Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.43510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43510 | −1.72188 | −0.860938 | − | 0.508710i | \(-0.830123\pi\) | ||||
−0.860938 | + | 0.508710i | \(0.830123\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.92972 | 1.96486 | ||||||||
\(5\) | −3.49556 | −1.56326 | −0.781632 | − | 0.623740i | \(-0.785612\pi\) | ||||
−0.781632 | + | 0.623740i | \(0.785612\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.87125 | −1.84116 | −0.920581 | − | 0.390553i | \(-0.872284\pi\) | ||||
−0.920581 | + | 0.390553i | \(0.872284\pi\) | |||||||
\(8\) | −4.69905 | −1.66137 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.51205 | 2.69175 | ||||||||
\(11\) | 1.63115 | 0.491810 | 0.245905 | − | 0.969294i | \(-0.420915\pi\) | ||||
0.245905 | + | 0.969294i | \(0.420915\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07695 | −1.40809 | −0.704046 | − | 0.710155i | \(-0.748625\pi\) | ||||
−0.704046 | + | 0.710155i | \(0.748625\pi\) | |||||||
\(14\) | 11.8620 | 3.17025 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.58324 | 0.895809 | ||||||||
\(17\) | −7.41068 | −1.79735 | −0.898677 | − | 0.438611i | \(-0.855471\pi\) | ||||
−0.898677 | + | 0.438611i | \(0.855471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.289958 | 0.0665210 | 0.0332605 | − | 0.999447i | \(-0.489411\pi\) | ||||
0.0332605 | + | 0.999447i | \(0.489411\pi\) | |||||||
\(20\) | −13.7366 | −3.07159 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.97201 | −0.846836 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.21896 | 1.44379 | ||||||||
\(26\) | 12.3629 | 2.42456 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −19.1426 | −3.61762 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20829 | −0.217016 | −0.108508 | − | 0.994096i | \(-0.534607\pi\) | ||||
−0.108508 | + | 0.994096i | \(0.534607\pi\) | |||||||
\(32\) | 0.672566 | 0.118894 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.0458 | 3.09482 | ||||||||
\(35\) | 17.0278 | 2.87822 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.03076 | 0.333855 | 0.166927 | − | 0.985969i | \(-0.446615\pi\) | ||||
0.166927 | + | 0.985969i | \(0.446615\pi\) | |||||||
\(38\) | −0.706078 | −0.114541 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 16.4258 | 2.59715 | ||||||||
\(41\) | 10.9339 | 1.70758 | 0.853792 | − | 0.520615i | \(-0.174297\pi\) | ||||
0.853792 | + | 0.520615i | \(0.174297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.66129 | 0.863339 | 0.431670 | − | 0.902032i | \(-0.357925\pi\) | ||||
0.431670 | + | 0.902032i | \(0.357925\pi\) | |||||||
\(44\) | 6.40996 | 0.966337 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.43510 | −0.359036 | ||||||||
\(47\) | −5.12682 | −0.747823 | −0.373912 | − | 0.927464i | \(-0.621984\pi\) | ||||
−0.373912 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.7291 | 2.38987 | ||||||||
\(50\) | −17.5789 | −2.48603 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.9510 | −2.76670 | ||||||||
\(53\) | −7.16900 | −0.984737 | −0.492369 | − | 0.870387i | \(-0.663869\pi\) | ||||
−0.492369 | + | 0.870387i | \(0.663869\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.70179 | −0.768829 | ||||||||
\(56\) | 22.8903 | 3.05884 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.43510 | 0.319744 | ||||||||
\(59\) | 0.758039 | 0.0986883 | 0.0493441 | − | 0.998782i | \(-0.484287\pi\) | ||||
0.0493441 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5695 | 1.48133 | 0.740663 | − | 0.671876i | \(-0.234511\pi\) | ||||
0.740663 | + | 0.671876i | \(0.234511\pi\) | |||||||
\(62\) | 2.94232 | 0.373675 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.80424 | −1.10053 | ||||||||
\(65\) | 17.7468 | 2.20122 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.60778 | 0.440761 | 0.220380 | − | 0.975414i | \(-0.429270\pi\) | ||||
0.220380 | + | 0.975414i | \(0.429270\pi\) | |||||||
\(68\) | −29.1219 | −3.53155 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −41.4644 | −4.95594 | ||||||||
\(71\) | −8.89620 | −1.05579 | −0.527893 | − | 0.849311i | \(-0.677018\pi\) | ||||
−0.527893 | + | 0.849311i | \(0.677018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.62827 | −0.307616 | −0.153808 | − | 0.988101i | \(-0.549154\pi\) | ||||
−0.153808 | + | 0.988101i | \(0.549154\pi\) | |||||||
\(74\) | −4.94510 | −0.574857 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.13945 | 0.130704 | ||||||||
\(77\) | −7.94575 | −0.905502 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.77211 | −0.424395 | −0.212198 | − | 0.977227i | \(-0.568062\pi\) | ||||
−0.212198 | + | 0.977227i | \(0.568062\pi\) | |||||||
\(80\) | −12.5254 | −1.40039 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −26.6251 | −2.94025 | ||||||||
\(83\) | 10.7050 | 1.17502 | 0.587510 | − | 0.809217i | \(-0.300108\pi\) | ||||
0.587510 | + | 0.809217i | \(0.300108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.9045 | 2.80974 | ||||||||
\(86\) | −13.7858 | −1.48656 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.66486 | −0.817077 | ||||||||
\(89\) | 4.54315 | 0.481573 | 0.240786 | − | 0.970578i | \(-0.422595\pi\) | ||||
0.240786 | + | 0.970578i | \(0.422595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.7311 | 2.59252 | ||||||||
\(92\) | 3.92972 | 0.409701 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.4843 | 1.28766 | ||||||||
\(95\) | −1.01357 | −0.103990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.62406 | −0.266433 | −0.133217 | − | 0.991087i | \(-0.542531\pi\) | ||||
−0.133217 | + | 0.991087i | \(0.542531\pi\) | |||||||
\(98\) | −40.7371 | −4.11507 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.3685 | 2.83685 | ||||||||
\(101\) | −18.5441 | −1.84521 | −0.922604 | − | 0.385748i | \(-0.873943\pi\) | ||||
−0.922604 | + | 0.385748i | \(0.873943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.66490 | 0.656712 | 0.328356 | − | 0.944554i | \(-0.393505\pi\) | ||||
0.328356 | + | 0.944554i | \(0.393505\pi\) | |||||||
\(104\) | 23.8568 | 2.33936 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.4572 | 1.69560 | ||||||||
\(107\) | 13.0781 | 1.26431 | 0.632156 | − | 0.774841i | \(-0.282170\pi\) | ||||
0.632156 | + | 0.774841i | \(0.282170\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.3526 | 1.27895 | 0.639476 | − | 0.768811i | \(-0.279152\pi\) | ||||
0.639476 | + | 0.768811i | \(0.279152\pi\) | |||||||
\(110\) | 13.8844 | 1.32383 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.4549 | −1.64933 | ||||||||
\(113\) | −4.16536 | −0.391844 | −0.195922 | − | 0.980619i | \(-0.562770\pi\) | ||||
−0.195922 | + | 0.980619i | \(0.562770\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.49556 | −0.325963 | ||||||||
\(116\) | −3.92972 | −0.364865 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.84590 | −0.169929 | ||||||||
\(119\) | 36.0993 | 3.30922 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.33935 | −0.758123 | ||||||||
\(122\) | −28.1730 | −2.55066 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.74825 | −0.426405 | ||||||||
\(125\) | −7.75651 | −0.693763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0964 | −0.895909 | −0.447954 | − | 0.894056i | \(-0.647847\pi\) | ||||
−0.447954 | + | 0.894056i | \(0.647847\pi\) | |||||||
\(128\) | 20.0941 | 1.77608 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −43.2152 | −3.79023 | ||||||||
\(131\) | 20.4223 | 1.78430 | 0.892151 | − | 0.451736i | \(-0.149195\pi\) | ||||
0.892151 | + | 0.451736i | \(0.149195\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41246 | −0.122476 | ||||||||
\(134\) | −8.78531 | −0.758935 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34.8232 | 2.98606 | ||||||||
\(137\) | 10.9157 | 0.932591 | 0.466296 | − | 0.884629i | \(-0.345588\pi\) | ||||
0.466296 | + | 0.884629i | \(0.345588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.60677 | −0.814836 | −0.407418 | − | 0.913242i | \(-0.633571\pi\) | ||||
−0.407418 | + | 0.913242i | \(0.633571\pi\) | |||||||
\(140\) | 66.9143 | 5.65529 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.6632 | 1.81793 | ||||||||
\(143\) | −8.28126 | −0.692514 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.49556 | 0.290291 | ||||||||
\(146\) | 6.40011 | 0.529677 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.98031 | 0.655977 | ||||||||
\(149\) | 3.92991 | 0.321950 | 0.160975 | − | 0.986958i | \(-0.448536\pi\) | ||||
0.160975 | + | 0.986958i | \(0.448536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.79351 | 0.796985 | 0.398492 | − | 0.917172i | \(-0.369534\pi\) | ||||
0.398492 | + | 0.917172i | \(0.369534\pi\) | |||||||
\(152\) | −1.36253 | −0.110516 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.3487 | 1.55916 | ||||||||
\(155\) | 4.22367 | 0.339253 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.60539 | −0.128124 | −0.0640621 | − | 0.997946i | \(-0.520406\pi\) | ||||
−0.0640621 | + | 0.997946i | \(0.520406\pi\) | |||||||
\(158\) | 9.18546 | 0.730756 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.35100 | −0.185863 | ||||||||
\(161\) | −4.87125 | −0.383909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5495 | −1.21793 | −0.608964 | − | 0.793198i | \(-0.708414\pi\) | ||||
−0.608964 | + | 0.793198i | \(0.708414\pi\) | |||||||
\(164\) | 42.9670 | 3.35516 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.0676 | −2.02324 | ||||||||
\(167\) | −0.764987 | −0.0591965 | −0.0295982 | − | 0.999562i | \(-0.509423\pi\) | ||||
−0.0295982 | + | 0.999562i | \(0.509423\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7754 | 0.982722 | ||||||||
\(170\) | −63.0801 | −4.83802 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.2473 | 1.69634 | ||||||||
\(173\) | −2.00062 | −0.152104 | −0.0760521 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760521 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −35.1654 | −2.65825 | ||||||||
\(176\) | 5.84480 | 0.440568 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.0630 | −0.829209 | ||||||||
\(179\) | −20.3309 | −1.51961 | −0.759803 | − | 0.650154i | \(-0.774704\pi\) | ||||
−0.759803 | + | 0.650154i | \(0.774704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46867 | 0.406483 | 0.203242 | − | 0.979129i | \(-0.434852\pi\) | ||||
0.203242 | + | 0.979129i | \(0.434852\pi\) | |||||||
\(182\) | −60.2227 | −4.46401 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.69905 | −0.346419 | ||||||||
\(185\) | −7.09865 | −0.521903 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0879 | −0.883957 | ||||||||
\(188\) | −20.1469 | −1.46937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.46814 | 0.179058 | ||||||||
\(191\) | −6.82852 | −0.494095 | −0.247047 | − | 0.969003i | \(-0.579460\pi\) | ||||
−0.247047 | + | 0.969003i | \(0.579460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.2138 | 1.38304 | 0.691518 | − | 0.722359i | \(-0.256942\pi\) | ||||
0.691518 | + | 0.722359i | \(0.256942\pi\) | |||||||
\(194\) | 6.38986 | 0.458765 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 65.7407 | 4.69576 | ||||||||
\(197\) | 10.5750 | 0.753440 | 0.376720 | − | 0.926327i | \(-0.377052\pi\) | ||||
0.376720 | + | 0.926327i | \(0.377052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0141811 | −0.00100527 | −0.000502634 | − | 1.00000i | \(-0.500160\pi\) | ||||
−0.000502634 | 1.00000i | \(0.500160\pi\) | ||||||||
\(200\) | −33.9223 | −2.39867 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45.1568 | 3.17722 | ||||||||
\(203\) | 4.87125 | 0.341895 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38.2200 | −2.66940 | ||||||||
\(206\) | −16.2297 | −1.13078 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.1919 | −1.26138 | ||||||||
\(209\) | 0.472966 | 0.0327157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.93797 | −0.615316 | −0.307658 | − | 0.951497i | \(-0.599545\pi\) | ||||
−0.307658 | + | 0.951497i | \(0.599545\pi\) | |||||||
\(212\) | −28.1721 | −1.93487 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31.8466 | −2.17699 | ||||||||
\(215\) | −19.7894 | −1.34963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.88591 | 0.399561 | ||||||||
\(218\) | −32.5150 | −2.20220 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22.4064 | −1.51064 | ||||||||
\(221\) | 37.6236 | 2.53084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4912 | 1.50612 | 0.753062 | − | 0.657950i | \(-0.228576\pi\) | ||||
0.753062 | + | 0.657950i | \(0.228576\pi\) | |||||||
\(224\) | −3.27624 | −0.218903 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1431 | 0.674707 | ||||||||
\(227\) | −12.6937 | −0.842510 | −0.421255 | − | 0.906942i | \(-0.638410\pi\) | ||||
−0.421255 | + | 0.906942i | \(0.638410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9279 | −1.31687 | −0.658437 | − | 0.752636i | \(-0.728782\pi\) | ||||
−0.658437 | + | 0.752636i | \(0.728782\pi\) | |||||||
\(230\) | 8.51205 | 0.561268 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.69905 | 0.308508 | ||||||||
\(233\) | −15.8089 | −1.03568 | −0.517838 | − | 0.855479i | \(-0.673263\pi\) | ||||
−0.517838 | + | 0.855479i | \(0.673263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.9211 | 1.16904 | ||||||||
\(236\) | 2.97888 | 0.193908 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −87.9055 | −5.69807 | ||||||||
\(239\) | 28.5189 | 1.84474 | 0.922368 | − | 0.386313i | \(-0.126252\pi\) | ||||
0.922368 | + | 0.386313i | \(0.126252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4957 | −0.676087 | −0.338044 | − | 0.941130i | \(-0.609765\pi\) | ||||
−0.338044 | + | 0.941130i | \(0.609765\pi\) | |||||||
\(242\) | 20.3072 | 1.30539 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 45.4650 | 2.91060 | ||||||||
\(245\) | −58.4777 | −3.73600 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47210 | −0.0936677 | ||||||||
\(248\) | 5.67783 | 0.360543 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.8879 | 1.19457 | ||||||||
\(251\) | −0.515831 | −0.0325589 | −0.0162795 | − | 0.999867i | \(-0.505182\pi\) | ||||
−0.0162795 | + | 0.999867i | \(0.505182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.63115 | 0.102550 | ||||||||
\(254\) | 24.5857 | 1.54264 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.3226 | −1.95766 | ||||||||
\(257\) | −11.5127 | −0.718142 | −0.359071 | − | 0.933310i | \(-0.616906\pi\) | ||||
−0.359071 | + | 0.933310i | \(0.616906\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.89234 | −0.614680 | ||||||||
\(260\) | 69.7398 | 4.32508 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −49.7303 | −3.07235 | ||||||||
\(263\) | 3.77657 | 0.232873 | 0.116437 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116437 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.0597 | 1.53940 | ||||||||
\(266\) | 3.43949 | 0.210888 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.1776 | 0.866032 | ||||||||
\(269\) | 13.0119 | 0.793348 | 0.396674 | − | 0.917960i | \(-0.370164\pi\) | ||||
0.396674 | + | 0.917960i | \(0.370164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5566 | −1.43096 | −0.715480 | − | 0.698633i | \(-0.753792\pi\) | ||||
−0.715480 | + | 0.698633i | \(0.753792\pi\) | |||||||
\(272\) | −26.5542 | −1.61009 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.5808 | −1.60581 | ||||||||
\(275\) | 11.7752 | 0.710072 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.30189 | 0.498812 | 0.249406 | − | 0.968399i | \(-0.419765\pi\) | ||||
0.249406 | + | 0.968399i | \(0.419765\pi\) | |||||||
\(278\) | 23.3935 | 1.40305 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −80.0144 | −4.78178 | ||||||||
\(281\) | 24.5091 | 1.46209 | 0.731046 | − | 0.682328i | \(-0.239032\pi\) | ||||
0.731046 | + | 0.682328i | \(0.239032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8683 | 1.00271 | 0.501357 | − | 0.865240i | \(-0.332834\pi\) | ||||
0.501357 | + | 0.865240i | \(0.332834\pi\) | |||||||
\(284\) | −34.9596 | −2.07447 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.1657 | 1.19242 | ||||||||
\(287\) | −53.2617 | −3.14394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.9182 | 2.23048 | ||||||||
\(290\) | −8.51205 | −0.499845 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.3284 | −0.604422 | ||||||||
\(293\) | −9.99230 | −0.583756 | −0.291878 | − | 0.956456i | \(-0.594280\pi\) | ||||
−0.291878 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64977 | −0.154276 | ||||||||
\(296\) | −9.54264 | −0.554655 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.56972 | −0.554359 | ||||||||
\(299\) | −5.07695 | −0.293607 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.5776 | −1.58955 | ||||||||
\(302\) | −23.8482 | −1.37231 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.03899 | 0.0595901 | ||||||||
\(305\) | −40.4420 | −2.31570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3287 | −0.589488 | −0.294744 | − | 0.955576i | \(-0.595234\pi\) | ||||
−0.294744 | + | 0.955576i | \(0.595234\pi\) | |||||||
\(308\) | −31.2245 | −1.77918 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.2851 | −0.584152 | ||||||||
\(311\) | −21.5343 | −1.22110 | −0.610550 | − | 0.791978i | \(-0.709051\pi\) | ||||
−0.610550 | + | 0.791978i | \(0.709051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23924 | −0.0700459 | −0.0350229 | − | 0.999387i | \(-0.511150\pi\) | ||||
−0.0350229 | + | 0.999387i | \(0.511150\pi\) | |||||||
\(314\) | 3.90929 | 0.220614 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.8233 | −0.833876 | ||||||||
\(317\) | 24.4749 | 1.37465 | 0.687325 | − | 0.726350i | \(-0.258785\pi\) | ||||
0.687325 | + | 0.726350i | \(0.258785\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.63115 | −0.0913269 | ||||||||
\(320\) | 30.7758 | 1.72042 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.8620 | 0.661043 | ||||||||
\(323\) | −2.14879 | −0.119562 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −36.6503 | −2.03299 | ||||||||
\(326\) | 37.8645 | 2.09712 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −51.3788 | −2.83692 | ||||||||
\(329\) | 24.9740 | 1.37686 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.08020 | 0.279233 | 0.139616 | − | 0.990206i | \(-0.455413\pi\) | ||||
0.139616 | + | 0.990206i | \(0.455413\pi\) | |||||||
\(332\) | 42.0674 | 2.30875 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.86282 | 0.101929 | ||||||||
\(335\) | −12.6112 | −0.689025 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1891 | −1.64450 | −0.822252 | − | 0.569124i | \(-0.807282\pi\) | ||||
−0.822252 | + | 0.569124i | \(0.807282\pi\) | |||||||
\(338\) | −31.1094 | −1.69213 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 101.797 | 5.52074 | ||||||||
\(341\) | −1.97091 | −0.106731 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −47.3930 | −2.55898 | ||||||||
\(344\) | −26.6027 | −1.43432 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.87171 | 0.261905 | ||||||||
\(347\) | 15.1414 | 0.812831 | 0.406416 | − | 0.913688i | \(-0.366779\pi\) | ||||
0.406416 | + | 0.913688i | \(0.366779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.2696 | 1.35265 | 0.676325 | − | 0.736603i | \(-0.263571\pi\) | ||||
0.676325 | + | 0.736603i | \(0.263571\pi\) | |||||||
\(350\) | 85.6313 | 4.57718 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.09706 | 0.0584733 | ||||||||
\(353\) | 21.9355 | 1.16751 | 0.583755 | − | 0.811930i | \(-0.301583\pi\) | ||||
0.583755 | + | 0.811930i | \(0.301583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.0972 | 1.65047 | ||||||||
\(356\) | 17.8533 | 0.946222 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 49.5079 | 2.61657 | ||||||||
\(359\) | 11.5228 | 0.608148 | 0.304074 | − | 0.952648i | \(-0.401653\pi\) | ||||
0.304074 | + | 0.952648i | \(0.401653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9159 | −0.995575 | ||||||||
\(362\) | −13.3168 | −0.699914 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 97.1862 | 5.09394 | ||||||||
\(365\) | 9.18729 | 0.480885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.2955 | 1.58141 | 0.790707 | − | 0.612195i | \(-0.209713\pi\) | ||||
0.790707 | + | 0.612195i | \(0.209713\pi\) | |||||||
\(368\) | 3.58324 | 0.186789 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.2859 | 0.898652 | ||||||||
\(371\) | 34.9220 | 1.81306 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2767 | 0.635664 | 0.317832 | − | 0.948147i | \(-0.397045\pi\) | ||||
0.317832 | + | 0.948147i | \(0.397045\pi\) | |||||||
\(374\) | 29.4353 | 1.52207 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.0912 | 1.24241 | ||||||||
\(377\) | 5.07695 | 0.261476 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3849 | −0.533438 | −0.266719 | − | 0.963774i | \(-0.585940\pi\) | ||||
−0.266719 | + | 0.963774i | \(0.585940\pi\) | |||||||
\(380\) | −3.98303 | −0.204325 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.6281 | 0.850770 | ||||||||
\(383\) | −22.4826 | −1.14880 | −0.574402 | − | 0.818573i | \(-0.694766\pi\) | ||||
−0.574402 | + | 0.818573i | \(0.694766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.7749 | 1.41554 | ||||||||
\(386\) | −46.7874 | −2.38142 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.3118 | −0.523504 | ||||||||
\(389\) | 9.81702 | 0.497743 | 0.248871 | − | 0.968537i | \(-0.419940\pi\) | ||||
0.248871 | + | 0.968537i | \(0.419940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.41068 | −0.374774 | ||||||||
\(392\) | −78.6110 | −3.97046 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.7513 | −1.29733 | ||||||||
\(395\) | 13.1856 | 0.663441 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.40591 | 0.0705608 | 0.0352804 | − | 0.999377i | \(-0.488768\pi\) | ||||
0.0352804 | + | 0.999377i | \(0.488768\pi\) | |||||||
\(398\) | 0.0345323 | 0.00173095 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 25.8672 | 1.29336 | ||||||||
\(401\) | 12.9350 | 0.645943 | 0.322971 | − | 0.946409i | \(-0.395318\pi\) | ||||
0.322971 | + | 0.946409i | \(0.395318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.13444 | 0.305578 | ||||||||
\(404\) | −72.8731 | −3.62557 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.8620 | −0.588701 | ||||||||
\(407\) | 3.31247 | 0.164193 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.6740 | 1.26950 | 0.634748 | − | 0.772720i | \(-0.281104\pi\) | ||||
0.634748 | + | 0.772720i | \(0.281104\pi\) | |||||||
\(410\) | 93.0696 | 4.59638 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.1912 | 1.29035 | ||||||||
\(413\) | −3.69260 | −0.181701 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.4198 | −1.83687 | ||||||||
\(416\) | −3.41458 | −0.167414 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.15172 | −0.0563324 | ||||||||
\(419\) | −2.80144 | −0.136859 | −0.0684297 | − | 0.997656i | \(-0.521799\pi\) | ||||
−0.0684297 | + | 0.997656i | \(0.521799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0333 | 1.12258 | 0.561288 | − | 0.827621i | \(-0.310306\pi\) | ||||
0.561288 | + | 0.827621i | \(0.310306\pi\) | |||||||
\(422\) | 21.7649 | 1.05950 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 33.6875 | 1.63601 | ||||||||
\(425\) | −53.4974 | −2.59501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −56.3581 | −2.72736 | ||||||||
\(428\) | 51.3934 | 2.48419 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.1892 | 2.32389 | ||||||||
\(431\) | −11.6913 | −0.563150 | −0.281575 | − | 0.959539i | \(-0.590857\pi\) | ||||
−0.281575 | + | 0.959539i | \(0.590857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.89512 | 0.475529 | 0.237765 | − | 0.971323i | \(-0.423585\pi\) | ||||
0.237765 | + | 0.971323i | \(0.423585\pi\) | |||||||
\(434\) | −14.3328 | −0.687995 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 52.4721 | 2.51296 | ||||||||
\(437\) | 0.289958 | 0.0138706 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3217 | −1.20854 | −0.604269 | − | 0.796780i | \(-0.706535\pi\) | ||||
−0.604269 | + | 0.796780i | \(0.706535\pi\) | |||||||
\(440\) | 26.7930 | 1.27731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −91.6174 | −4.35779 | ||||||||
\(443\) | −35.7692 | −1.69944 | −0.849722 | − | 0.527230i | \(-0.823231\pi\) | ||||
−0.849722 | + | 0.527230i | \(0.823231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.8809 | −0.752825 | ||||||||
\(446\) | −54.7684 | −2.59336 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 42.8877 | 2.02625 | ||||||||
\(449\) | −22.9074 | −1.08106 | −0.540532 | − | 0.841323i | \(-0.681777\pi\) | ||||
−0.540532 | + | 0.841323i | \(0.681777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8348 | 0.839807 | ||||||||
\(452\) | −16.3687 | −0.769918 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 30.9104 | 1.45070 | ||||||||
\(455\) | −86.4491 | −4.05280 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8884 | 0.790005 | 0.395002 | − | 0.918680i | \(-0.370744\pi\) | ||||
0.395002 | + | 0.918680i | \(0.370744\pi\) | |||||||
\(458\) | 48.5265 | 2.26749 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.7366 | −0.640471 | ||||||||
\(461\) | −28.9020 | −1.34610 | −0.673050 | − | 0.739597i | \(-0.735016\pi\) | ||||
−0.673050 | + | 0.739597i | \(0.735016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8535 | −0.597351 | −0.298675 | − | 0.954355i | \(-0.596545\pi\) | ||||
−0.298675 | + | 0.954355i | \(0.596545\pi\) | |||||||
\(464\) | −3.58324 | −0.166348 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.4963 | 1.78330 | ||||||||
\(467\) | 7.93973 | 0.367407 | 0.183703 | − | 0.982982i | \(-0.441191\pi\) | ||||
0.183703 | + | 0.982982i | \(0.441191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5744 | −0.811511 | ||||||||
\(470\) | −43.6397 | −2.01295 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.56207 | −0.163957 | ||||||||
\(473\) | 9.23442 | 0.424599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.09320 | 0.0960425 | ||||||||
\(476\) | 141.860 | 6.50215 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −69.4464 | −3.17641 | ||||||||
\(479\) | −32.7143 | −1.49475 | −0.747377 | − | 0.664400i | \(-0.768687\pi\) | ||||
−0.747377 | + | 0.664400i | \(0.768687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3101 | −0.470098 | ||||||||
\(482\) | 25.5581 | 1.16414 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.7713 | −1.48960 | ||||||||
\(485\) | 9.17258 | 0.416505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.76700 | 0.306642 | 0.153321 | − | 0.988176i | \(-0.451003\pi\) | ||||
0.153321 | + | 0.988176i | \(0.451003\pi\) | |||||||
\(488\) | −54.3658 | −2.46103 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 142.399 | 6.43294 | ||||||||
\(491\) | 14.2398 | 0.642634 | 0.321317 | − | 0.946972i | \(-0.395874\pi\) | ||||
0.321317 | + | 0.946972i | \(0.395874\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.41068 | 0.333760 | ||||||||
\(494\) | 3.58472 | 0.161284 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.32960 | −0.194405 | ||||||||
\(497\) | 43.3357 | 1.94387 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.53838 | −0.247932 | −0.123966 | − | 0.992286i | \(-0.539561\pi\) | ||||
−0.123966 | + | 0.992286i | \(0.539561\pi\) | |||||||
\(500\) | −30.4809 | −1.36315 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.25610 | 0.0560625 | ||||||||
\(503\) | −35.3182 | −1.57476 | −0.787381 | − | 0.616466i | \(-0.788564\pi\) | ||||
−0.787381 | + | 0.616466i | \(0.788564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.8221 | 2.88455 | ||||||||
\(506\) | −3.97201 | −0.176578 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.6759 | −1.76033 | ||||||||
\(509\) | 24.8206 | 1.10015 | 0.550076 | − | 0.835114i | \(-0.314599\pi\) | ||||
0.550076 | + | 0.835114i | \(0.314599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8030 | 0.566371 | ||||||||
\(512\) | 36.0856 | 1.59477 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.0346 | 1.23655 | ||||||||
\(515\) | −23.2976 | −1.02661 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.36261 | −0.367787 | ||||||||
\(518\) | 24.0889 | 1.05840 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −83.3931 | −3.65703 | ||||||||
\(521\) | −25.3463 | −1.11044 | −0.555221 | − | 0.831703i | \(-0.687366\pi\) | ||||
−0.555221 | + | 0.831703i | \(0.687366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.12658 | −0.0492617 | −0.0246309 | − | 0.999697i | \(-0.507841\pi\) | ||||
−0.0246309 | + | 0.999697i | \(0.507841\pi\) | |||||||
\(524\) | 80.2538 | 3.50590 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.19633 | −0.400979 | ||||||||
\(527\) | 8.95428 | 0.390054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −61.0228 | −2.65066 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.55057 | −0.240648 | ||||||||
\(533\) | −55.5107 | −2.40443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −45.7154 | −1.97645 | ||||||||
\(536\) | −16.9532 | −0.732265 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.6852 | −1.36605 | ||||||||
\(539\) | 27.2877 | 1.17536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.1099 | −1.59548 | −0.797740 | − | 0.603001i | \(-0.793972\pi\) | ||||
−0.797740 | + | 0.603001i | \(0.793972\pi\) | |||||||
\(542\) | 57.3626 | 2.46394 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.98417 | −0.213695 | ||||||||
\(545\) | −46.6750 | −1.99934 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.86456 | 0.207993 | 0.103997 | − | 0.994578i | \(-0.466837\pi\) | ||||
0.103997 | + | 0.994578i | \(0.466837\pi\) | |||||||
\(548\) | 42.8956 | 1.83241 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −28.6738 | −1.22266 | ||||||||
\(551\) | −0.289958 | −0.0123526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.3749 | 0.781380 | ||||||||
\(554\) | −20.2159 | −0.858893 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.7519 | −1.60104 | ||||||||
\(557\) | 23.4839 | 0.995043 | 0.497521 | − | 0.867452i | \(-0.334244\pi\) | ||||
0.497521 | + | 0.867452i | \(0.334244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.7421 | −1.21566 | ||||||||
\(560\) | 61.0145 | 2.57833 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −59.6822 | −2.51754 | ||||||||
\(563\) | 42.1697 | 1.77724 | 0.888620 | − | 0.458645i | \(-0.151665\pi\) | ||||
0.888620 | + | 0.458645i | \(0.151665\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.5603 | 0.612555 | ||||||||
\(566\) | −41.0759 | −1.72655 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41.8037 | 1.75405 | ||||||||
\(569\) | 2.21802 | 0.0929842 | 0.0464921 | − | 0.998919i | \(-0.485196\pi\) | ||||
0.0464921 | + | 0.998919i | \(0.485196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4117 | 0.812353 | 0.406177 | − | 0.913795i | \(-0.366862\pi\) | ||||
0.406177 | + | 0.913795i | \(0.366862\pi\) | |||||||
\(572\) | −32.5430 | −1.36069 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 129.698 | 5.41347 | ||||||||
\(575\) | 7.21896 | 0.301051 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.65159 | −0.0687565 | −0.0343782 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343782 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(578\) | −92.3346 | −3.84061 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.7366 | 0.570380 | ||||||||
\(581\) | −52.1465 | −2.16340 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6937 | −0.484304 | ||||||||
\(584\) | 12.3504 | 0.511063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.3322 | 1.00516 | ||||||||
\(587\) | 17.7277 | 0.731698 | 0.365849 | − | 0.930674i | \(-0.380779\pi\) | ||||
0.365849 | + | 0.930674i | \(0.380779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.350355 | −0.0144361 | ||||||||
\(590\) | 6.45246 | 0.265644 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.27669 | 0.299070 | ||||||||
\(593\) | 1.20316 | 0.0494078 | 0.0247039 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247039 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −126.187 | −5.17318 | ||||||||
\(596\) | 15.4434 | 0.632587 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.3629 | 0.505556 | ||||||||
\(599\) | 36.3309 | 1.48444 | 0.742221 | − | 0.670155i | \(-0.233773\pi\) | ||||
0.742221 | + | 0.670155i | \(0.233773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.62167 | −0.106940 | −0.0534701 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534701 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(602\) | 67.1543 | 2.73700 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 38.4857 | 1.56596 | ||||||||
\(605\) | 29.1507 | 1.18515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.15983 | −0.250020 | −0.125010 | − | 0.992155i | \(-0.539896\pi\) | ||||
−0.125010 | + | 0.992155i | \(0.539896\pi\) | |||||||
\(608\) | 0.195016 | 0.00790895 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 98.4804 | 3.98735 | ||||||||
\(611\) | 26.0286 | 1.05300 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2042 | 0.735259 | 0.367630 | − | 0.929972i | \(-0.380169\pi\) | ||||
0.367630 | + | 0.929972i | \(0.380169\pi\) | |||||||
\(614\) | 25.1513 | 1.01502 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.3375 | 1.50437 | ||||||||
\(617\) | −7.55796 | −0.304272 | −0.152136 | − | 0.988360i | \(-0.548615\pi\) | ||||
−0.152136 | + | 0.988360i | \(0.548615\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36490 | −0.135247 | −0.0676233 | − | 0.997711i | \(-0.521542\pi\) | ||||
−0.0676233 | + | 0.997711i | \(0.521542\pi\) | |||||||
\(620\) | 16.5978 | 0.666584 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 52.4382 | 2.10258 | ||||||||
\(623\) | −22.1308 | −0.886653 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.98142 | −0.359257 | ||||||||
\(626\) | 3.01767 | 0.120610 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.30873 | −0.251746 | ||||||||
\(629\) | −15.0493 | −0.600055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.41948 | 0.175937 | 0.0879684 | − | 0.996123i | \(-0.471963\pi\) | ||||
0.0879684 | + | 0.996123i | \(0.471963\pi\) | |||||||
\(632\) | 17.7253 | 0.705076 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −59.5989 | −2.36698 | ||||||||
\(635\) | 35.2925 | 1.40054 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −84.9329 | −3.36516 | ||||||||
\(638\) | 3.97201 | 0.157254 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −70.2401 | −2.77648 | ||||||||
\(641\) | −27.1330 | −1.07169 | −0.535845 | − | 0.844316i | \(-0.680007\pi\) | ||||
−0.535845 | + | 0.844316i | \(0.680007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4069 | 0.725896 | 0.362948 | − | 0.931809i | \(-0.381770\pi\) | ||||
0.362948 | + | 0.931809i | \(0.381770\pi\) | |||||||
\(644\) | −19.1426 | −0.754326 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.23252 | 0.205871 | ||||||||
\(647\) | −31.4390 | −1.23600 | −0.617998 | − | 0.786180i | \(-0.712056\pi\) | ||||
−0.617998 | + | 0.786180i | \(0.712056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23648 | 0.0485359 | ||||||||
\(650\) | 89.2471 | 3.50056 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −61.1049 | −2.39305 | ||||||||
\(653\) | 3.57315 | 0.139828 | 0.0699140 | − | 0.997553i | \(-0.477728\pi\) | ||||
0.0699140 | + | 0.997553i | \(0.477728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −71.3874 | −2.78934 | ||||||||
\(656\) | 39.1786 | 1.52967 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −60.8143 | −2.37079 | ||||||||
\(659\) | −4.59543 | −0.179012 | −0.0895062 | − | 0.995986i | \(-0.528529\pi\) | ||||
−0.0895062 | + | 0.995986i | \(0.528529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.4071 | −1.14380 | −0.571901 | − | 0.820322i | \(-0.693794\pi\) | ||||
−0.571901 | + | 0.820322i | \(0.693794\pi\) | |||||||
\(662\) | −12.3708 | −0.480804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −50.3031 | −1.95214 | ||||||||
\(665\) | 4.93735 | 0.191462 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −3.00618 | −0.116313 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 30.7096 | 1.18642 | ||||||||
\(671\) | 18.8716 | 0.728532 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.9468 | 1.00018 | 0.500088 | − | 0.865975i | \(-0.333301\pi\) | ||||
0.500088 | + | 0.865975i | \(0.333301\pi\) | |||||||
\(674\) | 73.5134 | 2.83163 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 50.2037 | 1.93091 | ||||||||
\(677\) | −12.6758 | −0.487170 | −0.243585 | − | 0.969880i | \(-0.578323\pi\) | ||||
−0.243585 | + | 0.969880i | \(0.578323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7825 | 0.490547 | ||||||||
\(680\) | −121.727 | −4.66800 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.79936 | 0.183777 | ||||||||
\(683\) | −41.1437 | −1.57432 | −0.787159 | − | 0.616750i | \(-0.788449\pi\) | ||||
−0.787159 | + | 0.616750i | \(0.788449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.1565 | −1.45789 | ||||||||
\(686\) | 115.407 | 4.40625 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.2858 | 0.773387 | ||||||||
\(689\) | 36.3966 | 1.38660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.6369 | −1.69807 | −0.849035 | − | 0.528337i | \(-0.822816\pi\) | ||||
−0.849035 | + | 0.528337i | \(0.822816\pi\) | |||||||
\(692\) | −7.86187 | −0.298863 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.8708 | −1.39959 | ||||||||
\(695\) | 33.5811 | 1.27380 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −81.0274 | −3.06913 | ||||||||
\(698\) | −61.5340 | −2.32910 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −138.190 | −5.22309 | ||||||||
\(701\) | 18.9701 | 0.716489 | 0.358244 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358244 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.588836 | 0.0222084 | ||||||||
\(704\) | −14.3610 | −0.541252 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −53.4152 | −2.01031 | ||||||||
\(707\) | 90.3331 | 3.39733 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2432 | −0.459802 | −0.229901 | − | 0.973214i | \(-0.573840\pi\) | ||||
−0.229901 | + | 0.973214i | \(0.573840\pi\) | |||||||
\(710\) | −75.7249 | −2.84191 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.3485 | −0.800069 | ||||||||
\(713\) | −1.20829 | −0.0452509 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.9477 | 1.08258 | ||||||||
\(716\) | −79.8948 | −2.98581 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.0591 | −1.04716 | ||||||||
\(719\) | −6.46404 | −0.241068 | −0.120534 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120534 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.4664 | −1.20911 | ||||||||
\(722\) | 46.0622 | 1.71426 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.4903 | 0.798682 | ||||||||
\(725\) | −7.21896 | −0.268105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3230 | 0.457034 | 0.228517 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228517 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(728\) | −116.213 | −4.30713 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.3720 | −0.828024 | ||||||||
\(731\) | −41.9541 | −1.55173 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1603 | 0.707702 | 0.353851 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353851 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(734\) | −73.7726 | −2.72300 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.672566 | 0.0247911 | ||||||||
\(737\) | 5.88483 | 0.216771 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4622 | 1.19414 | 0.597071 | − | 0.802189i | \(-0.296331\pi\) | ||||
0.597071 | + | 0.802189i | \(0.296331\pi\) | |||||||
\(740\) | −27.8957 | −1.02546 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −85.0386 | −3.12187 | ||||||||
\(743\) | 13.5331 | 0.496481 | 0.248240 | − | 0.968698i | \(-0.420148\pi\) | ||||
0.248240 | + | 0.968698i | \(0.420148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.7372 | −0.503293 | ||||||||
\(746\) | −29.8950 | −1.09453 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −47.5021 | −1.73685 | ||||||||
\(749\) | −63.7069 | −2.32780 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8722 | −1.01707 | −0.508535 | − | 0.861041i | \(-0.669813\pi\) | ||||
−0.508535 | + | 0.861041i | \(0.669813\pi\) | |||||||
\(752\) | −18.3706 | −0.669907 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.3629 | −0.450229 | ||||||||
\(755\) | −34.2338 | −1.24590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.0638 | −1.49249 | −0.746245 | − | 0.665672i | \(-0.768145\pi\) | ||||
−0.746245 | + | 0.665672i | \(0.768145\pi\) | |||||||
\(758\) | 25.2883 | 0.918514 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.76281 | 0.172765 | ||||||||
\(761\) | −38.0521 | −1.37939 | −0.689694 | − | 0.724101i | \(-0.742255\pi\) | ||||
−0.689694 | + | 0.724101i | \(0.742255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −65.0441 | −2.35476 | ||||||||
\(764\) | −26.8342 | −0.970826 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.7473 | 1.97810 | ||||||||
\(767\) | −3.84852 | −0.138962 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2151 | 0.801097 | 0.400549 | − | 0.916276i | \(-0.368820\pi\) | ||||
0.400549 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(770\) | −67.6346 | −2.43738 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 75.5046 | 2.71747 | ||||||||
\(773\) | −42.9479 | −1.54473 | −0.772365 | − | 0.635179i | \(-0.780926\pi\) | ||||
−0.772365 | + | 0.635179i | \(0.780926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.72262 | −0.313326 | ||||||||
\(776\) | 12.3306 | 0.442643 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.9054 | −0.857051 | ||||||||
\(779\) | 3.17037 | 0.113590 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.5110 | −0.519246 | ||||||||
\(782\) | 18.0458 | 0.645315 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 59.9444 | 2.14087 | ||||||||
\(785\) | 5.61175 | 0.200292 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1228 | 1.10941 | 0.554703 | − | 0.832048i | \(-0.312832\pi\) | ||||
0.554703 | + | 0.832048i | \(0.312832\pi\) | |||||||
\(788\) | 41.5569 | 1.48040 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.1084 | −1.14236 | ||||||||
\(791\) | 20.2905 | 0.721448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.7379 | −2.08584 | ||||||||
\(794\) | −3.42354 | −0.121497 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0557275 | −0.00197521 | ||||||||
\(797\) | −24.1202 | −0.854383 | −0.427191 | − | 0.904161i | \(-0.640497\pi\) | ||||
−0.427191 | + | 0.904161i | \(0.640497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.9932 | 1.34410 | ||||||||
\(800\) | 4.85523 | 0.171658 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.4980 | −1.11223 | ||||||||
\(803\) | −4.28711 | −0.151289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.0278 | 0.600150 | ||||||||
\(806\) | −14.9380 | −0.526168 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 87.1398 | 3.06557 | ||||||||
\(809\) | 22.2731 | 0.783081 | 0.391541 | − | 0.920161i | \(-0.371942\pi\) | ||||
0.391541 | + | 0.920161i | \(0.371942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.2815 | −1.34424 | −0.672122 | − | 0.740440i | \(-0.734617\pi\) | ||||
−0.672122 | + | 0.740440i | \(0.734617\pi\) | |||||||
\(812\) | 19.1426 | 0.671775 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.06621 | −0.282720 | ||||||||
\(815\) | 54.3541 | 1.90394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.64154 | 0.0574302 | ||||||||
\(818\) | −62.5187 | −2.18591 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −150.194 | −5.24500 | ||||||||
\(821\) | −17.3465 | −0.605395 | −0.302698 | − | 0.953087i | \(-0.597887\pi\) | ||||
−0.302698 | + | 0.953087i | \(0.597887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.80452 | 0.202333 | 0.101166 | − | 0.994870i | \(-0.467743\pi\) | ||||
0.101166 | + | 0.994870i | \(0.467743\pi\) | |||||||
\(824\) | −31.3187 | −1.09104 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.99186 | 0.312867 | ||||||||
\(827\) | 27.5059 | 0.956475 | 0.478237 | − | 0.878231i | \(-0.341276\pi\) | ||||
0.478237 | + | 0.878231i | \(0.341276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3056 | 0.635779 | 0.317890 | − | 0.948128i | \(-0.397026\pi\) | ||||
0.317890 | + | 0.948128i | \(0.397026\pi\) | |||||||
\(830\) | 91.1210 | 3.16286 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 44.6986 | 1.54965 | ||||||||
\(833\) | −123.974 | −4.29545 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.67406 | 0.0925397 | ||||||||
\(836\) | 1.85862 | 0.0642817 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.82179 | 0.235655 | ||||||||
\(839\) | 0.291572 | 0.0100662 | 0.00503308 | − | 0.999987i | \(-0.498398\pi\) | ||||
0.00503308 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −56.0885 | −1.93294 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.1237 | −1.20901 | ||||||||
\(845\) | −44.6572 | −1.53625 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.6231 | 1.39583 | ||||||||
\(848\) | −25.6882 | −0.882136 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 130.272 | 4.46828 | ||||||||
\(851\) | 2.03076 | 0.0696135 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.6773 | −0.879175 | −0.439587 | − | 0.898200i | \(-0.644875\pi\) | ||||
−0.439587 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(854\) | 137.238 | 4.69618 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −61.4549 | −2.10048 | ||||||||
\(857\) | 40.3915 | 1.37975 | 0.689874 | − | 0.723930i | \(-0.257666\pi\) | ||||
0.689874 | + | 0.723930i | \(0.257666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.56391 | −0.189838 | −0.0949191 | − | 0.995485i | \(-0.530259\pi\) | ||||
−0.0949191 | + | 0.995485i | \(0.530259\pi\) | |||||||
\(860\) | −77.7668 | −2.65182 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.4695 | 0.969674 | ||||||||
\(863\) | −42.7773 | −1.45616 | −0.728078 | − | 0.685494i | \(-0.759586\pi\) | ||||
−0.728078 | + | 0.685494i | \(0.759586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.99329 | 0.237779 | ||||||||
\(866\) | −24.0956 | −0.818802 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.1299 | 0.785081 | ||||||||
\(869\) | −6.15287 | −0.208722 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.3165 | −0.620631 | ||||||||
\(872\) | −62.7448 | −2.12481 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.706078 | −0.0238834 | ||||||||
\(875\) | 37.7839 | 1.27733 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.3278 | −1.49684 | −0.748422 | − | 0.663223i | \(-0.769188\pi\) | ||||
−0.748422 | + | 0.663223i | \(0.769188\pi\) | |||||||
\(878\) | 61.6609 | 2.08095 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.4308 | −0.688724 | ||||||||
\(881\) | 30.0372 | 1.01198 | 0.505990 | − | 0.862539i | \(-0.331127\pi\) | ||||
0.505990 | + | 0.862539i | \(0.331127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.4304 | −0.990411 | −0.495205 | − | 0.868776i | \(-0.664907\pi\) | ||||
−0.495205 | + | 0.868776i | \(0.664907\pi\) | |||||||
\(884\) | 147.850 | 4.97274 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 87.1016 | 2.92623 | ||||||||
\(887\) | 57.8556 | 1.94260 | 0.971301 | − | 0.237854i | \(-0.0764439\pi\) | ||||
0.971301 | + | 0.237854i | \(0.0764439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.1820 | 1.64951 | ||||||||
\(890\) | 38.6715 | 1.29627 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 88.3841 | 2.95932 | ||||||||
\(893\) | −1.48656 | −0.0497460 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.0681 | 2.37554 | ||||||||
\(896\) | −97.8833 | −3.27005 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 55.7817 | 1.86146 | ||||||||
\(899\) | 1.20829 | 0.0402988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.1271 | 1.76992 | ||||||||
\(902\) | −43.4295 | −1.44604 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.5732 | 0.650996 | ||||||||
\(905\) | −19.1161 | −0.635440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.2768 | −0.905710 | −0.452855 | − | 0.891584i | \(-0.649595\pi\) | ||||
−0.452855 | + | 0.891584i | \(0.649595\pi\) | |||||||
\(908\) | −49.8826 | −1.65541 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 210.512 | 6.97842 | ||||||||
\(911\) | 24.0599 | 0.797139 | 0.398569 | − | 0.917138i | \(-0.369507\pi\) | ||||
0.398569 | + | 0.917138i | \(0.369507\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4614 | 0.577887 | ||||||||
\(914\) | −41.1249 | −1.36029 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −78.3110 | −2.58747 | ||||||||
\(917\) | −99.4821 | −3.28519 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.2959 | −1.26326 | −0.631632 | − | 0.775269i | \(-0.717615\pi\) | ||||
−0.631632 | + | 0.775269i | \(0.717615\pi\) | |||||||
\(920\) | 16.4258 | 0.541544 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 70.3792 | 2.31782 | ||||||||
\(923\) | 45.1656 | 1.48664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6600 | 0.482017 | ||||||||
\(926\) | 31.2995 | 1.02856 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.672566 | −0.0220781 | ||||||||
\(929\) | −16.9016 | −0.554523 | −0.277262 | − | 0.960794i | \(-0.589427\pi\) | ||||
−0.277262 | + | 0.960794i | \(0.589427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.85075 | 0.158977 | ||||||||
\(932\) | −62.1245 | −2.03495 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.3340 | −0.632629 | ||||||||
\(935\) | 42.2541 | 1.38186 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.00392697 | 0.000128289 0 | 6.41443e−5 | − | 1.00000i | \(-0.499980\pi\) | ||||
6.41443e−5 | 1.00000i | \(0.499980\pi\) | ||||||||
\(938\) | 42.7955 | 1.39732 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 70.4249 | 2.29701 | ||||||||
\(941\) | 25.9434 | 0.845731 | 0.422865 | − | 0.906193i | \(-0.361024\pi\) | ||||
0.422865 | + | 0.906193i | \(0.361024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9339 | 0.356056 | ||||||||
\(944\) | 2.71623 | 0.0884058 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.4867 | −0.731107 | ||||||||
\(947\) | −17.3620 | −0.564188 | −0.282094 | − | 0.959387i | \(-0.591029\pi\) | ||||
−0.282094 | + | 0.959387i | \(0.591029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.3436 | 0.433151 | ||||||||
\(950\) | −5.09715 | −0.165373 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −169.633 | −5.49782 | ||||||||
\(953\) | −28.5774 | −0.925713 | −0.462857 | − | 0.886433i | \(-0.653175\pi\) | ||||
−0.462857 | + | 0.886433i | \(0.653175\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.8695 | 0.772400 | ||||||||
\(956\) | 112.071 | 3.62464 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 79.6626 | 2.57378 | ||||||||
\(959\) | −53.1732 | −1.71705 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5400 | −0.952904 | ||||||||
\(962\) | 25.1060 | 0.809451 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.2451 | −1.32842 | ||||||||
\(965\) | −67.1629 | −2.16205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.08127 | −0.0990869 | −0.0495435 | − | 0.998772i | \(-0.515777\pi\) | ||||
−0.0495435 | + | 0.998772i | \(0.515777\pi\) | |||||||
\(968\) | 39.1870 | 1.25952 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.3362 | −0.717171 | ||||||||
\(971\) | 10.1788 | 0.326652 | 0.163326 | − | 0.986572i | \(-0.447778\pi\) | ||||
0.163326 | + | 0.986572i | \(0.447778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.7970 | 1.50024 | ||||||||
\(974\) | −16.4783 | −0.528000 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.4563 | 1.32699 | ||||||||
\(977\) | 51.5899 | 1.65051 | 0.825253 | − | 0.564763i | \(-0.191032\pi\) | ||||
0.825253 | + | 0.564763i | \(0.191032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.41056 | 0.236843 | ||||||||
\(980\) | −229.801 | −7.34072 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.6754 | −1.10654 | ||||||||
\(983\) | 40.0166 | 1.27633 | 0.638166 | − | 0.769899i | \(-0.279693\pi\) | ||||
0.638166 | + | 0.769899i | \(0.279693\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.9657 | −1.17783 | ||||||||
\(986\) | −18.0458 | −0.574694 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.78495 | −0.184044 | ||||||||
\(989\) | 5.66129 | 0.180019 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9438 | −0.538238 | −0.269119 | − | 0.963107i | \(-0.586733\pi\) | ||||
−0.269119 | + | 0.963107i | \(0.586733\pi\) | |||||||
\(992\) | −0.812657 | −0.0258019 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −105.527 | −3.34710 | ||||||||
\(995\) | 0.0495708 | 0.00157150 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0505 | 0.476655 | 0.238327 | − | 0.971185i | \(-0.423401\pi\) | ||||
0.238327 | + | 0.971185i | \(0.423401\pi\) | |||||||
\(998\) | 13.4865 | 0.426908 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.o.1.2 | 13 | ||
3.2 | odd | 2 | 667.2.a.c.1.12 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.c.1.12 | ✓ | 13 | 3.2 | odd | 2 | ||
6003.2.a.o.1.2 | 13 | 1.1 | even | 1 | trivial |