Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(51,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 51.1 | ||
Root | \(1.66044 + 1.66044i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.51 |
Dual form | 325.2.c.g.51.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.51414i | − | 1.77776i | −0.458137 | − | 0.888882i | \(-0.651483\pi\) | ||
0.458137 | − | 0.888882i | \(-0.348517\pi\) | |||||||
\(3\) | −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 | ||||||||
\(6\) | 3.80675i | 1.55410i | ||||||||
\(7\) | 3.32088i | 1.25518i | 0.778545 | + | 0.627588i | \(0.215958\pi\) | ||||
−0.778545 | + | 0.627588i | \(0.784042\pi\) | |||||||
\(8\) | 5.83502i | 2.06299i | ||||||||
\(9\) | −0.707389 | −0.235796 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.83502i | 0.854791i | 0.904065 | + | 0.427396i | \(0.140569\pi\) | ||||
−0.904065 | + | 0.427396i | \(0.859431\pi\) | |||||||
\(12\) | 6.54241 | 1.88863 | ||||||||
\(13\) | 3.51414 | − | 0.806748i | 0.974646 | − | 0.223752i | ||||
\(14\) | 8.34916 | 2.23141 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.02827 | 1.50707 | ||||||||
\(17\) | −6.64177 | −1.61087 | −0.805433 | − | 0.592687i | \(-0.798067\pi\) | ||||
−0.805433 | + | 0.592687i | \(0.798067\pi\) | |||||||
\(18\) | 1.77847i | 0.419190i | ||||||||
\(19\) | 2.19325i | 0.503167i | 0.967836 | + | 0.251583i | \(0.0809512\pi\) | ||||
−0.967836 | + | 0.251583i | \(0.919049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.02827i | − | 1.09726i | ||||||
\(22\) | 7.12763 | 1.51962 | ||||||||
\(23\) | −0.485863 | −0.101309 | −0.0506547 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506547 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(24\) | − | 8.83502i | − | 1.80344i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.02827 | − | 8.83502i | −0.397777 | − | 1.73269i | ||||
\(27\) | 5.61350 | 1.08032 | ||||||||
\(28\) | − | 14.3492i | − | 2.71174i | ||||||
\(29\) | −3.32088 | −0.616673 | −0.308336 | − | 0.951277i | \(-0.599772\pi\) | ||||
−0.308336 | + | 0.951277i | \(0.599772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.80675i | 0.683712i | 0.939752 | + | 0.341856i | \(0.111056\pi\) | ||||
−0.939752 | + | 0.341856i | \(0.888944\pi\) | |||||||
\(32\) | − | 3.48586i | − | 0.616219i | ||||||
\(33\) | − | 4.29261i | − | 0.747248i | ||||||
\(34\) | 16.6983i | 2.86374i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.05655 | 0.509425 | ||||||||
\(37\) | 9.32088i | 1.53234i | 0.642636 | + | 0.766172i | \(0.277841\pi\) | ||||
−0.642636 | + | 0.766172i | \(0.722159\pi\) | |||||||
\(38\) | 5.51414 | 0.894511 | ||||||||
\(39\) | −5.32088 | + | 1.22153i | −0.852023 | + | 0.195601i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.61350i | − | 0.251986i | −0.992031 | − | 0.125993i | \(-0.959788\pi\) | ||
0.992031 | − | 0.125993i | \(-0.0402116\pi\) | |||||||
\(42\) | −12.6418 | −1.95067 | ||||||||
\(43\) | −0.872368 | −0.133035 | −0.0665174 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665174 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(44\) | − | 12.2498i | − | 1.84673i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.22153i | 0.180104i | ||||||||
\(47\) | − | 3.32088i | − | 0.484401i | −0.970226 | − | 0.242200i | \(-0.922131\pi\) | ||
0.970226 | − | 0.242200i | \(-0.0778691\pi\) | |||||||
\(48\) | −9.12763 | −1.31746 | ||||||||
\(49\) | −4.02827 | −0.575468 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0565 | 1.40820 | ||||||||
\(52\) | −15.1842 | + | 3.48586i | −2.10567 | + | 0.483402i | ||||
\(53\) | −11.6700 | −1.60300 | −0.801502 | − | 0.597992i | \(-0.795965\pi\) | ||||
−0.801502 | + | 0.597992i | \(0.795965\pi\) | |||||||
\(54\) | − | 14.1131i | − | 1.92055i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.3774 | −2.58942 | ||||||||
\(57\) | − | 3.32088i | − | 0.439862i | ||||||
\(58\) | 8.34916i | 1.09630i | ||||||||
\(59\) | 8.83502i | 1.15022i | 0.818075 | + | 0.575111i | \(0.195041\pi\) | ||||
−0.818075 | + | 0.575111i | \(0.804959\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | − | 2.34916i | − | 0.295966i | ||||||
\(64\) | 3.29261 | 0.411576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.7922 | −1.32843 | ||||||||
\(67\) | − | 4.29261i | − | 0.524426i | −0.965010 | − | 0.262213i | \(-0.915548\pi\) | ||
0.965010 | − | 0.262213i | \(-0.0844523\pi\) | |||||||
\(68\) | 28.6983 | 3.48018 | ||||||||
\(69\) | 0.735663 | 0.0885634 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19325i | 0.260291i | 0.991495 | + | 0.130146i | \(0.0415445\pi\) | ||||
−0.991495 | + | 0.130146i | \(0.958456\pi\) | |||||||
\(72\) | − | 4.12763i | − | 0.486446i | ||||||
\(73\) | 12.7357i | 1.49060i | 0.666731 | + | 0.745298i | \(0.267693\pi\) | ||||
−0.666731 | + | 0.745298i | \(0.732307\pi\) | |||||||
\(74\) | 23.4340 | 2.72414 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 9.47679i | − | 1.08706i | ||||||
\(77\) | −9.41478 | −1.07291 | ||||||||
\(78\) | 3.07108 | + | 13.3774i | 0.347732 | + | 1.51470i | ||||
\(79\) | 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 | ||||||||
\(83\) | − | 7.70739i | − | 0.845996i | −0.906131 | − | 0.422998i | \(-0.860978\pi\) | ||
0.906131 | − | 0.422998i | \(-0.139022\pi\) | |||||||
\(84\) | 21.7266i | 2.37057i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.19325i | 0.236504i | ||||||||
\(87\) | 5.02827 | 0.539088 | ||||||||
\(88\) | −16.5424 | −1.76343 | ||||||||
\(89\) | − | 3.41478i | − | 0.361966i | −0.983486 | − | 0.180983i | \(-0.942072\pi\) | ||
0.983486 | − | 0.180983i | \(-0.0579279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.67912 | + | 11.6700i | 0.280848 | + | 1.22335i | ||||
\(92\) | 2.09936 | 0.218873 | ||||||||
\(93\) | − | 5.76394i | − | 0.597692i | ||||||
\(94\) | −8.34916 | −0.861150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.27807i | 0.538691i | ||||||||
\(97\) | − | 0.641769i | − | 0.0651618i | −0.999469 | − | 0.0325809i | \(-0.989627\pi\) | ||
0.999469 | − | 0.0325809i | \(-0.0103727\pi\) | |||||||
\(98\) | 10.1276i | 1.02305i | ||||||||
\(99\) | − | 2.00546i | − | 0.201557i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.97173 | −0.693713 | −0.346856 | − | 0.937918i | \(-0.612751\pi\) | ||||
−0.346856 | + | 0.937918i | \(0.612751\pi\) | |||||||
\(102\) | − | 25.2835i | − | 2.50344i | ||||||
\(103\) | −7.18418 | −0.707878 | −0.353939 | − | 0.935268i | \(-0.615158\pi\) | ||||
−0.353939 | + | 0.935268i | \(0.615158\pi\) | |||||||
\(104\) | 4.70739 | + | 20.5051i | 0.461598 | + | 2.01069i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.3401i | 2.84976i | ||||||||
\(107\) | 9.57068 | 0.925233 | 0.462617 | − | 0.886558i | \(-0.346911\pi\) | ||||
0.462617 | + | 0.886558i | \(0.346911\pi\) | |||||||
\(108\) | −24.2553 | −2.33396 | ||||||||
\(109\) | − | 10.6983i | − | 1.02471i | −0.858773 | − | 0.512356i | \(-0.828773\pi\) | ||
0.858773 | − | 0.512356i | \(-0.171227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 14.1131i | − | 1.33956i | ||||||
\(112\) | 20.0192i | 1.89164i | ||||||||
\(113\) | 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 | ||||||||
\(117\) | −2.48586 | + | 0.570685i | −0.229818 | + | 0.0527598i | ||||
\(118\) | 22.2125 | 2.04482 | ||||||||
\(119\) | − | 22.0565i | − | 2.02192i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.96265 | 0.269332 | ||||||||
\(122\) | 9.32088i | 0.843873i | ||||||||
\(123\) | 2.44305i | 0.220283i | ||||||||
\(124\) | − | 16.4485i | − | 1.47712i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.90611 | −0.526158 | ||||||||
\(127\) | 5.90064 | 0.523597 | 0.261799 | − | 0.965123i | \(-0.415684\pi\) | ||||
0.261799 | + | 0.965123i | \(0.415684\pi\) | |||||||
\(128\) | − | 15.2498i | − | 1.34790i | ||||||
\(129\) | 1.32088 | 0.116297 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.41478 | 0.298351 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(132\) | 18.5479i | 1.61439i | ||||||||
\(133\) | −7.28354 | −0.631563 | ||||||||
\(134\) | −10.7922 | −0.932305 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 38.7549i | − | 3.32320i | ||||||
\(137\) | − | 15.0848i | − | 1.28878i | −0.764696 | − | 0.644392i | \(-0.777111\pi\) | ||
0.764696 | − | 0.644392i | \(-0.222889\pi\) | |||||||
\(138\) | − | 1.84956i | − | 0.157445i | ||||||
\(139\) | −20.6983 | −1.75561 | −0.877804 | − | 0.479020i | \(-0.840992\pi\) | ||||
−0.877804 | + | 0.479020i | \(0.840992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.02827i | 0.423457i | ||||||||
\(142\) | 5.51414 | 0.462736 | ||||||||
\(143\) | 2.28715 | + | 9.96265i | 0.191261 | + | 0.833119i | ||||
\(144\) | −4.26434 | −0.355361 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 32.0192 | 2.64993 | ||||||||
\(147\) | 6.09936 | 0.503067 | ||||||||
\(148\) | − | 40.2745i | − | 3.31054i | ||||||
\(149\) | 0.641769i | 0.0525758i | 0.999654 | + | 0.0262879i | \(0.00836866\pi\) | ||||
−0.999654 | + | 0.0262879i | \(0.991631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.6363i | − | 1.35384i | −0.736055 | − | 0.676922i | \(-0.763314\pi\) | ||
0.736055 | − | 0.676922i | \(-0.236686\pi\) | |||||||
\(152\) | −12.7977 | −1.03803 | ||||||||
\(153\) | 4.69832 | 0.379836 | ||||||||
\(154\) | 23.6700i | 1.90739i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.9909 | − | 5.27807i | 1.84075 | − | 0.422584i | ||||
\(157\) | −10.2553 | −0.818459 | −0.409230 | − | 0.912431i | \(-0.634202\pi\) | ||||
−0.409230 | + | 0.912431i | \(0.634202\pi\) | |||||||
\(158\) | − | 1.47133i | − | 0.117052i | ||||||
\(159\) | 17.6700 | 1.40133 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.61350i | − | 0.127161i | ||||||
\(162\) | 16.0337i | 1.25973i | ||||||||
\(163\) | − | 1.37743i | − | 0.107889i | −0.998544 | − | 0.0539444i | \(-0.982821\pi\) | ||
0.998544 | − | 0.0539444i | \(-0.0171794\pi\) | |||||||
\(164\) | 6.97173i | 0.544400i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.3774 | −1.50398 | ||||||||
\(167\) | 17.5761i | 1.36008i | 0.733174 | + | 0.680042i | \(0.238038\pi\) | ||||
−0.733174 | + | 0.680042i | \(0.761962\pi\) | |||||||
\(168\) | 29.3401 | 2.26364 | ||||||||
\(169\) | 11.6983 | − | 5.67004i | 0.899871 | − | 0.436157i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.55148i | − | 0.118645i | ||||||
\(172\) | 3.76940 | 0.287414 | ||||||||
\(173\) | 6.31181 | 0.479878 | 0.239939 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239939 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(174\) | − | 12.6418i | − | 0.958370i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.0903i | 1.28823i | ||||||||
\(177\) | − | 13.3774i | − | 1.00551i | ||||||
\(178\) | −8.58522 | −0.643490 | ||||||||
\(179\) | 9.08482 | 0.679031 | 0.339516 | − | 0.940600i | \(-0.389737\pi\) | ||||
0.339516 | + | 0.940600i | \(0.389737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0192 | −0.893380 | −0.446690 | − | 0.894689i | \(-0.647397\pi\) | ||||
−0.446690 | + | 0.894689i | \(0.647397\pi\) | |||||||
\(182\) | 29.3401 | − | 6.73566i | 2.17483 | − | 0.499281i | ||||
\(183\) | 5.61350 | 0.414962 | ||||||||
\(184\) | − | 2.83502i | − | 0.209001i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.4913 | −1.06256 | ||||||||
\(187\) | − | 18.8296i | − | 1.37695i | ||||||
\(188\) | 14.3492i | 1.04652i | ||||||||
\(189\) | 18.6418i | 1.35599i | ||||||||
\(190\) | 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 | ||||||||
\(193\) | 16.3684i | 1.17822i | 0.808053 | + | 0.589110i | \(0.200522\pi\) | ||||
−0.808053 | + | 0.589110i | \(0.799478\pi\) | |||||||
\(194\) | −1.61350 | −0.115842 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.4057 | 1.24326 | ||||||||
\(197\) | − | 14.8970i | − | 1.06137i | −0.847569 | − | 0.530685i | \(-0.821935\pi\) | ||
0.847569 | − | 0.530685i | \(-0.178065\pi\) | |||||||
\(198\) | −5.04201 | −0.358320 | ||||||||
\(199\) | 16.3118 | 1.15631 | 0.578157 | − | 0.815926i | \(-0.303772\pi\) | ||||
0.578157 | + | 0.815926i | \(0.303772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.49960i | 0.458446i | ||||||||
\(202\) | 17.5279i | 1.23326i | ||||||||
\(203\) | − | 11.0283i | − | 0.774033i | ||||||
\(204\) | −43.4532 | −3.04233 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.0620i | 1.25844i | ||||||||
\(207\) | 0.343694 | 0.0238884 | ||||||||
\(208\) | 21.1842 | − | 4.86330i | 1.46886 | − | 0.337209i | ||||
\(209\) | −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 | ||||||||
\(213\) | − | 3.32088i | − | 0.227543i | ||||||
\(214\) | − | 24.0620i | − | 1.64485i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32.7549i | 2.22869i | ||||||||
\(217\) | −12.6418 | −0.858179 | ||||||||
\(218\) | −26.8970 | −1.82170 | ||||||||
\(219\) | − | 19.2835i | − | 1.30306i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.3401 | + | 5.35823i | −1.57002 | + | 0.360434i | ||||
\(222\) | −35.4823 | −2.38141 | ||||||||
\(223\) | 20.0192i | 1.34058i | 0.742097 | + | 0.670292i | \(0.233831\pi\) | ||||
−0.742097 | + | 0.670292i | \(0.766169\pi\) | |||||||
\(224\) | 11.5761 | 0.773464 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 8.11310i | − | 0.539675i | ||||||
\(227\) | 22.4623i | 1.49087i | 0.666577 | + | 0.745436i | \(0.267759\pi\) | ||||
−0.666577 | + | 0.745436i | \(0.732241\pi\) | |||||||
\(228\) | 14.3492i | 0.950296i | ||||||||
\(229\) | 10.3684i | 0.685160i | 0.939489 | + | 0.342580i | \(0.111301\pi\) | ||||
−0.939489 | + | 0.342580i | \(0.888699\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.2553 | 0.937928 | ||||||||
\(232\) | − | 19.3774i | − | 1.27219i | ||||||
\(233\) | 11.3582 | 0.744102 | 0.372051 | − | 0.928212i | \(-0.378655\pi\) | ||||
0.372051 | + | 0.928212i | \(0.378655\pi\) | |||||||
\(234\) | 1.43478 | + | 6.24980i | 0.0937945 | + | 0.408562i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 38.1751i | − | 2.48499i | ||||||
\(237\) | −0.886105 | −0.0575587 | ||||||||
\(238\) | −55.4532 | −3.59450 | ||||||||
\(239\) | 28.1186i | 1.81884i | 0.415881 | + | 0.909419i | \(0.363473\pi\) | ||||
−0.415881 | + | 0.909419i | \(0.636527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0848i | 0.971699i | 0.874043 | + | 0.485849i | \(0.161490\pi\) | ||||
−0.874043 | + | 0.485849i | \(0.838510\pi\) | |||||||
\(242\) | − | 7.44852i | − | 0.478809i | ||||||
\(243\) | −7.18418 | −0.460865 | ||||||||
\(244\) | 16.0192 | 1.02552 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.14217 | 0.391610 | ||||||||
\(247\) | 1.76940 | + | 7.70739i | 0.112584 | + | 0.490409i | ||||
\(248\) | −22.2125 | −1.41049 | ||||||||
\(249\) | 11.6700i | 0.739559i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.15951 | −0.0731879 | −0.0365940 | − | 0.999330i | \(-0.511651\pi\) | ||||
−0.0365940 | + | 0.999330i | \(0.511651\pi\) | |||||||
\(252\) | 10.1504i | 0.639418i | ||||||||
\(253\) | − | 1.37743i | − | 0.0865984i | ||||||
\(254\) | − | 14.8350i | − | 0.930832i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.7549 | −1.98468 | ||||||||
\(257\) | −0.829557 | −0.0517464 | −0.0258732 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258732 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(258\) | − | 3.32088i | − | 0.206749i | ||||||
\(259\) | −30.9536 | −1.92336 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34916 | 0.145409 | ||||||||
\(262\) | − | 8.58522i | − | 0.530397i | ||||||
\(263\) | 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 | ||||||||
\(266\) | 18.3118i | 1.12277i | ||||||||
\(267\) | 5.17044i | 0.316426i | ||||||||
\(268\) | 18.5479i | 1.13299i | ||||||||
\(269\) | 5.02827 | 0.306579 | 0.153290 | − | 0.988181i | \(-0.451013\pi\) | ||||
0.153290 | + | 0.988181i | \(0.451013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8916i | 1.14758i | 0.819002 | + | 0.573791i | \(0.194528\pi\) | ||||
−0.819002 | + | 0.573791i | \(0.805472\pi\) | |||||||
\(272\) | −40.0384 | −2.42768 | ||||||||
\(273\) | −4.05655 | − | 17.6700i | −0.245513 | − | 1.06944i | ||||
\(274\) | −37.9253 | −2.29115 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.17872 | −0.191336 | ||||||||
\(277\) | 23.7831 | 1.42899 | 0.714495 | − | 0.699640i | \(-0.246656\pi\) | ||||
0.714495 | + | 0.699640i | \(0.246656\pi\) | |||||||
\(278\) | 52.0384i | 3.12106i | ||||||||
\(279\) | − | 2.69285i | − | 0.161217i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 31.5953i | − | 1.88482i | −0.334459 | − | 0.942410i | \(-0.608554\pi\) | ||
0.334459 | − | 0.942410i | \(-0.391446\pi\) | |||||||
\(282\) | 12.6418 | 0.752806 | ||||||||
\(283\) | 6.35462 | 0.377743 | 0.188872 | − | 0.982002i | \(-0.439517\pi\) | ||||
0.188872 | + | 0.982002i | \(0.439517\pi\) | |||||||
\(284\) | − | 9.47679i | − | 0.562344i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 25.0475 | − | 5.75020i | 1.48109 | − | 0.340016i | ||||
\(287\) | 5.35823 | 0.316286 | ||||||||
\(288\) | 2.46586i | 0.145302i | ||||||||
\(289\) | 27.1131 | 1.59489 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.971726i | 0.0569636i | ||||||||
\(292\) | − | 55.0293i | − | 3.22035i | ||||||
\(293\) | − | 8.03735i | − | 0.469547i | −0.972050 | − | 0.234773i | \(-0.924565\pi\) | ||
0.972050 | − | 0.234773i | \(-0.0754348\pi\) | |||||||
\(294\) | − | 15.3346i | − | 0.894333i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −54.3876 | −3.16121 | ||||||||
\(297\) | 15.9144i | 0.923446i | ||||||||
\(298\) | 1.61350 | 0.0934673 | ||||||||
\(299\) | −1.70739 | + | 0.391969i | −0.0987409 | + | 0.0226681i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.89703i | − | 0.166982i | ||||||
\(302\) | −41.8259 | −2.40681 | ||||||||
\(303\) | 10.5561 | 0.606435 | ||||||||
\(304\) | 13.2215i | 0.758307i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 11.8122i | − | 0.675259i | ||||||
\(307\) | − | 15.8205i | − | 0.902923i | −0.892291 | − | 0.451461i | \(-0.850903\pi\) | ||
0.892291 | − | 0.451461i | \(-0.149097\pi\) | |||||||
\(308\) | 40.6802 | 2.31797 | ||||||||
\(309\) | 10.8778 | 0.618818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3118 | −1.37860 | −0.689298 | − | 0.724478i | \(-0.742081\pi\) | ||||
−0.689298 | + | 0.724478i | \(0.742081\pi\) | |||||||
\(312\) | −7.12763 | − | 31.0475i | −0.403523 | − | 1.75772i | ||||
\(313\) | 11.2270 | 0.634587 | 0.317294 | − | 0.948327i | \(-0.397226\pi\) | ||||
0.317294 | + | 0.948327i | \(0.397226\pi\) | |||||||
\(314\) | 25.7831i | 1.45503i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.52867 | −0.142249 | ||||||||
\(317\) | 16.1504i | 0.907099i | 0.891231 | + | 0.453550i | \(0.149843\pi\) | ||||
−0.891231 | + | 0.453550i | \(0.850157\pi\) | |||||||
\(318\) | − | 44.4249i | − | 2.49123i | ||||||
\(319\) | − | 9.41478i | − | 0.527126i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.4913 | −0.808827 | ||||||||
\(322\) | −4.05655 | −0.226063 | ||||||||
\(323\) | − | 14.5671i | − | 0.810534i | ||||||
\(324\) | 27.5561 | 1.53090 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.46305 | −0.191801 | ||||||||
\(327\) | 16.1987i | 0.895791i | ||||||||
\(328\) | 9.41478 | 0.519844 | ||||||||
\(329\) | 11.0283 | 0.608008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0620i | 1.65236i | 0.563408 | + | 0.826179i | \(0.309490\pi\) | ||||
−0.563408 | + | 0.826179i | \(0.690510\pi\) | |||||||
\(332\) | 33.3027i | 1.82773i | ||||||||
\(333\) | − | 6.59349i | − | 0.361321i | ||||||
\(334\) | 44.1888 | 2.41791 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 30.3118i | − | 1.65364i | ||||||
\(337\) | −17.4713 | −0.951724 | −0.475862 | − | 0.879520i | \(-0.657864\pi\) | ||||
−0.475862 | + | 0.879520i | \(0.657864\pi\) | |||||||
\(338\) | −14.2553 | − | 29.4112i | −0.775384 | − | 1.59976i | ||||
\(339\) | −4.88611 | −0.265377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7922 | −0.584431 | ||||||||
\(342\) | −3.90064 | −0.210923 | ||||||||
\(343\) | 9.86876i | 0.532863i | ||||||||
\(344\) | − | 5.09029i | − | 0.274450i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.8688i | − | 0.853110i | ||||||
\(347\) | −33.2407 | −1.78446 | −0.892228 | − | 0.451585i | \(-0.850859\pi\) | ||||
−0.892228 | + | 0.451585i | \(0.850859\pi\) | |||||||
\(348\) | −21.7266 | −1.16467 | ||||||||
\(349\) | 20.8970i | 1.11859i | 0.828968 | + | 0.559296i | \(0.188929\pi\) | ||||
−0.828968 | + | 0.559296i | \(0.811071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.7266 | − | 4.52867i | 1.05293 | − | 0.241723i | ||||
\(352\) | 9.88250 | 0.526739 | ||||||||
\(353\) | − | 12.5479i | − | 0.667856i | −0.942599 | − | 0.333928i | \(-0.891626\pi\) | ||
0.942599 | − | 0.333928i | \(-0.108374\pi\) | |||||||
\(354\) | −33.6327 | −1.78756 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.7549i | 0.782006i | ||||||||
\(357\) | 33.3966i | 1.76754i | ||||||||
\(358\) | − | 22.8405i | − | 1.20716i | ||||||
\(359\) | 2.97719i | 0.157130i | 0.996909 | + | 0.0785650i | \(0.0250338\pi\) | ||||
−0.996909 | + | 0.0785650i | \(0.974966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1896 | 0.746823 | ||||||||
\(362\) | 30.2179i | 1.58822i | ||||||||
\(363\) | −4.48586 | −0.235447 | ||||||||
\(364\) | −11.5761 | − | 50.4249i | −0.606755 | − | 2.64298i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 14.1131i | − | 0.737703i | ||||||
\(367\) | 30.5990 | 1.59725 | 0.798626 | − | 0.601827i | \(-0.205560\pi\) | ||||
0.798626 | + | 0.601827i | \(0.205560\pi\) | |||||||
\(368\) | −2.92892 | −0.152680 | ||||||||
\(369\) | 1.14137i | 0.0594173i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 38.7549i | − | 2.01205i | ||||||
\(372\) | 24.9053i | 1.29128i | ||||||||
\(373\) | −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 | ||||||||
\(377\) | −11.6700 | + | 2.67912i | −0.601038 | + | 0.137981i | ||||
\(378\) | 46.8680 | 2.41063 | ||||||||
\(379\) | 15.9945i | 0.821584i | 0.911729 | + | 0.410792i | \(0.134748\pi\) | ||||
−0.911729 | + | 0.410792i | \(0.865252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.93438 | −0.457722 | ||||||||
\(382\) | − | 33.3966i | − | 1.70872i | ||||||
\(383\) | 2.16137i | 0.110441i | 0.998474 | + | 0.0552204i | \(0.0175862\pi\) | ||||
−0.998474 | + | 0.0552204i | \(0.982414\pi\) | |||||||
\(384\) | 23.0903i | 1.17832i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.1523 | 2.09460 | ||||||||
\(387\) | 0.617104 | 0.0313691 | ||||||||
\(388\) | 2.77301i | 0.140778i | ||||||||
\(389\) | 0.453981 | 0.0230177 | 0.0115089 | − | 0.999934i | \(-0.496337\pi\) | ||||
0.0115089 | + | 0.999934i | \(0.496337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22699 | 0.163196 | ||||||||
\(392\) | − | 23.5051i | − | 1.18719i | ||||||
\(393\) | −5.17044 | −0.260814 | ||||||||
\(394\) | −37.4532 | −1.88686 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.66538i | 0.435452i | ||||||||
\(397\) | − | 29.2462i | − | 1.46782i | −0.679244 | − | 0.733912i | \(-0.737692\pi\) | ||
0.679244 | − | 0.733912i | \(-0.262308\pi\) | |||||||
\(398\) | − | 41.0101i | − | 2.05565i | ||||||
\(399\) | 11.0283 | 0.552104 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 15.2270i | − | 0.760400i | −0.924904 | − | 0.380200i | \(-0.875855\pi\) | ||
0.924904 | − | 0.380200i | \(-0.124145\pi\) | |||||||
\(402\) | 16.3409 | 0.815009 | ||||||||
\(403\) | 3.07108 | + | 13.3774i | 0.152982 | + | 0.666377i | ||||
\(404\) | 30.1240 | 1.49873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.7266 | −1.37605 | ||||||||
\(407\) | −26.4249 | −1.30983 | ||||||||
\(408\) | 58.6802i | 2.90510i | ||||||||
\(409\) | − | 23.6700i | − | 1.17041i | −0.810886 | − | 0.585204i | \(-0.801014\pi\) | ||
0.810886 | − | 0.585204i | \(-0.198986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.8405i | 1.12664i | ||||||||
\(412\) | 31.0420 | 1.52933 | ||||||||
\(413\) | −29.3401 | −1.44373 | ||||||||
\(414\) | − | 0.864095i | − | 0.0424679i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.81221 | − | 12.2498i | −0.137880 | − | 0.600596i | ||||
\(417\) | 31.3401 | 1.53473 | ||||||||
\(418\) | 15.6327i | 0.764620i | ||||||||
\(419\) | −5.67004 | −0.277000 | −0.138500 | − | 0.990362i | \(-0.544228\pi\) | ||||
−0.138500 | + | 0.990362i | \(0.544228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3009i | − | 1.28183i | −0.767613 | − | 0.640913i | \(-0.778556\pi\) | ||
0.767613 | − | 0.640913i | \(-0.221444\pi\) | |||||||
\(422\) | − | 29.6700i | − | 1.44432i | ||||||
\(423\) | 2.34916i | 0.114220i | ||||||||
\(424\) | − | 68.0950i | − | 3.30698i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.34916 | −0.404518 | ||||||||
\(427\) | − | 12.3118i | − | 0.595810i | ||||||
\(428\) | −41.3538 | −1.99891 | ||||||||
\(429\) | −3.46305 | − | 15.0848i | −0.167198 | − | 0.728302i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.09029i | 0.245190i | 0.992457 | + | 0.122595i | \(0.0391217\pi\) | ||||
−0.992457 | + | 0.122595i | \(0.960878\pi\) | |||||||
\(432\) | 33.8397 | 1.62811 | ||||||||
\(433\) | 24.0565 | 1.15608 | 0.578042 | − | 0.816007i | \(-0.303817\pi\) | ||||
0.578042 | + | 0.816007i | \(0.303817\pi\) | |||||||
\(434\) | 31.7831i | 1.52564i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 46.2262i | 2.21383i | ||||||||
\(437\) | − | 1.06562i | − | 0.0509755i | ||||||
\(438\) | −48.4815 | −2.31653 | ||||||||
\(439\) | 7.21606 | 0.344404 | 0.172202 | − | 0.985062i | \(-0.444912\pi\) | ||||
0.172202 | + | 0.985062i | \(0.444912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.84956 | 0.135693 | ||||||||
\(442\) | 13.4713 | + | 58.6802i | 0.640766 | + | 2.79113i | ||||
\(443\) | −27.3829 | −1.30100 | −0.650500 | − | 0.759506i | \(-0.725441\pi\) | ||||
−0.650500 | + | 0.759506i | \(0.725441\pi\) | |||||||
\(444\) | 60.9811i | 2.89403i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 50.3310 | 2.38324 | ||||||||
\(447\) | − | 0.971726i | − | 0.0459611i | ||||||
\(448\) | 10.9344i | 0.516601i | ||||||||
\(449\) | − | 1.42571i | − | 0.0672833i | −0.999434 | − | 0.0336416i | \(-0.989290\pi\) | ||
0.999434 | − | 0.0336416i | \(-0.0107105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.57429 | 0.215395 | ||||||||
\(452\) | −13.9435 | −0.655845 | ||||||||
\(453\) | 25.1896i | 1.18351i | ||||||||
\(454\) | 56.4732 | 2.65042 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.3774 | 0.907431 | ||||||||
\(457\) | 35.3219i | 1.65229i | 0.563457 | + | 0.826145i | \(0.309471\pi\) | ||||
−0.563457 | + | 0.826145i | \(0.690529\pi\) | |||||||
\(458\) | 26.0675 | 1.21805 | ||||||||
\(459\) | −37.2835 | −1.74025 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.1979i | 1.35988i | 0.733267 | + | 0.679941i | \(0.237995\pi\) | ||||
−0.733267 | + | 0.679941i | \(0.762005\pi\) | |||||||
\(462\) | − | 35.8397i | − | 1.66741i | ||||||
\(463\) | − | 3.32088i | − | 0.154335i | −0.997018 | − | 0.0771673i | \(-0.975412\pi\) | ||
0.997018 | − | 0.0771673i | \(-0.0245876\pi\) | |||||||
\(464\) | −20.0192 | −0.929368 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 28.5561i | − | 1.32284i | ||||||
\(467\) | 21.5525 | 0.997333 | 0.498666 | − | 0.866794i | \(-0.333823\pi\) | ||||
0.498666 | + | 0.866794i | \(0.333823\pi\) | |||||||
\(468\) | 10.7411 | − | 2.46586i | 0.496509 | − | 0.113985i | ||||
\(469\) | 14.2553 | 0.658247 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5279 | 0.715487 | ||||||||
\(472\) | −51.5525 | −2.37290 | ||||||||
\(473\) | − | 2.47318i | − | 0.113717i | ||||||
\(474\) | 2.22779i | 0.102326i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 95.3038i | 4.36824i | ||||||||
\(477\) | 8.25526 | 0.377983 | ||||||||
\(478\) | 70.6939 | 3.23346 | ||||||||
\(479\) | − | 5.42024i | − | 0.247657i | −0.992304 | − | 0.123829i | \(-0.960483\pi\) | ||
0.992304 | − | 0.123829i | \(-0.0395173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.51960 | + | 32.7549i | 0.342864 | + | 1.49349i | ||||
\(482\) | 37.9253 | 1.72745 | ||||||||
\(483\) | 2.44305i | 0.111163i | ||||||||
\(484\) | −12.8013 | −0.581877 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.0620i | 0.819309i | ||||||||
\(487\) | − | 17.4521i | − | 0.790831i | −0.918502 | − | 0.395416i | \(-0.870601\pi\) | ||
0.918502 | − | 0.395416i | \(-0.129399\pi\) | |||||||
\(488\) | − | 21.6327i | − | 0.979266i | ||||||
\(489\) | 2.08562i | 0.0943150i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.6236 | −1.11125 | −0.555624 | − | 0.831433i | \(-0.687521\pi\) | ||||
−0.555624 | + | 0.831433i | \(0.687521\pi\) | |||||||
\(492\) | − | 10.5561i | − | 0.475908i | ||||||
\(493\) | 22.0565 | 0.993377 | ||||||||
\(494\) | 19.3774 | − | 4.44852i | 0.871832 | − | 0.200148i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.9481i | 1.03040i | ||||||||
\(497\) | −7.28354 | −0.326711 | ||||||||
\(498\) | 29.3401 | 1.31476 | ||||||||
\(499\) | 32.3629i | 1.44876i | 0.689400 | + | 0.724381i | \(0.257874\pi\) | ||||
−0.689400 | + | 0.724381i | \(0.742126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 26.6127i | − | 1.18897i | ||||||
\(502\) | 2.91518i | 0.130111i | ||||||||
\(503\) | 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 | ||||||||
\(507\) | −17.7129 | + | 8.58522i | −0.786655 | + | 0.381283i | ||||
\(508\) | −25.4960 | −1.13120 | ||||||||
\(509\) | 9.74474i | 0.431928i | 0.976401 | + | 0.215964i | \(0.0692894\pi\) | ||||
−0.976401 | + | 0.215964i | \(0.930711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.2937 | −1.87096 | ||||||||
\(512\) | 49.3365i | 2.18038i | ||||||||
\(513\) | 12.3118i | 0.543580i | ||||||||
\(514\) | 2.08562i | 0.0919928i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.70739 | −0.251254 | ||||||||
\(517\) | 9.41478 | 0.414061 | ||||||||
\(518\) | 77.8215i | 3.41928i | ||||||||
\(519\) | −9.55695 | −0.419503 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4340 | −0.500932 | −0.250466 | − | 0.968125i | \(-0.580584\pi\) | ||||
−0.250466 | + | 0.968125i | \(0.580584\pi\) | |||||||
\(522\) | − | 5.90611i | − | 0.258503i | ||||||
\(523\) | −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 | ||||||||
\(526\) | − | 64.4304i | − | 2.80930i | ||||||
\(527\) | − | 25.2835i | − | 1.10137i | ||||||
\(528\) | − | 25.8770i | − | 1.12615i | ||||||
\(529\) | −22.7639 | −0.989736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.24980i | − | 0.271218i | ||||||
\(532\) | 31.4713 | 1.36446 | ||||||||
\(533\) | −1.30168 | − | 5.67004i | −0.0563822 | − | 0.245597i | ||||
\(534\) | 12.9992 | 0.562530 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.0475 | 1.08189 | ||||||||
\(537\) | −13.7557 | −0.593601 | ||||||||
\(538\) | − | 12.6418i | − | 0.545025i | ||||||
\(539\) | − | 11.4202i | − | 0.491905i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 26.4431i | − | 1.13688i | −0.822726 | − | 0.568438i | \(-0.807548\pi\) | ||
0.822726 | − | 0.568438i | \(-0.192452\pi\) | |||||||
\(542\) | 47.4960 | 2.04013 | ||||||||
\(543\) | 18.1987 | 0.780982 | ||||||||
\(544\) | 23.1523i | 0.992647i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −44.4249 | + | 10.1987i | −1.90121 | + | 0.436465i | ||||
\(547\) | 21.9681 | 0.939289 | 0.469644 | − | 0.882856i | \(-0.344382\pi\) | ||||
0.469644 | + | 0.882856i | \(0.344382\pi\) | |||||||
\(548\) | 65.1798i | 2.78434i | ||||||||
\(549\) | 2.62257 | 0.111928 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.28354i | − | 0.310289i | ||||||
\(552\) | 4.29261i | 0.182706i | ||||||||
\(553\) | 1.94345i | 0.0826440i | ||||||||
\(554\) | − | 59.7941i | − | 2.54041i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 89.4350 | 3.79289 | ||||||||
\(557\) | − | 39.3027i | − | 1.66531i | −0.553792 | − | 0.832655i | \(-0.686820\pi\) | ||
0.553792 | − | 0.832655i | \(-0.313180\pi\) | |||||||
\(558\) | −6.77020 | −0.286605 | ||||||||
\(559\) | −3.06562 | + | 0.703781i | −0.129662 | + | 0.0297668i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.5105i | 1.20372i | ||||||||
\(562\) | −79.4350 | −3.35076 | ||||||||
\(563\) | −23.0420 | −0.971105 | −0.485552 | − | 0.874208i | \(-0.661382\pi\) | ||||
−0.485552 | + | 0.874208i | \(0.661382\pi\) | |||||||
\(564\) | − | 21.7266i | − | 0.914854i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 15.9764i | − | 0.671538i | ||||||
\(567\) | − | 21.1787i | − | 0.889422i | ||||||
\(568\) | −12.7977 | −0.536979 | ||||||||
\(569\) | 3.63270 | 0.152291 | 0.0761453 | − | 0.997097i | \(-0.475739\pi\) | ||||
0.0761453 | + | 0.997097i | \(0.475739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.3785 | 1.81533 | 0.907667 | − | 0.419692i | \(-0.137862\pi\) | ||||
0.907667 | + | 0.419692i | \(0.137862\pi\) | |||||||
\(572\) | −9.88250 | − | 43.0475i | −0.413208 | − | 1.79991i | ||||
\(573\) | −20.1131 | −0.840237 | ||||||||
\(574\) | − | 13.4713i | − | 0.562282i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.32916 | −0.0970482 | ||||||||
\(577\) | − | 8.84876i | − | 0.368379i | −0.982891 | − | 0.184189i | \(-0.941034\pi\) | ||
0.982891 | − | 0.184189i | \(-0.0589660\pi\) | |||||||
\(578\) | − | 68.1660i | − | 2.83533i | ||||||
\(579\) | − | 24.7839i | − | 1.02999i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.5953 | 1.06187 | ||||||||
\(582\) | 2.44305 | 0.101268 | ||||||||
\(583\) | − | 33.0848i | − | 1.37023i | ||||||
\(584\) | −74.3129 | −3.07509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.2070 | −0.834743 | ||||||||
\(587\) | 15.3209i | 0.632361i | 0.948699 | + | 0.316180i | \(0.102400\pi\) | ||||
−0.948699 | + | 0.316180i | \(0.897600\pi\) | |||||||
\(588\) | −26.3546 | −1.08685 | ||||||||
\(589\) | −8.34916 | −0.344021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.5561i | 0.927836i | ||||||||
\(592\) | 56.1888i | 2.30935i | ||||||||
\(593\) | − | 4.52867i | − | 0.185970i | −0.995667 | − | 0.0929852i | \(-0.970359\pi\) | ||
0.995667 | − | 0.0929852i | \(-0.0296409\pi\) | |||||||
\(594\) | 40.0109 | 1.64167 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.77301i | − | 0.113587i | ||||||
\(597\) | −24.6983 | −1.01083 | ||||||||
\(598\) | 0.985463 | + | 4.29261i | 0.0402986 | + | 0.175538i | ||||
\(599\) | 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 | ||||||||
\(603\) | 3.03655i | 0.123658i | ||||||||
\(604\) | 71.8836i | 2.92490i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 26.5396i | − | 1.07810i | ||||||
\(607\) | 8.99639 | 0.365152 | 0.182576 | − | 0.983192i | \(-0.441556\pi\) | ||||
0.182576 | + | 0.983192i | \(0.441556\pi\) | |||||||
\(608\) | 7.64538 | 0.310061 | ||||||||
\(609\) | 16.6983i | 0.676650i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.67912 | − | 11.6700i | −0.108385 | − | 0.472119i | ||||
\(612\) | −20.3009 | −0.820615 | ||||||||
\(613\) | 14.1131i | 0.570023i | 0.958524 | + | 0.285011i | \(0.0919973\pi\) | ||||
−0.958524 | + | 0.285011i | \(0.908003\pi\) | |||||||
\(614\) | −39.7749 | −1.60518 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 54.9354i | − | 2.21341i | ||||||
\(617\) | 2.46120i | 0.0990841i | 0.998772 | + | 0.0495420i | \(0.0157762\pi\) | ||||
−0.998772 | + | 0.0495420i | \(0.984224\pi\) | |||||||
\(618\) | − | 27.3484i | − | 1.10011i | ||||||
\(619\) | − | 5.73205i | − | 0.230391i | −0.993343 | − | 0.115195i | \(-0.963251\pi\) | ||
0.993343 | − | 0.115195i | \(-0.0367494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.72739 | −0.109446 | ||||||||
\(622\) | 61.1232i | 2.45082i | ||||||||
\(623\) | 11.3401 | 0.454331 | ||||||||
\(624\) | −32.0757 | + | 7.36369i | −1.28406 | + | 0.294784i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 28.2262i | − | 1.12815i | ||||||
\(627\) | 9.41478 | 0.375990 | ||||||||
\(628\) | 44.3118 | 1.76823 | ||||||||
\(629\) | − | 61.9072i | − | 2.46840i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.27807i | 0.210117i | 0.994466 | + | 0.105058i | \(0.0335030\pi\) | ||||
−0.994466 | + | 0.105058i | \(0.966497\pi\) | |||||||
\(632\) | 3.41478i | 0.135833i | ||||||||
\(633\) | −17.8688 | −0.710219 | ||||||||
\(634\) | 40.6044 | 1.61261 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −76.3502 | −3.02748 | ||||||||
\(637\) | −14.1559 | + | 3.24980i | −0.560877 | + | 0.128762i | ||||
\(638\) | −23.6700 | −0.937106 | ||||||||
\(639\) | − | 1.55148i | − | 0.0613757i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.9992 | 1.69837 | 0.849183 | − | 0.528098i | \(-0.177095\pi\) | ||||
0.849183 | + | 0.528098i | \(0.177095\pi\) | |||||||
\(642\) | 36.4332i | 1.43790i | ||||||||
\(643\) | − | 43.3593i | − | 1.70992i | −0.518691 | − | 0.854962i | \(-0.673581\pi\) | ||
0.518691 | − | 0.854962i | \(-0.326419\pi\) | |||||||
\(644\) | 6.97173i | 0.274724i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.6236 | −1.44094 | ||||||||
\(647\) | −19.6454 | −0.772339 | −0.386170 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386170 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(648\) | − | 37.2125i | − | 1.46184i | ||||||
\(649\) | −25.0475 | −0.983199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.1414 | 0.750209 | ||||||||
\(652\) | 5.95173i | 0.233088i | ||||||||
\(653\) | −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 | ||||||||
\(656\) | − | 9.72659i | − | 0.379760i | ||||||
\(657\) | − | 9.00907i | − | 0.351477i | ||||||
\(658\) | − | 27.7266i | − | 1.08090i | ||||||
\(659\) | 10.1806 | 0.396579 | 0.198289 | − | 0.980144i | \(-0.436461\pi\) | ||||
0.198289 | + | 0.980144i | \(0.436461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9427i | 1.28132i | 0.767824 | + | 0.640660i | \(0.221339\pi\) | ||||
−0.767824 | + | 0.640660i | \(0.778661\pi\) | |||||||
\(662\) | 75.5800 | 2.93750 | ||||||||
\(663\) | 35.3401 | − | 8.11310i | 1.37250 | − | 0.315087i | ||||
\(664\) | 44.9728 | 1.74528 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.5769 | −0.642344 | ||||||||
\(667\) | 1.61350 | 0.0624748 | ||||||||
\(668\) | − | 75.9445i | − | 2.93838i | ||||||
\(669\) | − | 30.3118i | − | 1.17192i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.5105i | − | 0.405754i | ||||||
\(672\) | −17.5279 | −0.676152 | ||||||||
\(673\) | −11.2270 | −0.432769 | −0.216384 | − | 0.976308i | \(-0.569426\pi\) | ||||
−0.216384 | + | 0.976308i | \(0.569426\pi\) | |||||||
\(674\) | 43.9253i | 1.69194i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −50.5471 | + | 24.4996i | −1.94412 | + | 0.942292i | ||||
\(677\) | 15.7447 | 0.605119 | 0.302560 | − | 0.953130i | \(-0.402159\pi\) | ||||
0.302560 | + | 0.953130i | \(0.402159\pi\) | |||||||
\(678\) | 12.2843i | 0.471777i | ||||||||
\(679\) | 2.13124 | 0.0817895 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 34.0109i | − | 1.30330i | ||||||
\(682\) | 27.1331i | 1.03898i | ||||||||
\(683\) | 50.3492i | 1.92656i | 0.268504 | + | 0.963279i | \(0.413471\pi\) | ||||
−0.268504 | + | 0.963279i | \(0.586529\pi\) | |||||||
\(684\) | 6.70378i | 0.256325i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.8114 | 0.947304 | ||||||||
\(687\) | − | 15.6991i | − | 0.598959i | ||||||
\(688\) | −5.25887 | −0.200493 | ||||||||
\(689\) | −41.0101 | + | 9.41478i | −1.56236 | + | 0.358675i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.19325i | 0.311686i | 0.987782 | + | 0.155843i | \(0.0498094\pi\) | ||||
−0.987782 | + | 0.155843i | \(0.950191\pi\) | |||||||
\(692\) | −27.2726 | −1.03675 | ||||||||
\(693\) | 6.65991 | 0.252989 | ||||||||
\(694\) | 83.5717i | 3.17234i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 29.3401i | 1.11213i | ||||||||
\(697\) | 10.7165i | 0.405915i | ||||||||
\(698\) | 52.5380 | 1.98859 | ||||||||
\(699\) | −17.1979 | −0.650485 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.25526 | 0.311797 | 0.155899 | − | 0.987773i | \(-0.450173\pi\) | ||||
0.155899 | + | 0.987773i | \(0.450173\pi\) | |||||||
\(702\) | −11.3857 | − | 49.5953i | −0.429726 | − | 1.87186i | ||||
\(703\) | −20.4431 | −0.771024 | ||||||||
\(704\) | 9.33462i | 0.351812i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.5471 | −1.18729 | ||||||||
\(707\) | − | 23.1523i | − | 0.870732i | ||||||
\(708\) | 57.8023i | 2.17234i | ||||||||
\(709\) | − | 37.7831i | − | 1.41898i | −0.704718 | − | 0.709488i | \(-0.748926\pi\) | ||
0.704718 | − | 0.709488i | \(-0.251074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.413979 | −0.0155254 | ||||||||
\(712\) | 19.9253 | 0.746732 | ||||||||
\(713\) | − | 1.84956i | − | 0.0692665i | ||||||
\(714\) | 83.9637 | 3.14226 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −39.2545 | −1.46701 | ||||||||
\(717\) | − | 42.5753i | − | 1.59001i | ||||||
\(718\) | 7.48506 | 0.279340 | ||||||||
\(719\) | 22.2443 | 0.829574 | 0.414787 | − | 0.909919i | \(-0.363856\pi\) | ||||
0.414787 | + | 0.909919i | \(0.363856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 23.8578i | − | 0.888512i | ||||||
\(722\) | − | 35.6747i | − | 1.32768i | ||||||
\(723\) | − | 22.8405i | − | 0.849447i | ||||||
\(724\) | 51.9336 | 1.93010 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.2781i | 0.418569i | ||||||||
\(727\) | −30.0812 | −1.11565 | −0.557825 | − | 0.829958i | \(-0.688364\pi\) | ||||
−0.557825 | + | 0.829958i | \(0.688364\pi\) | |||||||
\(728\) | −68.0950 | + | 15.6327i | −2.52377 | + | 0.579386i | ||||
\(729\) | 30.0101 | 1.11149 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.79407 | 0.214301 | ||||||||
\(732\) | −24.2553 | −0.896500 | ||||||||
\(733\) | 35.0101i | 1.29313i | 0.762859 | + | 0.646564i | \(0.223795\pi\) | ||||
−0.762859 | + | 0.646564i | \(0.776205\pi\) | |||||||
\(734\) | − | 76.9300i | − | 2.83954i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.69365i | 0.0624288i | ||||||||
\(737\) | 12.1696 | 0.448275 | ||||||||
\(738\) | 2.86956 | 0.105630 | ||||||||
\(739\) | − | 42.6856i | − | 1.57022i | −0.619359 | − | 0.785108i | \(-0.712607\pi\) | ||
0.619359 | − | 0.785108i | \(-0.287393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.67912 | − | 11.6700i | −0.0984198 | − | 0.428710i | ||||
\(742\) | −97.4350 | −3.57695 | ||||||||
\(743\) | − | 13.6892i | − | 0.502210i | −0.967960 | − | 0.251105i | \(-0.919206\pi\) | ||
0.967960 | − | 0.251105i | \(-0.0807939\pi\) | |||||||
\(744\) | 33.6327 | 1.23303 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.8962i | 1.68038i | ||||||||
\(747\) | 5.45213i | 0.199483i | ||||||||
\(748\) | 81.3603i | 2.97483i | ||||||||
\(749\) | 31.7831i | 1.16133i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.7831 | −0.648916 | −0.324458 | − | 0.945900i | \(-0.605182\pi\) | ||||
−0.324458 | + | 0.945900i | \(0.605182\pi\) | |||||||
\(752\) | − | 20.0192i | − | 0.730025i | ||||||
\(753\) | 1.75566 | 0.0639799 | ||||||||
\(754\) | 6.73566 | + | 29.3401i | 0.245298 | + | 1.06850i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 80.5489i | − | 2.92954i | ||||||
\(757\) | 26.9717 | 0.980304 | 0.490152 | − | 0.871637i | \(-0.336941\pi\) | ||||
0.490152 | + | 0.871637i | \(0.336941\pi\) | |||||||
\(758\) | 40.2125 | 1.46058 | ||||||||
\(759\) | 2.08562i | 0.0757032i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.1523i | 1.27427i | 0.770752 | + | 0.637135i | \(0.219881\pi\) | ||||
−0.770752 | + | 0.637135i | \(0.780119\pi\) | |||||||
\(762\) | 22.4623i | 0.813722i | ||||||||
\(763\) | 35.5279 | 1.28620 | ||||||||
\(764\) | −57.3966 | −2.07654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.43398 | 0.196338 | ||||||||
\(767\) | 7.12763 | + | 31.0475i | 0.257364 | + | 1.12106i | ||||
\(768\) | 48.0812 | 1.73498 | ||||||||
\(769\) | 23.1523i | 0.834893i | 0.908701 | + | 0.417447i | \(0.137075\pi\) | ||||
−0.908701 | + | 0.417447i | \(0.862925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.25606 | 0.0452360 | ||||||||
\(772\) | − | 70.7258i | − | 2.54548i | ||||||
\(773\) | 41.6218i | 1.49703i | 0.663117 | + | 0.748515i | \(0.269233\pi\) | ||||
−0.663117 | + | 0.748515i | \(0.730767\pi\) | |||||||
\(774\) | − | 1.55148i | − | 0.0557669i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.74474 | 0.134428 | ||||||||
\(777\) | 46.8680 | 1.68138 | ||||||||
\(778\) | − | 1.14137i | − | 0.0409201i | ||||||
\(779\) | 3.53880 | 0.126791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.21792 | −0.222495 | ||||||||
\(782\) | − | 8.11310i | − | 0.290124i | ||||||
\(783\) | −18.6418 | −0.666202 | ||||||||
\(784\) | −24.2835 | −0.867269 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.9992i | 0.463666i | ||||||||
\(787\) | 43.2353i | 1.54117i | 0.637337 | + | 0.770585i | \(0.280036\pi\) | ||||
−0.637337 | + | 0.770585i | \(0.719964\pi\) | |||||||
\(788\) | 64.3684i | 2.29303i | ||||||||
\(789\) | −38.8031 | −1.38143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7165i | 0.381034i | ||||||||
\(792\) | 11.7019 | 0.415810 | ||||||||
\(793\) | −13.0283 | + | 2.99093i | −0.462648 | + | 0.106211i | ||||
\(794\) | −73.5289 | −2.60944 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −70.4815 | −2.49815 | ||||||||
\(797\) | −14.4431 | −0.511599 | −0.255800 | − | 0.966730i | \(-0.582339\pi\) | ||||
−0.255800 | + | 0.966730i | \(0.582339\pi\) | |||||||
\(798\) | − | 27.7266i | − | 0.981511i | ||||||
\(799\) | 22.0565i | 0.780305i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.41558i | 0.0853503i | ||||||||
\(802\) | −38.2827 | −1.35181 | ||||||||
\(803\) | −36.1059 | −1.27415 | ||||||||
\(804\) | − | 28.0840i | − | 0.990447i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.6327 | − | 7.72113i | 1.18466 | − | 0.271965i | ||||
\(807\) | −7.61350 | −0.268008 | ||||||||
\(808\) | − | 40.6802i | − | 1.43112i | ||||||
\(809\) | 17.8880 | 0.628907 | 0.314454 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314454 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.69285i | − | 0.305247i | −0.988284 | − | 0.152624i | \(-0.951228\pi\) | ||
0.988284 | − | 0.152624i | \(-0.0487722\pi\) | |||||||
\(812\) | 47.6519i | 1.67225i | ||||||||
\(813\) | − | 28.6044i | − | 1.00320i | ||||||
\(814\) | 66.4358i | 2.32857i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 60.6236 | 2.12225 | ||||||||
\(817\) | − | 1.91332i | − | 0.0669387i | ||||||
\(818\) | −59.5097 | −2.08071 | ||||||||
\(819\) | −1.89518 | − | 8.25526i | −0.0662229 | − | 0.288462i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.41478i | − | 0.328578i | −0.986412 | − | 0.164289i | \(-0.947467\pi\) | ||
0.986412 | − | 0.164289i | \(-0.0525330\pi\) | |||||||
\(822\) | 57.4241 | 2.00290 | ||||||||
\(823\) | −30.3365 | −1.05746 | −0.528732 | − | 0.848789i | \(-0.677332\pi\) | ||||
−0.528732 | + | 0.848789i | \(0.677332\pi\) | |||||||
\(824\) | − | 41.9198i | − | 1.46035i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 73.7650i | 2.56661i | ||||||||
\(827\) | − | 18.2361i | − | 0.634130i | −0.948404 | − | 0.317065i | \(-0.897303\pi\) | ||
0.948404 | − | 0.317065i | \(-0.102697\pi\) | |||||||
\(828\) | −1.48506 | −0.0516095 | ||||||||
\(829\) | −29.8023 | −1.03508 | −0.517539 | − | 0.855660i | \(-0.673152\pi\) | ||||
−0.517539 | + | 0.855660i | \(0.673152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.0109 | −1.24921 | ||||||||
\(832\) | 11.5707 | − | 2.65631i | 0.401141 | − | 0.0920908i | ||||
\(833\) | 26.7549 | 0.927001 | ||||||||
\(834\) | − | 78.7933i | − | 2.72839i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.8669 | 0.929211 | ||||||||
\(837\) | 21.3692i | 0.738626i | ||||||||
\(838\) | 14.2553i | 0.492440i | ||||||||
\(839\) | 46.1004i | 1.59156i | 0.605584 | + | 0.795782i | \(0.292940\pi\) | ||||
−0.605584 | + | 0.795782i | \(0.707060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9717 | −0.619715 | ||||||||
\(842\) | −66.1240 | −2.27878 | ||||||||
\(843\) | 47.8397i | 1.64769i | ||||||||
\(844\) | −50.9920 | −1.75522 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.90611 | 0.203056 | ||||||||
\(847\) | 9.83863i | 0.338059i | ||||||||
\(848\) | −70.3502 | −2.41584 | ||||||||
\(849\) | −9.62177 | −0.330218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.52867i | − | 0.155241i | ||||||
\(852\) | 14.3492i | 0.491594i | ||||||||
\(853\) | − | 19.3774i | − | 0.663471i | −0.943373 | − | 0.331735i | \(-0.892366\pi\) | ||
0.943373 | − | 0.331735i | \(-0.107634\pi\) | |||||||
\(854\) | −30.9536 | −1.05921 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 55.8452i | 1.90875i | ||||||||
\(857\) | −43.4713 | −1.48495 | −0.742476 | − | 0.669873i | \(-0.766349\pi\) | ||||
−0.742476 | + | 0.669873i | \(0.766349\pi\) | |||||||
\(858\) | −37.9253 | + | 8.70659i | −1.29475 | + | 0.297238i | ||||
\(859\) | −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 | ||||||||
\(863\) | − | 3.69646i | − | 0.125829i | −0.998019 | − | 0.0629145i | \(-0.979960\pi\) | ||
0.998019 | − | 0.0629145i | \(-0.0200395\pi\) | |||||||
\(864\) | − | 19.5679i | − | 0.665713i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 60.4815i | − | 2.05524i | ||||||
\(867\) | −41.0529 | −1.39423 | ||||||||
\(868\) | 54.6236 | 1.85405 | ||||||||
\(869\) | 1.65911i | 0.0562816i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.46305 | − | 15.0848i | −0.117341 | − | 0.511130i | ||||
\(872\) | 62.4249 | 2.11397 | ||||||||
\(873\) | 0.453981i | 0.0153649i | ||||||||
\(874\) | −2.67912 | −0.0906224 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 83.3219i | 2.81519i | ||||||||
\(877\) | 20.5671i | 0.694501i | 0.937772 | + | 0.347250i | \(0.112885\pi\) | ||||
−0.937772 | + | 0.347250i | \(0.887115\pi\) | |||||||
\(878\) | − | 18.1422i | − | 0.612269i | ||||||
\(879\) | 12.1696i | 0.410472i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.5369 | 0.489762 | 0.244881 | − | 0.969553i | \(-0.421251\pi\) | ||||
0.244881 | + | 0.969553i | \(0.421251\pi\) | |||||||
\(882\) | − | 7.16418i | − | 0.241230i | ||||||
\(883\) | −36.2871 | −1.22116 | −0.610580 | − | 0.791955i | \(-0.709064\pi\) | ||||
−0.610580 | + | 0.791955i | \(0.709064\pi\) | |||||||
\(884\) | 100.850 | − | 23.1523i | 3.39195 | − | 0.778696i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 68.8444i | 2.31287i | ||||||||
\(887\) | 45.2407 | 1.51903 | 0.759517 | − | 0.650487i | \(-0.225435\pi\) | ||||
0.759517 | + | 0.650487i | \(0.225435\pi\) | |||||||
\(888\) | 82.3502 | 2.76349 | ||||||||
\(889\) | 19.5953i | 0.657207i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 18.0802i | − | 0.605708i | ||||||
\(892\) | − | 86.5007i | − | 2.89626i | ||||||
\(893\) | 7.28354 | 0.243734 | ||||||||
\(894\) | −2.44305 | −0.0817079 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.6428 | 1.69186 | ||||||||
\(897\) | 2.58522 | − | 0.593495i | 0.0863180 | − | 0.0198162i | ||||
\(898\) | −3.58442 | −0.119614 | ||||||||
\(899\) | − | 12.6418i | − | 0.421627i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 77.5097 | 2.58222 | ||||||||
\(902\) | − | 11.5004i | − | 0.382921i | ||||||
\(903\) | 4.38650i | 0.145974i | ||||||||
\(904\) | 18.8296i | 0.626262i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 63.3302 | 2.10401 | ||||||||
\(907\) | −11.2973 | −0.375120 | −0.187560 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187560 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(908\) | − | 97.0568i | − | 3.22094i | ||||||
\(909\) | 4.93172 | 0.163575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.1979 | −1.36495 | −0.682474 | − | 0.730910i | \(-0.739096\pi\) | ||||
−0.682474 | + | 0.730910i | \(0.739096\pi\) | |||||||
\(912\) | − | 20.0192i | − | 0.662902i | ||||||
\(913\) | 21.8506 | 0.723150 | ||||||||
\(914\) | 88.8042 | 2.93738 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 44.8005i | − | 1.48025i | ||||||
\(917\) | 11.3401i | 0.374483i | ||||||||
\(918\) | 93.7359i | 3.09375i | ||||||||
\(919\) | 1.74474 | 0.0575535 | 0.0287768 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287768 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.9544i | 0.789324i | ||||||||
\(922\) | 73.4076 | 2.41755 | ||||||||
\(923\) | 1.76940 | + | 7.70739i | 0.0582405 | + | 0.253692i | ||||
\(924\) | −61.5953 | −2.02634 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.34916 | −0.274370 | ||||||||
\(927\) | 5.08201 | 0.166915 | ||||||||
\(928\) | 11.5761i | 0.380006i | ||||||||
\(929\) | 15.5569i | 0.510407i | 0.966887 | + | 0.255203i | \(0.0821424\pi\) | ||||
−0.966887 | + | 0.255203i | \(0.917858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.83502i | − | 0.289556i | ||||||
\(932\) | −49.0776 | −1.60759 | ||||||||
\(933\) | 36.8114 | 1.20515 | ||||||||
\(934\) | − | 54.1860i | − | 1.77302i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.32996 | − | 14.5051i | −0.108843 | − | 0.474113i | ||||
\(937\) | −26.0384 | −0.850638 | −0.425319 | − | 0.905044i | \(-0.639838\pi\) | ||||
−0.425319 | + | 0.905044i | \(0.639838\pi\) | |||||||
\(938\) | − | 35.8397i | − | 1.17021i | ||||||
\(939\) | −16.9992 | −0.554748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.8789i | 1.65860i | 0.558800 | + | 0.829302i | \(0.311262\pi\) | ||||
−0.558800 | + | 0.829302i | \(0.688738\pi\) | |||||||
\(942\) | − | 39.0392i | − | 1.27197i | ||||||
\(943\) | 0.783938i | 0.0255285i | ||||||||
\(944\) | 53.2599i | 1.73346i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.21792 | −0.202162 | ||||||||
\(947\) | 37.8770i | 1.23084i | 0.788200 | + | 0.615419i | \(0.211013\pi\) | ||||
−0.788200 | + | 0.615419i | \(0.788987\pi\) | |||||||
\(948\) | 3.82876 | 0.124352 | ||||||||
\(949\) | 10.2745 | + | 44.7549i | 0.333523 | + | 1.45280i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 24.4540i | − | 0.792975i | ||||||
\(952\) | 128.700 | 4.17120 | ||||||||
\(953\) | −32.0950 | −1.03966 | −0.519829 | − | 0.854271i | \(-0.674004\pi\) | ||||
−0.519829 | + | 0.854271i | \(0.674004\pi\) | |||||||
\(954\) | − | 20.7549i | − | 0.671964i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 121.497i | − | 3.92950i | ||||||
\(957\) | 14.2553i | 0.460807i | ||||||||
\(958\) | −13.6272 | −0.440276 | ||||||||
\(959\) | 50.0950 | 1.61765 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.5087 | 0.532538 | ||||||||
\(962\) | 82.3502 | − | 18.9053i | 2.65508 | − | 0.609532i | ||||
\(963\) | −6.77020 | −0.218167 | ||||||||
\(964\) | − | 65.1798i | − | 2.09930i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.14217 | 0.197621 | ||||||||
\(967\) | 24.4057i | 0.784835i | 0.919787 | + | 0.392417i | \(0.128361\pi\) | ||||
−0.919787 | + | 0.392417i | \(0.871639\pi\) | |||||||
\(968\) | 17.2871i | 0.555630i | ||||||||
\(969\) | 22.0565i | 0.708558i | ||||||||
\(970\) | 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 | ||||||||
\(973\) | − | 68.7367i | − | 2.20360i | ||||||
\(974\) | −43.8770 | −1.40591 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.3492 | −0.715379 | ||||||||
\(977\) | 25.1715i | 0.805308i | 0.915352 | + | 0.402654i | \(0.131912\pi\) | ||||
−0.915352 | + | 0.402654i | \(0.868088\pi\) | |||||||
\(978\) | 5.24354 | 0.167670 | ||||||||
\(979\) | 9.68097 | 0.309405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.56788i | 0.241624i | ||||||||
\(982\) | 61.9072i | 1.97554i | ||||||||
\(983\) | 13.1896i | 0.420684i | 0.977628 | + | 0.210342i | \(0.0674578\pi\) | ||||
−0.977628 | + | 0.210342i | \(0.932542\pi\) | |||||||
\(984\) | −14.2553 | −0.454441 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 55.4532i | − | 1.76599i | ||||||
\(987\) | −16.6983 | −0.531513 | ||||||||
\(988\) | −7.64538 | − | 33.3027i | −0.243232 | − | 1.05950i | ||||
\(989\) | 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 | ||||||||
\(993\) | − | 45.5180i | − | 1.44447i | ||||||
\(994\) | 18.3118i | 0.580815i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 50.4249i | − | 1.59777i | ||||||
\(997\) | 0.630841 | 0.0199789 | 0.00998947 | − | 0.999950i | \(-0.496820\pi\) | ||||
0.00998947 | + | 0.999950i | \(0.496820\pi\) | |||||||
\(998\) | 81.3648 | 2.57556 | ||||||||
\(999\) | 52.3227i | 1.65542i |
(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 | 325.2.c.g.51.1 | 6 | ||
5.2 | odd | 4 | 325.2.d.f.324.6 | 6 | |||
5.3 | odd | 4 | 325.2.d.e.324.1 | 6 | |||
5.4 | even | 2 | 65.2.c.a.51.6 | yes | 6 | ||
13.5 | odd | 4 | 4225.2.a.bc.1.1 | 3 | |||
13.8 | odd | 4 | 4225.2.a.be.1.3 | 3 | |||
13.12 | even | 2 | inner | 325.2.c.g.51.6 | 6 | ||
15.14 | odd | 2 | 585.2.b.g.181.1 | 6 | |||
20.19 | odd | 2 | 1040.2.k.d.961.1 | 6 | |||
65.4 | even | 6 | 845.2.m.h.361.1 | 12 | |||
65.9 | even | 6 | 845.2.m.h.361.6 | 12 | |||
65.12 | odd | 4 | 325.2.d.e.324.2 | 6 | |||
65.19 | odd | 12 | 845.2.e.i.146.1 | 6 | |||
65.24 | odd | 12 | 845.2.e.k.191.3 | 6 | |||
65.29 | even | 6 | 845.2.m.h.316.1 | 12 | |||
65.34 | odd | 4 | 845.2.a.i.1.1 | 3 | |||
65.38 | odd | 4 | 325.2.d.f.324.5 | 6 | |||
65.44 | odd | 4 | 845.2.a.k.1.3 | 3 | |||
65.49 | even | 6 | 845.2.m.h.316.6 | 12 | |||
65.54 | odd | 12 | 845.2.e.i.191.1 | 6 | |||
65.59 | odd | 12 | 845.2.e.k.146.3 | 6 | |||
65.64 | even | 2 | 65.2.c.a.51.1 | ✓ | 6 | ||
195.44 | even | 4 | 7605.2.a.bs.1.1 | 3 | |||
195.164 | even | 4 | 7605.2.a.cc.1.3 | 3 | |||
195.194 | odd | 2 | 585.2.b.g.181.6 | 6 | |||
260.259 | odd | 2 | 1040.2.k.d.961.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.c.a.51.1 | ✓ | 6 | 65.64 | even | 2 | ||
65.2.c.a.51.6 | yes | 6 | 5.4 | even | 2 | ||
325.2.c.g.51.1 | 6 | 1.1 | even | 1 | trivial | ||
325.2.c.g.51.6 | 6 | 13.12 | even | 2 | inner | ||
325.2.d.e.324.1 | 6 | 5.3 | odd | 4 | |||
325.2.d.e.324.2 | 6 | 65.12 | odd | 4 | |||
325.2.d.f.324.5 | 6 | 65.38 | odd | 4 | |||
325.2.d.f.324.6 | 6 | 5.2 | odd | 4 | |||
585.2.b.g.181.1 | 6 | 15.14 | odd | 2 | |||
585.2.b.g.181.6 | 6 | 195.194 | odd | 2 | |||
845.2.a.i.1.1 | 3 | 65.34 | odd | 4 | |||
845.2.a.k.1.3 | 3 | 65.44 | odd | 4 | |||
845.2.e.i.146.1 | 6 | 65.19 | odd | 12 | |||
845.2.e.i.191.1 | 6 | 65.54 | odd | 12 | |||
845.2.e.k.146.3 | 6 | 65.59 | odd | 12 | |||
845.2.e.k.191.3 | 6 | 65.24 | odd | 12 | |||
845.2.m.h.316.1 | 12 | 65.29 | even | 6 | |||
845.2.m.h.316.6 | 12 | 65.49 | even | 6 | |||
845.2.m.h.361.1 | 12 | 65.4 | even | 6 | |||
845.2.m.h.361.6 | 12 | 65.9 | even | 6 | |||
1040.2.k.d.961.1 | 6 | 20.19 | odd | 2 | |||
1040.2.k.d.961.2 | 6 | 260.259 | odd | 2 | |||
4225.2.a.bc.1.1 | 3 | 13.5 | odd | 4 | |||
4225.2.a.be.1.3 | 3 | 13.8 | odd | 4 | |||
7605.2.a.bs.1.1 | 3 | 195.44 | even | 4 | |||
7605.2.a.cc.1.3 | 3 | 195.164 | even | 4 |