Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
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 | \(\chi\) | \(=\) | 845.1 |
$q$-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 | \(-0.356008\pi\) | ||||
0.437094 | + | 0.899416i | \(0.356008\pi\) | |||||||
\(4\) | 4.32088 | 2.16044 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 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 | ||||||||
\(10\) | −2.51414 | −0.795040 | ||||||||
\(11\) | −2.83502 | −0.854791 | −0.427396 | − | 0.904065i | \(-0.640569\pi\) | ||||
−0.427396 | + | 0.904065i | \(0.640569\pi\) | |||||||
\(12\) | 6.54241 | 1.88863 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 8.34916 | 2.23141 | ||||||||
\(15\) | −1.51414 | −0.390948 | ||||||||
\(16\) | 6.02827 | 1.50707 | ||||||||
\(17\) | −6.64177 | −1.61087 | −0.805433 | − | 0.592687i | \(-0.798067\pi\) | ||||
−0.805433 | + | 0.592687i | \(0.798067\pi\) | |||||||
\(18\) | −1.77847 | −0.419190 | ||||||||
\(19\) | 2.19325 | 0.503167 | 0.251583 | − | 0.967836i | \(-0.419049\pi\) | ||||
0.251583 | + | 0.967836i | \(0.419049\pi\) | |||||||
\(20\) | −4.32088 | −0.966179 | ||||||||
\(21\) | 5.02827 | 1.09726 | ||||||||
\(22\) | −7.12763 | −1.51962 | ||||||||
\(23\) | −0.485863 | −0.101309 | −0.0506547 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506547 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(24\) | 8.83502 | 1.80344 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 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 | \(0.599772\pi\) | |||||||
\(30\) | −3.80675 | −0.695014 | ||||||||
\(31\) | 3.80675 | 0.683712 | 0.341856 | − | 0.939752i | \(-0.388944\pi\) | ||||
0.341856 | + | 0.939752i | \(0.388944\pi\) | |||||||
\(32\) | 3.48586 | 0.616219 | ||||||||
\(33\) | −4.29261 | −0.747248 | ||||||||
\(34\) | −16.6983 | −2.86374 | ||||||||
\(35\) | −3.32088 | −0.561332 | ||||||||
\(36\) | −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 | ||||||||
\(40\) | −5.83502 | −0.922598 | ||||||||
\(41\) | −1.61350 | −0.251986 | −0.125993 | − | 0.992031i | \(-0.540212\pi\) | ||||
−0.125993 | + | 0.992031i | \(0.540212\pi\) | |||||||
\(42\) | 12.6418 | 1.95067 | ||||||||
\(43\) | −0.872368 | −0.133035 | −0.0665174 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665174 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(44\) | −12.2498 | −1.84673 | ||||||||
\(45\) | 0.707389 | 0.105451 | ||||||||
\(46\) | −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 | ||||||||
\(50\) | 2.51414 | 0.355553 | ||||||||
\(51\) | −10.0565 | −1.40820 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6700 | 1.60300 | 0.801502 | − | 0.597992i | \(-0.204035\pi\) | ||||
0.801502 | + | 0.597992i | \(0.204035\pi\) | |||||||
\(54\) | −14.1131 | −1.92055 | ||||||||
\(55\) | 2.83502 | 0.382274 | ||||||||
\(56\) | 19.3774 | 2.58942 | ||||||||
\(57\) | 3.32088 | 0.439862 | ||||||||
\(58\) | −8.34916 | −1.09630 | ||||||||
\(59\) | −8.83502 | −1.15022 | −0.575111 | − | 0.818075i | \(-0.695041\pi\) | ||||
−0.575111 | + | 0.818075i | \(0.695041\pi\) | |||||||
\(60\) | −6.54241 | −0.844622 | ||||||||
\(61\) | −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 | ||||||||
\(70\) | −8.34916 | −0.997915 | ||||||||
\(71\) | 2.19325 | 0.260291 | 0.130146 | − | 0.991495i | \(-0.458456\pi\) | ||||
0.130146 | + | 0.991495i | \(0.458456\pi\) | |||||||
\(72\) | −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 | ||||||||
\(75\) | 1.51414 | 0.174837 | ||||||||
\(76\) | 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 | \(0.489519\pi\) | |||||||
\(80\) | −6.02827 | −0.673982 | ||||||||
\(81\) | −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 | ||||||||
\(85\) | 6.64177 | 0.720401 | ||||||||
\(86\) | −2.19325 | −0.236504 | ||||||||
\(87\) | −5.02827 | −0.539088 | ||||||||
\(88\) | −16.5424 | −1.76343 | ||||||||
\(89\) | 3.41478 | 0.361966 | 0.180983 | − | 0.983486i | \(-0.442072\pi\) | ||||
0.180983 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(90\) | 1.77847 | 0.187468 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.09936 | −0.218873 | ||||||||
\(93\) | 5.76394 | 0.597692 | ||||||||
\(94\) | −8.34916 | −0.861150 | ||||||||
\(95\) | −2.19325 | −0.225023 | ||||||||
\(96\) | 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 | ||||||||
\(100\) | 4.32088 | 0.432088 | ||||||||
\(101\) | 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 | \(-0.615158\pi\) | ||||
−0.353939 | + | 0.935268i | \(0.615158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.02827 | −0.490709 | ||||||||
\(106\) | 29.3401 | 2.84976 | ||||||||
\(107\) | −9.57068 | −0.925233 | −0.462617 | − | 0.886558i | \(-0.653089\pi\) | ||||
−0.462617 | + | 0.886558i | \(0.653089\pi\) | |||||||
\(108\) | −24.2553 | −2.33396 | ||||||||
\(109\) | −10.6983 | −1.02471 | −0.512356 | − | 0.858773i | \(-0.671227\pi\) | ||||
−0.512356 | + | 0.858773i | \(0.671227\pi\) | |||||||
\(110\) | 7.12763 | 0.679593 | ||||||||
\(111\) | 14.1131 | 1.33956 | ||||||||
\(112\) | 20.0192 | 1.89164 | ||||||||
\(113\) | −3.22699 | −0.303570 | −0.151785 | − | 0.988414i | \(-0.548502\pi\) | ||||
−0.151785 | + | 0.988414i | \(0.548502\pi\) | |||||||
\(114\) | 8.34916 | 0.781970 | ||||||||
\(115\) | 0.485863 | 0.0453070 | ||||||||
\(116\) | −14.3492 | −1.33229 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −22.2125 | −2.04482 | ||||||||
\(119\) | −22.0565 | −2.02192 | ||||||||
\(120\) | −8.83502 | −0.806523 | ||||||||
\(121\) | −2.96265 | −0.269332 | ||||||||
\(122\) | −9.32088 | −0.843873 | ||||||||
\(123\) | −2.44305 | −0.220283 | ||||||||
\(124\) | 16.4485 | 1.47712 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.90611 | −0.526158 | ||||||||
\(127\) | 5.90064 | 0.523597 | 0.261799 | − | 0.965123i | \(-0.415684\pi\) | ||||
0.261799 | + | 0.965123i | \(0.415684\pi\) | |||||||
\(128\) | −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 | ||||||||
\(135\) | 5.61350 | 0.483133 | ||||||||
\(136\) | −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 | \(0.840992\pi\) | |||||||
\(140\) | −14.3492 | −1.21273 | ||||||||
\(141\) | −5.02827 | −0.423457 | ||||||||
\(142\) | 5.51414 | 0.462736 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.26434 | −0.355361 | ||||||||
\(145\) | 3.32088 | 0.275784 | ||||||||
\(146\) | 32.0192 | 2.64993 | ||||||||
\(147\) | 6.09936 | 0.503067 | ||||||||
\(148\) | 40.2745 | 3.31054 | ||||||||
\(149\) | 0.641769 | 0.0525758 | 0.0262879 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262879 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(150\) | 3.80675 | 0.310820 | ||||||||
\(151\) | 16.6363 | 1.35384 | 0.676922 | − | 0.736055i | \(-0.263314\pi\) | ||||
0.676922 | + | 0.736055i | \(0.263314\pi\) | |||||||
\(152\) | 12.7977 | 1.03803 | ||||||||
\(153\) | 4.69832 | 0.379836 | ||||||||
\(154\) | −23.6700 | −1.90739 | ||||||||
\(155\) | −3.80675 | −0.305765 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2553 | 0.818459 | 0.409230 | − | 0.912431i | \(-0.365798\pi\) | ||||
0.409230 | + | 0.912431i | \(0.365798\pi\) | |||||||
\(158\) | 1.47133 | 0.117052 | ||||||||
\(159\) | 17.6700 | 1.40133 | ||||||||
\(160\) | −3.48586 | −0.275582 | ||||||||
\(161\) | −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 | ||||||||
\(165\) | 4.29261 | 0.334179 | ||||||||
\(166\) | 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 | ||||||||
\(170\) | 16.6983 | 1.28070 | ||||||||
\(171\) | −1.55148 | −0.118645 | ||||||||
\(172\) | −3.76940 | −0.287414 | ||||||||
\(173\) | 6.31181 | 0.479878 | 0.239939 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239939 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(174\) | −12.6418 | −0.958370 | ||||||||
\(175\) | 3.32088 | 0.251035 | ||||||||
\(176\) | −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 | \(0.610263\pi\) | |||||||
\(180\) | 3.05655 | 0.227822 | ||||||||
\(181\) | 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 | ||||||||
\(185\) | −9.32088 | −0.685285 | ||||||||
\(186\) | 14.4913 | 1.06256 | ||||||||
\(187\) | 18.8296 | 1.37695 | ||||||||
\(188\) | −14.3492 | −1.04652 | ||||||||
\(189\) | −18.6418 | −1.35599 | ||||||||
\(190\) | −5.51414 | −0.400038 | ||||||||
\(191\) | 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 | \(0.696228\pi\) | |||||||
\(200\) | 5.83502 | 0.412598 | ||||||||
\(201\) | 6.49960 | 0.458446 | ||||||||
\(202\) | 17.5279 | 1.23326 | ||||||||
\(203\) | −11.0283 | −0.774033 | ||||||||
\(204\) | −43.4532 | −3.04233 | ||||||||
\(205\) | 1.61350 | 0.112691 | ||||||||
\(206\) | −18.0620 | −1.25844 | ||||||||
\(207\) | 0.343694 | 0.0238884 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.21792 | −0.430102 | ||||||||
\(210\) | −12.6418 | −0.872365 | ||||||||
\(211\) | 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 | ||||||||
\(215\) | 0.872368 | 0.0594950 | ||||||||
\(216\) | −32.7549 | −2.22869 | ||||||||
\(217\) | 12.6418 | 0.858179 | ||||||||
\(218\) | −26.8970 | −1.82170 | ||||||||
\(219\) | 19.2835 | 1.30306 | ||||||||
\(220\) | 12.2498 | 0.825881 | ||||||||
\(221\) | 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 | ||||||||
\(225\) | −0.707389 | −0.0471593 | ||||||||
\(226\) | −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 | \(-0.611301\pi\) | ||||
−0.342580 | + | 0.939489i | \(0.611301\pi\) | |||||||
\(230\) | 1.22153 | 0.0805451 | ||||||||
\(231\) | −14.2553 | −0.937928 | ||||||||
\(232\) | −19.3774 | −1.27219 | ||||||||
\(233\) | 11.3582 | 0.744102 | 0.372051 | − | 0.928212i | \(-0.378655\pi\) | ||||
0.372051 | + | 0.928212i | \(0.378655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.32088 | 0.216631 | ||||||||
\(236\) | −38.1751 | −2.48499 | ||||||||
\(237\) | 0.886105 | 0.0575587 | ||||||||
\(238\) | −55.4532 | −3.59450 | ||||||||
\(239\) | 28.1186 | 1.81884 | 0.909419 | − | 0.415881i | \(-0.136527\pi\) | ||||
0.909419 | + | 0.415881i | \(0.136527\pi\) | |||||||
\(240\) | −9.12763 | −0.589186 | ||||||||
\(241\) | −15.0848 | −0.971699 | −0.485849 | − | 0.874043i | \(-0.661490\pi\) | ||||
−0.485849 | + | 0.874043i | \(0.661490\pi\) | |||||||
\(242\) | −7.44852 | −0.478809 | ||||||||
\(243\) | 7.18418 | 0.460865 | ||||||||
\(244\) | −16.0192 | −1.02552 | ||||||||
\(245\) | −4.02827 | −0.257357 | ||||||||
\(246\) | −6.14217 | −0.391610 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 22.2125 | 1.41049 | ||||||||
\(249\) | 11.6700 | 0.739559 | ||||||||
\(250\) | −2.51414 | −0.159008 | ||||||||
\(251\) | 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 | ||||||||
\(255\) | 10.0565 | 0.629765 | ||||||||
\(256\) | −31.7549 | −1.98468 | ||||||||
\(257\) | −0.829557 | −0.0517464 | −0.0258732 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258732 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(258\) | −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 | \(-0.789983\pi\) | ||||
−0.790121 | + | 0.612950i | \(0.789983\pi\) | |||||||
\(264\) | −25.0475 | −1.54157 | ||||||||
\(265\) | −11.6700 | −0.716885 | ||||||||
\(266\) | 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 | \(0.451013\pi\) | |||||||
\(270\) | 14.1131 | 0.858896 | ||||||||
\(271\) | −18.8916 | −1.14758 | −0.573791 | − | 0.819002i | \(-0.694528\pi\) | ||||
−0.573791 | + | 0.819002i | \(0.694528\pi\) | |||||||
\(272\) | −40.0384 | −2.42768 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.9253 | −2.29115 | ||||||||
\(275\) | −2.83502 | −0.170958 | ||||||||
\(276\) | −3.17872 | −0.191336 | ||||||||
\(277\) | 23.7831 | 1.42899 | 0.714495 | − | 0.699640i | \(-0.246656\pi\) | ||||
0.714495 | + | 0.699640i | \(0.246656\pi\) | |||||||
\(278\) | −52.0384 | −3.12106 | ||||||||
\(279\) | −2.69285 | −0.161217 | ||||||||
\(280\) | −19.3774 | −1.15802 | ||||||||
\(281\) | 31.5953 | 1.88482 | 0.942410 | − | 0.334459i | \(-0.108554\pi\) | ||||
0.942410 | + | 0.334459i | \(0.108554\pi\) | |||||||
\(282\) | −12.6418 | −0.752806 | ||||||||
\(283\) | 6.35462 | 0.377743 | 0.188872 | − | 0.982002i | \(-0.439517\pi\) | ||||
0.188872 | + | 0.982002i | \(0.439517\pi\) | |||||||
\(284\) | 9.47679 | 0.562344 | ||||||||
\(285\) | −3.32088 | −0.196712 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.35823 | −0.316286 | ||||||||
\(288\) | −2.46586 | −0.145302 | ||||||||
\(289\) | 27.1131 | 1.59489 | ||||||||
\(290\) | 8.34916 | 0.490279 | ||||||||
\(291\) | 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 | ||||||||
\(295\) | 8.83502 | 0.514395 | ||||||||
\(296\) | 54.3876 | 3.16121 | ||||||||
\(297\) | 15.9144 | 0.923446 | ||||||||
\(298\) | 1.61350 | 0.0934673 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.54241 | 0.377726 | ||||||||
\(301\) | −2.89703 | −0.166982 | ||||||||
\(302\) | 41.8259 | 2.40681 | ||||||||
\(303\) | 10.5561 | 0.606435 | ||||||||
\(304\) | 13.2215 | 0.758307 | ||||||||
\(305\) | 3.70739 | 0.212284 | ||||||||
\(306\) | 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 | ||||||||
\(310\) | −9.57068 | −0.543578 | ||||||||
\(311\) | 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 | \(-0.602774\pi\) | ||||
−0.317294 | + | 0.948327i | \(0.602774\pi\) | |||||||
\(314\) | 25.7831 | 1.45503 | ||||||||
\(315\) | 2.34916 | 0.132360 | ||||||||
\(316\) | 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 | ||||||||
\(320\) | 3.29261 | 0.184063 | ||||||||
\(321\) | −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 | ||||||||
\(330\) | 10.7922 | 0.594092 | ||||||||
\(331\) | 30.0620 | 1.65236 | 0.826179 | − | 0.563408i | \(-0.190510\pi\) | ||||
0.826179 | + | 0.563408i | \(0.190510\pi\) | |||||||
\(332\) | 33.3027 | 1.82773 | ||||||||
\(333\) | −6.59349 | −0.361321 | ||||||||
\(334\) | 44.1888 | 2.41791 | ||||||||
\(335\) | −4.29261 | −0.234530 | ||||||||
\(336\) | 30.3118 | 1.65364 | ||||||||
\(337\) | −17.4713 | −0.951724 | −0.475862 | − | 0.879520i | \(-0.657864\pi\) | ||||
−0.475862 | + | 0.879520i | \(0.657864\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.88611 | −0.265377 | ||||||||
\(340\) | 28.6983 | 1.55638 | ||||||||
\(341\) | −10.7922 | −0.584431 | ||||||||
\(342\) | −3.90064 | −0.210923 | ||||||||
\(343\) | −9.86876 | −0.532863 | ||||||||
\(344\) | −5.09029 | −0.274450 | ||||||||
\(345\) | 0.735663 | 0.0396068 | ||||||||
\(346\) | 15.8688 | 0.853110 | ||||||||
\(347\) | 33.2407 | 1.78446 | 0.892228 | − | 0.451585i | \(-0.149141\pi\) | ||||
0.892228 | + | 0.451585i | \(0.149141\pi\) | |||||||
\(348\) | −21.7266 | −1.16467 | ||||||||
\(349\) | −20.8970 | −1.11859 | −0.559296 | − | 0.828968i | \(-0.688929\pi\) | ||||
−0.559296 | + | 0.828968i | \(0.688929\pi\) | |||||||
\(350\) | 8.34916 | 0.446281 | ||||||||
\(351\) | 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 | ||||||||
\(355\) | −2.19325 | −0.116406 | ||||||||
\(356\) | 14.7549 | 0.782006 | ||||||||
\(357\) | −33.3966 | −1.76754 | ||||||||
\(358\) | −22.8405 | −1.20716 | ||||||||
\(359\) | −2.97719 | −0.157130 | −0.0785650 | − | 0.996909i | \(-0.525034\pi\) | ||||
−0.0785650 | + | 0.996909i | \(0.525034\pi\) | |||||||
\(360\) | 4.12763 | 0.217545 | ||||||||
\(361\) | −14.1896 | −0.746823 | ||||||||
\(362\) | 30.2179 | 1.58822 | ||||||||
\(363\) | −4.48586 | −0.235447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7357 | −0.666615 | ||||||||
\(366\) | −14.1131 | −0.737703 | ||||||||
\(367\) | −30.5990 | −1.59725 | −0.798626 | − | 0.601827i | \(-0.794440\pi\) | ||||
−0.798626 | + | 0.601827i | \(0.794440\pi\) | |||||||
\(368\) | −2.92892 | −0.152680 | ||||||||
\(369\) | 1.14137 | 0.0594173 | ||||||||
\(370\) | −23.4340 | −1.21827 | ||||||||
\(371\) | 38.7549 | 2.01205 | ||||||||
\(372\) | 24.9053 | 1.29128 | ||||||||
\(373\) | 18.2553 | 0.945222 | 0.472611 | − | 0.881271i | \(-0.343312\pi\) | ||||
0.472611 | + | 0.881271i | \(0.343312\pi\) | |||||||
\(374\) | 47.3401 | 2.44790 | ||||||||
\(375\) | −1.51414 | −0.0781897 | ||||||||
\(376\) | −19.3774 | −0.999315 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −46.8680 | −2.41063 | ||||||||
\(379\) | 15.9945 | 0.821584 | 0.410792 | − | 0.911729i | \(-0.365252\pi\) | ||||
0.410792 | + | 0.911729i | \(0.365252\pi\) | |||||||
\(380\) | −9.47679 | −0.486149 | ||||||||
\(381\) | 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 | ||||||||
\(385\) | 9.41478 | 0.479822 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | −0.585221 | −0.0294457 | ||||||||
\(396\) | 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 | ||||||||
\(400\) | 6.02827 | 0.301414 | ||||||||
\(401\) | 15.2270 | 0.760400 | 0.380200 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380200 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(402\) | 16.3409 | 0.815009 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 30.1240 | 1.49873 | ||||||||
\(405\) | 6.37743 | 0.316897 | ||||||||
\(406\) | −27.7266 | −1.37605 | ||||||||
\(407\) | −26.4249 | −1.30983 | ||||||||
\(408\) | −58.6802 | −2.90510 | ||||||||
\(409\) | −23.6700 | −1.17041 | −0.585204 | − | 0.810886i | \(-0.698986\pi\) | ||||
−0.585204 | + | 0.810886i | \(0.698986\pi\) | |||||||
\(410\) | 4.05655 | 0.200339 | ||||||||
\(411\) | −22.8405 | −1.12664 | ||||||||
\(412\) | −31.0420 | −1.52933 | ||||||||
\(413\) | −29.3401 | −1.44373 | ||||||||
\(414\) | 0.864095 | 0.0424679 | ||||||||
\(415\) | −7.70739 | −0.378341 | ||||||||
\(416\) | 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 | \(0.544228\pi\) | |||||||
\(420\) | −21.7266 | −1.06015 | ||||||||
\(421\) | −26.3009 | −1.28183 | −0.640913 | − | 0.767613i | \(-0.721444\pi\) | ||||
−0.640913 | + | 0.767613i | \(0.721444\pi\) | |||||||
\(422\) | 29.6700 | 1.44432 | ||||||||
\(423\) | 2.34916 | 0.114220 | ||||||||
\(424\) | 68.0950 | 3.30698 | ||||||||
\(425\) | −6.64177 | −0.322173 | ||||||||
\(426\) | 8.34916 | 0.404518 | ||||||||
\(427\) | −12.3118 | −0.595810 | ||||||||
\(428\) | −41.3538 | −1.99891 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.19325 | 0.105768 | ||||||||
\(431\) | 5.09029 | 0.245190 | 0.122595 | − | 0.992457i | \(-0.460878\pi\) | ||||
0.122595 | + | 0.992457i | \(0.460878\pi\) | |||||||
\(432\) | −33.8397 | −1.62811 | ||||||||
\(433\) | 24.0565 | 1.15608 | 0.578042 | − | 0.816007i | \(-0.303817\pi\) | ||||
0.578042 | + | 0.816007i | \(0.303817\pi\) | |||||||
\(434\) | 31.7831 | 1.52564 | ||||||||
\(435\) | 5.02827 | 0.241087 | ||||||||
\(436\) | −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 | \(0.555088\pi\) | |||||||
\(440\) | 16.5424 | 0.788628 | ||||||||
\(441\) | −2.84956 | −0.135693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.3829 | 1.30100 | 0.650500 | − | 0.759506i | \(-0.274559\pi\) | ||||
0.650500 | + | 0.759506i | \(0.274559\pi\) | |||||||
\(444\) | 60.9811 | 2.89403 | ||||||||
\(445\) | −3.41478 | −0.161876 | ||||||||
\(446\) | −50.3310 | −2.38324 | ||||||||
\(447\) | 0.971726 | 0.0459611 | ||||||||
\(448\) | −10.9344 | −0.516601 | ||||||||
\(449\) | 1.42571 | 0.0672833 | 0.0336416 | − | 0.999434i | \(-0.489290\pi\) | ||||
0.0336416 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(450\) | −1.77847 | −0.0838381 | ||||||||
\(451\) | 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 | ||||||||
\(460\) | 2.09936 | 0.0978831 | ||||||||
\(461\) | 29.1979 | 1.35988 | 0.679941 | − | 0.733267i | \(-0.262005\pi\) | ||||
0.679941 | + | 0.733267i | \(0.262005\pi\) | |||||||
\(462\) | −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 | ||||||||
\(465\) | −5.76394 | −0.267296 | ||||||||
\(466\) | 28.5561 | 1.32284 | ||||||||
\(467\) | 21.5525 | 0.997333 | 0.498666 | − | 0.866794i | \(-0.333823\pi\) | ||||
0.498666 | + | 0.866794i | \(0.333823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2553 | 0.658247 | ||||||||
\(470\) | 8.34916 | 0.385118 | ||||||||
\(471\) | 15.5279 | 0.715487 | ||||||||
\(472\) | −51.5525 | −2.37290 | ||||||||
\(473\) | 2.47318 | 0.113717 | ||||||||
\(474\) | 2.22779 | 0.102326 | ||||||||
\(475\) | 2.19325 | 0.100633 | ||||||||
\(476\) | −95.3038 | −4.36824 | ||||||||
\(477\) | −8.25526 | −0.377983 | ||||||||
\(478\) | 70.6939 | 3.23346 | ||||||||
\(479\) | 5.42024 | 0.247657 | 0.123829 | − | 0.992304i | \(-0.460483\pi\) | ||||
0.123829 | + | 0.992304i | \(0.460483\pi\) | |||||||
\(480\) | −5.27807 | −0.240910 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −37.9253 | −1.72745 | ||||||||
\(483\) | −2.44305 | −0.111163 | ||||||||
\(484\) | −12.8013 | −0.581877 | ||||||||
\(485\) | −0.641769 | −0.0291412 | ||||||||
\(486\) | 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 | ||||||||
\(490\) | −10.1276 | −0.457520 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | −2.00546 | −0.0901389 | ||||||||
\(496\) | 22.9481 | 1.03040 | ||||||||
\(497\) | 7.28354 | 0.326711 | ||||||||
\(498\) | 29.3401 | 1.31476 | ||||||||
\(499\) | 32.3629 | 1.44876 | 0.724381 | − | 0.689400i | \(-0.242126\pi\) | ||||
0.724381 | + | 0.689400i | \(0.242126\pi\) | |||||||
\(500\) | −4.32088 | −0.193236 | ||||||||
\(501\) | 26.6127 | 1.18897 | ||||||||
\(502\) | 2.91518 | 0.130111 | ||||||||
\(503\) | −26.7411 | −1.19233 | −0.596164 | − | 0.802863i | \(-0.703309\pi\) | ||||
−0.596164 | + | 0.802863i | \(0.703309\pi\) | |||||||
\(504\) | −13.7074 | −0.610576 | ||||||||
\(505\) | −6.97173 | −0.310238 | ||||||||
\(506\) | 3.46305 | 0.153951 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.4960 | 1.13120 | ||||||||
\(509\) | 9.74474 | 0.431928 | 0.215964 | − | 0.976401i | \(-0.430711\pi\) | ||||
0.215964 | + | 0.976401i | \(0.430711\pi\) | |||||||
\(510\) | 25.2835 | 1.11957 | ||||||||
\(511\) | 42.2937 | 1.87096 | ||||||||
\(512\) | −49.3365 | −2.18038 | ||||||||
\(513\) | −12.3118 | −0.543580 | ||||||||
\(514\) | −2.08562 | −0.0919928 | ||||||||
\(515\) | 7.18418 | 0.316573 | ||||||||
\(516\) | −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 | \(-0.237084\pi\) | ||||
0.735208 | + | 0.677841i | \(0.237084\pi\) | |||||||
\(524\) | 14.7549 | 0.644569 | ||||||||
\(525\) | 5.02827 | 0.219452 | ||||||||
\(526\) | −64.4304 | −2.80930 | ||||||||
\(527\) | −25.2835 | −1.10137 | ||||||||
\(528\) | −25.8770 | −1.12615 | ||||||||
\(529\) | −22.7639 | −0.989736 | ||||||||
\(530\) | −29.3401 | −1.27445 | ||||||||
\(531\) | 6.24980 | 0.271218 | ||||||||
\(532\) | 31.4713 | 1.36446 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.9992 | 0.562530 | ||||||||
\(535\) | 9.57068 | 0.413777 | ||||||||
\(536\) | 25.0475 | 1.08189 | ||||||||
\(537\) | −13.7557 | −0.593601 | ||||||||
\(538\) | 12.6418 | 0.545025 | ||||||||
\(539\) | −11.4202 | −0.491905 | ||||||||
\(540\) | 24.2553 | 1.04378 | ||||||||
\(541\) | 26.4431 | 1.13688 | 0.568438 | − | 0.822726i | \(-0.307548\pi\) | ||||
0.568438 | + | 0.822726i | \(0.307548\pi\) | |||||||
\(542\) | −47.4960 | −2.04013 | ||||||||
\(543\) | 18.1987 | 0.780982 | ||||||||
\(544\) | −23.1523 | −0.992647 | ||||||||
\(545\) | 10.6983 | 0.458266 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.9681 | −0.939289 | −0.469644 | − | 0.882856i | \(-0.655618\pi\) | ||||
−0.469644 | + | 0.882856i | \(0.655618\pi\) | |||||||
\(548\) | −65.1798 | −2.78434 | ||||||||
\(549\) | 2.62257 | 0.111928 | ||||||||
\(550\) | −7.12763 | −0.303923 | ||||||||
\(551\) | −7.28354 | −0.310289 | ||||||||
\(552\) | −4.29261 | −0.182706 | ||||||||
\(553\) | 1.94345 | 0.0826440 | ||||||||
\(554\) | 59.7941 | 2.54041 | ||||||||
\(555\) | −14.1131 | −0.599068 | ||||||||
\(556\) | −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 | ||||||||
\(560\) | −20.0192 | −0.845966 | ||||||||
\(561\) | 28.5105 | 1.20372 | ||||||||
\(562\) | 79.4350 | 3.35076 | ||||||||
\(563\) | −23.0420 | −0.971105 | −0.485552 | − | 0.874208i | \(-0.661382\pi\) | ||||
−0.485552 | + | 0.874208i | \(0.661382\pi\) | |||||||
\(564\) | −21.7266 | −0.914854 | ||||||||
\(565\) | 3.22699 | 0.135761 | ||||||||
\(566\) | 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 | \(0.524261\pi\) | |||||||
\(570\) | −8.34916 | −0.349708 | ||||||||
\(571\) | −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 | ||||||||
\(575\) | −0.485863 | −0.0202619 | ||||||||
\(576\) | 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 | ||||||||
\(580\) | 14.3492 | 0.595816 | ||||||||
\(581\) | 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 | ||||||||
\(590\) | 22.2125 | 0.914472 | ||||||||
\(591\) | 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 | ||||||||
\(595\) | 22.0565 | 0.904230 | ||||||||
\(596\) | 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 | \(0.344090\pi\) | |||||||
\(600\) | 8.83502 | 0.360688 | ||||||||
\(601\) | −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 | ||||||||
\(605\) | 2.96265 | 0.120449 | ||||||||
\(606\) | 26.5396 | 1.07810 | ||||||||
\(607\) | −8.99639 | −0.365152 | −0.182576 | − | 0.983192i | \(-0.558444\pi\) | ||||
−0.182576 | + | 0.983192i | \(0.558444\pi\) | |||||||
\(608\) | 7.64538 | 0.310061 | ||||||||
\(609\) | −16.6983 | −0.676650 | ||||||||
\(610\) | 9.32088 | 0.377392 | ||||||||
\(611\) | 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 | ||||||||
\(615\) | 2.44305 | 0.0985134 | ||||||||
\(616\) | −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 | \(-0.463251\pi\) | ||||
0.115195 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(620\) | −16.4485 | −0.660588 | ||||||||
\(621\) | 2.72739 | 0.109446 | ||||||||
\(622\) | 61.1232 | 2.45082 | ||||||||
\(623\) | 11.3401 | 0.454331 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.2262 | −1.12815 | ||||||||
\(627\) | −9.41478 | −0.375990 | ||||||||
\(628\) | 44.3118 | 1.76823 | ||||||||
\(629\) | −61.9072 | −2.46840 | ||||||||
\(630\) | 5.90611 | 0.235305 | ||||||||
\(631\) | −5.27807 | −0.210117 | −0.105058 | − | 0.994466i | \(-0.533503\pi\) | ||||
−0.105058 | + | 0.994466i | \(0.533503\pi\) | |||||||
\(632\) | 3.41478 | 0.135833 | ||||||||
\(633\) | 17.8688 | 0.710219 | ||||||||
\(634\) | −40.6044 | −1.61261 | ||||||||
\(635\) | −5.90064 | −0.234160 | ||||||||
\(636\) | 76.3502 | 3.02748 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.6700 | 0.937106 | ||||||||
\(639\) | −1.55148 | −0.0613757 | ||||||||
\(640\) | 15.2498 | 0.602801 | ||||||||
\(641\) | −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 | ||||||||
\(645\) | 1.32088 | 0.0520098 | ||||||||
\(646\) | −36.6236 | −1.44094 | ||||||||
\(647\) | −19.6454 | −0.772339 | −0.386170 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386170 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(648\) | −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 | \(-0.437742\pi\) | ||||
0.194345 | + | 0.980933i | \(0.437742\pi\) | |||||||
\(654\) | −40.7258 | −1.59250 | ||||||||
\(655\) | −3.41478 | −0.133426 | ||||||||
\(656\) | −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 | \(0.436461\pi\) | |||||||
\(660\) | 18.5479 | 0.721975 | ||||||||
\(661\) | −32.9427 | −1.28132 | −0.640660 | − | 0.767824i | \(-0.721339\pi\) | ||||
−0.640660 | + | 0.767824i | \(0.721339\pi\) | |||||||
\(662\) | 75.5800 | 2.93750 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.9728 | 1.74528 | ||||||||
\(665\) | −7.28354 | −0.282443 | ||||||||
\(666\) | −16.5769 | −0.642344 | ||||||||
\(667\) | 1.61350 | 0.0624748 | ||||||||
\(668\) | 75.9445 | 2.93838 | ||||||||
\(669\) | −30.3118 | −1.17192 | ||||||||
\(670\) | −10.7922 | −0.416939 | ||||||||
\(671\) | 10.5105 | 0.405754 | ||||||||
\(672\) | 17.5279 | 0.676152 | ||||||||
\(673\) | −11.2270 | −0.432769 | −0.216384 | − | 0.976308i | \(-0.569426\pi\) | ||||
−0.216384 | + | 0.976308i | \(0.569426\pi\) | |||||||
\(674\) | −43.9253 | −1.69194 | ||||||||
\(675\) | −5.61350 | −0.216064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.7447 | −0.605119 | −0.302560 | − | 0.953130i | \(-0.597841\pi\) | ||||
−0.302560 | + | 0.953130i | \(0.597841\pi\) | |||||||
\(678\) | −12.2843 | −0.471777 | ||||||||
\(679\) | 2.13124 | 0.0817895 | ||||||||
\(680\) | 38.7549 | 1.48618 | ||||||||
\(681\) | −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 | ||||||||
\(685\) | 15.0848 | 0.576361 | ||||||||
\(686\) | −24.8114 | −0.947304 | ||||||||
\(687\) | −15.6991 | −0.598959 | ||||||||
\(688\) | −5.25887 | −0.200493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.84956 | 0.0704115 | ||||||||
\(691\) | 8.19325 | 0.311686 | 0.155843 | − | 0.987782i | \(-0.450191\pi\) | ||||
0.155843 | + | 0.987782i | \(0.450191\pi\) | |||||||
\(692\) | 27.2726 | 1.03675 | ||||||||
\(693\) | 6.65991 | 0.252989 | ||||||||
\(694\) | 83.5717 | 3.17234 | ||||||||
\(695\) | 20.6983 | 0.785132 | ||||||||
\(696\) | −29.3401 | −1.11213 | ||||||||
\(697\) | 10.7165 | 0.405915 | ||||||||
\(698\) | −52.5380 | −1.98859 | ||||||||
\(699\) | 17.1979 | 0.650485 | ||||||||
\(700\) | 14.3492 | 0.542347 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | 5.02827 | 0.189376 | ||||||||
\(706\) | 31.5471 | 1.18729 | ||||||||
\(707\) | 23.1523 | 0.870732 | ||||||||
\(708\) | −57.8023 | −2.17234 | ||||||||
\(709\) | 37.7831 | 1.41898 | 0.709488 | − | 0.704718i | \(-0.248926\pi\) | ||||
0.709488 | + | 0.704718i | \(0.248926\pi\) | |||||||
\(710\) | −5.51414 | −0.206942 | ||||||||
\(711\) | −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 | \(0.636144\pi\) | |||||||
\(720\) | 4.26434 | 0.158922 | ||||||||
\(721\) | −23.8578 | −0.888512 | ||||||||
\(722\) | −35.6747 | −1.32768 | ||||||||
\(723\) | −22.8405 | −0.849447 | ||||||||
\(724\) | 51.9336 | 1.93010 | ||||||||
\(725\) | −3.32088 | −0.123335 | ||||||||
\(726\) | −11.2781 | −0.418569 | ||||||||
\(727\) | −30.0812 | −1.11565 | −0.557825 | − | 0.829958i | \(-0.688364\pi\) | ||||
−0.557825 | + | 0.829958i | \(0.688364\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0101 | 1.11149 | ||||||||
\(730\) | −32.0192 | −1.18508 | ||||||||
\(731\) | 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 | ||||||||
\(735\) | −6.09936 | −0.224978 | ||||||||
\(736\) | −1.69365 | −0.0624288 | ||||||||
\(737\) | −12.1696 | −0.448275 | ||||||||
\(738\) | 2.86956 | 0.105630 | ||||||||
\(739\) | 42.6856 | 1.57022 | 0.785108 | − | 0.619359i | \(-0.212607\pi\) | ||||
0.785108 | + | 0.619359i | \(0.212607\pi\) | |||||||
\(740\) | −40.2745 | −1.48052 | ||||||||
\(741\) | 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 | ||||||||
\(745\) | −0.641769 | −0.0235126 | ||||||||
\(746\) | 45.8962 | 1.68038 | ||||||||
\(747\) | −5.45213 | −0.199483 | ||||||||
\(748\) | 81.3603 | 2.97483 | ||||||||
\(749\) | −31.7831 | −1.16133 | ||||||||
\(750\) | −3.80675 | −0.139003 | ||||||||
\(751\) | 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 | ||||||||
\(755\) | −16.6363 | −0.605457 | ||||||||
\(756\) | −80.5489 | −2.92954 | ||||||||
\(757\) | −26.9717 | −0.980304 | −0.490152 | − | 0.871637i | \(-0.663059\pi\) | ||||
−0.490152 | + | 0.871637i | \(0.663059\pi\) | |||||||
\(758\) | 40.2125 | 1.46058 | ||||||||
\(759\) | 2.08562 | 0.0757032 | ||||||||
\(760\) | −12.7977 | −0.464220 | ||||||||
\(761\) | −35.1523 | −1.27427 | −0.637135 | − | 0.770752i | \(-0.719881\pi\) | ||||
−0.637135 | + | 0.770752i | \(0.719881\pi\) | |||||||
\(762\) | 22.4623 | 0.813722 | ||||||||
\(763\) | −35.5279 | −1.28620 | ||||||||
\(764\) | 57.3966 | 2.07654 | ||||||||
\(765\) | −4.69832 | −0.169868 | ||||||||
\(766\) | −5.43398 | −0.196338 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −48.0812 | −1.73498 | ||||||||
\(769\) | 23.1523 | 0.834893 | 0.417447 | − | 0.908701i | \(-0.362925\pi\) | ||||
0.417447 | + | 0.908701i | \(0.362925\pi\) | |||||||
\(770\) | 23.6700 | 0.853009 | ||||||||
\(771\) | −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 | ||||||||
\(775\) | 3.80675 | 0.136742 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | −10.2553 | −0.366026 | ||||||||
\(786\) | 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 | ||||||||
\(790\) | −1.47133 | −0.0523474 | ||||||||
\(791\) | −10.7165 | −0.381034 | ||||||||
\(792\) | 11.7019 | 0.415810 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −73.5289 | −2.60944 | ||||||||
\(795\) | −17.6700 | −0.626692 | ||||||||
\(796\) | −70.4815 | −2.49815 | ||||||||
\(797\) | −14.4431 | −0.511599 | −0.255800 | − | 0.966730i | \(-0.582339\pi\) | ||||
−0.255800 | + | 0.966730i | \(0.582339\pi\) | |||||||
\(798\) | 27.7266 | 0.981511 | ||||||||
\(799\) | 22.0565 | 0.780305 | ||||||||
\(800\) | 3.48586 | 0.123244 | ||||||||
\(801\) | −2.41558 | −0.0853503 | ||||||||
\(802\) | 38.2827 | 1.35181 | ||||||||
\(803\) | −36.1059 | −1.27415 | ||||||||
\(804\) | 28.0840 | 0.990447 | ||||||||
\(805\) | 1.61350 | 0.0568682 | ||||||||
\(806\) | 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 | \(0.398179\pi\) | |||||||
\(810\) | 16.0337 | 0.563368 | ||||||||
\(811\) | −8.69285 | −0.305247 | −0.152624 | − | 0.988284i | \(-0.548772\pi\) | ||||
−0.152624 | + | 0.988284i | \(0.548772\pi\) | |||||||
\(812\) | −47.6519 | −1.67225 | ||||||||
\(813\) | −28.6044 | −1.00320 | ||||||||
\(814\) | −66.4358 | −2.32857 | ||||||||
\(815\) | 1.37743 | 0.0482493 | ||||||||
\(816\) | −60.6236 | −2.12225 | ||||||||
\(817\) | −1.91332 | −0.0669387 | ||||||||
\(818\) | −59.5097 | −2.08071 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.97173 | 0.243463 | ||||||||
\(821\) | −9.41478 | −0.328578 | −0.164289 | − | 0.986412i | \(-0.552533\pi\) | ||||
−0.164289 | + | 0.986412i | \(0.552533\pi\) | |||||||
\(822\) | −57.4241 | −2.00290 | ||||||||
\(823\) | −30.3365 | −1.05746 | −0.528732 | − | 0.848789i | \(-0.677332\pi\) | ||||
−0.528732 | + | 0.848789i | \(0.677332\pi\) | |||||||
\(824\) | −41.9198 | −1.46035 | ||||||||
\(825\) | −4.29261 | −0.149450 | ||||||||
\(826\) | −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 | \(0.326848\pi\) | |||||||
\(830\) | −19.3774 | −0.672600 | ||||||||
\(831\) | 36.0109 | 1.24921 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.7549 | −0.927001 | ||||||||
\(834\) | −78.7933 | −2.72839 | ||||||||
\(835\) | −17.5761 | −0.608248 | ||||||||
\(836\) | −26.8669 | −0.929211 | ||||||||
\(837\) | −21.3692 | −0.738626 | ||||||||
\(838\) | −14.2553 | −0.492440 | ||||||||
\(839\) | −46.1004 | −1.59156 | −0.795782 | − | 0.605584i | \(-0.792940\pi\) | ||||
−0.795782 | + | 0.605584i | \(0.792940\pi\) | |||||||
\(840\) | −29.3401 | −1.01233 | ||||||||
\(841\) | −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 | ||||||||
\(850\) | −16.6983 | −0.572748 | ||||||||
\(851\) | −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 | ||||||||
\(855\) | 1.55148 | 0.0530596 | ||||||||
\(856\) | −55.8452 | −1.90875 | ||||||||
\(857\) | −43.4713 | −1.48495 | −0.742476 | − | 0.669873i | \(-0.766349\pi\) | ||||
−0.742476 | + | 0.669873i | \(0.766349\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7375 | −0.946392 | −0.473196 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473196 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(860\) | 3.76940 | 0.128536 | ||||||||
\(861\) | −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 | ||||||||
\(865\) | −6.31181 | −0.214608 | ||||||||
\(866\) | 60.4815 | 2.05524 | ||||||||
\(867\) | 41.0529 | 1.39423 | ||||||||
\(868\) | 54.6236 | 1.85405 | ||||||||
\(869\) | −1.65911 | −0.0562816 | ||||||||
\(870\) | 12.6418 | 0.428596 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −62.4249 | −2.11397 | ||||||||
\(873\) | −0.453981 | −0.0153649 | ||||||||
\(874\) | −2.67912 | −0.0906224 | ||||||||
\(875\) | −3.32088 | −0.112266 | ||||||||
\(876\) | 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 | ||||||||
\(880\) | 17.0903 | 0.576113 | ||||||||
\(881\) | −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 | \(-0.709064\pi\) | ||||
−0.610580 | + | 0.791955i | \(0.709064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.3774 | 0.449677 | ||||||||
\(886\) | 68.8444 | 2.31287 | ||||||||
\(887\) | −45.2407 | −1.51903 | −0.759517 | − | 0.650487i | \(-0.774565\pi\) | ||||
−0.759517 | + | 0.650487i | \(0.774565\pi\) | |||||||
\(888\) | 82.3502 | 2.76349 | ||||||||
\(889\) | 19.5953 | 0.657207 | ||||||||
\(890\) | −8.58522 | −0.287777 | ||||||||
\(891\) | 18.0802 | 0.605708 | ||||||||
\(892\) | −86.5007 | −2.89626 | ||||||||
\(893\) | −7.28354 | −0.243734 | ||||||||
\(894\) | 2.44305 | 0.0817079 | ||||||||
\(895\) | 9.08482 | 0.303672 | ||||||||
\(896\) | −50.6428 | −1.69186 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.58442 | 0.119614 | ||||||||
\(899\) | −12.6418 | −0.421627 | ||||||||
\(900\) | −3.05655 | −0.101885 | ||||||||
\(901\) | −77.5097 | −2.58222 | ||||||||
\(902\) | 11.5004 | 0.382921 | ||||||||
\(903\) | −4.38650 | −0.145974 | ||||||||
\(904\) | −18.8296 | −0.626262 | ||||||||
\(905\) | −12.0192 | −0.399532 | ||||||||
\(906\) | 63.3302 | 2.10401 | ||||||||
\(907\) | −11.2973 | −0.375120 | −0.187560 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187560 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(908\) | −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 | ||||||||
\(915\) | 5.61350 | 0.185576 | ||||||||
\(916\) | −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 | \(0.490839\pi\) | |||||||
\(920\) | 2.83502 | 0.0934679 | ||||||||
\(921\) | −23.9544 | −0.789324 | ||||||||
\(922\) | 73.4076 | 2.41755 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −61.5953 | −2.02634 | ||||||||
\(925\) | 9.32088 | 0.306469 | ||||||||
\(926\) | −8.34916 | −0.274370 | ||||||||
\(927\) | 5.08201 | 0.166915 | ||||||||
\(928\) | −11.5761 | −0.380006 | ||||||||
\(929\) | 15.5569 | 0.510407 | 0.255203 | − | 0.966887i | \(-0.417858\pi\) | ||||
0.255203 | + | 0.966887i | \(0.417858\pi\) | |||||||
\(930\) | −14.4913 | −0.475189 | ||||||||
\(931\) | 8.83502 | 0.289556 | ||||||||
\(932\) | 49.0776 | 1.60759 | ||||||||
\(933\) | 36.8114 | 1.20515 | ||||||||
\(934\) | 54.1860 | 1.77302 | ||||||||
\(935\) | −18.8296 | −0.615792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0384 | 0.850638 | 0.425319 | − | 0.905044i | \(-0.360162\pi\) | ||||
0.425319 | + | 0.905044i | \(0.360162\pi\) | |||||||
\(938\) | 35.8397 | 1.17021 | ||||||||
\(939\) | −16.9992 | −0.554748 | ||||||||
\(940\) | 14.3492 | 0.468018 | ||||||||
\(941\) | 50.8789 | 1.65860 | 0.829302 | − | 0.558800i | \(-0.188738\pi\) | ||||
0.829302 | + | 0.558800i | \(0.188738\pi\) | |||||||
\(942\) | 39.0392 | 1.27197 | ||||||||
\(943\) | 0.783938 | 0.0255285 | ||||||||
\(944\) | −53.2599 | −1.73346 | ||||||||
\(945\) | 18.6418 | 0.606417 | ||||||||
\(946\) | 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 | ||||||||
\(950\) | 5.51414 | 0.178902 | ||||||||
\(951\) | −24.4540 | −0.792975 | ||||||||
\(952\) | −128.700 | −4.17120 | ||||||||
\(953\) | −32.0950 | −1.03966 | −0.519829 | − | 0.854271i | \(-0.674004\pi\) | ||||
−0.519829 | + | 0.854271i | \(0.674004\pi\) | |||||||
\(954\) | −20.7549 | −0.671964 | ||||||||
\(955\) | −13.2835 | −0.429845 | ||||||||
\(956\) | 121.497 | 3.92950 | ||||||||
\(957\) | 14.2553 | 0.460807 | ||||||||
\(958\) | 13.6272 | 0.440276 | ||||||||
\(959\) | −50.0950 | −1.61765 | ||||||||
\(960\) | 4.98546 | 0.160905 | ||||||||
\(961\) | −16.5087 | −0.532538 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.77020 | 0.218167 | ||||||||
\(964\) | −65.1798 | −2.09930 | ||||||||
\(965\) | −16.3684 | −0.526916 | ||||||||
\(966\) | −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 | ||||||||
\(970\) | −1.61350 | −0.0518062 | ||||||||
\(971\) | −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 | ||||||||
\(980\) | −17.4057 | −0.556005 | ||||||||
\(981\) | 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 | ||||||||
\(985\) | −14.8970 | −0.474659 | ||||||||
\(986\) | 55.4532 | 1.76599 | ||||||||
\(987\) | −16.6983 | −0.531513 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.423851 | 0.0134777 | ||||||||
\(990\) | −5.04201 | −0.160246 | ||||||||
\(991\) | 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 | ||||||||
\(995\) | 16.3118 | 0.517119 | ||||||||
\(996\) | 50.4249 | 1.59777 | ||||||||
\(997\) | −0.630841 | −0.0199789 | −0.00998947 | − | 0.999950i | \(-0.503180\pi\) | ||||
−0.00998947 | + | 0.999950i | \(0.503180\pi\) | |||||||
\(998\) | 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 | 845.2.a.k.1.3 | 3 | ||
3.2 | odd | 2 | 7605.2.a.bs.1.1 | 3 | |||
5.4 | even | 2 | 4225.2.a.bc.1.1 | 3 | |||
13.2 | odd | 12 | 845.2.m.h.316.6 | 12 | |||
13.3 | even | 3 | 845.2.e.i.191.1 | 6 | |||
13.4 | even | 6 | 845.2.e.k.146.3 | 6 | |||
13.5 | odd | 4 | 65.2.c.a.51.1 | ✓ | 6 | ||
13.6 | odd | 12 | 845.2.m.h.361.1 | 12 | |||
13.7 | odd | 12 | 845.2.m.h.361.6 | 12 | |||
13.8 | odd | 4 | 65.2.c.a.51.6 | yes | 6 | ||
13.9 | even | 3 | 845.2.e.i.146.1 | 6 | |||
13.10 | even | 6 | 845.2.e.k.191.3 | 6 | |||
13.11 | odd | 12 | 845.2.m.h.316.1 | 12 | |||
13.12 | even | 2 | 845.2.a.i.1.1 | 3 | |||
39.5 | even | 4 | 585.2.b.g.181.6 | 6 | |||
39.8 | even | 4 | 585.2.b.g.181.1 | 6 | |||
39.38 | odd | 2 | 7605.2.a.cc.1.3 | 3 | |||
52.31 | even | 4 | 1040.2.k.d.961.2 | 6 | |||
52.47 | even | 4 | 1040.2.k.d.961.1 | 6 | |||
65.8 | even | 4 | 325.2.d.f.324.6 | 6 | |||
65.18 | even | 4 | 325.2.d.e.324.2 | 6 | |||
65.34 | odd | 4 | 325.2.c.g.51.1 | 6 | |||
65.44 | odd | 4 | 325.2.c.g.51.6 | 6 | |||
65.47 | even | 4 | 325.2.d.e.324.1 | 6 | |||
65.57 | even | 4 | 325.2.d.f.324.5 | 6 | |||
65.64 | even | 2 | 4225.2.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.c.a.51.1 | ✓ | 6 | 13.5 | odd | 4 | ||
65.2.c.a.51.6 | yes | 6 | 13.8 | odd | 4 | ||
325.2.c.g.51.1 | 6 | 65.34 | odd | 4 | |||
325.2.c.g.51.6 | 6 | 65.44 | odd | 4 | |||
325.2.d.e.324.1 | 6 | 65.47 | even | 4 | |||
325.2.d.e.324.2 | 6 | 65.18 | even | 4 | |||
325.2.d.f.324.5 | 6 | 65.57 | even | 4 | |||
325.2.d.f.324.6 | 6 | 65.8 | even | 4 | |||
585.2.b.g.181.1 | 6 | 39.8 | even | 4 | |||
585.2.b.g.181.6 | 6 | 39.5 | even | 4 | |||
845.2.a.i.1.1 | 3 | 13.12 | even | 2 | |||
845.2.a.k.1.3 | 3 | 1.1 | even | 1 | trivial | ||
845.2.e.i.146.1 | 6 | 13.9 | even | 3 | |||
845.2.e.i.191.1 | 6 | 13.3 | even | 3 | |||
845.2.e.k.146.3 | 6 | 13.4 | even | 6 | |||
845.2.e.k.191.3 | 6 | 13.10 | even | 6 | |||
845.2.m.h.316.1 | 12 | 13.11 | odd | 12 | |||
845.2.m.h.316.6 | 12 | 13.2 | odd | 12 | |||
845.2.m.h.361.1 | 12 | 13.6 | odd | 12 | |||
845.2.m.h.361.6 | 12 | 13.7 | odd | 12 | |||
1040.2.k.d.961.1 | 6 | 52.47 | even | 4 | |||
1040.2.k.d.961.2 | 6 | 52.31 | even | 4 | |||
4225.2.a.bc.1.1 | 3 | 5.4 | even | 2 | |||
4225.2.a.be.1.3 | 3 | 65.64 | even | 2 | |||
7605.2.a.bs.1.1 | 3 | 3.2 | odd | 2 | |||
7605.2.a.cc.1.3 | 3 | 39.38 | odd | 2 |