Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(449,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.g (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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(1.32001 - 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.449 |
Dual form | 560.2.g.f.449.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.12489i | 1.80415i | 0.431576 | + | 0.902077i | \(0.357958\pi\) | ||||
−0.431576 | + | 0.902077i | \(0.642042\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.32001 | − | 1.80487i | 0.590327 | − | 0.807164i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.76491 | −2.25497 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.48486 | −0.749214 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.15516i | 1.15243i | 0.817297 | + | 0.576217i | \(0.195472\pi\) | ||||
−0.817297 | + | 0.576217i | \(0.804528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.64002 | + | 4.12489i | 1.45625 | + | 1.06504i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.76491i | 1.39820i | 0.715026 | + | 0.699098i | \(0.246415\pi\) | ||||
−0.715026 | + | 0.699098i | \(0.753585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.60975 | −0.369301 | −0.184651 | − | 0.982804i | \(-0.559115\pi\) | ||||
−0.184651 | + | 0.982804i | \(0.559115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12489 | −0.681906 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.28005i | 1.51799i | 0.651094 | + | 0.758997i | \(0.274310\pi\) | ||||
−0.651094 | + | 0.758997i | \(0.725690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.51514 | − | 4.76491i | −0.303028 | − | 0.952982i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 11.7649i | − | 2.26416i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45459 | −0.270110 | −0.135055 | − | 0.990838i | \(-0.543121\pi\) | ||||
−0.135055 | + | 0.990838i | \(0.543121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.24977 | 0.404071 | 0.202035 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202035 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 7.76491i | − | 1.35170i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.80487 | + | 1.32001i | 0.305079 | + | 0.223123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00000i | − | 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.9844 | −2.07917 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2800 | 1.76165 | 0.880824 | − | 0.473444i | \(-0.156990\pi\) | ||||
0.880824 | + | 0.473444i | \(0.156990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.28005i | − | 0.805200i | −0.915376 | − | 0.402600i | \(-0.868107\pi\) | ||
0.915376 | − | 0.402600i | \(-0.131893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.92976 | + | 12.2098i | −1.33117 | + | 1.82013i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.45459i | − | 0.503903i | −0.967740 | − | 0.251952i | \(-0.918928\pi\) | ||
0.967740 | − | 0.251952i | \(-0.0810724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.0147 | −2.52256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.21949i | 1.26639i | 0.773990 | + | 0.633197i | \(0.218258\pi\) | ||||
−0.773990 | + | 0.633197i | \(0.781742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.28005 | + | 4.48486i | −0.442281 | + | 0.604739i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.03028i | − | 0.666276i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.92007 | −0.770728 | −0.385364 | − | 0.922765i | \(-0.625924\pi\) | ||||
−0.385364 | + | 0.922765i | \(0.625924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.35998 | 0.686275 | 0.343137 | − | 0.939285i | \(-0.388510\pi\) | ||||
0.343137 | + | 0.939285i | \(0.388510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 6.76491i | − | 0.852298i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.49954 | + | 5.48486i | 0.930204 | + | 0.680313i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.52982i | 0.919914i | 0.887941 | + | 0.459957i | \(0.152135\pi\) | ||||
−0.887941 | + | 0.459957i | \(0.847865\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.7493 | −2.73870 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.24977 | 0.504355 | 0.252178 | − | 0.967681i | \(-0.418853\pi\) | ||||
0.252178 | + | 0.967681i | \(0.418853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.28005i | − | 0.852065i | −0.904708 | − | 0.426033i | \(-0.859911\pi\) | ||
0.904708 | − | 0.426033i | \(-0.140089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.8898 | − | 4.73463i | 1.71933 | − | 0.546708i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.48486i | − | 0.283176i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9844 | 1.91089 | 0.955447 | − | 0.295162i | \(-0.0953735\pi\) | ||||
0.955447 | + | 0.295162i | \(0.0953735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.4693 | 1.82992 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.1093i | − | 1.10964i | −0.831971 | − | 0.554819i | \(-0.812787\pi\) | ||
0.831971 | − | 0.554819i | \(-0.187213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.4049 | + | 7.60975i | 1.12857 | + | 0.825393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.54541i | − | 0.487320i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4693 | 1.21574 | 0.607870 | − | 0.794037i | \(-0.292024\pi\) | ||||
0.607870 | + | 0.794037i | \(0.292024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.15516 | −0.435579 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.03028i | 0.729006i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.12489 | + | 2.90539i | −0.218009 | + | 0.298087i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.73463i | − | 0.277660i | −0.990316 | − | 0.138830i | \(-0.955666\pi\) | ||
0.990316 | − | 0.138830i | \(-0.0443341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.8099 | 1.68945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.57947 | −0.455674 | −0.227837 | − | 0.973699i | \(-0.573165\pi\) | ||||
−0.227837 | + | 0.973699i | \(0.573165\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.48486i | − | 0.244841i | −0.992478 | − | 0.122420i | \(-0.960934\pi\) | ||
0.992478 | − | 0.122420i | \(-0.0390656\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.12489 | + | 5.64002i | −0.402548 | + | 0.550410i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.95413 | 0.953433 | 0.476716 | − | 0.879057i | \(-0.341827\pi\) | ||||
0.476716 | + | 0.879057i | \(0.341827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.7493 | 1.77961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4995i | 1.74029i | 0.492795 | + | 0.870145i | \(0.335975\pi\) | ||||
−0.492795 | + | 0.870145i | \(0.664025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.1396 | + | 9.60975i | 1.22527 | + | 0.896114i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 28.1093i | − | 2.59870i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.76491 | −0.528468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.82546 | −0.438678 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.2489i | 3.17828i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6001 | − | 3.55510i | −0.948098 | − | 0.317978i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.15894i | 0.635253i | 0.948216 | + | 0.317627i | \(0.102886\pi\) | ||||
−0.948216 | + | 0.317627i | \(0.897114\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.4995 | 1.45270 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.85952 | −0.686689 | −0.343345 | − | 0.939209i | \(-0.611560\pi\) | ||||
−0.343345 | + | 0.939209i | \(0.611560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.60975i | − | 0.139583i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.2342 | − | 15.5298i | −1.82755 | − | 1.33659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.5601i | − | 0.902210i | −0.892471 | − | 0.451105i | \(-0.851030\pi\) | ||
0.892471 | − | 0.451105i | \(-0.148970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.79897 | 0.831137 | 0.415569 | − | 0.909562i | \(-0.363583\pi\) | ||||
0.415569 | + | 0.909562i | \(0.363583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7952 | 0.909119 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 10.3250i | − | 0.863420i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.92007 | + | 2.62534i | −0.159453 | + | 0.218023i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 3.12489i | − | 0.257736i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.49954 | −0.204770 | −0.102385 | − | 0.994745i | \(-0.532647\pi\) | ||||
−0.102385 | + | 0.994745i | \(0.532647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.76491 | 0.306384 | 0.153192 | − | 0.988196i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 38.9991i | − | 3.15289i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.96972 | − | 4.06055i | 0.238534 | − | 0.326151i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.67030i | − | 0.452539i | −0.974065 | − | 0.226270i | \(-0.927347\pi\) | ||
0.974065 | − | 0.226270i | \(-0.0726530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.8099 | −2.28477 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.28005 | −0.573748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.2498i | − | 0.802824i | −0.915898 | − | 0.401412i | \(-0.868520\pi\) | ||
0.915898 | − | 0.401412i | \(-0.131480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.0147 | − | 10.2498i | −1.09104 | − | 0.797944i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.95504i | − | 0.228668i | −0.993442 | − | 0.114334i | \(-0.963527\pi\) | ||
0.993442 | − | 0.114334i | \(-0.0364734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.26537 | −0.328105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8898 | 0.832763 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4049i | 1.70342i | 0.524017 | + | 0.851708i | \(0.324433\pi\) | ||||
−0.524017 | + | 0.851708i | \(0.675567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.76491 | − | 1.51514i | 0.360193 | − | 0.114534i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 18.4995i | − | 1.39051i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5601 | 1.08827 | 0.544136 | − | 0.838997i | \(-0.316857\pi\) | ||||
0.544136 | + | 0.838997i | \(0.316857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.67030 | −0.718788 | −0.359394 | − | 0.933186i | \(-0.617017\pi\) | ||||
−0.359394 | + | 0.933186i | \(0.617017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.7493i | 1.23814i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8292 | − | 7.92007i | −0.796182 | − | 0.582295i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.3250i | − | 1.04755i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.7649 | 0.855771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.01468 | −0.579922 | −0.289961 | − | 0.957038i | \(-0.593642\pi\) | ||||
−0.289961 | + | 0.957038i | \(0.593642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.46927i | 0.249723i | 0.992174 | + | 0.124862i | \(0.0398487\pi\) | ||||
−0.992174 | + | 0.124862i | \(0.960151\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.1396 | + | 23.4352i | −1.22739 | + | 1.67823i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2791i | 1.15984i | 0.814673 | + | 0.579920i | \(0.196916\pi\) | ||||
−0.814673 | + | 0.579920i | \(0.803084\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.8704 | 1.90479 | 0.952397 | − | 0.304862i | \(-0.0986102\pi\) | ||||
0.952397 | + | 0.304862i | \(0.0986102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.5298 | −1.65967 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.45459i | − | 0.102092i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.8898 | − | 20.3591i | 1.03995 | − | 1.42194i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 49.2489i | − | 3.42303i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2342 | −1.18645 | −0.593225 | − | 0.805037i | \(-0.702145\pi\) | ||||
−0.593225 | + | 0.805037i | \(0.702145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2800i | 0.909934i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.52982 | − | 6.96972i | −0.649928 | − | 0.475331i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24977i | 0.152724i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.7493 | 1.53726 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.9541 | −1.61133 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.235091i | 0.0157429i | 0.999969 | + | 0.00787143i | \(0.00250558\pi\) | ||||
−0.999969 | + | 0.00787143i | \(0.997494\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.2498 | + | 32.2342i | 0.683318 | + | 2.14894i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 0.564792i | − | 0.0374865i | −0.999824 | − | 0.0187433i | \(-0.994033\pi\) | ||
0.999824 | − | 0.0187433i | \(-0.00596652\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.11021 | −0.469856 | −0.234928 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234928 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.76491 | 0.510893 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.49954i | 0.556823i | 0.960462 | + | 0.278412i | \(0.0898080\pi\) | ||||
−0.960462 | + | 0.278412i | \(0.910192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.23509 | − | 4.56009i | −0.406732 | − | 0.297468i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 53.0743i | 3.44755i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.26537 | −0.469958 | −0.234979 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234979 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.28005 | 0.468949 | 0.234475 | − | 0.972122i | \(-0.424663\pi\) | ||||
0.234475 | + | 0.972122i | \(0.424663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1698i | 1.03730i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.32001 | + | 1.80487i | −0.0843325 | + | 0.115309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.68876i | − | 0.425596i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.5904 | 2.00196 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9192 | −1.44664 | −0.723322 | − | 0.690511i | \(-0.757386\pi\) | ||||
−0.723322 | + | 0.690511i | \(0.757386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.0899i | − | 1.13730i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.7796 | + | 32.5142i | −1.48914 | + | 2.03612i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 0.719953i | − | 0.0449094i | −0.999748 | − | 0.0224547i | \(-0.992852\pi\) | ||
0.999748 | − | 0.0224547i | \(-0.00714816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.84014 | 0.609089 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.5601i | 1.14446i | 0.820092 | + | 0.572232i | \(0.193922\pi\) | ||||
−0.820092 | + | 0.572232i | \(0.806078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.6400 | + | 12.1698i | 1.02219 | + | 0.747587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.8401i | 2.19338i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1698 | 1.35172 | 0.675860 | − | 0.737030i | \(-0.263773\pi\) | ||||
0.675860 | + | 0.737030i | \(0.263773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.87890 | 0.478609 | 0.239304 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239304 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 12.9844i | − | 0.785852i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.76491 | + | 11.8401i | 0.227033 | + | 0.713987i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.78051i | 0.167064i | 0.996505 | + | 0.0835322i | \(0.0266201\pi\) | ||||
−0.996505 | + | 0.0835322i | \(0.973380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.2195 | −0.911167 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.7044 | −1.41408 | −0.707042 | − | 0.707172i | \(-0.749971\pi\) | ||||
−0.707042 | + | 0.707172i | \(0.749971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 26.8439i | − | 1.59571i | −0.602852 | − | 0.797853i | \(-0.705969\pi\) | ||
0.602852 | − | 0.797853i | \(-0.294031\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.07901 | − | 6.64002i | −0.537794 | − | 0.393321i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.2800i | 0.665840i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2342 | −0.954951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.54541 | 0.500941 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.93475i | − | 0.580394i | −0.956967 | − | 0.290197i | \(-0.906279\pi\) | ||
0.956967 | − | 0.290197i | \(-0.0937209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.81456 | + | 10.6850i | −0.454981 | + | 0.622104i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.2342i | 1.69634i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −30.2498 | −1.74939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.28005 | 0.304337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 14.3103i | − | 0.822107i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.07523 | − | 9.67408i | 0.405127 | − | 0.553936i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.0946i | − | 1.83174i | −0.401479 | − | 0.915868i | \(-0.631504\pi\) | ||
0.401479 | − | 0.915868i | \(-0.368496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.76491 | 0.441730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0606 | 0.570482 | 0.285241 | − | 0.958456i | \(-0.407926\pi\) | ||||
0.285241 | + | 0.958456i | \(0.407926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8245i | 1.17707i | 0.808471 | + | 0.588536i | \(0.200296\pi\) | ||||
−0.808471 | + | 0.588536i | \(0.799704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.2098 | − | 8.92976i | −0.687945 | − | 0.503135i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 15.7502i | − | 0.884621i | −0.896862 | − | 0.442311i | \(-0.854159\pi\) | ||
0.896862 | − | 0.442311i | \(-0.145841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.61445 | 0.202370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.28005i | − | 0.516356i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.7990 | − | 6.29564i | 1.09825 | − | 0.349219i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.1055i | 1.72014i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.45459 | 0.190457 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.7796 | 1.41697 | 0.708487 | − | 0.705724i | \(-0.249378\pi\) | ||||
0.708487 | + | 0.705724i | \(0.249378\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 40.5895i | 2.22429i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.5904 | + | 9.93945i | 0.742521 | + | 0.543050i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.0605522i | − | 0.00329849i | −0.999999 | − | 0.00164924i | \(-0.999475\pi\) | ||
0.999999 | − | 0.00164924i | \(-0.000524971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −57.8089 | −3.13975 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.59037 | −0.302736 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.0294 | + | 41.0596i | −1.61673 | + | 2.21058i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.9310i | − | 1.12363i | −0.827262 | − | 0.561817i | \(-0.810103\pi\) | ||
0.827262 | − | 0.561817i | \(-0.189897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.48108 | −0.293396 | −0.146698 | − | 0.989181i | \(-0.546864\pi\) | ||||
−0.146698 | + | 0.989181i | \(0.546864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 48.8851 | 2.60929 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.9239i | − | 1.43301i | −0.697581 | − | 0.716506i | \(-0.745740\pi\) | ||
0.697581 | − | 0.716506i | \(-0.254260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.60975 | − | 7.67030i | 0.297734 | − | 0.407097i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 18.0147i | − | 0.953438i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.06055 | 0.319864 | 0.159932 | − | 0.987128i | \(-0.448873\pi\) | ||||
0.159932 | + | 0.987128i | \(0.448873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4087 | −0.863616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.0790i | − | 0.791443i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.1396 | − | 9.60975i | −0.687756 | − | 0.502997i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7034i | 1.60271i | 0.598191 | + | 0.801353i | \(0.295886\pi\) | ||||
−0.598191 | + | 0.801353i | \(0.704114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −76.3085 | −3.97246 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.21949 | −0.478652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.8099i | − | 0.559714i | −0.960042 | − | 0.279857i | \(-0.909713\pi\) | ||
0.960042 | − | 0.279857i | \(-0.0902870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1093 | − | 33.1240i | 0.573681 | − | 1.71051i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.04404i | − | 0.311284i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.28005 | −0.476684 | −0.238342 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238342 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.3709 | −1.14609 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.28005i | 0.269798i | 0.990859 | + | 0.134899i | \(0.0430710\pi\) | ||||
−0.990859 | + | 0.134899i | \(0.956929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.48486 | − | 3.28005i | −0.228570 | − | 0.167167i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 35.7190i | 1.81570i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.48395 | −0.278047 | −0.139024 | − | 0.990289i | \(-0.544396\pi\) | ||||
−0.139024 | + | 0.990289i | \(0.544396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.9688 | −2.12245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.5601i | − | 1.23889i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.4196 | − | 30.6547i | 1.12805 | − | 1.54241i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.40493i | − | 0.321454i | −0.986999 | − | 0.160727i | \(-0.948616\pi\) | ||
0.986999 | − | 0.160727i | \(-0.0513839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.03028 | 0.251829 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.20482 | −0.0601656 | −0.0300828 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300828 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.34816i | 0.465665i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.7396 | − | 29.7249i | 1.08025 | − | 1.47704i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9092i | 0.739020i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.31032 | 0.114238 | 0.0571191 | − | 0.998367i | \(-0.481809\pi\) | ||||
0.0571191 | + | 0.998367i | \(0.481809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.9991 | 1.62772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.92007i | − | 0.291308i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2460 | − | 13.3444i | −0.895660 | − | 0.655050i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.6206i | 1.49950i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.7384 | −0.964285 | −0.482142 | − | 0.876093i | \(-0.660141\pi\) | ||||
−0.482142 | + | 0.876093i | \(0.660141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1433 | 1.46910 | 0.734548 | − | 0.678556i | \(-0.237394\pi\) | ||||
0.734548 | + | 0.678556i | \(0.237394\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.3700i | 1.13629i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.4693 | − | 8.73463i | 1.33246 | − | 0.423692i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.35998i | 0.259387i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.2645 | 1.55774 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.61353 | 0.222226 | 0.111113 | − | 0.993808i | \(-0.464558\pi\) | ||||
0.111113 | + | 0.993808i | \(0.464558\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.4399i | − | 0.549767i | −0.961478 | − | 0.274883i | \(-0.911361\pi\) | ||
0.961478 | − | 0.274883i | \(-0.0886393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.20390 | − | 6.00000i | −0.393347 | − | 0.287678i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11.7190i | − | 0.560598i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0294 | 0.574130 | 0.287065 | − | 0.957911i | \(-0.407320\pi\) | ||||
0.287065 | + | 0.957911i | \(0.407320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76491 | 0.322139 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4390i | 0.686017i | 0.939332 | + | 0.343009i | \(0.111446\pi\) | ||||
−0.939332 | + | 0.343009i | \(0.888554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.1396 | − | 20.7006i | 0.717684 | − | 0.981301i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.81078i | − | 0.369437i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.2342 | −0.907717 | −0.453858 | − | 0.891074i | \(-0.649953\pi\) | ||||
−0.453858 | + | 0.891074i | \(0.649953\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.0294 | −1.31985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.7649i | 0.552764i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.48486 | + | 7.49954i | −0.257134 | + | 0.351584i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 34.8780i | − | 1.63152i | −0.578388 | − | 0.815762i | \(-0.696318\pi\) | ||
0.578388 | − | 0.815762i | \(-0.303682\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 67.8236 | 3.16574 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2607 | −0.710760 | −0.355380 | − | 0.934722i | \(-0.615649\pi\) | ||||
−0.355380 | + | 0.934722i | \(0.615649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.9991i | − | 1.16181i | −0.813973 | − | 0.580903i | \(-0.802700\pi\) | ||
0.813973 | − | 0.580903i | \(-0.197300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.6888 | + | 9.28005i | 0.588427 | + | 0.430352i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.06433i | 0.234349i | 0.993111 | + | 0.117175i | \(0.0373837\pi\) | ||||
−0.993111 | + | 0.117175i | \(0.962616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.52982 | −0.347695 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7190 | 0.816450 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.1202i | 0.603267i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.43899 | + | 7.67030i | 0.111909 | + | 0.351937i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 62.3690i | − | 2.85568i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.8089 | 1.91030 | 0.955150 | − | 0.296123i | \(-0.0956938\pi\) | ||||
0.955150 | + | 0.296123i | \(0.0956938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.9310 | 1.13675 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 22.7493i | − | 1.03513i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.93567 | − | 3.60975i | −0.224117 | − | 0.163910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3406i | 0.967035i | 0.875335 | + | 0.483517i | \(0.160641\pi\) | ||||
−0.875335 | + | 0.483517i | \(0.839359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.0294 | 1.44842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.35620 | −0.377110 | −0.188555 | − | 0.982063i | \(-0.560380\pi\) | ||||
−0.188555 | + | 0.982063i | \(0.560380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.38555i | − | 0.377666i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.1892 | − | 30.3397i | 0.997331 | − | 1.36367i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.24977i | 0.190628i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8539 | −1.73934 | −0.869670 | − | 0.493634i | \(-0.835668\pi\) | ||||
−0.869670 | + | 0.493634i | \(0.835668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.23417 | 0.412552 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.7044i | 0.789398i | 0.918810 | + | 0.394699i | \(0.129151\pi\) | ||||
−0.918810 | + | 0.394699i | \(0.870849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.04496 | + | 8.26537i | −0.268997 | + | 0.367804i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 13.3288i | − | 0.591952i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.11021 | −0.315154 | −0.157577 | − | 0.987507i | \(-0.550368\pi\) | ||||
−0.157577 | + | 0.987507i | \(0.550368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.28005 | 0.322050 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9385i | 0.836157i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.48486 | − | 3.28005i | −0.197627 | − | 0.144536i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.58417i | 0.377531i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −70.0128 | −3.07322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1892 | 0.796884 | 0.398442 | − | 0.917194i | \(-0.369551\pi\) | ||||
0.398442 | + | 0.917194i | \(0.369551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9882i | 0.611661i | 0.952086 | + | 0.305830i | \(0.0989340\pi\) | ||||
−0.952086 | + | 0.305830i | \(0.901066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.73463 | + | 14.8898i | 0.206636 | + | 0.649844i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9697i | 0.564970i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.9991 | −1.30431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.0487 | 1.73797 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.8704i | 2.03018i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.4986i | 1.96341i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.48486 | 0.107031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.8245 | −0.895317 | −0.447659 | − | 0.894205i | \(-0.647742\pi\) | ||||
−0.447659 | + | 0.894205i | \(0.647742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 30.2186i | − | 1.29680i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.1396 | − | 17.9659i | 0.562837 | − | 0.769576i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.09839i | − | 0.132478i | −0.997804 | − | 0.0662388i | \(-0.978900\pi\) | ||
0.997804 | − | 0.0662388i | \(-0.0210999\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.2598 | −1.54753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.34152 | 0.0997519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.9844i | 0.722250i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.7493 | − | 33.8401i | 1.05055 | − | 1.43643i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.8099i | − | 0.797000i | −0.917168 | − | 0.398500i | \(-0.869531\pi\) | ||
0.917168 | − | 0.398500i | \(-0.130469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9394 | 0.927940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.7640 | 1.88994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9503i | 1.22011i | 0.792358 | + | 0.610056i | \(0.208853\pi\) | ||||
−0.792358 | + | 0.610056i | \(0.791147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.3893 | + | 24.4196i | 1.40470 | + | 1.02734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.4693i | 0.691644i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.9688 | 1.25636 | 0.628179 | − | 0.778069i | \(-0.283801\pi\) | ||||
0.628179 | + | 0.778069i | \(0.283801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.280964 | −0.0117580 | −0.00587898 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587898 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 25.0450i | − | 1.04627i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.6888 | − | 11.0303i | 1.44662 | − | 0.459994i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.9541i | 1.08048i | 0.841510 | + | 0.540242i | \(0.181667\pi\) | ||||
−0.841510 | + | 0.540242i | \(0.818333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8411 | −0.450539 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.1093 | 0.419404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.9092i | − | 0.948801i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −50.7337 | − | 37.1046i | −2.09758 | − | 1.53409i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2304i | 0.917547i | 0.888553 | + | 0.458773i | \(0.151711\pi\) | ||||
−0.888553 | + | 0.458773i | \(0.848289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.62156 | −0.149224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.8704 | −2.09253 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.0743i | − | 1.44033i | −0.693803 | − | 0.720165i | \(-0.744066\pi\) | ||
0.693803 | − | 0.720165i | \(-0.255934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.60975 | + | 10.4049i | −0.311969 | + | 0.426561i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 83.9670i | 3.43654i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.7262 | −0.887707 | −0.443853 | − | 0.896099i | \(-0.646389\pi\) | ||||
−0.443853 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.9688 | −0.977708 | −0.488854 | − | 0.872366i | \(-0.662585\pi\) | ||||
−0.488854 | + | 0.872366i | \(0.662585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 50.9385i | − | 2.07438i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.36967 | + | 8.70935i | −0.258964 | + | 0.354085i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 43.3241i | − | 1.75847i | −0.476388 | − | 0.879235i | \(-0.658054\pi\) | ||
0.476388 | − | 0.879235i | \(-0.341946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.54541 | 0.184189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3544 | 0.580715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.90917i | 0.359838i | 0.983681 | + | 0.179919i | \(0.0575836\pi\) | ||||
−0.983681 | + | 0.179919i | \(0.942416\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.6197 | + | 46.5289i | 2.56540 | + | 1.87623i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.2413i | 1.09669i | 0.836251 | + | 0.548347i | \(0.184743\pi\) | ||||
−0.836251 | + | 0.548347i | \(0.815257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1405 | 0.970288 | 0.485144 | − | 0.874434i | \(-0.338767\pi\) | ||||
0.485144 | + | 0.874434i | \(0.338767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 85.6491 | 3.43698 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4693i | 0.459506i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.4087 | + | 14.4390i | −0.816349 | + | 0.577560i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.4995i | 0.499184i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.5895 | 1.37917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.01468 | −0.319059 | −0.159530 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159530 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 53.8548i | − | 2.14054i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9210 | + | 9.44989i | 0.512754 | + | 0.375007i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.15516i | − | 0.164633i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.7493 | −1.13731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.1495 | −1.94129 | −0.970645 | − | 0.240516i | \(-0.922683\pi\) | ||||
−0.970645 | + | 0.240516i | \(0.922683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.24599i | 0.285754i | 0.989740 | + | 0.142877i | \(0.0456353\pi\) | ||||
−0.989740 | + | 0.142877i | \(0.954365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.7796 | − | 29.7796i | 0.857570 | − | 1.17257i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.2791i | − | 1.19040i | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||
0.803579 | − | 0.595198i | \(-0.202926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7106 | 0.577440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.03028 | −0.275538 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 7.96881i | − | 0.311844i | −0.987769 | − | 0.155922i | \(-0.950165\pi\) | ||
0.987769 | − | 0.155922i | \(-0.0498348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3747 | + | 14.1854i | −0.405371 | + | 0.554271i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 49.2489i | 1.92138i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9239 | 0.815078 | 0.407539 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407539 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1992 | 1.79694 | 0.898470 | − | 0.439034i | \(-0.144679\pi\) | ||||
0.898470 | + | 0.439034i | \(0.144679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 74.8539i | − | 2.90708i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.90539 | − | 2.12489i | −0.112666 | − | 0.0823995i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.5895i | − | 0.410025i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.734633 | −0.0284025 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.3188 | −0.514167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 40.3784i | − | 1.55647i | −0.627970 | − | 0.778237i | \(-0.716114\pi\) | ||
0.627970 | − | 0.778237i | \(-0.283886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −56.0587 | + | 17.8255i | −2.15770 | + | 0.686102i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 44.3737i | − | 1.70542i | −0.522383 | − | 0.852711i | \(-0.674957\pi\) | ||
0.522383 | − | 0.852711i | \(-0.325043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.73463 | 0.104946 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.76491 | 0.0676315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9394i | 0.686434i | 0.939256 | + | 0.343217i | \(0.111517\pi\) | ||||
−0.939256 | + | 0.343217i | \(0.888483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.0596 | − | 13.9394i | −0.728231 | − | 0.532599i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.2186i | − | 0.847692i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.3085 | −1.45944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7905 | 0.486573 | 0.243287 | − | 0.969954i | \(-0.421774\pi\) | ||||
0.243287 | + | 0.969954i | \(0.421774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.8099i | 0.638554i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9348 | − | 17.6859i | 0.490643 | − | 0.670864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 65.0284i | 2.46313i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.5601 | −1.00460 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.4234 | −0.733611 | −0.366806 | − | 0.930298i | \(-0.619549\pi\) | ||||
−0.366806 | + | 0.930298i | \(0.619549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.65848i | 0.364277i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.2498 | − | 19.4839i | 0.536677 | − | 0.733808i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.57947i | − | 0.172229i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.4839 | 0.506400 | 0.253200 | − | 0.967414i | \(-0.418517\pi\) | ||||
0.253200 | + | 0.967414i | \(0.418517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −114.898 | −4.30901 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3784i | 0.613377i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.6353 | − | 13.6291i | −0.696922 | − | 0.509700i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 22.7034i | − | 0.847876i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.3700 | 0.573203 | 0.286601 | − | 0.958050i | \(-0.407474\pi\) | ||||
0.286601 | + | 0.958050i | \(0.407474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48486 | 0.0925411 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.7493i | 0.846056i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.20390 | + | 6.93097i | 0.0818507 | + | 0.257410i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1589i | 0.488038i | 0.969770 | + | 0.244019i | \(0.0784660\pi\) | ||||
−0.969770 | + | 0.244019i | \(0.921534\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.12110 | −0.0415224 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.4390 | 1.12583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.0265i | − | 0.370337i | −0.982707 | − | 0.185169i | \(-0.940717\pi\) | ||
0.982707 | − | 0.185169i | \(-0.0592831\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.64002 | − | 4.12489i | −0.208035 | − | 0.152149i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18.7106i | − | 0.689212i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2266 | 0.707262 | 0.353631 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353631 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.9016 | 0.767840 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.21949i | 0.191485i | 0.995406 | + | 0.0957423i | \(0.0305225\pi\) | ||||
−0.995406 | + | 0.0957423i | \(0.969478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.29942 | + | 4.51136i | −0.120882 | + | 0.165283i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 68.3884i | 2.50220i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8548 | −1.08942 | −0.544709 | − | 0.838625i | \(-0.683360\pi\) | ||||
−0.544709 | + | 0.838625i | \(0.683360\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 71.6197i | − | 2.60997i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.96972 | − | 6.79518i | 0.180867 | − | 0.247302i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.0294i | 0.655288i | 0.944801 | + | 0.327644i | \(0.106255\pi\) | ||||
−0.944801 | + | 0.327644i | \(0.893745\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 56.5289 | 2.05187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.22041 | 0.297990 | 0.148995 | − | 0.988838i | \(-0.452396\pi\) | ||||
0.148995 | + | 0.988838i | \(0.452396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.95413i | 0.360364i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −70.3884 | − | 51.4792i | −2.54490 | − | 1.86124i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.5988i | − | 0.888213i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.6888 | −1.82788 | −0.913942 | − | 0.405845i | \(-0.866977\pi\) | ||||
−0.913942 | + | 0.405845i | \(0.866977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.24977 | 0.0810235 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.99622i | 0.251637i | 0.992053 | + | 0.125818i | \(0.0401556\pi\) | ||||
−0.992053 | + | 0.125818i | \(0.959844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.40871 | − | 10.7200i | −0.122445 | − | 0.385072i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.7493i | 0.672628i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1580 | −0.650579 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5601 | −0.377870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.1131i | 0.611571i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.2342 | − | 7.48486i | −0.365273 | − | 0.267146i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 14.3444i | − | 0.511322i | −0.966767 | − | 0.255661i | \(-0.917707\pi\) | ||
0.966767 | − | 0.255661i | \(-0.0822931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −57.9982 | −2.06479 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.4995 | −0.657768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.2716i | 0.790887i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.0294 | + | 51.9982i | −1.34876 | + | 1.84418i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.9348i | 0.493594i | 0.969067 | + | 0.246797i | \(0.0793781\pi\) | ||||
−0.969067 | + | 0.246797i | \(0.920622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.9154 | 0.704555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −77.5885 | −2.74146 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0899i | 0.638379i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.60975 | + | 13.1396i | −0.338699 | + | 0.463109i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 69.2782i | 2.43871i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.58325 | 0.196297 | 0.0981483 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981483 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.57947 | 0.231036 | 0.115518 | − | 0.993305i | \(-0.463147\pi\) | ||||
0.115518 | + | 0.993305i | \(0.463147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.6206i | 0.863484i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.4995 | − | 13.5298i | −0.648011 | − | 0.473929i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.49954i | 0.297361i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.1093 | 0.982218 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3250 | 0.569747 | 0.284873 | − | 0.958565i | \(-0.408048\pi\) | ||||
0.284873 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12.3491i | − | 0.430462i | −0.976563 | − | 0.215231i | \(-0.930950\pi\) | ||
0.976563 | − | 0.215231i | \(-0.0690504\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.9991 | + | 11.7649i | −1.28814 | + | 0.409602i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.40963i | 0.222885i | 0.993771 | + | 0.111442i | \(0.0355470\pi\) | ||||
−0.993771 | + | 0.111442i | \(0.964453\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1698 | 0.908916 | 0.454458 | − | 0.890768i | \(-0.349833\pi\) | ||||
0.454458 | + | 0.890768i | \(0.349833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.68876 | −0.301410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.76491i | − | 0.199742i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.33348 | − | 3.90069i | −0.184573 | − | 0.134989i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 26.4683i | − | 0.914880i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.12958 | −0.0389975 | −0.0194988 | − | 0.999810i | \(-0.506207\pi\) | ||||
−0.0194988 | + | 0.999810i | \(0.506207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8842 | −0.927041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 74.0734i | − | 2.55122i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.63033 | + | 7.69845i | −0.193689 | + | 0.264835i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.82546i | − | 0.165805i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 83.8842 | 2.87890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.6803 | 1.49734 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.29095i | 0.215398i | 0.994184 | + | 0.107699i | \(0.0343483\pi\) | ||||
−0.994184 | + | 0.107699i | \(0.965652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.3747 | − | 19.6547i | 0.491603 | − | 0.672177i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0596i | 0.856021i | 0.903774 | + | 0.428010i | \(0.140785\pi\) | ||||
−0.903774 | + | 0.428010i | \(0.859215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.7896 | 1.83528 | 0.917638 | − | 0.397417i | \(-0.130093\pi\) | ||||
0.917638 | + | 0.397417i | \(0.130093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.2489 | −1.20128 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 58.0899i | 1.97740i | 0.149896 | + | 0.988702i | \(0.452106\pi\) | ||||
−0.149896 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.4381 | + | 29.5748i | 1.37494 | + | 1.00557i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 50.7299i | − | 1.72288i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.2039 | −1.43167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.2876 | −1.06014 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4995i | 0.626115i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.55510 | − | 10.6001i | 0.120184 | − | 0.358347i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0899i | 0.813459i | 0.913549 | + | 0.406729i | \(0.133331\pi\) | ||||
−0.913549 | + | 0.406729i | \(0.866669\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.0450 | 1.04712 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9679 | 1.38024 | 0.690122 | − | 0.723693i | \(-0.257557\pi\) | ||||
0.690122 | + | 0.723693i | \(0.257557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.8014i | 1.47403i | 0.675874 | + | 0.737017i | \(0.263766\pi\) | ||||
−0.675874 | + | 0.737017i | \(0.736234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.3893 | − | 24.4196i | −1.12237 | − | 0.820856i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.77959i | − | 0.0597527i | −0.999554 | − | 0.0298764i | \(-0.990489\pi\) | ||
0.999554 | − | 0.0298764i | \(-0.00951136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.15894 | −0.240103 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.9239 | −1.37100 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.56101i | 0.186092i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.2195 | − | 26.2791i | 0.642437 | − | 0.878414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 94.5271i | − | 3.15617i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.27248 | −0.109143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.1495 | −1.77067 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.4995i | 0.549070i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.7649 | + | 17.4537i | −0.424320 | + | 0.580180i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.0284i | 1.76078i | 0.474250 | + | 0.880390i | \(0.342719\pi\) | ||||
−0.474250 | + | 0.880390i | \(0.657281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.9797 | 1.02753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.1798 | −0.933639 | −0.466820 | − | 0.884353i | \(-0.654600\pi\) | ||||
−0.466820 | + | 0.884353i | \(0.654600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1202i | 0.831357i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.2304 | + | 22.1093i | 0.999386 | + | 0.730911i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.85952i | − | 0.259544i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4243 | 1.26750 | 0.633751 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633751 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 100.292 | 3.30473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.6585i | 0.581236i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5895 | + | 9.09083i | −0.940015 | + | 0.298905i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.8099i | 0.552108i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.6576 | 1.20270 | 0.601348 | − | 0.798987i | \(-0.294631\pi\) | ||||
0.601348 | + | 0.798987i | \(0.294631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60975 | 0.0527573 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.4381i | 1.02924i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.8548 | − | 18.9092i | −0.845543 | − | 0.618396i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.83302i | − | 0.190557i | −0.995451 | − | 0.0952783i | \(-0.969626\pi\) | ||
0.995451 | − | 0.0952783i | \(-0.0303741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.0743 | −2.12362 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.23796 | −0.0729553 | −0.0364776 | − | 0.999334i | \(-0.511614\pi\) | ||||
−0.0364776 | + | 0.999334i | \(0.511614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.1193i | 2.67417i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.5298 | − | 21.2342i | 0.505185 | − | 0.690748i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 17.7502i | − | 0.576805i | −0.957509 | − | 0.288402i | \(-0.906876\pi\) | ||
0.957509 | − | 0.288402i | \(-0.0931241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.2498 | 0.981949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.2177 | 1.59599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32.0294i | − | 1.03753i | −0.854916 | − | 0.518766i | \(-0.826391\pi\) | ||
0.854916 | − | 0.518766i | \(-0.173609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5795 | + | 14.4655i | −0.342344 | + | 0.468092i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.2947i | 0.365107i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5601 | 0.341003 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9385 | −0.836727 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.26159 | + | 4.57947i | 0.201568 | + | 0.147418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4305i | 1.39663i | 0.715790 | + | 0.698316i | \(0.246067\pi\) | ||||
−0.715790 | + | 0.698316i | \(0.753933\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.9991 | 0.931585 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.79897 | 0.0577316 | 0.0288658 | − | 0.999583i | \(-0.490810\pi\) | ||||
0.0288658 | + | 0.999583i | \(0.490810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.79897i | 0.314140i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.6732 | + | 61.8695i | 0.630045 | + | 1.98141i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4390i | 0.717887i | 0.933359 | + | 0.358943i | \(0.116863\pi\) | ||||
−0.933359 | + | 0.358943i | \(0.883137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4995 | −0.910849 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.3388 | −2.14996 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.6950i | − | 1.20228i | −0.799143 | − | 0.601141i | \(-0.794713\pi\) | ||
0.799143 | − | 0.601141i | \(-0.205287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3818 | + | 21.4886i | 0.936181 | + | 0.684685i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7952i | 0.343615i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.4390 | 1.22229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.5686 | −0.431020 | −0.215510 | − | 0.976502i | \(-0.569141\pi\) | ||||
−0.215510 | + | 0.976502i | \(0.569141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 80.5583i | 2.55644i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.4693 | − | 48.4977i | 1.12445 | − | 1.53748i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 14.2838i | − | 0.452373i | −0.974084 | − | 0.226187i | \(-0.927374\pi\) | ||
0.974084 | − | 0.226187i | \(-0.0726259\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −70.5895 | −2.23335 |
(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 | 560.2.g.f.449.6 | 6 | ||
3.2 | odd | 2 | 5040.2.t.y.1009.2 | 6 | |||
4.3 | odd | 2 | 280.2.g.b.169.1 | ✓ | 6 | ||
5.2 | odd | 4 | 2800.2.a.br.1.3 | 3 | |||
5.3 | odd | 4 | 2800.2.a.bq.1.1 | 3 | |||
5.4 | even | 2 | inner | 560.2.g.f.449.1 | 6 | ||
8.3 | odd | 2 | 2240.2.g.l.449.6 | 6 | |||
8.5 | even | 2 | 2240.2.g.m.449.1 | 6 | |||
12.11 | even | 2 | 2520.2.t.g.1009.2 | 6 | |||
15.14 | odd | 2 | 5040.2.t.y.1009.1 | 6 | |||
20.3 | even | 4 | 1400.2.a.t.1.3 | 3 | |||
20.7 | even | 4 | 1400.2.a.s.1.1 | 3 | |||
20.19 | odd | 2 | 280.2.g.b.169.6 | yes | 6 | ||
28.27 | even | 2 | 1960.2.g.c.1569.6 | 6 | |||
40.19 | odd | 2 | 2240.2.g.l.449.1 | 6 | |||
40.29 | even | 2 | 2240.2.g.m.449.6 | 6 | |||
60.59 | even | 2 | 2520.2.t.g.1009.1 | 6 | |||
140.27 | odd | 4 | 9800.2.a.cg.1.3 | 3 | |||
140.83 | odd | 4 | 9800.2.a.cd.1.1 | 3 | |||
140.139 | even | 2 | 1960.2.g.c.1569.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.1 | ✓ | 6 | 4.3 | odd | 2 | ||
280.2.g.b.169.6 | yes | 6 | 20.19 | odd | 2 | ||
560.2.g.f.449.1 | 6 | 5.4 | even | 2 | inner | ||
560.2.g.f.449.6 | 6 | 1.1 | even | 1 | trivial | ||
1400.2.a.s.1.1 | 3 | 20.7 | even | 4 | |||
1400.2.a.t.1.3 | 3 | 20.3 | even | 4 | |||
1960.2.g.c.1569.1 | 6 | 140.139 | even | 2 | |||
1960.2.g.c.1569.6 | 6 | 28.27 | even | 2 | |||
2240.2.g.l.449.1 | 6 | 40.19 | odd | 2 | |||
2240.2.g.l.449.6 | 6 | 8.3 | odd | 2 | |||
2240.2.g.m.449.1 | 6 | 8.5 | even | 2 | |||
2240.2.g.m.449.6 | 6 | 40.29 | even | 2 | |||
2520.2.t.g.1009.1 | 6 | 60.59 | even | 2 | |||
2520.2.t.g.1009.2 | 6 | 12.11 | even | 2 | |||
2800.2.a.bq.1.1 | 3 | 5.3 | odd | 4 | |||
2800.2.a.br.1.3 | 3 | 5.2 | odd | 4 | |||
5040.2.t.y.1009.1 | 6 | 15.14 | odd | 2 | |||
5040.2.t.y.1009.2 | 6 | 3.2 | odd | 2 | |||
9800.2.a.cd.1.1 | 3 | 140.83 | odd | 4 | |||
9800.2.a.cg.1.3 | 3 | 140.27 | odd | 4 |