Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.2.b.g.337.5 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.24698i | − 0.881748i | −0.897569 | − | 0.440874i | \(-0.854669\pi\) | ||||
0.897569 | − | 0.440874i | \(-0.145331\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.445042 | 0.222521 | ||||||||
\(5\) | 2.80194i | 1.25306i | 0.779395 | + | 0.626532i | \(0.215526\pi\) | ||||
−0.779395 | + | 0.626532i | \(0.784474\pi\) | |||||||
\(6\) | − 1.24698i | − 0.509077i | ||||||||
\(7\) | − 4.80194i | − 1.81496i | −0.420093 | − | 0.907481i | \(-0.638003\pi\) | ||||
0.420093 | − | 0.907481i | \(-0.361997\pi\) | |||||||
\(8\) | − 3.04892i | − 1.07796i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.49396 | 1.10489 | ||||||||
\(11\) | 1.46681i | 0.442260i | 0.975244 | + | 0.221130i | \(0.0709746\pi\) | ||||
−0.975244 | + | 0.221130i | \(0.929025\pi\) | |||||||
\(12\) | 0.445042 | 0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.98792 | −1.60034 | ||||||||
\(15\) | 2.80194i | 0.723457i | ||||||||
\(16\) | −2.91185 | −0.727963 | ||||||||
\(17\) | 2.44504 | 0.593010 | 0.296505 | − | 0.955031i | \(-0.404179\pi\) | ||||
0.296505 | + | 0.955031i | \(0.404179\pi\) | |||||||
\(18\) | − 1.24698i | − 0.293916i | ||||||||
\(19\) | − 2.54288i | − 0.583376i | −0.956514 | − | 0.291688i | \(-0.905783\pi\) | ||||
0.956514 | − | 0.291688i | \(-0.0942169\pi\) | |||||||
\(20\) | 1.24698i | 0.278833i | ||||||||
\(21\) | − 4.80194i | − 1.04787i | ||||||||
\(22\) | 1.82908 | 0.389962 | ||||||||
\(23\) | 3.51573 | 0.733080 | 0.366540 | − | 0.930402i | \(-0.380542\pi\) | ||||
0.366540 | + | 0.930402i | \(0.380542\pi\) | |||||||
\(24\) | − 3.04892i | − 0.622358i | ||||||||
\(25\) | −2.85086 | −0.570171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 2.13706i | − 0.403867i | ||||||||
\(29\) | 1.85086 | 0.343695 | 0.171848 | − | 0.985124i | \(-0.445026\pi\) | ||||
0.171848 | + | 0.985124i | \(0.445026\pi\) | |||||||
\(30\) | 3.49396 | 0.637907 | ||||||||
\(31\) | 7.63102i | 1.37057i | 0.728274 | + | 0.685286i | \(0.240323\pi\) | ||||
−0.728274 | + | 0.685286i | \(0.759677\pi\) | |||||||
\(32\) | − 2.46681i | − 0.436075i | ||||||||
\(33\) | 1.46681i | 0.255339i | ||||||||
\(34\) | − 3.04892i | − 0.522885i | ||||||||
\(35\) | 13.4547 | 2.27426 | ||||||||
\(36\) | 0.445042 | 0.0741736 | ||||||||
\(37\) | − 4.55496i | − 0.748831i | −0.927261 | − | 0.374415i | \(-0.877843\pi\) | ||||
0.927261 | − | 0.374415i | \(-0.122157\pi\) | |||||||
\(38\) | −3.17092 | −0.514390 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.54288 | 1.35075 | ||||||||
\(41\) | − 1.24698i | − 0.194745i | −0.995248 | − | 0.0973727i | \(-0.968956\pi\) | ||||
0.995248 | − | 0.0973727i | \(-0.0310439\pi\) | |||||||
\(42\) | −5.98792 | −0.923956 | ||||||||
\(43\) | −2.38404 | −0.363563 | −0.181782 | − | 0.983339i | \(-0.558186\pi\) | ||||
−0.181782 | + | 0.983339i | \(0.558186\pi\) | |||||||
\(44\) | 0.652793i | 0.0984122i | ||||||||
\(45\) | 2.80194i | 0.417688i | ||||||||
\(46\) | − 4.38404i | − 0.646392i | ||||||||
\(47\) | 12.8170i | 1.86955i | 0.355238 | + | 0.934776i | \(0.384400\pi\) | ||||
−0.355238 | + | 0.934776i | \(0.615600\pi\) | |||||||
\(48\) | −2.91185 | −0.420290 | ||||||||
\(49\) | −16.0586 | −2.29409 | ||||||||
\(50\) | 3.55496i | 0.502747i | ||||||||
\(51\) | 2.44504 | 0.342374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.85086 | −1.21576 | −0.607879 | − | 0.794030i | \(-0.707980\pi\) | ||||
−0.607879 | + | 0.794030i | \(0.707980\pi\) | |||||||
\(54\) | − 1.24698i | − 0.169692i | ||||||||
\(55\) | −4.10992 | −0.554181 | ||||||||
\(56\) | −14.6407 | −1.95645 | ||||||||
\(57\) | − 2.54288i | − 0.336812i | ||||||||
\(58\) | − 2.30798i | − 0.303052i | ||||||||
\(59\) | 2.17629i | 0.283329i | 0.989915 | + | 0.141665i | \(0.0452454\pi\) | ||||
−0.989915 | + | 0.141665i | \(0.954755\pi\) | |||||||
\(60\) | 1.24698i | 0.160984i | ||||||||
\(61\) | −7.82908 | −1.00241 | −0.501206 | − | 0.865328i | \(-0.667110\pi\) | ||||
−0.501206 | + | 0.865328i | \(0.667110\pi\) | |||||||
\(62\) | 9.51573 | 1.20850 | ||||||||
\(63\) | − 4.80194i | − 0.604987i | ||||||||
\(64\) | −8.89977 | −1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.82908 | 0.225145 | ||||||||
\(67\) | 3.58211i | 0.437624i | 0.975767 | + | 0.218812i | \(0.0702181\pi\) | ||||
−0.975767 | + | 0.218812i | \(0.929782\pi\) | |||||||
\(68\) | 1.08815 | 0.131957 | ||||||||
\(69\) | 3.51573 | 0.423244 | ||||||||
\(70\) | − 16.7778i | − 2.00533i | ||||||||
\(71\) | 8.83877i | 1.04897i | 0.851420 | + | 0.524485i | \(0.175742\pi\) | ||||
−0.851420 | + | 0.524485i | \(0.824258\pi\) | |||||||
\(72\) | − 3.04892i | − 0.359318i | ||||||||
\(73\) | − 7.69202i | − 0.900283i | −0.892957 | − | 0.450142i | \(-0.851374\pi\) | ||||
0.892957 | − | 0.450142i | \(-0.148626\pi\) | |||||||
\(74\) | −5.67994 | −0.660280 | ||||||||
\(75\) | −2.85086 | −0.329188 | ||||||||
\(76\) | − 1.13169i | − 0.129813i | ||||||||
\(77\) | 7.04354 | 0.802686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.02177 | −0.452485 | −0.226242 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226242 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(80\) | − 8.15883i | − 0.912185i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.55496 | −0.171716 | ||||||||
\(83\) | 0.652793i | 0.0716533i | 0.999358 | + | 0.0358267i | \(0.0114064\pi\) | ||||
−0.999358 | + | 0.0358267i | \(0.988594\pi\) | |||||||
\(84\) | − 2.13706i | − 0.233173i | ||||||||
\(85\) | 6.85086i | 0.743080i | ||||||||
\(86\) | 2.97285i | 0.320571i | ||||||||
\(87\) | 1.85086 | 0.198432 | ||||||||
\(88\) | 4.47219 | 0.476737 | ||||||||
\(89\) | 6.29590i | 0.667364i | 0.942686 | + | 0.333682i | \(0.108291\pi\) | ||||
−0.942686 | + | 0.333682i | \(0.891709\pi\) | |||||||
\(90\) | 3.49396 | 0.368296 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.56465 | 0.163126 | ||||||||
\(93\) | 7.63102i | 0.791300i | ||||||||
\(94\) | 15.9825 | 1.64847 | ||||||||
\(95\) | 7.12498 | 0.731008 | ||||||||
\(96\) | − 2.46681i | − 0.251768i | ||||||||
\(97\) | 10.0315i | 1.01854i | 0.860607 | + | 0.509270i | \(0.170085\pi\) | ||||
−0.860607 | + | 0.509270i | \(0.829915\pi\) | |||||||
\(98\) | 20.0248i | 2.02281i | ||||||||
\(99\) | 1.46681i | 0.147420i | ||||||||
\(100\) | −1.26875 | −0.126875 | ||||||||
\(101\) | −13.8877 | −1.38188 | −0.690938 | − | 0.722914i | \(-0.742802\pi\) | ||||
−0.690938 | + | 0.722914i | \(0.742802\pi\) | |||||||
\(102\) | − 3.04892i | − 0.301888i | ||||||||
\(103\) | 17.4034 | 1.71481 | 0.857405 | − | 0.514642i | \(-0.172075\pi\) | ||||
0.857405 | + | 0.514642i | \(0.172075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.4547 | 1.31305 | ||||||||
\(106\) | 11.0368i | 1.07199i | ||||||||
\(107\) | 10.5526 | 1.02015 | 0.510077 | − | 0.860128i | \(-0.329617\pi\) | ||||
0.510077 | + | 0.860128i | \(0.329617\pi\) | |||||||
\(108\) | 0.445042 | 0.0428242 | ||||||||
\(109\) | − 1.07069i | − 0.102553i | −0.998684 | − | 0.0512766i | \(-0.983671\pi\) | ||||
0.998684 | − | 0.0512766i | \(-0.0163290\pi\) | |||||||
\(110\) | 5.12498i | 0.488648i | ||||||||
\(111\) | − 4.55496i | − 0.432337i | ||||||||
\(112\) | 13.9825i | 1.32123i | ||||||||
\(113\) | −16.5308 | −1.55509 | −0.777543 | − | 0.628830i | \(-0.783534\pi\) | ||||
−0.777543 | + | 0.628830i | \(0.783534\pi\) | |||||||
\(114\) | −3.17092 | −0.296983 | ||||||||
\(115\) | 9.85086i | 0.918597i | ||||||||
\(116\) | 0.823708 | 0.0764794 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.71379 | 0.249825 | ||||||||
\(119\) | − 11.7409i | − 1.07629i | ||||||||
\(120\) | 8.54288 | 0.779854 | ||||||||
\(121\) | 8.84846 | 0.804406 | ||||||||
\(122\) | 9.76271i | 0.883874i | ||||||||
\(123\) | − 1.24698i | − 0.112436i | ||||||||
\(124\) | 3.39612i | 0.304981i | ||||||||
\(125\) | 6.02177i | 0.538604i | ||||||||
\(126\) | −5.98792 | −0.533446 | ||||||||
\(127\) | 9.53750 | 0.846316 | 0.423158 | − | 0.906056i | \(-0.360921\pi\) | ||||
0.423158 | + | 0.906056i | \(0.360921\pi\) | |||||||
\(128\) | 6.16421i | 0.544844i | ||||||||
\(129\) | −2.38404 | −0.209903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.50902 | −0.481326 | −0.240663 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240663 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(132\) | 0.652793i | 0.0568183i | ||||||||
\(133\) | −12.2107 | −1.05880 | ||||||||
\(134\) | 4.46681 | 0.385874 | ||||||||
\(135\) | 2.80194i | 0.241152i | ||||||||
\(136\) | − 7.45473i | − 0.639238i | ||||||||
\(137\) | − 16.1836i | − 1.38266i | −0.722540 | − | 0.691329i | \(-0.757026\pi\) | ||||
0.722540 | − | 0.691329i | \(-0.242974\pi\) | |||||||
\(138\) | − 4.38404i | − 0.373195i | ||||||||
\(139\) | −10.5090 | −0.891364 | −0.445682 | − | 0.895191i | \(-0.647039\pi\) | ||||
−0.445682 | + | 0.895191i | \(0.647039\pi\) | |||||||
\(140\) | 5.98792 | 0.506071 | ||||||||
\(141\) | 12.8170i | 1.07939i | ||||||||
\(142\) | 11.0218 | 0.924926 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | 5.18598i | 0.430672i | ||||||||
\(146\) | −9.59179 | −0.793823 | ||||||||
\(147\) | −16.0586 | −1.32449 | ||||||||
\(148\) | − 2.02715i | − 0.166630i | ||||||||
\(149\) | − 14.3502i | − 1.17561i | −0.809001 | − | 0.587807i | \(-0.799992\pi\) | ||||
0.809001 | − | 0.587807i | \(-0.200008\pi\) | |||||||
\(150\) | 3.55496i | 0.290261i | ||||||||
\(151\) | 1.96615i | 0.160003i | 0.996795 | + | 0.0800014i | \(0.0254925\pi\) | ||||
−0.996795 | + | 0.0800014i | \(0.974508\pi\) | |||||||
\(152\) | −7.75302 | −0.628853 | ||||||||
\(153\) | 2.44504 | 0.197670 | ||||||||
\(154\) | − 8.78315i | − 0.707767i | ||||||||
\(155\) | −21.3817 | −1.71742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7017 | 0.854089 | 0.427045 | − | 0.904231i | \(-0.359555\pi\) | ||||
0.427045 | + | 0.904231i | \(0.359555\pi\) | |||||||
\(158\) | 5.01507i | 0.398977i | ||||||||
\(159\) | −8.85086 | −0.701918 | ||||||||
\(160\) | 6.91185 | 0.546430 | ||||||||
\(161\) | − 16.8823i | − 1.33051i | ||||||||
\(162\) | − 1.24698i | − 0.0979720i | ||||||||
\(163\) | 3.89977i | 0.305454i | 0.988268 | + | 0.152727i | \(0.0488055\pi\) | ||||
−0.988268 | + | 0.152727i | \(0.951195\pi\) | |||||||
\(164\) | − 0.554958i | − 0.0433349i | ||||||||
\(165\) | −4.10992 | −0.319957 | ||||||||
\(166\) | 0.814019 | 0.0631802 | ||||||||
\(167\) | 21.0194i | 1.62653i | 0.581895 | + | 0.813264i | \(0.302312\pi\) | ||||
−0.581895 | + | 0.813264i | \(0.697688\pi\) | |||||||
\(168\) | −14.6407 | −1.12956 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.54288 | 0.655209 | ||||||||
\(171\) | − 2.54288i | − 0.194459i | ||||||||
\(172\) | −1.06100 | −0.0809004 | ||||||||
\(173\) | −13.2349 | −1.00623 | −0.503115 | − | 0.864219i | \(-0.667813\pi\) | ||||
−0.503115 | + | 0.864219i | \(0.667813\pi\) | |||||||
\(174\) | − 2.30798i | − 0.174967i | ||||||||
\(175\) | 13.6896i | 1.03484i | ||||||||
\(176\) | − 4.27114i | − 0.321950i | ||||||||
\(177\) | 2.17629i | 0.163580i | ||||||||
\(178\) | 7.85086 | 0.588446 | ||||||||
\(179\) | −8.52781 | −0.637399 | −0.318699 | − | 0.947856i | \(-0.603246\pi\) | ||||
−0.318699 | + | 0.947856i | \(0.603246\pi\) | |||||||
\(180\) | 1.24698i | 0.0929444i | ||||||||
\(181\) | 3.63640 | 0.270291 | 0.135146 | − | 0.990826i | \(-0.456850\pi\) | ||||
0.135146 | + | 0.990826i | \(0.456850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.82908 | −0.578743 | ||||||||
\(184\) | − 10.7192i | − 0.790228i | ||||||||
\(185\) | 12.7627 | 0.938333 | ||||||||
\(186\) | 9.51573 | 0.697727 | ||||||||
\(187\) | 3.58642i | 0.262265i | ||||||||
\(188\) | 5.70410i | 0.416014i | ||||||||
\(189\) | − 4.80194i | − 0.349290i | ||||||||
\(190\) | − 8.88471i | − 0.644564i | ||||||||
\(191\) | 21.3817 | 1.54712 | 0.773561 | − | 0.633722i | \(-0.218474\pi\) | ||||
0.773561 | + | 0.633722i | \(0.218474\pi\) | |||||||
\(192\) | −8.89977 | −0.642286 | ||||||||
\(193\) | − 8.42758i | − 0.606631i | −0.952890 | − | 0.303315i | \(-0.901906\pi\) | ||||
0.952890 | − | 0.303315i | \(-0.0980936\pi\) | |||||||
\(194\) | 12.5090 | 0.898096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.14675 | −0.510482 | ||||||||
\(197\) | 26.4765i | 1.88637i | 0.332264 | + | 0.943186i | \(0.392187\pi\) | ||||
−0.332264 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(198\) | 1.82908 | 0.129987 | ||||||||
\(199\) | 14.2524 | 1.01032 | 0.505161 | − | 0.863025i | \(-0.331433\pi\) | ||||
0.505161 | + | 0.863025i | \(0.331433\pi\) | |||||||
\(200\) | 8.69202i | 0.614619i | ||||||||
\(201\) | 3.58211i | 0.252662i | ||||||||
\(202\) | 17.3177i | 1.21847i | ||||||||
\(203\) | − 8.88769i | − 0.623794i | ||||||||
\(204\) | 1.08815 | 0.0761855 | ||||||||
\(205\) | 3.49396 | 0.244029 | ||||||||
\(206\) | − 21.7017i | − 1.51203i | ||||||||
\(207\) | 3.51573 | 0.244360 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.72992 | 0.258004 | ||||||||
\(210\) | − 16.7778i | − 1.15778i | ||||||||
\(211\) | 1.85086 | 0.127418 | 0.0637091 | − | 0.997969i | \(-0.479707\pi\) | ||||
0.0637091 | + | 0.997969i | \(0.479707\pi\) | |||||||
\(212\) | −3.93900 | −0.270532 | ||||||||
\(213\) | 8.83877i | 0.605623i | ||||||||
\(214\) | − 13.1588i | − 0.899519i | ||||||||
\(215\) | − 6.67994i | − 0.455568i | ||||||||
\(216\) | − 3.04892i | − 0.207453i | ||||||||
\(217\) | 36.6437 | 2.48754 | ||||||||
\(218\) | −1.33513 | −0.0904261 | ||||||||
\(219\) | − 7.69202i | − 0.519779i | ||||||||
\(220\) | −1.82908 | −0.123317 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.67994 | −0.381213 | ||||||||
\(223\) | − 18.6504i | − 1.24892i | −0.781056 | − | 0.624462i | \(-0.785318\pi\) | ||||
0.781056 | − | 0.624462i | \(-0.214682\pi\) | |||||||
\(224\) | −11.8455 | −0.791459 | ||||||||
\(225\) | −2.85086 | −0.190057 | ||||||||
\(226\) | 20.6136i | 1.37119i | ||||||||
\(227\) | − 9.75733i | − 0.647617i | −0.946123 | − | 0.323808i | \(-0.895037\pi\) | ||||
0.946123 | − | 0.323808i | \(-0.104963\pi\) | |||||||
\(228\) | − 1.13169i | − 0.0749478i | ||||||||
\(229\) | − 2.86294i | − 0.189188i | −0.995516 | − | 0.0945941i | \(-0.969845\pi\) | ||||
0.995516 | − | 0.0945941i | \(-0.0301553\pi\) | |||||||
\(230\) | 12.2838 | 0.809971 | ||||||||
\(231\) | 7.04354 | 0.463431 | ||||||||
\(232\) | − 5.64310i | − 0.370488i | ||||||||
\(233\) | 5.78554 | 0.379024 | 0.189512 | − | 0.981878i | \(-0.439309\pi\) | ||||
0.189512 | + | 0.981878i | \(0.439309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9124 | −2.34267 | ||||||||
\(236\) | 0.968541i | 0.0630467i | ||||||||
\(237\) | −4.02177 | −0.261242 | ||||||||
\(238\) | −14.6407 | −0.949016 | ||||||||
\(239\) | − 7.09246i | − 0.458773i | −0.973335 | − | 0.229386i | \(-0.926328\pi\) | ||||
0.973335 | − | 0.229386i | \(-0.0736720\pi\) | |||||||
\(240\) | − 8.15883i | − 0.526650i | ||||||||
\(241\) | 3.89977i | 0.251206i | 0.992081 | + | 0.125603i | \(0.0400866\pi\) | ||||
−0.992081 | + | 0.125603i | \(0.959913\pi\) | |||||||
\(242\) | − 11.0339i | − 0.709283i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.48427 | −0.223058 | ||||||||
\(245\) | − 44.9952i | − 2.87464i | ||||||||
\(246\) | −1.55496 | −0.0991405 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.2664 | 1.47742 | ||||||||
\(249\) | 0.652793i | 0.0413691i | ||||||||
\(250\) | 7.50902 | 0.474912 | ||||||||
\(251\) | 2.44504 | 0.154330 | 0.0771648 | − | 0.997018i | \(-0.475413\pi\) | ||||
0.0771648 | + | 0.997018i | \(0.475413\pi\) | |||||||
\(252\) | − 2.13706i | − 0.134622i | ||||||||
\(253\) | 5.15691i | 0.324212i | ||||||||
\(254\) | − 11.8931i | − 0.746237i | ||||||||
\(255\) | 6.85086i | 0.429017i | ||||||||
\(256\) | −10.1129 | −0.632056 | ||||||||
\(257\) | 14.1304 | 0.881428 | 0.440714 | − | 0.897648i | \(-0.354725\pi\) | ||||
0.440714 | + | 0.897648i | \(0.354725\pi\) | |||||||
\(258\) | 2.97285i | 0.185082i | ||||||||
\(259\) | −21.8726 | −1.35910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.85086 | 0.114565 | ||||||||
\(262\) | 6.86964i | 0.424408i | ||||||||
\(263\) | −23.7235 | −1.46285 | −0.731426 | − | 0.681921i | \(-0.761145\pi\) | ||||
−0.731426 | + | 0.681921i | \(0.761145\pi\) | |||||||
\(264\) | 4.47219 | 0.275244 | ||||||||
\(265\) | − 24.7995i | − 1.52342i | ||||||||
\(266\) | 15.2265i | 0.933599i | ||||||||
\(267\) | 6.29590i | 0.385303i | ||||||||
\(268\) | 1.59419i | 0.0973805i | ||||||||
\(269\) | −5.91617 | −0.360715 | −0.180357 | − | 0.983601i | \(-0.557725\pi\) | ||||
−0.180357 | + | 0.983601i | \(0.557725\pi\) | |||||||
\(270\) | 3.49396 | 0.212636 | ||||||||
\(271\) | 3.19029i | 0.193796i | 0.995294 | + | 0.0968982i | \(0.0308921\pi\) | ||||
−0.995294 | + | 0.0968982i | \(0.969108\pi\) | |||||||
\(272\) | −7.11960 | −0.431689 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1806 | −1.21915 | ||||||||
\(275\) | − 4.18167i | − 0.252164i | ||||||||
\(276\) | 1.56465 | 0.0941807 | ||||||||
\(277\) | −21.9366 | −1.31804 | −0.659022 | − | 0.752124i | \(-0.729029\pi\) | ||||
−0.659022 | + | 0.752124i | \(0.729029\pi\) | |||||||
\(278\) | 13.1045i | 0.785958i | ||||||||
\(279\) | 7.63102i | 0.456857i | ||||||||
\(280\) | − 41.0224i | − 2.45155i | ||||||||
\(281\) | − 11.9903i | − 0.715282i | −0.933859 | − | 0.357641i | \(-0.883581\pi\) | ||||
0.933859 | − | 0.357641i | \(-0.116419\pi\) | |||||||
\(282\) | 15.9825 | 0.951747 | ||||||||
\(283\) | 14.3666 | 0.854005 | 0.427002 | − | 0.904250i | \(-0.359570\pi\) | ||||
0.427002 | + | 0.904250i | \(0.359570\pi\) | |||||||
\(284\) | 3.93362i | 0.233418i | ||||||||
\(285\) | 7.12498 | 0.422047 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.98792 | −0.353456 | ||||||||
\(288\) | − 2.46681i | − 0.145358i | ||||||||
\(289\) | −11.0218 | −0.648339 | ||||||||
\(290\) | 6.46681 | 0.379744 | ||||||||
\(291\) | 10.0315i | 0.588055i | ||||||||
\(292\) | − 3.42327i | − 0.200332i | ||||||||
\(293\) | − 18.7584i | − 1.09588i | −0.836519 | − | 0.547939i | \(-0.815413\pi\) | ||||
0.836519 | − | 0.547939i | \(-0.184587\pi\) | |||||||
\(294\) | 20.0248i | 1.16787i | ||||||||
\(295\) | −6.09783 | −0.355030 | ||||||||
\(296\) | −13.8877 | −0.807206 | ||||||||
\(297\) | 1.46681i | 0.0851131i | ||||||||
\(298\) | −17.8944 | −1.03659 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.26875 | −0.0732513 | ||||||||
\(301\) | 11.4480i | 0.659853i | ||||||||
\(302\) | 2.45175 | 0.141082 | ||||||||
\(303\) | −13.8877 | −0.797827 | ||||||||
\(304\) | 7.40449i | 0.424676i | ||||||||
\(305\) | − 21.9366i | − 1.25609i | ||||||||
\(306\) | − 3.04892i | − 0.174295i | ||||||||
\(307\) | − 25.6262i | − 1.46257i | −0.682074 | − | 0.731283i | \(-0.738922\pi\) | ||||
0.682074 | − | 0.731283i | \(-0.261078\pi\) | |||||||
\(308\) | 3.13467 | 0.178614 | ||||||||
\(309\) | 17.4034 | 0.990046 | ||||||||
\(310\) | 26.6625i | 1.51433i | ||||||||
\(311\) | −11.3817 | −0.645394 | −0.322697 | − | 0.946502i | \(-0.604590\pi\) | ||||
−0.322697 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.5743 | 1.55859 | 0.779297 | − | 0.626655i | \(-0.215576\pi\) | ||||
0.779297 | + | 0.626655i | \(0.215576\pi\) | |||||||
\(314\) | − 13.3448i | − 0.753091i | ||||||||
\(315\) | 13.4547 | 0.758088 | ||||||||
\(316\) | −1.78986 | −0.100687 | ||||||||
\(317\) | − 11.2597i | − 0.632405i | −0.948692 | − | 0.316203i | \(-0.897592\pi\) | ||||
0.948692 | − | 0.316203i | \(-0.102408\pi\) | |||||||
\(318\) | 11.0368i | 0.618915i | ||||||||
\(319\) | 2.71486i | 0.152003i | ||||||||
\(320\) | − 24.9366i | − 1.39400i | ||||||||
\(321\) | 10.5526 | 0.588987 | ||||||||
\(322\) | −21.0519 | −1.17318 | ||||||||
\(323\) | − 6.21744i | − 0.345948i | ||||||||
\(324\) | 0.445042 | 0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.86294 | 0.269333 | ||||||||
\(327\) | − 1.07069i | − 0.0592092i | ||||||||
\(328\) | −3.80194 | −0.209927 | ||||||||
\(329\) | 61.5465 | 3.39317 | ||||||||
\(330\) | 5.12498i | 0.282121i | ||||||||
\(331\) | − 11.9065i | − 0.654439i | −0.944948 | − | 0.327220i | \(-0.893888\pi\) | ||||
0.944948 | − | 0.327220i | \(-0.106112\pi\) | |||||||
\(332\) | 0.290520i | 0.0159444i | ||||||||
\(333\) | − 4.55496i | − 0.249610i | ||||||||
\(334\) | 26.2107 | 1.43419 | ||||||||
\(335\) | −10.0368 | −0.548371 | ||||||||
\(336\) | 13.9825i | 0.762810i | ||||||||
\(337\) | −17.1672 | −0.935157 | −0.467578 | − | 0.883952i | \(-0.654873\pi\) | ||||
−0.467578 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5308 | −0.897830 | ||||||||
\(340\) | 3.04892i | 0.165351i | ||||||||
\(341\) | −11.1933 | −0.606150 | ||||||||
\(342\) | −3.17092 | −0.171463 | ||||||||
\(343\) | 43.4989i | 2.34872i | ||||||||
\(344\) | 7.26875i | 0.391905i | ||||||||
\(345\) | 9.85086i | 0.530352i | ||||||||
\(346\) | 16.5036i | 0.887242i | ||||||||
\(347\) | −24.2760 | −1.30321 | −0.651603 | − | 0.758560i | \(-0.725903\pi\) | ||||
−0.651603 | + | 0.758560i | \(0.725903\pi\) | |||||||
\(348\) | 0.823708 | 0.0441554 | ||||||||
\(349\) | 4.57242i | 0.244756i | 0.992484 | + | 0.122378i | \(0.0390520\pi\) | ||||
−0.992484 | + | 0.122378i | \(0.960948\pi\) | |||||||
\(350\) | 17.0707 | 0.912467 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.61835 | 0.192859 | ||||||||
\(353\) | − 6.07606i | − 0.323396i | −0.986840 | − | 0.161698i | \(-0.948303\pi\) | ||||
0.986840 | − | 0.161698i | \(-0.0516971\pi\) | |||||||
\(354\) | 2.71379 | 0.144236 | ||||||||
\(355\) | −24.7657 | −1.31443 | ||||||||
\(356\) | 2.80194i | 0.148502i | ||||||||
\(357\) | − 11.7409i | − 0.621396i | ||||||||
\(358\) | 10.6340i | 0.562025i | ||||||||
\(359\) | 14.9661i | 0.789883i | 0.918706 | + | 0.394942i | \(0.129235\pi\) | ||||
−0.918706 | + | 0.394942i | \(0.870765\pi\) | |||||||
\(360\) | 8.54288 | 0.450249 | ||||||||
\(361\) | 12.5338 | 0.659673 | ||||||||
\(362\) | − 4.53452i | − 0.238329i | ||||||||
\(363\) | 8.84846 | 0.464424 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.5526 | 1.12811 | ||||||||
\(366\) | 9.76271i | 0.510305i | ||||||||
\(367\) | 37.0834 | 1.93574 | 0.967868 | − | 0.251459i | \(-0.0809105\pi\) | ||||
0.967868 | + | 0.251459i | \(0.0809105\pi\) | |||||||
\(368\) | −10.2373 | −0.533656 | ||||||||
\(369\) | − 1.24698i | − 0.0649152i | ||||||||
\(370\) | − 15.9148i | − 0.827373i | ||||||||
\(371\) | 42.5013i | 2.20656i | ||||||||
\(372\) | 3.39612i | 0.176081i | ||||||||
\(373\) | −36.5090 | −1.89037 | −0.945183 | − | 0.326542i | \(-0.894117\pi\) | ||||
−0.945183 | + | 0.326542i | \(0.894117\pi\) | |||||||
\(374\) | 4.47219 | 0.231251 | ||||||||
\(375\) | 6.02177i | 0.310963i | ||||||||
\(376\) | 39.0780 | 2.01529 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.98792 | −0.307985 | ||||||||
\(379\) | − 26.5851i | − 1.36558i | −0.730613 | − | 0.682792i | \(-0.760765\pi\) | ||||
0.730613 | − | 0.682792i | \(-0.239235\pi\) | |||||||
\(380\) | 3.17092 | 0.162665 | ||||||||
\(381\) | 9.53750 | 0.488621 | ||||||||
\(382\) | − 26.6625i | − 1.36417i | ||||||||
\(383\) | − 14.3502i | − 0.733261i | −0.930367 | − | 0.366630i | \(-0.880511\pi\) | ||||
0.930367 | − | 0.366630i | \(-0.119489\pi\) | |||||||
\(384\) | 6.16421i | 0.314566i | ||||||||
\(385\) | 19.7356i | 1.00582i | ||||||||
\(386\) | −10.5090 | −0.534895 | ||||||||
\(387\) | −2.38404 | −0.121188 | ||||||||
\(388\) | 4.46442i | 0.226647i | ||||||||
\(389\) | 22.6582 | 1.14881 | 0.574407 | − | 0.818570i | \(-0.305233\pi\) | ||||
0.574407 | + | 0.818570i | \(0.305233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.59611 | 0.434724 | ||||||||
\(392\) | 48.9614i | 2.47292i | ||||||||
\(393\) | −5.50902 | −0.277894 | ||||||||
\(394\) | 33.0157 | 1.66330 | ||||||||
\(395\) | − 11.2687i | − 0.566992i | ||||||||
\(396\) | 0.652793i | 0.0328041i | ||||||||
\(397\) | − 7.90754i | − 0.396868i | −0.980114 | − | 0.198434i | \(-0.936414\pi\) | ||||
0.980114 | − | 0.198434i | \(-0.0635856\pi\) | |||||||
\(398\) | − 17.7724i | − 0.890850i | ||||||||
\(399\) | −12.2107 | −0.611301 | ||||||||
\(400\) | 8.30127 | 0.415064 | ||||||||
\(401\) | − 2.93661i | − 0.146647i | −0.997308 | − | 0.0733236i | \(-0.976639\pi\) | ||||
0.997308 | − | 0.0733236i | \(-0.0233606\pi\) | |||||||
\(402\) | 4.46681 | 0.222784 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.18060 | −0.307497 | ||||||||
\(405\) | 2.80194i | 0.139229i | ||||||||
\(406\) | −11.0828 | −0.550029 | ||||||||
\(407\) | 6.68127 | 0.331178 | ||||||||
\(408\) | − 7.45473i | − 0.369064i | ||||||||
\(409\) | 11.7549i | 0.581244i | 0.956838 | + | 0.290622i | \(0.0938623\pi\) | ||||
−0.956838 | + | 0.290622i | \(0.906138\pi\) | |||||||
\(410\) | − 4.35690i | − 0.215172i | ||||||||
\(411\) | − 16.1836i | − 0.798278i | ||||||||
\(412\) | 7.74525 | 0.381581 | ||||||||
\(413\) | 10.4504 | 0.514231 | ||||||||
\(414\) | − 4.38404i | − 0.215464i | ||||||||
\(415\) | −1.82908 | −0.0897862 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.5090 | −0.514629 | ||||||||
\(418\) | − 4.65114i | − 0.227495i | ||||||||
\(419\) | 7.34183 | 0.358672 | 0.179336 | − | 0.983788i | \(-0.442605\pi\) | ||||
0.179336 | + | 0.983788i | \(0.442605\pi\) | |||||||
\(420\) | 5.98792 | 0.292181 | ||||||||
\(421\) | 25.6963i | 1.25236i | 0.779677 | + | 0.626181i | \(0.215383\pi\) | ||||
−0.779677 | + | 0.626181i | \(0.784617\pi\) | |||||||
\(422\) | − 2.30798i | − 0.112351i | ||||||||
\(423\) | 12.8170i | 0.623184i | ||||||||
\(424\) | 26.9855i | 1.31053i | ||||||||
\(425\) | −6.97046 | −0.338117 | ||||||||
\(426\) | 11.0218 | 0.534007 | ||||||||
\(427\) | 37.5948i | 1.81934i | ||||||||
\(428\) | 4.69633 | 0.227006 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.32975 | −0.401696 | ||||||||
\(431\) | 8.94198i | 0.430720i | 0.976535 | + | 0.215360i | \(0.0690925\pi\) | ||||
−0.976535 | + | 0.215360i | \(0.930907\pi\) | |||||||
\(432\) | −2.91185 | −0.140097 | ||||||||
\(433\) | −2.91484 | −0.140078 | −0.0700391 | − | 0.997544i | \(-0.522312\pi\) | ||||
−0.0700391 | + | 0.997544i | \(0.522312\pi\) | |||||||
\(434\) | − 45.6939i | − 2.19338i | ||||||||
\(435\) | 5.18598i | 0.248649i | ||||||||
\(436\) | − 0.476501i | − 0.0228203i | ||||||||
\(437\) | − 8.94007i | − 0.427661i | ||||||||
\(438\) | −9.59179 | −0.458314 | ||||||||
\(439\) | −9.05861 | −0.432344 | −0.216172 | − | 0.976355i | \(-0.569357\pi\) | ||||
−0.216172 | + | 0.976355i | \(0.569357\pi\) | |||||||
\(440\) | 12.5308i | 0.597382i | ||||||||
\(441\) | −16.0586 | −0.764696 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2325 | 0.533672 | 0.266836 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266836 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(444\) | − 2.02715i | − 0.0962041i | ||||||||
\(445\) | −17.6407 | −0.836250 | ||||||||
\(446\) | −23.2567 | −1.10124 | ||||||||
\(447\) | − 14.3502i | − 0.678741i | ||||||||
\(448\) | 42.7362i | 2.01909i | ||||||||
\(449\) | − 28.7579i | − 1.35717i | −0.734522 | − | 0.678585i | \(-0.762593\pi\) | ||||
0.734522 | − | 0.678585i | \(-0.237407\pi\) | |||||||
\(450\) | 3.55496i | 0.167582i | ||||||||
\(451\) | 1.82908 | 0.0861282 | ||||||||
\(452\) | −7.35690 | −0.346039 | ||||||||
\(453\) | 1.96615i | 0.0923777i | ||||||||
\(454\) | −12.1672 | −0.571035 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.75302 | −0.363068 | ||||||||
\(457\) | − 19.0761i | − 0.892341i | −0.894948 | − | 0.446170i | \(-0.852788\pi\) | ||||
0.894948 | − | 0.446170i | \(-0.147212\pi\) | |||||||
\(458\) | −3.57002 | −0.166816 | ||||||||
\(459\) | 2.44504 | 0.114125 | ||||||||
\(460\) | 4.38404i | 0.204407i | ||||||||
\(461\) | 31.7332i | 1.47796i | 0.673727 | + | 0.738981i | \(0.264692\pi\) | ||||
−0.673727 | + | 0.738981i | \(0.735308\pi\) | |||||||
\(462\) | − 8.78315i | − 0.408629i | ||||||||
\(463\) | 36.4784i | 1.69530i | 0.530559 | + | 0.847648i | \(0.321982\pi\) | ||||
−0.530559 | + | 0.847648i | \(0.678018\pi\) | |||||||
\(464\) | −5.38942 | −0.250198 | ||||||||
\(465\) | −21.3817 | −0.991550 | ||||||||
\(466\) | − 7.21446i | − 0.334203i | ||||||||
\(467\) | −13.0000 | −0.601568 | −0.300784 | − | 0.953692i | \(-0.597248\pi\) | ||||
−0.300784 | + | 0.953692i | \(0.597248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.2010 | 0.794271 | ||||||||
\(470\) | 44.7821i | 2.06564i | ||||||||
\(471\) | 10.7017 | 0.493109 | ||||||||
\(472\) | 6.63533 | 0.305416 | ||||||||
\(473\) | − 3.49694i | − 0.160790i | ||||||||
\(474\) | 5.01507i | 0.230350i | ||||||||
\(475\) | 7.24937i | 0.332624i | ||||||||
\(476\) | − 5.22521i | − 0.239497i | ||||||||
\(477\) | −8.85086 | −0.405253 | ||||||||
\(478\) | −8.84415 | −0.404522 | ||||||||
\(479\) | − 5.61655i | − 0.256627i | −0.991734 | − | 0.128313i | \(-0.959044\pi\) | ||||
0.991734 | − | 0.128313i | \(-0.0409563\pi\) | |||||||
\(480\) | 6.91185 | 0.315482 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.86294 | 0.221501 | ||||||||
\(483\) | − 16.8823i | − 0.768172i | ||||||||
\(484\) | 3.93794 | 0.178997 | ||||||||
\(485\) | −28.1075 | −1.27630 | ||||||||
\(486\) | − 1.24698i | − 0.0565641i | ||||||||
\(487\) | − 9.75733i | − 0.442147i | −0.975257 | − | 0.221073i | \(-0.929044\pi\) | ||||
0.975257 | − | 0.221073i | \(-0.0709561\pi\) | |||||||
\(488\) | 23.8702i | 1.08055i | ||||||||
\(489\) | 3.89977i | 0.176354i | ||||||||
\(490\) | −56.1081 | −2.53471 | ||||||||
\(491\) | 7.38835 | 0.333432 | 0.166716 | − | 0.986005i | \(-0.446684\pi\) | ||||
0.166716 | + | 0.986005i | \(0.446684\pi\) | |||||||
\(492\) | − 0.554958i | − 0.0250194i | ||||||||
\(493\) | 4.52542 | 0.203815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.10992 | −0.184727 | ||||||||
\(496\) | − 22.2204i | − 0.997726i | ||||||||
\(497\) | 42.4432 | 1.90384 | ||||||||
\(498\) | 0.814019 | 0.0364771 | ||||||||
\(499\) | − 43.2814i | − 1.93754i | −0.247956 | − | 0.968771i | \(-0.579759\pi\) | ||||
0.247956 | − | 0.968771i | \(-0.420241\pi\) | |||||||
\(500\) | 2.67994i | 0.119851i | ||||||||
\(501\) | 21.0194i | 0.939077i | ||||||||
\(502\) | − 3.04892i | − 0.136080i | ||||||||
\(503\) | 10.7670 | 0.480078 | 0.240039 | − | 0.970763i | \(-0.422840\pi\) | ||||
0.240039 | + | 0.970763i | \(0.422840\pi\) | |||||||
\(504\) | −14.6407 | −0.652149 | ||||||||
\(505\) | − 38.9124i | − 1.73158i | ||||||||
\(506\) | 6.43057 | 0.285874 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.24459 | 0.188323 | ||||||||
\(509\) | − 41.5448i | − 1.84144i | −0.390223 | − | 0.920720i | \(-0.627602\pi\) | ||||
0.390223 | − | 0.920720i | \(-0.372398\pi\) | |||||||
\(510\) | 8.54288 | 0.378285 | ||||||||
\(511\) | −36.9366 | −1.63398 | ||||||||
\(512\) | 24.9390i | 1.10216i | ||||||||
\(513\) | − 2.54288i | − 0.112271i | ||||||||
\(514\) | − 17.6203i | − 0.777197i | ||||||||
\(515\) | 48.7633i | 2.14877i | ||||||||
\(516\) | −1.06100 | −0.0467079 | ||||||||
\(517\) | −18.8001 | −0.826829 | ||||||||
\(518\) | 27.2747i | 1.19838i | ||||||||
\(519\) | −13.2349 | −0.580948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7198 | 1.12680 | 0.563402 | − | 0.826183i | \(-0.309492\pi\) | ||||
0.563402 | + | 0.826183i | \(0.309492\pi\) | |||||||
\(522\) | − 2.30798i | − 0.101017i | ||||||||
\(523\) | 8.59286 | 0.375739 | 0.187870 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187870 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(524\) | −2.45175 | −0.107105 | ||||||||
\(525\) | 13.6896i | 0.597464i | ||||||||
\(526\) | 29.5827i | 1.28987i | ||||||||
\(527\) | 18.6582i | 0.812763i | ||||||||
\(528\) | − 4.27114i | − 0.185878i | ||||||||
\(529\) | −10.6396 | −0.462593 | ||||||||
\(530\) | −30.9245 | −1.34328 | ||||||||
\(531\) | 2.17629i | 0.0944430i | ||||||||
\(532\) | −5.43429 | −0.235606 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.85086 | 0.339740 | ||||||||
\(535\) | 29.5676i | 1.27832i | ||||||||
\(536\) | 10.9215 | 0.471739 | ||||||||
\(537\) | −8.52781 | −0.368002 | ||||||||
\(538\) | 7.37734i | 0.318060i | ||||||||
\(539\) | − 23.5550i | − 1.01458i | ||||||||
\(540\) | 1.24698i | 0.0536615i | ||||||||
\(541\) | − 31.3534i | − 1.34799i | −0.738736 | − | 0.673995i | \(-0.764577\pi\) | ||||
0.738736 | − | 0.673995i | \(-0.235423\pi\) | |||||||
\(542\) | 3.97823 | 0.170880 | ||||||||
\(543\) | 3.63640 | 0.156053 | ||||||||
\(544\) | − 6.03146i | − 0.258597i | ||||||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9342 | 0.852325 | 0.426163 | − | 0.904647i | \(-0.359865\pi\) | ||||
0.426163 | + | 0.904647i | \(0.359865\pi\) | |||||||
\(548\) | − 7.20237i | − 0.307670i | ||||||||
\(549\) | −7.82908 | −0.334137 | ||||||||
\(550\) | −5.21446 | −0.222345 | ||||||||
\(551\) | − 4.70650i | − 0.200503i | ||||||||
\(552\) | − 10.7192i | − 0.456238i | ||||||||
\(553\) | 19.3123i | 0.821242i | ||||||||
\(554\) | 27.3545i | 1.16218i | ||||||||
\(555\) | 12.7627 | 0.541747 | ||||||||
\(556\) | −4.67696 | −0.198347 | ||||||||
\(557\) | − 33.2349i | − 1.40821i | −0.710097 | − | 0.704104i | \(-0.751349\pi\) | ||||
0.710097 | − | 0.704104i | \(-0.248651\pi\) | |||||||
\(558\) | 9.51573 | 0.402833 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −39.1782 | −1.65558 | ||||||||
\(561\) | 3.58642i | 0.151419i | ||||||||
\(562\) | −14.9517 | −0.630698 | ||||||||
\(563\) | −3.87130 | −0.163156 | −0.0815779 | − | 0.996667i | \(-0.525996\pi\) | ||||
−0.0815779 | + | 0.996667i | \(0.525996\pi\) | |||||||
\(564\) | 5.70410i | 0.240186i | ||||||||
\(565\) | − 46.3183i | − 1.94862i | ||||||||
\(566\) | − 17.9148i | − 0.753017i | ||||||||
\(567\) | − 4.80194i | − 0.201662i | ||||||||
\(568\) | 26.9487 | 1.13074 | ||||||||
\(569\) | −20.1457 | −0.844551 | −0.422276 | − | 0.906468i | \(-0.638769\pi\) | ||||
−0.422276 | + | 0.906468i | \(0.638769\pi\) | |||||||
\(570\) | − 8.88471i | − 0.372139i | ||||||||
\(571\) | 32.1269 | 1.34447 | 0.672234 | − | 0.740338i | \(-0.265335\pi\) | ||||
0.672234 | + | 0.740338i | \(0.265335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3817 | 0.893231 | ||||||||
\(574\) | 7.46681i | 0.311659i | ||||||||
\(575\) | −10.0228 | −0.417981 | ||||||||
\(576\) | −8.89977 | −0.370824 | ||||||||
\(577\) | − 16.7506i | − 0.697338i | −0.937246 | − | 0.348669i | \(-0.886634\pi\) | ||||
0.937246 | − | 0.348669i | \(-0.113366\pi\) | |||||||
\(578\) | 13.7439i | 0.571672i | ||||||||
\(579\) | − 8.42758i | − 0.350238i | ||||||||
\(580\) | 2.30798i | 0.0958336i | ||||||||
\(581\) | 3.13467 | 0.130048 | ||||||||
\(582\) | 12.5090 | 0.518516 | ||||||||
\(583\) | − 12.9825i | − 0.537682i | ||||||||
\(584\) | −23.4523 | −0.970465 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.3913 | −0.966287 | ||||||||
\(587\) | − 6.73795i | − 0.278105i | −0.990285 | − | 0.139053i | \(-0.955594\pi\) | ||||
0.990285 | − | 0.139053i | \(-0.0444057\pi\) | |||||||
\(588\) | −7.14675 | −0.294727 | ||||||||
\(589\) | 19.4047 | 0.799559 | ||||||||
\(590\) | 7.60388i | 0.313047i | ||||||||
\(591\) | 26.4765i | 1.08910i | ||||||||
\(592\) | 13.2634i | 0.545121i | ||||||||
\(593\) | − 18.1172i | − 0.743985i | −0.928236 | − | 0.371992i | \(-0.878675\pi\) | ||||
0.928236 | − | 0.371992i | \(-0.121325\pi\) | |||||||
\(594\) | 1.82908 | 0.0750483 | ||||||||
\(595\) | 32.8974 | 1.34866 | ||||||||
\(596\) | − 6.38644i | − 0.261599i | ||||||||
\(597\) | 14.2524 | 0.583310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7851 | −1.09441 | −0.547204 | − | 0.836999i | \(-0.684308\pi\) | ||||
−0.547204 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(600\) | 8.69202i | 0.354850i | ||||||||
\(601\) | −4.70171 | −0.191787 | −0.0958934 | − | 0.995392i | \(-0.530571\pi\) | ||||
−0.0958934 | + | 0.995392i | \(0.530571\pi\) | |||||||
\(602\) | 14.2755 | 0.581824 | ||||||||
\(603\) | 3.58211i | 0.145875i | ||||||||
\(604\) | 0.875018i | 0.0356040i | ||||||||
\(605\) | 24.7928i | 1.00797i | ||||||||
\(606\) | 17.3177i | 0.703482i | ||||||||
\(607\) | 27.6396 | 1.12186 | 0.560929 | − | 0.827864i | \(-0.310444\pi\) | ||||
0.560929 | + | 0.827864i | \(0.310444\pi\) | |||||||
\(608\) | −6.27280 | −0.254396 | ||||||||
\(609\) | − 8.88769i | − 0.360147i | ||||||||
\(610\) | −27.3545 | −1.10755 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.08815 | 0.0439857 | ||||||||
\(613\) | 48.1782i | 1.94590i | 0.231017 | + | 0.972950i | \(0.425795\pi\) | ||||
−0.231017 | + | 0.972950i | \(0.574205\pi\) | |||||||
\(614\) | −31.9554 | −1.28961 | ||||||||
\(615\) | 3.49396 | 0.140890 | ||||||||
\(616\) | − 21.4752i | − 0.865259i | ||||||||
\(617\) | 30.3043i | 1.22000i | 0.792400 | + | 0.610002i | \(0.208831\pi\) | ||||
−0.792400 | + | 0.610002i | \(0.791169\pi\) | |||||||
\(618\) | − 21.7017i | − 0.872971i | ||||||||
\(619\) | 10.9041i | 0.438272i | 0.975694 | + | 0.219136i | \(0.0703239\pi\) | ||||
−0.975694 | + | 0.219136i | \(0.929676\pi\) | |||||||
\(620\) | −9.51573 | −0.382161 | ||||||||
\(621\) | 3.51573 | 0.141081 | ||||||||
\(622\) | 14.1927i | 0.569075i | ||||||||
\(623\) | 30.2325 | 1.21124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1269 | −1.24508 | ||||||||
\(626\) | − 34.3846i | − 1.37429i | ||||||||
\(627\) | 3.72992 | 0.148959 | ||||||||
\(628\) | 4.76271 | 0.190053 | ||||||||
\(629\) | − 11.1371i | − 0.444064i | ||||||||
\(630\) | − 16.7778i | − 0.668443i | ||||||||
\(631\) | 10.4523i | 0.416101i | 0.978118 | + | 0.208050i | \(0.0667118\pi\) | ||||
−0.978118 | + | 0.208050i | \(0.933288\pi\) | |||||||
\(632\) | 12.2620i | 0.487758i | ||||||||
\(633\) | 1.85086 | 0.0735649 | ||||||||
\(634\) | −14.0406 | −0.557622 | ||||||||
\(635\) | 26.7235i | 1.06049i | ||||||||
\(636\) | −3.93900 | −0.156192 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.38537 | 0.134028 | ||||||||
\(639\) | 8.83877i | 0.349656i | ||||||||
\(640\) | −17.2717 | −0.682725 | ||||||||
\(641\) | 17.5942 | 0.694929 | 0.347464 | − | 0.937693i | \(-0.387043\pi\) | ||||
0.347464 | + | 0.937693i | \(0.387043\pi\) | |||||||
\(642\) | − 13.1588i | − 0.519338i | ||||||||
\(643\) | 22.6058i | 0.891486i | 0.895161 | + | 0.445743i | \(0.147060\pi\) | ||||
−0.895161 | + | 0.445743i | \(0.852940\pi\) | |||||||
\(644\) | − 7.51334i | − 0.296067i | ||||||||
\(645\) | − 6.67994i | − 0.263022i | ||||||||
\(646\) | −7.75302 | −0.305039 | ||||||||
\(647\) | 24.7918 | 0.974665 | 0.487333 | − | 0.873216i | \(-0.337970\pi\) | ||||
0.487333 | + | 0.873216i | \(0.337970\pi\) | |||||||
\(648\) | − 3.04892i | − 0.119773i | ||||||||
\(649\) | −3.19221 | −0.125305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6437 | 1.43618 | ||||||||
\(652\) | 1.73556i | 0.0679699i | ||||||||
\(653\) | −21.8106 | −0.853513 | −0.426757 | − | 0.904367i | \(-0.640344\pi\) | ||||
−0.426757 | + | 0.904367i | \(0.640344\pi\) | |||||||
\(654\) | −1.33513 | −0.0522075 | ||||||||
\(655\) | − 15.4359i | − 0.603132i | ||||||||
\(656\) | 3.63102i | 0.141768i | ||||||||
\(657\) | − 7.69202i | − 0.300094i | ||||||||
\(658\) | − 76.7472i | − 2.99192i | ||||||||
\(659\) | 16.5526 | 0.644796 | 0.322398 | − | 0.946604i | \(-0.395511\pi\) | ||||
0.322398 | + | 0.946604i | \(0.395511\pi\) | |||||||
\(660\) | −1.82908 | −0.0711970 | ||||||||
\(661\) | 15.9541i | 0.620541i | 0.950648 | + | 0.310271i | \(0.100420\pi\) | ||||
−0.950648 | + | 0.310271i | \(0.899580\pi\) | |||||||
\(662\) | −14.8471 | −0.577050 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.99031 | 0.0772391 | ||||||||
\(665\) | − 34.2137i | − 1.32675i | ||||||||
\(666\) | −5.67994 | −0.220093 | ||||||||
\(667\) | 6.50711 | 0.251956 | ||||||||
\(668\) | 9.35450i | 0.361937i | ||||||||
\(669\) | − 18.6504i | − 0.721066i | ||||||||
\(670\) | 12.5157i | 0.483525i | ||||||||
\(671\) | − 11.4838i | − 0.443327i | ||||||||
\(672\) | −11.8455 | −0.456949 | ||||||||
\(673\) | 7.38835 | 0.284800 | 0.142400 | − | 0.989809i | \(-0.454518\pi\) | ||||
0.142400 | + | 0.989809i | \(0.454518\pi\) | |||||||
\(674\) | 21.4071i | 0.824572i | ||||||||
\(675\) | −2.85086 | −0.109729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1454 | −0.851118 | −0.425559 | − | 0.904931i | \(-0.639922\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639922\pi\) | |||||||
\(678\) | 20.6136i | 0.791659i | ||||||||
\(679\) | 48.1704 | 1.84861 | ||||||||
\(680\) | 20.8877 | 0.801006 | ||||||||
\(681\) | − 9.75733i | − 0.373902i | ||||||||
\(682\) | 13.9578i | 0.534471i | ||||||||
\(683\) | − 9.10023i | − 0.348211i | −0.984727 | − | 0.174105i | \(-0.944297\pi\) | ||||
0.984727 | − | 0.174105i | \(-0.0557033\pi\) | |||||||
\(684\) | − 1.13169i | − 0.0432711i | ||||||||
\(685\) | 45.3454 | 1.73256 | ||||||||
\(686\) | 54.2422 | 2.07098 | ||||||||
\(687\) | − 2.86294i | − 0.109228i | ||||||||
\(688\) | 6.94198 | 0.264661 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.2838 | 0.467637 | ||||||||
\(691\) | 13.7711i | 0.523876i | 0.965085 | + | 0.261938i | \(0.0843616\pi\) | ||||
−0.965085 | + | 0.261938i | \(0.915638\pi\) | |||||||
\(692\) | −5.89008 | −0.223907 | ||||||||
\(693\) | 7.04354 | 0.267562 | ||||||||
\(694\) | 30.2717i | 1.14910i | ||||||||
\(695\) | − 29.4456i | − 1.11694i | ||||||||
\(696\) | − 5.64310i | − 0.213901i | ||||||||
\(697\) | − 3.04892i | − 0.115486i | ||||||||
\(698\) | 5.70171 | 0.215813 | ||||||||
\(699\) | 5.78554 | 0.218829 | ||||||||
\(700\) | 6.09246i | 0.230273i | ||||||||
\(701\) | −46.5090 | −1.75662 | −0.878311 | − | 0.478090i | \(-0.841329\pi\) | ||||
−0.878311 | + | 0.478090i | \(0.841329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5827 | −0.436850 | ||||||||
\(704\) | − 13.0543i | − 0.492002i | ||||||||
\(705\) | −35.9124 | −1.35254 | ||||||||
\(706\) | −7.57673 | −0.285154 | ||||||||
\(707\) | 66.6878i | 2.50805i | ||||||||
\(708\) | 0.968541i | 0.0364000i | ||||||||
\(709\) | − 7.24565i | − 0.272116i | −0.990701 | − | 0.136058i | \(-0.956557\pi\) | ||||
0.990701 | − | 0.136058i | \(-0.0434434\pi\) | |||||||
\(710\) | 30.8823i | 1.15899i | ||||||||
\(711\) | −4.02177 | −0.150828 | ||||||||
\(712\) | 19.1957 | 0.719388 | ||||||||
\(713\) | 26.8286i | 1.00474i | ||||||||
\(714\) | −14.6407 | −0.547915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.79523 | −0.141835 | ||||||||
\(717\) | − 7.09246i | − 0.264873i | ||||||||
\(718\) | 18.6625 | 0.696478 | ||||||||
\(719\) | −25.5147 | −0.951536 | −0.475768 | − | 0.879571i | \(-0.657830\pi\) | ||||
−0.475768 | + | 0.879571i | \(0.657830\pi\) | |||||||
\(720\) | − 8.15883i | − 0.304062i | ||||||||
\(721\) | − 83.5701i | − 3.11231i | ||||||||
\(722\) | − 15.6294i | − 0.581665i | ||||||||
\(723\) | 3.89977i | 0.145034i | ||||||||
\(724\) | 1.61835 | 0.0601455 | ||||||||
\(725\) | −5.27652 | −0.195965 | ||||||||
\(726\) | − 11.0339i | − 0.409505i | ||||||||
\(727\) | 14.4873 | 0.537303 | 0.268651 | − | 0.963238i | \(-0.413422\pi\) | ||||
0.268651 | + | 0.963238i | \(0.413422\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 26.8756i | − 0.994711i | ||||||||
\(731\) | −5.82908 | −0.215596 | ||||||||
\(732\) | −3.48427 | −0.128782 | ||||||||
\(733\) | 37.5036i | 1.38523i | 0.721308 | + | 0.692614i | \(0.243541\pi\) | ||||
−0.721308 | + | 0.692614i | \(0.756459\pi\) | |||||||
\(734\) | − 46.2422i | − 1.70683i | ||||||||
\(735\) | − 44.9952i | − 1.65967i | ||||||||
\(736\) | − 8.67264i | − 0.319678i | ||||||||
\(737\) | −5.25428 | −0.193544 | ||||||||
\(738\) | −1.55496 | −0.0572388 | ||||||||
\(739\) | − 43.1876i | − 1.58868i | −0.607472 | − | 0.794341i | \(-0.707816\pi\) | ||||
0.607472 | − | 0.794341i | \(-0.292184\pi\) | |||||||
\(740\) | 5.67994 | 0.208799 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.9982 | 1.94563 | ||||||||
\(743\) | 13.4765i | 0.494405i | 0.968964 | + | 0.247202i | \(0.0795113\pi\) | ||||
−0.968964 | + | 0.247202i | \(0.920489\pi\) | |||||||
\(744\) | 23.2664 | 0.852986 | ||||||||
\(745\) | 40.2083 | 1.47312 | ||||||||
\(746\) | 45.5260i | 1.66683i | ||||||||
\(747\) | 0.652793i | 0.0238844i | ||||||||
\(748\) | 1.59611i | 0.0583594i | ||||||||
\(749\) | − 50.6728i | − 1.85154i | ||||||||
\(750\) | 7.50902 | 0.274191 | ||||||||
\(751\) | −35.5894 | −1.29868 | −0.649338 | − | 0.760500i | \(-0.724954\pi\) | ||||
−0.649338 | + | 0.760500i | \(0.724954\pi\) | |||||||
\(752\) | − 37.3212i | − 1.36097i | ||||||||
\(753\) | 2.44504 | 0.0891023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.50902 | −0.200494 | ||||||||
\(756\) | − 2.13706i | − 0.0777242i | ||||||||
\(757\) | −12.2107 | −0.443807 | −0.221903 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221903 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(758\) | −33.1511 | −1.20410 | ||||||||
\(759\) | 5.15691i | 0.187184i | ||||||||
\(760\) | − 21.7235i | − 0.787993i | ||||||||
\(761\) | − 30.9071i | − 1.12038i | −0.828364 | − | 0.560190i | \(-0.810728\pi\) | ||||
0.828364 | − | 0.560190i | \(-0.189272\pi\) | |||||||
\(762\) | − 11.8931i | − 0.430840i | ||||||||
\(763\) | −5.14138 | −0.186130 | ||||||||
\(764\) | 9.51573 | 0.344267 | ||||||||
\(765\) | 6.85086i | 0.247693i | ||||||||
\(766\) | −17.8944 | −0.646551 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.1129 | −0.364918 | ||||||||
\(769\) | 11.9892i | 0.432343i | 0.976355 | + | 0.216172i | \(0.0693571\pi\) | ||||
−0.976355 | + | 0.216172i | \(0.930643\pi\) | |||||||
\(770\) | 24.6098 | 0.886877 | ||||||||
\(771\) | 14.1304 | 0.508892 | ||||||||
\(772\) | − 3.75063i | − 0.134988i | ||||||||
\(773\) | 43.9661i | 1.58135i | 0.612235 | + | 0.790676i | \(0.290271\pi\) | ||||
−0.612235 | + | 0.790676i | \(0.709729\pi\) | |||||||
\(774\) | 2.97285i | 0.106857i | ||||||||
\(775\) | − 21.7549i | − 0.781460i | ||||||||
\(776\) | 30.5851 | 1.09794 | ||||||||
\(777\) | −21.8726 | −0.784676 | ||||||||
\(778\) | − 28.2543i | − 1.01296i | ||||||||
\(779\) | −3.17092 | −0.113610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9648 | −0.463918 | ||||||||
\(782\) | − 10.7192i | − 0.383317i | ||||||||
\(783\) | 1.85086 | 0.0661442 | ||||||||
\(784\) | 46.7603 | 1.67001 | ||||||||
\(785\) | 29.9855i | 1.07023i | ||||||||
\(786\) | 6.86964i | 0.245032i | ||||||||
\(787\) | − 30.3763i | − 1.08280i | −0.840766 | − | 0.541399i | \(-0.817895\pi\) | ||||
0.840766 | − | 0.541399i | \(-0.182105\pi\) | |||||||
\(788\) | 11.7832i | 0.419757i | ||||||||
\(789\) | −23.7235 | −0.844578 | ||||||||
\(790\) | −14.0519 | −0.499944 | ||||||||
\(791\) | 79.3798i | 2.82242i | ||||||||
\(792\) | 4.47219 | 0.158912 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.86054 | −0.349938 | ||||||||
\(795\) | − 24.7995i | − 0.879549i | ||||||||
\(796\) | 6.34290 | 0.224818 | ||||||||
\(797\) | −52.5763 | −1.86235 | −0.931173 | − | 0.364577i | \(-0.881214\pi\) | ||||
−0.931173 | + | 0.364577i | \(0.881214\pi\) | |||||||
\(798\) | 15.2265i | 0.539014i | ||||||||
\(799\) | 31.3381i | 1.10866i | ||||||||
\(800\) | 7.03252i | 0.248637i | ||||||||
\(801\) | 6.29590i | 0.222455i | ||||||||
\(802\) | −3.66189 | −0.129306 | ||||||||
\(803\) | 11.2828 | 0.398160 | ||||||||
\(804\) | 1.59419i | 0.0562226i | ||||||||
\(805\) | 47.3032 | 1.66722 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.91617 | −0.208259 | ||||||||
\(808\) | 42.3424i | 1.48960i | ||||||||
\(809\) | 49.4215 | 1.73757 | 0.868783 | − | 0.495193i | \(-0.164903\pi\) | ||||
0.868783 | + | 0.495193i | \(0.164903\pi\) | |||||||
\(810\) | 3.49396 | 0.122765 | ||||||||
\(811\) | − 1.36526i | − 0.0479406i | −0.999713 | − | 0.0239703i | \(-0.992369\pi\) | ||||
0.999713 | − | 0.0239703i | \(-0.00763072\pi\) | |||||||
\(812\) | − 3.95539i | − 0.138807i | ||||||||
\(813\) | 3.19029i | 0.111888i | ||||||||
\(814\) | − 8.33140i | − 0.292016i | ||||||||
\(815\) | −10.9269 | −0.382753 | ||||||||
\(816\) | −7.11960 | −0.249236 | ||||||||
\(817\) | 6.06233i | 0.212094i | ||||||||
\(818\) | 14.6582 | 0.512511 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.55496 | 0.0543015 | ||||||||
\(821\) | 0.665939i | 0.0232414i | 0.999932 | + | 0.0116207i | \(0.00369907\pi\) | ||||
−0.999932 | + | 0.0116207i | \(0.996301\pi\) | |||||||
\(822\) | −20.1806 | −0.703879 | ||||||||
\(823\) | 10.0592 | 0.350642 | 0.175321 | − | 0.984511i | \(-0.443904\pi\) | ||||
0.175321 | + | 0.984511i | \(0.443904\pi\) | |||||||
\(824\) | − 53.0616i | − 1.84849i | ||||||||
\(825\) | − 4.18167i | − 0.145587i | ||||||||
\(826\) | − 13.0315i | − 0.453422i | ||||||||
\(827\) | 37.3038i | 1.29718i | 0.761138 | + | 0.648590i | \(0.224641\pi\) | ||||
−0.761138 | + | 0.648590i | \(0.775359\pi\) | |||||||
\(828\) | 1.56465 | 0.0543752 | ||||||||
\(829\) | 42.6209 | 1.48028 | 0.740142 | − | 0.672451i | \(-0.234758\pi\) | ||||
0.740142 | + | 0.672451i | \(0.234758\pi\) | |||||||
\(830\) | 2.28083i | 0.0791688i | ||||||||
\(831\) | −21.9366 | −0.760973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.2640 | −1.36042 | ||||||||
\(834\) | 13.1045i | 0.453773i | ||||||||
\(835\) | −58.8950 | −2.03815 | ||||||||
\(836\) | 1.65997 | 0.0574113 | ||||||||
\(837\) | 7.63102i | 0.263767i | ||||||||
\(838\) | − 9.15511i | − 0.316258i | ||||||||
\(839\) | − 4.14005i | − 0.142930i | −0.997443 | − | 0.0714652i | \(-0.977233\pi\) | ||||
0.997443 | − | 0.0714652i | \(-0.0227675\pi\) | |||||||
\(840\) | − 41.0224i | − 1.41541i | ||||||||
\(841\) | −25.5743 | −0.881874 | ||||||||
\(842\) | 32.0428 | 1.10427 | ||||||||
\(843\) | − 11.9903i | − 0.412968i | ||||||||
\(844\) | 0.823708 | 0.0283532 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.9825 | 0.549491 | ||||||||
\(847\) | − 42.4898i | − 1.45997i | ||||||||
\(848\) | 25.7724 | 0.885028 | ||||||||
\(849\) | 14.3666 | 0.493060 | ||||||||
\(850\) | 8.69202i | 0.298134i | ||||||||
\(851\) | − 16.0140i | − 0.548953i | ||||||||
\(852\) | 3.93362i | 0.134764i | ||||||||
\(853\) | − 17.3502i | − 0.594059i | −0.954868 | − | 0.297030i | \(-0.904004\pi\) | ||||
0.954868 | − | 0.297030i | \(-0.0959960\pi\) | |||||||
\(854\) | 46.8799 | 1.60420 | ||||||||
\(855\) | 7.12498 | 0.243669 | ||||||||
\(856\) | − 32.1739i | − 1.09968i | ||||||||
\(857\) | −41.0180 | −1.40115 | −0.700575 | − | 0.713579i | \(-0.747073\pi\) | ||||
−0.700575 | + | 0.713579i | \(0.747073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.59286 | 0.224945 | 0.112473 | − | 0.993655i | \(-0.464123\pi\) | ||||
0.112473 | + | 0.993655i | \(0.464123\pi\) | |||||||
\(860\) | − 2.97285i | − 0.101373i | ||||||||
\(861\) | −5.98792 | −0.204068 | ||||||||
\(862\) | 11.1505 | 0.379787 | ||||||||
\(863\) | − 16.6455i | − 0.566619i | −0.959028 | − | 0.283310i | \(-0.908568\pi\) | ||||
0.959028 | − | 0.283310i | \(-0.0914324\pi\) | |||||||
\(864\) | − 2.46681i | − 0.0839227i | ||||||||
\(865\) | − 37.0834i | − 1.26087i | ||||||||
\(866\) | 3.63474i | 0.123514i | ||||||||
\(867\) | −11.0218 | −0.374319 | ||||||||
\(868\) | 16.3080 | 0.553529 | ||||||||
\(869\) | − 5.89918i | − 0.200116i | ||||||||
\(870\) | 6.46681 | 0.219245 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.26444 | −0.110548 | ||||||||
\(873\) | 10.0315i | 0.339513i | ||||||||
\(874\) | −11.1481 | −0.377089 | ||||||||
\(875\) | 28.9162 | 0.977545 | ||||||||
\(876\) | − 3.42327i | − 0.115662i | ||||||||
\(877\) | 54.4965i | 1.84022i | 0.391666 | + | 0.920108i | \(0.371899\pi\) | ||||
−0.391666 | + | 0.920108i | \(0.628101\pi\) | |||||||
\(878\) | 11.2959i | 0.381218i | ||||||||
\(879\) | − 18.7584i | − 0.632705i | ||||||||
\(880\) | 11.9675 | 0.403424 | ||||||||
\(881\) | 9.00670 | 0.303444 | 0.151722 | − | 0.988423i | \(-0.451518\pi\) | ||||
0.151722 | + | 0.988423i | \(0.451518\pi\) | |||||||
\(882\) | 20.0248i | 0.674269i | ||||||||
\(883\) | −18.8907 | −0.635722 | −0.317861 | − | 0.948137i | \(-0.602965\pi\) | ||||
−0.317861 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.09783 | −0.204976 | ||||||||
\(886\) | − 14.0067i | − 0.470564i | ||||||||
\(887\) | −46.9124 | −1.57517 | −0.787583 | − | 0.616209i | \(-0.788668\pi\) | ||||
−0.787583 | + | 0.616209i | \(0.788668\pi\) | |||||||
\(888\) | −13.8877 | −0.466040 | ||||||||
\(889\) | − 45.7985i | − 1.53603i | ||||||||
\(890\) | 21.9976i | 0.737361i | ||||||||
\(891\) | 1.46681i | 0.0491401i | ||||||||
\(892\) | − 8.30021i | − 0.277912i | ||||||||
\(893\) | 32.5921 | 1.09065 | ||||||||
\(894\) | −17.8944 | −0.598478 | ||||||||
\(895\) | − 23.8944i | − 0.798702i | ||||||||
\(896\) | 29.6002 | 0.988872 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.8605 | −1.19668 | ||||||||
\(899\) | 14.1239i | 0.471059i | ||||||||
\(900\) | −1.26875 | −0.0422917 | ||||||||
\(901\) | −21.6407 | −0.720957 | ||||||||
\(902\) | − 2.28083i | − 0.0759434i | ||||||||
\(903\) | 11.4480i | 0.380966i | ||||||||
\(904\) | 50.4010i | 1.67631i | ||||||||
\(905\) | 10.1890i | 0.338693i | ||||||||
\(906\) | 2.45175 | 0.0814538 | ||||||||
\(907\) | 35.3013 | 1.17216 | 0.586080 | − | 0.810253i | \(-0.300671\pi\) | ||||
0.586080 | + | 0.810253i | \(0.300671\pi\) | |||||||
\(908\) | − 4.34242i | − 0.144108i | ||||||||
\(909\) | −13.8877 | −0.460626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.80731 | −0.324931 | −0.162465 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162465 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(912\) | 7.40449i | 0.245187i | ||||||||
\(913\) | −0.957524 | −0.0316894 | ||||||||
\(914\) | −23.7875 | −0.786819 | ||||||||
\(915\) | − 21.9366i | − 0.725202i | ||||||||
\(916\) | − 1.27413i | − 0.0420983i | ||||||||
\(917\) | 26.4540i | 0.873588i | ||||||||
\(918\) | − 3.04892i | − 0.100629i | ||||||||
\(919\) | 18.4655 | 0.609120 | 0.304560 | − | 0.952493i | \(-0.401491\pi\) | ||||
0.304560 | + | 0.952493i | \(0.401491\pi\) | |||||||
\(920\) | 30.0344 | 0.990206 | ||||||||
\(921\) | − 25.6262i | − 0.844413i | ||||||||
\(922\) | 39.5706 | 1.30319 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.13467 | 0.103123 | ||||||||
\(925\) | 12.9855i | 0.426961i | ||||||||
\(926\) | 45.4878 | 1.49482 | ||||||||
\(927\) | 17.4034 | 0.571603 | ||||||||
\(928\) | − 4.56571i | − 0.149877i | ||||||||
\(929\) | − 25.6267i | − 0.840785i | −0.907342 | − | 0.420393i | \(-0.861892\pi\) | ||||
0.907342 | − | 0.420393i | \(-0.138108\pi\) | |||||||
\(930\) | 26.6625i | 0.874297i | ||||||||
\(931\) | 40.8351i | 1.33831i | ||||||||
\(932\) | 2.57481 | 0.0843407 | ||||||||
\(933\) | −11.3817 | −0.372618 | ||||||||
\(934\) | 16.2107i | 0.530431i | ||||||||
\(935\) | −10.0489 | −0.328635 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.54932 | 0.246625 | 0.123313 | − | 0.992368i | \(-0.460648\pi\) | ||||
0.123313 | + | 0.992368i | \(0.460648\pi\) | |||||||
\(938\) | − 21.4494i | − 0.700346i | ||||||||
\(939\) | 27.5743 | 0.899854 | ||||||||
\(940\) | −15.9825 | −0.521293 | ||||||||
\(941\) | − 12.6418i | − 0.412110i | −0.978540 | − | 0.206055i | \(-0.933937\pi\) | ||||
0.978540 | − | 0.206055i | \(-0.0660626\pi\) | |||||||
\(942\) | − 13.3448i | − 0.434798i | ||||||||
\(943\) | − 4.38404i | − 0.142764i | ||||||||
\(944\) | − 6.33704i | − 0.206253i | ||||||||
\(945\) | 13.4547 | 0.437682 | ||||||||
\(946\) | −4.36062 | −0.141776 | ||||||||
\(947\) | − 27.9801i | − 0.909233i | −0.890687 | − | 0.454616i | \(-0.849776\pi\) | ||||
0.890687 | − | 0.454616i | \(-0.150224\pi\) | |||||||
\(948\) | −1.78986 | −0.0581318 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.03982 | 0.293290 | ||||||||
\(951\) | − 11.2597i | − 0.365119i | ||||||||
\(952\) | −35.7972 | −1.16019 | ||||||||
\(953\) | −4.00239 | −0.129650 | −0.0648251 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648251 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(954\) | 11.0368i | 0.357331i | ||||||||
\(955\) | 59.9101i | 1.93864i | ||||||||
\(956\) | − 3.15644i | − 0.102087i | ||||||||
\(957\) | 2.71486i | 0.0877589i | ||||||||
\(958\) | −7.00372 | −0.226280 | ||||||||
\(959\) | −77.7126 | −2.50947 | ||||||||
\(960\) | − 24.9366i | − 0.804826i | ||||||||
\(961\) | −27.2325 | −0.878468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5526 | 0.340052 | ||||||||
\(964\) | 1.73556i | 0.0558987i | ||||||||
\(965\) | 23.6136 | 0.760148 | ||||||||
\(966\) | −21.0519 | −0.677334 | ||||||||
\(967\) | 12.2239i | 0.393094i | 0.980494 | + | 0.196547i | \(0.0629728\pi\) | ||||
−0.980494 | + | 0.196547i | \(0.937027\pi\) | |||||||
\(968\) | − 26.9782i | − 0.867113i | ||||||||
\(969\) | − 6.21744i | − 0.199733i | ||||||||
\(970\) | 35.0495i | 1.12537i | ||||||||
\(971\) | −23.6401 | −0.758648 | −0.379324 | − | 0.925264i | \(-0.623843\pi\) | ||||
−0.379324 | + | 0.925264i | \(0.623843\pi\) | |||||||
\(972\) | 0.445042 | 0.0142747 | ||||||||
\(973\) | 50.4637i | 1.61779i | ||||||||
\(974\) | −12.1672 | −0.389862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7972 | 0.729719 | ||||||||
\(977\) | 18.7313i | 0.599266i | 0.954055 | + | 0.299633i | \(0.0968642\pi\) | ||||
−0.954055 | + | 0.299633i | \(0.903136\pi\) | |||||||
\(978\) | 4.86294 | 0.155500 | ||||||||
\(979\) | −9.23490 | −0.295149 | ||||||||
\(980\) | − 20.0248i | − 0.639667i | ||||||||
\(981\) | − 1.07069i | − 0.0341844i | ||||||||
\(982\) | − 9.21313i | − 0.294003i | ||||||||
\(983\) | − 12.0954i | − 0.385785i | −0.981220 | − | 0.192892i | \(-0.938213\pi\) | ||||
0.981220 | − | 0.192892i | \(-0.0617868\pi\) | |||||||
\(984\) | −3.80194 | −0.121201 | ||||||||
\(985\) | −74.1855 | −2.36375 | ||||||||
\(986\) | − 5.64310i | − 0.179713i | ||||||||
\(987\) | 61.5465 | 1.95905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.38165 | −0.266521 | ||||||||
\(990\) | 5.12498i | 0.162883i | ||||||||
\(991\) | −28.5526 | −0.907002 | −0.453501 | − | 0.891256i | \(-0.649825\pi\) | ||||
−0.453501 | + | 0.891256i | \(0.649825\pi\) | |||||||
\(992\) | 18.8243 | 0.597672 | ||||||||
\(993\) | − 11.9065i | − 0.377841i | ||||||||
\(994\) | − 52.9259i | − 1.67871i | ||||||||
\(995\) | 39.9342i | 1.26600i | ||||||||
\(996\) | 0.290520i | 0.00920548i | ||||||||
\(997\) | −23.9347 | −0.758019 | −0.379010 | − | 0.925393i | \(-0.623735\pi\) | ||||
−0.379010 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(998\) | −53.9711 | −1.70842 | ||||||||
\(999\) | − 4.55496i | − 0.144112i |
(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 | 507.2.b.g.337.2 | 6 | ||
3.2 | odd | 2 | 1521.2.b.m.1351.5 | 6 | |||
13.2 | odd | 12 | 507.2.e.j.22.3 | 6 | |||
13.3 | even | 3 | 507.2.j.h.316.5 | 12 | |||
13.4 | even | 6 | 507.2.j.h.361.5 | 12 | |||
13.5 | odd | 4 | 507.2.a.k.1.1 | yes | 3 | ||
13.6 | odd | 12 | 507.2.e.j.484.3 | 6 | |||
13.7 | odd | 12 | 507.2.e.k.484.1 | 6 | |||
13.8 | odd | 4 | 507.2.a.j.1.3 | ✓ | 3 | ||
13.9 | even | 3 | 507.2.j.h.361.2 | 12 | |||
13.10 | even | 6 | 507.2.j.h.316.2 | 12 | |||
13.11 | odd | 12 | 507.2.e.k.22.1 | 6 | |||
13.12 | even | 2 | inner | 507.2.b.g.337.5 | 6 | ||
39.5 | even | 4 | 1521.2.a.p.1.3 | 3 | |||
39.8 | even | 4 | 1521.2.a.q.1.1 | 3 | |||
39.38 | odd | 2 | 1521.2.b.m.1351.2 | 6 | |||
52.31 | even | 4 | 8112.2.a.cf.1.3 | 3 | |||
52.47 | even | 4 | 8112.2.a.by.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
507.2.a.k.1.1 | yes | 3 | 13.5 | odd | 4 | ||
507.2.b.g.337.2 | 6 | 1.1 | even | 1 | trivial | ||
507.2.b.g.337.5 | 6 | 13.12 | even | 2 | inner | ||
507.2.e.j.22.3 | 6 | 13.2 | odd | 12 | |||
507.2.e.j.484.3 | 6 | 13.6 | odd | 12 | |||
507.2.e.k.22.1 | 6 | 13.11 | odd | 12 | |||
507.2.e.k.484.1 | 6 | 13.7 | odd | 12 | |||
507.2.j.h.316.2 | 12 | 13.10 | even | 6 | |||
507.2.j.h.316.5 | 12 | 13.3 | even | 3 | |||
507.2.j.h.361.2 | 12 | 13.9 | even | 3 | |||
507.2.j.h.361.5 | 12 | 13.4 | even | 6 | |||
1521.2.a.p.1.3 | 3 | 39.5 | even | 4 | |||
1521.2.a.q.1.1 | 3 | 39.8 | even | 4 | |||
1521.2.b.m.1351.2 | 6 | 39.38 | odd | 2 | |||
1521.2.b.m.1351.5 | 6 | 3.2 | odd | 2 | |||
8112.2.a.by.1.1 | 3 | 52.47 | even | 4 | |||
8112.2.a.cf.1.3 | 3 | 52.31 | even | 4 |