Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.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: | \(25.3445176016\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.30972\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.88612 | −1.73793 | −0.868963 | − | 0.494876i | \(-0.835213\pi\) | ||||
−0.868963 | + | 0.494876i | \(0.835213\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.16140 | 1.57286 | 0.786430 | − | 0.617679i | \(-0.211927\pi\) | ||||
0.786430 | + | 0.617679i | \(0.211927\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.88612 | −1.22890 | ||||||||
\(11\) | 4.52825 | 1.36532 | 0.682659 | − | 0.730737i | \(-0.260823\pi\) | ||||
0.682659 | + | 0.730737i | \(0.260823\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.26315 | −0.905036 | −0.452518 | − | 0.891755i | \(-0.649474\pi\) | ||||
−0.452518 | + | 0.891755i | \(0.649474\pi\) | |||||||
\(14\) | 4.16140 | 1.11218 | ||||||||
\(15\) | 3.88612 | 1.00339 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.82862 | −0.443505 | −0.221753 | − | 0.975103i | \(-0.571178\pi\) | ||||
−0.221753 | + | 0.975103i | \(0.571178\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.36564 | 0.313300 | 0.156650 | − | 0.987654i | \(-0.449931\pi\) | ||||
0.156650 | + | 0.987654i | \(0.449931\pi\) | |||||||
\(20\) | −3.88612 | −0.868963 | ||||||||
\(21\) | −4.16140 | −0.908092 | ||||||||
\(22\) | 4.52825 | 0.965426 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 10.1019 | 2.02039 | ||||||||
\(26\) | −3.26315 | −0.639957 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.16140 | 0.786430 | ||||||||
\(29\) | 0.561114 | 0.104196 | 0.0520981 | − | 0.998642i | \(-0.483409\pi\) | ||||
0.0520981 | + | 0.998642i | \(0.483409\pi\) | |||||||
\(30\) | 3.88612 | 0.709506 | ||||||||
\(31\) | −4.63657 | −0.832752 | −0.416376 | − | 0.909192i | \(-0.636700\pi\) | ||||
−0.416376 | + | 0.909192i | \(0.636700\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.52825 | −0.788267 | ||||||||
\(34\) | −1.82862 | −0.313605 | ||||||||
\(35\) | −16.1717 | −2.73352 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.51890 | 0.414104 | 0.207052 | − | 0.978330i | \(-0.433613\pi\) | ||||
0.207052 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(38\) | 1.36564 | 0.221537 | ||||||||
\(39\) | 3.26315 | 0.522523 | ||||||||
\(40\) | −3.88612 | −0.614450 | ||||||||
\(41\) | −6.11749 | −0.955392 | −0.477696 | − | 0.878525i | \(-0.658528\pi\) | ||||
−0.477696 | + | 0.878525i | \(0.658528\pi\) | |||||||
\(42\) | −4.16140 | −0.642118 | ||||||||
\(43\) | 9.85240 | 1.50248 | 0.751238 | − | 0.660031i | \(-0.229457\pi\) | ||||
0.751238 | + | 0.660031i | \(0.229457\pi\) | |||||||
\(44\) | 4.52825 | 0.682659 | ||||||||
\(45\) | −3.88612 | −0.579309 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.38128 | 0.347345 | 0.173672 | − | 0.984803i | \(-0.444437\pi\) | ||||
0.173672 | + | 0.984803i | \(0.444437\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 10.3172 | 1.47389 | ||||||||
\(50\) | 10.1019 | 1.42863 | ||||||||
\(51\) | 1.82862 | 0.256058 | ||||||||
\(52\) | −3.26315 | −0.452518 | ||||||||
\(53\) | 10.6102 | 1.45743 | 0.728713 | − | 0.684820i | \(-0.240119\pi\) | ||||
0.728713 | + | 0.684820i | \(0.240119\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −17.5973 | −2.37282 | ||||||||
\(56\) | 4.16140 | 0.556090 | ||||||||
\(57\) | −1.36564 | −0.180884 | ||||||||
\(58\) | 0.561114 | 0.0736778 | ||||||||
\(59\) | −7.15262 | −0.931192 | −0.465596 | − | 0.884997i | \(-0.654160\pi\) | ||||
−0.465596 | + | 0.884997i | \(0.654160\pi\) | |||||||
\(60\) | 3.88612 | 0.501696 | ||||||||
\(61\) | −3.25684 | −0.416995 | −0.208498 | − | 0.978023i | \(-0.566857\pi\) | ||||
−0.208498 | + | 0.978023i | \(0.566857\pi\) | |||||||
\(62\) | −4.63657 | −0.588845 | ||||||||
\(63\) | 4.16140 | 0.524287 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.6810 | 1.57289 | ||||||||
\(66\) | −4.52825 | −0.557389 | ||||||||
\(67\) | −6.28762 | −0.768154 | −0.384077 | − | 0.923301i | \(-0.625480\pi\) | ||||
−0.384077 | + | 0.923301i | \(0.625480\pi\) | |||||||
\(68\) | −1.82862 | −0.221753 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.1717 | −1.93289 | ||||||||
\(71\) | −6.45399 | −0.765948 | −0.382974 | − | 0.923759i | \(-0.625100\pi\) | ||||
−0.382974 | + | 0.923759i | \(0.625100\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 12.3533 | 1.44584 | 0.722920 | − | 0.690932i | \(-0.242799\pi\) | ||||
0.722920 | + | 0.690932i | \(0.242799\pi\) | |||||||
\(74\) | 2.51890 | 0.292816 | ||||||||
\(75\) | −10.1019 | −1.16647 | ||||||||
\(76\) | 1.36564 | 0.156650 | ||||||||
\(77\) | 18.8439 | 2.14746 | ||||||||
\(78\) | 3.26315 | 0.369479 | ||||||||
\(79\) | 8.43720 | 0.949259 | 0.474629 | − | 0.880186i | \(-0.342582\pi\) | ||||
0.474629 | + | 0.880186i | \(0.342582\pi\) | |||||||
\(80\) | −3.88612 | −0.434482 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.11749 | −0.675564 | ||||||||
\(83\) | −0.377030 | −0.0413845 | −0.0206922 | − | 0.999786i | \(-0.506587\pi\) | ||||
−0.0206922 | + | 0.999786i | \(0.506587\pi\) | |||||||
\(84\) | −4.16140 | −0.454046 | ||||||||
\(85\) | 7.10623 | 0.770779 | ||||||||
\(86\) | 9.85240 | 1.06241 | ||||||||
\(87\) | −0.561114 | −0.0601577 | ||||||||
\(88\) | 4.52825 | 0.482713 | ||||||||
\(89\) | 15.2049 | 1.61172 | 0.805860 | − | 0.592106i | \(-0.201703\pi\) | ||||
0.805860 | + | 0.592106i | \(0.201703\pi\) | |||||||
\(90\) | −3.88612 | −0.409633 | ||||||||
\(91\) | −13.5793 | −1.42350 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.63657 | 0.480790 | ||||||||
\(94\) | 2.38128 | 0.245610 | ||||||||
\(95\) | −5.30706 | −0.544493 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 18.8759 | 1.91656 | 0.958278 | − | 0.285838i | \(-0.0922721\pi\) | ||||
0.958278 | + | 0.285838i | \(0.0922721\pi\) | |||||||
\(98\) | 10.3172 | 1.04220 | ||||||||
\(99\) | 4.52825 | 0.455106 | ||||||||
\(100\) | 10.1019 | 1.01019 | ||||||||
\(101\) | −1.10306 | −0.109759 | −0.0548793 | − | 0.998493i | \(-0.517477\pi\) | ||||
−0.0548793 | + | 0.998493i | \(0.517477\pi\) | |||||||
\(102\) | 1.82862 | 0.181060 | ||||||||
\(103\) | 3.36648 | 0.331709 | 0.165854 | − | 0.986150i | \(-0.446962\pi\) | ||||
0.165854 | + | 0.986150i | \(0.446962\pi\) | |||||||
\(104\) | −3.26315 | −0.319978 | ||||||||
\(105\) | 16.1717 | 1.57820 | ||||||||
\(106\) | 10.6102 | 1.03056 | ||||||||
\(107\) | −10.4984 | −1.01492 | −0.507458 | − | 0.861676i | \(-0.669415\pi\) | ||||
−0.507458 | + | 0.861676i | \(0.669415\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.27668 | −0.122284 | −0.0611418 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611418 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(110\) | −17.5973 | −1.67784 | ||||||||
\(111\) | −2.51890 | −0.239083 | ||||||||
\(112\) | 4.16140 | 0.393215 | ||||||||
\(113\) | 17.6913 | 1.66425 | 0.832127 | − | 0.554585i | \(-0.187123\pi\) | ||||
0.832127 | + | 0.554585i | \(0.187123\pi\) | |||||||
\(114\) | −1.36564 | −0.127904 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.561114 | 0.0520981 | ||||||||
\(117\) | −3.26315 | −0.301679 | ||||||||
\(118\) | −7.15262 | −0.658452 | ||||||||
\(119\) | −7.60961 | −0.697572 | ||||||||
\(120\) | 3.88612 | 0.354753 | ||||||||
\(121\) | 9.50505 | 0.864096 | ||||||||
\(122\) | −3.25684 | −0.294860 | ||||||||
\(123\) | 6.11749 | 0.551596 | ||||||||
\(124\) | −4.63657 | −0.416376 | ||||||||
\(125\) | −19.8268 | −1.77336 | ||||||||
\(126\) | 4.16140 | 0.370727 | ||||||||
\(127\) | 10.0980 | 0.896050 | 0.448025 | − | 0.894021i | \(-0.352128\pi\) | ||||
0.448025 | + | 0.894021i | \(0.352128\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.85240 | −0.867455 | ||||||||
\(130\) | 12.6810 | 1.11220 | ||||||||
\(131\) | 7.51893 | 0.656932 | 0.328466 | − | 0.944516i | \(-0.393468\pi\) | ||||
0.328466 | + | 0.944516i | \(0.393468\pi\) | |||||||
\(132\) | −4.52825 | −0.394134 | ||||||||
\(133\) | 5.68299 | 0.492778 | ||||||||
\(134\) | −6.28762 | −0.543167 | ||||||||
\(135\) | 3.88612 | 0.334464 | ||||||||
\(136\) | −1.82862 | −0.156803 | ||||||||
\(137\) | −14.3005 | −1.22178 | −0.610888 | − | 0.791717i | \(-0.709188\pi\) | ||||
−0.610888 | + | 0.791717i | \(0.709188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8003 | 1.84907 | 0.924537 | − | 0.381092i | \(-0.124452\pi\) | ||||
0.924537 | + | 0.381092i | \(0.124452\pi\) | |||||||
\(140\) | −16.1717 | −1.36676 | ||||||||
\(141\) | −2.38128 | −0.200540 | ||||||||
\(142\) | −6.45399 | −0.541607 | ||||||||
\(143\) | −14.7764 | −1.23566 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.18056 | −0.181085 | ||||||||
\(146\) | 12.3533 | 1.02236 | ||||||||
\(147\) | −10.3172 | −0.850951 | ||||||||
\(148\) | 2.51890 | 0.207052 | ||||||||
\(149\) | −2.08094 | −0.170477 | −0.0852385 | − | 0.996361i | \(-0.527165\pi\) | ||||
−0.0852385 | + | 0.996361i | \(0.527165\pi\) | |||||||
\(150\) | −10.1019 | −0.824821 | ||||||||
\(151\) | 18.7684 | 1.52735 | 0.763675 | − | 0.645600i | \(-0.223393\pi\) | ||||
0.763675 | + | 0.645600i | \(0.223393\pi\) | |||||||
\(152\) | 1.36564 | 0.110768 | ||||||||
\(153\) | −1.82862 | −0.147835 | ||||||||
\(154\) | 18.8439 | 1.51848 | ||||||||
\(155\) | 18.0183 | 1.44726 | ||||||||
\(156\) | 3.26315 | 0.261261 | ||||||||
\(157\) | −1.99513 | −0.159228 | −0.0796142 | − | 0.996826i | \(-0.525369\pi\) | ||||
−0.0796142 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(158\) | 8.43720 | 0.671227 | ||||||||
\(159\) | −10.6102 | −0.841445 | ||||||||
\(160\) | −3.88612 | −0.307225 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.698970 | 0.0547475 | 0.0273738 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273738 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(164\) | −6.11749 | −0.477696 | ||||||||
\(165\) | 17.5973 | 1.36995 | ||||||||
\(166\) | −0.377030 | −0.0292632 | ||||||||
\(167\) | 5.02836 | 0.389106 | 0.194553 | − | 0.980892i | \(-0.437674\pi\) | ||||
0.194553 | + | 0.980892i | \(0.437674\pi\) | |||||||
\(168\) | −4.16140 | −0.321059 | ||||||||
\(169\) | −2.35183 | −0.180910 | ||||||||
\(170\) | 7.10623 | 0.545023 | ||||||||
\(171\) | 1.36564 | 0.104433 | ||||||||
\(172\) | 9.85240 | 0.751238 | ||||||||
\(173\) | −8.68258 | −0.660124 | −0.330062 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330062 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(174\) | −0.561114 | −0.0425379 | ||||||||
\(175\) | 42.0382 | 3.17779 | ||||||||
\(176\) | 4.52825 | 0.341330 | ||||||||
\(177\) | 7.15262 | 0.537624 | ||||||||
\(178\) | 15.2049 | 1.13966 | ||||||||
\(179\) | −11.5753 | −0.865176 | −0.432588 | − | 0.901592i | \(-0.642400\pi\) | ||||
−0.432588 | + | 0.901592i | \(0.642400\pi\) | |||||||
\(180\) | −3.88612 | −0.289654 | ||||||||
\(181\) | −2.61369 | −0.194274 | −0.0971370 | − | 0.995271i | \(-0.530968\pi\) | ||||
−0.0971370 | + | 0.995271i | \(0.530968\pi\) | |||||||
\(182\) | −13.5793 | −1.00656 | ||||||||
\(183\) | 3.25684 | 0.240752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.78874 | −0.719683 | ||||||||
\(186\) | 4.63657 | 0.339970 | ||||||||
\(187\) | −8.28044 | −0.605526 | ||||||||
\(188\) | 2.38128 | 0.173672 | ||||||||
\(189\) | −4.16140 | −0.302697 | ||||||||
\(190\) | −5.30706 | −0.385015 | ||||||||
\(191\) | 6.15128 | 0.445091 | 0.222546 | − | 0.974922i | \(-0.428563\pi\) | ||||
0.222546 | + | 0.974922i | \(0.428563\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.53015 | 0.614014 | 0.307007 | − | 0.951707i | \(-0.400673\pi\) | ||||
0.307007 | + | 0.951707i | \(0.400673\pi\) | |||||||
\(194\) | 18.8759 | 1.35521 | ||||||||
\(195\) | −12.6810 | −0.908106 | ||||||||
\(196\) | 10.3172 | 0.736946 | ||||||||
\(197\) | 3.29008 | 0.234409 | 0.117204 | − | 0.993108i | \(-0.462607\pi\) | ||||
0.117204 | + | 0.993108i | \(0.462607\pi\) | |||||||
\(198\) | 4.52825 | 0.321809 | ||||||||
\(199\) | 20.0262 | 1.41962 | 0.709810 | − | 0.704393i | \(-0.248781\pi\) | ||||
0.709810 | + | 0.704393i | \(0.248781\pi\) | |||||||
\(200\) | 10.1019 | 0.714316 | ||||||||
\(201\) | 6.28762 | 0.443494 | ||||||||
\(202\) | −1.10306 | −0.0776110 | ||||||||
\(203\) | 2.33502 | 0.163886 | ||||||||
\(204\) | 1.82862 | 0.128029 | ||||||||
\(205\) | 23.7733 | 1.66040 | ||||||||
\(206\) | 3.36648 | 0.234554 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.26315 | −0.226259 | ||||||||
\(209\) | 6.18398 | 0.427755 | ||||||||
\(210\) | 16.1717 | 1.11595 | ||||||||
\(211\) | 2.62325 | 0.180592 | 0.0902959 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902959 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(212\) | 10.6102 | 0.728713 | ||||||||
\(213\) | 6.45399 | 0.442220 | ||||||||
\(214\) | −10.4984 | −0.717654 | ||||||||
\(215\) | −38.2876 | −2.61119 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −19.2946 | −1.30980 | ||||||||
\(218\) | −1.27668 | −0.0864676 | ||||||||
\(219\) | −12.3533 | −0.834756 | ||||||||
\(220\) | −17.5973 | −1.18641 | ||||||||
\(221\) | 5.96706 | 0.401388 | ||||||||
\(222\) | −2.51890 | −0.169057 | ||||||||
\(223\) | 3.40900 | 0.228283 | 0.114142 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114142 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(224\) | 4.16140 | 0.278045 | ||||||||
\(225\) | 10.1019 | 0.673463 | ||||||||
\(226\) | 17.6913 | 1.17681 | ||||||||
\(227\) | 14.8065 | 0.982745 | 0.491372 | − | 0.870950i | \(-0.336495\pi\) | ||||
0.491372 | + | 0.870950i | \(0.336495\pi\) | |||||||
\(228\) | −1.36564 | −0.0904420 | ||||||||
\(229\) | 9.79565 | 0.647315 | 0.323657 | − | 0.946174i | \(-0.395088\pi\) | ||||
0.323657 | + | 0.946174i | \(0.395088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.8439 | −1.23983 | ||||||||
\(232\) | 0.561114 | 0.0368389 | ||||||||
\(233\) | −3.95532 | −0.259122 | −0.129561 | − | 0.991571i | \(-0.541357\pi\) | ||||
−0.129561 | + | 0.991571i | \(0.541357\pi\) | |||||||
\(234\) | −3.26315 | −0.213319 | ||||||||
\(235\) | −9.25393 | −0.603660 | ||||||||
\(236\) | −7.15262 | −0.465596 | ||||||||
\(237\) | −8.43720 | −0.548055 | ||||||||
\(238\) | −7.60961 | −0.493258 | ||||||||
\(239\) | −9.82751 | −0.635689 | −0.317844 | − | 0.948143i | \(-0.602959\pi\) | ||||
−0.317844 | + | 0.948143i | \(0.602959\pi\) | |||||||
\(240\) | 3.88612 | 0.250848 | ||||||||
\(241\) | 21.6867 | 1.39697 | 0.698483 | − | 0.715627i | \(-0.253859\pi\) | ||||
0.698483 | + | 0.715627i | \(0.253859\pi\) | |||||||
\(242\) | 9.50505 | 0.611008 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.25684 | −0.208498 | ||||||||
\(245\) | −40.0941 | −2.56151 | ||||||||
\(246\) | 6.11749 | 0.390037 | ||||||||
\(247\) | −4.45630 | −0.283548 | ||||||||
\(248\) | −4.63657 | −0.294422 | ||||||||
\(249\) | 0.377030 | 0.0238933 | ||||||||
\(250\) | −19.8268 | −1.25396 | ||||||||
\(251\) | −7.45090 | −0.470297 | −0.235148 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235148 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(252\) | 4.16140 | 0.262143 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.0980 | 0.633603 | ||||||||
\(255\) | −7.10623 | −0.445010 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.10261 | 0.255914 | 0.127957 | − | 0.991780i | \(-0.459158\pi\) | ||||
0.127957 | + | 0.991780i | \(0.459158\pi\) | |||||||
\(258\) | −9.85240 | −0.613383 | ||||||||
\(259\) | 10.4821 | 0.651328 | ||||||||
\(260\) | 12.6810 | 0.786443 | ||||||||
\(261\) | 0.561114 | 0.0347321 | ||||||||
\(262\) | 7.51893 | 0.464521 | ||||||||
\(263\) | −26.8046 | −1.65284 | −0.826420 | − | 0.563054i | \(-0.809626\pi\) | ||||
−0.826420 | + | 0.563054i | \(0.809626\pi\) | |||||||
\(264\) | −4.52825 | −0.278695 | ||||||||
\(265\) | −41.2326 | −2.53290 | ||||||||
\(266\) | 5.68299 | 0.348446 | ||||||||
\(267\) | −15.2049 | −0.930527 | ||||||||
\(268\) | −6.28762 | −0.384077 | ||||||||
\(269\) | −5.74299 | −0.350156 | −0.175078 | − | 0.984555i | \(-0.556018\pi\) | ||||
−0.175078 | + | 0.984555i | \(0.556018\pi\) | |||||||
\(270\) | 3.88612 | 0.236502 | ||||||||
\(271\) | 6.93596 | 0.421330 | 0.210665 | − | 0.977558i | \(-0.432437\pi\) | ||||
0.210665 | + | 0.977558i | \(0.432437\pi\) | |||||||
\(272\) | −1.82862 | −0.110876 | ||||||||
\(273\) | 13.5793 | 0.821855 | ||||||||
\(274\) | −14.3005 | −0.863927 | ||||||||
\(275\) | 45.7442 | 2.75848 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.81024 | −0.228935 | −0.114468 | − | 0.993427i | \(-0.536516\pi\) | ||||
−0.114468 | + | 0.993427i | \(0.536516\pi\) | |||||||
\(278\) | 21.8003 | 1.30749 | ||||||||
\(279\) | −4.63657 | −0.277584 | ||||||||
\(280\) | −16.1717 | −0.966444 | ||||||||
\(281\) | 18.1727 | 1.08409 | 0.542047 | − | 0.840348i | \(-0.317649\pi\) | ||||
0.542047 | + | 0.840348i | \(0.317649\pi\) | |||||||
\(282\) | −2.38128 | −0.141803 | ||||||||
\(283\) | −17.0969 | −1.01631 | −0.508153 | − | 0.861267i | \(-0.669672\pi\) | ||||
−0.508153 | + | 0.861267i | \(0.669672\pi\) | |||||||
\(284\) | −6.45399 | −0.382974 | ||||||||
\(285\) | 5.30706 | 0.314363 | ||||||||
\(286\) | −14.7764 | −0.873745 | ||||||||
\(287\) | −25.4573 | −1.50270 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.6562 | −0.803303 | ||||||||
\(290\) | −2.18056 | −0.128047 | ||||||||
\(291\) | −18.8759 | −1.10652 | ||||||||
\(292\) | 12.3533 | 0.722920 | ||||||||
\(293\) | −13.0545 | −0.762650 | −0.381325 | − | 0.924441i | \(-0.624532\pi\) | ||||
−0.381325 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(294\) | −10.3172 | −0.601714 | ||||||||
\(295\) | 27.7960 | 1.61834 | ||||||||
\(296\) | 2.51890 | 0.146408 | ||||||||
\(297\) | −4.52825 | −0.262756 | ||||||||
\(298\) | −2.08094 | −0.120545 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.1019 | −0.583236 | ||||||||
\(301\) | 40.9997 | 2.36319 | ||||||||
\(302\) | 18.7684 | 1.08000 | ||||||||
\(303\) | 1.10306 | 0.0633691 | ||||||||
\(304\) | 1.36564 | 0.0783250 | ||||||||
\(305\) | 12.6565 | 0.724707 | ||||||||
\(306\) | −1.82862 | −0.104535 | ||||||||
\(307\) | −24.0856 | −1.37464 | −0.687320 | − | 0.726355i | \(-0.741213\pi\) | ||||
−0.687320 | + | 0.726355i | \(0.741213\pi\) | |||||||
\(308\) | 18.8439 | 1.07373 | ||||||||
\(309\) | −3.36648 | −0.191512 | ||||||||
\(310\) | 18.0183 | 1.02337 | ||||||||
\(311\) | 2.64709 | 0.150103 | 0.0750513 | − | 0.997180i | \(-0.476088\pi\) | ||||
0.0750513 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(312\) | 3.26315 | 0.184740 | ||||||||
\(313\) | −25.0150 | −1.41393 | −0.706965 | − | 0.707248i | \(-0.749936\pi\) | ||||
−0.706965 | + | 0.707248i | \(0.749936\pi\) | |||||||
\(314\) | −1.99513 | −0.112591 | ||||||||
\(315\) | −16.1717 | −0.911172 | ||||||||
\(316\) | 8.43720 | 0.474629 | ||||||||
\(317\) | −2.94022 | −0.165139 | −0.0825695 | − | 0.996585i | \(-0.526313\pi\) | ||||
−0.0825695 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(318\) | −10.6102 | −0.594991 | ||||||||
\(319\) | 2.54086 | 0.142261 | ||||||||
\(320\) | −3.88612 | −0.217241 | ||||||||
\(321\) | 10.4984 | 0.585962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.49724 | −0.138950 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −32.9642 | −1.82853 | ||||||||
\(326\) | 0.698970 | 0.0387124 | ||||||||
\(327\) | 1.27668 | 0.0706005 | ||||||||
\(328\) | −6.11749 | −0.337782 | ||||||||
\(329\) | 9.90943 | 0.546325 | ||||||||
\(330\) | 17.5973 | 0.968702 | ||||||||
\(331\) | −1.21838 | −0.0669682 | −0.0334841 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334841 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(332\) | −0.377030 | −0.0206922 | ||||||||
\(333\) | 2.51890 | 0.138035 | ||||||||
\(334\) | 5.02836 | 0.275140 | ||||||||
\(335\) | 24.4344 | 1.33500 | ||||||||
\(336\) | −4.16140 | −0.227023 | ||||||||
\(337\) | 19.0636 | 1.03846 | 0.519230 | − | 0.854635i | \(-0.326219\pi\) | ||||
0.519230 | + | 0.854635i | \(0.326219\pi\) | |||||||
\(338\) | −2.35183 | −0.127923 | ||||||||
\(339\) | −17.6913 | −0.960858 | ||||||||
\(340\) | 7.10623 | 0.385390 | ||||||||
\(341\) | −20.9955 | −1.13697 | ||||||||
\(342\) | 1.36564 | 0.0738456 | ||||||||
\(343\) | 13.8043 | 0.745365 | ||||||||
\(344\) | 9.85240 | 0.531206 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.68258 | −0.466778 | ||||||||
\(347\) | −12.3566 | −0.663340 | −0.331670 | − | 0.943396i | \(-0.607612\pi\) | ||||
−0.331670 | + | 0.943396i | \(0.607612\pi\) | |||||||
\(348\) | −0.561114 | −0.0300789 | ||||||||
\(349\) | −15.6813 | −0.839400 | −0.419700 | − | 0.907663i | \(-0.637865\pi\) | ||||
−0.419700 | + | 0.907663i | \(0.637865\pi\) | |||||||
\(350\) | 42.0382 | 2.24704 | ||||||||
\(351\) | 3.26315 | 0.174174 | ||||||||
\(352\) | 4.52825 | 0.241357 | ||||||||
\(353\) | 30.5143 | 1.62411 | 0.812057 | − | 0.583578i | \(-0.198348\pi\) | ||||
0.812057 | + | 0.583578i | \(0.198348\pi\) | |||||||
\(354\) | 7.15262 | 0.380158 | ||||||||
\(355\) | 25.0810 | 1.33116 | ||||||||
\(356\) | 15.2049 | 0.805860 | ||||||||
\(357\) | 7.60961 | 0.402743 | ||||||||
\(358\) | −11.5753 | −0.611772 | ||||||||
\(359\) | 16.4977 | 0.870713 | 0.435357 | − | 0.900258i | \(-0.356622\pi\) | ||||
0.435357 | + | 0.900258i | \(0.356622\pi\) | |||||||
\(360\) | −3.88612 | −0.204817 | ||||||||
\(361\) | −17.1350 | −0.901843 | ||||||||
\(362\) | −2.61369 | −0.137372 | ||||||||
\(363\) | −9.50505 | −0.498886 | ||||||||
\(364\) | −13.5793 | −0.711748 | ||||||||
\(365\) | −48.0063 | −2.51276 | ||||||||
\(366\) | 3.25684 | 0.170238 | ||||||||
\(367\) | −27.6912 | −1.44547 | −0.722736 | − | 0.691125i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691125i | \(0.757116\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.11749 | −0.318464 | ||||||||
\(370\) | −9.78874 | −0.508892 | ||||||||
\(371\) | 44.1533 | 2.29233 | ||||||||
\(372\) | 4.63657 | 0.240395 | ||||||||
\(373\) | −20.3626 | −1.05433 | −0.527167 | − | 0.849762i | \(-0.676746\pi\) | ||||
−0.527167 | + | 0.849762i | \(0.676746\pi\) | |||||||
\(374\) | −8.28044 | −0.428171 | ||||||||
\(375\) | 19.8268 | 1.02385 | ||||||||
\(376\) | 2.38128 | 0.122805 | ||||||||
\(377\) | −1.83100 | −0.0943013 | ||||||||
\(378\) | −4.16140 | −0.214039 | ||||||||
\(379\) | −15.3289 | −0.787391 | −0.393695 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393695 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(380\) | −5.30706 | −0.272246 | ||||||||
\(381\) | −10.0980 | −0.517335 | ||||||||
\(382\) | 6.15128 | 0.314727 | ||||||||
\(383\) | −20.7059 | −1.05802 | −0.529011 | − | 0.848615i | \(-0.677437\pi\) | ||||
−0.529011 | + | 0.848615i | \(0.677437\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −73.2295 | −3.73212 | ||||||||
\(386\) | 8.53015 | 0.434173 | ||||||||
\(387\) | 9.85240 | 0.500825 | ||||||||
\(388\) | 18.8759 | 0.958278 | ||||||||
\(389\) | −34.4334 | −1.74584 | −0.872920 | − | 0.487863i | \(-0.837777\pi\) | ||||
−0.872920 | + | 0.487863i | \(0.837777\pi\) | |||||||
\(390\) | −12.6810 | −0.642128 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 10.3172 | 0.521099 | ||||||||
\(393\) | −7.51893 | −0.379280 | ||||||||
\(394\) | 3.29008 | 0.165752 | ||||||||
\(395\) | −32.7880 | −1.64974 | ||||||||
\(396\) | 4.52825 | 0.227553 | ||||||||
\(397\) | −26.4490 | −1.32744 | −0.663718 | − | 0.747983i | \(-0.731022\pi\) | ||||
−0.663718 | + | 0.747983i | \(0.731022\pi\) | |||||||
\(398\) | 20.0262 | 1.00382 | ||||||||
\(399\) | −5.68299 | −0.284505 | ||||||||
\(400\) | 10.1019 | 0.505097 | ||||||||
\(401\) | −17.8995 | −0.893857 | −0.446928 | − | 0.894570i | \(-0.647482\pi\) | ||||
−0.446928 | + | 0.894570i | \(0.647482\pi\) | |||||||
\(402\) | 6.28762 | 0.313598 | ||||||||
\(403\) | 15.1298 | 0.753671 | ||||||||
\(404\) | −1.10306 | −0.0548793 | ||||||||
\(405\) | −3.88612 | −0.193103 | ||||||||
\(406\) | 2.33502 | 0.115885 | ||||||||
\(407\) | 11.4062 | 0.565384 | ||||||||
\(408\) | 1.82862 | 0.0905301 | ||||||||
\(409\) | −9.47776 | −0.468645 | −0.234323 | − | 0.972159i | \(-0.575287\pi\) | ||||
−0.234323 | + | 0.972159i | \(0.575287\pi\) | |||||||
\(410\) | 23.7733 | 1.17408 | ||||||||
\(411\) | 14.3005 | 0.705393 | ||||||||
\(412\) | 3.36648 | 0.165854 | ||||||||
\(413\) | −29.7649 | −1.46464 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.46519 | 0.0719232 | ||||||||
\(416\) | −3.26315 | −0.159989 | ||||||||
\(417\) | −21.8003 | −1.06756 | ||||||||
\(418\) | 6.18398 | 0.302468 | ||||||||
\(419\) | −22.4130 | −1.09495 | −0.547474 | − | 0.836822i | \(-0.684411\pi\) | ||||
−0.547474 | + | 0.836822i | \(0.684411\pi\) | |||||||
\(420\) | 16.1717 | 0.789098 | ||||||||
\(421\) | −1.53019 | −0.0745770 | −0.0372885 | − | 0.999305i | \(-0.511872\pi\) | ||||
−0.0372885 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(422\) | 2.62325 | 0.127698 | ||||||||
\(423\) | 2.38128 | 0.115782 | ||||||||
\(424\) | 10.6102 | 0.515278 | ||||||||
\(425\) | −18.4726 | −0.896053 | ||||||||
\(426\) | 6.45399 | 0.312697 | ||||||||
\(427\) | −13.5530 | −0.655875 | ||||||||
\(428\) | −10.4984 | −0.507458 | ||||||||
\(429\) | 14.7764 | 0.713410 | ||||||||
\(430\) | −38.2876 | −1.84639 | ||||||||
\(431\) | 0.121649 | 0.00585962 | 0.00292981 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00292981 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 34.9931 | 1.68166 | 0.840830 | − | 0.541300i | \(-0.182068\pi\) | ||||
0.840830 | + | 0.541300i | \(0.182068\pi\) | |||||||
\(434\) | −19.2946 | −0.926171 | ||||||||
\(435\) | 2.18056 | 0.104550 | ||||||||
\(436\) | −1.27668 | −0.0611418 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −12.3533 | −0.590262 | ||||||||
\(439\) | −21.5673 | −1.02935 | −0.514676 | − | 0.857385i | \(-0.672088\pi\) | ||||
−0.514676 | + | 0.857385i | \(0.672088\pi\) | |||||||
\(440\) | −17.5973 | −0.838920 | ||||||||
\(441\) | 10.3172 | 0.491297 | ||||||||
\(442\) | 5.96706 | 0.283824 | ||||||||
\(443\) | −3.30287 | −0.156924 | −0.0784620 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784620 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(444\) | −2.51890 | −0.119542 | ||||||||
\(445\) | −59.0883 | −2.80105 | ||||||||
\(446\) | 3.40900 | 0.161421 | ||||||||
\(447\) | 2.08094 | 0.0984250 | ||||||||
\(448\) | 4.16140 | 0.196608 | ||||||||
\(449\) | 22.2893 | 1.05190 | 0.525949 | − | 0.850516i | \(-0.323710\pi\) | ||||
0.525949 | + | 0.850516i | \(0.323710\pi\) | |||||||
\(450\) | 10.1019 | 0.476210 | ||||||||
\(451\) | −27.7015 | −1.30441 | ||||||||
\(452\) | 17.6913 | 0.832127 | ||||||||
\(453\) | −18.7684 | −0.881816 | ||||||||
\(454\) | 14.8065 | 0.694906 | ||||||||
\(455\) | 52.7707 | 2.47393 | ||||||||
\(456\) | −1.36564 | −0.0639521 | ||||||||
\(457\) | −36.1129 | −1.68929 | −0.844645 | − | 0.535327i | \(-0.820188\pi\) | ||||
−0.844645 | + | 0.535327i | \(0.820188\pi\) | |||||||
\(458\) | 9.79565 | 0.457721 | ||||||||
\(459\) | 1.82862 | 0.0853526 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5662 | 1.47018 | 0.735091 | − | 0.677968i | \(-0.237139\pi\) | ||||
0.735091 | + | 0.677968i | \(0.237139\pi\) | |||||||
\(462\) | −18.8439 | −0.876695 | ||||||||
\(463\) | −27.8475 | −1.29418 | −0.647092 | − | 0.762412i | \(-0.724015\pi\) | ||||
−0.647092 | + | 0.762412i | \(0.724015\pi\) | |||||||
\(464\) | 0.561114 | 0.0260490 | ||||||||
\(465\) | −18.0183 | −0.835577 | ||||||||
\(466\) | −3.95532 | −0.183227 | ||||||||
\(467\) | 0.589854 | 0.0272952 | 0.0136476 | − | 0.999907i | \(-0.495656\pi\) | ||||
0.0136476 | + | 0.999907i | \(0.495656\pi\) | |||||||
\(468\) | −3.26315 | −0.150839 | ||||||||
\(469\) | −26.1653 | −1.20820 | ||||||||
\(470\) | −9.25393 | −0.426852 | ||||||||
\(471\) | 1.99513 | 0.0919305 | ||||||||
\(472\) | −7.15262 | −0.329226 | ||||||||
\(473\) | 44.6141 | 2.05136 | ||||||||
\(474\) | −8.43720 | −0.387533 | ||||||||
\(475\) | 13.7957 | 0.632988 | ||||||||
\(476\) | −7.60961 | −0.348786 | ||||||||
\(477\) | 10.6102 | 0.485808 | ||||||||
\(478\) | −9.82751 | −0.449500 | ||||||||
\(479\) | −10.2856 | −0.469960 | −0.234980 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234980 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(480\) | 3.88612 | 0.177376 | ||||||||
\(481\) | −8.21955 | −0.374779 | ||||||||
\(482\) | 21.6867 | 0.987804 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.50505 | 0.432048 | ||||||||
\(485\) | −73.3540 | −3.33083 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −27.5042 | −1.24633 | −0.623167 | − | 0.782089i | \(-0.714154\pi\) | ||||
−0.623167 | + | 0.782089i | \(0.714154\pi\) | |||||||
\(488\) | −3.25684 | −0.147430 | ||||||||
\(489\) | −0.698970 | −0.0316085 | ||||||||
\(490\) | −40.0941 | −1.81126 | ||||||||
\(491\) | 8.79100 | 0.396732 | 0.198366 | − | 0.980128i | \(-0.436436\pi\) | ||||
0.198366 | + | 0.980128i | \(0.436436\pi\) | |||||||
\(492\) | 6.11749 | 0.275798 | ||||||||
\(493\) | −1.02606 | −0.0462115 | ||||||||
\(494\) | −4.45630 | −0.200499 | ||||||||
\(495\) | −17.5973 | −0.790941 | ||||||||
\(496\) | −4.63657 | −0.208188 | ||||||||
\(497\) | −26.8576 | −1.20473 | ||||||||
\(498\) | 0.377030 | 0.0168951 | ||||||||
\(499\) | 23.5520 | 1.05433 | 0.527167 | − | 0.849762i | \(-0.323254\pi\) | ||||
0.527167 | + | 0.849762i | \(0.323254\pi\) | |||||||
\(500\) | −19.8268 | −0.886682 | ||||||||
\(501\) | −5.02836 | −0.224651 | ||||||||
\(502\) | −7.45090 | −0.332550 | ||||||||
\(503\) | 6.82809 | 0.304450 | 0.152225 | − | 0.988346i | \(-0.451356\pi\) | ||||
0.152225 | + | 0.988346i | \(0.451356\pi\) | |||||||
\(504\) | 4.16140 | 0.185363 | ||||||||
\(505\) | 4.28663 | 0.190752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.35183 | 0.104449 | ||||||||
\(508\) | 10.0980 | 0.448025 | ||||||||
\(509\) | 18.7374 | 0.830522 | 0.415261 | − | 0.909702i | \(-0.363690\pi\) | ||||
0.415261 | + | 0.909702i | \(0.363690\pi\) | |||||||
\(510\) | −7.10623 | −0.314669 | ||||||||
\(511\) | 51.4069 | 2.27411 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.36564 | −0.0602946 | ||||||||
\(514\) | 4.10261 | 0.180958 | ||||||||
\(515\) | −13.0825 | −0.576486 | ||||||||
\(516\) | −9.85240 | −0.433728 | ||||||||
\(517\) | 10.7830 | 0.474236 | ||||||||
\(518\) | 10.4821 | 0.460558 | ||||||||
\(519\) | 8.68258 | 0.381123 | ||||||||
\(520\) | 12.6810 | 0.556099 | ||||||||
\(521\) | 31.2416 | 1.36872 | 0.684360 | − | 0.729144i | \(-0.260082\pi\) | ||||
0.684360 | + | 0.729144i | \(0.260082\pi\) | |||||||
\(522\) | 0.561114 | 0.0245593 | ||||||||
\(523\) | 13.6962 | 0.598892 | 0.299446 | − | 0.954113i | \(-0.403198\pi\) | ||||
0.299446 | + | 0.954113i | \(0.403198\pi\) | |||||||
\(524\) | 7.51893 | 0.328466 | ||||||||
\(525\) | −42.0382 | −1.83470 | ||||||||
\(526\) | −26.8046 | −1.16873 | ||||||||
\(527\) | 8.47851 | 0.369330 | ||||||||
\(528\) | −4.52825 | −0.197067 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −41.2326 | −1.79103 | ||||||||
\(531\) | −7.15262 | −0.310397 | ||||||||
\(532\) | 5.68299 | 0.246389 | ||||||||
\(533\) | 19.9623 | 0.864664 | ||||||||
\(534\) | −15.2049 | −0.657982 | ||||||||
\(535\) | 40.7980 | 1.76385 | ||||||||
\(536\) | −6.28762 | −0.271584 | ||||||||
\(537\) | 11.5753 | 0.499510 | ||||||||
\(538\) | −5.74299 | −0.247598 | ||||||||
\(539\) | 46.7190 | 2.01233 | ||||||||
\(540\) | 3.88612 | 0.167232 | ||||||||
\(541\) | 23.8228 | 1.02422 | 0.512111 | − | 0.858919i | \(-0.328864\pi\) | ||||
0.512111 | + | 0.858919i | \(0.328864\pi\) | |||||||
\(542\) | 6.93596 | 0.297925 | ||||||||
\(543\) | 2.61369 | 0.112164 | ||||||||
\(544\) | −1.82862 | −0.0784014 | ||||||||
\(545\) | 4.96133 | 0.212520 | ||||||||
\(546\) | 13.5793 | 0.581140 | ||||||||
\(547\) | −22.0310 | −0.941977 | −0.470988 | − | 0.882139i | \(-0.656103\pi\) | ||||
−0.470988 | + | 0.882139i | \(0.656103\pi\) | |||||||
\(548\) | −14.3005 | −0.610888 | ||||||||
\(549\) | −3.25684 | −0.138998 | ||||||||
\(550\) | 45.7442 | 1.95054 | ||||||||
\(551\) | 0.766281 | 0.0326447 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.1105 | 1.49305 | ||||||||
\(554\) | −3.81024 | −0.161882 | ||||||||
\(555\) | 9.78874 | 0.415509 | ||||||||
\(556\) | 21.8003 | 0.924537 | ||||||||
\(557\) | 10.0072 | 0.424019 | 0.212010 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212010 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(558\) | −4.63657 | −0.196282 | ||||||||
\(559\) | −32.1499 | −1.35979 | ||||||||
\(560\) | −16.1717 | −0.683379 | ||||||||
\(561\) | 8.28044 | 0.349600 | ||||||||
\(562\) | 18.1727 | 0.766571 | ||||||||
\(563\) | 13.6494 | 0.575252 | 0.287626 | − | 0.957743i | \(-0.407134\pi\) | ||||
0.287626 | + | 0.957743i | \(0.407134\pi\) | |||||||
\(564\) | −2.38128 | −0.100270 | ||||||||
\(565\) | −68.7504 | −2.89235 | ||||||||
\(566\) | −17.0969 | −0.718638 | ||||||||
\(567\) | 4.16140 | 0.174762 | ||||||||
\(568\) | −6.45399 | −0.270804 | ||||||||
\(569\) | 20.5236 | 0.860394 | 0.430197 | − | 0.902735i | \(-0.358444\pi\) | ||||
0.430197 | + | 0.902735i | \(0.358444\pi\) | |||||||
\(570\) | 5.30706 | 0.222288 | ||||||||
\(571\) | −10.3256 | −0.432114 | −0.216057 | − | 0.976381i | \(-0.569320\pi\) | ||||
−0.216057 | + | 0.976381i | \(0.569320\pi\) | |||||||
\(572\) | −14.7764 | −0.617831 | ||||||||
\(573\) | −6.15128 | −0.256974 | ||||||||
\(574\) | −25.4573 | −1.06257 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 40.8152 | 1.69916 | 0.849579 | − | 0.527461i | \(-0.176856\pi\) | ||||
0.849579 | + | 0.527461i | \(0.176856\pi\) | |||||||
\(578\) | −13.6562 | −0.568021 | ||||||||
\(579\) | −8.53015 | −0.354501 | ||||||||
\(580\) | −2.18056 | −0.0905427 | ||||||||
\(581\) | −1.56897 | −0.0650920 | ||||||||
\(582\) | −18.8759 | −0.782431 | ||||||||
\(583\) | 48.0457 | 1.98985 | ||||||||
\(584\) | 12.3533 | 0.511182 | ||||||||
\(585\) | 12.6810 | 0.524295 | ||||||||
\(586\) | −13.0545 | −0.539275 | ||||||||
\(587\) | 42.9852 | 1.77419 | 0.887095 | − | 0.461587i | \(-0.152720\pi\) | ||||
0.887095 | + | 0.461587i | \(0.152720\pi\) | |||||||
\(588\) | −10.3172 | −0.425476 | ||||||||
\(589\) | −6.33190 | −0.260901 | ||||||||
\(590\) | 27.7960 | 1.14434 | ||||||||
\(591\) | −3.29008 | −0.135336 | ||||||||
\(592\) | 2.51890 | 0.103526 | ||||||||
\(593\) | −24.9472 | −1.02446 | −0.512229 | − | 0.858849i | \(-0.671180\pi\) | ||||
−0.512229 | + | 0.858849i | \(0.671180\pi\) | |||||||
\(594\) | −4.52825 | −0.185796 | ||||||||
\(595\) | 29.5719 | 1.21233 | ||||||||
\(596\) | −2.08094 | −0.0852385 | ||||||||
\(597\) | −20.0262 | −0.819618 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7284 | 1.37811 | 0.689053 | − | 0.724711i | \(-0.258027\pi\) | ||||
0.689053 | + | 0.724711i | \(0.258027\pi\) | |||||||
\(600\) | −10.1019 | −0.412410 | ||||||||
\(601\) | 39.8604 | 1.62594 | 0.812970 | − | 0.582306i | \(-0.197849\pi\) | ||||
0.812970 | + | 0.582306i | \(0.197849\pi\) | |||||||
\(602\) | 40.9997 | 1.67102 | ||||||||
\(603\) | −6.28762 | −0.256051 | ||||||||
\(604\) | 18.7684 | 0.763675 | ||||||||
\(605\) | −36.9378 | −1.50174 | ||||||||
\(606\) | 1.10306 | 0.0448087 | ||||||||
\(607\) | 28.8082 | 1.16929 | 0.584645 | − | 0.811289i | \(-0.301234\pi\) | ||||
0.584645 | + | 0.811289i | \(0.301234\pi\) | |||||||
\(608\) | 1.36564 | 0.0553842 | ||||||||
\(609\) | −2.33502 | −0.0946197 | ||||||||
\(610\) | 12.6565 | 0.512445 | ||||||||
\(611\) | −7.77047 | −0.314359 | ||||||||
\(612\) | −1.82862 | −0.0739175 | ||||||||
\(613\) | −28.9620 | −1.16977 | −0.584883 | − | 0.811118i | \(-0.698860\pi\) | ||||
−0.584883 | + | 0.811118i | \(0.698860\pi\) | |||||||
\(614\) | −24.0856 | −0.972017 | ||||||||
\(615\) | −23.7733 | −0.958633 | ||||||||
\(616\) | 18.8439 | 0.759241 | ||||||||
\(617\) | −26.0167 | −1.04739 | −0.523696 | − | 0.851905i | \(-0.675447\pi\) | ||||
−0.523696 | + | 0.851905i | \(0.675447\pi\) | |||||||
\(618\) | −3.36648 | −0.135420 | ||||||||
\(619\) | 21.2470 | 0.853989 | 0.426995 | − | 0.904254i | \(-0.359572\pi\) | ||||
0.426995 | + | 0.904254i | \(0.359572\pi\) | |||||||
\(620\) | 18.0183 | 0.723631 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.64709 | 0.106139 | ||||||||
\(623\) | 63.2738 | 2.53501 | ||||||||
\(624\) | 3.26315 | 0.130631 | ||||||||
\(625\) | 26.5396 | 1.06159 | ||||||||
\(626\) | −25.0150 | −0.999800 | ||||||||
\(627\) | −6.18398 | −0.246964 | ||||||||
\(628\) | −1.99513 | −0.0796142 | ||||||||
\(629\) | −4.60610 | −0.183657 | ||||||||
\(630\) | −16.1717 | −0.644296 | ||||||||
\(631\) | 17.1772 | 0.683813 | 0.341906 | − | 0.939734i | \(-0.388927\pi\) | ||||
0.341906 | + | 0.939734i | \(0.388927\pi\) | |||||||
\(632\) | 8.43720 | 0.335614 | ||||||||
\(633\) | −2.62325 | −0.104265 | ||||||||
\(634\) | −2.94022 | −0.116771 | ||||||||
\(635\) | −39.2420 | −1.55727 | ||||||||
\(636\) | −10.6102 | −0.420722 | ||||||||
\(637\) | −33.6667 | −1.33392 | ||||||||
\(638\) | 2.54086 | 0.100594 | ||||||||
\(639\) | −6.45399 | −0.255316 | ||||||||
\(640\) | −3.88612 | −0.153612 | ||||||||
\(641\) | −2.37406 | −0.0937697 | −0.0468848 | − | 0.998900i | \(-0.514929\pi\) | ||||
−0.0468848 | + | 0.998900i | \(0.514929\pi\) | |||||||
\(642\) | 10.4984 | 0.414338 | ||||||||
\(643\) | 46.5640 | 1.83630 | 0.918152 | − | 0.396229i | \(-0.129681\pi\) | ||||
0.918152 | + | 0.396229i | \(0.129681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.2876 | 1.50757 | ||||||||
\(646\) | −2.49724 | −0.0982526 | ||||||||
\(647\) | −9.57063 | −0.376260 | −0.188130 | − | 0.982144i | \(-0.560243\pi\) | ||||
−0.188130 | + | 0.982144i | \(0.560243\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −32.3889 | −1.27137 | ||||||||
\(650\) | −32.9642 | −1.29296 | ||||||||
\(651\) | 19.2946 | 0.756215 | ||||||||
\(652\) | 0.698970 | 0.0273738 | ||||||||
\(653\) | −32.1688 | −1.25886 | −0.629432 | − | 0.777056i | \(-0.716712\pi\) | ||||
−0.629432 | + | 0.777056i | \(0.716712\pi\) | |||||||
\(654\) | 1.27668 | 0.0499221 | ||||||||
\(655\) | −29.2195 | −1.14170 | ||||||||
\(656\) | −6.11749 | −0.238848 | ||||||||
\(657\) | 12.3533 | 0.481947 | ||||||||
\(658\) | 9.90943 | 0.386310 | ||||||||
\(659\) | 1.81861 | 0.0708431 | 0.0354216 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354216 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(660\) | 17.5973 | 0.684975 | ||||||||
\(661\) | 40.7121 | 1.58352 | 0.791760 | − | 0.610833i | \(-0.209165\pi\) | ||||
0.791760 | + | 0.610833i | \(0.209165\pi\) | |||||||
\(662\) | −1.21838 | −0.0473537 | ||||||||
\(663\) | −5.96706 | −0.231741 | ||||||||
\(664\) | −0.377030 | −0.0146316 | ||||||||
\(665\) | −22.0848 | −0.856411 | ||||||||
\(666\) | 2.51890 | 0.0976053 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.02836 | 0.194553 | ||||||||
\(669\) | −3.40900 | −0.131799 | ||||||||
\(670\) | 24.4344 | 0.943985 | ||||||||
\(671\) | −14.7478 | −0.569331 | ||||||||
\(672\) | −4.16140 | −0.160529 | ||||||||
\(673\) | −12.9279 | −0.498335 | −0.249167 | − | 0.968460i | \(-0.580157\pi\) | ||||
−0.249167 | + | 0.968460i | \(0.580157\pi\) | |||||||
\(674\) | 19.0636 | 0.734302 | ||||||||
\(675\) | −10.1019 | −0.388824 | ||||||||
\(676\) | −2.35183 | −0.0904551 | ||||||||
\(677\) | 6.82478 | 0.262298 | 0.131149 | − | 0.991363i | \(-0.458133\pi\) | ||||
0.131149 | + | 0.991363i | \(0.458133\pi\) | |||||||
\(678\) | −17.6913 | −0.679429 | ||||||||
\(679\) | 78.5501 | 3.01448 | ||||||||
\(680\) | 7.10623 | 0.272512 | ||||||||
\(681\) | −14.8065 | −0.567388 | ||||||||
\(682\) | −20.9955 | −0.803961 | ||||||||
\(683\) | 1.89490 | 0.0725064 | 0.0362532 | − | 0.999343i | \(-0.488458\pi\) | ||||
0.0362532 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(684\) | 1.36564 | 0.0522167 | ||||||||
\(685\) | 55.5736 | 2.12336 | ||||||||
\(686\) | 13.8043 | 0.527052 | ||||||||
\(687\) | −9.79565 | −0.373727 | ||||||||
\(688\) | 9.85240 | 0.375619 | ||||||||
\(689\) | −34.6228 | −1.31902 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4219 | −0.548635 | −0.274317 | − | 0.961639i | \(-0.588452\pi\) | ||||
−0.274317 | + | 0.961639i | \(0.588452\pi\) | |||||||
\(692\) | −8.68258 | −0.330062 | ||||||||
\(693\) | 18.8439 | 0.715819 | ||||||||
\(694\) | −12.3566 | −0.469052 | ||||||||
\(695\) | −84.7185 | −3.21356 | ||||||||
\(696\) | −0.561114 | −0.0212690 | ||||||||
\(697\) | 11.1866 | 0.423721 | ||||||||
\(698\) | −15.6813 | −0.593545 | ||||||||
\(699\) | 3.95532 | 0.149604 | ||||||||
\(700\) | 42.0382 | 1.58890 | ||||||||
\(701\) | 36.1516 | 1.36543 | 0.682713 | − | 0.730687i | \(-0.260800\pi\) | ||||
0.682713 | + | 0.730687i | \(0.260800\pi\) | |||||||
\(702\) | 3.26315 | 0.123160 | ||||||||
\(703\) | 3.43992 | 0.129739 | ||||||||
\(704\) | 4.52825 | 0.170665 | ||||||||
\(705\) | 9.25393 | 0.348523 | ||||||||
\(706\) | 30.5143 | 1.14842 | ||||||||
\(707\) | −4.59027 | −0.172635 | ||||||||
\(708\) | 7.15262 | 0.268812 | ||||||||
\(709\) | 19.0207 | 0.714337 | 0.357168 | − | 0.934040i | \(-0.383742\pi\) | ||||
0.357168 | + | 0.934040i | \(0.383742\pi\) | |||||||
\(710\) | 25.0810 | 0.941274 | ||||||||
\(711\) | 8.43720 | 0.316420 | ||||||||
\(712\) | 15.2049 | 0.569829 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 7.60961 | 0.284782 | ||||||||
\(715\) | 57.4228 | 2.14749 | ||||||||
\(716\) | −11.5753 | −0.432588 | ||||||||
\(717\) | 9.82751 | 0.367015 | ||||||||
\(718\) | 16.4977 | 0.615687 | ||||||||
\(719\) | −11.0635 | −0.412600 | −0.206300 | − | 0.978489i | \(-0.566142\pi\) | ||||
−0.206300 | + | 0.978489i | \(0.566142\pi\) | |||||||
\(720\) | −3.88612 | −0.144827 | ||||||||
\(721\) | 14.0093 | 0.521732 | ||||||||
\(722\) | −17.1350 | −0.637699 | ||||||||
\(723\) | −21.6867 | −0.806538 | ||||||||
\(724\) | −2.61369 | −0.0971370 | ||||||||
\(725\) | 5.66834 | 0.210517 | ||||||||
\(726\) | −9.50505 | −0.352766 | ||||||||
\(727\) | −5.79278 | −0.214843 | −0.107421 | − | 0.994214i | \(-0.534259\pi\) | ||||
−0.107421 | + | 0.994214i | \(0.534259\pi\) | |||||||
\(728\) | −13.5793 | −0.503282 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −48.0063 | −1.77679 | ||||||||
\(731\) | −18.0163 | −0.666356 | ||||||||
\(732\) | 3.25684 | 0.120376 | ||||||||
\(733\) | −14.8050 | −0.546836 | −0.273418 | − | 0.961895i | \(-0.588154\pi\) | ||||
−0.273418 | + | 0.961895i | \(0.588154\pi\) | |||||||
\(734\) | −27.6912 | −1.02210 | ||||||||
\(735\) | 40.0941 | 1.47889 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.4719 | −1.04878 | ||||||||
\(738\) | −6.11749 | −0.225188 | ||||||||
\(739\) | 3.68448 | 0.135536 | 0.0677679 | − | 0.997701i | \(-0.478412\pi\) | ||||
0.0677679 | + | 0.997701i | \(0.478412\pi\) | |||||||
\(740\) | −9.78874 | −0.359841 | ||||||||
\(741\) | 4.45630 | 0.163706 | ||||||||
\(742\) | 44.1533 | 1.62092 | ||||||||
\(743\) | −40.5510 | −1.48767 | −0.743835 | − | 0.668363i | \(-0.766995\pi\) | ||||
−0.743835 | + | 0.668363i | \(0.766995\pi\) | |||||||
\(744\) | 4.63657 | 0.169985 | ||||||||
\(745\) | 8.08678 | 0.296277 | ||||||||
\(746\) | −20.3626 | −0.745526 | ||||||||
\(747\) | −0.377030 | −0.0137948 | ||||||||
\(748\) | −8.28044 | −0.302763 | ||||||||
\(749\) | −43.6879 | −1.59632 | ||||||||
\(750\) | 19.8268 | 0.723972 | ||||||||
\(751\) | 16.0575 | 0.585947 | 0.292974 | − | 0.956120i | \(-0.405355\pi\) | ||||
0.292974 | + | 0.956120i | \(0.405355\pi\) | |||||||
\(752\) | 2.38128 | 0.0868362 | ||||||||
\(753\) | 7.45090 | 0.271526 | ||||||||
\(754\) | −1.83100 | −0.0666811 | ||||||||
\(755\) | −72.9363 | −2.65442 | ||||||||
\(756\) | −4.16140 | −0.151349 | ||||||||
\(757\) | −46.6087 | −1.69402 | −0.847011 | − | 0.531575i | \(-0.821600\pi\) | ||||
−0.847011 | + | 0.531575i | \(0.821600\pi\) | |||||||
\(758\) | −15.3289 | −0.556769 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.30706 | −0.192507 | ||||||||
\(761\) | −24.2888 | −0.880467 | −0.440234 | − | 0.897883i | \(-0.645104\pi\) | ||||
−0.440234 | + | 0.897883i | \(0.645104\pi\) | |||||||
\(762\) | −10.0980 | −0.365811 | ||||||||
\(763\) | −5.31277 | −0.192335 | ||||||||
\(764\) | 6.15128 | 0.222546 | ||||||||
\(765\) | 7.10623 | 0.256926 | ||||||||
\(766\) | −20.7059 | −0.748135 | ||||||||
\(767\) | 23.3401 | 0.842762 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 18.4202 | 0.664250 | 0.332125 | − | 0.943235i | \(-0.392234\pi\) | ||||
0.332125 | + | 0.943235i | \(0.392234\pi\) | |||||||
\(770\) | −73.2295 | −2.63901 | ||||||||
\(771\) | −4.10261 | −0.147752 | ||||||||
\(772\) | 8.53015 | 0.307007 | ||||||||
\(773\) | 0.914757 | 0.0329015 | 0.0164508 | − | 0.999865i | \(-0.494763\pi\) | ||||
0.0164508 | + | 0.999865i | \(0.494763\pi\) | |||||||
\(774\) | 9.85240 | 0.354137 | ||||||||
\(775\) | −46.8384 | −1.68248 | ||||||||
\(776\) | 18.8759 | 0.677605 | ||||||||
\(777\) | −10.4821 | −0.376044 | ||||||||
\(778\) | −34.4334 | −1.23450 | ||||||||
\(779\) | −8.35432 | −0.299324 | ||||||||
\(780\) | −12.6810 | −0.454053 | ||||||||
\(781\) | −29.2253 | −1.04576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.561114 | −0.0200526 | ||||||||
\(784\) | 10.3172 | 0.368473 | ||||||||
\(785\) | 7.75330 | 0.276727 | ||||||||
\(786\) | −7.51893 | −0.268191 | ||||||||
\(787\) | −23.8906 | −0.851608 | −0.425804 | − | 0.904815i | \(-0.640009\pi\) | ||||
−0.425804 | + | 0.904815i | \(0.640009\pi\) | |||||||
\(788\) | 3.29008 | 0.117204 | ||||||||
\(789\) | 26.8046 | 0.954268 | ||||||||
\(790\) | −32.7880 | −1.16654 | ||||||||
\(791\) | 73.6204 | 2.61764 | ||||||||
\(792\) | 4.52825 | 0.160904 | ||||||||
\(793\) | 10.6276 | 0.377395 | ||||||||
\(794\) | −26.4490 | −0.938638 | ||||||||
\(795\) | 41.2326 | 1.46237 | ||||||||
\(796\) | 20.0262 | 0.709810 | ||||||||
\(797\) | −32.1264 | −1.13798 | −0.568988 | − | 0.822346i | \(-0.692665\pi\) | ||||
−0.568988 | + | 0.822346i | \(0.692665\pi\) | |||||||
\(798\) | −5.68299 | −0.201176 | ||||||||
\(799\) | −4.35444 | −0.154049 | ||||||||
\(800\) | 10.1019 | 0.357158 | ||||||||
\(801\) | 15.2049 | 0.537240 | ||||||||
\(802\) | −17.8995 | −0.632052 | ||||||||
\(803\) | 55.9387 | 1.97403 | ||||||||
\(804\) | 6.28762 | 0.221747 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.1298 | 0.532926 | ||||||||
\(807\) | 5.74299 | 0.202163 | ||||||||
\(808\) | −1.10306 | −0.0388055 | ||||||||
\(809\) | −52.3359 | −1.84003 | −0.920017 | − | 0.391879i | \(-0.871825\pi\) | ||||
−0.920017 | + | 0.391879i | \(0.871825\pi\) | |||||||
\(810\) | −3.88612 | −0.136544 | ||||||||
\(811\) | −46.4728 | −1.63188 | −0.815941 | − | 0.578135i | \(-0.803781\pi\) | ||||
−0.815941 | + | 0.578135i | \(0.803781\pi\) | |||||||
\(812\) | 2.33502 | 0.0819431 | ||||||||
\(813\) | −6.93596 | −0.243255 | ||||||||
\(814\) | 11.4062 | 0.399787 | ||||||||
\(815\) | −2.71628 | −0.0951472 | ||||||||
\(816\) | 1.82862 | 0.0640144 | ||||||||
\(817\) | 13.4549 | 0.470726 | ||||||||
\(818\) | −9.47776 | −0.331382 | ||||||||
\(819\) | −13.5793 | −0.474498 | ||||||||
\(820\) | 23.7733 | 0.830201 | ||||||||
\(821\) | −16.0165 | −0.558981 | −0.279491 | − | 0.960148i | \(-0.590166\pi\) | ||||
−0.279491 | + | 0.960148i | \(0.590166\pi\) | |||||||
\(822\) | 14.3005 | 0.498788 | ||||||||
\(823\) | 48.9112 | 1.70494 | 0.852469 | − | 0.522778i | \(-0.175104\pi\) | ||||
0.852469 | + | 0.522778i | \(0.175104\pi\) | |||||||
\(824\) | 3.36648 | 0.117277 | ||||||||
\(825\) | −45.7442 | −1.59261 | ||||||||
\(826\) | −29.7649 | −1.03565 | ||||||||
\(827\) | 10.4217 | 0.362400 | 0.181200 | − | 0.983446i | \(-0.442002\pi\) | ||||
0.181200 | + | 0.983446i | \(0.442002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.753780 | −0.0261799 | −0.0130899 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130899 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(830\) | 1.46519 | 0.0508574 | ||||||||
\(831\) | 3.81024 | 0.132176 | ||||||||
\(832\) | −3.26315 | −0.113129 | ||||||||
\(833\) | −18.8663 | −0.653678 | ||||||||
\(834\) | −21.8003 | −0.754882 | ||||||||
\(835\) | −19.5408 | −0.676239 | ||||||||
\(836\) | 6.18398 | 0.213877 | ||||||||
\(837\) | 4.63657 | 0.160263 | ||||||||
\(838\) | −22.4130 | −0.774246 | ||||||||
\(839\) | 9.19175 | 0.317335 | 0.158667 | − | 0.987332i | \(-0.449280\pi\) | ||||
0.158667 | + | 0.987332i | \(0.449280\pi\) | |||||||
\(840\) | 16.1717 | 0.557977 | ||||||||
\(841\) | −28.6852 | −0.989143 | ||||||||
\(842\) | −1.53019 | −0.0527339 | ||||||||
\(843\) | −18.1727 | −0.625902 | ||||||||
\(844\) | 2.62325 | 0.0902959 | ||||||||
\(845\) | 9.13951 | 0.314409 | ||||||||
\(846\) | 2.38128 | 0.0818699 | ||||||||
\(847\) | 39.5543 | 1.35910 | ||||||||
\(848\) | 10.6102 | 0.364356 | ||||||||
\(849\) | 17.0969 | 0.586765 | ||||||||
\(850\) | −18.4726 | −0.633605 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 6.45399 | 0.221110 | ||||||||
\(853\) | −37.5833 | −1.28683 | −0.643414 | − | 0.765518i | \(-0.722483\pi\) | ||||
−0.643414 | + | 0.765518i | \(0.722483\pi\) | |||||||
\(854\) | −13.5530 | −0.463774 | ||||||||
\(855\) | −5.30706 | −0.181498 | ||||||||
\(856\) | −10.4984 | −0.358827 | ||||||||
\(857\) | 39.2383 | 1.34036 | 0.670178 | − | 0.742200i | \(-0.266218\pi\) | ||||
0.670178 | + | 0.742200i | \(0.266218\pi\) | |||||||
\(858\) | 14.7764 | 0.504457 | ||||||||
\(859\) | 25.8456 | 0.881842 | 0.440921 | − | 0.897546i | \(-0.354652\pi\) | ||||
0.440921 | + | 0.897546i | \(0.354652\pi\) | |||||||
\(860\) | −38.2876 | −1.30560 | ||||||||
\(861\) | 25.4573 | 0.867583 | ||||||||
\(862\) | 0.121649 | 0.00414337 | ||||||||
\(863\) | −54.5197 | −1.85587 | −0.927936 | − | 0.372740i | \(-0.878419\pi\) | ||||
−0.927936 | + | 0.372740i | \(0.878419\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 33.7416 | 1.14725 | ||||||||
\(866\) | 34.9931 | 1.18911 | ||||||||
\(867\) | 13.6562 | 0.463787 | ||||||||
\(868\) | −19.2946 | −0.654902 | ||||||||
\(869\) | 38.2057 | 1.29604 | ||||||||
\(870\) | 2.18056 | 0.0739278 | ||||||||
\(871\) | 20.5175 | 0.695207 | ||||||||
\(872\) | −1.27668 | −0.0432338 | ||||||||
\(873\) | 18.8759 | 0.638852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −82.5072 | −2.78925 | ||||||||
\(876\) | −12.3533 | −0.417378 | ||||||||
\(877\) | −24.0009 | −0.810451 | −0.405226 | − | 0.914217i | \(-0.632807\pi\) | ||||
−0.405226 | + | 0.914217i | \(0.632807\pi\) | |||||||
\(878\) | −21.5673 | −0.727862 | ||||||||
\(879\) | 13.0545 | 0.440316 | ||||||||
\(880\) | −17.5973 | −0.593206 | ||||||||
\(881\) | 19.3576 | 0.652175 | 0.326088 | − | 0.945340i | \(-0.394270\pi\) | ||||
0.326088 | + | 0.945340i | \(0.394270\pi\) | |||||||
\(882\) | 10.3172 | 0.347399 | ||||||||
\(883\) | −37.7107 | −1.26907 | −0.634534 | − | 0.772895i | \(-0.718808\pi\) | ||||
−0.634534 | + | 0.772895i | \(0.718808\pi\) | |||||||
\(884\) | 5.96706 | 0.200694 | ||||||||
\(885\) | −27.7960 | −0.934351 | ||||||||
\(886\) | −3.30287 | −0.110962 | ||||||||
\(887\) | 5.07878 | 0.170529 | 0.0852643 | − | 0.996358i | \(-0.472827\pi\) | ||||
0.0852643 | + | 0.996358i | \(0.472827\pi\) | |||||||
\(888\) | −2.51890 | −0.0845286 | ||||||||
\(889\) | 42.0217 | 1.40936 | ||||||||
\(890\) | −59.0883 | −1.98064 | ||||||||
\(891\) | 4.52825 | 0.151702 | ||||||||
\(892\) | 3.40900 | 0.114142 | ||||||||
\(893\) | 3.25197 | 0.108823 | ||||||||
\(894\) | 2.08094 | 0.0695970 | ||||||||
\(895\) | 44.9829 | 1.50361 | ||||||||
\(896\) | 4.16140 | 0.139023 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2893 | 0.743804 | ||||||||
\(899\) | −2.60164 | −0.0867696 | ||||||||
\(900\) | 10.1019 | 0.336732 | ||||||||
\(901\) | −19.4020 | −0.646375 | ||||||||
\(902\) | −27.7015 | −0.922360 | ||||||||
\(903\) | −40.9997 | −1.36439 | ||||||||
\(904\) | 17.6913 | 0.588403 | ||||||||
\(905\) | 10.1571 | 0.337634 | ||||||||
\(906\) | −18.7684 | −0.623538 | ||||||||
\(907\) | −36.5683 | −1.21423 | −0.607115 | − | 0.794614i | \(-0.707673\pi\) | ||||
−0.607115 | + | 0.794614i | \(0.707673\pi\) | |||||||
\(908\) | 14.8065 | 0.491372 | ||||||||
\(909\) | −1.10306 | −0.0365862 | ||||||||
\(910\) | 52.7707 | 1.74933 | ||||||||
\(911\) | 28.6820 | 0.950277 | 0.475139 | − | 0.879911i | \(-0.342398\pi\) | ||||
0.475139 | + | 0.879911i | \(0.342398\pi\) | |||||||
\(912\) | −1.36564 | −0.0452210 | ||||||||
\(913\) | −1.70729 | −0.0565030 | ||||||||
\(914\) | −36.1129 | −1.19451 | ||||||||
\(915\) | −12.6565 | −0.418410 | ||||||||
\(916\) | 9.79565 | 0.323657 | ||||||||
\(917\) | 31.2893 | 1.03326 | ||||||||
\(918\) | 1.82862 | 0.0603534 | ||||||||
\(919\) | −16.5221 | −0.545013 | −0.272507 | − | 0.962154i | \(-0.587853\pi\) | ||||
−0.272507 | + | 0.962154i | \(0.587853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0856 | 0.793649 | ||||||||
\(922\) | 31.5662 | 1.03958 | ||||||||
\(923\) | 21.0604 | 0.693211 | ||||||||
\(924\) | −18.8439 | −0.619917 | ||||||||
\(925\) | 25.4458 | 0.836652 | ||||||||
\(926\) | −27.8475 | −0.915126 | ||||||||
\(927\) | 3.36648 | 0.110570 | ||||||||
\(928\) | 0.561114 | 0.0184195 | ||||||||
\(929\) | −3.55998 | −0.116799 | −0.0583996 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0583996 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(930\) | −18.0183 | −0.590842 | ||||||||
\(931\) | 14.0897 | 0.461770 | ||||||||
\(932\) | −3.95532 | −0.129561 | ||||||||
\(933\) | −2.64709 | −0.0866618 | ||||||||
\(934\) | 0.589854 | 0.0193006 | ||||||||
\(935\) | 32.1788 | 1.05236 | ||||||||
\(936\) | −3.26315 | −0.106659 | ||||||||
\(937\) | −50.5231 | −1.65052 | −0.825258 | − | 0.564756i | \(-0.808970\pi\) | ||||
−0.825258 | + | 0.564756i | \(0.808970\pi\) | |||||||
\(938\) | −26.1653 | −0.854326 | ||||||||
\(939\) | 25.0150 | 0.816333 | ||||||||
\(940\) | −9.25393 | −0.301830 | ||||||||
\(941\) | 60.0089 | 1.95623 | 0.978116 | − | 0.208059i | \(-0.0667146\pi\) | ||||
0.978116 | + | 0.208059i | \(0.0667146\pi\) | |||||||
\(942\) | 1.99513 | 0.0650047 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.15262 | −0.232798 | ||||||||
\(945\) | 16.1717 | 0.526066 | ||||||||
\(946\) | 44.6141 | 1.45053 | ||||||||
\(947\) | 10.3111 | 0.335067 | 0.167533 | − | 0.985866i | \(-0.446420\pi\) | ||||
0.167533 | + | 0.985866i | \(0.446420\pi\) | |||||||
\(948\) | −8.43720 | −0.274027 | ||||||||
\(949\) | −40.3106 | −1.30854 | ||||||||
\(950\) | 13.7957 | 0.447590 | ||||||||
\(951\) | 2.94022 | 0.0953431 | ||||||||
\(952\) | −7.60961 | −0.246629 | ||||||||
\(953\) | 42.2831 | 1.36968 | 0.684842 | − | 0.728692i | \(-0.259871\pi\) | ||||
0.684842 | + | 0.728692i | \(0.259871\pi\) | |||||||
\(954\) | 10.6102 | 0.343518 | ||||||||
\(955\) | −23.9046 | −0.773536 | ||||||||
\(956\) | −9.82751 | −0.317844 | ||||||||
\(957\) | −2.54086 | −0.0821344 | ||||||||
\(958\) | −10.2856 | −0.332312 | ||||||||
\(959\) | −59.5102 | −1.92168 | ||||||||
\(960\) | 3.88612 | 0.125424 | ||||||||
\(961\) | −9.50223 | −0.306524 | ||||||||
\(962\) | −8.21955 | −0.265009 | ||||||||
\(963\) | −10.4984 | −0.338305 | ||||||||
\(964\) | 21.6867 | 0.698483 | ||||||||
\(965\) | −33.1492 | −1.06711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.6393 | −0.599399 | −0.299700 | − | 0.954034i | \(-0.596886\pi\) | ||||
−0.299700 | + | 0.954034i | \(0.596886\pi\) | |||||||
\(968\) | 9.50505 | 0.305504 | ||||||||
\(969\) | 2.49724 | 0.0802229 | ||||||||
\(970\) | −73.3540 | −2.35526 | ||||||||
\(971\) | 7.59445 | 0.243718 | 0.121859 | − | 0.992547i | \(-0.461115\pi\) | ||||
0.121859 | + | 0.992547i | \(0.461115\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 90.7196 | 2.90834 | ||||||||
\(974\) | −27.5042 | −0.881291 | ||||||||
\(975\) | 32.9642 | 1.05570 | ||||||||
\(976\) | −3.25684 | −0.104249 | ||||||||
\(977\) | 12.9508 | 0.414332 | 0.207166 | − | 0.978306i | \(-0.433576\pi\) | ||||
0.207166 | + | 0.978306i | \(0.433576\pi\) | |||||||
\(978\) | −0.698970 | −0.0223506 | ||||||||
\(979\) | 68.8518 | 2.20051 | ||||||||
\(980\) | −40.0941 | −1.28076 | ||||||||
\(981\) | −1.27668 | −0.0407612 | ||||||||
\(982\) | 8.79100 | 0.280532 | ||||||||
\(983\) | −36.3780 | −1.16028 | −0.580139 | − | 0.814518i | \(-0.697002\pi\) | ||||
−0.580139 | + | 0.814518i | \(0.697002\pi\) | |||||||
\(984\) | 6.11749 | 0.195019 | ||||||||
\(985\) | −12.7857 | −0.407385 | ||||||||
\(986\) | −1.02606 | −0.0326765 | ||||||||
\(987\) | −9.90943 | −0.315421 | ||||||||
\(988\) | −4.45630 | −0.141774 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −17.5973 | −0.559280 | ||||||||
\(991\) | −31.3165 | −0.994801 | −0.497400 | − | 0.867521i | \(-0.665712\pi\) | ||||
−0.497400 | + | 0.867521i | \(0.665712\pi\) | |||||||
\(992\) | −4.63657 | −0.147211 | ||||||||
\(993\) | 1.21838 | 0.0386641 | ||||||||
\(994\) | −26.8576 | −0.851873 | ||||||||
\(995\) | −77.8243 | −2.46720 | ||||||||
\(996\) | 0.377030 | 0.0119467 | ||||||||
\(997\) | −19.4478 | −0.615920 | −0.307960 | − | 0.951399i | \(-0.599646\pi\) | ||||
−0.307960 | + | 0.951399i | \(0.599646\pi\) | |||||||
\(998\) | 23.5520 | 0.745526 | ||||||||
\(999\) | −2.51890 | −0.0796944 |
(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 | 3174.2.a.ba.1.1 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bs.1.5 | 5 | |||
23.4 | even | 11 | 138.2.e.b.85.1 | yes | 10 | ||
23.6 | even | 11 | 138.2.e.b.13.1 | ✓ | 10 | ||
23.22 | odd | 2 | 3174.2.a.bb.1.5 | 5 | |||
69.29 | odd | 22 | 414.2.i.e.289.1 | 10 | |||
69.50 | odd | 22 | 414.2.i.e.361.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.br.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.b.13.1 | ✓ | 10 | 23.6 | even | 11 | ||
138.2.e.b.85.1 | yes | 10 | 23.4 | even | 11 | ||
414.2.i.e.289.1 | 10 | 69.29 | odd | 22 | |||
414.2.i.e.361.1 | 10 | 69.50 | odd | 22 | |||
3174.2.a.ba.1.1 | 5 | 1.1 | even | 1 | trivial | ||
3174.2.a.bb.1.5 | 5 | 23.22 | odd | 2 | |||
9522.2.a.br.1.1 | 5 | 69.68 | even | 2 | |||
9522.2.a.bs.1.5 | 5 | 3.2 | odd | 2 |