Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, 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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51414 | 1.77776 | 0.888882 | − | 0.458137i | \(-0.151483\pi\) | ||||
0.888882 | + | 0.458137i | \(0.151483\pi\) | |||||||
\(3\) | −1.51414 | −0.874187 | −0.437094 | − | 0.899416i | \(-0.643992\pi\) | ||||
−0.437094 | + | 0.899416i | \(0.643992\pi\) | |||||||
\(4\) | 4.32088 | 2.16044 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.80675 | −1.55410 | ||||||||
\(7\) | 3.32088 | 1.25518 | 0.627588 | − | 0.778545i | \(-0.284042\pi\) | ||||
0.627588 | + | 0.778545i | \(0.284042\pi\) | |||||||
\(8\) | 5.83502 | 2.06299 | ||||||||
\(9\) | −0.707389 | −0.235796 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.83502 | 0.854791 | 0.427396 | − | 0.904065i | \(-0.359431\pi\) | ||||
0.427396 | + | 0.904065i | \(0.359431\pi\) | |||||||
\(12\) | −6.54241 | −1.88863 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 8.34916 | 2.23141 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.02827 | 1.50707 | ||||||||
\(17\) | 6.64177 | 1.61087 | 0.805433 | − | 0.592687i | \(-0.201933\pi\) | ||||
0.805433 | + | 0.592687i | \(0.201933\pi\) | |||||||
\(18\) | −1.77847 | −0.419190 | ||||||||
\(19\) | −2.19325 | −0.503167 | −0.251583 | − | 0.967836i | \(-0.580951\pi\) | ||||
−0.251583 | + | 0.967836i | \(0.580951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.02827 | −1.09726 | ||||||||
\(22\) | 7.12763 | 1.51962 | ||||||||
\(23\) | 0.485863 | 0.101309 | 0.0506547 | − | 0.998716i | \(-0.483869\pi\) | ||||
0.0506547 | + | 0.998716i | \(0.483869\pi\) | |||||||
\(24\) | −8.83502 | −1.80344 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61350 | 1.08032 | ||||||||
\(28\) | 14.3492 | 2.71174 | ||||||||
\(29\) | −3.32088 | −0.616673 | −0.308336 | − | 0.951277i | \(-0.599772\pi\) | ||||
−0.308336 | + | 0.951277i | \(0.599772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.80675 | −0.683712 | −0.341856 | − | 0.939752i | \(-0.611056\pi\) | ||||
−0.341856 | + | 0.939752i | \(0.611056\pi\) | |||||||
\(32\) | 3.48586 | 0.616219 | ||||||||
\(33\) | −4.29261 | −0.747248 | ||||||||
\(34\) | 16.6983 | 2.86374 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.05655 | −0.509425 | ||||||||
\(37\) | 9.32088 | 1.53234 | 0.766172 | − | 0.642636i | \(-0.222159\pi\) | ||||
0.766172 | + | 0.642636i | \(0.222159\pi\) | |||||||
\(38\) | −5.51414 | −0.894511 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.61350 | 0.251986 | 0.125993 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125993 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(42\) | −12.6418 | −1.95067 | ||||||||
\(43\) | 0.872368 | 0.133035 | 0.0665174 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665174 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(44\) | 12.2498 | 1.84673 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.22153 | 0.180104 | ||||||||
\(47\) | −3.32088 | −0.484401 | −0.242200 | − | 0.970226i | \(-0.577869\pi\) | ||||
−0.242200 | + | 0.970226i | \(0.577869\pi\) | |||||||
\(48\) | −9.12763 | −1.31746 | ||||||||
\(49\) | 4.02827 | 0.575468 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0565 | −1.40820 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6700 | −1.60300 | −0.801502 | − | 0.597992i | \(-0.795965\pi\) | ||||
−0.801502 | + | 0.597992i | \(0.795965\pi\) | |||||||
\(54\) | 14.1131 | 1.92055 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.3774 | 2.58942 | ||||||||
\(57\) | 3.32088 | 0.439862 | ||||||||
\(58\) | −8.34916 | −1.09630 | ||||||||
\(59\) | 8.83502 | 1.15022 | 0.575111 | − | 0.818075i | \(-0.304959\pi\) | ||||
0.575111 | + | 0.818075i | \(0.304959\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.70739 | −0.474683 | −0.237341 | − | 0.971426i | \(-0.576276\pi\) | ||||
−0.237341 | + | 0.971426i | \(0.576276\pi\) | |||||||
\(62\) | −9.57068 | −1.21548 | ||||||||
\(63\) | −2.34916 | −0.295966 | ||||||||
\(64\) | −3.29261 | −0.411576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.7922 | −1.32843 | ||||||||
\(67\) | 4.29261 | 0.524426 | 0.262213 | − | 0.965010i | \(-0.415548\pi\) | ||||
0.262213 | + | 0.965010i | \(0.415548\pi\) | |||||||
\(68\) | 28.6983 | 3.48018 | ||||||||
\(69\) | −0.735663 | −0.0885634 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19325 | −0.260291 | −0.130146 | − | 0.991495i | \(-0.541544\pi\) | ||||
−0.130146 | + | 0.991495i | \(0.541544\pi\) | |||||||
\(72\) | −4.12763 | −0.486446 | ||||||||
\(73\) | 12.7357 | 1.49060 | 0.745298 | − | 0.666731i | \(-0.232307\pi\) | ||||
0.745298 | + | 0.666731i | \(0.232307\pi\) | |||||||
\(74\) | 23.4340 | 2.72414 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.47679 | −1.08706 | ||||||||
\(77\) | 9.41478 | 1.07291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.585221 | 0.0658425 | 0.0329213 | − | 0.999458i | \(-0.489519\pi\) | ||||
0.0329213 | + | 0.999458i | \(0.489519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.37743 | −0.708604 | ||||||||
\(82\) | 4.05655 | 0.447971 | ||||||||
\(83\) | 7.70739 | 0.845996 | 0.422998 | − | 0.906131i | \(-0.360978\pi\) | ||||
0.422998 | + | 0.906131i | \(0.360978\pi\) | |||||||
\(84\) | −21.7266 | −2.37057 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.19325 | 0.236504 | ||||||||
\(87\) | 5.02827 | 0.539088 | ||||||||
\(88\) | 16.5424 | 1.76343 | ||||||||
\(89\) | −3.41478 | −0.361966 | −0.180983 | − | 0.983486i | \(-0.557928\pi\) | ||||
−0.180983 | + | 0.983486i | \(0.557928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.09936 | 0.218873 | ||||||||
\(93\) | 5.76394 | 0.597692 | ||||||||
\(94\) | −8.34916 | −0.861150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.27807 | −0.538691 | ||||||||
\(97\) | 0.641769 | 0.0651618 | 0.0325809 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325809 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(98\) | 10.1276 | 1.02305 | ||||||||
\(99\) | −2.00546 | −0.201557 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.97173 | 0.693713 | 0.346856 | − | 0.937918i | \(-0.387249\pi\) | ||||
0.346856 | + | 0.937918i | \(0.387249\pi\) | |||||||
\(102\) | −25.2835 | −2.50344 | ||||||||
\(103\) | 7.18418 | 0.707878 | 0.353939 | − | 0.935268i | \(-0.384842\pi\) | ||||
0.353939 | + | 0.935268i | \(0.384842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.3401 | −2.84976 | ||||||||
\(107\) | 9.57068 | 0.925233 | 0.462617 | − | 0.886558i | \(-0.346911\pi\) | ||||
0.462617 | + | 0.886558i | \(0.346911\pi\) | |||||||
\(108\) | 24.2553 | 2.33396 | ||||||||
\(109\) | 10.6983 | 1.02471 | 0.512356 | − | 0.858773i | \(-0.328773\pi\) | ||||
0.512356 | + | 0.858773i | \(0.328773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1131 | −1.33956 | ||||||||
\(112\) | 20.0192 | 1.89164 | ||||||||
\(113\) | 3.22699 | 0.303570 | 0.151785 | − | 0.988414i | \(-0.451498\pi\) | ||||
0.151785 | + | 0.988414i | \(0.451498\pi\) | |||||||
\(114\) | 8.34916 | 0.781970 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.3492 | −1.33229 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.2125 | 2.04482 | ||||||||
\(119\) | 22.0565 | 2.02192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.96265 | −0.269332 | ||||||||
\(122\) | −9.32088 | −0.843873 | ||||||||
\(123\) | −2.44305 | −0.220283 | ||||||||
\(124\) | −16.4485 | −1.47712 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.90611 | −0.526158 | ||||||||
\(127\) | −5.90064 | −0.523597 | −0.261799 | − | 0.965123i | \(-0.584316\pi\) | ||||
−0.261799 | + | 0.965123i | \(0.584316\pi\) | |||||||
\(128\) | −15.2498 | −1.34790 | ||||||||
\(129\) | −1.32088 | −0.116297 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.41478 | 0.298351 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(132\) | −18.5479 | −1.61439 | ||||||||
\(133\) | −7.28354 | −0.631563 | ||||||||
\(134\) | 10.7922 | 0.932305 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.7549 | 3.32320 | ||||||||
\(137\) | −15.0848 | −1.28878 | −0.644392 | − | 0.764696i | \(-0.722889\pi\) | ||||
−0.644392 | + | 0.764696i | \(0.722889\pi\) | |||||||
\(138\) | −1.84956 | −0.157445 | ||||||||
\(139\) | −20.6983 | −1.75561 | −0.877804 | − | 0.479020i | \(-0.840992\pi\) | ||||
−0.877804 | + | 0.479020i | \(0.840992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.02827 | 0.423457 | ||||||||
\(142\) | −5.51414 | −0.462736 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.26434 | −0.355361 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 32.0192 | 2.64993 | ||||||||
\(147\) | −6.09936 | −0.503067 | ||||||||
\(148\) | 40.2745 | 3.31054 | ||||||||
\(149\) | −0.641769 | −0.0525758 | −0.0262879 | − | 0.999654i | \(-0.508369\pi\) | ||||
−0.0262879 | + | 0.999654i | \(0.508369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6363 | −1.35384 | −0.676922 | − | 0.736055i | \(-0.736686\pi\) | ||||
−0.676922 | + | 0.736055i | \(0.736686\pi\) | |||||||
\(152\) | −12.7977 | −1.03803 | ||||||||
\(153\) | −4.69832 | −0.379836 | ||||||||
\(154\) | 23.6700 | 1.90739 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2553 | −0.818459 | −0.409230 | − | 0.912431i | \(-0.634202\pi\) | ||||
−0.409230 | + | 0.912431i | \(0.634202\pi\) | |||||||
\(158\) | 1.47133 | 0.117052 | ||||||||
\(159\) | 17.6700 | 1.40133 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61350 | 0.127161 | ||||||||
\(162\) | −16.0337 | −1.25973 | ||||||||
\(163\) | −1.37743 | −0.107889 | −0.0539444 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539444 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(164\) | 6.97173 | 0.544400 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.3774 | 1.50398 | ||||||||
\(167\) | 17.5761 | 1.36008 | 0.680042 | − | 0.733174i | \(-0.261962\pi\) | ||||
0.680042 | + | 0.733174i | \(0.261962\pi\) | |||||||
\(168\) | −29.3401 | −2.26364 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.55148 | 0.118645 | ||||||||
\(172\) | 3.76940 | 0.287414 | ||||||||
\(173\) | −6.31181 | −0.479878 | −0.239939 | − | 0.970788i | \(-0.577127\pi\) | ||||
−0.239939 | + | 0.970788i | \(0.577127\pi\) | |||||||
\(174\) | 12.6418 | 0.958370 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.0903 | 1.28823 | ||||||||
\(177\) | −13.3774 | −1.00551 | ||||||||
\(178\) | −8.58522 | −0.643490 | ||||||||
\(179\) | −9.08482 | −0.679031 | −0.339516 | − | 0.940600i | \(-0.610263\pi\) | ||||
−0.339516 | + | 0.940600i | \(0.610263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0192 | 0.893380 | 0.446690 | − | 0.894689i | \(-0.352603\pi\) | ||||
0.446690 | + | 0.894689i | \(0.352603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.61350 | 0.414962 | ||||||||
\(184\) | 2.83502 | 0.209001 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.4913 | 1.06256 | ||||||||
\(187\) | 18.8296 | 1.37695 | ||||||||
\(188\) | −14.3492 | −1.04652 | ||||||||
\(189\) | 18.6418 | 1.35599 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2835 | 0.961163 | 0.480582 | − | 0.876950i | \(-0.340426\pi\) | ||||
0.480582 | + | 0.876950i | \(0.340426\pi\) | |||||||
\(192\) | 4.98546 | 0.359795 | ||||||||
\(193\) | 16.3684 | 1.17822 | 0.589110 | − | 0.808053i | \(-0.299478\pi\) | ||||
0.589110 | + | 0.808053i | \(0.299478\pi\) | |||||||
\(194\) | 1.61350 | 0.115842 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.4057 | 1.24326 | ||||||||
\(197\) | 14.8970 | 1.06137 | 0.530685 | − | 0.847569i | \(-0.321935\pi\) | ||||
0.530685 | + | 0.847569i | \(0.321935\pi\) | |||||||
\(198\) | −5.04201 | −0.358320 | ||||||||
\(199\) | −16.3118 | −1.15631 | −0.578157 | − | 0.815926i | \(-0.696228\pi\) | ||||
−0.578157 | + | 0.815926i | \(0.696228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.49960 | −0.458446 | ||||||||
\(202\) | 17.5279 | 1.23326 | ||||||||
\(203\) | −11.0283 | −0.774033 | ||||||||
\(204\) | −43.4532 | −3.04233 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.0620 | 1.25844 | ||||||||
\(207\) | −0.343694 | −0.0238884 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.21792 | −0.430102 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8013 | 0.812434 | 0.406217 | − | 0.913777i | \(-0.366848\pi\) | ||||
0.406217 | + | 0.913777i | \(0.366848\pi\) | |||||||
\(212\) | −50.4249 | −3.46320 | ||||||||
\(213\) | 3.32088 | 0.227543 | ||||||||
\(214\) | 24.0620 | 1.64485 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32.7549 | 2.22869 | ||||||||
\(217\) | −12.6418 | −0.858179 | ||||||||
\(218\) | 26.8970 | 1.82170 | ||||||||
\(219\) | −19.2835 | −1.30306 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −35.4823 | −2.38141 | ||||||||
\(223\) | −20.0192 | −1.34058 | −0.670292 | − | 0.742097i | \(-0.733831\pi\) | ||||
−0.670292 | + | 0.742097i | \(0.733831\pi\) | |||||||
\(224\) | 11.5761 | 0.773464 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.11310 | 0.539675 | ||||||||
\(227\) | −22.4623 | −1.49087 | −0.745436 | − | 0.666577i | \(-0.767759\pi\) | ||||
−0.745436 | + | 0.666577i | \(0.767759\pi\) | |||||||
\(228\) | 14.3492 | 0.950296 | ||||||||
\(229\) | 10.3684 | 0.685160 | 0.342580 | − | 0.939489i | \(-0.388699\pi\) | ||||
0.342580 | + | 0.939489i | \(0.388699\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.2553 | −0.937928 | ||||||||
\(232\) | −19.3774 | −1.27219 | ||||||||
\(233\) | −11.3582 | −0.744102 | −0.372051 | − | 0.928212i | \(-0.621345\pi\) | ||||
−0.372051 | + | 0.928212i | \(0.621345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 38.1751 | 2.48499 | ||||||||
\(237\) | −0.886105 | −0.0575587 | ||||||||
\(238\) | 55.4532 | 3.59450 | ||||||||
\(239\) | −28.1186 | −1.81884 | −0.909419 | − | 0.415881i | \(-0.863473\pi\) | ||||
−0.909419 | + | 0.415881i | \(0.863473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0848 | 0.971699 | 0.485849 | − | 0.874043i | \(-0.338510\pi\) | ||||
0.485849 | + | 0.874043i | \(0.338510\pi\) | |||||||
\(242\) | −7.44852 | −0.478809 | ||||||||
\(243\) | −7.18418 | −0.460865 | ||||||||
\(244\) | −16.0192 | −1.02552 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.14217 | −0.391610 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −22.2125 | −1.41049 | ||||||||
\(249\) | −11.6700 | −0.739559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.15951 | 0.0731879 | 0.0365940 | − | 0.999330i | \(-0.488349\pi\) | ||||
0.0365940 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(252\) | −10.1504 | −0.639418 | ||||||||
\(253\) | 1.37743 | 0.0865984 | ||||||||
\(254\) | −14.8350 | −0.930832 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.7549 | −1.98468 | ||||||||
\(257\) | 0.829557 | 0.0517464 | 0.0258732 | − | 0.999665i | \(-0.491763\pi\) | ||||
0.0258732 | + | 0.999665i | \(0.491763\pi\) | |||||||
\(258\) | −3.32088 | −0.206749 | ||||||||
\(259\) | 30.9536 | 1.92336 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34916 | 0.145409 | ||||||||
\(262\) | 8.58522 | 0.530397 | ||||||||
\(263\) | 25.6272 | 1.58024 | 0.790121 | − | 0.612950i | \(-0.210017\pi\) | ||||
0.790121 | + | 0.612950i | \(0.210017\pi\) | |||||||
\(264\) | −25.0475 | −1.54157 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.3118 | −1.12277 | ||||||||
\(267\) | 5.17044 | 0.316426 | ||||||||
\(268\) | 18.5479 | 1.13299 | ||||||||
\(269\) | 5.02827 | 0.306579 | 0.153290 | − | 0.988181i | \(-0.451013\pi\) | ||||
0.153290 | + | 0.988181i | \(0.451013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8916 | 1.14758 | 0.573791 | − | 0.819002i | \(-0.305472\pi\) | ||||
0.573791 | + | 0.819002i | \(0.305472\pi\) | |||||||
\(272\) | 40.0384 | 2.42768 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.9253 | −2.29115 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.17872 | −0.191336 | ||||||||
\(277\) | −23.7831 | −1.42899 | −0.714495 | − | 0.699640i | \(-0.753344\pi\) | ||||
−0.714495 | + | 0.699640i | \(0.753344\pi\) | |||||||
\(278\) | −52.0384 | −3.12106 | ||||||||
\(279\) | 2.69285 | 0.161217 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.5953 | −1.88482 | −0.942410 | − | 0.334459i | \(-0.891446\pi\) | ||||
−0.942410 | + | 0.334459i | \(0.891446\pi\) | |||||||
\(282\) | 12.6418 | 0.752806 | ||||||||
\(283\) | −6.35462 | −0.377743 | −0.188872 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188872 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(284\) | −9.47679 | −0.562344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.35823 | 0.316286 | ||||||||
\(288\) | −2.46586 | −0.145302 | ||||||||
\(289\) | 27.1131 | 1.59489 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.971726 | −0.0569636 | ||||||||
\(292\) | 55.0293 | 3.22035 | ||||||||
\(293\) | −8.03735 | −0.469547 | −0.234773 | − | 0.972050i | \(-0.575435\pi\) | ||||
−0.234773 | + | 0.972050i | \(0.575435\pi\) | |||||||
\(294\) | −15.3346 | −0.894333 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 54.3876 | 3.16121 | ||||||||
\(297\) | 15.9144 | 0.923446 | ||||||||
\(298\) | −1.61350 | −0.0934673 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.89703 | 0.166982 | ||||||||
\(302\) | −41.8259 | −2.40681 | ||||||||
\(303\) | −10.5561 | −0.606435 | ||||||||
\(304\) | −13.2215 | −0.758307 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.8122 | −0.675259 | ||||||||
\(307\) | −15.8205 | −0.902923 | −0.451461 | − | 0.892291i | \(-0.649097\pi\) | ||||
−0.451461 | + | 0.892291i | \(0.649097\pi\) | |||||||
\(308\) | 40.6802 | 2.31797 | ||||||||
\(309\) | −10.8778 | −0.618818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3118 | 1.37860 | 0.689298 | − | 0.724478i | \(-0.257919\pi\) | ||||
0.689298 | + | 0.724478i | \(0.257919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2270 | 0.634587 | 0.317294 | − | 0.948327i | \(-0.397226\pi\) | ||||
0.317294 | + | 0.948327i | \(0.397226\pi\) | |||||||
\(314\) | −25.7831 | −1.45503 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.52867 | 0.142249 | ||||||||
\(317\) | −16.1504 | −0.907099 | −0.453550 | − | 0.891231i | \(-0.649843\pi\) | ||||
−0.453550 | + | 0.891231i | \(0.649843\pi\) | |||||||
\(318\) | 44.4249 | 2.49123 | ||||||||
\(319\) | −9.41478 | −0.527126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.4913 | −0.808827 | ||||||||
\(322\) | 4.05655 | 0.226063 | ||||||||
\(323\) | −14.5671 | −0.810534 | ||||||||
\(324\) | −27.5561 | −1.53090 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.46305 | −0.191801 | ||||||||
\(327\) | −16.1987 | −0.895791 | ||||||||
\(328\) | 9.41478 | 0.519844 | ||||||||
\(329\) | −11.0283 | −0.608008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0620 | −1.65236 | −0.826179 | − | 0.563408i | \(-0.809490\pi\) | ||||
−0.826179 | + | 0.563408i | \(0.809490\pi\) | |||||||
\(332\) | 33.3027 | 1.82773 | ||||||||
\(333\) | −6.59349 | −0.361321 | ||||||||
\(334\) | 44.1888 | 2.41791 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −30.3118 | −1.65364 | ||||||||
\(337\) | 17.4713 | 0.951724 | 0.475862 | − | 0.879520i | \(-0.342136\pi\) | ||||
0.475862 | + | 0.879520i | \(0.342136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.88611 | −0.265377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7922 | −0.584431 | ||||||||
\(342\) | 3.90064 | 0.210923 | ||||||||
\(343\) | −9.86876 | −0.532863 | ||||||||
\(344\) | 5.09029 | 0.274450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.8688 | −0.853110 | ||||||||
\(347\) | −33.2407 | −1.78446 | −0.892228 | − | 0.451585i | \(-0.850859\pi\) | ||||
−0.892228 | + | 0.451585i | \(0.850859\pi\) | |||||||
\(348\) | 21.7266 | 1.16467 | ||||||||
\(349\) | 20.8970 | 1.11859 | 0.559296 | − | 0.828968i | \(-0.311071\pi\) | ||||
0.559296 | + | 0.828968i | \(0.311071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.88250 | 0.526739 | ||||||||
\(353\) | 12.5479 | 0.667856 | 0.333928 | − | 0.942599i | \(-0.391626\pi\) | ||||
0.333928 | + | 0.942599i | \(0.391626\pi\) | |||||||
\(354\) | −33.6327 | −1.78756 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.7549 | −0.782006 | ||||||||
\(357\) | −33.3966 | −1.76754 | ||||||||
\(358\) | −22.8405 | −1.20716 | ||||||||
\(359\) | 2.97719 | 0.157130 | 0.0785650 | − | 0.996909i | \(-0.474966\pi\) | ||||
0.0785650 | + | 0.996909i | \(0.474966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1896 | −0.746823 | ||||||||
\(362\) | 30.2179 | 1.58822 | ||||||||
\(363\) | 4.48586 | 0.235447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.1131 | 0.737703 | ||||||||
\(367\) | 30.5990 | 1.59725 | 0.798626 | − | 0.601827i | \(-0.205560\pi\) | ||||
0.798626 | + | 0.601827i | \(0.205560\pi\) | |||||||
\(368\) | 2.92892 | 0.152680 | ||||||||
\(369\) | −1.14137 | −0.0594173 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −38.7549 | −2.01205 | ||||||||
\(372\) | 24.9053 | 1.29128 | ||||||||
\(373\) | −18.2553 | −0.945222 | −0.472611 | − | 0.881271i | \(-0.656688\pi\) | ||||
−0.472611 | + | 0.881271i | \(0.656688\pi\) | |||||||
\(374\) | 47.3401 | 2.44790 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.3774 | −0.999315 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 46.8680 | 2.41063 | ||||||||
\(379\) | −15.9945 | −0.821584 | −0.410792 | − | 0.911729i | \(-0.634748\pi\) | ||||
−0.410792 | + | 0.911729i | \(0.634748\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.93438 | 0.457722 | ||||||||
\(382\) | 33.3966 | 1.70872 | ||||||||
\(383\) | −2.16137 | −0.110441 | −0.0552204 | − | 0.998474i | \(-0.517586\pi\) | ||||
−0.0552204 | + | 0.998474i | \(0.517586\pi\) | |||||||
\(384\) | 23.0903 | 1.17832 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.1523 | 2.09460 | ||||||||
\(387\) | −0.617104 | −0.0313691 | ||||||||
\(388\) | 2.77301 | 0.140778 | ||||||||
\(389\) | −0.453981 | −0.0230177 | −0.0115089 | − | 0.999934i | \(-0.503663\pi\) | ||||
−0.0115089 | + | 0.999934i | \(0.503663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22699 | 0.163196 | ||||||||
\(392\) | 23.5051 | 1.18719 | ||||||||
\(393\) | −5.17044 | −0.260814 | ||||||||
\(394\) | 37.4532 | 1.88686 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.66538 | −0.435452 | ||||||||
\(397\) | −29.2462 | −1.46782 | −0.733912 | − | 0.679244i | \(-0.762308\pi\) | ||||
−0.733912 | + | 0.679244i | \(0.762308\pi\) | |||||||
\(398\) | −41.0101 | −2.05565 | ||||||||
\(399\) | 11.0283 | 0.552104 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2270 | −0.760400 | −0.380200 | − | 0.924904i | \(-0.624145\pi\) | ||||
−0.380200 | + | 0.924904i | \(0.624145\pi\) | |||||||
\(402\) | −16.3409 | −0.815009 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 30.1240 | 1.49873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.7266 | −1.37605 | ||||||||
\(407\) | 26.4249 | 1.30983 | ||||||||
\(408\) | −58.6802 | −2.90510 | ||||||||
\(409\) | 23.6700 | 1.17041 | 0.585204 | − | 0.810886i | \(-0.301014\pi\) | ||||
0.585204 | + | 0.810886i | \(0.301014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.8405 | 1.12664 | ||||||||
\(412\) | 31.0420 | 1.52933 | ||||||||
\(413\) | 29.3401 | 1.44373 | ||||||||
\(414\) | −0.864095 | −0.0424679 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.3401 | 1.53473 | ||||||||
\(418\) | −15.6327 | −0.764620 | ||||||||
\(419\) | −5.67004 | −0.277000 | −0.138500 | − | 0.990362i | \(-0.544228\pi\) | ||||
−0.138500 | + | 0.990362i | \(0.544228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.3009 | 1.28183 | 0.640913 | − | 0.767613i | \(-0.278556\pi\) | ||||
0.640913 | + | 0.767613i | \(0.278556\pi\) | |||||||
\(422\) | 29.6700 | 1.44432 | ||||||||
\(423\) | 2.34916 | 0.114220 | ||||||||
\(424\) | −68.0950 | −3.30698 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.34916 | 0.404518 | ||||||||
\(427\) | −12.3118 | −0.595810 | ||||||||
\(428\) | 41.3538 | 1.99891 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.09029 | −0.245190 | −0.122595 | − | 0.992457i | \(-0.539122\pi\) | ||||
−0.122595 | + | 0.992457i | \(0.539122\pi\) | |||||||
\(432\) | 33.8397 | 1.62811 | ||||||||
\(433\) | −24.0565 | −1.15608 | −0.578042 | − | 0.816007i | \(-0.696183\pi\) | ||||
−0.578042 | + | 0.816007i | \(0.696183\pi\) | |||||||
\(434\) | −31.7831 | −1.52564 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 46.2262 | 2.21383 | ||||||||
\(437\) | −1.06562 | −0.0509755 | ||||||||
\(438\) | −48.4815 | −2.31653 | ||||||||
\(439\) | −7.21606 | −0.344404 | −0.172202 | − | 0.985062i | \(-0.555088\pi\) | ||||
−0.172202 | + | 0.985062i | \(0.555088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.84956 | −0.135693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.3829 | −1.30100 | −0.650500 | − | 0.759506i | \(-0.725441\pi\) | ||||
−0.650500 | + | 0.759506i | \(0.725441\pi\) | |||||||
\(444\) | −60.9811 | −2.89403 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −50.3310 | −2.38324 | ||||||||
\(447\) | 0.971726 | 0.0459611 | ||||||||
\(448\) | −10.9344 | −0.516601 | ||||||||
\(449\) | −1.42571 | −0.0672833 | −0.0336416 | − | 0.999434i | \(-0.510710\pi\) | ||||
−0.0336416 | + | 0.999434i | \(0.510710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.57429 | 0.215395 | ||||||||
\(452\) | 13.9435 | 0.655845 | ||||||||
\(453\) | 25.1896 | 1.18351 | ||||||||
\(454\) | −56.4732 | −2.65042 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.3774 | 0.907431 | ||||||||
\(457\) | −35.3219 | −1.65229 | −0.826145 | − | 0.563457i | \(-0.809471\pi\) | ||||
−0.826145 | + | 0.563457i | \(0.809471\pi\) | |||||||
\(458\) | 26.0675 | 1.21805 | ||||||||
\(459\) | 37.2835 | 1.74025 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.1979 | −1.35988 | −0.679941 | − | 0.733267i | \(-0.737995\pi\) | ||||
−0.679941 | + | 0.733267i | \(0.737995\pi\) | |||||||
\(462\) | −35.8397 | −1.66741 | ||||||||
\(463\) | −3.32088 | −0.154335 | −0.0771673 | − | 0.997018i | \(-0.524588\pi\) | ||||
−0.0771673 | + | 0.997018i | \(0.524588\pi\) | |||||||
\(464\) | −20.0192 | −0.929368 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.5561 | −1.32284 | ||||||||
\(467\) | −21.5525 | −0.997333 | −0.498666 | − | 0.866794i | \(-0.666177\pi\) | ||||
−0.498666 | + | 0.866794i | \(0.666177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2553 | 0.658247 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5279 | 0.715487 | ||||||||
\(472\) | 51.5525 | 2.37290 | ||||||||
\(473\) | 2.47318 | 0.113717 | ||||||||
\(474\) | −2.22779 | −0.102326 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 95.3038 | 4.36824 | ||||||||
\(477\) | 8.25526 | 0.377983 | ||||||||
\(478\) | −70.6939 | −3.23346 | ||||||||
\(479\) | −5.42024 | −0.247657 | −0.123829 | − | 0.992304i | \(-0.539517\pi\) | ||||
−0.123829 | + | 0.992304i | \(0.539517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 37.9253 | 1.72745 | ||||||||
\(483\) | −2.44305 | −0.111163 | ||||||||
\(484\) | −12.8013 | −0.581877 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.0620 | −0.819309 | ||||||||
\(487\) | 17.4521 | 0.790831 | 0.395416 | − | 0.918502i | \(-0.370601\pi\) | ||||
0.395416 | + | 0.918502i | \(0.370601\pi\) | |||||||
\(488\) | −21.6327 | −0.979266 | ||||||||
\(489\) | 2.08562 | 0.0943150 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6236 | 1.11125 | 0.555624 | − | 0.831433i | \(-0.312479\pi\) | ||||
0.555624 | + | 0.831433i | \(0.312479\pi\) | |||||||
\(492\) | −10.5561 | −0.475908 | ||||||||
\(493\) | −22.0565 | −0.993377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.9481 | −1.03040 | ||||||||
\(497\) | −7.28354 | −0.326711 | ||||||||
\(498\) | −29.3401 | −1.31476 | ||||||||
\(499\) | −32.3629 | −1.44876 | −0.724381 | − | 0.689400i | \(-0.757874\pi\) | ||||
−0.724381 | + | 0.689400i | \(0.757874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6127 | −1.18897 | ||||||||
\(502\) | 2.91518 | 0.130111 | ||||||||
\(503\) | 26.7411 | 1.19233 | 0.596164 | − | 0.802863i | \(-0.296691\pi\) | ||||
0.596164 | + | 0.802863i | \(0.296691\pi\) | |||||||
\(504\) | −13.7074 | −0.610576 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.46305 | 0.153951 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.4960 | −1.13120 | ||||||||
\(509\) | −9.74474 | −0.431928 | −0.215964 | − | 0.976401i | \(-0.569289\pi\) | ||||
−0.215964 | + | 0.976401i | \(0.569289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.2937 | 1.87096 | ||||||||
\(512\) | −49.3365 | −2.18038 | ||||||||
\(513\) | −12.3118 | −0.543580 | ||||||||
\(514\) | 2.08562 | 0.0919928 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.70739 | −0.251254 | ||||||||
\(517\) | −9.41478 | −0.414061 | ||||||||
\(518\) | 77.8215 | 3.41928 | ||||||||
\(519\) | 9.55695 | 0.419503 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4340 | −0.500932 | −0.250466 | − | 0.968125i | \(-0.580584\pi\) | ||||
−0.250466 | + | 0.968125i | \(0.580584\pi\) | |||||||
\(522\) | 5.90611 | 0.258503 | ||||||||
\(523\) | −33.6272 | −1.47042 | −0.735208 | − | 0.677841i | \(-0.762916\pi\) | ||||
−0.735208 | + | 0.677841i | \(0.762916\pi\) | |||||||
\(524\) | 14.7549 | 0.644569 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 64.4304 | 2.80930 | ||||||||
\(527\) | −25.2835 | −1.10137 | ||||||||
\(528\) | −25.8770 | −1.12615 | ||||||||
\(529\) | −22.7639 | −0.989736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.24980 | −0.271218 | ||||||||
\(532\) | −31.4713 | −1.36446 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.9992 | 0.562530 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.0475 | 1.08189 | ||||||||
\(537\) | 13.7557 | 0.593601 | ||||||||
\(538\) | 12.6418 | 0.545025 | ||||||||
\(539\) | 11.4202 | 0.491905 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.4431 | −1.13688 | −0.568438 | − | 0.822726i | \(-0.692452\pi\) | ||||
−0.568438 | + | 0.822726i | \(0.692452\pi\) | |||||||
\(542\) | 47.4960 | 2.04013 | ||||||||
\(543\) | −18.1987 | −0.780982 | ||||||||
\(544\) | 23.1523 | 0.992647 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9681 | 0.939289 | 0.469644 | − | 0.882856i | \(-0.344382\pi\) | ||||
0.469644 | + | 0.882856i | \(0.344382\pi\) | |||||||
\(548\) | −65.1798 | −2.78434 | ||||||||
\(549\) | 2.62257 | 0.111928 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.28354 | 0.310289 | ||||||||
\(552\) | −4.29261 | −0.182706 | ||||||||
\(553\) | 1.94345 | 0.0826440 | ||||||||
\(554\) | −59.7941 | −2.54041 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −89.4350 | −3.79289 | ||||||||
\(557\) | −39.3027 | −1.66531 | −0.832655 | − | 0.553792i | \(-0.813180\pi\) | ||||
−0.832655 | + | 0.553792i | \(0.813180\pi\) | |||||||
\(558\) | 6.77020 | 0.286605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.5105 | −1.20372 | ||||||||
\(562\) | −79.4350 | −3.35076 | ||||||||
\(563\) | 23.0420 | 0.971105 | 0.485552 | − | 0.874208i | \(-0.338618\pi\) | ||||
0.485552 | + | 0.874208i | \(0.338618\pi\) | |||||||
\(564\) | 21.7266 | 0.914854 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.9764 | −0.671538 | ||||||||
\(567\) | −21.1787 | −0.889422 | ||||||||
\(568\) | −12.7977 | −0.536979 | ||||||||
\(569\) | −3.63270 | −0.152291 | −0.0761453 | − | 0.997097i | \(-0.524261\pi\) | ||||
−0.0761453 | + | 0.997097i | \(0.524261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.3785 | −1.81533 | −0.907667 | − | 0.419692i | \(-0.862138\pi\) | ||||
−0.907667 | + | 0.419692i | \(0.862138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.1131 | −0.840237 | ||||||||
\(574\) | 13.4713 | 0.562282 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.32916 | 0.0970482 | ||||||||
\(577\) | 8.84876 | 0.368379 | 0.184189 | − | 0.982891i | \(-0.441034\pi\) | ||||
0.184189 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(578\) | 68.1660 | 2.83533 | ||||||||
\(579\) | −24.7839 | −1.02999 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.5953 | 1.06187 | ||||||||
\(582\) | −2.44305 | −0.101268 | ||||||||
\(583\) | −33.0848 | −1.37023 | ||||||||
\(584\) | 74.3129 | 3.07509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.2070 | −0.834743 | ||||||||
\(587\) | −15.3209 | −0.632361 | −0.316180 | − | 0.948699i | \(-0.602400\pi\) | ||||
−0.316180 | + | 0.948699i | \(0.602400\pi\) | |||||||
\(588\) | −26.3546 | −1.08685 | ||||||||
\(589\) | 8.34916 | 0.344021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.5561 | −0.927836 | ||||||||
\(592\) | 56.1888 | 2.30935 | ||||||||
\(593\) | −4.52867 | −0.185970 | −0.0929852 | − | 0.995667i | \(-0.529641\pi\) | ||||
−0.0929852 | + | 0.995667i | \(0.529641\pi\) | |||||||
\(594\) | 40.0109 | 1.64167 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.77301 | −0.113587 | ||||||||
\(597\) | 24.6983 | 1.01083 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.0283 | 0.940910 | 0.470455 | − | 0.882424i | \(-0.344090\pi\) | ||||
0.470455 | + | 0.882424i | \(0.344090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0565 | −0.491797 | −0.245898 | − | 0.969296i | \(-0.579083\pi\) | ||||
−0.245898 | + | 0.969296i | \(0.579083\pi\) | |||||||
\(602\) | 7.28354 | 0.296855 | ||||||||
\(603\) | −3.03655 | −0.123658 | ||||||||
\(604\) | −71.8836 | −2.92490 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −26.5396 | −1.07810 | ||||||||
\(607\) | 8.99639 | 0.365152 | 0.182576 | − | 0.983192i | \(-0.441556\pi\) | ||||
0.182576 | + | 0.983192i | \(0.441556\pi\) | |||||||
\(608\) | −7.64538 | −0.310061 | ||||||||
\(609\) | 16.6983 | 0.676650 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −20.3009 | −0.820615 | ||||||||
\(613\) | −14.1131 | −0.570023 | −0.285011 | − | 0.958524i | \(-0.591997\pi\) | ||||
−0.285011 | + | 0.958524i | \(0.591997\pi\) | |||||||
\(614\) | −39.7749 | −1.60518 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 54.9354 | 2.21341 | ||||||||
\(617\) | −2.46120 | −0.0990841 | −0.0495420 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495420 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(618\) | −27.3484 | −1.10011 | ||||||||
\(619\) | −5.73205 | −0.230391 | −0.115195 | − | 0.993343i | \(-0.536749\pi\) | ||||
−0.115195 | + | 0.993343i | \(0.536749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.72739 | 0.109446 | ||||||||
\(622\) | 61.1232 | 2.45082 | ||||||||
\(623\) | −11.3401 | −0.454331 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.2262 | 1.12815 | ||||||||
\(627\) | 9.41478 | 0.375990 | ||||||||
\(628\) | −44.3118 | −1.76823 | ||||||||
\(629\) | 61.9072 | 2.46840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.27807 | 0.210117 | 0.105058 | − | 0.994466i | \(-0.466497\pi\) | ||||
0.105058 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(632\) | 3.41478 | 0.135833 | ||||||||
\(633\) | −17.8688 | −0.710219 | ||||||||
\(634\) | −40.6044 | −1.61261 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 76.3502 | 3.02748 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.6700 | −0.937106 | ||||||||
\(639\) | 1.55148 | 0.0613757 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9992 | −1.69837 | −0.849183 | − | 0.528098i | \(-0.822905\pi\) | ||||
−0.849183 | + | 0.528098i | \(0.822905\pi\) | |||||||
\(642\) | −36.4332 | −1.43790 | ||||||||
\(643\) | 43.3593 | 1.70992 | 0.854962 | − | 0.518691i | \(-0.173581\pi\) | ||||
0.854962 | + | 0.518691i | \(0.173581\pi\) | |||||||
\(644\) | 6.97173 | 0.274724 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.6236 | −1.44094 | ||||||||
\(647\) | 19.6454 | 0.772339 | 0.386170 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386170 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(648\) | −37.2125 | −1.46184 | ||||||||
\(649\) | 25.0475 | 0.983199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.1414 | 0.750209 | ||||||||
\(652\) | −5.95173 | −0.233088 | ||||||||
\(653\) | −9.93252 | −0.388690 | −0.194345 | − | 0.980933i | \(-0.562258\pi\) | ||||
−0.194345 | + | 0.980933i | \(0.562258\pi\) | |||||||
\(654\) | −40.7258 | −1.59250 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.72659 | 0.379760 | ||||||||
\(657\) | −9.00907 | −0.351477 | ||||||||
\(658\) | −27.7266 | −1.08090 | ||||||||
\(659\) | 10.1806 | 0.396579 | 0.198289 | − | 0.980144i | \(-0.436461\pi\) | ||||
0.198289 | + | 0.980144i | \(0.436461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9427 | 1.28132 | 0.640660 | − | 0.767824i | \(-0.278661\pi\) | ||||
0.640660 | + | 0.767824i | \(0.278661\pi\) | |||||||
\(662\) | −75.5800 | −2.93750 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.9728 | 1.74528 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.5769 | −0.642344 | ||||||||
\(667\) | −1.61350 | −0.0624748 | ||||||||
\(668\) | 75.9445 | 2.93838 | ||||||||
\(669\) | 30.3118 | 1.17192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.5105 | −0.405754 | ||||||||
\(672\) | −17.5279 | −0.676152 | ||||||||
\(673\) | 11.2270 | 0.432769 | 0.216384 | − | 0.976308i | \(-0.430574\pi\) | ||||
0.216384 | + | 0.976308i | \(0.430574\pi\) | |||||||
\(674\) | 43.9253 | 1.69194 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7447 | 0.605119 | 0.302560 | − | 0.953130i | \(-0.402159\pi\) | ||||
0.302560 | + | 0.953130i | \(0.402159\pi\) | |||||||
\(678\) | −12.2843 | −0.471777 | ||||||||
\(679\) | 2.13124 | 0.0817895 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.0109 | 1.30330 | ||||||||
\(682\) | −27.1331 | −1.03898 | ||||||||
\(683\) | 50.3492 | 1.92656 | 0.963279 | − | 0.268504i | \(-0.0865293\pi\) | ||||
0.963279 | + | 0.268504i | \(0.0865293\pi\) | |||||||
\(684\) | 6.70378 | 0.256325 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.8114 | −0.947304 | ||||||||
\(687\) | −15.6991 | −0.598959 | ||||||||
\(688\) | 5.25887 | 0.200493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.19325 | −0.311686 | −0.155843 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155843 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(692\) | −27.2726 | −1.03675 | ||||||||
\(693\) | −6.65991 | −0.252989 | ||||||||
\(694\) | −83.5717 | −3.17234 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 29.3401 | 1.11213 | ||||||||
\(697\) | 10.7165 | 0.405915 | ||||||||
\(698\) | 52.5380 | 1.98859 | ||||||||
\(699\) | 17.1979 | 0.650485 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.25526 | −0.311797 | −0.155899 | − | 0.987773i | \(-0.549827\pi\) | ||||
−0.155899 | + | 0.987773i | \(0.549827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.4431 | −0.771024 | ||||||||
\(704\) | −9.33462 | −0.351812 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.5471 | 1.18729 | ||||||||
\(707\) | 23.1523 | 0.870732 | ||||||||
\(708\) | −57.8023 | −2.17234 | ||||||||
\(709\) | −37.7831 | −1.41898 | −0.709488 | − | 0.704718i | \(-0.751074\pi\) | ||||
−0.709488 | + | 0.704718i | \(0.751074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.413979 | −0.0155254 | ||||||||
\(712\) | −19.9253 | −0.746732 | ||||||||
\(713\) | −1.84956 | −0.0692665 | ||||||||
\(714\) | −83.9637 | −3.14226 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −39.2545 | −1.46701 | ||||||||
\(717\) | 42.5753 | 1.59001 | ||||||||
\(718\) | 7.48506 | 0.279340 | ||||||||
\(719\) | −22.2443 | −0.829574 | −0.414787 | − | 0.909919i | \(-0.636144\pi\) | ||||
−0.414787 | + | 0.909919i | \(0.636144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8578 | 0.888512 | ||||||||
\(722\) | −35.6747 | −1.32768 | ||||||||
\(723\) | −22.8405 | −0.849447 | ||||||||
\(724\) | 51.9336 | 1.93010 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.2781 | 0.418569 | ||||||||
\(727\) | 30.0812 | 1.11565 | 0.557825 | − | 0.829958i | \(-0.311636\pi\) | ||||
0.557825 | + | 0.829958i | \(0.311636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0101 | 1.11149 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.79407 | 0.214301 | ||||||||
\(732\) | 24.2553 | 0.896500 | ||||||||
\(733\) | −35.0101 | −1.29313 | −0.646564 | − | 0.762859i | \(-0.723795\pi\) | ||||
−0.646564 | + | 0.762859i | \(0.723795\pi\) | |||||||
\(734\) | 76.9300 | 2.83954 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.69365 | 0.0624288 | ||||||||
\(737\) | 12.1696 | 0.448275 | ||||||||
\(738\) | −2.86956 | −0.105630 | ||||||||
\(739\) | −42.6856 | −1.57022 | −0.785108 | − | 0.619359i | \(-0.787393\pi\) | ||||
−0.785108 | + | 0.619359i | \(0.787393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −97.4350 | −3.57695 | ||||||||
\(743\) | 13.6892 | 0.502210 | 0.251105 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251105 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(744\) | 33.6327 | 1.23303 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.8962 | −1.68038 | ||||||||
\(747\) | −5.45213 | −0.199483 | ||||||||
\(748\) | 81.3603 | 2.97483 | ||||||||
\(749\) | 31.7831 | 1.16133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7831 | 0.648916 | 0.324458 | − | 0.945900i | \(-0.394818\pi\) | ||||
0.324458 | + | 0.945900i | \(0.394818\pi\) | |||||||
\(752\) | −20.0192 | −0.730025 | ||||||||
\(753\) | −1.75566 | −0.0639799 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 80.5489 | 2.92954 | ||||||||
\(757\) | 26.9717 | 0.980304 | 0.490152 | − | 0.871637i | \(-0.336941\pi\) | ||||
0.490152 | + | 0.871637i | \(0.336941\pi\) | |||||||
\(758\) | −40.2125 | −1.46058 | ||||||||
\(759\) | −2.08562 | −0.0757032 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.1523 | 1.27427 | 0.637135 | − | 0.770752i | \(-0.280119\pi\) | ||||
0.637135 | + | 0.770752i | \(0.280119\pi\) | |||||||
\(762\) | 22.4623 | 0.813722 | ||||||||
\(763\) | 35.5279 | 1.28620 | ||||||||
\(764\) | 57.3966 | 2.07654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.43398 | −0.196338 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 48.0812 | 1.73498 | ||||||||
\(769\) | −23.1523 | −0.834893 | −0.417447 | − | 0.908701i | \(-0.637075\pi\) | ||||
−0.417447 | + | 0.908701i | \(0.637075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.25606 | −0.0452360 | ||||||||
\(772\) | 70.7258 | 2.54548 | ||||||||
\(773\) | −41.6218 | −1.49703 | −0.748515 | − | 0.663117i | \(-0.769233\pi\) | ||||
−0.748515 | + | 0.663117i | \(0.769233\pi\) | |||||||
\(774\) | −1.55148 | −0.0557669 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.74474 | 0.134428 | ||||||||
\(777\) | −46.8680 | −1.68138 | ||||||||
\(778\) | −1.14137 | −0.0409201 | ||||||||
\(779\) | −3.53880 | −0.126791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.21792 | −0.222495 | ||||||||
\(782\) | 8.11310 | 0.290124 | ||||||||
\(783\) | −18.6418 | −0.666202 | ||||||||
\(784\) | 24.2835 | 0.867269 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.9992 | −0.463666 | ||||||||
\(787\) | 43.2353 | 1.54117 | 0.770585 | − | 0.637337i | \(-0.219964\pi\) | ||||
0.770585 | + | 0.637337i | \(0.219964\pi\) | |||||||
\(788\) | 64.3684 | 2.29303 | ||||||||
\(789\) | −38.8031 | −1.38143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7165 | 0.381034 | ||||||||
\(792\) | −11.7019 | −0.415810 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −73.5289 | −2.60944 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −70.4815 | −2.49815 | ||||||||
\(797\) | 14.4431 | 0.511599 | 0.255800 | − | 0.966730i | \(-0.417661\pi\) | ||||
0.255800 | + | 0.966730i | \(0.417661\pi\) | |||||||
\(798\) | 27.7266 | 0.981511 | ||||||||
\(799\) | −22.0565 | −0.780305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.41558 | 0.0853503 | ||||||||
\(802\) | −38.2827 | −1.35181 | ||||||||
\(803\) | 36.1059 | 1.27415 | ||||||||
\(804\) | −28.0840 | −0.990447 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.61350 | −0.268008 | ||||||||
\(808\) | 40.6802 | 1.43112 | ||||||||
\(809\) | 17.8880 | 0.628907 | 0.314454 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314454 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.69285 | 0.305247 | 0.152624 | − | 0.988284i | \(-0.451228\pi\) | ||||
0.152624 | + | 0.988284i | \(0.451228\pi\) | |||||||
\(812\) | −47.6519 | −1.67225 | ||||||||
\(813\) | −28.6044 | −1.00320 | ||||||||
\(814\) | 66.4358 | 2.32857 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −60.6236 | −2.12225 | ||||||||
\(817\) | −1.91332 | −0.0669387 | ||||||||
\(818\) | 59.5097 | 2.08071 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.41478 | 0.328578 | 0.164289 | − | 0.986412i | \(-0.447467\pi\) | ||||
0.164289 | + | 0.986412i | \(0.447467\pi\) | |||||||
\(822\) | 57.4241 | 2.00290 | ||||||||
\(823\) | 30.3365 | 1.05746 | 0.528732 | − | 0.848789i | \(-0.322668\pi\) | ||||
0.528732 | + | 0.848789i | \(0.322668\pi\) | |||||||
\(824\) | 41.9198 | 1.46035 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 73.7650 | 2.56661 | ||||||||
\(827\) | −18.2361 | −0.634130 | −0.317065 | − | 0.948404i | \(-0.602697\pi\) | ||||
−0.317065 | + | 0.948404i | \(0.602697\pi\) | |||||||
\(828\) | −1.48506 | −0.0516095 | ||||||||
\(829\) | 29.8023 | 1.03508 | 0.517539 | − | 0.855660i | \(-0.326848\pi\) | ||||
0.517539 | + | 0.855660i | \(0.326848\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.0109 | 1.24921 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.7549 | 0.927001 | ||||||||
\(834\) | 78.7933 | 2.72839 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.8669 | −0.929211 | ||||||||
\(837\) | −21.3692 | −0.738626 | ||||||||
\(838\) | −14.2553 | −0.492440 | ||||||||
\(839\) | 46.1004 | 1.59156 | 0.795782 | − | 0.605584i | \(-0.207060\pi\) | ||||
0.795782 | + | 0.605584i | \(0.207060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9717 | −0.619715 | ||||||||
\(842\) | 66.1240 | 2.27878 | ||||||||
\(843\) | 47.8397 | 1.64769 | ||||||||
\(844\) | 50.9920 | 1.75522 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.90611 | 0.203056 | ||||||||
\(847\) | −9.83863 | −0.338059 | ||||||||
\(848\) | −70.3502 | −2.41584 | ||||||||
\(849\) | 9.62177 | 0.330218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.52867 | 0.155241 | ||||||||
\(852\) | 14.3492 | 0.491594 | ||||||||
\(853\) | −19.3774 | −0.663471 | −0.331735 | − | 0.943373i | \(-0.607634\pi\) | ||||
−0.331735 | + | 0.943373i | \(0.607634\pi\) | |||||||
\(854\) | −30.9536 | −1.05921 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 55.8452 | 1.90875 | ||||||||
\(857\) | 43.4713 | 1.48495 | 0.742476 | − | 0.669873i | \(-0.233651\pi\) | ||||
0.742476 | + | 0.669873i | \(0.233651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7375 | −0.946392 | −0.473196 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473196 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.11310 | −0.276494 | ||||||||
\(862\) | −12.7977 | −0.435891 | ||||||||
\(863\) | 3.69646 | 0.125829 | 0.0629145 | − | 0.998019i | \(-0.479960\pi\) | ||||
0.0629145 | + | 0.998019i | \(0.479960\pi\) | |||||||
\(864\) | 19.5679 | 0.665713 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −60.4815 | −2.05524 | ||||||||
\(867\) | −41.0529 | −1.39423 | ||||||||
\(868\) | −54.6236 | −1.85405 | ||||||||
\(869\) | 1.65911 | 0.0562816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 62.4249 | 2.11397 | ||||||||
\(873\) | −0.453981 | −0.0153649 | ||||||||
\(874\) | −2.67912 | −0.0906224 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −83.3219 | −2.81519 | ||||||||
\(877\) | −20.5671 | −0.694501 | −0.347250 | − | 0.937772i | \(-0.612885\pi\) | ||||
−0.347250 | + | 0.937772i | \(0.612885\pi\) | |||||||
\(878\) | −18.1422 | −0.612269 | ||||||||
\(879\) | 12.1696 | 0.410472 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.5369 | −0.489762 | −0.244881 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244881 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(882\) | −7.16418 | −0.241230 | ||||||||
\(883\) | 36.2871 | 1.22116 | 0.610580 | − | 0.791955i | \(-0.290936\pi\) | ||||
0.610580 | + | 0.791955i | \(0.290936\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −68.8444 | −2.31287 | ||||||||
\(887\) | 45.2407 | 1.51903 | 0.759517 | − | 0.650487i | \(-0.225435\pi\) | ||||
0.759517 | + | 0.650487i | \(0.225435\pi\) | |||||||
\(888\) | −82.3502 | −2.76349 | ||||||||
\(889\) | −19.5953 | −0.657207 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0802 | −0.605708 | ||||||||
\(892\) | −86.5007 | −2.89626 | ||||||||
\(893\) | 7.28354 | 0.243734 | ||||||||
\(894\) | 2.44305 | 0.0817079 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −50.6428 | −1.69186 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.58442 | −0.119614 | ||||||||
\(899\) | 12.6418 | 0.421627 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.5097 | −2.58222 | ||||||||
\(902\) | 11.5004 | 0.382921 | ||||||||
\(903\) | −4.38650 | −0.145974 | ||||||||
\(904\) | 18.8296 | 0.626262 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 63.3302 | 2.10401 | ||||||||
\(907\) | 11.2973 | 0.375120 | 0.187560 | − | 0.982253i | \(-0.439942\pi\) | ||||
0.187560 | + | 0.982253i | \(0.439942\pi\) | |||||||
\(908\) | −97.0568 | −3.22094 | ||||||||
\(909\) | −4.93172 | −0.163575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.1979 | −1.36495 | −0.682474 | − | 0.730910i | \(-0.739096\pi\) | ||||
−0.682474 | + | 0.730910i | \(0.739096\pi\) | |||||||
\(912\) | 20.0192 | 0.662902 | ||||||||
\(913\) | 21.8506 | 0.723150 | ||||||||
\(914\) | −88.8042 | −2.93738 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.8005 | 1.48025 | ||||||||
\(917\) | 11.3401 | 0.374483 | ||||||||
\(918\) | 93.7359 | 3.09375 | ||||||||
\(919\) | 1.74474 | 0.0575535 | 0.0287768 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287768 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.9544 | 0.789324 | ||||||||
\(922\) | −73.4076 | −2.41755 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −61.5953 | −2.02634 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.34916 | −0.274370 | ||||||||
\(927\) | −5.08201 | −0.166915 | ||||||||
\(928\) | −11.5761 | −0.380006 | ||||||||
\(929\) | −15.5569 | −0.510407 | −0.255203 | − | 0.966887i | \(-0.582142\pi\) | ||||
−0.255203 | + | 0.966887i | \(0.582142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.83502 | −0.289556 | ||||||||
\(932\) | −49.0776 | −1.60759 | ||||||||
\(933\) | −36.8114 | −1.20515 | ||||||||
\(934\) | −54.1860 | −1.77302 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0384 | −0.850638 | −0.425319 | − | 0.905044i | \(-0.639838\pi\) | ||||
−0.425319 | + | 0.905044i | \(0.639838\pi\) | |||||||
\(938\) | 35.8397 | 1.17021 | ||||||||
\(939\) | −16.9992 | −0.554748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.8789 | −1.65860 | −0.829302 | − | 0.558800i | \(-0.811262\pi\) | ||||
−0.829302 | + | 0.558800i | \(0.811262\pi\) | |||||||
\(942\) | 39.0392 | 1.27197 | ||||||||
\(943\) | 0.783938 | 0.0255285 | ||||||||
\(944\) | 53.2599 | 1.73346 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.21792 | 0.202162 | ||||||||
\(947\) | 37.8770 | 1.23084 | 0.615419 | − | 0.788200i | \(-0.288987\pi\) | ||||
0.615419 | + | 0.788200i | \(0.288987\pi\) | |||||||
\(948\) | −3.82876 | −0.124352 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.4540 | 0.792975 | ||||||||
\(952\) | 128.700 | 4.17120 | ||||||||
\(953\) | 32.0950 | 1.03966 | 0.519829 | − | 0.854271i | \(-0.325996\pi\) | ||||
0.519829 | + | 0.854271i | \(0.325996\pi\) | |||||||
\(954\) | 20.7549 | 0.671964 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −121.497 | −3.92950 | ||||||||
\(957\) | 14.2553 | 0.460807 | ||||||||
\(958\) | −13.6272 | −0.440276 | ||||||||
\(959\) | −50.0950 | −1.61765 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5087 | −0.532538 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.77020 | −0.218167 | ||||||||
\(964\) | 65.1798 | 2.09930 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.14217 | −0.197621 | ||||||||
\(967\) | −24.4057 | −0.784835 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(968\) | −17.2871 | −0.555630 | ||||||||
\(969\) | 22.0565 | 0.708558 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.9354 | −1.18531 | −0.592657 | − | 0.805455i | \(-0.701921\pi\) | ||||
−0.592657 | + | 0.805455i | \(0.701921\pi\) | |||||||
\(972\) | −31.0420 | −0.995673 | ||||||||
\(973\) | −68.7367 | −2.20360 | ||||||||
\(974\) | 43.8770 | 1.40591 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.3492 | −0.715379 | ||||||||
\(977\) | −25.1715 | −0.805308 | −0.402654 | − | 0.915352i | \(-0.631912\pi\) | ||||
−0.402654 | + | 0.915352i | \(0.631912\pi\) | |||||||
\(978\) | 5.24354 | 0.167670 | ||||||||
\(979\) | −9.68097 | −0.309405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.56788 | −0.241624 | ||||||||
\(982\) | 61.9072 | 1.97554 | ||||||||
\(983\) | 13.1896 | 0.420684 | 0.210342 | − | 0.977628i | \(-0.432542\pi\) | ||||
0.210342 | + | 0.977628i | \(0.432542\pi\) | |||||||
\(984\) | −14.2553 | −0.454441 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −55.4532 | −1.76599 | ||||||||
\(987\) | 16.6983 | 0.531513 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.423851 | 0.0134777 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.0667 | 0.732737 | 0.366369 | − | 0.930470i | \(-0.380601\pi\) | ||||
0.366369 | + | 0.930470i | \(0.380601\pi\) | |||||||
\(992\) | −13.2698 | −0.421317 | ||||||||
\(993\) | 45.5180 | 1.44447 | ||||||||
\(994\) | −18.3118 | −0.580815 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −50.4249 | −1.59777 | ||||||||
\(997\) | 0.630841 | 0.0199789 | 0.00998947 | − | 0.999950i | \(-0.496820\pi\) | ||||
0.00998947 | + | 0.999950i | \(0.496820\pi\) | |||||||
\(998\) | −81.3648 | −2.57556 | ||||||||
\(999\) | 52.3227 | 1.65542 |
(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 | 4225.2.a.be.1.3 | 3 | ||
5.4 | even | 2 | 845.2.a.i.1.1 | 3 | |||
13.5 | odd | 4 | 325.2.c.g.51.1 | 6 | |||
13.8 | odd | 4 | 325.2.c.g.51.6 | 6 | |||
13.12 | even | 2 | 4225.2.a.bc.1.1 | 3 | |||
15.14 | odd | 2 | 7605.2.a.cc.1.3 | 3 | |||
65.4 | even | 6 | 845.2.e.i.146.1 | 6 | |||
65.8 | even | 4 | 325.2.d.f.324.5 | 6 | |||
65.9 | even | 6 | 845.2.e.k.146.3 | 6 | |||
65.18 | even | 4 | 325.2.d.e.324.1 | 6 | |||
65.19 | odd | 12 | 845.2.m.h.361.6 | 12 | |||
65.24 | odd | 12 | 845.2.m.h.316.6 | 12 | |||
65.29 | even | 6 | 845.2.e.k.191.3 | 6 | |||
65.34 | odd | 4 | 65.2.c.a.51.1 | ✓ | 6 | ||
65.44 | odd | 4 | 65.2.c.a.51.6 | yes | 6 | ||
65.47 | even | 4 | 325.2.d.e.324.2 | 6 | |||
65.49 | even | 6 | 845.2.e.i.191.1 | 6 | |||
65.54 | odd | 12 | 845.2.m.h.316.1 | 12 | |||
65.57 | even | 4 | 325.2.d.f.324.6 | 6 | |||
65.59 | odd | 12 | 845.2.m.h.361.1 | 12 | |||
65.64 | even | 2 | 845.2.a.k.1.3 | 3 | |||
195.44 | even | 4 | 585.2.b.g.181.1 | 6 | |||
195.164 | even | 4 | 585.2.b.g.181.6 | 6 | |||
195.194 | odd | 2 | 7605.2.a.bs.1.1 | 3 | |||
260.99 | even | 4 | 1040.2.k.d.961.2 | 6 | |||
260.239 | even | 4 | 1040.2.k.d.961.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.c.a.51.1 | ✓ | 6 | 65.34 | odd | 4 | ||
65.2.c.a.51.6 | yes | 6 | 65.44 | odd | 4 | ||
325.2.c.g.51.1 | 6 | 13.5 | odd | 4 | |||
325.2.c.g.51.6 | 6 | 13.8 | odd | 4 | |||
325.2.d.e.324.1 | 6 | 65.18 | even | 4 | |||
325.2.d.e.324.2 | 6 | 65.47 | even | 4 | |||
325.2.d.f.324.5 | 6 | 65.8 | even | 4 | |||
325.2.d.f.324.6 | 6 | 65.57 | even | 4 | |||
585.2.b.g.181.1 | 6 | 195.44 | even | 4 | |||
585.2.b.g.181.6 | 6 | 195.164 | even | 4 | |||
845.2.a.i.1.1 | 3 | 5.4 | even | 2 | |||
845.2.a.k.1.3 | 3 | 65.64 | even | 2 | |||
845.2.e.i.146.1 | 6 | 65.4 | even | 6 | |||
845.2.e.i.191.1 | 6 | 65.49 | even | 6 | |||
845.2.e.k.146.3 | 6 | 65.9 | even | 6 | |||
845.2.e.k.191.3 | 6 | 65.29 | even | 6 | |||
845.2.m.h.316.1 | 12 | 65.54 | odd | 12 | |||
845.2.m.h.316.6 | 12 | 65.24 | odd | 12 | |||
845.2.m.h.361.1 | 12 | 65.59 | odd | 12 | |||
845.2.m.h.361.6 | 12 | 65.19 | odd | 12 | |||
1040.2.k.d.961.1 | 6 | 260.239 | even | 4 | |||
1040.2.k.d.961.2 | 6 | 260.99 | even | 4 | |||
4225.2.a.bc.1.1 | 3 | 13.12 | even | 2 | |||
4225.2.a.be.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7605.2.a.bs.1.1 | 3 | 195.194 | odd | 2 | |||
7605.2.a.cc.1.3 | 3 | 15.14 | odd | 2 |