Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58711 | −1.82936 | −0.914680 | − | 0.404178i | \(-0.867557\pi\) | ||||
−0.914680 | + | 0.404178i | \(0.867557\pi\) | |||||||
\(3\) | −3.26786 | −1.88670 | −0.943351 | − | 0.331796i | \(-0.892345\pi\) | ||||
−0.943351 | + | 0.331796i | \(0.892345\pi\) | |||||||
\(4\) | 4.69312 | 2.34656 | ||||||||
\(5\) | 2.66521 | 1.19192 | 0.595958 | − | 0.803015i | \(-0.296772\pi\) | ||||
0.595958 | + | 0.803015i | \(0.296772\pi\) | |||||||
\(6\) | 8.45431 | 3.45146 | ||||||||
\(7\) | 2.69955 | 1.02033 | 0.510167 | − | 0.860075i | \(-0.329584\pi\) | ||||
0.510167 | + | 0.860075i | \(0.329584\pi\) | |||||||
\(8\) | −6.96738 | −2.46334 | ||||||||
\(9\) | 7.67894 | 2.55965 | ||||||||
\(10\) | −6.89517 | −2.18045 | ||||||||
\(11\) | 1.78104 | 0.537004 | 0.268502 | − | 0.963279i | \(-0.413471\pi\) | ||||
0.268502 | + | 0.963279i | \(0.413471\pi\) | |||||||
\(12\) | −15.3365 | −4.42726 | ||||||||
\(13\) | 0.833324 | 0.231123 | 0.115561 | − | 0.993300i | \(-0.463133\pi\) | ||||
0.115561 | + | 0.993300i | \(0.463133\pi\) | |||||||
\(14\) | −6.98403 | −1.86656 | ||||||||
\(15\) | −8.70953 | −2.24879 | ||||||||
\(16\) | 8.63912 | 2.15978 | ||||||||
\(17\) | 5.88299 | 1.42683 | 0.713417 | − | 0.700740i | \(-0.247147\pi\) | ||||
0.713417 | + | 0.700740i | \(0.247147\pi\) | |||||||
\(18\) | −19.8662 | −4.68252 | ||||||||
\(19\) | 3.75980 | 0.862558 | 0.431279 | − | 0.902219i | \(-0.358063\pi\) | ||||
0.431279 | + | 0.902219i | \(0.358063\pi\) | |||||||
\(20\) | 12.5081 | 2.79690 | ||||||||
\(21\) | −8.82177 | −1.92507 | ||||||||
\(22\) | −4.60774 | −0.982374 | ||||||||
\(23\) | 5.86102 | 1.22211 | 0.611053 | − | 0.791589i | \(-0.290746\pi\) | ||||
0.611053 | + | 0.791589i | \(0.290746\pi\) | |||||||
\(24\) | 22.7685 | 4.64759 | ||||||||
\(25\) | 2.10333 | 0.420665 | ||||||||
\(26\) | −2.15590 | −0.422807 | ||||||||
\(27\) | −15.2901 | −2.94259 | ||||||||
\(28\) | 12.6693 | 2.39428 | ||||||||
\(29\) | −4.40811 | −0.818566 | −0.409283 | − | 0.912407i | \(-0.634221\pi\) | ||||
−0.409283 | + | 0.912407i | \(0.634221\pi\) | |||||||
\(30\) | 22.5325 | 4.11385 | ||||||||
\(31\) | −8.58372 | −1.54168 | −0.770841 | − | 0.637028i | \(-0.780164\pi\) | ||||
−0.770841 | + | 0.637028i | \(0.780164\pi\) | |||||||
\(32\) | −8.41557 | −1.48768 | ||||||||
\(33\) | −5.82020 | −1.01317 | ||||||||
\(34\) | −15.2199 | −2.61019 | ||||||||
\(35\) | 7.19486 | 1.21615 | ||||||||
\(36\) | 36.0382 | 6.00636 | ||||||||
\(37\) | 7.29770 | 1.19973 | 0.599867 | − | 0.800099i | \(-0.295220\pi\) | ||||
0.599867 | + | 0.800099i | \(0.295220\pi\) | |||||||
\(38\) | −9.72700 | −1.57793 | ||||||||
\(39\) | −2.72319 | −0.436060 | ||||||||
\(40\) | −18.5695 | −2.93610 | ||||||||
\(41\) | −10.9515 | −1.71034 | −0.855171 | − | 0.518346i | \(-0.826548\pi\) | ||||
−0.855171 | + | 0.518346i | \(0.826548\pi\) | |||||||
\(42\) | 22.8228 | 3.52164 | ||||||||
\(43\) | 1.81334 | 0.276532 | 0.138266 | − | 0.990395i | \(-0.455847\pi\) | ||||
0.138266 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(44\) | 8.35863 | 1.26011 | ||||||||
\(45\) | 20.4660 | 3.05088 | ||||||||
\(46\) | −15.1631 | −2.23567 | ||||||||
\(47\) | −5.45378 | −0.795515 | −0.397758 | − | 0.917491i | \(-0.630211\pi\) | ||||
−0.397758 | + | 0.917491i | \(0.630211\pi\) | |||||||
\(48\) | −28.2315 | −4.07486 | ||||||||
\(49\) | 0.287576 | 0.0410823 | ||||||||
\(50\) | −5.44153 | −0.769548 | ||||||||
\(51\) | −19.2248 | −2.69201 | ||||||||
\(52\) | 3.91089 | 0.542343 | ||||||||
\(53\) | −1.35833 | −0.186581 | −0.0932905 | − | 0.995639i | \(-0.529739\pi\) | ||||
−0.0932905 | + | 0.995639i | \(0.529739\pi\) | |||||||
\(54\) | 39.5572 | 5.38305 | ||||||||
\(55\) | 4.74684 | 0.640064 | ||||||||
\(56\) | −18.8088 | −2.51343 | ||||||||
\(57\) | −12.2865 | −1.62739 | ||||||||
\(58\) | 11.4043 | 1.49745 | ||||||||
\(59\) | 6.16715 | 0.802895 | 0.401447 | − | 0.915882i | \(-0.368507\pi\) | ||||
0.401447 | + | 0.915882i | \(0.368507\pi\) | |||||||
\(60\) | −40.8749 | −5.27692 | ||||||||
\(61\) | −13.5682 | −1.73723 | −0.868613 | − | 0.495491i | \(-0.834988\pi\) | ||||
−0.868613 | + | 0.495491i | \(0.834988\pi\) | |||||||
\(62\) | 22.2070 | 2.82029 | ||||||||
\(63\) | 20.7297 | 2.61169 | ||||||||
\(64\) | 4.49371 | 0.561714 | ||||||||
\(65\) | 2.22098 | 0.275479 | ||||||||
\(66\) | 15.0575 | 1.85345 | ||||||||
\(67\) | 1.49479 | 0.182617 | 0.0913087 | − | 0.995823i | \(-0.470895\pi\) | ||||
0.0913087 | + | 0.995823i | \(0.470895\pi\) | |||||||
\(68\) | 27.6096 | 3.34815 | ||||||||
\(69\) | −19.1530 | −2.30575 | ||||||||
\(70\) | −18.6139 | −2.22478 | ||||||||
\(71\) | 13.0574 | 1.54963 | 0.774813 | − | 0.632190i | \(-0.217844\pi\) | ||||
0.774813 | + | 0.632190i | \(0.217844\pi\) | |||||||
\(72\) | −53.5021 | −6.30528 | ||||||||
\(73\) | 5.94246 | 0.695513 | 0.347756 | − | 0.937585i | \(-0.386944\pi\) | ||||
0.347756 | + | 0.937585i | \(0.386944\pi\) | |||||||
\(74\) | −18.8799 | −2.19475 | ||||||||
\(75\) | −6.87339 | −0.793670 | ||||||||
\(76\) | 17.6452 | 2.02404 | ||||||||
\(77\) | 4.80801 | 0.547924 | ||||||||
\(78\) | 7.04519 | 0.797710 | ||||||||
\(79\) | 15.6967 | 1.76602 | 0.883011 | − | 0.469352i | \(-0.155512\pi\) | ||||
0.883011 | + | 0.469352i | \(0.155512\pi\) | |||||||
\(80\) | 23.0251 | 2.57428 | ||||||||
\(81\) | 26.9293 | 2.99214 | ||||||||
\(82\) | 28.3328 | 3.12883 | ||||||||
\(83\) | 15.5119 | 1.70266 | 0.851328 | − | 0.524634i | \(-0.175798\pi\) | ||||
0.851328 | + | 0.524634i | \(0.175798\pi\) | |||||||
\(84\) | −41.4016 | −4.51728 | ||||||||
\(85\) | 15.6794 | 1.70067 | ||||||||
\(86\) | −4.69131 | −0.505877 | ||||||||
\(87\) | 14.4051 | 1.54439 | ||||||||
\(88\) | −12.4092 | −1.32282 | ||||||||
\(89\) | 4.85742 | 0.514885 | 0.257442 | − | 0.966294i | \(-0.417120\pi\) | ||||
0.257442 | + | 0.966294i | \(0.417120\pi\) | |||||||
\(90\) | −52.9476 | −5.58117 | ||||||||
\(91\) | 2.24960 | 0.235822 | ||||||||
\(92\) | 27.5064 | 2.86775 | ||||||||
\(93\) | 28.0504 | 2.90869 | ||||||||
\(94\) | 14.1095 | 1.45528 | ||||||||
\(95\) | 10.0206 | 1.02810 | ||||||||
\(96\) | 27.5009 | 2.80680 | ||||||||
\(97\) | −11.1935 | −1.13653 | −0.568263 | − | 0.822847i | \(-0.692384\pi\) | ||||
−0.568263 | + | 0.822847i | \(0.692384\pi\) | |||||||
\(98\) | −0.743990 | −0.0751544 | ||||||||
\(99\) | 13.6765 | 1.37454 | ||||||||
\(100\) | 9.87116 | 0.987116 | ||||||||
\(101\) | −6.38725 | −0.635555 | −0.317778 | − | 0.948165i | \(-0.602937\pi\) | ||||
−0.317778 | + | 0.948165i | \(0.602937\pi\) | |||||||
\(102\) | 49.7366 | 4.92466 | ||||||||
\(103\) | 7.55629 | 0.744543 | 0.372272 | − | 0.928124i | \(-0.378579\pi\) | ||||
0.372272 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(104\) | −5.80609 | −0.569334 | ||||||||
\(105\) | −23.5118 | −2.29452 | ||||||||
\(106\) | 3.51414 | 0.341324 | ||||||||
\(107\) | 20.2302 | 1.95573 | 0.977863 | − | 0.209246i | \(-0.0671010\pi\) | ||||
0.977863 | + | 0.209246i | \(0.0671010\pi\) | |||||||
\(108\) | −71.7584 | −6.90496 | ||||||||
\(109\) | 5.37553 | 0.514882 | 0.257441 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257441 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(110\) | −12.2806 | −1.17091 | ||||||||
\(111\) | −23.8479 | −2.26354 | ||||||||
\(112\) | 23.3218 | 2.20370 | ||||||||
\(113\) | −9.18266 | −0.863832 | −0.431916 | − | 0.901914i | \(-0.642162\pi\) | ||||
−0.431916 | + | 0.901914i | \(0.642162\pi\) | |||||||
\(114\) | 31.7865 | 2.97708 | ||||||||
\(115\) | 15.6208 | 1.45665 | ||||||||
\(116\) | −20.6878 | −1.92081 | ||||||||
\(117\) | 6.39905 | 0.591592 | ||||||||
\(118\) | −15.9551 | −1.46878 | ||||||||
\(119\) | 15.8814 | 1.45585 | ||||||||
\(120\) | 60.6827 | 5.53954 | ||||||||
\(121\) | −7.82790 | −0.711627 | ||||||||
\(122\) | 35.1023 | 3.17801 | ||||||||
\(123\) | 35.7881 | 3.22691 | ||||||||
\(124\) | −40.2844 | −3.61765 | ||||||||
\(125\) | −7.72023 | −0.690519 | ||||||||
\(126\) | −53.6299 | −4.77773 | ||||||||
\(127\) | 13.3228 | 1.18220 | 0.591102 | − | 0.806597i | \(-0.298693\pi\) | ||||
0.591102 | + | 0.806597i | \(0.298693\pi\) | |||||||
\(128\) | 5.20542 | 0.460098 | ||||||||
\(129\) | −5.92576 | −0.521734 | ||||||||
\(130\) | −5.74592 | −0.503950 | ||||||||
\(131\) | −8.33750 | −0.728451 | −0.364226 | − | 0.931311i | \(-0.618666\pi\) | ||||
−0.364226 | + | 0.931311i | \(0.618666\pi\) | |||||||
\(132\) | −27.3149 | −2.37746 | ||||||||
\(133\) | 10.1498 | 0.880097 | ||||||||
\(134\) | −3.86717 | −0.334073 | ||||||||
\(135\) | −40.7514 | −3.50732 | ||||||||
\(136\) | −40.9890 | −3.51478 | ||||||||
\(137\) | −0.0440816 | −0.00376615 | −0.00188307 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188307 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(138\) | 49.5509 | 4.21805 | ||||||||
\(139\) | −8.15248 | −0.691484 | −0.345742 | − | 0.938330i | \(-0.612373\pi\) | ||||
−0.345742 | + | 0.938330i | \(0.612373\pi\) | |||||||
\(140\) | 33.7663 | 2.85378 | ||||||||
\(141\) | 17.8222 | 1.50090 | ||||||||
\(142\) | −33.7808 | −2.83482 | ||||||||
\(143\) | 1.48418 | 0.124114 | ||||||||
\(144\) | 66.3393 | 5.52828 | ||||||||
\(145\) | −11.7485 | −0.975663 | ||||||||
\(146\) | −15.3738 | −1.27234 | ||||||||
\(147\) | −0.939760 | −0.0775101 | ||||||||
\(148\) | 34.2490 | 2.81525 | ||||||||
\(149\) | 13.9625 | 1.14385 | 0.571926 | − | 0.820305i | \(-0.306197\pi\) | ||||
0.571926 | + | 0.820305i | \(0.306197\pi\) | |||||||
\(150\) | 17.7822 | 1.45191 | ||||||||
\(151\) | −11.1285 | −0.905627 | −0.452814 | − | 0.891605i | \(-0.649580\pi\) | ||||
−0.452814 | + | 0.891605i | \(0.649580\pi\) | |||||||
\(152\) | −26.1960 | −2.12477 | ||||||||
\(153\) | 45.1751 | 3.65219 | ||||||||
\(154\) | −12.4388 | −1.00235 | ||||||||
\(155\) | −22.8774 | −1.83756 | ||||||||
\(156\) | −12.7803 | −1.02324 | ||||||||
\(157\) | 9.71956 | 0.775705 | 0.387853 | − | 0.921721i | \(-0.373217\pi\) | ||||
0.387853 | + | 0.921721i | \(0.373217\pi\) | |||||||
\(158\) | −40.6092 | −3.23069 | ||||||||
\(159\) | 4.43884 | 0.352023 | ||||||||
\(160\) | −22.4292 | −1.77319 | ||||||||
\(161\) | 15.8221 | 1.24696 | ||||||||
\(162\) | −69.6689 | −5.47371 | ||||||||
\(163\) | −14.0085 | −1.09723 | −0.548616 | − | 0.836075i | \(-0.684845\pi\) | ||||
−0.548616 | + | 0.836075i | \(0.684845\pi\) | |||||||
\(164\) | −51.3968 | −4.01342 | ||||||||
\(165\) | −15.5120 | −1.20761 | ||||||||
\(166\) | −40.1310 | −3.11477 | ||||||||
\(167\) | −14.4959 | −1.12173 | −0.560864 | − | 0.827908i | \(-0.689531\pi\) | ||||
−0.560864 | + | 0.827908i | \(0.689531\pi\) | |||||||
\(168\) | 61.4646 | 4.74210 | ||||||||
\(169\) | −12.3056 | −0.946582 | ||||||||
\(170\) | −40.5642 | −3.11113 | ||||||||
\(171\) | 28.8713 | 2.20784 | ||||||||
\(172\) | 8.51024 | 0.648900 | ||||||||
\(173\) | −8.85267 | −0.673056 | −0.336528 | − | 0.941673i | \(-0.609253\pi\) | ||||
−0.336528 | + | 0.941673i | \(0.609253\pi\) | |||||||
\(174\) | −37.2676 | −2.82525 | ||||||||
\(175\) | 5.67804 | 0.429219 | ||||||||
\(176\) | 15.3866 | 1.15981 | ||||||||
\(177\) | −20.1534 | −1.51482 | ||||||||
\(178\) | −12.5666 | −0.941910 | ||||||||
\(179\) | 15.2719 | 1.14148 | 0.570739 | − | 0.821131i | \(-0.306657\pi\) | ||||
0.570739 | + | 0.821131i | \(0.306657\pi\) | |||||||
\(180\) | 96.0492 | 7.15908 | ||||||||
\(181\) | 11.4202 | 0.848860 | 0.424430 | − | 0.905461i | \(-0.360475\pi\) | ||||
0.424430 | + | 0.905461i | \(0.360475\pi\) | |||||||
\(182\) | −5.81996 | −0.431404 | ||||||||
\(183\) | 44.3389 | 3.27763 | ||||||||
\(184\) | −40.8360 | −3.01047 | ||||||||
\(185\) | 19.4499 | 1.42998 | ||||||||
\(186\) | −72.5694 | −5.32105 | ||||||||
\(187\) | 10.4778 | 0.766215 | ||||||||
\(188\) | −25.5952 | −1.86672 | ||||||||
\(189\) | −41.2765 | −3.00242 | ||||||||
\(190\) | −25.9245 | −1.88076 | ||||||||
\(191\) | 21.7398 | 1.57304 | 0.786519 | − | 0.617566i | \(-0.211881\pi\) | ||||
0.786519 | + | 0.617566i | \(0.211881\pi\) | |||||||
\(192\) | −14.6848 | −1.05979 | ||||||||
\(193\) | 13.6555 | 0.982947 | 0.491473 | − | 0.870893i | \(-0.336459\pi\) | ||||
0.491473 | + | 0.870893i | \(0.336459\pi\) | |||||||
\(194\) | 28.9587 | 2.07911 | ||||||||
\(195\) | −7.25787 | −0.519747 | ||||||||
\(196\) | 1.34963 | 0.0964021 | ||||||||
\(197\) | 3.84837 | 0.274185 | 0.137092 | − | 0.990558i | \(-0.456224\pi\) | ||||
0.137092 | + | 0.990558i | \(0.456224\pi\) | |||||||
\(198\) | −35.3826 | −2.51453 | ||||||||
\(199\) | 6.90982 | 0.489824 | 0.244912 | − | 0.969545i | \(-0.421241\pi\) | ||||
0.244912 | + | 0.969545i | \(0.421241\pi\) | |||||||
\(200\) | −14.6547 | −1.03624 | ||||||||
\(201\) | −4.88476 | −0.344545 | ||||||||
\(202\) | 16.5245 | 1.16266 | ||||||||
\(203\) | −11.8999 | −0.835211 | ||||||||
\(204\) | −90.2243 | −6.31696 | ||||||||
\(205\) | −29.1881 | −2.03859 | ||||||||
\(206\) | −19.5489 | −1.36204 | ||||||||
\(207\) | 45.0064 | 3.12816 | ||||||||
\(208\) | 7.19919 | 0.499174 | ||||||||
\(209\) | 6.69636 | 0.463197 | ||||||||
\(210\) | 60.8276 | 4.19750 | ||||||||
\(211\) | −22.2344 | −1.53068 | −0.765341 | − | 0.643625i | \(-0.777430\pi\) | ||||
−0.765341 | + | 0.643625i | \(0.777430\pi\) | |||||||
\(212\) | −6.37480 | −0.437823 | ||||||||
\(213\) | −42.6698 | −2.92368 | ||||||||
\(214\) | −52.3376 | −3.57773 | ||||||||
\(215\) | 4.83294 | 0.329604 | ||||||||
\(216\) | 106.532 | 7.24860 | ||||||||
\(217\) | −23.1722 | −1.57303 | ||||||||
\(218\) | −13.9071 | −0.941905 | ||||||||
\(219\) | −19.4192 | −1.31223 | ||||||||
\(220\) | 22.2775 | 1.50195 | ||||||||
\(221\) | 4.90244 | 0.329774 | ||||||||
\(222\) | 61.6971 | 4.14084 | ||||||||
\(223\) | −2.65269 | −0.177637 | −0.0888185 | − | 0.996048i | \(-0.528309\pi\) | ||||
−0.0888185 | + | 0.996048i | \(0.528309\pi\) | |||||||
\(224\) | −22.7183 | −1.51793 | ||||||||
\(225\) | 16.1513 | 1.07675 | ||||||||
\(226\) | 23.7565 | 1.58026 | ||||||||
\(227\) | 7.90391 | 0.524601 | 0.262301 | − | 0.964986i | \(-0.415519\pi\) | ||||
0.262301 | + | 0.964986i | \(0.415519\pi\) | |||||||
\(228\) | −57.6621 | −3.81877 | ||||||||
\(229\) | 24.0296 | 1.58792 | 0.793961 | − | 0.607969i | \(-0.208016\pi\) | ||||
0.793961 | + | 0.607969i | \(0.208016\pi\) | |||||||
\(230\) | −40.4127 | −2.66474 | ||||||||
\(231\) | −15.7119 | −1.03377 | ||||||||
\(232\) | 30.7130 | 2.01641 | ||||||||
\(233\) | −2.81518 | −0.184429 | −0.0922143 | − | 0.995739i | \(-0.529394\pi\) | ||||
−0.0922143 | + | 0.995739i | \(0.529394\pi\) | |||||||
\(234\) | −16.5550 | −1.08224 | ||||||||
\(235\) | −14.5354 | −0.948188 | ||||||||
\(236\) | 28.9432 | 1.88404 | ||||||||
\(237\) | −51.2948 | −3.33196 | ||||||||
\(238\) | −41.0869 | −2.66327 | ||||||||
\(239\) | 26.2813 | 1.70000 | 0.849999 | − | 0.526784i | \(-0.176602\pi\) | ||||
0.849999 | + | 0.526784i | \(0.176602\pi\) | |||||||
\(240\) | −75.2428 | −4.85690 | ||||||||
\(241\) | −22.9326 | −1.47722 | −0.738610 | − | 0.674133i | \(-0.764518\pi\) | ||||
−0.738610 | + | 0.674133i | \(0.764518\pi\) | |||||||
\(242\) | 20.2516 | 1.30182 | ||||||||
\(243\) | −42.1308 | −2.70269 | ||||||||
\(244\) | −63.6770 | −4.07650 | ||||||||
\(245\) | 0.766450 | 0.0489667 | ||||||||
\(246\) | −92.5877 | −5.90318 | ||||||||
\(247\) | 3.13313 | 0.199357 | ||||||||
\(248\) | 59.8061 | 3.79769 | ||||||||
\(249\) | −50.6909 | −3.21240 | ||||||||
\(250\) | 19.9731 | 1.26321 | ||||||||
\(251\) | −2.89924 | −0.182998 | −0.0914991 | − | 0.995805i | \(-0.529166\pi\) | ||||
−0.0914991 | + | 0.995805i | \(0.529166\pi\) | |||||||
\(252\) | 97.2869 | 6.12850 | ||||||||
\(253\) | 10.4387 | 0.656276 | ||||||||
\(254\) | −34.4674 | −2.16268 | ||||||||
\(255\) | −51.2381 | −3.20865 | ||||||||
\(256\) | −22.4544 | −1.40340 | ||||||||
\(257\) | 14.4049 | 0.898555 | 0.449277 | − | 0.893392i | \(-0.351681\pi\) | ||||
0.449277 | + | 0.893392i | \(0.351681\pi\) | |||||||
\(258\) | 15.3306 | 0.954440 | ||||||||
\(259\) | 19.7005 | 1.22413 | ||||||||
\(260\) | 10.4233 | 0.646428 | ||||||||
\(261\) | −33.8496 | −2.09524 | ||||||||
\(262\) | 21.5700 | 1.33260 | ||||||||
\(263\) | 29.5009 | 1.81910 | 0.909551 | − | 0.415592i | \(-0.136425\pi\) | ||||
0.909551 | + | 0.415592i | \(0.136425\pi\) | |||||||
\(264\) | 40.5516 | 2.49578 | ||||||||
\(265\) | −3.62023 | −0.222389 | ||||||||
\(266\) | −26.2585 | −1.61001 | ||||||||
\(267\) | −15.8734 | −0.971435 | ||||||||
\(268\) | 7.01521 | 0.428522 | ||||||||
\(269\) | 16.0481 | 0.978470 | 0.489235 | − | 0.872152i | \(-0.337276\pi\) | ||||
0.489235 | + | 0.872152i | \(0.337276\pi\) | |||||||
\(270\) | 105.428 | 6.41615 | ||||||||
\(271\) | −12.7876 | −0.776790 | −0.388395 | − | 0.921493i | \(-0.626970\pi\) | ||||
−0.388395 | + | 0.921493i | \(0.626970\pi\) | |||||||
\(272\) | 50.8239 | 3.08165 | ||||||||
\(273\) | −7.35139 | −0.444927 | ||||||||
\(274\) | 0.114044 | 0.00688964 | ||||||||
\(275\) | 3.74611 | 0.225899 | ||||||||
\(276\) | −89.8873 | −5.41058 | ||||||||
\(277\) | 4.98817 | 0.299710 | 0.149855 | − | 0.988708i | \(-0.452119\pi\) | ||||
0.149855 | + | 0.988708i | \(0.452119\pi\) | |||||||
\(278\) | 21.0913 | 1.26497 | ||||||||
\(279\) | −65.9138 | −3.94616 | ||||||||
\(280\) | −50.1294 | −2.99580 | ||||||||
\(281\) | −13.6316 | −0.813190 | −0.406595 | − | 0.913608i | \(-0.633284\pi\) | ||||
−0.406595 | + | 0.913608i | \(0.633284\pi\) | |||||||
\(282\) | −46.1079 | −2.74569 | ||||||||
\(283\) | −12.9069 | −0.767236 | −0.383618 | − | 0.923492i | \(-0.625322\pi\) | ||||
−0.383618 | + | 0.923492i | \(0.625322\pi\) | |||||||
\(284\) | 61.2798 | 3.63629 | ||||||||
\(285\) | −32.7461 | −1.93971 | ||||||||
\(286\) | −3.83974 | −0.227049 | ||||||||
\(287\) | −29.5642 | −1.74512 | ||||||||
\(288\) | −64.6226 | −3.80792 | ||||||||
\(289\) | 17.6095 | 1.03586 | ||||||||
\(290\) | 30.3947 | 1.78484 | ||||||||
\(291\) | 36.5788 | 2.14428 | ||||||||
\(292\) | 27.8887 | 1.63206 | ||||||||
\(293\) | −7.69534 | −0.449567 | −0.224783 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224783 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(294\) | 2.43126 | 0.141794 | ||||||||
\(295\) | 16.4367 | 0.956984 | ||||||||
\(296\) | −50.8459 | −2.95536 | ||||||||
\(297\) | −27.2323 | −1.58018 | ||||||||
\(298\) | −36.1224 | −2.09252 | ||||||||
\(299\) | 4.88413 | 0.282456 | ||||||||
\(300\) | −32.2576 | −1.86239 | ||||||||
\(301\) | 4.89521 | 0.282155 | ||||||||
\(302\) | 28.7907 | 1.65672 | ||||||||
\(303\) | 20.8727 | 1.19910 | ||||||||
\(304\) | 32.4814 | 1.86294 | ||||||||
\(305\) | −36.1620 | −2.07063 | ||||||||
\(306\) | −116.873 | −6.68117 | ||||||||
\(307\) | −8.54169 | −0.487500 | −0.243750 | − | 0.969838i | \(-0.578378\pi\) | ||||
−0.243750 | + | 0.969838i | \(0.578378\pi\) | |||||||
\(308\) | 22.5646 | 1.28574 | ||||||||
\(309\) | −24.6929 | −1.40473 | ||||||||
\(310\) | 59.1862 | 3.36155 | ||||||||
\(311\) | 13.0024 | 0.737296 | 0.368648 | − | 0.929569i | \(-0.379821\pi\) | ||||
0.368648 | + | 0.929569i | \(0.379821\pi\) | |||||||
\(312\) | 18.9735 | 1.07416 | ||||||||
\(313\) | −0.527559 | −0.0298194 | −0.0149097 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149097 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(314\) | −25.1455 | −1.41904 | ||||||||
\(315\) | 55.2489 | 3.11292 | ||||||||
\(316\) | 73.6667 | 4.14408 | ||||||||
\(317\) | 8.85398 | 0.497289 | 0.248644 | − | 0.968595i | \(-0.420015\pi\) | ||||
0.248644 | + | 0.968595i | \(0.420015\pi\) | |||||||
\(318\) | −11.4837 | −0.643977 | ||||||||
\(319\) | −7.85103 | −0.439573 | ||||||||
\(320\) | 11.9767 | 0.669516 | ||||||||
\(321\) | −66.1095 | −3.68987 | ||||||||
\(322\) | −40.9335 | −2.28113 | ||||||||
\(323\) | 22.1189 | 1.23073 | ||||||||
\(324\) | 126.382 | 7.02124 | ||||||||
\(325\) | 1.75275 | 0.0972253 | ||||||||
\(326\) | 36.2415 | 2.00723 | ||||||||
\(327\) | −17.5665 | −0.971430 | ||||||||
\(328\) | 76.3035 | 4.21316 | ||||||||
\(329\) | −14.7228 | −0.811692 | ||||||||
\(330\) | 40.1313 | 2.20915 | ||||||||
\(331\) | 4.38103 | 0.240803 | 0.120402 | − | 0.992725i | \(-0.461582\pi\) | ||||
0.120402 | + | 0.992725i | \(0.461582\pi\) | |||||||
\(332\) | 72.7993 | 3.99538 | ||||||||
\(333\) | 56.0386 | 3.07090 | ||||||||
\(334\) | 37.5025 | 2.05205 | ||||||||
\(335\) | 3.98392 | 0.217665 | ||||||||
\(336\) | −76.2123 | −4.15772 | ||||||||
\(337\) | −14.5867 | −0.794589 | −0.397294 | − | 0.917691i | \(-0.630051\pi\) | ||||
−0.397294 | + | 0.917691i | \(0.630051\pi\) | |||||||
\(338\) | 31.8358 | 1.73164 | ||||||||
\(339\) | 30.0077 | 1.62979 | ||||||||
\(340\) | 73.5852 | 3.99072 | ||||||||
\(341\) | −15.2880 | −0.827889 | ||||||||
\(342\) | −74.6931 | −4.03894 | ||||||||
\(343\) | −18.1205 | −0.978417 | ||||||||
\(344\) | −12.6343 | −0.681194 | ||||||||
\(345\) | −51.0467 | −2.74826 | ||||||||
\(346\) | 22.9028 | 1.23126 | ||||||||
\(347\) | −4.34547 | −0.233277 | −0.116638 | − | 0.993174i | \(-0.537212\pi\) | ||||
−0.116638 | + | 0.993174i | \(0.537212\pi\) | |||||||
\(348\) | 67.6049 | 3.62401 | ||||||||
\(349\) | −20.7044 | −1.10828 | −0.554142 | − | 0.832422i | \(-0.686953\pi\) | ||||
−0.554142 | + | 0.832422i | \(0.686953\pi\) | |||||||
\(350\) | −14.6897 | −0.785197 | ||||||||
\(351\) | −12.7416 | −0.680099 | ||||||||
\(352\) | −14.9885 | −0.798888 | ||||||||
\(353\) | −18.4882 | −0.984030 | −0.492015 | − | 0.870587i | \(-0.663739\pi\) | ||||
−0.492015 | + | 0.870587i | \(0.663739\pi\) | |||||||
\(354\) | 52.1390 | 2.77116 | ||||||||
\(355\) | 34.8006 | 1.84703 | ||||||||
\(356\) | 22.7964 | 1.20821 | ||||||||
\(357\) | −51.8984 | −2.74675 | ||||||||
\(358\) | −39.5101 | −2.08817 | ||||||||
\(359\) | −0.00828583 | −0.000437310 0 | −0.000218655 | − | 1.00000i | \(-0.500070\pi\) | ||||
−0.000218655 | 1.00000i | \(0.500070\pi\) | ||||||||
\(360\) | −142.594 | −7.51537 | ||||||||
\(361\) | −4.86390 | −0.255995 | ||||||||
\(362\) | −29.5454 | −1.55287 | ||||||||
\(363\) | 25.5805 | 1.34263 | ||||||||
\(364\) | 10.5576 | 0.553371 | ||||||||
\(365\) | 15.8379 | 0.828993 | ||||||||
\(366\) | −114.710 | −5.99596 | ||||||||
\(367\) | −17.8359 | −0.931029 | −0.465514 | − | 0.885040i | \(-0.654131\pi\) | ||||
−0.465514 | + | 0.885040i | \(0.654131\pi\) | |||||||
\(368\) | 50.6341 | 2.63948 | ||||||||
\(369\) | −84.0961 | −4.37787 | ||||||||
\(370\) | −50.3189 | −2.61596 | ||||||||
\(371\) | −3.66688 | −0.190375 | ||||||||
\(372\) | 131.644 | 6.82542 | ||||||||
\(373\) | −7.06112 | −0.365611 | −0.182805 | − | 0.983149i | \(-0.558518\pi\) | ||||
−0.182805 | + | 0.983149i | \(0.558518\pi\) | |||||||
\(374\) | −27.1073 | −1.40168 | ||||||||
\(375\) | 25.2287 | 1.30280 | ||||||||
\(376\) | 37.9986 | 1.95963 | ||||||||
\(377\) | −3.67339 | −0.189189 | ||||||||
\(378\) | 106.787 | 5.49252 | ||||||||
\(379\) | −16.1473 | −0.829432 | −0.414716 | − | 0.909951i | \(-0.636119\pi\) | ||||
−0.414716 | + | 0.909951i | \(0.636119\pi\) | |||||||
\(380\) | 47.0281 | 2.41249 | ||||||||
\(381\) | −43.5370 | −2.23047 | ||||||||
\(382\) | −56.2432 | −2.87765 | ||||||||
\(383\) | 32.7186 | 1.67184 | 0.835922 | − | 0.548849i | \(-0.184934\pi\) | ||||
0.835922 | + | 0.548849i | \(0.184934\pi\) | |||||||
\(384\) | −17.0106 | −0.868069 | ||||||||
\(385\) | 12.8143 | 0.653079 | ||||||||
\(386\) | −35.3283 | −1.79816 | ||||||||
\(387\) | 13.9246 | 0.707825 | ||||||||
\(388\) | −52.5323 | −2.66692 | ||||||||
\(389\) | 34.3002 | 1.73909 | 0.869545 | − | 0.493853i | \(-0.164412\pi\) | ||||
0.869545 | + | 0.493853i | \(0.164412\pi\) | |||||||
\(390\) | 18.7769 | 0.950804 | ||||||||
\(391\) | 34.4803 | 1.74374 | ||||||||
\(392\) | −2.00365 | −0.101200 | ||||||||
\(393\) | 27.2458 | 1.37437 | ||||||||
\(394\) | −9.95614 | −0.501583 | ||||||||
\(395\) | 41.8351 | 2.10495 | ||||||||
\(396\) | 64.1854 | 3.22544 | ||||||||
\(397\) | 7.76342 | 0.389635 | 0.194817 | − | 0.980840i | \(-0.437589\pi\) | ||||
0.194817 | + | 0.980840i | \(0.437589\pi\) | |||||||
\(398\) | −17.8764 | −0.896064 | ||||||||
\(399\) | −33.1681 | −1.66048 | ||||||||
\(400\) | 18.1709 | 0.908545 | ||||||||
\(401\) | −25.1007 | −1.25347 | −0.626735 | − | 0.779233i | \(-0.715609\pi\) | ||||
−0.626735 | + | 0.779233i | \(0.715609\pi\) | |||||||
\(402\) | 12.6374 | 0.630296 | ||||||||
\(403\) | −7.15302 | −0.356317 | ||||||||
\(404\) | −29.9761 | −1.49137 | ||||||||
\(405\) | 71.7721 | 3.56638 | ||||||||
\(406\) | 30.7864 | 1.52790 | ||||||||
\(407\) | 12.9975 | 0.644262 | ||||||||
\(408\) | 133.947 | 6.63135 | ||||||||
\(409\) | 38.2637 | 1.89202 | 0.946009 | − | 0.324141i | \(-0.105075\pi\) | ||||
0.946009 | + | 0.324141i | \(0.105075\pi\) | |||||||
\(410\) | 75.5127 | 3.72931 | ||||||||
\(411\) | 0.144053 | 0.00710560 | ||||||||
\(412\) | 35.4626 | 1.74712 | ||||||||
\(413\) | 16.6485 | 0.819221 | ||||||||
\(414\) | −116.436 | −5.72253 | ||||||||
\(415\) | 41.3425 | 2.02942 | ||||||||
\(416\) | −7.01290 | −0.343836 | ||||||||
\(417\) | 26.6412 | 1.30462 | ||||||||
\(418\) | −17.3242 | −0.847354 | ||||||||
\(419\) | −3.99514 | −0.195175 | −0.0975877 | − | 0.995227i | \(-0.531113\pi\) | ||||
−0.0975877 | + | 0.995227i | \(0.531113\pi\) | |||||||
\(420\) | −110.344 | −5.38423 | ||||||||
\(421\) | 18.7870 | 0.915624 | 0.457812 | − | 0.889049i | \(-0.348633\pi\) | ||||
0.457812 | + | 0.889049i | \(0.348633\pi\) | |||||||
\(422\) | 57.5228 | 2.80017 | ||||||||
\(423\) | −41.8792 | −2.03624 | ||||||||
\(424\) | 9.46401 | 0.459613 | ||||||||
\(425\) | 12.3738 | 0.600220 | ||||||||
\(426\) | 110.391 | 5.34847 | ||||||||
\(427\) | −36.6280 | −1.77255 | ||||||||
\(428\) | 94.9427 | 4.58923 | ||||||||
\(429\) | −4.85011 | −0.234166 | ||||||||
\(430\) | −12.5033 | −0.602964 | ||||||||
\(431\) | 38.7169 | 1.86493 | 0.932463 | − | 0.361266i | \(-0.117656\pi\) | ||||
0.932463 | + | 0.361266i | \(0.117656\pi\) | |||||||
\(432\) | −132.093 | −6.35535 | ||||||||
\(433\) | 17.3288 | 0.832769 | 0.416385 | − | 0.909189i | \(-0.363297\pi\) | ||||
0.416385 | + | 0.909189i | \(0.363297\pi\) | |||||||
\(434\) | 59.9489 | 2.87764 | ||||||||
\(435\) | 38.3926 | 1.84079 | ||||||||
\(436\) | 25.2280 | 1.20820 | ||||||||
\(437\) | 22.0363 | 1.05414 | ||||||||
\(438\) | 50.2394 | 2.40053 | ||||||||
\(439\) | 0.353601 | 0.0168765 | 0.00843823 | − | 0.999964i | \(-0.497314\pi\) | ||||
0.00843823 | + | 0.999964i | \(0.497314\pi\) | |||||||
\(440\) | −33.0731 | −1.57670 | ||||||||
\(441\) | 2.20828 | 0.105156 | ||||||||
\(442\) | −12.6831 | −0.603275 | ||||||||
\(443\) | 24.8597 | 1.18112 | 0.590561 | − | 0.806993i | \(-0.298907\pi\) | ||||
0.590561 | + | 0.806993i | \(0.298907\pi\) | |||||||
\(444\) | −111.921 | −5.31154 | ||||||||
\(445\) | 12.9460 | 0.613700 | ||||||||
\(446\) | 6.86278 | 0.324962 | ||||||||
\(447\) | −45.6275 | −2.15811 | ||||||||
\(448\) | 12.1310 | 0.573136 | ||||||||
\(449\) | −29.2334 | −1.37961 | −0.689804 | − | 0.723997i | \(-0.742303\pi\) | ||||
−0.689804 | + | 0.723997i | \(0.742303\pi\) | |||||||
\(450\) | −41.7852 | −1.96977 | ||||||||
\(451\) | −19.5051 | −0.918460 | ||||||||
\(452\) | −43.0953 | −2.02703 | ||||||||
\(453\) | 36.3665 | 1.70865 | ||||||||
\(454\) | −20.4483 | −0.959685 | ||||||||
\(455\) | 5.99565 | 0.281081 | ||||||||
\(456\) | 85.6049 | 4.00882 | ||||||||
\(457\) | 34.5762 | 1.61741 | 0.808704 | − | 0.588216i | \(-0.200169\pi\) | ||||
0.808704 | + | 0.588216i | \(0.200169\pi\) | |||||||
\(458\) | −62.1671 | −2.90488 | ||||||||
\(459\) | −89.9517 | −4.19859 | ||||||||
\(460\) | 73.3104 | 3.41811 | ||||||||
\(461\) | −18.0049 | −0.838571 | −0.419286 | − | 0.907854i | \(-0.637719\pi\) | ||||
−0.419286 | + | 0.907854i | \(0.637719\pi\) | |||||||
\(462\) | 40.6484 | 1.89114 | ||||||||
\(463\) | −31.9655 | −1.48556 | −0.742782 | − | 0.669533i | \(-0.766494\pi\) | ||||
−0.742782 | + | 0.669533i | \(0.766494\pi\) | |||||||
\(464\) | −38.0823 | −1.76792 | ||||||||
\(465\) | 74.7602 | 3.46692 | ||||||||
\(466\) | 7.28317 | 0.337386 | ||||||||
\(467\) | −37.9096 | −1.75425 | −0.877123 | − | 0.480266i | \(-0.840540\pi\) | ||||
−0.877123 | + | 0.480266i | \(0.840540\pi\) | |||||||
\(468\) | 30.0315 | 1.38821 | ||||||||
\(469\) | 4.03525 | 0.186331 | ||||||||
\(470\) | 37.6047 | 1.73458 | ||||||||
\(471\) | −31.7622 | −1.46352 | ||||||||
\(472\) | −42.9689 | −1.97780 | ||||||||
\(473\) | 3.22964 | 0.148499 | ||||||||
\(474\) | 132.705 | 6.09535 | ||||||||
\(475\) | 7.90809 | 0.362848 | ||||||||
\(476\) | 74.5334 | 3.41623 | ||||||||
\(477\) | −10.4305 | −0.477581 | ||||||||
\(478\) | −67.9926 | −3.10991 | ||||||||
\(479\) | −5.03277 | −0.229953 | −0.114977 | − | 0.993368i | \(-0.536679\pi\) | ||||
−0.114977 | + | 0.993368i | \(0.536679\pi\) | |||||||
\(480\) | 73.2957 | 3.34547 | ||||||||
\(481\) | 6.08135 | 0.277286 | ||||||||
\(482\) | 59.3291 | 2.70237 | ||||||||
\(483\) | −51.7045 | −2.35264 | ||||||||
\(484\) | −36.7372 | −1.66987 | ||||||||
\(485\) | −29.8329 | −1.35464 | ||||||||
\(486\) | 108.997 | 4.94420 | ||||||||
\(487\) | 16.6581 | 0.754849 | 0.377424 | − | 0.926040i | \(-0.376810\pi\) | ||||
0.377424 | + | 0.926040i | \(0.376810\pi\) | |||||||
\(488\) | 94.5347 | 4.27938 | ||||||||
\(489\) | 45.7779 | 2.07015 | ||||||||
\(490\) | −1.98289 | −0.0895778 | ||||||||
\(491\) | 3.05886 | 0.138044 | 0.0690221 | − | 0.997615i | \(-0.478012\pi\) | ||||
0.0690221 | + | 0.997615i | \(0.478012\pi\) | |||||||
\(492\) | 167.958 | 7.57213 | ||||||||
\(493\) | −25.9329 | −1.16796 | ||||||||
\(494\) | −8.10575 | −0.364695 | ||||||||
\(495\) | 36.4507 | 1.63834 | ||||||||
\(496\) | −74.1558 | −3.32969 | ||||||||
\(497\) | 35.2491 | 1.58114 | ||||||||
\(498\) | 131.143 | 5.87665 | ||||||||
\(499\) | −14.9054 | −0.667258 | −0.333629 | − | 0.942704i | \(-0.608273\pi\) | ||||
−0.333629 | + | 0.942704i | \(0.608273\pi\) | |||||||
\(500\) | −36.2320 | −1.62034 | ||||||||
\(501\) | 47.3707 | 2.11637 | ||||||||
\(502\) | 7.50063 | 0.334770 | ||||||||
\(503\) | −20.2347 | −0.902220 | −0.451110 | − | 0.892468i | \(-0.648972\pi\) | ||||
−0.451110 | + | 0.892468i | \(0.648972\pi\) | |||||||
\(504\) | −144.432 | −6.43350 | ||||||||
\(505\) | −17.0233 | −0.757529 | ||||||||
\(506\) | −27.0060 | −1.20057 | ||||||||
\(507\) | 40.2129 | 1.78592 | ||||||||
\(508\) | 62.5253 | 2.77411 | ||||||||
\(509\) | 31.5475 | 1.39832 | 0.699159 | − | 0.714966i | \(-0.253558\pi\) | ||||
0.699159 | + | 0.714966i | \(0.253558\pi\) | |||||||
\(510\) | 132.558 | 5.86978 | ||||||||
\(511\) | 16.0420 | 0.709655 | ||||||||
\(512\) | 47.6811 | 2.10723 | ||||||||
\(513\) | −57.4879 | −2.53815 | ||||||||
\(514\) | −37.2671 | −1.64378 | ||||||||
\(515\) | 20.1391 | 0.887434 | ||||||||
\(516\) | −27.8103 | −1.22428 | ||||||||
\(517\) | −9.71340 | −0.427195 | ||||||||
\(518\) | −50.9673 | −2.23938 | ||||||||
\(519\) | 28.9293 | 1.26986 | ||||||||
\(520\) | −15.4744 | −0.678599 | ||||||||
\(521\) | −4.88434 | −0.213987 | −0.106993 | − | 0.994260i | \(-0.534122\pi\) | ||||
−0.106993 | + | 0.994260i | \(0.534122\pi\) | |||||||
\(522\) | 87.5726 | 3.83295 | ||||||||
\(523\) | 18.5613 | 0.811630 | 0.405815 | − | 0.913955i | \(-0.366988\pi\) | ||||
0.405815 | + | 0.913955i | \(0.366988\pi\) | |||||||
\(524\) | −39.1289 | −1.70935 | ||||||||
\(525\) | −18.5551 | −0.809809 | ||||||||
\(526\) | −76.3219 | −3.32779 | ||||||||
\(527\) | −50.4979 | −2.19972 | ||||||||
\(528\) | −50.2814 | −2.18822 | ||||||||
\(529\) | 11.3515 | 0.493544 | ||||||||
\(530\) | 9.36592 | 0.406830 | ||||||||
\(531\) | 47.3572 | 2.05513 | ||||||||
\(532\) | 47.6341 | 2.06520 | ||||||||
\(533\) | −9.12618 | −0.395299 | ||||||||
\(534\) | 41.0661 | 1.77710 | ||||||||
\(535\) | 53.9176 | 2.33106 | ||||||||
\(536\) | −10.4148 | −0.449849 | ||||||||
\(537\) | −49.9066 | −2.15363 | ||||||||
\(538\) | −41.5182 | −1.78997 | ||||||||
\(539\) | 0.512185 | 0.0220614 | ||||||||
\(540\) | −191.251 | −8.23013 | ||||||||
\(541\) | −7.28670 | −0.313280 | −0.156640 | − | 0.987656i | \(-0.550066\pi\) | ||||
−0.156640 | + | 0.987656i | \(0.550066\pi\) | |||||||
\(542\) | 33.0828 | 1.42103 | ||||||||
\(543\) | −37.3198 | −1.60155 | ||||||||
\(544\) | −49.5087 | −2.12267 | ||||||||
\(545\) | 14.3269 | 0.613697 | ||||||||
\(546\) | 19.0188 | 0.813931 | ||||||||
\(547\) | 7.29380 | 0.311860 | 0.155930 | − | 0.987768i | \(-0.450163\pi\) | ||||
0.155930 | + | 0.987768i | \(0.450163\pi\) | |||||||
\(548\) | −0.206880 | −0.00883749 | ||||||||
\(549\) | −104.189 | −4.44668 | ||||||||
\(550\) | −9.69158 | −0.413250 | ||||||||
\(551\) | −16.5736 | −0.706060 | ||||||||
\(552\) | 133.446 | 5.67985 | ||||||||
\(553\) | 42.3742 | 1.80193 | ||||||||
\(554\) | −12.9049 | −0.548278 | ||||||||
\(555\) | −63.5596 | −2.69795 | ||||||||
\(556\) | −38.2605 | −1.62261 | ||||||||
\(557\) | 4.00018 | 0.169493 | 0.0847465 | − | 0.996403i | \(-0.472992\pi\) | ||||
0.0847465 | + | 0.996403i | \(0.472992\pi\) | |||||||
\(558\) | 170.526 | 7.21895 | ||||||||
\(559\) | 1.51110 | 0.0639129 | ||||||||
\(560\) | 62.1573 | 2.62663 | ||||||||
\(561\) | −34.2402 | −1.44562 | ||||||||
\(562\) | 35.2663 | 1.48762 | ||||||||
\(563\) | −14.4938 | −0.610840 | −0.305420 | − | 0.952218i | \(-0.598797\pi\) | ||||
−0.305420 | + | 0.952218i | \(0.598797\pi\) | |||||||
\(564\) | 83.6417 | 3.52195 | ||||||||
\(565\) | −24.4737 | −1.02962 | ||||||||
\(566\) | 33.3915 | 1.40355 | ||||||||
\(567\) | 72.6970 | 3.05299 | ||||||||
\(568\) | −90.9758 | −3.81726 | ||||||||
\(569\) | −25.7920 | −1.08125 | −0.540627 | − | 0.841262i | \(-0.681813\pi\) | ||||
−0.540627 | + | 0.841262i | \(0.681813\pi\) | |||||||
\(570\) | 84.7177 | 3.54843 | ||||||||
\(571\) | 6.09385 | 0.255020 | 0.127510 | − | 0.991837i | \(-0.459302\pi\) | ||||
0.127510 | + | 0.991837i | \(0.459302\pi\) | |||||||
\(572\) | 6.96545 | 0.291240 | ||||||||
\(573\) | −71.0428 | −2.96785 | ||||||||
\(574\) | 76.4858 | 3.19246 | ||||||||
\(575\) | 12.3276 | 0.514098 | ||||||||
\(576\) | 34.5069 | 1.43779 | ||||||||
\(577\) | 2.74582 | 0.114310 | 0.0571550 | − | 0.998365i | \(-0.481797\pi\) | ||||
0.0571550 | + | 0.998365i | \(0.481797\pi\) | |||||||
\(578\) | −45.5578 | −1.89495 | ||||||||
\(579\) | −44.6244 | −1.85453 | ||||||||
\(580\) | −55.1373 | −2.28945 | ||||||||
\(581\) | 41.8753 | 1.73728 | ||||||||
\(582\) | −94.6331 | −3.92267 | ||||||||
\(583\) | −2.41924 | −0.100195 | ||||||||
\(584\) | −41.4034 | −1.71329 | ||||||||
\(585\) | 17.0548 | 0.705128 | ||||||||
\(586\) | 19.9087 | 0.822419 | ||||||||
\(587\) | −6.17044 | −0.254681 | −0.127341 | − | 0.991859i | \(-0.540644\pi\) | ||||
−0.127341 | + | 0.991859i | \(0.540644\pi\) | |||||||
\(588\) | −4.41041 | −0.181882 | ||||||||
\(589\) | −32.2731 | −1.32979 | ||||||||
\(590\) | −42.5236 | −1.75067 | ||||||||
\(591\) | −12.5759 | −0.517305 | ||||||||
\(592\) | 63.0458 | 2.59116 | ||||||||
\(593\) | −5.34173 | −0.219359 | −0.109679 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109679 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(594\) | 70.4530 | 2.89072 | ||||||||
\(595\) | 42.3273 | 1.73525 | ||||||||
\(596\) | 65.5276 | 2.68412 | ||||||||
\(597\) | −22.5803 | −0.924152 | ||||||||
\(598\) | −12.6358 | −0.516715 | ||||||||
\(599\) | −21.3099 | −0.870700 | −0.435350 | − | 0.900261i | \(-0.643375\pi\) | ||||
−0.435350 | + | 0.900261i | \(0.643375\pi\) | |||||||
\(600\) | 47.8895 | 1.95508 | ||||||||
\(601\) | −0.757251 | −0.0308889 | −0.0154444 | − | 0.999881i | \(-0.504916\pi\) | ||||
−0.0154444 | + | 0.999881i | \(0.504916\pi\) | |||||||
\(602\) | −12.6644 | −0.516164 | ||||||||
\(603\) | 11.4784 | 0.467436 | ||||||||
\(604\) | −52.2275 | −2.12511 | ||||||||
\(605\) | −20.8630 | −0.848200 | ||||||||
\(606\) | −53.9998 | −2.19359 | ||||||||
\(607\) | 23.4434 | 0.951539 | 0.475770 | − | 0.879570i | \(-0.342170\pi\) | ||||
0.475770 | + | 0.879570i | \(0.342170\pi\) | |||||||
\(608\) | −31.6409 | −1.28321 | ||||||||
\(609\) | 38.8874 | 1.57580 | ||||||||
\(610\) | 93.5549 | 3.78793 | ||||||||
\(611\) | −4.54477 | −0.183862 | ||||||||
\(612\) | 212.012 | 8.57008 | ||||||||
\(613\) | 16.8473 | 0.680454 | 0.340227 | − | 0.940343i | \(-0.389496\pi\) | ||||
0.340227 | + | 0.940343i | \(0.389496\pi\) | |||||||
\(614\) | 22.0982 | 0.891813 | ||||||||
\(615\) | 95.3828 | 3.84620 | ||||||||
\(616\) | −33.4992 | −1.34972 | ||||||||
\(617\) | 12.3191 | 0.495949 | 0.247975 | − | 0.968767i | \(-0.420235\pi\) | ||||
0.247975 | + | 0.968767i | \(0.420235\pi\) | |||||||
\(618\) | 63.8832 | 2.56976 | ||||||||
\(619\) | −37.2520 | −1.49728 | −0.748642 | − | 0.662975i | \(-0.769294\pi\) | ||||
−0.748642 | + | 0.662975i | \(0.769294\pi\) | |||||||
\(620\) | −107.366 | −4.31193 | ||||||||
\(621\) | −89.6157 | −3.59616 | ||||||||
\(622\) | −33.6385 | −1.34878 | ||||||||
\(623\) | 13.1128 | 0.525355 | ||||||||
\(624\) | −23.5260 | −0.941793 | ||||||||
\(625\) | −31.0927 | −1.24371 | ||||||||
\(626\) | 1.36485 | 0.0545505 | ||||||||
\(627\) | −21.8828 | −0.873914 | ||||||||
\(628\) | 45.6150 | 1.82024 | ||||||||
\(629\) | 42.9323 | 1.71182 | ||||||||
\(630\) | −142.935 | −5.69466 | ||||||||
\(631\) | −3.03001 | −0.120623 | −0.0603114 | − | 0.998180i | \(-0.519209\pi\) | ||||
−0.0603114 | + | 0.998180i | \(0.519209\pi\) | |||||||
\(632\) | −109.365 | −4.35032 | ||||||||
\(633\) | 72.6591 | 2.88794 | ||||||||
\(634\) | −22.9062 | −0.909721 | ||||||||
\(635\) | 35.5079 | 1.40909 | ||||||||
\(636\) | 20.8320 | 0.826042 | ||||||||
\(637\) | 0.239644 | 0.00949505 | ||||||||
\(638\) | 20.3114 | 0.804138 | ||||||||
\(639\) | 100.267 | 3.96649 | ||||||||
\(640\) | 13.8735 | 0.548399 | ||||||||
\(641\) | −19.3417 | −0.763951 | −0.381975 | − | 0.924172i | \(-0.624756\pi\) | ||||
−0.381975 | + | 0.924172i | \(0.624756\pi\) | |||||||
\(642\) | 171.032 | 6.75011 | ||||||||
\(643\) | −8.14343 | −0.321146 | −0.160573 | − | 0.987024i | \(-0.551334\pi\) | ||||
−0.160573 | + | 0.987024i | \(0.551334\pi\) | |||||||
\(644\) | 74.2551 | 2.92606 | ||||||||
\(645\) | −15.7934 | −0.621864 | ||||||||
\(646\) | −57.2239 | −2.25144 | ||||||||
\(647\) | 3.17502 | 0.124823 | 0.0624116 | − | 0.998050i | \(-0.480121\pi\) | ||||
0.0624116 | + | 0.998050i | \(0.480121\pi\) | |||||||
\(648\) | −187.627 | −7.37067 | ||||||||
\(649\) | 10.9839 | 0.431158 | ||||||||
\(650\) | −4.53456 | −0.177860 | ||||||||
\(651\) | 75.7236 | 2.96784 | ||||||||
\(652\) | −65.7436 | −2.57472 | ||||||||
\(653\) | 18.5415 | 0.725586 | 0.362793 | − | 0.931870i | \(-0.381823\pi\) | ||||
0.362793 | + | 0.931870i | \(0.381823\pi\) | |||||||
\(654\) | 45.4464 | 1.77709 | ||||||||
\(655\) | −22.2212 | −0.868253 | ||||||||
\(656\) | −94.6117 | −3.69396 | ||||||||
\(657\) | 45.6318 | 1.78027 | ||||||||
\(658\) | 38.0893 | 1.48488 | ||||||||
\(659\) | 22.8098 | 0.888542 | 0.444271 | − | 0.895892i | \(-0.353463\pi\) | ||||
0.444271 | + | 0.895892i | \(0.353463\pi\) | |||||||
\(660\) | −72.7998 | −2.83373 | ||||||||
\(661\) | 10.6933 | 0.415922 | 0.207961 | − | 0.978137i | \(-0.433317\pi\) | ||||
0.207961 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(662\) | −11.3342 | −0.440516 | ||||||||
\(663\) | −16.0205 | −0.622185 | ||||||||
\(664\) | −108.078 | −4.19422 | ||||||||
\(665\) | 27.0512 | 1.04900 | ||||||||
\(666\) | −144.978 | −5.61778 | ||||||||
\(667\) | −25.8360 | −1.00038 | ||||||||
\(668\) | −68.0311 | −2.63220 | ||||||||
\(669\) | 8.66862 | 0.335148 | ||||||||
\(670\) | −10.3068 | −0.398187 | ||||||||
\(671\) | −24.1655 | −0.932897 | ||||||||
\(672\) | 74.2402 | 2.86388 | ||||||||
\(673\) | −28.0836 | −1.08254 | −0.541272 | − | 0.840847i | \(-0.682057\pi\) | ||||
−0.541272 | + | 0.840847i | \(0.682057\pi\) | |||||||
\(674\) | 37.7374 | 1.45359 | ||||||||
\(675\) | −32.1601 | −1.23784 | ||||||||
\(676\) | −57.7515 | −2.22121 | ||||||||
\(677\) | 6.95352 | 0.267246 | 0.133623 | − | 0.991032i | \(-0.457339\pi\) | ||||
0.133623 | + | 0.991032i | \(0.457339\pi\) | |||||||
\(678\) | −77.6331 | −2.98148 | ||||||||
\(679\) | −30.2174 | −1.15964 | ||||||||
\(680\) | −109.244 | −4.18933 | ||||||||
\(681\) | −25.8289 | −0.989766 | ||||||||
\(682\) | 39.5516 | 1.51451 | ||||||||
\(683\) | −15.0221 | −0.574803 | −0.287402 | − | 0.957810i | \(-0.592791\pi\) | ||||
−0.287402 | + | 0.957810i | \(0.592791\pi\) | |||||||
\(684\) | 135.496 | 5.18083 | ||||||||
\(685\) | −0.117487 | −0.00448894 | ||||||||
\(686\) | 46.8797 | 1.78988 | ||||||||
\(687\) | −78.5255 | −2.99593 | ||||||||
\(688\) | 15.6657 | 0.597249 | ||||||||
\(689\) | −1.13193 | −0.0431231 | ||||||||
\(690\) | 132.063 | 5.02756 | ||||||||
\(691\) | 15.2745 | 0.581069 | 0.290534 | − | 0.956865i | \(-0.406167\pi\) | ||||
0.290534 | + | 0.956865i | \(0.406167\pi\) | |||||||
\(692\) | −41.5466 | −1.57937 | ||||||||
\(693\) | 36.9204 | 1.40249 | ||||||||
\(694\) | 11.2422 | 0.426748 | ||||||||
\(695\) | −21.7280 | −0.824191 | ||||||||
\(696\) | −100.366 | −3.80436 | ||||||||
\(697\) | −64.4277 | −2.44037 | ||||||||
\(698\) | 53.5646 | 2.02745 | ||||||||
\(699\) | 9.19963 | 0.347962 | ||||||||
\(700\) | 26.6477 | 1.00719 | ||||||||
\(701\) | 33.3521 | 1.25969 | 0.629845 | − | 0.776721i | \(-0.283118\pi\) | ||||
0.629845 | + | 0.776721i | \(0.283118\pi\) | |||||||
\(702\) | 32.9640 | 1.24415 | ||||||||
\(703\) | 27.4379 | 1.03484 | ||||||||
\(704\) | 8.00348 | 0.301643 | ||||||||
\(705\) | 47.4999 | 1.78895 | ||||||||
\(706\) | 47.8310 | 1.80014 | ||||||||
\(707\) | −17.2427 | −0.648479 | ||||||||
\(708\) | −94.5824 | −3.55462 | ||||||||
\(709\) | 0.766159 | 0.0287737 | 0.0143869 | − | 0.999897i | \(-0.495420\pi\) | ||||
0.0143869 | + | 0.999897i | \(0.495420\pi\) | |||||||
\(710\) | −90.0329 | −3.37888 | ||||||||
\(711\) | 120.534 | 4.52039 | ||||||||
\(712\) | −33.8435 | −1.26834 | ||||||||
\(713\) | −50.3093 | −1.88410 | ||||||||
\(714\) | 134.267 | 5.02480 | ||||||||
\(715\) | 3.95566 | 0.147933 | ||||||||
\(716\) | 71.6730 | 2.67855 | ||||||||
\(717\) | −85.8838 | −3.20739 | ||||||||
\(718\) | 0.0214363 | 0.000799997 0 | ||||||||
\(719\) | 7.74131 | 0.288702 | 0.144351 | − | 0.989527i | \(-0.453891\pi\) | ||||
0.144351 | + | 0.989527i | \(0.453891\pi\) | |||||||
\(720\) | 176.808 | 6.58924 | ||||||||
\(721\) | 20.3986 | 0.759683 | ||||||||
\(722\) | 12.5834 | 0.468306 | ||||||||
\(723\) | 74.9407 | 2.78708 | ||||||||
\(724\) | 53.5965 | 1.99190 | ||||||||
\(725\) | −9.27170 | −0.344342 | ||||||||
\(726\) | −66.1795 | −2.45615 | ||||||||
\(727\) | −15.7242 | −0.583177 | −0.291588 | − | 0.956544i | \(-0.594184\pi\) | ||||
−0.291588 | + | 0.956544i | \(0.594184\pi\) | |||||||
\(728\) | −15.6738 | −0.580911 | ||||||||
\(729\) | 56.8900 | 2.10704 | ||||||||
\(730\) | −40.9743 | −1.51653 | ||||||||
\(731\) | 10.6679 | 0.394566 | ||||||||
\(732\) | 208.088 | 7.69115 | ||||||||
\(733\) | 16.5868 | 0.612648 | 0.306324 | − | 0.951927i | \(-0.400901\pi\) | ||||
0.306324 | + | 0.951927i | \(0.400901\pi\) | |||||||
\(734\) | 46.1435 | 1.70319 | ||||||||
\(735\) | −2.50466 | −0.0923856 | ||||||||
\(736\) | −49.3238 | −1.81810 | ||||||||
\(737\) | 2.66228 | 0.0980662 | ||||||||
\(738\) | 217.566 | 8.00870 | ||||||||
\(739\) | 24.1154 | 0.887098 | 0.443549 | − | 0.896250i | \(-0.353719\pi\) | ||||
0.443549 | + | 0.896250i | \(0.353719\pi\) | |||||||
\(740\) | 91.2806 | 3.35554 | ||||||||
\(741\) | −10.2387 | −0.376126 | ||||||||
\(742\) | 9.48661 | 0.348264 | ||||||||
\(743\) | 3.34156 | 0.122590 | 0.0612950 | − | 0.998120i | \(-0.480477\pi\) | ||||
0.0612950 | + | 0.998120i | \(0.480477\pi\) | |||||||
\(744\) | −195.438 | −7.16511 | ||||||||
\(745\) | 37.2129 | 1.36338 | ||||||||
\(746\) | 18.2679 | 0.668834 | ||||||||
\(747\) | 119.115 | 4.35820 | ||||||||
\(748\) | 49.1737 | 1.79797 | ||||||||
\(749\) | 54.6124 | 1.99549 | ||||||||
\(750\) | −65.2693 | −2.38330 | ||||||||
\(751\) | −9.36166 | −0.341612 | −0.170806 | − | 0.985305i | \(-0.554637\pi\) | ||||
−0.170806 | + | 0.985305i | \(0.554637\pi\) | |||||||
\(752\) | −47.1159 | −1.71814 | ||||||||
\(753\) | 9.47431 | 0.345263 | ||||||||
\(754\) | 9.50345 | 0.346095 | ||||||||
\(755\) | −29.6598 | −1.07943 | ||||||||
\(756\) | −193.716 | −7.04537 | ||||||||
\(757\) | 16.1336 | 0.586384 | 0.293192 | − | 0.956054i | \(-0.405282\pi\) | ||||
0.293192 | + | 0.956054i | \(0.405282\pi\) | |||||||
\(758\) | 41.7748 | 1.51733 | ||||||||
\(759\) | −34.1123 | −1.23820 | ||||||||
\(760\) | −69.8177 | −2.53255 | ||||||||
\(761\) | 1.12341 | 0.0407236 | 0.0203618 | − | 0.999793i | \(-0.493518\pi\) | ||||
0.0203618 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(762\) | 112.635 | 4.08033 | ||||||||
\(763\) | 14.5115 | 0.525352 | ||||||||
\(764\) | 102.028 | 3.69123 | ||||||||
\(765\) | 120.401 | 4.35311 | ||||||||
\(766\) | −84.6466 | −3.05840 | ||||||||
\(767\) | 5.13924 | 0.185567 | ||||||||
\(768\) | 73.3779 | 2.64780 | ||||||||
\(769\) | −0.928771 | −0.0334924 | −0.0167462 | − | 0.999860i | \(-0.505331\pi\) | ||||
−0.0167462 | + | 0.999860i | \(0.505331\pi\) | |||||||
\(770\) | −33.1521 | −1.19472 | ||||||||
\(771\) | −47.0734 | −1.69531 | ||||||||
\(772\) | 64.0870 | 2.30654 | ||||||||
\(773\) | 53.6704 | 1.93039 | 0.965194 | − | 0.261534i | \(-0.0842283\pi\) | ||||
0.965194 | + | 0.261534i | \(0.0842283\pi\) | |||||||
\(774\) | −36.0243 | −1.29487 | ||||||||
\(775\) | −18.0544 | −0.648532 | ||||||||
\(776\) | 77.9892 | 2.79965 | ||||||||
\(777\) | −64.3786 | −2.30957 | ||||||||
\(778\) | −88.7383 | −3.18142 | ||||||||
\(779\) | −41.1756 | −1.47527 | ||||||||
\(780\) | −34.0620 | −1.21962 | ||||||||
\(781\) | 23.2557 | 0.832155 | ||||||||
\(782\) | −89.2042 | −3.18994 | ||||||||
\(783\) | 67.4007 | 2.40870 | ||||||||
\(784\) | 2.48441 | 0.0887288 | ||||||||
\(785\) | 25.9046 | 0.924576 | ||||||||
\(786\) | −70.4879 | −2.51422 | ||||||||
\(787\) | −2.19248 | −0.0781535 | −0.0390768 | − | 0.999236i | \(-0.512442\pi\) | ||||
−0.0390768 | + | 0.999236i | \(0.512442\pi\) | |||||||
\(788\) | 18.0608 | 0.643391 | ||||||||
\(789\) | −96.4049 | −3.43211 | ||||||||
\(790\) | −108.232 | −3.85071 | ||||||||
\(791\) | −24.7891 | −0.881398 | ||||||||
\(792\) | −95.2894 | −3.38596 | ||||||||
\(793\) | −11.3067 | −0.401512 | ||||||||
\(794\) | −20.0848 | −0.712782 | ||||||||
\(795\) | 11.8304 | 0.419582 | ||||||||
\(796\) | 32.4286 | 1.14940 | ||||||||
\(797\) | 20.9898 | 0.743498 | 0.371749 | − | 0.928333i | \(-0.378758\pi\) | ||||
0.371749 | + | 0.928333i | \(0.378758\pi\) | |||||||
\(798\) | 85.8094 | 3.03762 | ||||||||
\(799\) | −32.0845 | −1.13507 | ||||||||
\(800\) | −17.7007 | −0.625814 | ||||||||
\(801\) | 37.2998 | 1.31792 | ||||||||
\(802\) | 64.9382 | 2.29305 | ||||||||
\(803\) | 10.5838 | 0.373493 | ||||||||
\(804\) | −22.9248 | −0.808494 | ||||||||
\(805\) | 42.1692 | 1.48627 | ||||||||
\(806\) | 18.5056 | 0.651833 | ||||||||
\(807\) | −52.4430 | −1.84608 | ||||||||
\(808\) | 44.5024 | 1.56559 | ||||||||
\(809\) | 16.9903 | 0.597346 | 0.298673 | − | 0.954356i | \(-0.403456\pi\) | ||||
0.298673 | + | 0.954356i | \(0.403456\pi\) | |||||||
\(810\) | −185.682 | −6.52420 | ||||||||
\(811\) | 41.4830 | 1.45666 | 0.728332 | − | 0.685224i | \(-0.240296\pi\) | ||||
0.728332 | + | 0.685224i | \(0.240296\pi\) | |||||||
\(812\) | −55.8478 | −1.95987 | ||||||||
\(813\) | 41.7881 | 1.46557 | ||||||||
\(814\) | −33.6259 | −1.17859 | ||||||||
\(815\) | −37.3356 | −1.30781 | ||||||||
\(816\) | −166.086 | −5.81416 | ||||||||
\(817\) | 6.81781 | 0.238525 | ||||||||
\(818\) | −98.9922 | −3.46118 | ||||||||
\(819\) | 17.2746 | 0.603622 | ||||||||
\(820\) | −136.983 | −4.78366 | ||||||||
\(821\) | 35.6149 | 1.24297 | 0.621485 | − | 0.783426i | \(-0.286530\pi\) | ||||
0.621485 | + | 0.783426i | \(0.286530\pi\) | |||||||
\(822\) | −0.372680 | −0.0129987 | ||||||||
\(823\) | −53.5314 | −1.86599 | −0.932993 | − | 0.359895i | \(-0.882813\pi\) | ||||
−0.932993 | + | 0.359895i | \(0.882813\pi\) | |||||||
\(824\) | −52.6476 | −1.83406 | ||||||||
\(825\) | −12.2418 | −0.426204 | ||||||||
\(826\) | −43.0716 | −1.49865 | ||||||||
\(827\) | −16.9070 | −0.587914 | −0.293957 | − | 0.955819i | \(-0.594972\pi\) | ||||
−0.293957 | + | 0.955819i | \(0.594972\pi\) | |||||||
\(828\) | 211.220 | 7.34041 | ||||||||
\(829\) | 6.72781 | 0.233666 | 0.116833 | − | 0.993152i | \(-0.462726\pi\) | ||||
0.116833 | + | 0.993152i | \(0.462726\pi\) | |||||||
\(830\) | −106.957 | −3.71255 | ||||||||
\(831\) | −16.3007 | −0.565464 | ||||||||
\(832\) | 3.74472 | 0.129825 | ||||||||
\(833\) | 1.69181 | 0.0586177 | ||||||||
\(834\) | −68.9236 | −2.38663 | ||||||||
\(835\) | −38.6347 | −1.33701 | ||||||||
\(836\) | 31.4268 | 1.08692 | ||||||||
\(837\) | 131.246 | 4.53653 | ||||||||
\(838\) | 10.3358 | 0.357046 | ||||||||
\(839\) | 49.9522 | 1.72454 | 0.862271 | − | 0.506447i | \(-0.169041\pi\) | ||||
0.862271 | + | 0.506447i | \(0.169041\pi\) | |||||||
\(840\) | 163.816 | 5.65219 | ||||||||
\(841\) | −9.56853 | −0.329949 | ||||||||
\(842\) | −48.6041 | −1.67501 | ||||||||
\(843\) | 44.5461 | 1.53425 | ||||||||
\(844\) | −104.349 | −3.59183 | ||||||||
\(845\) | −32.7969 | −1.12825 | ||||||||
\(846\) | 108.346 | 3.72501 | ||||||||
\(847\) | −21.1318 | −0.726097 | ||||||||
\(848\) | −11.7348 | −0.402974 | ||||||||
\(849\) | 42.1780 | 1.44755 | ||||||||
\(850\) | −32.0125 | −1.09802 | ||||||||
\(851\) | 42.7720 | 1.46620 | ||||||||
\(852\) | −200.254 | −6.86060 | ||||||||
\(853\) | 10.5211 | 0.360235 | 0.180118 | − | 0.983645i | \(-0.442352\pi\) | ||||
0.180118 | + | 0.983645i | \(0.442352\pi\) | |||||||
\(854\) | 94.7605 | 3.24264 | ||||||||
\(855\) | 76.9479 | 2.63156 | ||||||||
\(856\) | −140.951 | −4.81762 | ||||||||
\(857\) | −13.9617 | −0.476924 | −0.238462 | − | 0.971152i | \(-0.576643\pi\) | ||||
−0.238462 | + | 0.971152i | \(0.576643\pi\) | |||||||
\(858\) | 12.5478 | 0.428373 | ||||||||
\(859\) | −37.0411 | −1.26383 | −0.631913 | − | 0.775039i | \(-0.717730\pi\) | ||||
−0.631913 | + | 0.775039i | \(0.717730\pi\) | |||||||
\(860\) | 22.6815 | 0.773434 | ||||||||
\(861\) | 96.6119 | 3.29252 | ||||||||
\(862\) | −100.165 | −3.41162 | ||||||||
\(863\) | 45.5752 | 1.55140 | 0.775699 | − | 0.631103i | \(-0.217398\pi\) | ||||
0.775699 | + | 0.631103i | \(0.217398\pi\) | |||||||
\(864\) | 128.675 | 4.37762 | ||||||||
\(865\) | −23.5942 | −0.802227 | ||||||||
\(866\) | −44.8315 | −1.52344 | ||||||||
\(867\) | −57.5456 | −1.95435 | ||||||||
\(868\) | −108.750 | −3.69121 | ||||||||
\(869\) | 27.9565 | 0.948361 | ||||||||
\(870\) | −99.3258 | −3.36746 | ||||||||
\(871\) | 1.24564 | 0.0422070 | ||||||||
\(872\) | −37.4534 | −1.26833 | ||||||||
\(873\) | −85.9540 | −2.90910 | ||||||||
\(874\) | −57.0101 | −1.92840 | ||||||||
\(875\) | −20.8412 | −0.704560 | ||||||||
\(876\) | −91.1364 | −3.07921 | ||||||||
\(877\) | −31.3022 | −1.05700 | −0.528500 | − | 0.848933i | \(-0.677245\pi\) | ||||
−0.528500 | + | 0.848933i | \(0.677245\pi\) | |||||||
\(878\) | −0.914803 | −0.0308731 | ||||||||
\(879\) | 25.1473 | 0.848198 | ||||||||
\(880\) | 41.0085 | 1.38240 | ||||||||
\(881\) | 31.0217 | 1.04515 | 0.522574 | − | 0.852594i | \(-0.324972\pi\) | ||||
0.522574 | + | 0.852594i | \(0.324972\pi\) | |||||||
\(882\) | −5.71306 | −0.192369 | ||||||||
\(883\) | 48.4340 | 1.62993 | 0.814967 | − | 0.579508i | \(-0.196755\pi\) | ||||
0.814967 | + | 0.579508i | \(0.196755\pi\) | |||||||
\(884\) | 23.0077 | 0.773833 | ||||||||
\(885\) | −53.7130 | −1.80554 | ||||||||
\(886\) | −64.3148 | −2.16070 | ||||||||
\(887\) | −34.6113 | −1.16213 | −0.581067 | − | 0.813856i | \(-0.697364\pi\) | ||||
−0.581067 | + | 0.813856i | \(0.697364\pi\) | |||||||
\(888\) | 166.157 | 5.57588 | ||||||||
\(889\) | 35.9655 | 1.20624 | ||||||||
\(890\) | −33.4927 | −1.12268 | ||||||||
\(891\) | 47.9621 | 1.60679 | ||||||||
\(892\) | −12.4494 | −0.416836 | ||||||||
\(893\) | −20.5051 | −0.686178 | ||||||||
\(894\) | 118.043 | 3.94796 | ||||||||
\(895\) | 40.7029 | 1.36055 | ||||||||
\(896\) | 14.0523 | 0.469454 | ||||||||
\(897\) | −15.9607 | −0.532911 | ||||||||
\(898\) | 75.6298 | 2.52380 | ||||||||
\(899\) | 37.8380 | 1.26197 | ||||||||
\(900\) | 75.8000 | 2.52667 | ||||||||
\(901\) | −7.99104 | −0.266220 | ||||||||
\(902\) | 50.4618 | 1.68019 | ||||||||
\(903\) | −15.9969 | −0.532343 | ||||||||
\(904\) | 63.9791 | 2.12791 | ||||||||
\(905\) | 30.4373 | 1.01177 | ||||||||
\(906\) | −94.0841 | −3.12573 | ||||||||
\(907\) | 2.20511 | 0.0732194 | 0.0366097 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366097 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(908\) | 37.0940 | 1.23101 | ||||||||
\(909\) | −49.0473 | −1.62680 | ||||||||
\(910\) | −15.5114 | −0.514198 | ||||||||
\(911\) | 27.6735 | 0.916864 | 0.458432 | − | 0.888730i | \(-0.348411\pi\) | ||||
0.458432 | + | 0.888730i | \(0.348411\pi\) | |||||||
\(912\) | −106.145 | −3.51480 | ||||||||
\(913\) | 27.6274 | 0.914333 | ||||||||
\(914\) | −89.4524 | −2.95882 | ||||||||
\(915\) | 118.172 | 3.90666 | ||||||||
\(916\) | 112.774 | 3.72615 | ||||||||
\(917\) | −22.5075 | −0.743264 | ||||||||
\(918\) | 232.715 | 7.68073 | ||||||||
\(919\) | −59.5447 | −1.96420 | −0.982100 | − | 0.188362i | \(-0.939682\pi\) | ||||
−0.982100 | + | 0.188362i | \(0.939682\pi\) | |||||||
\(920\) | −108.836 | −3.58823 | ||||||||
\(921\) | 27.9131 | 0.919767 | ||||||||
\(922\) | 46.5805 | 1.53405 | ||||||||
\(923\) | 10.8810 | 0.358154 | ||||||||
\(924\) | −73.7379 | −2.42580 | ||||||||
\(925\) | 15.3495 | 0.504687 | ||||||||
\(926\) | 82.6983 | 2.71763 | ||||||||
\(927\) | 58.0243 | 1.90577 | ||||||||
\(928\) | 37.0968 | 1.21776 | ||||||||
\(929\) | −22.5651 | −0.740336 | −0.370168 | − | 0.928965i | \(-0.620700\pi\) | ||||
−0.370168 | + | 0.928965i | \(0.620700\pi\) | |||||||
\(930\) | −193.413 | −6.34225 | ||||||||
\(931\) | 1.08123 | 0.0354359 | ||||||||
\(932\) | −13.2120 | −0.432773 | ||||||||
\(933\) | −42.4900 | −1.39106 | ||||||||
\(934\) | 98.0761 | 3.20915 | ||||||||
\(935\) | 27.9256 | 0.913265 | ||||||||
\(936\) | −44.5846 | −1.45729 | ||||||||
\(937\) | 14.5724 | 0.476059 | 0.238029 | − | 0.971258i | \(-0.423499\pi\) | ||||
0.238029 | + | 0.971258i | \(0.423499\pi\) | |||||||
\(938\) | −10.4396 | −0.340866 | ||||||||
\(939\) | 1.72399 | 0.0562604 | ||||||||
\(940\) | −68.2166 | −2.22498 | ||||||||
\(941\) | −43.6673 | −1.42351 | −0.711756 | − | 0.702426i | \(-0.752100\pi\) | ||||
−0.711756 | + | 0.702426i | \(0.752100\pi\) | |||||||
\(942\) | 82.1722 | 2.67731 | ||||||||
\(943\) | −64.1871 | −2.09022 | ||||||||
\(944\) | 53.2788 | 1.73408 | ||||||||
\(945\) | −110.010 | −3.57864 | ||||||||
\(946\) | −8.35542 | −0.271658 | ||||||||
\(947\) | −31.0708 | −1.00967 | −0.504833 | − | 0.863217i | \(-0.668446\pi\) | ||||
−0.504833 | + | 0.863217i | \(0.668446\pi\) | |||||||
\(948\) | −240.733 | −7.81864 | ||||||||
\(949\) | 4.95200 | 0.160749 | ||||||||
\(950\) | −20.4591 | −0.663780 | ||||||||
\(951\) | −28.9336 | −0.938236 | ||||||||
\(952\) | −110.652 | −3.58625 | ||||||||
\(953\) | −36.1505 | −1.17103 | −0.585515 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585515 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(954\) | 26.9849 | 0.873668 | ||||||||
\(955\) | 57.9411 | 1.87493 | ||||||||
\(956\) | 123.341 | 3.98915 | ||||||||
\(957\) | 25.6561 | 0.829344 | ||||||||
\(958\) | 13.0203 | 0.420667 | ||||||||
\(959\) | −0.119001 | −0.00384273 | ||||||||
\(960\) | −39.1381 | −1.26318 | ||||||||
\(961\) | 42.6802 | 1.37678 | ||||||||
\(962\) | −15.7331 | −0.507256 | ||||||||
\(963\) | 155.346 | 5.00597 | ||||||||
\(964\) | −107.626 | −3.46639 | ||||||||
\(965\) | 36.3948 | 1.17159 | ||||||||
\(966\) | 133.765 | 4.30382 | ||||||||
\(967\) | −38.6408 | −1.24261 | −0.621303 | − | 0.783571i | \(-0.713396\pi\) | ||||
−0.621303 | + | 0.783571i | \(0.713396\pi\) | |||||||
\(968\) | 54.5400 | 1.75298 | ||||||||
\(969\) | −72.2814 | −2.32201 | ||||||||
\(970\) | 77.1809 | 2.47813 | ||||||||
\(971\) | 34.0568 | 1.09293 | 0.546467 | − | 0.837481i | \(-0.315972\pi\) | ||||
0.546467 | + | 0.837481i | \(0.315972\pi\) | |||||||
\(972\) | −197.725 | −6.34203 | ||||||||
\(973\) | −22.0080 | −0.705545 | ||||||||
\(974\) | −43.0962 | −1.38089 | ||||||||
\(975\) | −5.72776 | −0.183435 | ||||||||
\(976\) | −117.217 | −3.75203 | ||||||||
\(977\) | −35.4380 | −1.13376 | −0.566881 | − | 0.823800i | \(-0.691850\pi\) | ||||
−0.566881 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(978\) | −118.432 | −3.78705 | ||||||||
\(979\) | 8.65125 | 0.276495 | ||||||||
\(980\) | 3.59704 | 0.114903 | ||||||||
\(981\) | 41.2784 | 1.31792 | ||||||||
\(982\) | −7.91358 | −0.252533 | ||||||||
\(983\) | −20.1776 | −0.643566 | −0.321783 | − | 0.946814i | \(-0.604282\pi\) | ||||
−0.321783 | + | 0.946814i | \(0.604282\pi\) | |||||||
\(984\) | −249.350 | −7.94898 | ||||||||
\(985\) | 10.2567 | 0.326806 | ||||||||
\(986\) | 67.0911 | 2.13662 | ||||||||
\(987\) | 48.1120 | 1.53142 | ||||||||
\(988\) | 14.7042 | 0.467802 | ||||||||
\(989\) | 10.6280 | 0.337952 | ||||||||
\(990\) | −94.3018 | −2.99711 | ||||||||
\(991\) | 22.6238 | 0.718669 | 0.359334 | − | 0.933209i | \(-0.383004\pi\) | ||||
0.359334 | + | 0.933209i | \(0.383004\pi\) | |||||||
\(992\) | 72.2369 | 2.29352 | ||||||||
\(993\) | −14.3166 | −0.454324 | ||||||||
\(994\) | −91.1931 | −2.89247 | ||||||||
\(995\) | 18.4161 | 0.583829 | ||||||||
\(996\) | −237.898 | −7.53810 | ||||||||
\(997\) | 25.7781 | 0.816401 | 0.408200 | − | 0.912892i | \(-0.366157\pi\) | ||||
0.408200 | + | 0.912892i | \(0.366157\pi\) | |||||||
\(998\) | 38.5619 | 1.22066 | ||||||||
\(999\) | −111.583 | −3.53033 |
(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 | 6037.2.a.b.1.10 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.10 | ✓ | 259 | 1.1 | even | 1 | trivial |