Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.1 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.c.364.4 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.23607i | − | 1.58114i | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||
0.612372 | − | 0.790569i | \(-0.290215\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | −2.23607 | −0.912871 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.47214 | + | 2.23607i | −1.41421 | + | 0.707107i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000i | 0.866025i | ||||||||
\(13\) | − | 4.47214i | − | 1.24035i | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||
0.784465 | − | 0.620174i | \(-0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 2.23607i | 0.527046i | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 3.00000 | + | 6.00000i | 0.670820 | + | 1.34164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −10.0000 | −1.96116 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.94427 | −1.66091 | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 2.23607 | + | 4.47214i | 0.408248 | + | 0.816497i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 6.70820i | 1.18585i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000 | 1.71499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | − | 8.00000i | − | 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 4.47214 | − | 2.23607i | 0.707107 | − | 0.353553i | ||||
\(41\) | −8.94427 | −1.39686 | −0.698430 | − | 0.715678i | \(-0.746118\pi\) | ||||
−0.698430 | + | 0.715678i | \(0.746118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427i | 1.36399i | 0.731357 | + | 0.681994i | \(0.238887\pi\) | ||||
−0.731357 | + | 0.681994i | \(0.761113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 2.00000i | 0.149071 | + | 0.298142i | ||||
\(46\) | 8.94427 | 1.31876 | ||||||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 8.94427 | + | 6.70820i | 1.26491 | + | 0.948683i | ||||
\(51\) | 4.47214 | 0.626224 | ||||||||
\(52\) | 13.4164i | 1.86052i | ||||||||
\(53\) | 4.00000i | 0.549442i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.0000i | 2.62613i | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 6.00000 | − | 3.00000i | 0.774597 | − | 0.387298i | ||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | −8.94427 | + | 4.47214i | −1.10940 | + | 0.554700i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | − | 13.4164i | − | 1.62698i | ||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | − | 2.23607i | − | 0.263523i | ||||||
\(73\) | 13.4164i | 1.57027i | 0.619324 | + | 0.785136i | \(0.287407\pi\) | ||||
−0.619324 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(74\) | −17.8885 | −2.07950 | ||||||||
\(75\) | 4.00000 | + | 3.00000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0000i | 1.13228i | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.0000i | 2.20863i | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94427 | − | 4.47214i | 0.970143 | − | 0.485071i | ||||
\(86\) | 20.0000 | 2.15666 | ||||||||
\(87\) | 8.94427i | 0.958927i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 4.47214 | − | 2.23607i | 0.471405 | − | 0.235702i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 12.0000i | − | 1.25109i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −26.8328 | −2.76759 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.70820 | 0.684653 | ||||||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | − | 15.6525i | − | 1.58114i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.00000 | − | 12.0000i | 0.900000 | − | 1.20000i | ||||
\(101\) | −8.94427 | −0.889988 | −0.444994 | − | 0.895533i | \(-0.646794\pi\) | ||||
−0.444994 | + | 0.895533i | \(0.646794\pi\) | |||||||
\(102\) | − | 10.0000i | − | 0.990148i | ||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 10.0000 | 0.980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.94427 | 0.868744 | ||||||||
\(107\) | − | 17.8885i | − | 1.72935i | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||
0.502331 | − | 0.864675i | \(-0.332476\pi\) | |||||||
\(108\) | − | 3.00000i | − | 0.288675i | ||||||
\(109\) | 17.8885 | 1.71341 | 0.856706 | − | 0.515805i | \(-0.172507\pi\) | ||||
0.856706 | + | 0.515805i | \(0.172507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | − | 4.00000i | 0.746004 | − | 0.373002i | ||||
\(116\) | 26.8328 | 2.49136 | ||||||||
\(117\) | 4.47214i | 0.413449i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.23607 | − | 4.47214i | −0.204124 | − | 0.408248i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.94427i | 0.806478i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | − | 15.6525i | − | 1.38350i | ||||||
\(129\) | 8.94427 | 0.787499 | ||||||||
\(130\) | 10.0000 | + | 20.0000i | 0.877058 | + | 1.75412i | ||||
\(131\) | −17.8885 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −26.8328 | −2.31800 | ||||||||
\(135\) | 2.00000 | − | 1.00000i | 0.172133 | − | 0.0860663i | ||||
\(136\) | −10.0000 | −0.857493 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | − | 8.94427i | − | 0.761387i | ||||||
\(139\) | −17.8885 | −1.51729 | −0.758643 | − | 0.651506i | \(-0.774137\pi\) | ||||
−0.758643 | + | 0.651506i | \(0.774137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | − | 26.8328i | − | 2.25176i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.94427 | + | 17.8885i | 0.742781 | + | 1.48556i | ||||
\(146\) | 30.0000 | 2.48282 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | 24.0000i | 1.97279i | ||||||||
\(149\) | −8.94427 | −0.732743 | −0.366372 | − | 0.930469i | \(-0.619400\pi\) | ||||
−0.366372 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(150\) | 6.70820 | − | 8.94427i | 0.547723 | − | 0.730297i | ||||
\(151\) | 17.8885 | 1.45575 | 0.727875 | − | 0.685710i | \(-0.240508\pi\) | ||||
0.727875 | + | 0.685710i | \(0.240508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.47214i | − | 0.361551i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.4164 | 1.07417 | ||||||||
\(157\) | − | 8.00000i | − | 0.638470i | −0.947676 | − | 0.319235i | \(-0.896574\pi\) | ||
0.947676 | − | 0.319235i | \(-0.103426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 13.4164 | − | 6.70820i | 1.06066 | − | 0.530330i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 2.23607i | − | 0.175682i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 26.8328 | 2.09529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.94427i | 0.692129i | 0.938211 | + | 0.346064i | \(0.112482\pi\) | ||||
−0.938211 | + | 0.346064i | \(0.887518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | −10.0000 | − | 20.0000i | −0.766965 | − | 1.53393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 26.8328i | − | 2.04598i | ||||||
\(173\) | − | 13.4164i | − | 1.02003i | −0.860165 | − | 0.510015i | \(-0.829640\pi\) | ||
0.860165 | − | 0.510015i | \(-0.170360\pi\) | |||||||
\(174\) | 20.0000 | 1.51620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.4164i | 1.00560i | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | −3.00000 | − | 6.00000i | −0.223607 | − | 0.447214i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.94427 | −0.659380 | ||||||||
\(185\) | −16.0000 | + | 8.00000i | −1.17634 | + | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 36.0000i | 2.62557i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | − | 13.0000i | − | 0.938194i | ||||||
\(193\) | − | 4.47214i | − | 0.321911i | −0.986962 | − | 0.160956i | \(-0.948542\pi\) | ||
0.986962 | − | 0.160956i | \(-0.0514576\pi\) | |||||||
\(194\) | −17.8885 | −1.28432 | ||||||||
\(195\) | 4.47214 | + | 8.94427i | 0.320256 | + | 0.640513i | ||||
\(196\) | −21.0000 | −1.50000 | ||||||||
\(197\) | − | 4.47214i | − | 0.318626i | −0.987228 | − | 0.159313i | \(-0.949072\pi\) | ||
0.987228 | − | 0.159313i | \(-0.0509280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −8.94427 | − | 6.70820i | −0.632456 | − | 0.474342i | ||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | 20.0000i | 1.40720i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.4164 | −0.939336 | ||||||||
\(205\) | 8.94427 | + | 17.8885i | 0.624695 | + | 1.24939i | ||||
\(206\) | 8.94427 | 0.623177 | ||||||||
\(207\) | − | 4.00000i | − | 0.278019i | ||||||
\(208\) | 4.47214i | 0.310087i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8885 | −1.23150 | −0.615749 | − | 0.787942i | \(-0.711146\pi\) | ||||
−0.615749 | + | 0.787942i | \(0.711146\pi\) | |||||||
\(212\) | − | 12.0000i | − | 0.824163i | ||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | −40.0000 | −2.73434 | ||||||||
\(215\) | 17.8885 | − | 8.94427i | 1.21999 | − | 0.609994i | ||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 40.0000i | − | 2.70914i | ||||||
\(219\) | 13.4164 | 0.906597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 17.8885i | 1.20060i | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 8.94427 | 0.594964 | ||||||||
\(227\) | 17.8885i | 1.18730i | 0.804722 | + | 0.593652i | \(0.202314\pi\) | ||||
−0.804722 | + | 0.593652i | \(0.797686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −8.94427 | − | 17.8885i | −0.589768 | − | 1.17954i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 20.0000i | − | 1.31306i | ||||||
\(233\) | 22.3607i | 1.46490i | 0.680823 | + | 0.732448i | \(0.261622\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(234\) | 10.0000 | 0.653720 | ||||||||
\(235\) | −24.0000 | + | 12.0000i | −1.56559 | + | 0.782794i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8885 | −1.15711 | −0.578557 | − | 0.815642i | \(-0.696384\pi\) | ||||
−0.578557 | + | 0.815642i | \(0.696384\pi\) | |||||||
\(240\) | 2.00000 | − | 1.00000i | 0.129099 | − | 0.0645497i | ||||
\(241\) | −17.8885 | −1.15230 | −0.576151 | − | 0.817343i | \(-0.695446\pi\) | ||||
−0.576151 | + | 0.817343i | \(0.695446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.00000 | − | 14.0000i | −0.447214 | − | 0.894427i | ||||
\(246\) | 20.0000 | 1.27515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.47214 | − | 24.5967i | 0.282843 | − | 1.55563i | ||||
\(251\) | 8.00000 | 0.504956 | 0.252478 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252478 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.47214 | − | 8.94427i | −0.280056 | − | 0.560112i | ||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | − | 12.0000i | − | 0.748539i | −0.927320 | − | 0.374270i | \(-0.877893\pi\) | ||
0.927320 | − | 0.374270i | \(-0.122107\pi\) | |||||||
\(258\) | − | 20.0000i | − | 1.24515i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 26.8328 | − | 13.4164i | 1.66410 | − | 0.832050i | ||||
\(261\) | 8.94427 | 0.553637 | ||||||||
\(262\) | 40.0000i | 2.47121i | ||||||||
\(263\) | − | 8.94427i | − | 0.551527i | −0.961225 | − | 0.275764i | \(-0.911069\pi\) | ||
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | − | 4.00000i | 0.491436 | − | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | 36.0000i | 2.19905i | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | −2.23607 | − | 4.47214i | −0.136083 | − | 0.272166i | ||||
\(271\) | 17.8885 | 1.08665 | 0.543326 | − | 0.839522i | \(-0.317165\pi\) | ||||
0.543326 | + | 0.839522i | \(0.317165\pi\) | |||||||
\(272\) | − | 4.47214i | − | 0.271163i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.8328 | 1.62103 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.0000 | −0.722315 | ||||||||
\(277\) | − | 13.4164i | − | 0.806114i | −0.915175 | − | 0.403057i | \(-0.867948\pi\) | ||
0.915175 | − | 0.403057i | \(-0.132052\pi\) | |||||||
\(278\) | 40.0000i | 2.39904i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.94427 | −0.533571 | −0.266785 | − | 0.963756i | \(-0.585961\pi\) | ||||
−0.266785 | + | 0.963756i | \(0.585961\pi\) | |||||||
\(282\) | 26.8328i | 1.59787i | ||||||||
\(283\) | − | 8.94427i | − | 0.531682i | −0.964017 | − | 0.265841i | \(-0.914350\pi\) | ||
0.964017 | − | 0.265841i | \(-0.0856496\pi\) | |||||||
\(284\) | −36.0000 | −2.13621 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 6.70820i | − | 0.395285i | ||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 40.0000 | − | 20.0000i | 2.34888 | − | 1.17444i | ||||
\(291\) | −8.00000 | −0.468968 | ||||||||
\(292\) | − | 40.2492i | − | 2.35541i | ||||||
\(293\) | − | 4.47214i | − | 0.261265i | −0.991431 | − | 0.130632i | \(-0.958299\pi\) | ||
0.991431 | − | 0.130632i | \(-0.0417008\pi\) | |||||||
\(294\) | −15.6525 | −0.912871 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.8885 | 1.03975 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0000i | 1.15857i | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | −12.0000 | − | 9.00000i | −0.692820 | − | 0.519615i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 40.0000i | − | 2.30174i | ||||||
\(303\) | 8.94427i | 0.513835i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.0000 | −0.571662 | ||||||||
\(307\) | − | 8.94427i | − | 0.510477i | −0.966878 | − | 0.255238i | \(-0.917846\pi\) | ||
0.966878 | − | 0.255238i | \(-0.0821539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | − | 10.0000i | − | 0.566139i | ||||||
\(313\) | 16.0000i | 0.904373i | 0.891923 | + | 0.452187i | \(0.149356\pi\) | ||||
−0.891923 | + | 0.452187i | \(0.850644\pi\) | |||||||
\(314\) | −17.8885 | −1.00951 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | − | 8.94427i | − | 0.501570i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −13.0000 | − | 26.0000i | −0.726722 | − | 1.45344i | ||||
\(321\) | −17.8885 | −0.998441 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.00000 | −0.166667 | ||||||||
\(325\) | 17.8885 | + | 13.4164i | 0.992278 | + | 0.744208i | ||||
\(326\) | −8.94427 | −0.495377 | ||||||||
\(327\) | − | 17.8885i | − | 0.989239i | ||||||
\(328\) | − | 20.0000i | − | 1.10432i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000i | 0.438397i | ||||||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | −24.0000 | + | 12.0000i | −1.31126 | + | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 31.3050i | − | 1.70529i | −0.522491 | − | 0.852645i | \(-0.674997\pi\) | ||
0.522491 | − | 0.852645i | \(-0.325003\pi\) | |||||||
\(338\) | 15.6525i | 0.851382i | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | −26.8328 | + | 13.4164i | −1.45521 | + | 0.727607i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | −4.00000 | − | 8.00000i | −0.215353 | − | 0.430706i | ||||
\(346\) | −30.0000 | −1.61281 | ||||||||
\(347\) | 17.8885i | 0.960307i | 0.877184 | + | 0.480154i | \(0.159419\pi\) | ||||
−0.877184 | + | 0.480154i | \(0.840581\pi\) | |||||||
\(348\) | − | 26.8328i | − | 1.43839i | ||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000i | 0.212899i | 0.994318 | + | 0.106449i | \(0.0339482\pi\) | ||||
−0.994318 | + | 0.106449i | \(0.966052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | − | 24.0000i | −0.636894 | − | 1.27379i | ||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 35.7771i | 1.89088i | ||||||||
\(359\) | −17.8885 | −0.944121 | −0.472061 | − | 0.881566i | \(-0.656490\pi\) | ||||
−0.472061 | + | 0.881566i | \(0.656490\pi\) | |||||||
\(360\) | −4.47214 | + | 2.23607i | −0.235702 | + | 0.117851i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 22.3607i | 1.17525i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.8328 | − | 13.4164i | 1.40449 | − | 0.702247i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0000i | 1.46159i | 0.682598 | + | 0.730794i | \(0.260850\pi\) | ||||
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | 8.94427 | 0.465620 | ||||||||
\(370\) | 17.8885 | + | 35.7771i | 0.929981 | + | 1.85996i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.3607i | 1.15779i | 0.815401 | + | 0.578896i | \(0.196516\pi\) | ||||
−0.815401 | + | 0.578896i | \(0.803484\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | 26.8328 | 1.38380 | ||||||||
\(377\) | 40.0000i | 2.06010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 44.7214i | 2.28814i | ||||||||
\(383\) | − | 4.00000i | − | 0.204390i | −0.994764 | − | 0.102195i | \(-0.967413\pi\) | ||
0.994764 | − | 0.102195i | \(-0.0325866\pi\) | |||||||
\(384\) | −15.6525 | −0.798762 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | − | 8.94427i | − | 0.454663i | ||||||
\(388\) | 24.0000i | 1.21842i | ||||||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 20.0000 | − | 10.0000i | 1.01274 | − | 0.506370i | ||||
\(391\) | −17.8885 | −0.904663 | ||||||||
\(392\) | 15.6525i | 0.790569i | ||||||||
\(393\) | 17.8885i | 0.902358i | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.00000i | − | 0.401508i | −0.979642 | − | 0.200754i | \(-0.935661\pi\) | ||
0.979642 | − | 0.200754i | \(-0.0643393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 26.8328i | 1.33830i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 26.8328 | 1.33498 | ||||||||
\(405\) | −1.00000 | − | 2.00000i | −0.0496904 | − | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.0000i | 0.495074i | ||||||||
\(409\) | −17.8885 | −0.884532 | −0.442266 | − | 0.896884i | \(-0.645825\pi\) | ||||
−0.442266 | + | 0.896884i | \(0.645825\pi\) | |||||||
\(410\) | 40.0000 | − | 20.0000i | 1.97546 | − | 0.987730i | ||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | − | 12.0000i | − | 0.591198i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.94427 | −0.439587 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 30.0000 | 1.47087 | ||||||||
\(417\) | 17.8885i | 0.876006i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 40.0000i | 1.94717i | ||||||||
\(423\) | 12.0000i | 0.583460i | ||||||||
\(424\) | −8.94427 | −0.434372 | ||||||||
\(425\) | −17.8885 | − | 13.4164i | −0.867722 | − | 0.650791i | ||||
\(426\) | −26.8328 | −1.30005 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 53.6656i | 2.59403i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.0000 | − | 40.0000i | −0.964486 | − | 1.92897i | ||||
\(431\) | 17.8885 | 0.861661 | 0.430830 | − | 0.902433i | \(-0.358221\pi\) | ||||
0.430830 | + | 0.902433i | \(0.358221\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 16.0000i | 0.768911i | 0.923144 | + | 0.384455i | \(0.125611\pi\) | ||||
−0.923144 | + | 0.384455i | \(0.874389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8885 | − | 8.94427i | 0.857690 | − | 0.428845i | ||||
\(436\) | −53.6656 | −2.57012 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 30.0000i | − | 1.43346i | ||||||
\(439\) | −17.8885 | −0.853774 | −0.426887 | − | 0.904305i | \(-0.640390\pi\) | ||||
−0.426887 | + | 0.904305i | \(0.640390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | − | 44.7214i | − | 2.12718i | ||||||
\(443\) | − | 36.0000i | − | 1.71041i | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||
0.518289 | − | 0.855206i | \(-0.326569\pi\) | |||||||
\(444\) | 24.0000 | 1.13899 | ||||||||
\(445\) | 6.00000 | + | 12.0000i | 0.284427 | + | 0.568855i | ||||
\(446\) | −8.94427 | −0.423524 | ||||||||
\(447\) | 8.94427i | 0.423050i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | −8.94427 | − | 6.70820i | −0.421637 | − | 0.316228i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | − | 17.8885i | − | 0.840477i | ||||||
\(454\) | 40.0000 | 1.87729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4164i | 0.627593i | 0.949490 | + | 0.313797i | \(0.101601\pi\) | ||||
−0.949490 | + | 0.313797i | \(0.898399\pi\) | |||||||
\(458\) | 22.3607i | 1.04485i | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | −24.0000 | + | 12.0000i | −1.11901 | + | 0.559503i | ||||
\(461\) | −26.8328 | −1.24973 | −0.624864 | − | 0.780733i | \(-0.714846\pi\) | ||||
−0.624864 | + | 0.780733i | \(0.714846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | 8.94427 | 0.415227 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 50.0000 | 2.31621 | ||||||||
\(467\) | − | 28.0000i | − | 1.29569i | −0.761774 | − | 0.647843i | \(-0.775671\pi\) | ||
0.761774 | − | 0.647843i | \(-0.224329\pi\) | |||||||
\(468\) | − | 13.4164i | − | 0.620174i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 26.8328 | + | 53.6656i | 1.23771 | + | 2.47541i | ||||
\(471\) | −8.00000 | −0.368621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.00000i | − | 0.183147i | ||||||
\(478\) | 40.0000i | 1.82956i | ||||||||
\(479\) | −17.8885 | −0.817348 | −0.408674 | − | 0.912680i | \(-0.634009\pi\) | ||||
−0.408674 | + | 0.912680i | \(0.634009\pi\) | |||||||
\(480\) | −6.70820 | − | 13.4164i | −0.306186 | − | 0.612372i | ||||
\(481\) | −35.7771 | −1.63129 | ||||||||
\(482\) | 40.0000i | 1.82195i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | + | 8.00000i | −0.726523 | + | 0.363261i | ||||
\(486\) | −2.23607 | −0.101430 | ||||||||
\(487\) | 28.0000i | 1.26880i | 0.773004 | + | 0.634401i | \(0.218753\pi\) | ||||
−0.773004 | + | 0.634401i | \(0.781247\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −31.3050 | + | 15.6525i | −1.41421 | + | 0.707107i | ||||
\(491\) | 35.7771 | 1.61460 | 0.807299 | − | 0.590143i | \(-0.200929\pi\) | ||||
0.807299 | + | 0.590143i | \(0.200929\pi\) | |||||||
\(492\) | − | 26.8328i | − | 1.20972i | ||||||
\(493\) | − | 40.0000i | − | 1.80151i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | −33.0000 | − | 6.00000i | −1.47580 | − | 0.268328i | ||||
\(501\) | 8.94427 | 0.399601 | ||||||||
\(502\) | − | 17.8885i | − | 0.798405i | ||||||
\(503\) | 26.8328i | 1.19642i | 0.801341 | + | 0.598208i | \(0.204120\pi\) | ||||
−0.801341 | + | 0.598208i | \(0.795880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.94427 | + | 17.8885i | 0.398015 | + | 0.796030i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000i | 0.310881i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0000 | −0.443242 | −0.221621 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221621 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(510\) | −20.0000 | + | 10.0000i | −0.885615 | + | 0.442807i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11.1803i | − | 0.494106i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.8328 | −1.18354 | ||||||||
\(515\) | 8.00000 | − | 4.00000i | 0.352522 | − | 0.176261i | ||||
\(516\) | −26.8328 | −1.18125 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.4164 | −0.588915 | ||||||||
\(520\) | −10.0000 | − | 20.0000i | −0.438529 | − | 0.877058i | ||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | − | 20.0000i | − | 0.875376i | ||||||
\(523\) | − | 8.94427i | − | 0.391106i | −0.980693 | − | 0.195553i | \(-0.937350\pi\) | ||
0.980693 | − | 0.195553i | \(-0.0626501\pi\) | |||||||
\(524\) | 53.6656 | 2.34439 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0000 | −0.872041 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | −8.94427 | − | 17.8885i | −0.388514 | − | 0.777029i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.0000i | 1.73259i | ||||||||
\(534\) | 13.4164 | 0.580585 | ||||||||
\(535\) | −35.7771 | + | 17.8885i | −1.54678 | + | 0.773389i | ||||
\(536\) | 26.8328 | 1.15900 | ||||||||
\(537\) | 16.0000i | 0.690451i | ||||||||
\(538\) | − | 22.3607i | − | 0.964037i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.00000 | + | 3.00000i | −0.258199 | + | 0.129099i | ||||
\(541\) | −17.8885 | −0.769089 | −0.384544 | − | 0.923107i | \(-0.625641\pi\) | ||||
−0.384544 | + | 0.923107i | \(0.625641\pi\) | |||||||
\(542\) | − | 40.0000i | − | 1.71815i | ||||||
\(543\) | 10.0000i | 0.429141i | ||||||||
\(544\) | −30.0000 | −1.28624 | ||||||||
\(545\) | −17.8885 | − | 35.7771i | −0.766261 | − | 1.53252i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.7214i | 1.91215i | 0.293127 | + | 0.956074i | \(0.405304\pi\) | ||||
−0.293127 | + | 0.956074i | \(0.594696\pi\) | |||||||
\(548\) | − | 36.0000i | − | 1.53784i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.94427i | 0.380693i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −30.0000 | −1.27458 | ||||||||
\(555\) | 8.00000 | + | 16.0000i | 0.339581 | + | 0.679162i | ||||
\(556\) | 53.6656 | 2.27593 | ||||||||
\(557\) | 13.4164i | 0.568471i | 0.958754 | + | 0.284236i | \(0.0917398\pi\) | ||||
−0.958754 | + | 0.284236i | \(0.908260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.0000i | 0.843649i | ||||||||
\(563\) | − | 17.8885i | − | 0.753912i | −0.926231 | − | 0.376956i | \(-0.876971\pi\) | ||
0.926231 | − | 0.376956i | \(-0.123029\pi\) | |||||||
\(564\) | 36.0000 | 1.51587 | ||||||||
\(565\) | 8.00000 | − | 4.00000i | 0.336563 | − | 0.168281i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.8328i | 1.12588i | ||||||||
\(569\) | 8.94427 | 0.374963 | 0.187482 | − | 0.982268i | \(-0.439967\pi\) | ||||
0.187482 | + | 0.982268i | \(0.439967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.7771 | 1.49722 | 0.748612 | − | 0.663008i | \(-0.230720\pi\) | ||||
0.748612 | + | 0.663008i | \(0.230720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.0000i | 0.835512i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0000 | − | 12.0000i | −0.667246 | − | 0.500435i | ||||
\(576\) | −13.0000 | −0.541667 | ||||||||
\(577\) | − | 32.0000i | − | 1.33218i | −0.745873 | − | 0.666089i | \(-0.767967\pi\) | ||
0.745873 | − | 0.666089i | \(-0.232033\pi\) | |||||||
\(578\) | 6.70820i | 0.279024i | ||||||||
\(579\) | −4.47214 | −0.185856 | ||||||||
\(580\) | −26.8328 | − | 53.6656i | −1.11417 | − | 2.22834i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.8885i | 0.741504i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −30.0000 | −1.24141 | ||||||||
\(585\) | 8.94427 | − | 4.47214i | 0.369800 | − | 0.184900i | ||||
\(586\) | −10.0000 | −0.413096 | ||||||||
\(587\) | − | 28.0000i | − | 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(588\) | 21.0000i | 0.866025i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.47214 | −0.183959 | ||||||||
\(592\) | 8.00000i | 0.328798i | ||||||||
\(593\) | − | 4.47214i | − | 0.183649i | −0.995775 | − | 0.0918243i | \(-0.970730\pi\) | ||
0.995775 | − | 0.0918243i | \(-0.0292698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.8328 | 1.09911 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 40.0000i | − | 1.63572i | ||||||
\(599\) | −4.00000 | −0.163436 | −0.0817178 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817178 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(600\) | −6.70820 | + | 8.94427i | −0.273861 | + | 0.365148i | ||||
\(601\) | 35.7771 | 1.45938 | 0.729689 | − | 0.683779i | \(-0.239665\pi\) | ||||
0.729689 | + | 0.683779i | \(0.239665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | −53.6656 | −2.18362 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.0000 | 0.812444 | ||||||||
\(607\) | − | 17.8885i | − | 0.726074i | −0.931775 | − | 0.363037i | \(-0.881740\pi\) | ||
0.931775 | − | 0.363037i | \(-0.118260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.6656 | −2.17108 | ||||||||
\(612\) | 13.4164i | 0.542326i | ||||||||
\(613\) | − | 13.4164i | − | 0.541884i | −0.962596 | − | 0.270942i | \(-0.912665\pi\) | ||
0.962596 | − | 0.270942i | \(-0.0873351\pi\) | |||||||
\(614\) | −20.0000 | −0.807134 | ||||||||
\(615\) | 17.8885 | − | 8.94427i | 0.721336 | − | 0.360668i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | − | 8.94427i | − | 0.359791i | ||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 26.8328i | 1.07590i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.47214 | 0.179029 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 35.7771 | 1.42994 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.0000i | 0.957704i | ||||||||
\(629\) | 35.7771 | 1.42653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8885i | 0.711006i | ||||||||
\(634\) | −26.8328 | −1.06567 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | − | 31.3050i | − | 1.24035i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | −31.3050 | + | 15.6525i | −1.23744 | + | 0.618718i | ||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 40.0000i | 1.57867i | ||||||||
\(643\) | − | 36.0000i | − | 1.41970i | −0.704352 | − | 0.709851i | \(-0.748762\pi\) | ||
0.704352 | − | 0.709851i | \(-0.251238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.94427 | − | 17.8885i | −0.352180 | − | 0.704361i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0000i | 1.10079i | 0.834903 | + | 0.550397i | \(0.185524\pi\) | ||||
−0.834903 | + | 0.550397i | \(0.814476\pi\) | |||||||
\(648\) | 2.23607i | 0.0878410i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 30.0000 | − | 40.0000i | 1.17670 | − | 1.56893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | 4.00000i | 0.156532i | 0.996933 | + | 0.0782660i | \(0.0249384\pi\) | ||||
−0.996933 | + | 0.0782660i | \(0.975062\pi\) | |||||||
\(654\) | −40.0000 | −1.56412 | ||||||||
\(655\) | 17.8885 | + | 35.7771i | 0.698963 | + | 1.39793i | ||||
\(656\) | 8.94427 | 0.349215 | ||||||||
\(657\) | − | 13.4164i | − | 0.523424i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0000 | 1.47803 | 0.739014 | − | 0.673690i | \(-0.235292\pi\) | ||||
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 44.7214i | 1.73814i | ||||||||
\(663\) | − | 20.0000i | − | 0.776736i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.8885 | 0.693167 | ||||||||
\(667\) | − | 35.7771i | − | 1.38529i | ||||||
\(668\) | − | 26.8328i | − | 1.03819i | ||||||
\(669\) | −4.00000 | −0.154649 | ||||||||
\(670\) | 26.8328 | + | 53.6656i | 1.03664 | + | 2.07328i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.47214i | − | 0.172388i | −0.996278 | − | 0.0861941i | \(-0.972529\pi\) | ||
0.996278 | − | 0.0861941i | \(-0.0274705\pi\) | |||||||
\(674\) | −70.0000 | −2.69630 | ||||||||
\(675\) | −4.00000 | − | 3.00000i | −0.153960 | − | 0.115470i | ||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | − | 31.3050i | − | 1.20315i | −0.798817 | − | 0.601574i | \(-0.794541\pi\) | ||
0.798817 | − | 0.601574i | \(-0.205459\pi\) | |||||||
\(678\) | − | 8.94427i | − | 0.343503i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.0000 | + | 20.0000i | 0.383482 | + | 0.766965i | ||||
\(681\) | 17.8885 | 0.685490 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | − | 12.0000i | 0.916993 | − | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000i | 0.381524i | ||||||||
\(688\) | − | 8.94427i | − | 0.340997i | ||||||
\(689\) | 17.8885 | 0.681499 | ||||||||
\(690\) | −17.8885 | + | 8.94427i | −0.681005 | + | 0.340503i | ||||
\(691\) | 12.0000 | 0.456502 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | 40.2492i | 1.53005i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.0000 | 1.51838 | ||||||||
\(695\) | 17.8885 | + | 35.7771i | 0.678551 | + | 1.35710i | ||||
\(696\) | −20.0000 | −0.758098 | ||||||||
\(697\) | − | 40.0000i | − | 1.51511i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.3607 | 0.845759 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.94427 | −0.337820 | −0.168910 | − | 0.985631i | \(-0.554025\pi\) | ||||
−0.168910 | + | 0.985631i | \(0.554025\pi\) | |||||||
\(702\) | − | 10.0000i | − | 0.377426i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.0000 | + | 24.0000i | 0.451946 | + | 0.903892i | ||||
\(706\) | 8.94427 | 0.336622 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | −53.6656 | + | 26.8328i | −2.01404 | + | 1.00702i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 13.4164i | − | 0.502801i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 48.0000 | 1.79384 | ||||||||
\(717\) | 17.8885i | 0.668060i | ||||||||
\(718\) | 40.0000i | 1.49279i | ||||||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | −1.00000 | − | 2.00000i | −0.0372678 | − | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 42.4853i | 1.58114i | ||||||||
\(723\) | 17.8885i | 0.665282i | ||||||||
\(724\) | 30.0000 | 1.11494 | ||||||||
\(725\) | 26.8328 | − | 35.7771i | 0.996546 | − | 1.32873i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0000i | − | 1.03846i | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||
0.854634 | − | 0.519231i | \(-0.173782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −30.0000 | − | 60.0000i | −1.11035 | − | 2.22070i | ||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.3050i | − | 1.15627i | −0.815939 | − | 0.578137i | \(-0.803780\pi\) | ||
0.815939 | − | 0.578137i | \(-0.196220\pi\) | |||||||
\(734\) | 62.6099 | 2.31097 | ||||||||
\(735\) | −14.0000 | + | 7.00000i | −0.516398 | + | 0.258199i | ||||
\(736\) | −26.8328 | −0.989071 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 20.0000i | − | 0.736210i | ||||||
\(739\) | 17.8885 | 0.658041 | 0.329020 | − | 0.944323i | \(-0.393282\pi\) | ||||
0.329020 | + | 0.944323i | \(0.393282\pi\) | |||||||
\(740\) | 48.0000 | − | 24.0000i | 1.76452 | − | 0.882258i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 26.8328i | − | 0.984401i | −0.870482 | − | 0.492200i | \(-0.836193\pi\) | ||
0.870482 | − | 0.492200i | \(-0.163807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.94427 | + | 17.8885i | 0.327693 | + | 0.655386i | ||||
\(746\) | 50.0000 | 1.83063 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −24.5967 | − | 4.47214i | −0.898146 | − | 0.163299i | ||||
\(751\) | −48.0000 | −1.75154 | −0.875772 | − | 0.482724i | \(-0.839647\pi\) | ||||
−0.875772 | + | 0.482724i | \(0.839647\pi\) | |||||||
\(752\) | 12.0000i | 0.437595i | ||||||||
\(753\) | − | 8.00000i | − | 0.291536i | ||||||
\(754\) | 89.4427 | 3.25731 | ||||||||
\(755\) | −17.8885 | − | 35.7771i | −0.651031 | − | 1.30206i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.0000i | − | 1.74459i | −0.488980 | − | 0.872295i | \(-0.662631\pi\) | ||
0.488980 | − | 0.872295i | \(-0.337369\pi\) | |||||||
\(758\) | − | 44.7214i | − | 1.62435i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.94427 | −0.324230 | −0.162115 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162115 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 60.0000 | 2.17072 | ||||||||
\(765\) | −8.94427 | + | 4.47214i | −0.323381 | + | 0.161690i | ||||
\(766\) | −8.94427 | −0.323170 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9.00000i | 0.324760i | ||||||||
\(769\) | 35.7771 | 1.29015 | 0.645077 | − | 0.764117i | \(-0.276825\pi\) | ||||
0.645077 | + | 0.764117i | \(0.276825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 13.4164i | 0.482867i | ||||||||
\(773\) | 36.0000i | 1.29483i | 0.762138 | + | 0.647415i | \(0.224150\pi\) | ||||
−0.762138 | + | 0.647415i | \(0.775850\pi\) | |||||||
\(774\) | −20.0000 | −0.718885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.8885 | 0.642161 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 67.0820i | − | 2.40501i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −13.4164 | − | 26.8328i | −0.480384 | − | 0.960769i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 40.0000i | 1.43040i | ||||||||
\(783\) | − | 8.94427i | − | 0.319642i | ||||||
\(784\) | −7.00000 | −0.250000 | ||||||||
\(785\) | −16.0000 | + | 8.00000i | −0.571064 | + | 0.285532i | ||||
\(786\) | 40.0000 | 1.42675 | ||||||||
\(787\) | − | 26.8328i | − | 0.956487i | −0.878227 | − | 0.478243i | \(-0.841274\pi\) | ||
0.878227 | − | 0.478243i | \(-0.158726\pi\) | |||||||
\(788\) | 13.4164i | 0.477940i | ||||||||
\(789\) | −8.94427 | −0.318425 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17.8885 | −0.634841 | ||||||||
\(795\) | −4.00000 | − | 8.00000i | −0.141865 | − | 0.283731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.6656 | 1.89855 | ||||||||
\(800\) | −26.8328 | − | 20.1246i | −0.948683 | − | 0.711512i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | − | 67.0820i | − | 2.36875i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 36.0000 | 1.26962 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 10.0000i | − | 0.352017i | ||||||
\(808\) | − | 20.0000i | − | 0.703598i | ||||||
\(809\) | 26.8328 | 0.943392 | 0.471696 | − | 0.881761i | \(-0.343642\pi\) | ||||
0.471696 | + | 0.881761i | \(0.343642\pi\) | |||||||
\(810\) | −4.47214 | + | 2.23607i | −0.157135 | + | 0.0785674i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.8885i | − | 0.627379i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | + | 4.00000i | −0.280228 | + | 0.140114i | ||||
\(816\) | −4.47214 | −0.156556 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 40.0000i | 1.39857i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.8328 | − | 53.6656i | −0.937043 | − | 1.87409i | ||||
\(821\) | 8.94427 | 0.312157 | 0.156079 | − | 0.987745i | \(-0.450115\pi\) | ||||
0.156079 | + | 0.987745i | \(0.450115\pi\) | |||||||
\(822\) | − | 26.8328i | − | 0.935902i | ||||||
\(823\) | 4.00000i | 0.139431i | 0.997567 | + | 0.0697156i | \(0.0222092\pi\) | ||||
−0.997567 | + | 0.0697156i | \(0.977791\pi\) | |||||||
\(824\) | −8.94427 | −0.311588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8885i | 0.622046i | 0.950402 | + | 0.311023i | \(0.100672\pi\) | ||||
−0.950402 | + | 0.311023i | \(0.899328\pi\) | |||||||
\(828\) | 12.0000i | 0.417029i | ||||||||
\(829\) | 46.0000 | 1.59765 | 0.798823 | − | 0.601566i | \(-0.205456\pi\) | ||||
0.798823 | + | 0.601566i | \(0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4164 | −0.465410 | ||||||||
\(832\) | − | 58.1378i | − | 2.01556i | ||||||
\(833\) | 31.3050i | 1.08465i | ||||||||
\(834\) | 40.0000 | 1.38509 | ||||||||
\(835\) | 17.8885 | − | 8.94427i | 0.619059 | − | 0.309529i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 53.6656i | 1.85385i | ||||||||
\(839\) | 20.0000 | 0.690477 | 0.345238 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345238 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.0000 | 1.75862 | ||||||||
\(842\) | 22.3607i | 0.770600i | ||||||||
\(843\) | 8.94427i | 0.308057i | ||||||||
\(844\) | 53.6656 | 1.84725 | ||||||||
\(845\) | 7.00000 | + | 14.0000i | 0.240807 | + | 0.481615i | ||||
\(846\) | 26.8328 | 0.922531 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4.00000i | − | 0.137361i | ||||||
\(849\) | −8.94427 | −0.306967 | ||||||||
\(850\) | −30.0000 | + | 40.0000i | −1.02899 | + | 1.37199i | ||||
\(851\) | 32.0000 | 1.09695 | ||||||||
\(852\) | 36.0000i | 1.23334i | ||||||||
\(853\) | − | 49.1935i | − | 1.68435i | −0.539202 | − | 0.842177i | \(-0.681274\pi\) | ||
0.539202 | − | 0.842177i | \(-0.318726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40.0000 | 1.36717 | ||||||||
\(857\) | − | 13.4164i | − | 0.458296i | −0.973392 | − | 0.229148i | \(-0.926406\pi\) | ||
0.973392 | − | 0.229148i | \(-0.0735939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0000 | −1.50126 | −0.750630 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(860\) | −53.6656 | + | 26.8328i | −1.82998 | + | 0.914991i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 40.0000i | − | 1.36241i | ||||||
\(863\) | − | 4.00000i | − | 0.136162i | −0.997680 | − | 0.0680808i | \(-0.978312\pi\) | ||
0.997680 | − | 0.0680808i | \(-0.0216876\pi\) | |||||||
\(864\) | −6.70820 | −0.228218 | ||||||||
\(865\) | −26.8328 | + | 13.4164i | −0.912343 | + | 0.456172i | ||||
\(866\) | 35.7771 | 1.21575 | ||||||||
\(867\) | 3.00000i | 0.101885i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −20.0000 | − | 40.0000i | −0.678064 | − | 1.35613i | ||||
\(871\) | −53.6656 | −1.81839 | ||||||||
\(872\) | 40.0000i | 1.35457i | ||||||||
\(873\) | 8.00000i | 0.270759i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −40.2492 | −1.35990 | ||||||||
\(877\) | 31.3050i | 1.05709i | 0.848904 | + | 0.528547i | \(0.177263\pi\) | ||||
−0.848904 | + | 0.528547i | \(0.822737\pi\) | |||||||
\(878\) | 40.0000i | 1.34993i | ||||||||
\(879\) | −4.47214 | −0.150841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 15.6525i | 0.527046i | ||||||||
\(883\) | − | 4.00000i | − | 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | −60.0000 | −2.01802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −80.4984 | −2.70440 | ||||||||
\(887\) | − | 44.7214i | − | 1.50160i | −0.660532 | − | 0.750798i | \(-0.729669\pi\) | ||
0.660532 | − | 0.750798i | \(-0.270331\pi\) | |||||||
\(888\) | − | 17.8885i | − | 0.600300i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 26.8328 | − | 13.4164i | 0.899438 | − | 0.449719i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.0000i | 0.401790i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 20.0000 | 0.668900 | ||||||||
\(895\) | 16.0000 | + | 32.0000i | 0.534821 | + | 1.06964i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 17.8885i | − | 0.597281i | ||||||
\(898\) | 76.0263i | 2.53703i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −9.00000 | + | 12.0000i | −0.300000 | + | 0.400000i | ||||
\(901\) | −17.8885 | −0.595954 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.94427 | −0.297482 | ||||||||
\(905\) | 10.0000 | + | 20.0000i | 0.332411 | + | 0.664822i | ||||
\(906\) | −40.0000 | −1.32891 | ||||||||
\(907\) | − | 12.0000i | − | 0.398453i | −0.979953 | − | 0.199227i | \(-0.936157\pi\) | ||
0.979953 | − | 0.199227i | \(-0.0638430\pi\) | |||||||
\(908\) | − | 53.6656i | − | 1.78096i | ||||||
\(909\) | 8.94427 | 0.296663 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.0000 | −0.662630 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 30.0000 | 0.992312 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.0000 | 0.991228 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.0000i | 0.330049i | ||||||||
\(919\) | 53.6656 | 1.77027 | 0.885133 | − | 0.465338i | \(-0.154067\pi\) | ||||
0.885133 | + | 0.465338i | \(0.154067\pi\) | |||||||
\(920\) | 8.94427 | + | 17.8885i | 0.294884 | + | 0.589768i | ||||
\(921\) | −8.94427 | −0.294724 | ||||||||
\(922\) | 60.0000i | 1.97599i | ||||||||
\(923\) | − | 53.6656i | − | 1.76643i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | + | 24.0000i | 1.05215 | + | 0.789115i | ||||
\(926\) | −8.94427 | −0.293927 | ||||||||
\(927\) | − | 4.00000i | − | 0.131377i | ||||||
\(928\) | − | 60.0000i | − | 1.96960i | ||||||
\(929\) | 50.0000 | 1.64045 | 0.820223 | − | 0.572043i | \(-0.193849\pi\) | ||||
0.820223 | + | 0.572043i | \(0.193849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 67.0820i | − | 2.19735i | ||||||
\(933\) | 12.0000i | 0.392862i | ||||||||
\(934\) | −62.6099 | −2.04866 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.0000 | −0.326860 | ||||||||
\(937\) | − | 22.3607i | − | 0.730492i | −0.930911 | − | 0.365246i | \(-0.880985\pi\) | ||
0.930911 | − | 0.365246i | \(-0.119015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 72.0000 | − | 36.0000i | 2.34838 | − | 1.17419i | ||||
\(941\) | −8.94427 | −0.291575 | −0.145787 | − | 0.989316i | \(-0.546572\pi\) | ||||
−0.145787 | + | 0.989316i | \(0.546572\pi\) | |||||||
\(942\) | 17.8885i | 0.582840i | ||||||||
\(943\) | − | 35.7771i | − | 1.16506i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28.0000i | − | 0.909878i | −0.890523 | − | 0.454939i | \(-0.849661\pi\) | ||
0.890523 | − | 0.454939i | \(-0.150339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0000 | 1.94768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.4164i | − | 0.434600i | −0.976105 | − | 0.217300i | \(-0.930275\pi\) | ||
0.976105 | − | 0.217300i | \(-0.0697250\pi\) | |||||||
\(954\) | −8.94427 | −0.289581 | ||||||||
\(955\) | 20.0000 | + | 40.0000i | 0.647185 | + | 1.29437i | ||||
\(956\) | 53.6656 | 1.73567 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.0000i | 1.29234i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.0000 | + | 13.0000i | −0.839146 | + | 0.419573i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 80.0000i | 2.57930i | ||||||||
\(963\) | 17.8885i | 0.576450i | ||||||||
\(964\) | 53.6656 | 1.72845 | ||||||||
\(965\) | −8.94427 | + | 4.47214i | −0.287926 | + | 0.143963i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.8885i | − | 0.575257i | −0.957742 | − | 0.287628i | \(-0.907133\pi\) | ||
0.957742 | − | 0.287628i | \(-0.0928668\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.8885 | + | 35.7771i | 0.574367 | + | 1.14873i | ||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 3.00000i | 0.0962250i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 62.6099 | 2.00615 | ||||||||
\(975\) | 13.4164 | − | 17.8885i | 0.429669 | − | 0.572892i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 8.94427i | 0.286006i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 21.0000 | + | 42.0000i | 0.670820 | + | 1.34164i | ||||
\(981\) | −17.8885 | −0.571137 | ||||||||
\(982\) | − | 80.0000i | − | 2.55290i | ||||||
\(983\) | − | 36.0000i | − | 1.14822i | −0.818778 | − | 0.574111i | \(-0.805348\pi\) | ||
0.818778 | − | 0.574111i | \(-0.194652\pi\) | |||||||
\(984\) | −20.0000 | −0.637577 | ||||||||
\(985\) | −8.94427 | + | 4.47214i | −0.284988 | + | 0.142494i | ||||
\(986\) | −89.4427 | −2.84844 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.7771 | −1.13765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000i | 0.634681i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4164i | 0.424902i | 0.977172 | + | 0.212451i | \(0.0681446\pi\) | ||||
−0.977172 | + | 0.212451i | \(0.931855\pi\) | |||||||
\(998\) | 44.7214i | 1.41563i | ||||||||
\(999\) | 8.00000 | 0.253109 |
(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 | 1815.2.c.c.364.1 | ✓ | 4 | |
5.2 | odd | 4 | 9075.2.a.bj.1.2 | 2 | |||
5.3 | odd | 4 | 9075.2.a.bq.1.1 | 2 | |||
5.4 | even | 2 | inner | 1815.2.c.c.364.4 | yes | 4 | |
11.10 | odd | 2 | inner | 1815.2.c.c.364.3 | yes | 4 | |
55.32 | even | 4 | 9075.2.a.bj.1.1 | 2 | |||
55.43 | even | 4 | 9075.2.a.bq.1.2 | 2 | |||
55.54 | odd | 2 | inner | 1815.2.c.c.364.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.c.364.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1815.2.c.c.364.2 | yes | 4 | 55.54 | odd | 2 | inner | |
1815.2.c.c.364.3 | yes | 4 | 11.10 | odd | 2 | inner | |
1815.2.c.c.364.4 | yes | 4 | 5.4 | even | 2 | inner | |
9075.2.a.bj.1.1 | 2 | 55.32 | even | 4 | |||
9075.2.a.bj.1.2 | 2 | 5.2 | odd | 4 | |||
9075.2.a.bq.1.1 | 2 | 5.3 | odd | 4 | |||
9075.2.a.bq.1.2 | 2 | 55.43 | even | 4 |