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: | \(3\) |
Coefficient field: | 3.3.307532.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 76x + 168 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30119\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.30119 | −0.760350 | −0.380175 | − | 0.924915i | \(-0.624136\pi\) | ||||
−0.380175 | + | 0.924915i | \(0.624136\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −13.4998 | −0.421868 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −38.7107 | −0.438988 | ||||||||
\(7\) | 148.216 | 1.14327 | 0.571635 | − | 0.820508i | \(-0.306309\pi\) | ||||
0.571635 | + | 0.820508i | \(0.306309\pi\) | |||||||
\(8\) | 195.703 | 1.08112 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −121.498 | −0.243565 | ||||||||
\(13\) | −234.137 | −0.384247 | −0.192124 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192124 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(14\) | −637.504 | −0.869286 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −409.764 | −0.400160 | ||||||||
\(17\) | −1031.76 | −0.865875 | −0.432937 | − | 0.901424i | \(-0.642523\pi\) | ||||
−0.432937 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(18\) | −348.396 | −0.253450 | ||||||||
\(19\) | 1266.29 | 0.804729 | 0.402365 | − | 0.915480i | \(-0.368188\pi\) | ||||
0.402365 | + | 0.915480i | \(0.368188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1333.94 | 0.660068 | ||||||||
\(22\) | −520.444 | −0.229254 | ||||||||
\(23\) | −384.710 | −0.151640 | −0.0758201 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758201 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(24\) | 1761.33 | 0.624183 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1007.07 | 0.292163 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −2000.88 | −0.482309 | ||||||||
\(29\) | −4484.85 | −0.990268 | −0.495134 | − | 0.868817i | \(-0.664881\pi\) | ||||
−0.495134 | + | 0.868817i | \(0.664881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −997.235 | −0.186377 | −0.0931887 | − | 0.995648i | \(-0.529706\pi\) | ||||
−0.0931887 | + | 0.995648i | \(0.529706\pi\) | |||||||
\(32\) | −4500.03 | −0.776856 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 4437.78 | 0.658368 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1093.48 | −0.140623 | ||||||||
\(37\) | −5168.11 | −0.620622 | −0.310311 | − | 0.950635i | \(-0.600433\pi\) | ||||
−0.310311 | + | 0.950635i | \(0.600433\pi\) | |||||||
\(38\) | −5446.56 | −0.611876 | ||||||||
\(39\) | −2107.23 | −0.221845 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2259.17 | 0.209889 | 0.104944 | − | 0.994478i | \(-0.466534\pi\) | ||||
0.104944 | + | 0.994478i | \(0.466534\pi\) | |||||||
\(42\) | −5737.54 | −0.501883 | ||||||||
\(43\) | −15818.9 | −1.30469 | −0.652343 | − | 0.757924i | \(-0.726214\pi\) | ||||
−0.652343 | + | 0.757924i | \(0.726214\pi\) | |||||||
\(44\) | −1633.47 | −0.127198 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1654.71 | 0.115300 | ||||||||
\(47\) | −12033.2 | −0.794577 | −0.397289 | − | 0.917694i | \(-0.630049\pi\) | ||||
−0.397289 | + | 0.917694i | \(0.630049\pi\) | |||||||
\(48\) | −3687.87 | −0.231032 | ||||||||
\(49\) | 5160.90 | 0.307069 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9285.81 | −0.499913 | ||||||||
\(52\) | 3160.79 | 0.162102 | ||||||||
\(53\) | 3851.67 | 0.188347 | 0.0941737 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941737 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(54\) | −3135.57 | −0.146329 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 29006.3 | 1.23601 | ||||||||
\(57\) | 11396.6 | 0.464611 | ||||||||
\(58\) | 19290.2 | 0.752950 | ||||||||
\(59\) | −20261.0 | −0.757760 | −0.378880 | − | 0.925446i | \(-0.623691\pi\) | ||||
−0.378880 | + | 0.925446i | \(0.623691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2006.88 | 0.0690553 | 0.0345276 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345276 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(62\) | 4289.30 | 0.141712 | ||||||||
\(63\) | 12005.5 | 0.381090 | ||||||||
\(64\) | 32467.9 | 0.990842 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4684.00 | −0.132360 | ||||||||
\(67\) | −40945.6 | −1.11435 | −0.557173 | − | 0.830397i | \(-0.688114\pi\) | ||||
−0.557173 | + | 0.830397i | \(0.688114\pi\) | |||||||
\(68\) | 13928.5 | 0.365285 | ||||||||
\(69\) | −3462.39 | −0.0875495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16970.8 | 0.399537 | 0.199769 | − | 0.979843i | \(-0.435981\pi\) | ||||
0.199769 | + | 0.979843i | \(0.435981\pi\) | |||||||
\(72\) | 15852.0 | 0.360372 | ||||||||
\(73\) | 56640.5 | 1.24400 | 0.621999 | − | 0.783018i | \(-0.286321\pi\) | ||||
0.621999 | + | 0.783018i | \(0.286321\pi\) | |||||||
\(74\) | 22229.0 | 0.471890 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17094.6 | −0.339489 | ||||||||
\(77\) | 17934.1 | 0.344709 | ||||||||
\(78\) | 9063.59 | 0.168680 | ||||||||
\(79\) | 58507.9 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323178\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −9717.12 | −0.159589 | ||||||||
\(83\) | 52243.8 | 0.832415 | 0.416207 | − | 0.909270i | \(-0.363359\pi\) | ||||
0.416207 | + | 0.909270i | \(0.363359\pi\) | |||||||
\(84\) | −18007.9 | −0.278461 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 68040.2 | 0.992018 | ||||||||
\(87\) | −40363.6 | −0.571732 | ||||||||
\(88\) | 23680.1 | 0.325969 | ||||||||
\(89\) | 55114.4 | 0.737548 | 0.368774 | − | 0.929519i | \(-0.379778\pi\) | ||||
0.368774 | + | 0.929519i | \(0.379778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34702.7 | −0.439299 | ||||||||
\(92\) | 5193.50 | 0.0639721 | ||||||||
\(93\) | −8975.11 | −0.107605 | ||||||||
\(94\) | 51757.0 | 0.604157 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −40500.3 | −0.448518 | ||||||||
\(97\) | −99383.8 | −1.07247 | −0.536237 | − | 0.844068i | \(-0.680154\pi\) | ||||
−0.536237 | + | 0.844068i | \(0.680154\pi\) | |||||||
\(98\) | −22198.0 | −0.233480 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −25334.3 | −0.247118 | −0.123559 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123559 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(102\) | 39940.0 | 0.380109 | ||||||||
\(103\) | 93216.6 | 0.865766 | 0.432883 | − | 0.901450i | \(-0.357496\pi\) | ||||
0.432883 | + | 0.901450i | \(0.357496\pi\) | |||||||
\(104\) | −45821.3 | −0.415416 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16566.8 | −0.143210 | ||||||||
\(107\) | −205830. | −1.73799 | −0.868997 | − | 0.494817i | \(-0.835235\pi\) | ||||
−0.868997 | + | 0.494817i | \(0.835235\pi\) | |||||||
\(108\) | −9841.33 | −0.0811885 | ||||||||
\(109\) | −155901. | −1.25684 | −0.628422 | − | 0.777872i | \(-0.716299\pi\) | ||||
−0.628422 | + | 0.777872i | \(0.716299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −46513.0 | −0.358316 | ||||||||
\(112\) | −60733.4 | −0.457491 | ||||||||
\(113\) | −40304.5 | −0.296932 | −0.148466 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148466 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(114\) | −49019.0 | −0.353267 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 60544.4 | 0.417762 | ||||||||
\(117\) | −18965.1 | −0.128082 | ||||||||
\(118\) | 87146.6 | 0.576163 | ||||||||
\(119\) | −152923. | −0.989929 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −8631.97 | −0.0525062 | ||||||||
\(123\) | 20332.5 | 0.121179 | ||||||||
\(124\) | 13462.4 | 0.0786266 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −51637.8 | −0.289762 | ||||||||
\(127\) | −120825. | −0.664733 | −0.332367 | − | 0.943150i | \(-0.607847\pi\) | ||||
−0.332367 | + | 0.943150i | \(0.607847\pi\) | |||||||
\(128\) | 4350.25 | 0.0234687 | ||||||||
\(129\) | −142370. | −0.753260 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 266474. | 1.35668 | 0.678338 | − | 0.734750i | \(-0.262701\pi\) | ||||
0.678338 | + | 0.734750i | \(0.262701\pi\) | |||||||
\(132\) | −14701.2 | −0.0734377 | ||||||||
\(133\) | 187684. | 0.920023 | ||||||||
\(134\) | 176115. | 0.847292 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −201918. | −0.936112 | ||||||||
\(137\) | −17176.5 | −0.0781866 | −0.0390933 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390933 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(138\) | 14892.4 | 0.0665682 | ||||||||
\(139\) | −5031.99 | −0.0220903 | −0.0110452 | − | 0.999939i | \(-0.503516\pi\) | ||||
−0.0110452 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −108299. | −0.458749 | ||||||||
\(142\) | −72994.7 | −0.303788 | ||||||||
\(143\) | −28330.5 | −0.115855 | ||||||||
\(144\) | −33190.9 | −0.133387 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −243621. | −0.945874 | ||||||||
\(147\) | 46448.1 | 0.177286 | ||||||||
\(148\) | 69768.3 | 0.261820 | ||||||||
\(149\) | −37407.9 | −0.138038 | −0.0690188 | − | 0.997615i | \(-0.521987\pi\) | ||||
−0.0690188 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −225853. | −0.806091 | −0.403046 | − | 0.915180i | \(-0.632048\pi\) | ||||
−0.403046 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(152\) | 247817. | 0.870006 | ||||||||
\(153\) | −83572.3 | −0.288625 | ||||||||
\(154\) | −77138.0 | −0.262100 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 28447.1 | 0.0935894 | ||||||||
\(157\) | 205537. | 0.665489 | 0.332744 | − | 0.943017i | \(-0.392025\pi\) | ||||
0.332744 | + | 0.943017i | \(0.392025\pi\) | |||||||
\(158\) | −251654. | −0.801974 | ||||||||
\(159\) | 34665.1 | 0.108742 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −57020.1 | −0.173366 | ||||||||
\(162\) | −28220.1 | −0.0844833 | ||||||||
\(163\) | 639398. | 1.88496 | 0.942481 | − | 0.334261i | \(-0.108487\pi\) | ||||
0.942481 | + | 0.334261i | \(0.108487\pi\) | |||||||
\(164\) | −30498.3 | −0.0885453 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −224711. | −0.632927 | ||||||||
\(167\) | −416990. | −1.15700 | −0.578502 | − | 0.815681i | \(-0.696363\pi\) | ||||
−0.578502 | + | 0.815681i | \(0.696363\pi\) | |||||||
\(168\) | 261057. | 0.713611 | ||||||||
\(169\) | −316473. | −0.852354 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 102570. | 0.268243 | ||||||||
\(172\) | 213552. | 0.550405 | ||||||||
\(173\) | −608651. | −1.54615 | −0.773077 | − | 0.634312i | \(-0.781284\pi\) | ||||
−0.773077 | + | 0.634312i | \(0.781284\pi\) | |||||||
\(174\) | 173612. | 0.434716 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −49581.4 | −0.120653 | ||||||||
\(177\) | −182349. | −0.437493 | ||||||||
\(178\) | −237058. | −0.560795 | ||||||||
\(179\) | 511566. | 1.19335 | 0.596676 | − | 0.802482i | \(-0.296488\pi\) | ||||
0.596676 | + | 0.802482i | \(0.296488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56369.0 | 0.127892 | 0.0639460 | − | 0.997953i | \(-0.479631\pi\) | ||||
0.0639460 | + | 0.997953i | \(0.479631\pi\) | |||||||
\(182\) | 149263. | 0.334021 | ||||||||
\(183\) | 18061.9 | 0.0398691 | ||||||||
\(184\) | −75289.0 | −0.163941 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 38603.7 | 0.0818175 | ||||||||
\(187\) | −124843. | −0.261071 | ||||||||
\(188\) | 162445. | 0.335206 | ||||||||
\(189\) | 108049. | 0.220023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 45986.9 | 0.0912117 | 0.0456059 | − | 0.998960i | \(-0.485478\pi\) | ||||
0.0456059 | + | 0.998960i | \(0.485478\pi\) | |||||||
\(192\) | 292211. | 0.572063 | ||||||||
\(193\) | −360889. | −0.697398 | −0.348699 | − | 0.937235i | \(-0.613376\pi\) | ||||
−0.348699 | + | 0.937235i | \(0.613376\pi\) | |||||||
\(194\) | 427469. | 0.815455 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −69671.0 | −0.129542 | ||||||||
\(197\) | −978922. | −1.79714 | −0.898571 | − | 0.438828i | \(-0.855394\pi\) | ||||
−0.898571 | + | 0.438828i | \(0.855394\pi\) | |||||||
\(198\) | −42156.0 | −0.0764181 | ||||||||
\(199\) | 902328. | 1.61522 | 0.807610 | − | 0.589717i | \(-0.200761\pi\) | ||||
0.807610 | + | 0.589717i | \(0.200761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −368510. | −0.643367 | ||||||||
\(202\) | 108968. | 0.187897 | ||||||||
\(203\) | −664725. | −1.13214 | ||||||||
\(204\) | 125356. | 0.210897 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −400942. | −0.658285 | ||||||||
\(207\) | −31161.5 | −0.0505467 | ||||||||
\(208\) | 95940.7 | 0.153760 | ||||||||
\(209\) | 153221. | 0.242635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 318392. | 0.492330 | 0.246165 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246165 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(212\) | −51996.7 | −0.0794577 | ||||||||
\(213\) | 152737. | 0.230673 | ||||||||
\(214\) | 885312. | 1.32148 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 142668. | 0.208061 | ||||||||
\(217\) | −147806. | −0.213080 | ||||||||
\(218\) | 670558. | 0.955642 | ||||||||
\(219\) | 509764. | 0.718223 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 241572. | 0.332710 | ||||||||
\(222\) | 200061. | 0.272446 | ||||||||
\(223\) | −661352. | −0.890575 | −0.445287 | − | 0.895388i | \(-0.646899\pi\) | ||||
−0.445287 | + | 0.895388i | \(0.646899\pi\) | |||||||
\(224\) | −666975. | −0.888157 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 173357. | 0.225773 | ||||||||
\(227\) | −606704. | −0.781470 | −0.390735 | − | 0.920503i | \(-0.627779\pi\) | ||||
−0.390735 | + | 0.920503i | \(0.627779\pi\) | |||||||
\(228\) | −153852. | −0.196004 | ||||||||
\(229\) | −352377. | −0.444036 | −0.222018 | − | 0.975043i | \(-0.571264\pi\) | ||||
−0.222018 | + | 0.975043i | \(0.571264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 161407. | 0.199018 | ||||||||
\(232\) | −877699. | −1.07060 | ||||||||
\(233\) | −1.49288e6 | −1.80151 | −0.900755 | − | 0.434328i | \(-0.856986\pi\) | ||||
−0.900755 | + | 0.434328i | \(0.856986\pi\) | |||||||
\(234\) | 81572.3 | 0.0973875 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 273519. | 0.319675 | ||||||||
\(237\) | 526571. | 0.608956 | ||||||||
\(238\) | 657749. | 0.752693 | ||||||||
\(239\) | 388141. | 0.439536 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −75337.2 | −0.0835540 | −0.0417770 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417770 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(242\) | −62973.7 | −0.0691227 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −27092.4 | −0.0291322 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −87454.1 | −0.0921388 | ||||||||
\(247\) | −296485. | −0.309215 | ||||||||
\(248\) | −195162. | −0.201496 | ||||||||
\(249\) | 470194. | 0.480595 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −346975. | −0.347627 | −0.173814 | − | 0.984779i | \(-0.555609\pi\) | ||||
−0.173814 | + | 0.984779i | \(0.555609\pi\) | |||||||
\(252\) | −162071. | −0.160770 | ||||||||
\(253\) | −46549.9 | −0.0457212 | ||||||||
\(254\) | 519691. | 0.505430 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.05768e6 | −1.00869 | ||||||||
\(257\) | −1.97267e6 | −1.86304 | −0.931518 | − | 0.363696i | \(-0.881515\pi\) | ||||
−0.931518 | + | 0.363696i | \(0.881515\pi\) | |||||||
\(258\) | 612362. | 0.572742 | ||||||||
\(259\) | −765995. | −0.709539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −363273. | −0.330089 | ||||||||
\(262\) | −1.14615e6 | −1.03155 | ||||||||
\(263\) | 190986. | 0.170260 | 0.0851300 | − | 0.996370i | \(-0.472869\pi\) | ||||
0.0851300 | + | 0.996370i | \(0.472869\pi\) | |||||||
\(264\) | 213121. | 0.188198 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −807266. | −0.699540 | ||||||||
\(267\) | 496030. | 0.425823 | ||||||||
\(268\) | 552755. | 0.470106 | ||||||||
\(269\) | 933912. | 0.786911 | 0.393455 | − | 0.919344i | \(-0.371280\pi\) | ||||
0.393455 | + | 0.919344i | \(0.371280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17171e6 | −0.969163 | −0.484582 | − | 0.874746i | \(-0.661028\pi\) | ||||
−0.484582 | + | 0.874746i | \(0.661028\pi\) | |||||||
\(272\) | 422776. | 0.346488 | ||||||||
\(273\) | −312325. | −0.253629 | ||||||||
\(274\) | 73879.3 | 0.0594492 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 46741.5 | 0.0369343 | ||||||||
\(277\) | 472512. | 0.370010 | 0.185005 | − | 0.982738i | \(-0.440770\pi\) | ||||
0.185005 | + | 0.982738i | \(0.440770\pi\) | |||||||
\(278\) | 21643.5 | 0.0167964 | ||||||||
\(279\) | −80776.0 | −0.0621258 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.05374e6 | −1.55160 | −0.775798 | − | 0.630981i | \(-0.782652\pi\) | ||||
−0.775798 | + | 0.630981i | \(0.782652\pi\) | |||||||
\(282\) | 465813. | 0.348810 | ||||||||
\(283\) | −465578. | −0.345562 | −0.172781 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172781 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(284\) | −229102. | −0.168552 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 121855. | 0.0880903 | ||||||||
\(287\) | 334845. | 0.239960 | ||||||||
\(288\) | −364502. | −0.258952 | ||||||||
\(289\) | −355335. | −0.250261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −894454. | −0.619193 | ||||||||
\(292\) | −764633. | −0.524803 | ||||||||
\(293\) | 1.19434e6 | 0.812751 | 0.406376 | − | 0.913706i | \(-0.366792\pi\) | ||||
0.406376 | + | 0.913706i | \(0.366792\pi\) | |||||||
\(294\) | −199782. | −0.134800 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.01141e6 | −0.670965 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 160898. | 0.104957 | ||||||||
\(299\) | 90074.7 | 0.0582673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.34461e6 | −1.49161 | ||||||||
\(302\) | 971438. | 0.612912 | ||||||||
\(303\) | −228009. | −0.142674 | ||||||||
\(304\) | −518880. | −0.322020 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 359460. | 0.219456 | ||||||||
\(307\) | −1.72251e6 | −1.04308 | −0.521538 | − | 0.853228i | \(-0.674641\pi\) | ||||
−0.521538 | + | 0.853228i | \(0.674641\pi\) | |||||||
\(308\) | −242106. | −0.145422 | ||||||||
\(309\) | 838950. | 0.499850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.60616e6 | −1.52792 | −0.763960 | − | 0.645263i | \(-0.776748\pi\) | ||||
−0.763960 | + | 0.645263i | \(0.776748\pi\) | |||||||
\(312\) | −412391. | −0.239841 | ||||||||
\(313\) | −1.22311e6 | −0.705677 | −0.352839 | − | 0.935684i | \(-0.614784\pi\) | ||||
−0.352839 | + | 0.935684i | \(0.614784\pi\) | |||||||
\(314\) | −884053. | −0.506005 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −789843. | −0.444962 | ||||||||
\(317\) | 700043. | 0.391270 | 0.195635 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195635 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(318\) | −149101. | −0.0826824 | ||||||||
\(319\) | −542667. | −0.298577 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.85247e6 | −1.00343 | ||||||||
\(322\) | 245254. | 0.131819 | ||||||||
\(323\) | −1.30650e6 | −0.696794 | ||||||||
\(324\) | −88572.0 | −0.0468742 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.75017e6 | −1.43323 | ||||||||
\(327\) | −1.40311e6 | −0.725640 | ||||||||
\(328\) | 442127. | 0.226914 | ||||||||
\(329\) | −1.78351e6 | −0.908417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.78738e6 | 1.39839 | 0.699193 | − | 0.714933i | \(-0.253543\pi\) | ||||
0.699193 | + | 0.714933i | \(0.253543\pi\) | |||||||
\(332\) | −705279. | −0.351169 | ||||||||
\(333\) | −418617. | −0.206874 | ||||||||
\(334\) | 1.79355e6 | 0.879728 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −546601. | −0.264133 | ||||||||
\(337\) | 795333. | 0.381482 | 0.190741 | − | 0.981640i | \(-0.438911\pi\) | ||||
0.190741 | + | 0.981640i | \(0.438911\pi\) | |||||||
\(338\) | 1.36121e6 | 0.648087 | ||||||||
\(339\) | −362741. | −0.171434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −120665. | −0.0561949 | ||||||||
\(342\) | −441171. | −0.203959 | ||||||||
\(343\) | −1.72613e6 | −0.792208 | ||||||||
\(344\) | −3.09581e6 | −1.41052 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.61792e6 | 1.17562 | ||||||||
\(347\) | 3.80533e6 | 1.69656 | 0.848278 | − | 0.529551i | \(-0.177639\pi\) | ||||
0.848278 | + | 0.529551i | \(0.177639\pi\) | |||||||
\(348\) | 544900. | 0.241195 | ||||||||
\(349\) | −798008. | −0.350706 | −0.175353 | − | 0.984506i | \(-0.556107\pi\) | ||||
−0.175353 | + | 0.984506i | \(0.556107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −170686. | −0.0739484 | ||||||||
\(352\) | −544503. | −0.234231 | ||||||||
\(353\) | −2.48978e6 | −1.06347 | −0.531733 | − | 0.846912i | \(-0.678459\pi\) | ||||
−0.531733 | + | 0.846912i | \(0.678459\pi\) | |||||||
\(354\) | 784319. | 0.332648 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −744032. | −0.311148 | ||||||||
\(357\) | −1.37630e6 | −0.571536 | ||||||||
\(358\) | −2.20034e6 | −0.907366 | ||||||||
\(359\) | −2.15148e6 | −0.881050 | −0.440525 | − | 0.897740i | \(-0.645208\pi\) | ||||
−0.440525 | + | 0.897740i | \(0.645208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −872605. | −0.352411 | ||||||||
\(362\) | −242454. | −0.0972427 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 468479. | 0.185326 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −77687.8 | −0.0303145 | ||||||||
\(367\) | −1.47515e6 | −0.571705 | −0.285853 | − | 0.958274i | \(-0.592277\pi\) | ||||
−0.285853 | + | 0.958274i | \(0.592277\pi\) | |||||||
\(368\) | 157640. | 0.0606803 | ||||||||
\(369\) | 182993. | 0.0699630 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 570879. | 0.215332 | ||||||||
\(372\) | 121162. | 0.0453951 | ||||||||
\(373\) | 4.71290e6 | 1.75394 | 0.876972 | − | 0.480541i | \(-0.159560\pi\) | ||||
0.876972 | + | 0.480541i | \(0.159560\pi\) | |||||||
\(374\) | 536972. | 0.198505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.35493e6 | −0.859031 | ||||||||
\(377\) | 1.05007e6 | 0.380508 | ||||||||
\(378\) | −464740. | −0.167294 | ||||||||
\(379\) | 4.47900e6 | 1.60171 | 0.800853 | − | 0.598861i | \(-0.204380\pi\) | ||||
0.800853 | + | 0.598861i | \(0.204380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.08742e6 | −0.383784 | ||||||||
\(382\) | −197798. | −0.0693528 | ||||||||
\(383\) | 57968.7 | 0.0201928 | 0.0100964 | − | 0.999949i | \(-0.496786\pi\) | ||||
0.0100964 | + | 0.999949i | \(0.496786\pi\) | |||||||
\(384\) | 39152.3 | 0.0135497 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.55225e6 | 0.530267 | ||||||||
\(387\) | −1.28133e6 | −0.434895 | ||||||||
\(388\) | 1.34166e6 | 0.452442 | ||||||||
\(389\) | −4.53325e6 | −1.51892 | −0.759461 | − | 0.650553i | \(-0.774537\pi\) | ||||
−0.759461 | + | 0.650553i | \(0.774537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 396927. | 0.131301 | ||||||||
\(392\) | 1.01000e6 | 0.331977 | ||||||||
\(393\) | 2.39826e6 | 0.783277 | ||||||||
\(394\) | 4.21053e6 | 1.36646 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −132311. | −0.0423993 | ||||||||
\(397\) | −621573. | −0.197932 | −0.0989660 | − | 0.995091i | \(-0.531554\pi\) | ||||
−0.0989660 | + | 0.995091i | \(0.531554\pi\) | |||||||
\(398\) | −3.88108e6 | −1.22813 | ||||||||
\(399\) | 1.68916e6 | 0.531176 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 954326. | 0.296371 | 0.148186 | − | 0.988960i | \(-0.452657\pi\) | ||||
0.148186 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(402\) | 1.58503e6 | 0.489185 | ||||||||
\(403\) | 233489. | 0.0716150 | ||||||||
\(404\) | 342007. | 0.104251 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.85911e6 | 0.860826 | ||||||||
\(407\) | −625341. | −0.187125 | ||||||||
\(408\) | −1.81726e6 | −0.540465 | ||||||||
\(409\) | 3.19864e6 | 0.945491 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −154588. | −0.0451411 | ||||||||
\(412\) | −1.25840e6 | −0.365239 | ||||||||
\(413\) | −3.00301e6 | −0.866325 | ||||||||
\(414\) | 134032. | 0.0384332 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.05362e6 | 0.298505 | ||||||||
\(417\) | −45287.9 | −0.0127539 | ||||||||
\(418\) | −659034. | −0.184487 | ||||||||
\(419\) | −6.60122e6 | −1.83691 | −0.918457 | − | 0.395520i | \(-0.870564\pi\) | ||||
−0.918457 | + | 0.395520i | \(0.870564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22510e6 | −1.16180 | −0.580901 | − | 0.813974i | \(-0.697300\pi\) | ||||
−0.580901 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(422\) | −1.36946e6 | −0.374343 | ||||||||
\(423\) | −974688. | −0.264859 | ||||||||
\(424\) | 753785. | 0.203626 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −656953. | −0.175392 | ||||||||
\(427\) | 297451. | 0.0789489 | ||||||||
\(428\) | 2.77865e6 | 0.733204 | ||||||||
\(429\) | −254975. | −0.0668889 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.72300e6 | 1.22469 | 0.612344 | − | 0.790592i | \(-0.290227\pi\) | ||||
0.612344 | + | 0.790592i | \(0.290227\pi\) | |||||||
\(432\) | −298718. | −0.0770108 | ||||||||
\(433\) | 882129. | 0.226106 | 0.113053 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113053 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(434\) | 635741. | 0.162015 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.10462e6 | 0.530222 | ||||||||
\(437\) | −487155. | −0.122029 | ||||||||
\(438\) | −2.19259e6 | −0.546101 | ||||||||
\(439\) | −3.07514e6 | −0.761560 | −0.380780 | − | 0.924666i | \(-0.624344\pi\) | ||||
−0.380780 | + | 0.924666i | \(0.624344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 418033. | 0.102356 | ||||||||
\(442\) | −1.03905e6 | −0.252976 | ||||||||
\(443\) | −3.40381e6 | −0.824055 | −0.412028 | − | 0.911171i | \(-0.635179\pi\) | ||||
−0.412028 | + | 0.911171i | \(0.635179\pi\) | |||||||
\(444\) | 627914. | 0.151162 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.84460e6 | 0.677149 | ||||||||
\(447\) | −336671. | −0.0796961 | ||||||||
\(448\) | 4.81226e6 | 1.13280 | ||||||||
\(449\) | −605757. | −0.141802 | −0.0709010 | − | 0.997483i | \(-0.522587\pi\) | ||||
−0.0709010 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 273360. | 0.0632839 | ||||||||
\(452\) | 544102. | 0.125266 | ||||||||
\(453\) | −2.03268e6 | −0.465397 | ||||||||
\(454\) | 2.60955e6 | 0.594191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23035e6 | 0.502298 | ||||||||
\(457\) | 5.46329e6 | 1.22367 | 0.611834 | − | 0.790986i | \(-0.290432\pi\) | ||||
0.611834 | + | 0.790986i | \(0.290432\pi\) | |||||||
\(458\) | 1.51564e6 | 0.337623 | ||||||||
\(459\) | −752151. | −0.166638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.84223e6 | −0.622883 | −0.311441 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311441 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(462\) | −694242. | −0.151323 | ||||||||
\(463\) | 8.51652e6 | 1.84633 | 0.923166 | − | 0.384401i | \(-0.125592\pi\) | ||||
0.923166 | + | 0.384401i | \(0.125592\pi\) | |||||||
\(464\) | 1.83773e6 | 0.396266 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.42118e6 | 1.36978 | ||||||||
\(467\) | −7.00140e6 | −1.48557 | −0.742784 | − | 0.669531i | \(-0.766495\pi\) | ||||
−0.742784 | + | 0.669531i | \(0.766495\pi\) | |||||||
\(468\) | 256024. | 0.0540339 | ||||||||
\(469\) | −6.06877e6 | −1.27400 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.84983e6 | 0.384220 | ||||||||
\(472\) | −3.96515e6 | −0.819228 | ||||||||
\(473\) | −1.91409e6 | −0.393377 | ||||||||
\(474\) | −2.26488e6 | −0.463020 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.06442e6 | 0.417619 | ||||||||
\(477\) | 311986. | 0.0627825 | ||||||||
\(478\) | −1.66947e6 | −0.334201 | ||||||||
\(479\) | 1.06826e6 | 0.212734 | 0.106367 | − | 0.994327i | \(-0.466078\pi\) | ||||
0.106367 | + | 0.994327i | \(0.466078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.21004e6 | 0.238472 | ||||||||
\(482\) | 324040. | 0.0635303 | ||||||||
\(483\) | −513181. | −0.100093 | ||||||||
\(484\) | −197650. | −0.0383516 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −253981. | −0.0487765 | ||||||||
\(487\) | −1.00308e6 | −0.191652 | −0.0958260 | − | 0.995398i | \(-0.530549\pi\) | ||||
−0.0958260 | + | 0.995398i | \(0.530549\pi\) | |||||||
\(488\) | 392753. | 0.0746569 | ||||||||
\(489\) | 5.75458e6 | 1.08828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.23719e6 | 1.72916 | 0.864582 | − | 0.502491i | \(-0.167583\pi\) | ||||
0.864582 | + | 0.502491i | \(0.167583\pi\) | |||||||
\(492\) | −274484. | −0.0511217 | ||||||||
\(493\) | 4.62727e6 | 0.857448 | ||||||||
\(494\) | 1.27524e6 | 0.235112 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 408631. | 0.0745807 | ||||||||
\(497\) | 2.51534e6 | 0.456779 | ||||||||
\(498\) | −2.02240e6 | −0.365420 | ||||||||
\(499\) | 4.31532e6 | 0.775822 | 0.387911 | − | 0.921697i | \(-0.373197\pi\) | ||||
0.387911 | + | 0.921697i | \(0.373197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.75291e6 | −0.667997 | ||||||||
\(502\) | 1.49240e6 | 0.264318 | ||||||||
\(503\) | −3.28052e6 | −0.578127 | −0.289064 | − | 0.957310i | \(-0.593344\pi\) | ||||
−0.289064 | + | 0.957310i | \(0.593344\pi\) | |||||||
\(504\) | 2.34951e6 | 0.412003 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 200220. | 0.0347641 | ||||||||
\(507\) | −2.84826e6 | −0.492107 | ||||||||
\(508\) | 1.63111e6 | 0.280430 | ||||||||
\(509\) | −2.50882e6 | −0.429215 | −0.214608 | − | 0.976700i | \(-0.568847\pi\) | ||||
−0.214608 | + | 0.976700i | \(0.568847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.39501e6 | 1.42223 | ||||||||
\(512\) | 4.41009e6 | 0.743486 | ||||||||
\(513\) | 923126. | 0.154870 | ||||||||
\(514\) | 8.48482e6 | 1.41656 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.92197e6 | 0.317776 | ||||||||
\(517\) | −1.45602e6 | −0.239574 | ||||||||
\(518\) | 3.29469e6 | 0.539498 | ||||||||
\(519\) | −5.47786e6 | −0.892673 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.63347e6 | −0.586444 | −0.293222 | − | 0.956044i | \(-0.594728\pi\) | ||||
−0.293222 | + | 0.956044i | \(0.594728\pi\) | |||||||
\(522\) | 1.56250e6 | 0.250983 | ||||||||
\(523\) | 7.95990e6 | 1.27249 | 0.636243 | − | 0.771488i | \(-0.280487\pi\) | ||||
0.636243 | + | 0.771488i | \(0.280487\pi\) | |||||||
\(524\) | −3.59733e6 | −0.572338 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −821468. | −0.129457 | ||||||||
\(527\) | 1.02890e6 | 0.161379 | ||||||||
\(528\) | −446233. | −0.0696589 | ||||||||
\(529\) | −6.28834e6 | −0.977005 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.64114e6 | −0.252587 | ||||||||
\(532\) | −2.53369e6 | −0.388128 | ||||||||
\(533\) | −528954. | −0.0806492 | ||||||||
\(534\) | −2.13352e6 | −0.323775 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.01317e6 | −1.20474 | ||||||||
\(537\) | 4.60409e6 | 0.688983 | ||||||||
\(538\) | −4.01693e6 | −0.598328 | ||||||||
\(539\) | 624469. | 0.0925847 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20412e6 | 0.176879 | 0.0884395 | − | 0.996082i | \(-0.471812\pi\) | ||||
0.0884395 | + | 0.996082i | \(0.471812\pi\) | |||||||
\(542\) | 5.03975e6 | 0.736903 | ||||||||
\(543\) | 507321. | 0.0738385 | ||||||||
\(544\) | 4.64293e6 | 0.672660 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.34337e6 | 0.192847 | ||||||||
\(547\) | 1.04446e7 | 1.49254 | 0.746268 | − | 0.665646i | \(-0.231844\pi\) | ||||
0.746268 | + | 0.665646i | \(0.231844\pi\) | |||||||
\(548\) | 231878. | 0.0329844 | ||||||||
\(549\) | 162557. | 0.0230184 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.67912e6 | −0.796897 | ||||||||
\(552\) | −677601. | −0.0946512 | ||||||||
\(553\) | 8.67179e6 | 1.20586 | ||||||||
\(554\) | −2.03236e6 | −0.281337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 67930.6 | 0.00931920 | ||||||||
\(557\) | −8.45756e6 | −1.15507 | −0.577534 | − | 0.816367i | \(-0.695985\pi\) | ||||
−0.577534 | + | 0.816367i | \(0.695985\pi\) | |||||||
\(558\) | 347433. | 0.0472373 | ||||||||
\(559\) | 3.70379e6 | 0.501322 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.12358e6 | −0.150729 | ||||||||
\(562\) | 8.83350e6 | 1.17976 | ||||||||
\(563\) | −9.96372e6 | −1.32480 | −0.662401 | − | 0.749150i | \(-0.730462\pi\) | ||||
−0.662401 | + | 0.749150i | \(0.730462\pi\) | |||||||
\(564\) | 1.46201e6 | 0.193532 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.00254e6 | 0.262748 | ||||||||
\(567\) | 972443. | 0.127030 | ||||||||
\(568\) | 3.32124e6 | 0.431946 | ||||||||
\(569\) | −1.05157e7 | −1.36163 | −0.680813 | − | 0.732458i | \(-0.738373\pi\) | ||||
−0.680813 | + | 0.732458i | \(0.738373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.02900e6 | 1.15891 | 0.579454 | − | 0.815005i | \(-0.303266\pi\) | ||||
0.579454 | + | 0.815005i | \(0.303266\pi\) | |||||||
\(572\) | 382456. | 0.0488755 | ||||||||
\(573\) | 413882. | 0.0526611 | ||||||||
\(574\) | −1.44023e6 | −0.182453 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.62990e6 | 0.330281 | ||||||||
\(577\) | −6.65688e6 | −0.832398 | −0.416199 | − | 0.909273i | \(-0.636638\pi\) | ||||
−0.416199 | + | 0.909273i | \(0.636638\pi\) | |||||||
\(578\) | 1.52836e6 | 0.190286 | ||||||||
\(579\) | −3.24800e6 | −0.402643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.74336e6 | 0.951676 | ||||||||
\(582\) | 3.84722e6 | 0.470803 | ||||||||
\(583\) | 466053. | 0.0567889 | ||||||||
\(584\) | 1.10847e7 | 1.34491 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.13707e6 | −0.617975 | ||||||||
\(587\) | −2.20946e6 | −0.264661 | −0.132331 | − | 0.991206i | \(-0.542246\pi\) | ||||
−0.132331 | + | 0.991206i | \(0.542246\pi\) | |||||||
\(588\) | −627039. | −0.0747913 | ||||||||
\(589\) | −1.26279e6 | −0.149983 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.81030e6 | −1.03758 | ||||||||
\(592\) | 2.11770e6 | 0.248348 | ||||||||
\(593\) | 261524. | 0.0305404 | 0.0152702 | − | 0.999883i | \(-0.495139\pi\) | ||||
0.0152702 | + | 0.999883i | \(0.495139\pi\) | |||||||
\(594\) | −379404. | −0.0441200 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 504998. | 0.0582336 | ||||||||
\(597\) | 8.12095e6 | 0.932548 | ||||||||
\(598\) | −387429. | −0.0443036 | ||||||||
\(599\) | 7.09631e6 | 0.808101 | 0.404050 | − | 0.914737i | \(-0.367602\pi\) | ||||
0.404050 | + | 0.914737i | \(0.367602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.04793e6 | 0.683000 | 0.341500 | − | 0.939882i | \(-0.389065\pi\) | ||||
0.341500 | + | 0.939882i | \(0.389065\pi\) | |||||||
\(602\) | 1.00846e7 | 1.13414 | ||||||||
\(603\) | −3.31659e6 | −0.371448 | ||||||||
\(604\) | 3.04897e6 | 0.340064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 980708. | 0.108482 | ||||||||
\(607\) | 1.05203e7 | 1.15892 | 0.579461 | − | 0.815000i | \(-0.303263\pi\) | ||||
0.579461 | + | 0.815000i | \(0.303263\pi\) | |||||||
\(608\) | −5.69835e6 | −0.625158 | ||||||||
\(609\) | −5.98253e6 | −0.653644 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.81741e6 | 0.305314 | ||||||||
\(612\) | 1.12821e6 | 0.121762 | ||||||||
\(613\) | 8.55961e6 | 0.920032 | 0.460016 | − | 0.887911i | \(-0.347844\pi\) | ||||
0.460016 | + | 0.887911i | \(0.347844\pi\) | |||||||
\(614\) | 7.40884e6 | 0.793103 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.50976e6 | 0.372671 | ||||||||
\(617\) | 6.18055e6 | 0.653604 | 0.326802 | − | 0.945093i | \(-0.394029\pi\) | ||||
0.326802 | + | 0.945093i | \(0.394029\pi\) | |||||||
\(618\) | −3.60848e6 | −0.380061 | ||||||||
\(619\) | −1.12540e7 | −1.18053 | −0.590267 | − | 0.807208i | \(-0.700978\pi\) | ||||
−0.590267 | + | 0.807208i | \(0.700978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −280454. | −0.0291832 | ||||||||
\(622\) | 1.12096e7 | 1.16175 | ||||||||
\(623\) | 8.16882e6 | 0.843217 | ||||||||
\(624\) | 863466. | 0.0887736 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.26085e6 | 0.536562 | ||||||||
\(627\) | 1.37899e6 | 0.140085 | ||||||||
\(628\) | −2.77470e6 | −0.280748 | ||||||||
\(629\) | 5.33223e6 | 0.537381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.17369e7 | 1.17349 | 0.586746 | − | 0.809771i | \(-0.300409\pi\) | ||||
0.586746 | + | 0.809771i | \(0.300409\pi\) | |||||||
\(632\) | 1.14502e7 | 1.14030 | ||||||||
\(633\) | 2.86553e6 | 0.284247 | ||||||||
\(634\) | −3.01102e6 | −0.297502 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −467970. | −0.0458749 | ||||||||
\(637\) | −1.20836e6 | −0.117990 | ||||||||
\(638\) | 2.33411e6 | 0.227023 | ||||||||
\(639\) | 1.37464e6 | 0.133179 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.80878e6 | 0.654522 | 0.327261 | − | 0.944934i | \(-0.393874\pi\) | ||||
0.327261 | + | 0.944934i | \(0.393874\pi\) | |||||||
\(642\) | 7.96781e6 | 0.762959 | ||||||||
\(643\) | 1.16456e7 | 1.11080 | 0.555400 | − | 0.831583i | \(-0.312565\pi\) | ||||
0.555400 | + | 0.831583i | \(0.312565\pi\) | |||||||
\(644\) | 769758. | 0.0731374 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.61952e6 | 0.529808 | ||||||||
\(647\) | −2.61990e6 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(648\) | 1.28401e6 | 0.120124 | ||||||||
\(649\) | −2.45159e6 | −0.228473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.33025e6 | −0.123022 | ||||||||
\(652\) | −8.63173e6 | −0.795204 | ||||||||
\(653\) | −1.48492e7 | −1.36276 | −0.681379 | − | 0.731931i | \(-0.738619\pi\) | ||||
−0.681379 | + | 0.731931i | \(0.738619\pi\) | |||||||
\(654\) | 6.03502e6 | 0.551740 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −925726. | −0.0839891 | ||||||||
\(657\) | 4.58788e6 | 0.414666 | ||||||||
\(658\) | 7.67120e6 | 0.690715 | ||||||||
\(659\) | −2.47470e6 | −0.221977 | −0.110989 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110989 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.61212e6 | 0.677645 | 0.338822 | − | 0.940850i | \(-0.389971\pi\) | ||||
0.338822 | + | 0.940850i | \(0.389971\pi\) | |||||||
\(662\) | −1.19891e7 | −1.06326 | ||||||||
\(663\) | 2.17415e6 | 0.192090 | ||||||||
\(664\) | 1.02243e7 | 0.899938 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.80055e6 | 0.157297 | ||||||||
\(667\) | 1.72537e6 | 0.150164 | ||||||||
\(668\) | 5.62927e6 | 0.488103 | ||||||||
\(669\) | −5.95217e6 | −0.514174 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 242833. | 0.0208210 | ||||||||
\(672\) | −6.00278e6 | −0.512777 | ||||||||
\(673\) | −6.62472e6 | −0.563807 | −0.281903 | − | 0.959443i | \(-0.590966\pi\) | ||||
−0.281903 | + | 0.959443i | \(0.590966\pi\) | |||||||
\(674\) | −3.42088e6 | −0.290060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.27231e6 | 0.359581 | ||||||||
\(677\) | −228067. | −0.0191245 | −0.00956227 | − | 0.999954i | \(-0.503044\pi\) | ||||
−0.00956227 | + | 0.999954i | \(0.503044\pi\) | |||||||
\(678\) | 1.56022e6 | 0.130350 | ||||||||
\(679\) | −1.47302e7 | −1.22613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.46034e6 | −0.451182 | ||||||||
\(682\) | 519005. | 0.0427278 | ||||||||
\(683\) | 1.58370e6 | 0.129903 | 0.0649517 | − | 0.997888i | \(-0.479311\pi\) | ||||
0.0649517 | + | 0.997888i | \(0.479311\pi\) | |||||||
\(684\) | −1.38467e6 | −0.113163 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.42443e6 | 0.602356 | ||||||||
\(687\) | −3.17139e6 | −0.256364 | ||||||||
\(688\) | 6.48202e6 | 0.522083 | ||||||||
\(689\) | −901818. | −0.0723720 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.07411e7 | 1.65248 | 0.826241 | − | 0.563317i | \(-0.190475\pi\) | ||||
0.826241 | + | 0.563317i | \(0.190475\pi\) | |||||||
\(692\) | 8.21665e6 | 0.652273 | ||||||||
\(693\) | 1.45266e6 | 0.114903 | ||||||||
\(694\) | −1.63674e7 | −1.28998 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.89929e6 | −0.618109 | ||||||||
\(697\) | −2.33091e6 | −0.181737 | ||||||||
\(698\) | 3.43238e6 | 0.266660 | ||||||||
\(699\) | −1.34360e7 | −1.04010 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.54594e7 | −1.18822 | −0.594109 | − | 0.804384i | \(-0.702495\pi\) | ||||
−0.594109 | + | 0.804384i | \(0.702495\pi\) | |||||||
\(702\) | 734151. | 0.0562267 | ||||||||
\(703\) | −6.54433e6 | −0.499433 | ||||||||
\(704\) | 3.92862e6 | 0.298750 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.07090e7 | 0.808606 | ||||||||
\(707\) | −3.75494e6 | −0.282523 | ||||||||
\(708\) | 2.46167e6 | 0.184564 | ||||||||
\(709\) | −4.71237e6 | −0.352066 | −0.176033 | − | 0.984384i | \(-0.556327\pi\) | ||||
−0.176033 | + | 0.984384i | \(0.556327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.73914e6 | 0.351581 | ||||||||
\(712\) | 1.07861e7 | 0.797376 | ||||||||
\(713\) | 383646. | 0.0282623 | ||||||||
\(714\) | 5.91974e6 | 0.434567 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.90602e6 | −0.503437 | ||||||||
\(717\) | 3.49327e6 | 0.253766 | ||||||||
\(718\) | 9.25391e6 | 0.669906 | ||||||||
\(719\) | 2.29858e6 | 0.165820 | 0.0829099 | − | 0.996557i | \(-0.473579\pi\) | ||||
0.0829099 | + | 0.996557i | \(0.473579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.38162e7 | 0.989805 | ||||||||
\(722\) | 3.75324e6 | 0.267956 | ||||||||
\(723\) | −678035. | −0.0482399 | ||||||||
\(724\) | −760968. | −0.0539535 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −566763. | −0.0399080 | ||||||||
\(727\) | −2.81705e7 | −1.97678 | −0.988391 | − | 0.151933i | \(-0.951450\pi\) | ||||
−0.988391 | + | 0.151933i | \(0.951450\pi\) | |||||||
\(728\) | −6.79143e6 | −0.474934 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.63213e7 | 1.12969 | ||||||||
\(732\) | −243832. | −0.0168195 | ||||||||
\(733\) | 1.32094e7 | 0.908078 | 0.454039 | − | 0.890982i | \(-0.349983\pi\) | ||||
0.454039 | + | 0.890982i | \(0.349983\pi\) | |||||||
\(734\) | 6.34492e6 | 0.434696 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.73121e6 | 0.117802 | ||||||||
\(737\) | −4.95441e6 | −0.335988 | ||||||||
\(738\) | −787087. | −0.0531963 | ||||||||
\(739\) | −6.63649e6 | −0.447021 | −0.223510 | − | 0.974702i | \(-0.571752\pi\) | ||||
−0.223510 | + | 0.974702i | \(0.571752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.66837e6 | −0.178525 | ||||||||
\(742\) | −2.45546e6 | −0.163728 | ||||||||
\(743\) | 7.93013e6 | 0.526997 | 0.263499 | − | 0.964660i | \(-0.415124\pi\) | ||||
0.263499 | + | 0.964660i | \(0.415124\pi\) | |||||||
\(744\) | −1.75646e6 | −0.116334 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.02711e7 | −1.33361 | ||||||||
\(747\) | 4.23175e6 | 0.277472 | ||||||||
\(748\) | 1.68535e6 | 0.110137 | ||||||||
\(749\) | −3.05072e7 | −1.98700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.43446e7 | −0.928086 | −0.464043 | − | 0.885813i | \(-0.653602\pi\) | ||||
−0.464043 | + | 0.885813i | \(0.653602\pi\) | |||||||
\(752\) | 4.93076e6 | 0.317958 | ||||||||
\(753\) | −3.12277e6 | −0.200703 | ||||||||
\(754\) | −4.51654e6 | −0.289319 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.45864e6 | −0.0928204 | ||||||||
\(757\) | −8.38496e6 | −0.531816 | −0.265908 | − | 0.963998i | \(-0.585672\pi\) | ||||
−0.265908 | + | 0.963998i | \(0.585672\pi\) | |||||||
\(758\) | −1.92650e7 | −1.21786 | ||||||||
\(759\) | −418949. | −0.0263972 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.68159e7 | 1.67853 | 0.839267 | − | 0.543719i | \(-0.182984\pi\) | ||||
0.839267 | + | 0.543719i | \(0.182984\pi\) | |||||||
\(762\) | 4.67722e6 | 0.291810 | ||||||||
\(763\) | −2.31069e7 | −1.43691 | ||||||||
\(764\) | −620812. | −0.0384793 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −249334. | −0.0153536 | ||||||||
\(767\) | 4.74385e6 | 0.291167 | ||||||||
\(768\) | −9.51916e6 | −0.582365 | ||||||||
\(769\) | −2.82141e7 | −1.72049 | −0.860243 | − | 0.509884i | \(-0.829688\pi\) | ||||
−0.860243 | + | 0.509884i | \(0.829688\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.77540e7 | −1.07562 | ||||||||
\(772\) | 4.87192e6 | 0.294210 | ||||||||
\(773\) | −2.41553e7 | −1.45400 | −0.727000 | − | 0.686637i | \(-0.759086\pi\) | ||||
−0.727000 | + | 0.686637i | \(0.759086\pi\) | |||||||
\(774\) | 5.51125e6 | 0.330673 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.94497e7 | −1.15947 | ||||||||
\(777\) | −6.89395e6 | −0.409653 | ||||||||
\(778\) | 1.94983e7 | 1.15491 | ||||||||
\(779\) | 2.86077e6 | 0.168904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.05347e6 | 0.120465 | ||||||||
\(782\) | −1.70726e6 | −0.0998350 | ||||||||
\(783\) | −3.26945e6 | −0.190577 | ||||||||
\(784\) | −2.11475e6 | −0.122877 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.03154e7 | −0.595565 | ||||||||
\(787\) | −1.96829e7 | −1.13280 | −0.566400 | − | 0.824131i | \(-0.691664\pi\) | ||||
−0.566400 | + | 0.824131i | \(0.691664\pi\) | |||||||
\(788\) | 1.32152e7 | 0.758156 | ||||||||
\(789\) | 1.71888e6 | 0.0982997 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.97376e6 | −0.339474 | ||||||||
\(792\) | 1.91809e6 | 0.108656 | ||||||||
\(793\) | −469884. | −0.0265343 | ||||||||
\(794\) | 2.67351e6 | 0.150498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.21812e7 | −0.681409 | ||||||||
\(797\) | −2.41989e6 | −0.134943 | −0.0674714 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674714 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(798\) | −7.26539e6 | −0.403880 | ||||||||
\(799\) | 1.24153e7 | 0.688004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.46427e6 | 0.245849 | ||||||||
\(802\) | −4.10474e6 | −0.225346 | ||||||||
\(803\) | 6.85350e6 | 0.375080 | ||||||||
\(804\) | 4.97480e6 | 0.271416 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00428e6 | −0.0544525 | ||||||||
\(807\) | 8.40521e6 | 0.454323 | ||||||||
\(808\) | −4.95800e6 | −0.267164 | ||||||||
\(809\) | 2.06594e7 | 1.10981 | 0.554903 | − | 0.831915i | \(-0.312755\pi\) | ||||
0.554903 | + | 0.831915i | \(0.312755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38880e7 | 0.741461 | 0.370730 | − | 0.928741i | \(-0.379107\pi\) | ||||
0.370730 | + | 0.928741i | \(0.379107\pi\) | |||||||
\(812\) | 8.97363e6 | 0.477615 | ||||||||
\(813\) | −1.05454e7 | −0.559547 | ||||||||
\(814\) | 2.68971e6 | 0.142280 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.80499e6 | 0.200045 | ||||||||
\(817\) | −2.00314e7 | −1.04992 | ||||||||
\(818\) | −1.37580e7 | −0.718904 | ||||||||
\(819\) | −2.81092e6 | −0.146433 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.26859e6 | 0.272795 | 0.136398 | − | 0.990654i | \(-0.456448\pi\) | ||||
0.136398 | + | 0.990654i | \(0.456448\pi\) | |||||||
\(822\) | 664913. | 0.0343230 | ||||||||
\(823\) | −3.61766e7 | −1.86178 | −0.930890 | − | 0.365299i | \(-0.880967\pi\) | ||||
−0.930890 | + | 0.365299i | \(0.880967\pi\) | |||||||
\(824\) | 1.82428e7 | 0.935994 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.29165e7 | 0.658710 | ||||||||
\(827\) | −3.01917e7 | −1.53505 | −0.767527 | − | 0.641017i | \(-0.778513\pi\) | ||||
−0.767527 | + | 0.641017i | \(0.778513\pi\) | |||||||
\(828\) | 420673. | 0.0213240 | ||||||||
\(829\) | 2.93884e7 | 1.48522 | 0.742608 | − | 0.669727i | \(-0.233589\pi\) | ||||
0.742608 | + | 0.669727i | \(0.233589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.25261e6 | 0.213625 | ||||||||
\(832\) | −7.60193e6 | −0.380728 | ||||||||
\(833\) | −5.32479e6 | −0.265883 | ||||||||
\(834\) | 194792. | 0.00969740 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.06845e6 | −0.102360 | ||||||||
\(837\) | −726984. | −0.0358683 | ||||||||
\(838\) | 2.83931e7 | 1.39670 | ||||||||
\(839\) | 1.57845e7 | 0.774150 | 0.387075 | − | 0.922048i | \(-0.373485\pi\) | ||||
0.387075 | + | 0.922048i | \(0.373485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −397286. | −0.0193692 | ||||||||
\(842\) | 1.81730e7 | 0.883376 | ||||||||
\(843\) | −1.84836e7 | −0.895814 | ||||||||
\(844\) | −4.29822e6 | −0.207698 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.19232e6 | 0.201386 | ||||||||
\(847\) | 2.17003e6 | 0.103934 | ||||||||
\(848\) | −1.57828e6 | −0.0753691 | ||||||||
\(849\) | −4.19020e6 | −0.199510 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.98822e6 | 0.0941112 | ||||||||
\(852\) | −2.06192e6 | −0.0973134 | ||||||||
\(853\) | −2.68137e7 | −1.26178 | −0.630891 | − | 0.775871i | \(-0.717311\pi\) | ||||
−0.630891 | + | 0.775871i | \(0.717311\pi\) | |||||||
\(854\) | −1.27939e6 | −0.0600288 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.02815e7 | −1.87898 | ||||||||
\(857\) | 2.59115e7 | 1.20515 | 0.602574 | − | 0.798063i | \(-0.294142\pi\) | ||||
0.602574 | + | 0.798063i | \(0.294142\pi\) | |||||||
\(858\) | 1.09669e6 | 0.0508590 | ||||||||
\(859\) | 1.20430e7 | 0.556870 | 0.278435 | − | 0.960455i | \(-0.410184\pi\) | ||||
0.278435 | + | 0.960455i | \(0.410184\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.01360e6 | 0.138541 | ||||||||
\(862\) | −2.03145e7 | −0.931191 | ||||||||
\(863\) | −2.28033e7 | −1.04225 | −0.521125 | − | 0.853481i | \(-0.674487\pi\) | ||||
−0.521125 | + | 0.853481i | \(0.674487\pi\) | |||||||
\(864\) | −3.28052e6 | −0.149506 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.79420e6 | −0.171920 | ||||||||
\(867\) | −3.19801e6 | −0.144488 | ||||||||
\(868\) | 1.99534e6 | 0.0898915 | ||||||||
\(869\) | 7.07945e6 | 0.318017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.58685e6 | 0.428184 | ||||||||
\(872\) | −3.05102e7 | −1.35880 | ||||||||
\(873\) | −8.05009e6 | −0.357491 | ||||||||
\(874\) | 2.09535e6 | 0.0927849 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.88170e6 | −0.302995 | ||||||||
\(877\) | 3.10668e7 | 1.36395 | 0.681974 | − | 0.731376i | \(-0.261122\pi\) | ||||
0.681974 | + | 0.731376i | \(0.261122\pi\) | |||||||
\(878\) | 1.32268e7 | 0.579052 | ||||||||
\(879\) | 1.07490e7 | 0.469242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.45208e7 | −1.49844 | −0.749222 | − | 0.662319i | \(-0.769573\pi\) | ||||
−0.749222 | + | 0.662319i | \(0.769573\pi\) | |||||||
\(882\) | −1.79804e6 | −0.0778265 | ||||||||
\(883\) | 3.29428e7 | 1.42186 | 0.710932 | − | 0.703260i | \(-0.248273\pi\) | ||||
0.710932 | + | 0.703260i | \(0.248273\pi\) | |||||||
\(884\) | −3.26117e6 | −0.140360 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.46404e7 | 0.626571 | ||||||||
\(887\) | 2.11009e7 | 0.900519 | 0.450260 | − | 0.892898i | \(-0.351331\pi\) | ||||
0.450260 | + | 0.892898i | \(0.351331\pi\) | |||||||
\(888\) | −9.10273e6 | −0.387382 | ||||||||
\(889\) | −1.79082e7 | −0.759970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 8.92810e6 | 0.375705 | ||||||||
\(893\) | −1.52375e7 | −0.639419 | ||||||||
\(894\) | 1.44809e6 | 0.0605969 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 644775. | 0.0268311 | ||||||||
\(897\) | 810673. | 0.0336406 | ||||||||
\(898\) | 2.60547e6 | 0.107819 | ||||||||
\(899\) | 4.47245e6 | 0.184564 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.97399e6 | −0.163085 | ||||||||
\(902\) | −1.17577e6 | −0.0481179 | ||||||||
\(903\) | −2.11015e7 | −0.861181 | ||||||||
\(904\) | −7.88772e6 | −0.321019 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.74294e6 | 0.353865 | ||||||||
\(907\) | −1.30426e7 | −0.526438 | −0.263219 | − | 0.964736i | \(-0.584784\pi\) | ||||
−0.263219 | + | 0.964736i | \(0.584784\pi\) | |||||||
\(908\) | 8.19036e6 | 0.329677 | ||||||||
\(909\) | −2.05208e6 | −0.0823728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.09652e7 | −1.63538 | −0.817690 | − | 0.575658i | \(-0.804746\pi\) | ||||
−0.817690 | + | 0.575658i | \(0.804746\pi\) | |||||||
\(912\) | −4.66992e6 | −0.185918 | ||||||||
\(913\) | 6.32150e6 | 0.250982 | ||||||||
\(914\) | −2.34987e7 | −0.930417 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.75700e6 | 0.187325 | ||||||||
\(917\) | 3.94956e7 | 1.55105 | ||||||||
\(918\) | 3.23514e6 | 0.126703 | ||||||||
\(919\) | 5.59367e6 | 0.218478 | 0.109239 | − | 0.994016i | \(-0.465159\pi\) | ||||
0.109239 | + | 0.994016i | \(0.465159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.55026e7 | −0.602220 | ||||||||
\(922\) | 1.22250e7 | 0.473609 | ||||||||
\(923\) | −3.97349e6 | −0.153521 | ||||||||
\(924\) | −2.17896e6 | −0.0839592 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.66312e7 | −1.40386 | ||||||||
\(927\) | 7.55055e6 | 0.288589 | ||||||||
\(928\) | 2.01819e7 | 0.769295 | ||||||||
\(929\) | −4.15645e7 | −1.58010 | −0.790048 | − | 0.613045i | \(-0.789944\pi\) | ||||
−0.790048 | + | 0.613045i | \(0.789944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.53520e6 | 0.247107 | ||||||||
\(932\) | 2.01536e7 | 0.759999 | ||||||||
\(933\) | −2.34555e7 | −0.882145 | ||||||||
\(934\) | 3.01144e7 | 1.12955 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.71152e6 | −0.138472 | ||||||||
\(937\) | 1.62578e7 | 0.604941 | 0.302470 | − | 0.953159i | \(-0.402189\pi\) | ||||
0.302470 | + | 0.953159i | \(0.402189\pi\) | |||||||
\(938\) | 2.61030e7 | 0.968685 | ||||||||
\(939\) | −1.10080e7 | −0.407423 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.33538e7 | 0.491622 | 0.245811 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245811 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(942\) | −7.95648e6 | −0.292142 | ||||||||
\(943\) | −869126. | −0.0318276 | ||||||||
\(944\) | 8.30224e6 | 0.303225 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.23286e6 | 0.299105 | ||||||||
\(947\) | −1.36642e7 | −0.495117 | −0.247559 | − | 0.968873i | \(-0.579628\pi\) | ||||
−0.247559 | + | 0.968873i | \(0.579628\pi\) | |||||||
\(948\) | −7.10859e6 | −0.256899 | ||||||||
\(949\) | −1.32616e7 | −0.478003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.30038e6 | 0.225900 | ||||||||
\(952\) | −2.99274e7 | −1.07023 | ||||||||
\(953\) | 2.92858e7 | 1.04454 | 0.522270 | − | 0.852780i | \(-0.325085\pi\) | ||||
0.522270 | + | 0.852780i | \(0.325085\pi\) | |||||||
\(954\) | −1.34191e6 | −0.0477367 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.23981e6 | −0.185426 | ||||||||
\(957\) | −4.88400e6 | −0.172384 | ||||||||
\(958\) | −4.59478e6 | −0.161752 | ||||||||
\(959\) | −2.54582e6 | −0.0893885 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76347e7 | −0.965263 | ||||||||
\(962\) | −5.20462e6 | −0.181323 | ||||||||
\(963\) | −1.66722e7 | −0.579332 | ||||||||
\(964\) | 1.01704e6 | 0.0352487 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.20729e6 | 0.0761055 | ||||||||
\(967\) | 4.41255e7 | 1.51748 | 0.758741 | − | 0.651393i | \(-0.225815\pi\) | ||||
0.758741 | + | 0.651393i | \(0.225815\pi\) | |||||||
\(968\) | 2.86529e6 | 0.0982834 | ||||||||
\(969\) | −1.17585e7 | −0.402294 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.28334e7 | 0.777183 | 0.388592 | − | 0.921410i | \(-0.372962\pi\) | ||||
0.388592 | + | 0.921410i | \(0.372962\pi\) | |||||||
\(972\) | −797148. | −0.0270628 | ||||||||
\(973\) | −745819. | −0.0252552 | ||||||||
\(974\) | 4.31444e6 | 0.145723 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −822347. | −0.0276332 | ||||||||
\(977\) | 5.35594e7 | 1.79515 | 0.897573 | − | 0.440866i | \(-0.145329\pi\) | ||||
0.897573 | + | 0.440866i | \(0.145329\pi\) | |||||||
\(978\) | −2.47516e7 | −0.827476 | ||||||||
\(979\) | 6.66884e6 | 0.222379 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.26279e7 | −0.418948 | ||||||||
\(982\) | −3.97309e7 | −1.31477 | ||||||||
\(983\) | 2.25516e7 | 0.744378 | 0.372189 | − | 0.928157i | \(-0.378607\pi\) | ||||
0.372189 | + | 0.928157i | \(0.378607\pi\) | |||||||
\(984\) | 3.97914e6 | 0.131009 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.99028e7 | −0.651961 | ||||||||
\(987\) | −1.60516e7 | −0.524475 | ||||||||
\(988\) | 4.00248e6 | 0.130448 | ||||||||
\(989\) | 6.08570e6 | 0.197843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.10889e6 | 0.229942 | 0.114971 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114971 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(992\) | 4.48758e6 | 0.144788 | ||||||||
\(993\) | 2.50865e7 | 0.807358 | ||||||||
\(994\) | −1.08190e7 | −0.347312 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.34752e6 | −0.202747 | ||||||||
\(997\) | −3.59868e7 | −1.14658 | −0.573291 | − | 0.819352i | \(-0.694334\pi\) | ||||
−0.573291 | + | 0.819352i | \(0.694334\pi\) | |||||||
\(998\) | −1.85610e7 | −0.589896 | ||||||||
\(999\) | −3.76755e6 | −0.119439 |
(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.f.1.2 | 3 | ||
5.4 | even | 2 | 165.6.a.e.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 495.6.a.a.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.e.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
495.6.a.a.1.2 | 3 | 15.14 | odd | 2 | |||
825.6.a.f.1.2 | 3 | 1.1 | even | 1 | trivial |