Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,4,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("608.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(35.8731612835\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 28x^{3} - 8x^{2} + 73x - 12 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.31928\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.67449 | −0.707155 | −0.353578 | − | 0.935405i | \(-0.615035\pi\) | ||||
−0.353578 | + | 0.935405i | \(0.615035\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.12795 | −0.637543 | −0.318771 | − | 0.947832i | \(-0.603270\pi\) | ||||
−0.318771 | + | 0.947832i | \(0.603270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.511313 | −0.0276083 | −0.0138042 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138042 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.4981 | −0.499931 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.5714 | 0.481634 | 0.240817 | − | 0.970570i | \(-0.422585\pi\) | ||||
0.240817 | + | 0.970570i | \(0.422585\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.1247 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.1915 | 0.450842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68.1582 | 0.972399 | 0.486200 | − | 0.873848i | \(-0.338383\pi\) | ||||
0.486200 | + | 0.873848i | \(0.338383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.87881 | 0.0195234 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.8262 | 0.442651 | 0.221325 | − | 0.975200i | \(-0.428962\pi\) | ||||
0.221325 | + | 0.975200i | \(0.428962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −74.1924 | −0.593539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.810 | 1.06068 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −87.1627 | −0.558128 | −0.279064 | − | 0.960273i | \(-0.590024\pi\) | ||||
−0.279064 | + | 0.960273i | \(0.590024\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.2537 | 0.308537 | 0.154269 | − | 0.988029i | \(-0.450698\pi\) | ||||
0.154269 | + | 0.988029i | \(0.450698\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −64.5659 | −0.340590 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.64461 | 0.0176015 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −199.635 | −0.887020 | −0.443510 | − | 0.896269i | \(-0.646267\pi\) | ||||
−0.443510 | + | 0.896269i | \(0.646267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −191.532 | −0.786400 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −372.432 | −1.41864 | −0.709318 | − | 0.704889i | \(-0.750997\pi\) | ||||
−0.709318 | + | 0.704889i | \(0.750997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 416.493 | 1.47708 | 0.738542 | − | 0.674207i | \(-0.235515\pi\) | ||||
0.738542 | + | 0.674207i | \(0.235515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 96.2140 | 0.318728 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −221.394 | −0.687098 | −0.343549 | − | 0.939135i | \(-0.611629\pi\) | ||||
−0.343549 | + | 0.939135i | \(0.611629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.739 | −0.999238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −250.446 | −0.687637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 107.677 | 0.279066 | 0.139533 | − | 0.990217i | \(-0.455440\pi\) | ||||
0.139533 | + | 0.990217i | \(0.455440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −125.248 | −0.307063 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 69.8153 | 0.162233 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 155.785 | 0.343753 | 0.171877 | − | 0.985118i | \(-0.445017\pi\) | ||||
0.171877 | + | 0.985118i | \(0.445017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −229.061 | −0.480791 | −0.240395 | − | 0.970675i | \(-0.577277\pi\) | ||||
−0.240395 | + | 0.970675i | \(0.577277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.90178 | 0.0138023 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −371.542 | −0.708987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 580.065 | 1.05770 | 0.528852 | − | 0.848714i | \(-0.322623\pi\) | ||||
0.528852 | + | 0.848714i | \(0.322623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −179.411 | −0.313023 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38.2227 | −0.0638901 | −0.0319451 | − | 0.999490i | \(-0.510170\pi\) | ||||
−0.0319451 | + | 0.999490i | \(0.510170\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −803.910 | −1.28891 | −0.644456 | − | 0.764641i | \(-0.722916\pi\) | ||||
−0.644456 | + | 0.764641i | \(0.722916\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 272.619 | 0.419724 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.98449 | −0.0132971 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1034.63 | −1.47348 | −0.736739 | − | 0.676177i | \(-0.763635\pi\) | ||||
−0.736739 | + | 0.676177i | \(0.763635\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −182.350 | −0.250137 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1053.94 | −1.39379 | −0.696897 | − | 0.717171i | \(-0.745436\pi\) | ||||
−0.696897 | + | 0.717171i | \(0.745436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −485.828 | −0.619946 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 320.278 | 0.394683 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −641.103 | −0.763560 | −0.381780 | − | 0.924253i | \(-0.624689\pi\) | ||||
−0.381780 | + | 0.924253i | \(0.624689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.6521 | −0.0307021 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −195.680 | −0.218184 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 135.431 | 0.146262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.9998 | 0.0209348 | 0.0104674 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104674 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −237.181 | −0.240784 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −473.527 | −0.466512 | −0.233256 | − | 0.972415i | \(-0.574938\pi\) | ||||
−0.233256 | + | 0.972415i | \(0.574938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −289.467 | −0.276913 | −0.138456 | − | 0.990369i | \(-0.544214\pi\) | ||||
−0.138456 | + | 0.990369i | \(0.544214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.3921 | −0.0124470 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −390.982 | −0.353249 | −0.176625 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176625 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1268.65 | −1.11481 | −0.557407 | − | 0.830239i | \(-0.688204\pi\) | ||||
−0.557407 | + | 0.830239i | \(0.688204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 733.555 | 0.627261 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1100.46 | 0.916132 | 0.458066 | − | 0.888918i | \(-0.348542\pi\) | ||||
0.458066 | + | 0.888918i | \(0.348542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −348.030 | −0.282209 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −703.587 | −0.555954 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −34.8502 | −0.0268463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1022.25 | −0.768028 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1368.50 | 1.00320 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1419.83 | 1.01595 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2799.28 | −1.95587 | −0.977935 | − | 0.208907i | \(-0.933009\pi\) | ||||
−0.977935 | + | 0.208907i | \(0.933009\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1530.40 | −1.04453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 691.265 | 0.461039 | 0.230520 | − | 0.973068i | \(-0.425957\pi\) | ||||
0.230520 | + | 0.973068i | \(0.425957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.71495 | 0.00633378 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1060.71 | −0.676232 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1044.00 | 0.651057 | 0.325528 | − | 0.945532i | \(-0.394458\pi\) | ||||
0.325528 | + | 0.945532i | \(0.394458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1663.13 | 1.01486 | 0.507429 | − | 0.861694i | \(-0.330596\pi\) | ||||
0.507429 | + | 0.861694i | \(0.330596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 813.509 | 0.485885 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 915.904 | 0.535607 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 621.291 | 0.355830 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1259.39 | 0.706616 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −887.849 | −0.488157 | −0.244079 | − | 0.969755i | \(-0.578485\pi\) | ||||
−0.244079 | + | 0.969755i | \(0.578485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −55.6469 | −0.0299899 | −0.0149950 | − | 0.999888i | \(-0.504773\pi\) | ||||
−0.0149950 | + | 0.999888i | \(0.504773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −920.009 | −0.486133 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −379.590 | −0.196706 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1643.09 | −0.835239 | −0.417620 | − | 0.908622i | \(-0.637136\pi\) | ||||
−0.417620 | + | 0.908622i | \(0.637136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −395.656 | −0.197343 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.9655 | −0.0122208 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2241.78 | 1.07724 | 0.538619 | − | 0.842549i | \(-0.318946\pi\) | ||||
0.538619 | + | 0.842549i | \(0.318946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 460.222 | 0.217141 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2543.96 | −1.17879 | −0.589393 | − | 0.807847i | \(-0.700633\pi\) | ||||
−0.589393 | + | 0.807847i | \(0.700633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 519.985 | 0.236680 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 256.465 | 0.114692 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1084.28 | −0.476512 | −0.238256 | − | 0.971202i | \(-0.576576\pi\) | ||||
−0.238256 | + | 0.971202i | \(0.576576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 37.9356 | 0.0163866 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −572.429 | −0.243087 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2053.26 | 0.857362 | 0.428681 | − | 0.903456i | \(-0.358978\pi\) | ||||
0.428681 | + | 0.903456i | \(0.358978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2066.62 | −0.848676 | −0.424338 | − | 0.905504i | \(-0.639493\pi\) | ||||
−0.424338 | + | 0.905504i | \(0.639493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 841.681 | 0.339994 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1422.99 | 0.565513 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1197.64 | 0.468341 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −76.0885 | −0.0292837 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1250.64 | 0.473787 | 0.236893 | − | 0.971536i | \(-0.423871\pi\) | ||||
0.236893 | + | 0.971536i | \(0.423871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2815.01 | 1.04989 | 0.524945 | − | 0.851136i | \(-0.324086\pi\) | ||||
0.524945 | + | 0.851136i | \(0.324086\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1365.23 | 0.501364 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −593.857 | −0.214774 | −0.107387 | − | 0.994217i | \(-0.534248\pi\) | ||||
−0.107387 | + | 0.994217i | \(0.534248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4805 | −0.00551450 | −0.00275725 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275725 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2131.44 | −0.747961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44.5674 | 0.0154090 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2654.67 | 0.904441 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −659.063 | −0.221295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −333.857 | −0.110495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2228.10 | −0.726961 | −0.363481 | − | 0.931602i | \(-0.618412\pi\) | ||||
−0.363481 | + | 0.931602i | \(0.618412\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 140.449 | 0.0451802 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2968.74 | −0.941704 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.2293 | −0.00851819 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2953.96 | 0.911461 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3552.73 | 1.08137 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2068.17 | −0.621054 | −0.310527 | − | 0.950565i | \(-0.600506\pi\) | ||||
−0.310527 | + | 0.950565i | \(0.600506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1001.46 | 0.296729 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 591.946 | 0.173079 | 0.0865393 | − | 0.996248i | \(-0.472419\pi\) | ||||
0.0865393 | + | 0.996248i | \(0.472419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2519.07 | −0.726920 | −0.363460 | − | 0.931610i | \(-0.618405\pi\) | ||||
−0.363460 | + | 0.931610i | \(0.618405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.0134 | 0.00940313 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3985.94 | 1.12072 | 0.560359 | − | 0.828250i | \(-0.310663\pi\) | ||||
0.560359 | + | 0.828250i | \(0.310663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1578.08 | 0.438054 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3801.73 | 1.04198 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2371.73 | −0.641901 | −0.320951 | − | 0.947096i | \(-0.604002\pi\) | ||||
−0.320951 | + | 0.947096i | \(0.604002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5295.59 | 1.41543 | 0.707715 | − | 0.706498i | \(-0.249726\pi\) | ||||
0.707715 | + | 0.706498i | \(0.249726\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3347.82 | −0.883798 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2443.02 | 0.637057 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −990.369 | −0.255124 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3872.69 | 0.985629 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5766.76 | 1.45018 | 0.725088 | − | 0.688656i | \(-0.241799\pi\) | ||||
0.725088 | + | 0.688656i | \(0.241799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 857.945 | 0.213196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1785.17 | 0.438398 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3631.88 | 0.881518 | 0.440759 | − | 0.897625i | \(-0.354709\pi\) | ||||
0.440759 | + | 0.897625i | \(0.354709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 102.076 | 0.0244891 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1176.53 | 0.279025 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5848.72 | −1.37128 | −0.685641 | − | 0.727940i | \(-0.740478\pi\) | ||||
−0.685641 | + | 0.727940i | \(0.740478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −767.513 | −0.177917 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2355.73 | 0.539955 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4283.31 | −0.970848 | −0.485424 | − | 0.874279i | \(-0.661335\pi\) | ||||
−0.485424 | + | 0.874279i | \(0.661335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2350.55 | −0.526885 | −0.263443 | − | 0.964675i | \(-0.584858\pi\) | ||||
−0.263443 | + | 0.964675i | \(0.584858\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 97.9327 | 0.0217112 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1303.66 | −0.285869 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7901.74 | 1.71397 | 0.856985 | − | 0.515342i | \(-0.172335\pi\) | ||||
0.856985 | + | 0.515342i | \(0.172335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −718.826 | −0.154247 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1555.29 | −0.330180 | −0.165090 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165090 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3037.74 | −0.638073 | −0.319036 | − | 0.947742i | \(-0.603359\pi\) | ||||
−0.319036 | + | 0.947742i | \(0.603359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −497.639 | −0.103430 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 190.429 | 0.0391662 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −267.461 | −0.0544394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −73.4892 | −0.0148042 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4477.08 | 0.892676 | 0.446338 | − | 0.894864i | \(-0.352728\pi\) | ||||
0.446338 | + | 0.894864i | \(0.352728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1110.43 | −0.219157 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2614.80 | 0.510862 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2545.05 | 0.492254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −212.959 | −0.0407798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1739.97 | 0.329896 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1632.73 | 0.306525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1580.87 | −0.293893 | −0.146947 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1063.64 | 0.195820 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3241.23 | 0.590975 | 0.295488 | − | 0.955347i | \(-0.404518\pi\) | ||||
0.295488 | + | 0.955347i | \(0.404518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9579.34 | −1.72989 | −0.864946 | − | 0.501865i | \(-0.832647\pi\) | ||||
−0.864946 | + | 0.501865i | \(0.832647\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −49.1955 | −0.00879954 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5152.39 | 0.912894 | 0.456447 | − | 0.889751i | \(-0.349122\pi\) | ||||
0.456447 | + | 0.889751i | \(0.349122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1531.57 | −0.268813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1436.66 | 0.249802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1295.01 | −0.223084 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3867.26 | −0.660052 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4661.64 | 0.788347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 113.202 | 0.0189696 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4909.62 | −0.815278 | −0.407639 | − | 0.913143i | \(-0.633648\pi\) | ||||
−0.407639 | + | 0.913143i | \(0.633648\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2694.70 | 0.443449 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4134.67 | −0.674332 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5662.83 | −0.915353 | −0.457677 | − | 0.889119i | \(-0.651318\pi\) | ||||
−0.457677 | + | 0.889119i | \(0.651318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4043.64 | −0.647847 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 935.743 | 0.148602 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 350.627 | 0.0551956 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1278.83 | 0.199565 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12194.6 | −1.88658 | −0.943289 | − | 0.331973i | \(-0.892286\pi\) | ||||
−0.943289 | + | 0.331973i | \(0.892286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2887.35 | 0.442854 | 0.221427 | − | 0.975177i | \(-0.428929\pi\) | ||||
0.221427 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7756.67 | 1.17955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1828.06 | 0.275632 | 0.137816 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137816 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 272.449 | 0.0407327 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 128.057 | 0.0189845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2027.89 | −0.298128 | −0.149064 | − | 0.988828i | \(-0.547626\pi\) | ||||
−0.149064 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3756.23 | 0.543115 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5730.23 | 0.821737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3450.93 | 0.490836 | 0.245418 | − | 0.969417i | \(-0.421075\pi\) | ||||
0.245418 | + | 0.969417i | \(0.421075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5027.14 | 0.709220 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −55.0565 | −0.00770455 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5713.27 | −0.793089 | −0.396544 | − | 0.918016i | \(-0.629791\pi\) | ||||
−0.396544 | + | 0.918016i | \(0.629791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5217.16 | −0.718434 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4543.33 | −0.620672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7828.71 | 1.06104 | 0.530519 | − | 0.847673i | \(-0.321997\pi\) | ||||
0.530519 | + | 0.847673i | \(0.321997\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10285.9 | 1.38310 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11760.3 | 1.56898 | 0.784492 | − | 0.620139i | \(-0.212924\pi\) | ||||
0.784492 | + | 0.620139i | \(0.212924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 64.0410 | 0.00847748 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5621.89 | −0.738441 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6717.76 | −0.875589 | −0.437795 | − | 0.899075i | \(-0.644240\pi\) | ||||
−0.437795 | + | 0.899075i | \(0.644240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3327.90 | 0.430433 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2540.05 | −0.326026 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7374.78 | 0.939406 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12360.2 | −1.56257 | −0.781287 | − | 0.624172i | \(-0.785436\pi\) | ||||
−0.781287 | + | 0.624172i | \(0.785436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −35.6975 | −0.00447897 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2006.45 | 0.249869 | 0.124934 | − | 0.992165i | \(-0.460128\pi\) | ||||
0.124934 | + | 0.992165i | \(0.460128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2775.83 | 0.343112 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1299.78 | 0.159473 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3507.86 | −0.427219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5154.98 | 0.623221 | 0.311611 | − | 0.950210i | \(-0.399132\pi\) | ||||
0.311611 | + | 0.950210i | \(0.399132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3836.16 | −0.460398 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −79.6548 | −0.00949045 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7512.42 | 0.888603 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6111.17 | −0.717662 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5037.60 | 0.587357 | 0.293679 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293679 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4025.51 | −0.466013 | −0.233006 | − | 0.972475i | \(-0.574856\pi\) | ||||
−0.233006 | + | 0.972475i | \(0.574856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2988.41 | 0.343502 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5056.82 | −0.577157 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 117.122 | 0.0132738 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3365.48 | −0.378757 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2863.81 | −0.320057 | −0.160029 | − | 0.987112i | \(-0.551159\pi\) | ||||
−0.160029 | + | 0.987112i | \(0.551159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6617.66 | −0.734468 | −0.367234 | − | 0.930129i | \(-0.619695\pi\) | ||||
−0.367234 | + | 0.930129i | \(0.619695\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2282.93 | −0.251627 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −927.698 | −0.101551 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8810.03 | −0.957813 | −0.478907 | − | 0.877866i | \(-0.658967\pi\) | ||||
−0.478907 | + | 0.877866i | \(0.658967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4626.33 | 0.499550 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 202.487 | 0.0217165 | 0.0108583 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108583 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4569.75 | 0.486802 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3262.39 | 0.345203 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4619.26 | 0.485516 | 0.242758 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242758 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6544.15 | −0.683264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 204.474 | 0.0212075 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 189.974 | 0.0195739 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8196.37 | −0.838972 | −0.419486 | − | 0.907762i | \(-0.637790\pi\) | ||||
−0.419486 | + | 0.907762i | \(0.637790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10142.6 | 1.03141 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1269.48 | −0.128255 | −0.0641277 | − | 0.997942i | \(-0.520426\pi\) | ||||
−0.0641277 | + | 0.997942i | \(0.520426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8502.91 | 0.853485 | 0.426743 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426743 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1394.80 | 0.139101 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8132.55 | −0.805845 | −0.402923 | − | 0.915234i | \(-0.632006\pi\) | ||||
−0.402923 | + | 0.915234i | \(0.632006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −296.595 | −0.0292014 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6037.50 | 0.590644 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7318.37 | 0.711414 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1409.66 | 0.136167 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1453.43 | −0.139514 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15965.6 | 1.52293 | 0.761466 | − | 0.648205i | \(-0.224480\pi\) | ||||
0.761466 | + | 0.648205i | \(0.224480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10405.9 | −0.986421 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 91.7353 | 0.00864203 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −142.558 | −0.0133468 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11358.3 | −1.05687 | −0.528435 | − | 0.848974i | \(-0.677221\pi\) | ||||
−0.528435 | + | 0.848974i | \(0.677221\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8237.40 | −0.761775 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5256.31 | −0.483124 | −0.241562 | − | 0.970385i | \(-0.577660\pi\) | ||||
−0.241562 | + | 0.970385i | \(0.577660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5940.85 | −0.542723 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1690.62 | 0.153510 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.5438 | 0.00176390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11667.7 | −1.04673 | −0.523364 | − | 0.852109i | \(-0.675323\pi\) | ||||
−0.523364 | + | 0.852109i | \(0.675323\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9347.73 | 0.833585 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16902.2 | −1.49828 | −0.749139 | − | 0.662413i | \(-0.769533\pi\) | ||||
−0.749139 | + | 0.662413i | \(0.769533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3375.27 | 0.297421 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1910.68 | −0.167369 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2828.32 | 0.246293 | 0.123147 | − | 0.992388i | \(-0.460701\pi\) | ||||
0.123147 | + | 0.992388i | \(0.460701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 411.050 | 0.0355847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2827.39 | −0.243338 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2063.30 | 0.176544 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3890.20 | −0.330930 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3984.18 | 0.336968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6552.16 | 0.550970 | 0.275485 | − | 0.961305i | \(-0.411162\pi\) | ||||
0.275485 | + | 0.961305i | \(0.411162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7136.05 | 0.596631 | 0.298315 | − | 0.954467i | \(-0.403575\pi\) | ||||
0.298315 | + | 0.954467i | \(0.403575\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −139.394 | −0.0115879 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3629.68 | 0.300021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9783.00 | −0.804060 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2102.80 | −0.171853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19412.9 | −1.57761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2786.90 | 0.225212 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7544.68 | −0.606288 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6022.40 | −0.481267 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22860.0 | −1.81669 | −0.908343 | − | 0.418227i | \(-0.862652\pi\) | ||||
−0.908343 | + | 0.418227i | \(0.862652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7593.76 | 0.600146 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9042.88 | 0.710742 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9176.33 | −0.717279 | −0.358639 | − | 0.933476i | \(-0.616759\pi\) | ||||
−0.358639 | + | 0.933476i | \(0.616759\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3091.90 | 0.240362 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1656.09 | 0.128043 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 529.019 | 0.0406803 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5228.74 | −0.399906 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23966.7 | −1.82316 | −0.911581 | − | 0.411120i | \(-0.865138\pi\) | ||||
−0.911581 | + | 0.411120i | \(0.865138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21709.6 | 1.64261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4400.70 | −0.331190 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1356.83 | −0.101569 | −0.0507847 | − | 0.998710i | \(-0.516172\pi\) | ||||
−0.0507847 | + | 0.998710i | \(0.516172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7844.04 | −0.584073 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 93.2381 | 0.00690588 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16869.9 | −1.24292 | −0.621461 | − | 0.783445i | \(-0.713461\pi\) | ||||
−0.621461 | + | 0.783445i | \(0.713461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19377.3 | −1.42016 | −0.710082 | − | 0.704119i | \(-0.751342\pi\) | ||||
−0.710082 | + | 0.704119i | \(0.751342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4595.47 | −0.335041 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3622.53 | −0.262730 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16335.8 | −1.17863 | −0.589313 | − | 0.807905i | \(-0.700602\pi\) | ||||
−0.589313 | + | 0.807905i | \(0.700602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10343.7 | −0.742435 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 538.893 | 0.0384803 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1892.03 | 0.134408 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5015.13 | 0.354445 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9216.05 | −0.648019 | −0.324009 | − | 0.946054i | \(-0.605031\pi\) | ||||
−0.324009 | + | 0.946054i | \(0.605031\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1011.82 | −0.0707833 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2182.12 | 0.151879 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7176.76 | −0.496988 | −0.248494 | − | 0.968633i | \(-0.579936\pi\) | ||||
−0.248494 | + | 0.968633i | \(0.579936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 248.410 | 0.0171157 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 56.8830 | 0.00389961 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3445.62 | 0.235032 | 0.117516 | − | 0.993071i | \(-0.462507\pi\) | ||||
0.117516 | + | 0.993071i | \(0.462507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17940.3 | 1.21764 | 0.608820 | − | 0.793308i | \(-0.291643\pi\) | ||||
0.608820 | + | 0.793308i | \(0.291643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7829.80 | −0.528779 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7286.51 | 0.489651 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14232.0 | 0.951664 | 0.475832 | − | 0.879536i | \(-0.342147\pi\) | ||||
0.475832 | + | 0.879536i | \(0.342147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −163.763 | −0.0108965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11540.1 | −0.764095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19440.3 | 1.28089 | 0.640446 | − | 0.768003i | \(-0.278749\pi\) | ||||
0.640446 | + | 0.768003i | \(0.278749\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9754.56 | −0.639580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −359.820 | −0.0234778 | −0.0117389 | − | 0.999931i | \(-0.503737\pi\) | ||||
−0.0117389 | + | 0.999931i | \(0.503737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18561.5 | 1.20525 | 0.602624 | − | 0.798026i | \(-0.294122\pi\) | ||||
0.602624 | + | 0.798026i | \(0.294122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7265.82 | 0.469513 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 327.805 | 0.0210806 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −846.443 | −0.0541723 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1226.75 | 0.0781368 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13606.7 | −0.862538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9684.27 | −0.610974 | −0.305487 | − | 0.952196i | \(-0.598819\pi\) | ||||
−0.305487 | + | 0.952196i | \(0.598819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8187.13 | 0.514075 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19953.1 | 1.24695 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17865.1 | −1.11121 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 515.935 | 0.0319407 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4576.97 | −0.282027 | −0.141014 | − | 0.990008i | \(-0.545036\pi\) | ||||
−0.141014 | + | 0.990008i | \(0.545036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9722.95 | −0.596323 | −0.298161 | − | 0.954515i | \(-0.596373\pi\) | ||||
−0.298161 | + | 0.954515i | \(0.596373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10908.6 | 0.665931 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9150.86 | −0.556040 | −0.278020 | − | 0.960575i | \(-0.589678\pi\) | ||||
−0.278020 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2737.36 | 0.165563 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 100.054 | 0.00602369 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9202.67 | −0.551498 | −0.275749 | − | 0.961230i | \(-0.588926\pi\) | ||||
−0.275749 | + | 0.961230i | \(0.588926\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4927.30 | −0.293932 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10851.3 | 0.644367 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5007.55 | −0.296004 | −0.148002 | − | 0.988987i | \(-0.547284\pi\) | ||||
−0.148002 | + | 0.988987i | \(0.547284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21922.2 | −1.28998 | −0.644989 | − | 0.764192i | \(-0.723138\pi\) | ||||
−0.644989 | + | 0.764192i | \(0.723138\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13054.4 | −0.764695 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −69.2477 | −0.00403806 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4255.82 | −0.247056 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7599.47 | 0.439182 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4024.92 | −0.231565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13736.9 | 0.786806 | 0.393403 | − | 0.919366i | \(-0.371298\pi\) | ||||
0.393403 | + | 0.919366i | \(0.371298\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11040.6 | −0.629558 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20015.0 | 1.13625 | 0.568123 | − | 0.822944i | \(-0.307670\pi\) | ||||
0.568123 | + | 0.822944i | \(0.307670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2262 | −0.000577975 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2175.10 | −0.122393 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23674.0 | 1.32630 | 0.663148 | − | 0.748488i | \(-0.269220\pi\) | ||||
0.663148 | + | 0.748488i | \(0.269220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7441.56 | −0.415077 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9256.29 | 0.514046 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5612.61 | 0.310339 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2796.62 | 0.153963 | 0.0769815 | − | 0.997033i | \(-0.475472\pi\) | ||||
0.0769815 | + | 0.997033i | \(0.475472\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 121.274 | 0.00664765 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11854.7 | −0.647015 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25384.3 | −1.37948 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14646.3 | −0.792522 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −222.627 | −0.0119950 | −0.00599750 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599750 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3793.06 | 0.203496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5798.65 | −0.309773 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 242.121 | 0.0128796 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1068.75 | −0.0566119 | −0.0283059 | − | 0.999599i | \(-0.509011\pi\) | ||||
−0.0283059 | + | 0.999599i | \(0.509011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13965.6 | 0.736638 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2600.18 | 0.136574 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6528.52 | −0.341472 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8714.89 | 0.453924 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27102.1 | 1.40575 | 0.702876 | − | 0.711312i | \(-0.251899\pi\) | ||||
0.702876 | + | 0.711312i | \(0.251899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 148.008 | 0.00764509 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19458.6 | −1.00093 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6466.81 | 0.331271 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6285.65 | 0.320663 | 0.160331 | − | 0.987063i | \(-0.448744\pi\) | ||||
0.160331 | + | 0.987063i | \(0.448744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17225.0 | 0.875120 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28387.4 | 1.43632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1594.38 | 0.0803406 | 0.0401703 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401703 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8976.85 | −0.450498 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10192.6 | 0.509427 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11152.4 | −0.555141 | −0.277571 | − | 0.960705i | \(-0.589529\pi\) | ||||
−0.277571 | + | 0.960705i | \(0.589529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3639.10 | 0.180413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35565.1 | 1.75606 | 0.878032 | − | 0.478601i | \(-0.158856\pi\) | ||||
0.878032 | + | 0.478601i | \(0.158856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6328.54 | 0.311221 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14226.2 | 0.696801 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 199.915 | 0.00975263 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33922.2 | 1.64825 | 0.824126 | − | 0.566406i | \(-0.191667\pi\) | ||||
0.824126 | + | 0.566406i | \(0.191667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21189.9 | −1.02550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 396.648 | 0.0191199 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18859.2 | −0.905479 | −0.452740 | − | 0.891643i | \(-0.649553\pi\) | ||||
−0.452740 | + | 0.891643i | \(0.649553\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3152.51 | −0.150763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15707.4 | 0.748217 | 0.374109 | − | 0.927385i | \(-0.377949\pi\) | ||||
0.374109 | + | 0.927385i | \(0.377949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 648.679 | 0.0307782 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6557.78 | 0.309931 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8120.23 | 0.382275 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1292.73 | 0.0606202 | 0.0303101 | − | 0.999541i | \(-0.490351\pi\) | ||||
0.0303101 | + | 0.999541i | \(0.490351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13345.3 | −0.623370 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38483.0 | 1.79060 | 0.895301 | − | 0.445461i | \(-0.146960\pi\) | ||||
0.895301 | + | 0.445461i | \(0.146960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3951.02 | −0.183129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −375.077 | −0.0173176 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7076.20 | 0.325457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −671.626 | −0.0307717 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12970.7 | −0.591997 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11711.8 | 0.532501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18911.7 | −0.856579 | −0.428290 | − | 0.903641i | \(-0.640884\pi\) | ||||
−0.428290 | + | 0.903641i | \(0.640884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21491.0 | 0.969710 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −562.682 | −0.0252929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11939.7 | −0.534668 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2820.22 | 0.125815 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35376.1 | 1.57225 | 0.786127 | − | 0.618065i | \(-0.212083\pi\) | ||||
0.786127 | + | 0.618065i | \(0.212083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15089.8 | −0.668134 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8653.71 | 0.381727 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14125.8 | −0.620784 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 177.953 | 0.00779131 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15739.0 | 0.686541 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29057.9 | 1.26282 | 0.631411 | − | 0.775448i | \(-0.282476\pi\) | ||||
0.631411 | + | 0.775448i | \(0.282476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25476.2 | 1.10307 | 0.551534 | − | 0.834152i | \(-0.314043\pi\) | ||||
0.551534 | + | 0.834152i | \(0.314043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8637.07 | 0.372590 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15979.3 | −0.686786 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7913.37 | −0.338866 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 359.753 | 0.0153490 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41186.3 | 1.75081 | 0.875403 | − | 0.483394i | \(-0.160596\pi\) | ||||
0.875403 | + | 0.483394i | \(0.160596\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9004.24 | −0.381371 | −0.190685 | − | 0.981651i | \(-0.561071\pi\) | ||||
−0.190685 | + | 0.981651i | \(0.561071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4790.30 | 0.202154 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11943.7 | 0.502204 | 0.251102 | − | 0.967961i | \(-0.419207\pi\) | ||||
0.251102 | + | 0.967961i | \(0.419207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 869.327 | 0.0364209 | 0.0182105 | − | 0.999834i | \(-0.494203\pi\) | ||||
0.0182105 | + | 0.999834i | \(0.494203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29034.8 | −1.21204 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23360.4 | −0.971658 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18133.2 | 0.751526 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7924.68 | 0.327261 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1265.71 | −0.0520824 | −0.0260412 | − | 0.999661i | \(-0.508290\pi\) | ||||
−0.0260412 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16791.7 | −0.688493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5714.88 | 0.233489 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3706.43 | −0.150893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 522.688 | 0.0212040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11162.1 | 0.451217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9747.40 | −0.392640 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15823.2 | 0.635143 | 0.317572 | − | 0.948234i | \(-0.397133\pi\) | ||||
0.317572 | + | 0.948234i | \(0.397133\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1828.07 | −0.0731211 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36570.0 | 1.45765 | 0.728825 | − | 0.684700i | \(-0.240067\pi\) | ||||
0.728825 | + | 0.684700i | \(0.240067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18900.5 | 0.750731 | 0.375366 | − | 0.926877i | \(-0.377517\pi\) | ||||
0.375366 | + | 0.926877i | \(0.377517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −699.730 | −0.0276966 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30643.8 | 1.20872 | 0.604361 | − | 0.796710i | \(-0.293428\pi\) | ||||
0.604361 | + | 0.796710i | \(0.293428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7728.71 | 0.303797 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 982.780 | 0.0384971 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18179.9 | −0.709678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30235.7 | 1.17623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −269.961 | −0.0104660 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −725.979 | −0.0280487 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33839.9 | −1.30295 | −0.651477 | − | 0.758668i | \(-0.725850\pi\) | ||||
−0.651477 | + | 0.758668i | \(0.725850\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16451.0 | −0.631261 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3158.38 | −0.120781 | −0.0603907 | − | 0.998175i | \(-0.519235\pi\) | ||||
−0.0603907 | + | 0.998175i | \(0.519235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39820.3 | 1.51762 | 0.758810 | − | 0.651312i | \(-0.225781\pi\) | ||||
0.758810 | + | 0.651312i | \(0.225781\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4080.24 | 0.154978 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50176.9 | −1.89941 | −0.949705 | − | 0.313146i | \(-0.898617\pi\) | ||||
−0.949705 | + | 0.313146i | \(0.898617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1431.31 | 0.0539983 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3204.15 | −0.120475 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4206.48 | 0.157631 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14635.5 | −0.546605 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9351.76 | −0.348100 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4641.74 | −0.172203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7339.04 | 0.271364 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 782.513 | 0.0288377 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14730.7 | 0.541068 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42737.3 | −1.56457 | −0.782287 | − | 0.622918i | \(-0.785947\pi\) | ||||
−0.782287 | + | 0.622918i | \(0.785947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6391.74 | 0.233224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47034.3 | −1.71056 | −0.855278 | − | 0.518170i | \(-0.826614\pi\) | ||||
−0.855278 | + | 0.518170i | \(0.826614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18519.2 | −0.671299 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5999.46 | −0.216761 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −353.453 | −0.0127285 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35256.7 | 1.26552 | 0.632759 | − | 0.774349i | \(-0.281922\pi\) | ||||
0.632759 | + | 0.774349i | \(0.281922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5808.90 | 0.207828 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1992.35 | −0.0710497 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14811.4 | 0.526481 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3907.26 | 0.138437 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3588.82 | 0.126744 | 0.0633720 | − | 0.997990i | \(-0.479815\pi\) | ||||
0.0633720 | + | 0.997990i | \(0.479815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6512.03 | 0.229241 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11909.9 | −0.417911 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8536.68 | −0.298587 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13741.6 | −0.479101 | −0.239551 | − | 0.970884i | \(-0.577000\pi\) | ||||
−0.239551 | + | 0.970884i | \(0.577000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35199.1 | 1.22330 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31893.3 | 1.10488 | 0.552440 | − | 0.833553i | \(-0.313697\pi\) | ||||
0.552440 | + | 0.833553i | \(0.313697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18184.4 | −0.627960 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 542.355 | 0.0186696 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22540.6 | 0.773465 | 0.386733 | − | 0.922192i | \(-0.373604\pi\) | ||||
0.386733 | + | 0.922192i | \(0.373604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41903.6 | −1.43335 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18932.4 | −0.645558 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2204.23 | −0.0749233 | −0.0374617 | − | 0.999298i | \(-0.511927\pi\) | ||||
−0.0374617 | + | 0.999298i | \(0.511927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8914.51 | −0.302060 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5627.74 | 0.190093 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −533.810 | −0.0179746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26955.0 | −0.904805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5277.54 | 0.176600 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20065.2 | −0.669350 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56851.1 | −1.89060 | −0.945299 | − | 0.326205i | \(-0.894230\pi\) | ||||
−0.945299 | + | 0.326205i | \(0.894230\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4758.48 | 0.157755 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48267.9 | 1.59525 | 0.797627 | − | 0.603151i | \(-0.206088\pi\) | ||||
0.797627 | + | 0.603151i | \(0.206088\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −850.383 | −0.0280185 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14210.2 | 0.466759 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32914.4 | 1.07781 | 0.538907 | − | 0.842366i | \(-0.318838\pi\) | ||||
0.538907 | + | 0.842366i | \(0.318838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11265.1 | −0.367757 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17124.4 | 0.557331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29352.6 | −0.952394 | −0.476197 | − | 0.879338i | \(-0.657985\pi\) | ||||
−0.476197 | + | 0.879338i | \(0.657985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4232.98 | 0.136928 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −415.958 | −0.0134145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20335.8 | 0.653832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2460.63 | −0.0788744 | −0.0394372 | − | 0.999222i | \(-0.512557\pi\) | ||||
−0.0394372 | + | 0.999222i | \(0.512557\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18040.3 | 0.576528 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 110.344 | 0.00351573 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 971.621 | 0.0308641 | 0.0154321 | − | 0.999881i | \(-0.495088\pi\) | ||||
0.0154321 | + | 0.999881i | \(0.495088\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29707.6 | −0.940849 |
(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 | 608.4.a.h.1.2 | yes | 5 | |
4.3 | odd | 2 | 608.4.a.e.1.4 | ✓ | 5 | ||
8.3 | odd | 2 | 1216.4.a.bd.1.2 | 5 | |||
8.5 | even | 2 | 1216.4.a.y.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.e.1.4 | ✓ | 5 | 4.3 | odd | 2 | ||
608.4.a.h.1.2 | yes | 5 | 1.1 | even | 1 | trivial | |
1216.4.a.y.1.4 | 5 | 8.5 | even | 2 | |||
1216.4.a.bd.1.2 | 5 | 8.3 | odd | 2 |