329239 | ||||||||
\(809\) | −8.99554e6 | −0.483233 | −0.241616 | − | 0.970372i | \(-0.577678\pi\) | ||||
−0.241616 | + | 0.970372i | \(0.577678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.96119e7 | −1.58093 | −0.790467 | − | 0.612505i | \(-0.790162\pi\) | ||||
−0.790467 | + | 0.612505i | \(0.790162\pi\) | |||||||
\(812\) | −1.30989e6 | −0.0697180 | ||||||||
\(813\) | 1.70092e7 | 0.902523 | ||||||||
\(814\) | −4.48840e6 | −0.237427 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.54481e6 | 0.344090 | ||||||||
\(817\) | −1.20093e7 | −0.629455 | ||||||||
\(818\) | 2.37917e7 | 1.24320 | ||||||||
\(819\) | −399247. | −0.0207985 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.05145e7 | −1.06219 | −0.531097 | − | 0.847311i | \(-0.678220\pi\) | ||||
−0.531097 | + | 0.847311i | \(0.678220\pi\) | |||||||
\(822\) | 1.85189e7 | 0.955949 | ||||||||
\(823\) | −2.38536e7 | −1.22759 | −0.613796 | − | 0.789465i | \(-0.710358\pi\) | ||||
−0.613796 | + | 0.789465i | \(0.710358\pi\) | |||||||
\(824\) | −8.71781e6 | −0.447290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.73930e6 | −0.139698 | ||||||||
\(827\) | −1.89103e7 | −0.961468 | −0.480734 | − | 0.876866i | \(-0.659630\pi\) | ||||
−0.480734 | + | 0.876866i | \(0.659630\pi\) | |||||||
\(828\) | 961093. | 0.0487180 | ||||||||
\(829\) | 3.48075e7 | 1.75908 | 0.879541 | − | 0.475823i | \(-0.157850\pi\) | ||||
0.879541 | + | 0.475823i | \(0.157850\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.44045e6 | 0.223061 | ||||||||
\(832\) | 2.36692e6 | 0.118543 | ||||||||
\(833\) | −9.16540e6 | −0.457656 | ||||||||
\(834\) | −8.71961e6 | −0.434092 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 383266. | 0.0189664 | ||||||||
\(837\) | −1.89470e6 | −0.0934816 | ||||||||
\(838\) | −1.24529e7 | −0.612575 | ||||||||
\(839\) | −2.32033e7 | −1.13800 | −0.569002 | − | 0.822336i | \(-0.692670\pi\) | ||||
−0.569002 | + | 0.822336i | \(0.692670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.79863e6 | 0.233952 | ||||||||
\(842\) | −2.16002e7 | −1.04997 | ||||||||
\(843\) | −1.25206e7 | −0.606815 | ||||||||
\(844\) | 105916. | 0.00511807 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.65243e6 | −0.0793774 | ||||||||
\(847\) | −1.08343e6 | −0.0518911 | ||||||||
\(848\) | 4.36804e6 | 0.208591 | ||||||||
\(849\) | 1.73333e7 | 0.825299 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.34393e7 | −1.10949 | ||||||||
\(852\) | 442540. | 0.0208859 | ||||||||
\(853\) | −2.30500e7 | −1.08467 | −0.542336 | − | 0.840162i | \(-0.682460\pi\) | ||||
−0.542336 | + | 0.840162i | \(0.682460\pi\) | |||||||
\(854\) | −4.16185e6 | −0.195273 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.60159e6 | −0.354585 | ||||||||
\(857\) | 1.45809e7 | 0.678158 | 0.339079 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339079 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(858\) | 387111. | 0.0179522 | ||||||||
\(859\) | 4.26393e6 | 0.197164 | 0.0985818 | − | 0.995129i | \(-0.468569\pi\) | ||||
0.0985818 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 131727. | 0.00605572 | ||||||||
\(862\) | −1.27048e7 | −0.582370 | ||||||||
\(863\) | −9.80948e6 | −0.448352 | −0.224176 | − | 0.974549i | \(-0.571969\pi\) | ||||
−0.224176 | + | 0.974549i | \(0.571969\pi\) | |||||||
\(864\) | 924256. | 0.0421219 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.68102e7 | 1.21480 | ||||||||
\(867\) | 6.89019e6 | 0.311303 | ||||||||
\(868\) | 676711. | 0.0304863 | ||||||||
\(869\) | 3.50354e6 | 0.157383 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04940e6 | 0.0915337 | ||||||||
\(872\) | −8.46096e6 | −0.376815 | ||||||||
\(873\) | 5.10016e6 | 0.226489 | ||||||||
\(874\) | −1.62015e7 | −0.717427 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 434890. | 0.0191478 | ||||||||
\(877\) | −1.86437e7 | −0.818525 | −0.409263 | − | 0.912417i | \(-0.634214\pi\) | ||||
−0.409263 | + | 0.912417i | \(0.634214\pi\) | |||||||
\(878\) | 1.21367e7 | 0.531328 | ||||||||
\(879\) | −1.38300e7 | −0.603738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.42571e7 | −1.48700 | −0.743500 | − | 0.668736i | \(-0.766836\pi\) | ||||
−0.743500 | + | 0.668736i | \(0.766836\pi\) | |||||||
\(882\) | 4.89819e6 | 0.212014 | ||||||||
\(883\) | −1.57969e7 | −0.681818 | −0.340909 | − | 0.940096i | \(-0.610735\pi\) | ||||
−0.340909 | + | 0.940096i | \(0.610735\pi\) | |||||||
\(884\) | −189570. | −0.00815902 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −500014. | −0.0213992 | ||||||||
\(887\) | 2.96846e7 | 1.26684 | 0.633420 | − | 0.773808i | \(-0.281651\pi\) | ||||
0.633420 | + | 0.773808i | \(0.281651\pi\) | |||||||
\(888\) | −1.18578e7 | −0.504628 | ||||||||
\(889\) | 1.58700e7 | 0.673477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.89812e6 | 0.0798750 | ||||||||
\(893\) | −3.44121e6 | −0.144405 | ||||||||
\(894\) | −9.08268e6 | −0.380076 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.10314e7 | 0.459049 | ||||||||
\(897\) | 2.02157e6 | 0.0838895 | ||||||||
\(898\) | 3.18136e7 | 1.31650 | ||||||||
\(899\) | −1.30754e7 | −0.539582 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.93002e6 | −0.161281 | ||||||||
\(902\) | −127722. | −0.00522698 | ||||||||
\(903\) | 8.88460e6 | 0.362592 | ||||||||
\(904\) | 4.76271e7 | 1.93835 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.76814e6 | 0.354885 | ||||||||
\(907\) | −2.52650e7 | −1.01977 | −0.509884 | − | 0.860243i | \(-0.670312\pi\) | ||||
−0.509884 | + | 0.860243i | \(0.670312\pi\) | |||||||
\(908\) | 3.42013e6 | 0.137666 | ||||||||
\(909\) | 2.61089e6 | 0.104804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.64889e7 | −1.05747 | −0.528734 | − | 0.848787i | \(-0.677333\pi\) | ||||
−0.528734 | + | 0.848787i | \(0.677333\pi\) | |||||||
\(912\) | −7.28401e6 | −0.289990 | ||||||||
\(913\) | 1.25632e7 | 0.498797 | ||||||||
\(914\) | 4.68686e6 | 0.185574 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −607653. | −0.0239286 | ||||||||
\(917\) | −1.16471e7 | −0.457398 | ||||||||
\(918\) | 3.14696e6 | 0.123249 | ||||||||
\(919\) | 4.82111e6 | 0.188303 | 0.0941517 | − | 0.995558i | \(-0.469986\pi\) | ||||
0.0941517 | + | 0.995558i | \(0.469986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95983e7 | 0.761322 | ||||||||
\(922\) | 15802.0 | 0.000612188 0 | ||||||||
\(923\) | 930843. | 0.0359643 | ||||||||
\(924\) | −283543. | −0.0109254 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.28375e6 | −0.355792 | ||||||||
\(927\) | −3.72526e6 | −0.142383 | ||||||||
\(928\) | 6.37836e6 | 0.243130 | ||||||||
\(929\) | −5.00384e7 | −1.90224 | −0.951118 | − | 0.308828i | \(-0.900063\pi\) | ||||
−0.951118 | + | 0.308828i | \(0.900063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02006e7 | 0.385700 | ||||||||
\(932\) | 64589.3 | 0.00243568 | ||||||||
\(933\) | −5.62428e6 | −0.211526 | ||||||||
\(934\) | 1.26213e6 | 0.0473409 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.02270e6 | 0.0381556 | ||||||||
\(937\) | −3.70330e7 | −1.37797 | −0.688985 | − | 0.724775i | \(-0.741944\pi\) | ||||
−0.688985 | + | 0.724775i | \(0.741944\pi\) | |||||||
\(938\) | 1.21510e7 | 0.450926 | ||||||||
\(939\) | 6.81672e6 | 0.252296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.30398e7 | 1.21636 | 0.608182 | − | 0.793798i | \(-0.291899\pi\) | ||||
0.608182 | + | 0.793798i | \(0.291899\pi\) | |||||||
\(942\) | 1.43829e7 | 0.528104 | ||||||||
\(943\) | −666992. | −0.0244254 | ||||||||
\(944\) | 6.23593e6 | 0.227757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.61452e6 | −0.312970 | ||||||||
\(947\) | −410586. | −0.0148775 | −0.00743873 | − | 0.999972i | \(-0.502368\pi\) | ||||
−0.00743873 | + | 0.999972i | \(0.502368\pi\) | |||||||
\(948\) | 916905. | 0.0331363 | ||||||||
\(949\) | 914752. | 0.0329714 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.79198e7 | 1.00106 | ||||||||
\(952\) | −1.13462e7 | −0.405748 | ||||||||
\(953\) | 4.08733e7 | 1.45783 | 0.728915 | − | 0.684604i | \(-0.240025\pi\) | ||||
0.728915 | + | 0.684604i | \(0.240025\pi\) | |||||||
\(954\) | 2.10029e6 | 0.0747151 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 178750. | 0.00632560 | ||||||||
\(957\) | 5.47863e6 | 0.193371 | ||||||||
\(958\) | 6.59272e6 | 0.232087 | ||||||||
\(959\) | −2.85313e7 | −1.00179 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.18742e7 | −0.764052 | ||||||||
\(962\) | −2.47077e6 | −0.0860786 | ||||||||
\(963\) | −3.24828e6 | −0.112872 | ||||||||
\(964\) | −201557. | −0.00698564 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.19860e7 | 0.413268 | ||||||||
\(967\) | −1.34815e7 | −0.463629 | −0.231815 | − | 0.972760i | \(-0.574466\pi\) | ||||
−0.231815 | + | 0.972760i | \(0.574466\pi\) | |||||||
\(968\) | 2.77528e6 | 0.0951960 | ||||||||
\(969\) | 6.55359e6 | 0.224218 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.78750e7 | −1.62952 | −0.814761 | − | 0.579797i | \(-0.803132\pi\) | ||||
−0.814761 | + | 0.579797i | \(0.803132\pi\) | |||||||
\(972\) | 207765. | 0.00705354 | ||||||||
\(973\) | 1.34340e7 | 0.454906 | ||||||||
\(974\) | −2.54696e7 | −0.860250 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.47431e6 | 0.318363 | ||||||||
\(977\) | 1.03468e7 | 0.346793 | 0.173396 | − | 0.984852i | \(-0.444526\pi\) | ||||
0.173396 | + | 0.984852i | \(0.444526\pi\) | |||||||
\(978\) | 5.08218e6 | 0.169904 | ||||||||
\(979\) | −7.63146e6 | −0.254479 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.61550e6 | −0.119949 | ||||||||
\(982\) | −4.87080e7 | −1.61184 | ||||||||
\(983\) | −1.81075e7 | −0.597689 | −0.298844 | − | 0.954302i | \(-0.596601\pi\) | ||||
−0.298844 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(984\) | −337426. | −0.0111094 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.17174e7 | 0.711402 | ||||||||
\(987\) | 2.54583e6 | 0.0831835 | ||||||||
\(988\) | 210980. | 0.00687621 | ||||||||
\(989\) | −4.49867e7 | −1.46249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.58378e7 | −1.48265 | −0.741327 | − | 0.671144i | \(-0.765803\pi\) | ||||
−0.741327 | + | 0.671144i | \(0.765803\pi\) | |||||||
\(992\) | −3.29516e6 | −0.106316 | ||||||||
\(993\) | 1.43219e7 | 0.460921 | ||||||||
\(994\) | 5.51902e6 | 0.177172 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.28790e6 | 0.105019 | ||||||||
\(997\) | 3.02752e7 | 0.964605 | 0.482302 | − | 0.876005i | \(-0.339801\pi\) | ||||
0.482302 | + | 0.876005i | \(0.339801\pi\) | |||||||
\(998\) | −4.49844e7 | −1.42967 | ||||||||
\(999\) | −5.06702e6 | −0.160635 |
(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 | 825.6.a.o.1.2 | yes | 7 | |
5.4 | even | 2 | 825.6.a.m.1.6 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.m.1.6 | ✓ | 7 | 5.4 | even | 2 | ||
825.6.a.o.1.2 | yes | 7 | 1.1 | even | 1 | trivial |