Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(209,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.c (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: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.12 | ||
Root | \(4.54164i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.209 |
Dual form | 240.3.c.e.209.11 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.72256 | + | 1.26002i | 0.907521 | + | 0.420007i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.689011 | + | 4.95230i | 0.137802 | + | 0.990460i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.735748i | 0.105107i | 0.998618 | + | 0.0525534i | \(0.0167360\pi\) | ||||
−0.998618 | + | 0.0525534i | \(0.983264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.82469 | + | 6.86097i | 0.647188 | + | 0.762330i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.9451i | − | 0.995009i | −0.867461 | − | 0.497505i | \(-0.834250\pi\) | ||
0.867461 | − | 0.497505i | \(-0.165750\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.1901i | 1.63000i | 0.579458 | + | 0.815002i | \(0.303264\pi\) | ||||
−0.579458 | + | 0.815002i | \(0.696736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.36412 | + | 14.3511i | −0.290942 | + | 0.956741i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.03488 | 0.413816 | 0.206908 | − | 0.978360i | \(-0.433660\pi\) | ||||
0.206908 | + | 0.978360i | \(0.433660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.1529 | −1.21857 | −0.609287 | − | 0.792950i | \(-0.708544\pi\) | ||||
−0.609287 | + | 0.792950i | \(0.708544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.927058 | + | 2.00312i | −0.0441456 | + | 0.0953867i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.7483 | 1.07601 | 0.538006 | − | 0.842941i | \(-0.319178\pi\) | ||||
0.538006 | + | 0.842941i | \(0.319178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.0505 | + | 6.82438i | −0.962021 | + | 0.272975i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.21312 | + | 26.0187i | 0.267153 | + | 0.963654i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 32.3284i | − | 1.11477i | −0.830254 | − | 0.557386i | \(-0.811804\pi\) | ||
0.830254 | − | 0.557386i | \(-0.188196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.9482 | 1.12736 | 0.563680 | − | 0.825993i | \(-0.309385\pi\) | ||||
0.563680 | + | 0.825993i | \(0.309385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.7911 | − | 29.7987i | 0.417911 | − | 0.902992i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.64364 | + | 0.506939i | −0.104104 | + | 0.0144840i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.7818i | 1.02113i | 0.859839 | + | 0.510565i | \(0.170564\pi\) | ||||
−0.859839 | + | 0.510565i | \(0.829436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −26.6999 | + | 57.6912i | −0.684613 | + | 1.47926i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 39.0848i | − | 0.953288i | −0.879096 | − | 0.476644i | \(-0.841853\pi\) | ||
0.879096 | − | 0.476644i | \(-0.158147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 22.6804i | − | 0.527451i | −0.964598 | − | 0.263725i | \(-0.915049\pi\) | ||
0.964598 | − | 0.263725i | \(-0.0849513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −29.9643 | + | 33.5729i | −0.665873 | + | 0.746065i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −39.1076 | −0.832076 | −0.416038 | − | 0.909347i | \(-0.636582\pi\) | ||||
−0.416038 | + | 0.909347i | \(0.636582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.4587 | 0.988953 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.1529 | + | 8.86409i | 0.375547 | + | 0.173806i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 60.9179 | 1.14939 | 0.574697 | − | 0.818366i | \(-0.305120\pi\) | ||||
0.574697 | + | 0.818366i | \(0.305120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 54.2034 | − | 7.54130i | 0.985517 | − | 0.137115i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −63.0352 | − | 29.1731i | −1.10588 | − | 0.511809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.79696i | − | 0.132152i | −0.997815 | − | 0.0660759i | \(-0.978952\pi\) | ||
0.997815 | − | 0.0660759i | \(-0.0210480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1529 | −0.182834 | −0.0914171 | − | 0.995813i | \(-0.529140\pi\) | ||||
−0.0914171 | + | 0.995813i | \(0.529140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.04795 | + | 4.28551i | −0.0801262 | + | 0.0680239i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −104.939 | + | 14.6002i | −1.61445 | + | 0.224618i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 33.3485i | − | 0.497739i | −0.968537 | − | 0.248869i | \(-0.919941\pi\) | ||
0.968537 | − | 0.248869i | \(-0.0800590\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 67.3787 | + | 31.1833i | 0.976503 | + | 0.451933i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 96.9650i | − | 1.36570i | −0.730557 | − | 0.682852i | \(-0.760739\pi\) | ||
0.730557 | − | 0.682852i | \(-0.239261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 134.535i | − | 1.84295i | −0.388436 | − | 0.921476i | \(-0.626984\pi\) | ||
0.388436 | − | 0.921476i | \(-0.373016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −74.0779 | − | 11.7244i | −0.987706 | − | 0.156325i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.05284 | 0.104582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −121.049 | −1.53227 | −0.766134 | − | 0.642681i | \(-0.777822\pi\) | ||||
−0.766134 | + | 0.642681i | \(0.777822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −13.1459 | + | 79.9261i | −0.162295 | + | 0.986742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 90.2345 | 1.08716 | 0.543582 | − | 0.839356i | \(-0.317068\pi\) | ||||
0.543582 | + | 0.839356i | \(0.317068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.84711 | + | 34.8388i | 0.0570248 | + | 0.409868i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 40.7344 | − | 88.0160i | 0.468212 | − | 1.01168i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 53.1846i | − | 0.597579i | −0.954319 | − | 0.298790i | \(-0.903417\pi\) | ||
0.954319 | − | 0.298790i | \(-0.0965829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.5905 | −0.171325 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 95.1486 | + | 44.0354i | 1.02310 | + | 0.473499i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.9526 | − | 114.660i | −0.167922 | − | 1.20695i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 115.001i | − | 1.18557i | −0.805359 | − | 0.592787i | \(-0.798028\pi\) | ||
0.805359 | − | 0.592787i | \(-0.201972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 75.0940 | − | 63.7519i | 0.758526 | − | 0.643958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 29.1802i | 0.288913i | 0.989511 | + | 0.144457i | \(0.0461434\pi\) | ||||
−0.989511 | + | 0.144457i | \(0.953857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 89.9481i | − | 0.873283i | −0.899636 | − | 0.436641i | \(-0.856168\pi\) | ||
0.899636 | − | 0.436641i | \(-0.143832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.5588 | − | 3.21090i | −0.100560 | − | 0.0305800i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −153.586 | −1.43538 | −0.717689 | − | 0.696363i | \(-0.754800\pi\) | ||||
−0.717689 | + | 0.696363i | \(0.754800\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −59.5623 | −0.546444 | −0.273222 | − | 0.961951i | \(-0.588089\pi\) | ||||
−0.273222 | + | 0.961951i | \(0.588089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −47.6059 | + | 102.863i | −0.428882 | + | 0.926697i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.01796 | −0.00900851 | −0.00450426 | − | 0.999990i | \(-0.501434\pi\) | ||||
−0.00450426 | + | 0.999990i | \(0.501434\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.0518 | + | 122.561i | 0.148277 | + | 1.06575i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −145.384 | + | 123.426i | −1.24260 | + | 1.05492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.17590i | 0.0434949i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.20473 | 0.00995643 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 49.2477 | − | 106.411i | 0.400388 | − | 0.865129i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −50.3674 | − | 114.403i | −0.402940 | − | 0.915227i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.731i | 1.65142i | 0.564091 | + | 0.825712i | \(0.309227\pi\) | ||||
−0.564091 | + | 0.825712i | \(0.690773\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.5778 | − | 61.7488i | 0.221533 | − | 0.478672i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 210.051i | 1.60344i | 0.597698 | + | 0.801721i | \(0.296082\pi\) | ||||
−0.597698 | + | 0.801721i | \(0.703918\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 17.0347i | − | 0.128080i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −123.882 | + | 53.6487i | −0.917646 | + | 0.397398i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 168.688 | 1.23130 | 0.615648 | − | 0.788021i | \(-0.288894\pi\) | ||||
0.615648 | + | 0.788021i | \(0.288894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 129.251 | 0.929866 | 0.464933 | − | 0.885346i | \(-0.346078\pi\) | ||||
0.464933 | + | 0.885346i | \(0.346078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −106.473 | − | 49.2763i | −0.755126 | − | 0.349478i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 231.927 | 1.62187 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 160.100 | − | 22.2746i | 1.10414 | − | 0.153618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 131.932 | + | 61.0590i | 0.897495 | + | 0.415367i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 83.9655i | 0.563527i | 0.959484 | + | 0.281763i | \(0.0909193\pi\) | ||||
−0.959484 | + | 0.281763i | \(0.909081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.04922 | −0.0599286 | −0.0299643 | − | 0.999551i | \(-0.509539\pi\) | ||||
−0.0299643 | + | 0.999551i | \(0.509539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.9760 | + | 48.2661i | 0.267817 | + | 0.315465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.0797 | + | 173.074i | 0.155353 | + | 1.11660i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.054i | 1.03219i | 0.856530 | + | 0.516097i | \(0.172616\pi\) | ||||
−0.856530 | + | 0.516097i | \(0.827384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 165.853 | + | 76.7578i | 1.04310 | + | 0.482754i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2085i | 0.113096i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 136.172i | 0.835411i | 0.908583 | + | 0.417705i | \(0.137166\pi\) | ||||
−0.908583 | + | 0.417705i | \(0.862834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 157.074 | + | 47.7658i | 0.951966 | + | 0.289490i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −140.931 | −0.843898 | −0.421949 | − | 0.906620i | \(-0.638654\pi\) | ||||
−0.421949 | + | 0.906620i | \(0.638654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280.018 | −1.65691 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −134.859 | − | 158.851i | −0.788646 | − | 0.928955i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 132.351 | 0.765032 | 0.382516 | − | 0.923949i | \(-0.375058\pi\) | ||||
0.382516 | + | 0.923949i | \(0.375058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.02102 | − | 17.6951i | −0.0286916 | − | 0.101115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.82433 | − | 21.2277i | 0.0555047 | − | 0.119931i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 92.2499i | − | 0.515363i | −0.966230 | − | 0.257681i | \(-0.917042\pi\) | ||
0.966230 | − | 0.257681i | \(-0.0829585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.896 | 0.640311 | 0.320156 | − | 0.947365i | \(-0.396265\pi\) | ||||
0.320156 | + | 0.947365i | \(0.396265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.3644 | − | 14.0529i | −0.165926 | − | 0.0767917i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −187.107 | + | 26.0321i | −1.01139 | + | 0.140714i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 76.9974i | − | 0.411751i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.1432 | + | 5.30704i | −0.101287 | + | 0.0280796i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 53.1183i | − | 0.278106i | −0.990285 | − | 0.139053i | \(-0.955594\pi\) | ||
0.990285 | − | 0.139053i | \(-0.0444059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 271.315i | 1.40578i | 0.711299 | + | 0.702890i | \(0.248107\pi\) | ||||
−0.711299 | + | 0.702890i | \(0.751893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −304.101 | − | 92.4760i | −1.55949 | − | 0.474236i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −64.3941 | −0.326873 | −0.163437 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163437 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −72.0308 | −0.361964 | −0.180982 | − | 0.983486i | \(-0.557928\pi\) | ||||
−0.180982 | + | 0.983486i | \(0.557928\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.0198 | − | 90.7933i | 0.209054 | − | 0.451708i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.7855 | 0.117170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 193.560 | − | 26.9299i | 0.944194 | − | 0.131365i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 144.151 | + | 169.797i | 0.696382 | + | 0.820276i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 253.411i | 1.21249i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −108.583 | −0.514613 | −0.257307 | − | 0.966330i | \(-0.582835\pi\) | ||||
−0.257307 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 122.178 | − | 263.993i | 0.573605 | − | 1.23940i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 112.320 | − | 15.6270i | 0.522419 | − | 0.0726839i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.7130i | 0.118493i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 169.518 | − | 366.281i | 0.774053 | − | 1.67252i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 149.069i | 0.674522i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 83.6192i | 0.374974i | 0.982267 | + | 0.187487i | \(0.0600342\pi\) | ||||
−0.982267 | + | 0.187487i | \(0.939966\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −186.909 | − | 125.260i | −0.830706 | − | 0.556712i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −51.6591 | −0.227573 | −0.113787 | − | 0.993505i | \(-0.536298\pi\) | ||||
−0.113787 | + | 0.993505i | \(0.536298\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −280.974 | −1.22696 | −0.613480 | − | 0.789710i | \(-0.710231\pi\) | ||||
−0.613480 | + | 0.789710i | \(0.710231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.9244 | + | 10.1467i | 0.0949106 | + | 0.0439253i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −169.192 | −0.726148 | −0.363074 | − | 0.931760i | \(-0.618273\pi\) | ||||
−0.363074 | + | 0.931760i | \(0.618273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.9455 | − | 193.672i | −0.114662 | − | 0.824137i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −329.564 | − | 152.525i | −1.39057 | − | 0.643564i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.12039i | − | 0.00468782i | −0.999997 | − | 0.00234391i | \(-0.999254\pi\) | ||
0.999997 | − | 0.00234391i | \(-0.000746090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 153.254 | 0.635908 | 0.317954 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317954 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −136.499 | + | 201.040i | −0.561725 | + | 0.827324i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33.3886 | + | 239.982i | 0.136280 | + | 0.979518i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 490.611i | − | 1.98628i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 245.669 | + | 113.697i | 0.986623 | + | 0.456616i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 126.692i | 0.504751i | 0.967629 | + | 0.252375i | \(0.0812118\pi\) | ||||
−0.967629 | + | 0.252375i | \(0.918788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 270.872i | − | 1.07064i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −30.7011 | + | 100.958i | −0.120396 | + | 0.395915i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 396.692 | 1.54355 | 0.771774 | − | 0.635897i | \(-0.219370\pi\) | ||||
0.771774 | + | 0.635897i | \(0.219370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.7979 | −0.107328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 221.804 | − | 188.303i | 0.849824 | − | 0.721467i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −394.431 | −1.49974 | −0.749868 | − | 0.661587i | \(-0.769883\pi\) | ||||
−0.749868 | + | 0.661587i | \(0.769883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.9731 | + | 301.684i | 0.158389 | + | 1.13843i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 67.0137 | − | 144.798i | 0.250987 | − | 0.542316i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 104.802i | − | 0.389597i | −0.980843 | − | 0.194798i | \(-0.937595\pi\) | ||
0.980843 | − | 0.194798i | \(-0.0624053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 335.355 | 1.23747 | 0.618736 | − | 0.785599i | \(-0.287645\pi\) | ||||
0.618736 | + | 0.785599i | \(0.287645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.4462 | − | 19.6444i | −0.155481 | − | 0.0719576i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 74.6935 | + | 263.235i | 0.271613 | + | 0.957220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 167.790i | − | 0.605739i | −0.953032 | − | 0.302870i | \(-0.902055\pi\) | ||
0.953032 | − | 0.302870i | \(-0.0979447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 203.562 | + | 239.778i | 0.729614 | + | 0.859421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 99.4601i | − | 0.353950i | −0.984215 | − | 0.176975i | \(-0.943369\pi\) | ||
0.984215 | − | 0.176975i | \(-0.0566312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 487.022i | − | 1.72093i | −0.509512 | − | 0.860464i | \(-0.670174\pi\) | ||
0.509512 | − | 0.860464i | \(-0.329826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 101.042 | − | 332.270i | 0.354534 | − | 1.16586i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.7566 | 0.100197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −239.511 | −0.828756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 144.903 | − | 313.097i | 0.497950 | − | 1.07593i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −343.107 | −1.17101 | −0.585507 | − | 0.810667i | \(-0.699105\pi\) | ||||
−0.585507 | + | 0.810667i | \(0.699105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.6129 | − | 5.37219i | 0.130891 | − | 0.0182108i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 284.777 | − | 78.9484i | 0.958845 | − | 0.265819i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 524.417i | 1.75390i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6870 | 0.0554387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −36.7677 | + | 79.4450i | −0.121346 | + | 0.262195i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.68447 | − | 55.2325i | −0.0251950 | − | 0.181090i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 364.627i | 1.18771i | 0.804573 | + | 0.593854i | \(0.202394\pi\) | ||||
−0.804573 | + | 0.593854i | \(0.797606\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 113.337 | − | 244.889i | 0.366785 | − | 0.792522i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 121.963i | − | 0.392164i | −0.980587 | − | 0.196082i | \(-0.937178\pi\) | ||
0.980587 | − | 0.196082i | \(-0.0628219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 94.8060i | 0.302895i | 0.988465 | + | 0.151447i | \(0.0483934\pi\) | ||||
−0.988465 | + | 0.151447i | \(0.951607\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.7012 | − | 22.0462i | −0.0784165 | − | 0.0699879i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −511.282 | −1.61288 | −0.806438 | − | 0.591318i | \(-0.798608\pi\) | ||||
−0.806438 | + | 0.591318i | \(0.798608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −353.837 | −1.10921 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −418.146 | − | 193.521i | −1.30264 | − | 0.602869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −162.878 | −0.504265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −144.609 | − | 509.632i | −0.444951 | − | 1.56810i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −162.162 | − | 75.0498i | −0.495909 | − | 0.229510i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 28.7733i | − | 0.0874569i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 182.682 | 0.551909 | 0.275954 | − | 0.961171i | \(-0.411006\pi\) | ||||
0.275954 | + | 0.961171i | \(0.411006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −259.220 | + | 220.067i | −0.778438 | + | 0.660863i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 165.152 | − | 22.9775i | 0.492990 | − | 0.0685895i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 89.0617i | 0.264278i | 0.991231 | + | 0.132139i | \(0.0421845\pi\) | ||||
−0.991231 | + | 0.132139i | \(0.957815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.77147 | − | 1.28265i | −0.00817541 | − | 0.00378364i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 382.511i | − | 1.12173i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 71.7050i | 0.209053i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −108.005 | + | 355.165i | −0.313057 | + | 1.02946i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7180 | −0.0510605 | −0.0255303 | − | 0.999674i | \(-0.508127\pi\) | ||||
−0.0255303 | + | 0.999674i | \(0.508127\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 229.114 | 0.656488 | 0.328244 | − | 0.944593i | \(-0.393543\pi\) | ||||
0.328244 | + | 0.944593i | \(0.393543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −551.337 | + | 152.846i | −1.57076 | + | 0.435460i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −183.760 | −0.520566 | −0.260283 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260283 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 480.199 | − | 66.8099i | 1.35267 | − | 0.188197i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.52174 | + | 14.0917i | −0.0182682 | + | 0.0394726i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 537.837i | − | 1.49815i | −0.662484 | − | 0.749076i | \(-0.730498\pi\) | ||
0.662484 | − | 0.749076i | \(-0.269502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 175.056 | 0.484921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.27995 | + | 1.51798i | 0.00903567 | + | 0.00418177i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 666.260 | − | 92.6964i | 1.82537 | − | 0.253963i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 153.740i | 0.418909i | 0.977818 | + | 0.209455i | \(0.0671689\pi\) | ||||
−0.977818 | + | 0.209455i | \(0.932831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 268.160 | − | 227.657i | 0.726721 | − | 0.616957i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44.8202i | 0.120809i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 211.056i | 0.565833i | 0.959145 | + | 0.282917i | \(0.0913020\pi\) | ||||
−0.959145 | + | 0.282917i | \(0.908698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.02209 | − | 374.934i | 0.0187256 | − | 0.999825i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 685.040 | 1.81708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −699.345 | −1.84524 | −0.922618 | − | 0.385715i | \(-0.873955\pi\) | ||||
−0.922618 | + | 0.385715i | \(0.873955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −264.265 | + | 571.006i | −0.693610 | + | 1.49870i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 186.008 | 0.485662 | 0.242831 | − | 0.970069i | \(-0.421924\pi\) | ||||
0.242831 | + | 0.970069i | \(0.421924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.54850 | + | 39.8801i | 0.0144117 | + | 0.103585i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 155.609 | − | 132.106i | 0.402092 | − | 0.341360i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 288.194i | 0.740858i | 0.928861 | + | 0.370429i | \(0.120789\pi\) | ||||
−0.928861 | + | 0.370429i | \(0.879211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 174.101 | 0.445271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −264.669 | + | 571.877i | −0.673457 | + | 1.45516i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −83.4043 | − | 599.472i | −0.211150 | − | 1.51765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 64.3054i | − | 0.161978i | −0.996715 | − | 0.0809892i | \(-0.974192\pi\) | ||
0.996715 | − | 0.0809892i | \(-0.0258079\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.4641 | − | 46.3780i | 0.0537947 | − | 0.116236i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 659.774i | 1.64532i | 0.568533 | + | 0.822661i | \(0.307511\pi\) | ||||
−0.568533 | + | 0.822661i | \(0.692489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 740.553i | 1.83760i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −404.876 | − | 10.0324i | −0.999693 | − | 0.0247712i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 413.526 | 1.01603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 217.863 | 0.532672 | 0.266336 | − | 0.963880i | \(-0.414187\pi\) | ||||
0.266336 | + | 0.963880i | \(0.414187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 459.263 | + | 212.550i | 1.11743 | + | 0.517153i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.73660 | 0.0138901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 62.1726 | + | 446.868i | 0.149814 | + | 1.07679i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 351.895 | + | 162.859i | 0.843872 | + | 0.390550i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 407.129i | 0.971668i | 0.874051 | + | 0.485834i | \(0.161484\pi\) | ||||
−0.874051 | + | 0.485834i | \(0.838516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −69.1949 | −0.164359 | −0.0821793 | − | 0.996618i | \(-0.526188\pi\) | ||||
−0.0821793 | + | 0.996618i | \(0.526188\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −227.790 | − | 268.316i | −0.538510 | − | 0.634316i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −169.192 | + | 48.0087i | −0.398100 | + | 0.112962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.20572i | − | 0.0192171i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 631.437 | + | 292.233i | 1.47188 | + | 0.681197i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 452.663i | − | 1.05026i | −0.851021 | − | 0.525132i | \(-0.824016\pi\) | ||
0.851021 | − | 0.525132i | \(-0.175984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 226.323i | 0.522686i | 0.965246 | + | 0.261343i | \(0.0841654\pi\) | ||||
−0.965246 | + | 0.261343i | \(0.915835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 463.948 | + | 141.085i | 1.06655 | + | 0.324333i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −572.994 | −1.31120 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −188.642 | −0.429709 | −0.214855 | − | 0.976646i | \(-0.568928\pi\) | ||||
−0.214855 | + | 0.976646i | \(0.568928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 282.257 | + | 332.474i | 0.640038 | + | 0.753908i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −499.705 | −1.12800 | −0.564001 | − | 0.825774i | \(-0.690739\pi\) | ||||
−0.564001 | + | 0.825774i | \(0.690739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 263.386 | − | 36.6448i | 0.591878 | − | 0.0823478i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −105.798 | + | 228.601i | −0.236685 | + | 0.511412i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 818.928i | − | 1.82389i | −0.410310 | − | 0.911946i | \(-0.634579\pi\) | ||
0.410310 | − | 0.911946i | \(-0.365421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −427.787 | −0.948531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.6371 | − | 11.4022i | −0.0543864 | − | 0.0251704i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7421 | − | 77.2090i | −0.0236089 | − | 0.169690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 311.602i | − | 0.681842i | −0.940092 | − | 0.340921i | \(-0.889261\pi\) | ||
0.940092 | − | 0.340921i | \(-0.110739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 50.7434 | + | 183.038i | 0.110552 | + | 0.398776i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.18351i | 0.0155825i | 0.999970 | + | 0.00779123i | \(0.00248005\pi\) | ||||
−0.999970 | + | 0.00779123i | \(0.997520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 557.563i | 1.20424i | 0.798406 | + | 0.602120i | \(0.205677\pi\) | ||||
−0.798406 | + | 0.602120i | \(0.794323\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −152.518 | + | 501.545i | −0.327996 | + | 1.07859i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 659.257 | 1.41168 | 0.705842 | − | 0.708369i | \(-0.250569\pi\) | ||||
0.705842 | + | 0.708369i | \(0.250569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.5361 | 0.0523157 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −204.192 | + | 441.203i | −0.433529 | + | 0.936738i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −248.239 | −0.524818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 556.839 | − | 158.004i | 1.17229 | − | 0.332640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 354.828 | + | 417.956i | 0.743875 | + | 0.876218i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.3870i | 0.0634384i | 0.999497 | + | 0.0317192i | \(0.0100982\pi\) | ||||
−0.999497 | + | 0.0317192i | \(0.989902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −800.598 | −1.66445 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.9431 | + | 49.5738i | −0.0475012 | + | 0.102637i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 569.518 | − | 79.2368i | 1.17426 | − | 0.163375i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.5618i | 0.0545416i | 0.999628 | + | 0.0272708i | \(0.00868164\pi\) | ||||
−0.999628 | + | 0.0272708i | \(0.991318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −171.580 | + | 370.737i | −0.350878 | + | 0.758153i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3354i | 0.0393796i | 0.999806 | + | 0.0196898i | \(0.00626786\pi\) | ||||
−0.999806 | + | 0.0196898i | \(0.993732\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 227.426i | − | 0.461311i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 367.459 | + | 327.962i | 0.742341 | + | 0.662550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 71.3418 | 0.143545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −313.190 | −0.627635 | −0.313817 | − | 0.949483i | \(-0.601608\pi\) | ||||
−0.313817 | + | 0.949483i | \(0.601608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −383.693 | − | 177.576i | −0.765855 | − | 0.354443i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −551.684 | −1.09679 | −0.548394 | − | 0.836220i | \(-0.684760\pi\) | ||||
−0.548394 | + | 0.836220i | \(0.684760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −144.509 | + | 20.1055i | −0.286157 | + | 0.0398129i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −762.368 | − | 352.829i | −1.50368 | − | 0.695915i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 567.057i | − | 1.11406i | −0.830492 | − | 0.557031i | \(-0.811941\pi\) | ||
0.830492 | − | 0.557031i | \(-0.188059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 98.9842 | 0.193707 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −167.005 | − | 602.407i | −0.325545 | − | 1.17428i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 445.450 | − | 61.9753i | 0.864951 | − | 0.120340i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 428.036i | 0.827923i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 360.333 | + | 166.764i | 0.694283 | + | 0.321319i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 740.223i | − | 1.42077i | −0.703811 | − | 0.710387i | \(-0.748520\pi\) | ||
0.703811 | − | 0.710387i | \(-0.251480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.11805i | − | 0.00404981i | −0.999998 | − | 0.00202491i | \(-0.999355\pi\) | ||
0.999998 | − | 0.00202491i | \(-0.000644548\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.62619 | − | 54.5027i | 0.0164308 | − | 0.103815i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 245.856 | 0.466520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 83.4771 | 0.157802 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.4947 | − | 45.4149i | 0.100743 | − | 0.0855271i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 828.210 | 1.55386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −105.822 | − | 760.602i | −0.197798 | − | 1.42169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 116.237 | − | 251.156i | 0.216456 | − | 0.467702i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 530.385i | − | 0.984017i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.61681 | 0.0122307 | 0.00611535 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611535 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 315.535 | + | 146.032i | 0.581096 | + | 0.268935i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.0391 | − | 294.971i | −0.0753011 | − | 0.541230i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 230.092i | − | 0.420644i | −0.977632 | − | 0.210322i | \(-0.932549\pi\) | ||
0.977632 | − | 0.210322i | \(-0.0674512\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −64.9622 | − | 76.5197i | −0.118328 | − | 0.139380i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 748.495i | 1.35843i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 89.0617i | − | 0.161052i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −542.211 | − | 164.885i | −0.976957 | − | 0.297089i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −529.620 | −0.950844 | −0.475422 | − | 0.879758i | \(-0.657705\pi\) | ||||
−0.475422 | + | 0.879758i | \(0.657705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 480.598 | 0.859747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 97.0184 | − | 209.630i | 0.172938 | − | 0.373673i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −131.530 | −0.233623 | −0.116812 | − | 0.993154i | \(-0.537267\pi\) | ||||
−0.116812 | + | 0.993154i | \(0.537267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.701387 | − | 5.04125i | −0.00124139 | − | 0.00892257i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −58.8055 | − | 9.67206i | −0.103713 | − | 0.0170583i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 172.534i | 0.303224i | 0.988440 | + | 0.151612i | \(0.0484464\pi\) | ||||
−0.988440 | + | 0.151612i | \(0.951554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −197.935 | −0.346646 | −0.173323 | − | 0.984865i | \(-0.555450\pi\) | ||||
−0.173323 | + | 0.984865i | \(0.555450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 66.9302 | − | 144.618i | 0.116807 | − | 0.252387i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −595.209 | + | 168.892i | −1.03515 | + | 0.293724i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 865.374i | − | 1.49978i | −0.661562 | − | 0.749891i | \(-0.730106\pi\) | ||
0.661562 | − | 0.749891i | \(-0.269894\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −341.863 | + | 738.673i | −0.590437 | + | 1.27577i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.3899i | 0.114268i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 666.753i | − | 1.14366i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −711.412 | − | 634.945i | −1.21609 | − | 1.08538i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.8886 | 0.0526211 | 0.0263105 | − | 0.999654i | \(-0.491624\pi\) | ||||
0.0263105 | + | 0.999654i | \(0.491624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −809.151 | −1.37377 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −175.317 | − | 81.1379i | −0.296644 | − | 0.137289i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −511.286 | −0.862202 | −0.431101 | − | 0.902304i | \(-0.641875\pi\) | ||||
−0.431101 | + | 0.902304i | \(0.641875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.6326 | + | 3.56625i | −0.0430800 | + | 0.00599370i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −196.108 | − | 90.7603i | −0.328490 | − | 0.152027i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 514.866i | − | 0.859543i | −0.902938 | − | 0.429772i | \(-0.858594\pi\) | ||
0.902938 | − | 0.429772i | \(-0.141406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 853.532 | 1.42019 | 0.710093 | − | 0.704107i | \(-0.248653\pi\) | ||||
0.710093 | + | 0.704107i | \(0.248653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 228.803 | − | 194.245i | 0.379441 | − | 0.322131i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.830071 | + | 5.96618i | 0.00137202 | + | 0.00986145i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 88.0713i | − | 0.145093i | −0.997365 | − | 0.0725464i | \(-0.976887\pi\) | ||
0.997365 | − | 0.0725464i | \(-0.0231125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 64.7576 | + | 29.9703i | 0.106334 | + | 0.0492123i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 828.691i | − | 1.35629i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 403.346i | 0.657987i | 0.944332 | + | 0.328994i | \(0.106709\pi\) | ||||
−0.944332 | + | 0.328994i | \(0.893291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 560.911 | + | 170.571i | 0.912050 | + | 0.277351i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −365.738 | −0.592769 | −0.296384 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296384 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 399.495 | 0.645389 | 0.322694 | − | 0.946503i | \(-0.395411\pi\) | ||||
0.322694 | + | 0.946503i | \(0.395411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 178.512 | + | 643.917i | 0.287460 | + | 1.03690i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.1304 | 0.0628097 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 531.856 | − | 328.260i | 0.850969 | − | 0.525216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −319.303 | + | 689.927i | −0.509255 | + | 1.10036i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 265.790i | 0.422560i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 715.762 | 1.13433 | 0.567165 | − | 0.823604i | \(-0.308040\pi\) | ||||
0.567165 | + | 0.823604i | \(0.308040\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −295.625 | − | 136.817i | −0.467022 | − | 0.216141i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1038.65 | + | 144.507i | −1.63567 | + | 0.227570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1026.84i | 1.61200i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 665.274 | − | 564.791i | 1.04112 | − | 0.883867i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 627.158i | 0.978406i | 0.872170 | + | 0.489203i | \(0.162712\pi\) | ||||
−0.872170 | + | 0.489203i | \(0.837288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 802.039i | − | 1.24734i | −0.781688 | − | 0.623669i | \(-0.785641\pi\) | ||
0.781688 | − | 0.623669i | \(-0.214359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 325.489 | + | 98.9800i | 0.504634 | + | 0.153457i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.9275 | −0.0307998 | −0.0153999 | − | 0.999881i | \(-0.504902\pi\) | ||||
−0.0153999 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −85.3385 | −0.131492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.3990 | + | 70.0054i | −0.0497680 | + | 0.107535i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 78.4638 | 0.120159 | 0.0600795 | − | 0.998194i | \(-0.480865\pi\) | ||||
0.0600795 | + | 0.998194i | \(0.480865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1040.23 | + | 144.727i | −1.58815 | + | 0.220958i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 923.044 | − | 783.628i | 1.40494 | − | 1.19274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 371.793i | − | 0.564178i | −0.959388 | − | 0.282089i | \(-0.908973\pi\) | ||
0.959388 | − | 0.282089i | \(-0.0910274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 782.868 | 1.18437 | 0.592185 | − | 0.805802i | \(-0.298266\pi\) | ||||
0.592185 | + | 0.805802i | \(0.298266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −187.831 | + | 405.851i | −0.283304 | + | 0.612143i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 84.3609 | − | 11.7371i | 0.126859 | − | 0.0176498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 800.071i | − | 1.19951i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −105.362 | + | 227.658i | −0.157492 | + | 0.340297i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 122.070i | 0.181922i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 221.323i | − | 0.328860i | −0.986389 | − | 0.164430i | \(-0.947421\pi\) | ||
0.986389 | − | 0.164430i | \(-0.0525785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −351.041 | − | 576.537i | −0.520060 | − | 0.854130i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −576.855 | −0.852076 | −0.426038 | − | 0.904705i | \(-0.640091\pi\) | ||||
−0.426038 | + | 0.904705i | \(0.640091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 84.6116 | 0.124612 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −140.645 | − | 65.0916i | −0.206527 | − | 0.0955824i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1272.02 | 1.86239 | 0.931197 | − | 0.364516i | \(-0.118766\pi\) | ||||
0.931197 | + | 0.364516i | \(0.118766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 116.228 | + | 835.392i | 0.169675 | + | 1.21955i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −764.969 | − | 354.033i | −1.11349 | − | 0.515332i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1290.85i | 1.87352i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.61487 | −0.00233701 | −0.00116851 | − | 0.999999i | \(-0.500372\pi\) | ||||
−0.00116851 | + | 0.999999i | \(0.500372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.9053 | + | 55.2503i | 0.0676844 | + | 0.0797263i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 89.0556 | + | 640.091i | 0.128138 | + | 0.920995i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 274.957i | − | 0.394486i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −460.637 | − | 213.186i | −0.658994 | − | 0.304987i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 550.235i | − | 0.784929i | −0.919767 | − | 0.392465i | \(-0.871623\pi\) | ||
0.919767 | − | 0.392465i | \(-0.128377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 874.758i | − | 1.24432i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 170.670 | − | 561.237i | 0.242085 | − | 0.796081i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.4693 | −0.0303668 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −430.539 | −0.607249 | −0.303624 | − | 0.952792i | \(-0.598197\pi\) | ||||
−0.303624 | + | 0.952792i | \(0.598197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −705.075 | − | 830.515i | −0.991666 | − | 1.16809i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 864.907 | 1.21305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 159.801 | + | 1148.57i | 0.223497 | + | 1.60640i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.41171 | − | 3.05033i | 0.00196892 | − | 0.00425429i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 460.561i | 0.640558i | 0.947323 | + | 0.320279i | \(0.103777\pi\) | ||||
−0.947323 | + | 0.320279i | \(0.896223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 66.1792 | 0.0917880 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 417.243 | + | 193.103i | 0.577100 | + | 0.267086i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 220.621 | + | 777.514i | 0.304305 | + | 1.07243i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 413.275i | 0.568467i | 0.958755 | + | 0.284233i | \(0.0917390\pi\) | ||||
−0.958755 | + | 0.284233i | \(0.908261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −624.942 | + | 375.352i | −0.857259 | + | 0.514886i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 159.554i | − | 0.218268i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 307.003i | − | 0.418831i | −0.977827 | − | 0.209416i | \(-0.932844\pi\) | ||
0.977827 | − | 0.209416i | \(-0.0671562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −211.480 | + | 695.436i | −0.287727 | + | 0.946171i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −365.003 | −0.495255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 988.511 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 618.180 | − | 1335.72i | 0.834251 | − | 1.80259i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 652.187 | 0.877775 | 0.438887 | − | 0.898542i | \(-0.355373\pi\) | ||||
0.438887 | + | 0.898542i | \(0.355373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −415.822 | + | 57.8532i | −0.558151 | + | 0.0776552i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 525.589 | + | 619.097i | 0.703599 | + | 0.828777i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 113.000i | − | 0.150868i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −554.876 | −0.738850 | −0.369425 | − | 0.929261i | \(-0.620445\pi\) | ||||
−0.369425 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −159.635 | + | 344.928i | −0.211999 | + | 0.458072i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.23501 | − | 44.8144i | −0.00825829 | − | 0.0593569i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 547.156i | 0.722795i | 0.932412 | + | 0.361397i | \(0.117700\pi\) | ||||
−0.932412 | + | 0.361397i | \(0.882300\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 341.305 | − | 737.467i | 0.449677 | − | 0.971630i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1361.34i | − | 1.78888i | −0.447184 | − | 0.894442i | \(-0.647573\pi\) | ||
0.447184 | − | 0.894442i | \(-0.352427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 43.8229i | − | 0.0574350i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −210.795 | + | 236.181i | −0.275549 | + | 0.308734i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 165.218 | 0.215408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −396.180 | −0.515188 | −0.257594 | − | 0.966253i | \(-0.582930\pi\) | ||||
−0.257594 | + | 0.966253i | \(0.582930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1080.02 | + | 499.840i | 1.40080 | + | 0.648301i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 664.286 | 0.859361 | 0.429681 | − | 0.902981i | \(-0.358626\pi\) | ||||
0.429681 | + | 0.902981i | \(0.358626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −840.522 | + | 238.499i | −1.08454 | + | 0.307741i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −75.6815 | − | 35.0259i | −0.0974022 | − | 0.0450784i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 904.927i | 1.16165i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1061.29 | −1.35889 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 841.141 | − | 233.189i | 1.07425 | − | 0.297814i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −802.542 | + | 111.657i | −1.02235 | + | 0.142239i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 957.551i | 1.21671i | 0.793665 | + | 0.608355i | \(0.208170\pi\) | ||||
−0.793665 | + | 0.608355i | \(0.791830\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1073.86 | − | 496.991i | −1.36104 | − | 0.629900i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.748964i | − | 0.000946857i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 236.330i | − | 0.298021i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −265.853 | + | 874.240i | −0.334407 | + | 1.09967i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 643.860 | 0.807854 | 0.403927 | − | 0.914791i | \(-0.367645\pi\) | ||||
0.403927 | + | 0.914791i | \(0.367645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −275.117 | −0.344326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 364.898 | − | 309.784i | 0.455553 | − | 0.386746i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1472.50 | −1.83375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −90.1739 | + | 12.5459i | −0.112017 | + | 0.0155849i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 132.052 | − | 285.329i | 0.163633 | − | 0.353567i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 675.342i | − | 0.834786i | −0.908726 | − | 0.417393i | \(-0.862944\pi\) | ||
0.908726 | − | 0.417393i | \(-0.137056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −808.662 | −0.997117 | −0.498559 | − | 0.866856i | \(-0.666137\pi\) | ||||
−0.498559 | + | 0.866856i | \(0.666137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 913.025 | + | 422.554i | 1.12303 | + | 0.519747i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −674.364 | + | 93.8240i | −0.827441 | + | 0.115121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 525.116i | 0.642737i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −90.8101 | − | 106.966i | −0.110879 | − | 0.130606i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1348.63i | 1.64267i | 0.570445 | + | 0.821336i | \(0.306771\pi\) | ||||
−0.570445 | + | 0.821336i | \(0.693229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1433.75i | 1.74211i | 0.491188 | + | 0.871053i | \(0.336563\pi\) | ||||
−0.491188 | + | 0.871053i | \(0.663437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −128.324 | + | 810.790i | −0.155545 | + | 0.982776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5276 | −0.0332861 | −0.0166431 | − | 0.999861i | \(-0.505298\pi\) | ||||
−0.0166431 | + | 0.999861i | \(0.505298\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 374.884 | 0.452212 | 0.226106 | − | 0.974103i | \(-0.427400\pi\) | ||||
0.226106 | + | 0.974103i | \(0.427400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 211.419 | − | 456.818i | 0.254415 | − | 0.549721i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 340.901 | 0.409245 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −97.1030 | − | 697.932i | −0.116291 | − | 0.835847i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 252.085 | + | 909.304i | 0.301177 | + | 1.08639i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1173.68i | 1.39890i | 0.714681 | + | 0.699451i | \(0.246572\pi\) | ||||
−0.714681 | + | 0.699451i | \(0.753428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −204.123 | −0.242715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 125.322 | − | 270.786i | 0.148662 | − | 0.321217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −192.936 | − | 1386.73i | −0.228326 | − | 1.64111i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.886377i | 0.00104649i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 613.659 | − | 1325.95i | 0.722802 | − | 1.56178i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 935.034i | 1.09875i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 112.279i | 0.131629i | 0.997832 | + | 0.0658143i | \(0.0209645\pi\) | ||||
−0.997832 | + | 0.0658143i | \(0.979036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 693.760 | − | 777.310i | 0.811416 | − | 0.909134i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −619.631 | −0.723023 | −0.361511 | − | 0.932368i | \(-0.617739\pi\) | ||||
−0.361511 | + | 0.932368i | \(0.617739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1227.29 | 1.42875 | 0.714373 | − | 0.699765i | \(-0.246712\pi\) | ||||
0.714373 | + | 0.699765i | \(0.246712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 78.2916 | + | 36.2339i | 0.0909310 | + | 0.0420835i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 975.318 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 91.1910 | + | 655.439i | 0.105423 | + | 0.757734i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −652.082 | − | 301.788i | −0.752113 | − | 0.348083i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1324.90i | 1.52462i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 706.656 | 0.811316 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 789.017 | − | 669.844i | 0.903799 | − | 0.767290i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 84.1720 | − | 37.0578i | 0.0961966 | − | 0.0423517i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 991.857i | − | 1.13097i | −0.824760 | − | 0.565483i | \(-0.808690\pi\) | ||
0.824760 | − | 0.565483i | \(-0.191310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −934.131 | − | 432.322i | −1.06272 | − | 0.491834i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1024.25i | 1.16260i | 0.813690 | + | 0.581299i | \(0.197455\pi\) | ||||
−0.813690 | + | 0.581299i | \(0.802545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1170.22i | 1.32527i | 0.748941 | + | 0.662637i | \(0.230563\pi\) | ||||
−0.748941 | + | 0.662637i | \(0.769437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 111.895 | + | 34.0269i | 0.126435 | + | 0.0384485i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −540.358 | −0.609197 | −0.304599 | − | 0.952481i | \(-0.598522\pi\) | ||||
−0.304599 | + | 0.952481i | \(0.598522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −154.309 | −0.173576 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 874.800 | + | 143.883i | 0.981818 | + | 0.161485i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 905.453 | 1.01395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 456.849 | − | 63.5612i | 0.510446 | − | 0.0710181i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −660.777 | + | 1427.76i | −0.736652 | + | 1.59170i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1129.82i | − | 1.25675i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 428.550 | 0.475638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.4315 | + | 21.0260i | 0.0503118 | + | 0.0232846i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 79.8539 | + | 573.953i | 0.0882363 | + | 0.634202i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 682.738i | 0.752744i | 0.926469 | + | 0.376372i | \(0.122828\pi\) | ||||
−0.926469 | + | 0.376372i | \(0.877172\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −200.205 | + | 169.966i | −0.220247 | + | 0.186981i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1326.30i | 1.45587i | 0.685647 | + | 0.727934i | \(0.259519\pi\) | ||||
−0.685647 | + | 0.727934i | \(0.740481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 987.626i | − | 1.08174i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.6726 | − | 160.056i | 0.0531941 | − | 0.174925i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −154.545 | −0.168533 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −688.107 | −0.748756 | −0.374378 | − | 0.927276i | \(-0.622144\pi\) | ||||
−0.374378 | + | 0.927276i | \(0.622144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −459.437 | + | 992.719i | −0.498846 | + | 1.07787i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2054.69 | 2.22610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −257.837 | − | 908.672i | −0.278743 | − | 0.982348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 617.132 | − | 523.920i | 0.665730 | − | 0.565178i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 637.084i | 0.685774i | 0.939377 | + | 0.342887i | \(0.111405\pi\) | ||||
−0.939377 | + | 0.342887i | \(0.888595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1121.96 | −1.20511 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 153.676 | − | 332.052i | 0.164712 | − | 0.355897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 381.314 | − | 53.0521i | 0.407823 | − | 0.0567402i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 358.254i | 0.382341i | 0.981557 | + | 0.191171i | \(0.0612284\pi\) | ||||
−0.981557 | + | 0.191171i | \(0.938772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −119.458 | + | 258.115i | −0.127218 | + | 0.274883i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 124.973i | 0.132809i | 0.997793 | + | 0.0664043i | \(0.0211527\pi\) | ||||
−0.997793 | + | 0.0664043i | \(0.978847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 967.282i | − | 1.02575i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −39.4719 | − | 91.1462i | −0.0417692 | − | 0.0964510i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 378.826 | 0.400027 | 0.200014 | − | 0.979793i | \(-0.435901\pi\) | ||||
0.200014 | + | 0.979793i | \(0.435901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2850.81 | 3.00402 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1392.00 | − | 644.226i | −1.46372 | − | 0.677419i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.82139 | 0.00715780 | 0.00357890 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357890 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 263.058 | − | 36.5991i | 0.275453 | − | 0.0383237i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −963.344 | − | 445.842i | −1.00663 | − | 0.465875i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 124.112i | 0.129418i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 260.374 | 0.270941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −894.589 | − | 1053.75i | −0.928960 | − | 1.09423i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1343.63 | + | 186.939i | −1.39237 | + | 0.193719i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1193.53i | 1.23426i | 0.786861 | + | 0.617130i | \(0.211705\pi\) | ||||
−0.786861 | + | 0.617130i | \(0.788295\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −443.445 | − | 205.229i | −0.457631 | − | 0.211795i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1256.06i | − | 1.29357i | −0.762672 | − | 0.646785i | \(-0.776113\pi\) | ||
0.762672 | − | 0.646785i | \(-0.223887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 95.0964i | 0.0977353i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 248.440 | − | 1569.72i | 0.254810 | − | 1.60996i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 551.251 | 0.564228 | 0.282114 | − | 0.959381i | \(-0.408964\pi\) | ||||
0.282114 | + | 0.959381i | \(0.408964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −582.110 | −0.594597 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −346.932 | − | 408.656i | −0.353652 | − | 0.416570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1598.65 | −1.62630 | −0.813151 | − | 0.582053i | \(-0.802250\pi\) | ||||
−0.813151 | + | 0.582053i | \(0.802250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.3682 | − | 318.899i | −0.0450439 | − | 0.323755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.2550 | − | 78.3371i | 0.0367325 | − | 0.0793689i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 561.300i | − | 0.567543i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1734.40 | 1.75015 | 0.875077 | − | 0.483984i | \(-0.160811\pi\) | ||||
0.875077 | + | 0.483984i | \(0.160811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 497.363 | + | 230.183i | 0.500869 | + | 0.231806i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.6300 | − | 356.718i | −0.0498794 | − | 0.358511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1118.15i | − | 1.12151i | −0.827980 | − | 0.560757i | \(-0.810510\pi\) | ||
0.827980 | − | 0.560757i | \(-0.189490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −983.032 | + | 272.525i | −0.984016 | + | 0.272798i |
(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 | 240.3.c.e.209.12 | 12 | ||
3.2 | odd | 2 | inner | 240.3.c.e.209.2 | 12 | ||
4.3 | odd | 2 | 120.3.c.a.89.1 | ✓ | 12 | ||
5.2 | odd | 4 | 1200.3.l.y.401.7 | 12 | |||
5.3 | odd | 4 | 1200.3.l.y.401.6 | 12 | |||
5.4 | even | 2 | inner | 240.3.c.e.209.1 | 12 | ||
8.3 | odd | 2 | 960.3.c.k.449.12 | 12 | |||
8.5 | even | 2 | 960.3.c.j.449.1 | 12 | |||
12.11 | even | 2 | 120.3.c.a.89.11 | yes | 12 | ||
15.2 | even | 4 | 1200.3.l.y.401.8 | 12 | |||
15.8 | even | 4 | 1200.3.l.y.401.5 | 12 | |||
15.14 | odd | 2 | inner | 240.3.c.e.209.11 | 12 | ||
20.3 | even | 4 | 600.3.l.g.401.7 | 12 | |||
20.7 | even | 4 | 600.3.l.g.401.6 | 12 | |||
20.19 | odd | 2 | 120.3.c.a.89.12 | yes | 12 | ||
24.5 | odd | 2 | 960.3.c.j.449.11 | 12 | |||
24.11 | even | 2 | 960.3.c.k.449.2 | 12 | |||
40.19 | odd | 2 | 960.3.c.k.449.1 | 12 | |||
40.29 | even | 2 | 960.3.c.j.449.12 | 12 | |||
60.23 | odd | 4 | 600.3.l.g.401.8 | 12 | |||
60.47 | odd | 4 | 600.3.l.g.401.5 | 12 | |||
60.59 | even | 2 | 120.3.c.a.89.2 | yes | 12 | ||
120.29 | odd | 2 | 960.3.c.j.449.2 | 12 | |||
120.59 | even | 2 | 960.3.c.k.449.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.c.a.89.1 | ✓ | 12 | 4.3 | odd | 2 | ||
120.3.c.a.89.2 | yes | 12 | 60.59 | even | 2 | ||
120.3.c.a.89.11 | yes | 12 | 12.11 | even | 2 | ||
120.3.c.a.89.12 | yes | 12 | 20.19 | odd | 2 | ||
240.3.c.e.209.1 | 12 | 5.4 | even | 2 | inner | ||
240.3.c.e.209.2 | 12 | 3.2 | odd | 2 | inner | ||
240.3.c.e.209.11 | 12 | 15.14 | odd | 2 | inner | ||
240.3.c.e.209.12 | 12 | 1.1 | even | 1 | trivial | ||
600.3.l.g.401.5 | 12 | 60.47 | odd | 4 | |||
600.3.l.g.401.6 | 12 | 20.7 | even | 4 | |||
600.3.l.g.401.7 | 12 | 20.3 | even | 4 | |||
600.3.l.g.401.8 | 12 | 60.23 | odd | 4 | |||
960.3.c.j.449.1 | 12 | 8.5 | even | 2 | |||
960.3.c.j.449.2 | 12 | 120.29 | odd | 2 | |||
960.3.c.j.449.11 | 12 | 24.5 | odd | 2 | |||
960.3.c.j.449.12 | 12 | 40.29 | even | 2 | |||
960.3.c.k.449.1 | 12 | 40.19 | odd | 2 | |||
960.3.c.k.449.2 | 12 | 24.11 | even | 2 | |||
960.3.c.k.449.11 | 12 | 120.59 | even | 2 | |||
960.3.c.k.449.12 | 12 | 8.3 | odd | 2 | |||
1200.3.l.y.401.5 | 12 | 15.8 | even | 4 | |||
1200.3.l.y.401.6 | 12 | 5.3 | odd | 4 | |||
1200.3.l.y.401.7 | 12 | 5.2 | odd | 4 | |||
1200.3.l.y.401.8 | 12 | 15.2 | even | 4 |