Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(649,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.f (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.m.649.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −2.60555 | −0.984806 | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 3.60555i | − 1.00000i | ||||||||
\(14\) | 2.60555 | 0.696363 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.60555i | 0.631939i | 0.948769 | + | 0.315970i | \(0.102330\pi\) | ||||
−0.948769 | + | 0.315970i | \(0.897670\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.60555i | 0.597754i | 0.954292 | + | 0.298877i | \(0.0966121\pi\) | ||||
−0.954292 | + | 0.298877i | \(0.903388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.60555i | 0.568578i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.60555i | − 1.79438i | −0.441643 | − | 0.897191i | \(-0.645604\pi\) | ||||
0.441643 | − | 0.897191i | \(-0.354396\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.60555i | 0.707107i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.60555 | −0.492403 | ||||||||
\(29\) | 2.60555 | 0.483839 | 0.241919 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241919 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.00000i | − 1.07763i | −0.842424 | − | 0.538816i | \(-0.818872\pi\) | ||||
0.842424 | − | 0.538816i | \(-0.181128\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.60555i | − 0.446848i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −5.21110 | −0.856700 | −0.428350 | − | 0.903613i | \(-0.640905\pi\) | ||||
−0.428350 | + | 0.903613i | \(0.640905\pi\) | |||||||
\(38\) | − 2.60555i | − 0.422676i | ||||||||
\(39\) | −3.60555 | −0.577350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2111i | 1.75088i | 0.483327 | + | 0.875440i | \(0.339428\pi\) | ||||
−0.483327 | + | 0.875440i | \(0.660572\pi\) | |||||||
\(42\) | − 2.60555i | − 0.402045i | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.60555i | 1.26882i | ||||||||
\(47\) | −5.21110 | −0.760117 | −0.380059 | − | 0.924962i | \(-0.624096\pi\) | ||||
−0.380059 | + | 0.924962i | \(0.624096\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.60555 | 0.364850 | ||||||||
\(52\) | − 3.60555i | − 0.500000i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.60555 | 0.348181 | ||||||||
\(57\) | 2.60555 | 0.345114 | ||||||||
\(58\) | −2.60555 | −0.342126 | ||||||||
\(59\) | 5.21110i | 0.678428i | 0.940709 | + | 0.339214i | \(0.110161\pi\) | ||||
−0.940709 | + | 0.339214i | \(0.889839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.21110 | 0.411140 | 0.205570 | − | 0.978642i | \(-0.434095\pi\) | ||||
0.205570 | + | 0.978642i | \(0.434095\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 2.60555 | 0.328269 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2111 | −1.36965 | −0.684827 | − | 0.728706i | \(-0.740122\pi\) | ||||
−0.684827 | + | 0.728706i | \(0.740122\pi\) | |||||||
\(68\) | 2.60555i | 0.315970i | ||||||||
\(69\) | −8.60555 | −1.03599 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.21110i | 0.618444i | 0.950990 | + | 0.309222i | \(0.100069\pi\) | ||||
−0.950990 | + | 0.309222i | \(0.899931\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.60555 | −1.00720 | −0.503602 | − | 0.863936i | \(-0.667992\pi\) | ||||
−0.503602 | + | 0.863936i | \(0.667992\pi\) | |||||||
\(74\) | 5.21110 | 0.605778 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.60555i | 0.298877i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.60555 | 0.408248 | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 11.2111i | − 1.23806i | ||||||||
\(83\) | 17.2111 | 1.88916 | 0.944582 | − | 0.328276i | \(-0.106467\pi\) | ||||
0.944582 | + | 0.328276i | \(0.106467\pi\) | |||||||
\(84\) | 2.60555i | 0.284289i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 8.00000i | − 0.862662i | ||||||||
\(87\) | − 2.60555i | − 0.279344i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.788897i | 0.0836230i | 0.999126 | + | 0.0418115i | \(0.0133129\pi\) | ||||
−0.999126 | + | 0.0418115i | \(0.986687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.39445i | 0.984806i | ||||||||
\(92\) | − 8.60555i | − 0.897191i | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 5.21110 | 0.537484 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −8.60555 | −0.873761 | −0.436881 | − | 0.899519i | \(-0.643917\pi\) | ||||
−0.436881 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(98\) | 0.211103 | 0.0213246 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6056 | −1.45331 | −0.726653 | − | 0.687004i | \(-0.758925\pi\) | ||||
−0.726653 | + | 0.687004i | \(0.758925\pi\) | |||||||
\(102\) | −2.60555 | −0.257988 | ||||||||
\(103\) | − 4.00000i | − 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 3.60555i | 0.353553i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 6.00000i | − 0.582772i | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 8.60555i | 0.824262i | 0.911125 | + | 0.412131i | \(0.135215\pi\) | ||||
−0.911125 | + | 0.412131i | \(0.864785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.21110i | 0.494616i | ||||||||
\(112\) | −2.60555 | −0.246201 | ||||||||
\(113\) | 7.81665i | 0.735329i | 0.929959 | + | 0.367664i | \(0.119843\pi\) | ||||
−0.929959 | + | 0.367664i | \(0.880157\pi\) | |||||||
\(114\) | −2.60555 | −0.244032 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.60555 | 0.241919 | ||||||||
\(117\) | 3.60555i | 0.333333i | ||||||||
\(118\) | − 5.21110i | − 0.479721i | ||||||||
\(119\) | − 6.78890i | − 0.622337i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −3.21110 | −0.290720 | ||||||||
\(123\) | 11.2111 | 1.01087 | ||||||||
\(124\) | − 6.00000i | − 0.538816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.60555 | −0.232121 | ||||||||
\(127\) | 13.2111i | 1.17230i | 0.810204 | + | 0.586148i | \(0.199356\pi\) | ||||
−0.810204 | + | 0.586148i | \(0.800644\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3944 | 1.34502 | 0.672510 | − | 0.740088i | \(-0.265216\pi\) | ||||
0.672510 | + | 0.740088i | \(0.265216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.78890i | − 0.588672i | ||||||||
\(134\) | 11.2111 | 0.968492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 2.60555i | − 0.223424i | ||||||||
\(137\) | 11.2111 | 0.957829 | 0.478915 | − | 0.877862i | \(-0.341030\pi\) | ||||
0.478915 | + | 0.877862i | \(0.341030\pi\) | |||||||
\(138\) | 8.60555 | 0.732553 | ||||||||
\(139\) | −2.78890 | −0.236551 | −0.118276 | − | 0.992981i | \(-0.537737\pi\) | ||||
−0.118276 | + | 0.992981i | \(0.537737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.21110i | 0.438854i | ||||||||
\(142\) | − 5.21110i | − 0.437306i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.60555 | 0.712200 | ||||||||
\(147\) | 0.211103i | 0.0174114i | ||||||||
\(148\) | −5.21110 | −0.428350 | ||||||||
\(149\) | 0.788897i | 0.0646290i | 0.999478 | + | 0.0323145i | \(0.0102878\pi\) | ||||
−0.999478 | + | 0.0323145i | \(0.989712\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.00000i | − 0.488273i | −0.969741 | − | 0.244137i | \(-0.921495\pi\) | ||||
0.969741 | − | 0.244137i | \(-0.0785045\pi\) | |||||||
\(152\) | − 2.60555i | − 0.211338i | ||||||||
\(153\) | − 2.60555i | − 0.210646i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.60555 | −0.288675 | ||||||||
\(157\) | 8.42221i | 0.672165i | 0.941833 | + | 0.336083i | \(0.109102\pi\) | ||||
−0.941833 | + | 0.336083i | \(0.890898\pi\) | |||||||
\(158\) | 14.4222 | 1.14737 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.4222i | 1.76712i | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.42221 | −0.346374 | −0.173187 | − | 0.984889i | \(-0.555406\pi\) | ||||
−0.173187 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(164\) | 11.2111i | 0.875440i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2111 | −1.33584 | ||||||||
\(167\) | 5.21110 | 0.403247 | 0.201624 | − | 0.979463i | \(-0.435378\pi\) | ||||
0.201624 | + | 0.979463i | \(0.435378\pi\) | |||||||
\(168\) | − 2.60555i | − 0.201023i | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.60555i | − 0.199251i | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | 16.4222i | 1.24856i | 0.781202 | + | 0.624279i | \(0.214607\pi\) | ||||
−0.781202 | + | 0.624279i | \(0.785393\pi\) | |||||||
\(174\) | 2.60555i | 0.197526i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.21110 | 0.391690 | ||||||||
\(178\) | − 0.788897i | − 0.0591304i | ||||||||
\(179\) | −1.81665 | −0.135783 | −0.0678915 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678915 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4222 | −1.51797 | −0.758985 | − | 0.651108i | \(-0.774305\pi\) | ||||
−0.758985 | + | 0.651108i | \(0.774305\pi\) | |||||||
\(182\) | − 9.39445i | − 0.696363i | ||||||||
\(183\) | − 3.21110i | − 0.237372i | ||||||||
\(184\) | 8.60555i | 0.634410i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.21110 | −0.380059 | ||||||||
\(189\) | − 2.60555i | − 0.189526i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | −13.8167 | −0.994545 | −0.497272 | − | 0.867595i | \(-0.665665\pi\) | ||||
−0.497272 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(194\) | 8.60555 | 0.617843 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.42221 | 0.455258 | 0.227629 | − | 0.973748i | \(-0.426903\pi\) | ||||
0.227629 | + | 0.973748i | \(0.426903\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2111i | 0.790770i | ||||||||
\(202\) | 14.6056 | 1.02764 | ||||||||
\(203\) | −6.78890 | −0.476487 | ||||||||
\(204\) | 2.60555 | 0.182425 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000i | 0.278693i | ||||||||
\(207\) | 8.60555i | 0.598127i | ||||||||
\(208\) | − 3.60555i | − 0.250000i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.78890 | −0.191996 | −0.0959978 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959978 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 5.21110 | 0.357059 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 15.6333i | 1.06126i | ||||||||
\(218\) | − 8.60555i | − 0.582841i | ||||||||
\(219\) | 8.60555i | 0.581509i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.39445 | 0.631939 | ||||||||
\(222\) | − 5.21110i | − 0.349746i | ||||||||
\(223\) | −19.8167 | −1.32702 | −0.663511 | − | 0.748167i | \(-0.730934\pi\) | ||||
−0.663511 | + | 0.748167i | \(0.730934\pi\) | |||||||
\(224\) | 2.60555 | 0.174091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 7.81665i | − 0.519956i | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 2.60555 | 0.172557 | ||||||||
\(229\) | 1.81665i | 0.120048i | 0.998197 | + | 0.0600239i | \(0.0191177\pi\) | ||||
−0.998197 | + | 0.0600239i | \(0.980882\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.60555 | −0.171063 | ||||||||
\(233\) | 19.8167i | 1.29823i | 0.760689 | + | 0.649116i | \(0.224861\pi\) | ||||
−0.760689 | + | 0.649116i | \(0.775139\pi\) | |||||||
\(234\) | − 3.60555i | − 0.235702i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.21110i | 0.339214i | ||||||||
\(237\) | 14.4222i | 0.936823i | ||||||||
\(238\) | 6.78890i | 0.440059i | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 22.4222i | − 1.44434i | −0.691715 | − | 0.722171i | \(-0.743145\pi\) | ||||
0.691715 | − | 0.722171i | \(-0.256855\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 3.21110 | 0.205570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.2111 | −0.714794 | ||||||||
\(247\) | 9.39445 | 0.597754 | ||||||||
\(248\) | 6.00000i | 0.381000i | ||||||||
\(249\) | − 17.2111i | − 1.09071i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.6056 | −1.30061 | −0.650305 | − | 0.759673i | \(-0.725359\pi\) | ||||
−0.650305 | + | 0.759673i | \(0.725359\pi\) | |||||||
\(252\) | 2.60555 | 0.164134 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 13.2111i | − 0.828938i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.3944i | 1.33455i | 0.744812 | + | 0.667275i | \(0.232539\pi\) | ||||
−0.744812 | + | 0.667275i | \(0.767461\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 13.5778 | 0.843683 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.60555 | −0.161280 | ||||||||
\(262\) | −15.3944 | −0.951072 | ||||||||
\(263\) | 13.8167i | 0.851971i | 0.904730 | + | 0.425986i | \(0.140073\pi\) | ||||
−0.904730 | + | 0.425986i | \(0.859927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.78890i | 0.416254i | ||||||||
\(267\) | 0.788897 | 0.0482797 | ||||||||
\(268\) | −11.2111 | −0.684827 | ||||||||
\(269\) | −4.18335 | −0.255063 | −0.127532 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127532 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 28.4222i | − 1.72653i | −0.504754 | − | 0.863263i | \(-0.668417\pi\) | ||||
0.504754 | − | 0.863263i | \(-0.331583\pi\) | |||||||
\(272\) | 2.60555i | 0.157985i | ||||||||
\(273\) | 9.39445 | 0.568578 | ||||||||
\(274\) | −11.2111 | −0.677287 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.60555 | −0.517993 | ||||||||
\(277\) | − 12.4222i | − 0.746378i | −0.927755 | − | 0.373189i | \(-0.878264\pi\) | ||||
0.927755 | − | 0.373189i | \(-0.121736\pi\) | |||||||
\(278\) | 2.78890 | 0.167267 | ||||||||
\(279\) | 6.00000i | 0.359211i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 12.7889i | − 0.762922i | −0.924385 | − | 0.381461i | \(-0.875421\pi\) | ||||
0.924385 | − | 0.381461i | \(-0.124579\pi\) | |||||||
\(282\) | − 5.21110i | − 0.310317i | ||||||||
\(283\) | − 18.4222i | − 1.09509i | −0.836777 | − | 0.547543i | \(-0.815563\pi\) | ||||
0.836777 | − | 0.547543i | \(-0.184437\pi\) | |||||||
\(284\) | 5.21110i | 0.309222i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 29.2111i | − 1.72428i | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 10.2111 | 0.600653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.60555i | 0.504466i | ||||||||
\(292\) | −8.60555 | −0.503602 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | − 0.211103i | − 0.0123118i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.21110 | 0.302889 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 0.788897i | − 0.0456996i | ||||||||
\(299\) | −31.0278 | −1.79438 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 20.8444i | − 1.20145i | ||||||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | 14.6056i | 0.839067i | ||||||||
\(304\) | 2.60555i | 0.149439i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.60555i | 0.148949i | ||||||||
\(307\) | 23.2111 | 1.32473 | 0.662364 | − | 0.749182i | \(-0.269553\pi\) | ||||
0.662364 | + | 0.749182i | \(0.269553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 3.60555 | 0.204124 | ||||||||
\(313\) | 32.4222i | 1.83261i | 0.400480 | + | 0.916306i | \(0.368844\pi\) | ||||
−0.400480 | + | 0.916306i | \(0.631156\pi\) | |||||||
\(314\) | − 8.42221i | − 0.475293i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.4222 | −0.811312 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | −6.00000 | −0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 22.4222i | − 1.24954i | ||||||||
\(323\) | −6.78890 | −0.377744 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.42221 | 0.244923 | ||||||||
\(327\) | 8.60555 | 0.475888 | ||||||||
\(328\) | − 11.2111i | − 0.619030i | ||||||||
\(329\) | 13.5778 | 0.748568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.39445i | 0.516366i | 0.966096 | + | 0.258183i | \(0.0831237\pi\) | ||||
−0.966096 | + | 0.258183i | \(0.916876\pi\) | |||||||
\(332\) | 17.2111 | 0.944582 | ||||||||
\(333\) | 5.21110 | 0.285567 | ||||||||
\(334\) | −5.21110 | −0.285139 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.60555i | 0.142144i | ||||||||
\(337\) | 29.6333i | 1.61423i | 0.590395 | + | 0.807115i | \(0.298972\pi\) | ||||
−0.590395 | + | 0.807115i | \(0.701028\pi\) | |||||||
\(338\) | 13.0000 | 0.707107 | ||||||||
\(339\) | 7.81665 | 0.424542 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.60555i | 0.140892i | ||||||||
\(343\) | 18.7889 | 1.01451 | ||||||||
\(344\) | − 8.00000i | − 0.431331i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 16.4222i | − 0.882863i | ||||||||
\(347\) | − 15.6333i | − 0.839240i | −0.907700 | − | 0.419620i | \(-0.862163\pi\) | ||||
0.907700 | − | 0.419620i | \(-0.137837\pi\) | |||||||
\(348\) | − 2.60555i | − 0.139672i | ||||||||
\(349\) | 13.8167i | 0.739589i | 0.929114 | + | 0.369794i | \(0.120572\pi\) | ||||
−0.929114 | + | 0.369794i | \(0.879428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.60555 | 0.192450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2111 | −1.23540 | −0.617701 | − | 0.786413i | \(-0.711936\pi\) | ||||
−0.617701 | + | 0.786413i | \(0.711936\pi\) | |||||||
\(354\) | −5.21110 | −0.276967 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.788897i | 0.0418115i | ||||||||
\(357\) | −6.78890 | −0.359307 | ||||||||
\(358\) | 1.81665 | 0.0960131 | ||||||||
\(359\) | − 27.6333i | − 1.45843i | −0.684285 | − | 0.729215i | \(-0.739885\pi\) | ||||
0.684285 | − | 0.729215i | \(-0.260115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.2111 | 0.642690 | ||||||||
\(362\) | 20.4222 | 1.07337 | ||||||||
\(363\) | − 11.0000i | − 0.577350i | ||||||||
\(364\) | 9.39445i | 0.492403i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.21110i | 0.167847i | ||||||||
\(367\) | − 23.6333i | − 1.23365i | −0.787101 | − | 0.616824i | \(-0.788419\pi\) | ||||
0.787101 | − | 0.616824i | \(-0.211581\pi\) | |||||||
\(368\) | − 8.60555i | − 0.448595i | ||||||||
\(369\) | − 11.2111i | − 0.583627i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 15.6333i | − 0.811641i | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 8.42221i | 0.436085i | 0.975939 | + | 0.218043i | \(0.0699672\pi\) | ||||
−0.975939 | + | 0.218043i | \(0.930033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.21110 | 0.268742 | ||||||||
\(377\) | − 9.39445i | − 0.483839i | ||||||||
\(378\) | 2.60555i | 0.134015i | ||||||||
\(379\) | − 1.02776i | − 0.0527923i | −0.999652 | − | 0.0263961i | \(-0.991597\pi\) | ||||
0.999652 | − | 0.0263961i | \(-0.00840313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2111 | 0.676825 | ||||||||
\(382\) | 12.0000 | 0.613973 | ||||||||
\(383\) | 15.6333 | 0.798825 | 0.399412 | − | 0.916771i | \(-0.369214\pi\) | ||||
0.399412 | + | 0.916771i | \(0.369214\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8167 | 0.703249 | ||||||||
\(387\) | − 8.00000i | − 0.406663i | ||||||||
\(388\) | −8.60555 | −0.436881 | ||||||||
\(389\) | 2.60555 | 0.132107 | 0.0660533 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660533 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.4222 | 1.13394 | ||||||||
\(392\) | 0.211103 | 0.0106623 | ||||||||
\(393\) | − 15.3944i | − 0.776547i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.6333 | −1.98914 | −0.994569 | − | 0.104076i | \(-0.966811\pi\) | ||||
−0.994569 | + | 0.104076i | \(0.966811\pi\) | |||||||
\(398\) | −6.42221 | −0.321916 | ||||||||
\(399\) | −6.78890 | −0.339870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 23.2111i | − 1.15911i | −0.814934 | − | 0.579554i | \(-0.803227\pi\) | ||||
0.814934 | − | 0.579554i | \(-0.196773\pi\) | |||||||
\(402\) | − 11.2111i | − 0.559159i | ||||||||
\(403\) | −21.6333 | −1.07763 | ||||||||
\(404\) | −14.6056 | −0.726653 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.78890 | 0.336927 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.60555 | −0.128994 | ||||||||
\(409\) | − 29.2111i | − 1.44440i | −0.691686 | − | 0.722198i | \(-0.743132\pi\) | ||||
0.691686 | − | 0.722198i | \(-0.256868\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 11.2111i | − 0.553003i | ||||||||
\(412\) | − 4.00000i | − 0.197066i | ||||||||
\(413\) | − 13.5778i | − 0.668120i | ||||||||
\(414\) | − 8.60555i | − 0.422940i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60555i | 0.176777i | ||||||||
\(417\) | 2.78890i | 0.136573i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.8167 | −1.26123 | −0.630613 | − | 0.776097i | \(-0.717196\pi\) | ||||
−0.630613 | + | 0.776097i | \(0.717196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.81665i | − 0.0885383i | −0.999020 | − | 0.0442691i | \(-0.985904\pi\) | ||||
0.999020 | − | 0.0442691i | \(-0.0140959\pi\) | |||||||
\(422\) | 2.78890 | 0.135761 | ||||||||
\(423\) | 5.21110 | 0.253372 | ||||||||
\(424\) | − 6.00000i | − 0.291386i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.21110 | −0.252479 | ||||||||
\(427\) | −8.36669 | −0.404893 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 12.0000i | − 0.578020i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) | ||||
0.957326 | − | 0.289010i | \(-0.0933260\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 4.78890i | 0.230140i | 0.993357 | + | 0.115070i | \(0.0367092\pi\) | ||||
−0.993357 | + | 0.115070i | \(0.963291\pi\) | |||||||
\(434\) | − 15.6333i | − 0.750423i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.60555i | 0.412131i | ||||||||
\(437\) | 22.4222 | 1.07260 | ||||||||
\(438\) | − 8.60555i | − 0.411189i | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.211103 | 0.0100525 | ||||||||
\(442\) | −9.39445 | −0.446848 | ||||||||
\(443\) | − 27.6333i | − 1.31290i | −0.754370 | − | 0.656449i | \(-0.772058\pi\) | ||||
0.754370 | − | 0.656449i | \(-0.227942\pi\) | |||||||
\(444\) | 5.21110i | 0.247308i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.8167 | 0.938346 | ||||||||
\(447\) | 0.788897 | 0.0373136 | ||||||||
\(448\) | −2.60555 | −0.123101 | ||||||||
\(449\) | − 9.63331i | − 0.454624i | −0.973822 | − | 0.227312i | \(-0.927006\pi\) | ||||
0.973822 | − | 0.227312i | \(-0.0729937\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.81665i | 0.367664i | ||||||||
\(453\) | −6.00000 | −0.281905 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.60555 | −0.122016 | ||||||||
\(457\) | 12.2389 | 0.572510 | 0.286255 | − | 0.958154i | \(-0.407590\pi\) | ||||
0.286255 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(458\) | − 1.81665i | − 0.0848867i | ||||||||
\(459\) | −2.60555 | −0.121617 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9.63331i | − 0.448668i | −0.974512 | − | 0.224334i | \(-0.927979\pi\) | ||||
0.974512 | − | 0.224334i | \(-0.0720206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6056 | −1.79415 | −0.897076 | − | 0.441876i | \(-0.854313\pi\) | ||||
−0.897076 | + | 0.441876i | \(0.854313\pi\) | |||||||
\(464\) | 2.60555 | 0.120960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 19.8167i | − 0.917989i | ||||||||
\(467\) | 1.57779i | 0.0730116i | 0.999333 | + | 0.0365058i | \(0.0116227\pi\) | ||||
−0.999333 | + | 0.0365058i | \(0.988377\pi\) | |||||||
\(468\) | 3.60555i | 0.166667i | ||||||||
\(469\) | 29.2111 | 1.34884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.42221 | 0.388075 | ||||||||
\(472\) | − 5.21110i | − 0.239860i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − 14.4222i | − 0.662434i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 6.78890i | − 0.311169i | ||||||||
\(477\) | − 6.00000i | − 0.274721i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4222i | 1.57279i | 0.617724 | + | 0.786395i | \(0.288055\pi\) | ||||
−0.617724 | + | 0.786395i | \(0.711945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7889i | 0.856700i | ||||||||
\(482\) | 22.4222i | 1.02130i | ||||||||
\(483\) | 22.4222 | 1.02025 | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 37.0278 | 1.67789 | 0.838944 | − | 0.544218i | \(-0.183174\pi\) | ||||
0.838944 | + | 0.544218i | \(0.183174\pi\) | |||||||
\(488\) | −3.21110 | −0.145360 | ||||||||
\(489\) | 4.42221i | 0.199979i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8167 | −0.623537 | −0.311768 | − | 0.950158i | \(-0.600921\pi\) | ||||
−0.311768 | + | 0.950158i | \(0.600921\pi\) | |||||||
\(492\) | 11.2111 | 0.505436 | ||||||||
\(493\) | 6.78890i | 0.305757i | ||||||||
\(494\) | −9.39445 | −0.422676 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 6.00000i | − 0.269408i | ||||||||
\(497\) | − 13.5778i | − 0.609047i | ||||||||
\(498\) | 17.2111i | 0.771248i | ||||||||
\(499\) | − 13.0278i | − 0.583202i | −0.956540 | − | 0.291601i | \(-0.905812\pi\) | ||||
0.956540 | − | 0.291601i | \(-0.0941880\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.21110i | − 0.232815i | ||||||||
\(502\) | 20.6056 | 0.919671 | ||||||||
\(503\) | − 41.4500i | − 1.84816i | −0.382196 | − | 0.924081i | \(-0.624832\pi\) | ||||
0.382196 | − | 0.924081i | \(-0.375168\pi\) | |||||||
\(504\) | −2.60555 | −0.116060 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0000i | 0.577350i | ||||||||
\(508\) | 13.2111i | 0.586148i | ||||||||
\(509\) | 9.63331i | 0.426989i | 0.976944 | + | 0.213494i | \(0.0684845\pi\) | ||||
−0.976944 | + | 0.213494i | \(0.931515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4222 | 0.991900 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.60555 | −0.115038 | ||||||||
\(514\) | − 21.3944i | − 0.943669i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.5778 | −0.596574 | ||||||||
\(519\) | 16.4222 | 0.720855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6333 | −0.947772 | −0.473886 | − | 0.880586i | \(-0.657149\pi\) | ||||
−0.473886 | + | 0.880586i | \(0.657149\pi\) | |||||||
\(522\) | 2.60555 | 0.114042 | ||||||||
\(523\) | − 24.8444i | − 1.08637i | −0.839613 | − | 0.543185i | \(-0.817218\pi\) | ||||
0.839613 | − | 0.543185i | \(-0.182782\pi\) | |||||||
\(524\) | 15.3944 | 0.672510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 13.8167i | − 0.602435i | ||||||||
\(527\) | 15.6333 | 0.680998 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −51.0555 | −2.21980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.21110i | − 0.226143i | ||||||||
\(532\) | − 6.78890i | − 0.294336i | ||||||||
\(533\) | 40.4222 | 1.75088 | ||||||||
\(534\) | −0.788897 | −0.0341389 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.2111 | 0.484246 | ||||||||
\(537\) | 1.81665i | 0.0783944i | ||||||||
\(538\) | 4.18335 | 0.180357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 43.0278i | − 1.84991i | −0.380079 | − | 0.924954i | \(-0.624103\pi\) | ||||
0.380079 | − | 0.924954i | \(-0.375897\pi\) | |||||||
\(542\) | 28.4222i | 1.22084i | ||||||||
\(543\) | 20.4222i | 0.876401i | ||||||||
\(544\) | − 2.60555i | − 0.111712i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.39445 | −0.402045 | ||||||||
\(547\) | 14.4222i | 0.616649i | 0.951281 | + | 0.308324i | \(0.0997682\pi\) | ||||
−0.951281 | + | 0.308324i | \(0.900232\pi\) | |||||||
\(548\) | 11.2111 | 0.478915 | ||||||||
\(549\) | −3.21110 | −0.137047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.78890i | 0.289217i | ||||||||
\(552\) | 8.60555 | 0.366277 | ||||||||
\(553\) | 37.5778 | 1.59797 | ||||||||
\(554\) | 12.4222i | 0.527769i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.78890 | −0.118276 | ||||||||
\(557\) | −40.4222 | −1.71274 | −0.856372 | − | 0.516360i | \(-0.827287\pi\) | ||||
−0.856372 | + | 0.516360i | \(0.827287\pi\) | |||||||
\(558\) | − 6.00000i | − 0.254000i | ||||||||
\(559\) | 28.8444 | 1.21999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7889i | 0.539467i | ||||||||
\(563\) | − 38.0555i | − 1.60385i | −0.597426 | − | 0.801924i | \(-0.703810\pi\) | ||||
0.597426 | − | 0.801924i | \(-0.296190\pi\) | |||||||
\(564\) | 5.21110i | 0.219427i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.4222i | 0.774343i | ||||||||
\(567\) | −2.60555 | −0.109423 | ||||||||
\(568\) | − 5.21110i | − 0.218653i | ||||||||
\(569\) | 9.63331 | 0.403849 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.0555 | 1.75997 | 0.879984 | − | 0.475003i | \(-0.157553\pi\) | ||||
0.879984 | + | 0.475003i | \(0.157553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000i | 0.501307i | ||||||||
\(574\) | 29.2111i | 1.21925i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 44.6056 | 1.85695 | 0.928477 | − | 0.371391i | \(-0.121119\pi\) | ||||
0.928477 | + | 0.371391i | \(0.121119\pi\) | |||||||
\(578\) | −10.2111 | −0.424726 | ||||||||
\(579\) | 13.8167i | 0.574201i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.8444 | −1.86046 | ||||||||
\(582\) | − 8.60555i | − 0.356712i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.60555 | 0.356100 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −22.4222 | −0.925463 | −0.462732 | − | 0.886498i | \(-0.653131\pi\) | ||||
−0.462732 | + | 0.886498i | \(0.653131\pi\) | |||||||
\(588\) | 0.211103i | 0.00870572i | ||||||||
\(589\) | 15.6333 | 0.644159 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 6.00000i | − 0.246807i | ||||||||
\(592\) | −5.21110 | −0.214175 | ||||||||
\(593\) | 4.42221 | 0.181598 | 0.0907991 | − | 0.995869i | \(-0.471058\pi\) | ||||
0.0907991 | + | 0.995869i | \(0.471058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.788897i | 0.0323145i | ||||||||
\(597\) | − 6.42221i | − 0.262843i | ||||||||
\(598\) | 31.0278 | 1.26882 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.6333 | −1.69826 | −0.849129 | − | 0.528185i | \(-0.822873\pi\) | ||||
−0.849129 | + | 0.528185i | \(0.822873\pi\) | |||||||
\(602\) | 20.8444i | 0.849555i | ||||||||
\(603\) | 11.2111 | 0.456551 | ||||||||
\(604\) | − 6.00000i | − 0.244137i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − 14.6056i | − 0.593310i | ||||||||
\(607\) | − 2.78890i | − 0.113198i | −0.998397 | − | 0.0565989i | \(-0.981974\pi\) | ||||
0.998397 | − | 0.0565989i | \(-0.0180256\pi\) | |||||||
\(608\) | − 2.60555i | − 0.105669i | ||||||||
\(609\) | 6.78890i | 0.275100i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.7889i | 0.760117i | ||||||||
\(612\) | − 2.60555i | − 0.105323i | ||||||||
\(613\) | −18.7889 | −0.758876 | −0.379438 | − | 0.925217i | \(-0.623883\pi\) | ||||
−0.379438 | + | 0.925217i | \(0.623883\pi\) | |||||||
\(614\) | −23.2111 | −0.936724 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4222 | 0.661133 | 0.330567 | − | 0.943783i | \(-0.392760\pi\) | ||||
0.330567 | + | 0.943783i | \(0.392760\pi\) | |||||||
\(618\) | 4.00000 | 0.160904 | ||||||||
\(619\) | 4.18335i | 0.168143i | 0.996460 | + | 0.0840714i | \(0.0267924\pi\) | ||||
−0.996460 | + | 0.0840714i | \(0.973208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.60555 | 0.345329 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | − 2.05551i | − 0.0823524i | ||||||||
\(624\) | −3.60555 | −0.144338 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 32.4222i | − 1.29585i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.42221i | 0.336083i | ||||||||
\(629\) | − 13.5778i | − 0.541382i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2111i | 0.446307i | 0.974783 | + | 0.223153i | \(0.0716351\pi\) | ||||
−0.974783 | + | 0.223153i | \(0.928365\pi\) | |||||||
\(632\) | 14.4222 | 0.573685 | ||||||||
\(633\) | 2.78890i | 0.110849i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 0.761141i | 0.0301575i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 5.21110i | − 0.206148i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.4222 | −1.12261 | −0.561305 | − | 0.827609i | \(-0.689700\pi\) | ||||
−0.561305 | + | 0.827609i | \(0.689700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.6333 | −1.32637 | −0.663184 | − | 0.748456i | \(-0.730795\pi\) | ||||
−0.663184 | + | 0.748456i | \(0.730795\pi\) | |||||||
\(644\) | 22.4222i | 0.883559i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.78890 | 0.267106 | ||||||||
\(647\) | 27.3944i | 1.07699i | 0.842630 | + | 0.538493i | \(0.181006\pi\) | ||||
−0.842630 | + | 0.538493i | \(0.818994\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.6333 | 0.612718 | ||||||||
\(652\) | −4.42221 | −0.173187 | ||||||||
\(653\) | 24.7889i | 0.970065i | 0.874496 | + | 0.485032i | \(0.161192\pi\) | ||||
−0.874496 | + | 0.485032i | \(0.838808\pi\) | |||||||
\(654\) | −8.60555 | −0.336504 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.2111i | 0.437720i | ||||||||
\(657\) | 8.60555 | 0.335735 | ||||||||
\(658\) | −13.5778 | −0.529318 | ||||||||
\(659\) | −24.2389 | −0.944212 | −0.472106 | − | 0.881542i | \(-0.656506\pi\) | ||||
−0.472106 | + | 0.881542i | \(0.656506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.238859i | 0.00929054i | 0.999989 | + | 0.00464527i | \(0.00147864\pi\) | ||||
−0.999989 | + | 0.00464527i | \(0.998521\pi\) | |||||||
\(662\) | − 9.39445i | − 0.365126i | ||||||||
\(663\) | − 9.39445i | − 0.364850i | ||||||||
\(664\) | −17.2111 | −0.667920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.21110 | −0.201926 | ||||||||
\(667\) | − 22.4222i | − 0.868191i | ||||||||
\(668\) | 5.21110 | 0.201624 | ||||||||
\(669\) | 19.8167i | 0.766156i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − 2.60555i | − 0.100511i | ||||||||
\(673\) | 5.63331i | 0.217148i | 0.994088 | + | 0.108574i | \(0.0346284\pi\) | ||||
−0.994088 | + | 0.108574i | \(0.965372\pi\) | |||||||
\(674\) | − 29.6333i | − 1.14143i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | − 44.0555i | − 1.69319i | −0.532237 | − | 0.846595i | \(-0.678648\pi\) | ||||
0.532237 | − | 0.846595i | \(-0.321352\pi\) | |||||||
\(678\) | −7.81665 | −0.300197 | ||||||||
\(679\) | 22.4222 | 0.860485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000i | 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.21110 | −0.199397 | −0.0996986 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996986 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(684\) | − 2.60555i | − 0.0996257i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.7889 | −0.717363 | ||||||||
\(687\) | 1.81665 | 0.0693097 | ||||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | 21.6333 | 0.824163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.2389i | 1.15034i | 0.818034 | + | 0.575170i | \(0.195064\pi\) | ||||
−0.818034 | + | 0.575170i | \(0.804936\pi\) | |||||||
\(692\) | 16.4222i | 0.624279i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6333i | 0.593432i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.60555i | 0.0987632i | ||||||||
\(697\) | −29.2111 | −1.10645 | ||||||||
\(698\) | − 13.8167i | − 0.522968i | ||||||||
\(699\) | 19.8167 | 0.749535 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.9722 | 0.414416 | 0.207208 | − | 0.978297i | \(-0.433562\pi\) | ||||
0.207208 | + | 0.978297i | \(0.433562\pi\) | |||||||
\(702\) | −3.60555 | −0.136083 | ||||||||
\(703\) | − 13.5778i | − 0.512096i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.2111 | 0.873561 | ||||||||
\(707\) | 38.0555 | 1.43122 | ||||||||
\(708\) | 5.21110 | 0.195845 | ||||||||
\(709\) | − 8.60555i | − 0.323188i | −0.986857 | − | 0.161594i | \(-0.948336\pi\) | ||||
0.986857 | − | 0.161594i | \(-0.0516635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.4222 | 0.540875 | ||||||||
\(712\) | − 0.788897i | − 0.0295652i | ||||||||
\(713\) | −51.6333 | −1.93368 | ||||||||
\(714\) | 6.78890 | 0.254068 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.81665 | −0.0678915 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.6333i | 1.03127i | ||||||||
\(719\) | 8.36669 | 0.312025 | 0.156012 | − | 0.987755i | \(-0.450136\pi\) | ||||
0.156012 | + | 0.987755i | \(0.450136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4222i | 0.388143i | ||||||||
\(722\) | −12.2111 | −0.454450 | ||||||||
\(723\) | −22.4222 | −0.833891 | ||||||||
\(724\) | −20.4222 | −0.758985 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.0000i | 0.408248i | ||||||||
\(727\) | − 14.4222i | − 0.534890i | −0.963573 | − | 0.267445i | \(-0.913821\pi\) | ||||
0.963573 | − | 0.267445i | \(-0.0861794\pi\) | |||||||
\(728\) | − 9.39445i | − 0.348181i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.8444 | −0.770958 | ||||||||
\(732\) | − 3.21110i | − 0.118686i | ||||||||
\(733\) | 38.0555 | 1.40561 | 0.702806 | − | 0.711381i | \(-0.251930\pi\) | ||||
0.702806 | + | 0.711381i | \(0.251930\pi\) | |||||||
\(734\) | 23.6333i | 0.872321i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.60555i | 0.317205i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.2111i | 0.412686i | ||||||||
\(739\) | − 30.2389i | − 1.11235i | −0.831064 | − | 0.556177i | \(-0.812268\pi\) | ||||
0.831064 | − | 0.556177i | \(-0.187732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 9.39445i | − 0.345114i | ||||||||
\(742\) | 15.6333i | 0.573917i | ||||||||
\(743\) | −20.8444 | −0.764707 | −0.382354 | − | 0.924016i | \(-0.624886\pi\) | ||||
−0.382354 | + | 0.924016i | \(0.624886\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 8.42221i | − 0.308359i | ||||||||
\(747\) | −17.2111 | −0.629721 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.4222 | 0.672236 | 0.336118 | − | 0.941820i | \(-0.390886\pi\) | ||||
0.336118 | + | 0.941820i | \(0.390886\pi\) | |||||||
\(752\) | −5.21110 | −0.190029 | ||||||||
\(753\) | 20.6056i | 0.750908i | ||||||||
\(754\) | 9.39445i | 0.342126i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − 2.60555i | − 0.0947630i | ||||||||
\(757\) | − 27.2111i | − 0.989004i | −0.869176 | − | 0.494502i | \(-0.835350\pi\) | ||||
0.869176 | − | 0.494502i | \(-0.164650\pi\) | |||||||
\(758\) | 1.02776i | 0.0373298i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.63331i | 0.349207i | 0.984639 | + | 0.174604i | \(0.0558644\pi\) | ||||
−0.984639 | + | 0.174604i | \(0.944136\pi\) | |||||||
\(762\) | −13.2111 | −0.478588 | ||||||||
\(763\) | − 22.4222i | − 0.811738i | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.6333 | −0.564854 | ||||||||
\(767\) | 18.7889 | 0.678428 | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 44.8444i | 1.61713i | 0.588406 | + | 0.808565i | \(0.299756\pi\) | ||||
−0.588406 | + | 0.808565i | \(0.700244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.3944 | 0.770502 | ||||||||
\(772\) | −13.8167 | −0.497272 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 8.00000i | 0.287554i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.60555 | 0.308921 | ||||||||
\(777\) | − 13.5778i | − 0.487101i | ||||||||
\(778\) | −2.60555 | −0.0934135 | ||||||||
\(779\) | −29.2111 | −1.04660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −22.4222 | −0.801816 | ||||||||
\(783\) | 2.60555i | 0.0931148i | ||||||||
\(784\) | −0.211103 | −0.00753938 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.3944i | 0.549102i | ||||||||
\(787\) | 37.2666 | 1.32841 | 0.664206 | − | 0.747550i | \(-0.268770\pi\) | ||||
0.664206 | + | 0.747550i | \(0.268770\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 13.8167 | 0.491886 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 20.3667i | − 0.724156i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 11.5778i | − 0.411140i | ||||||||
\(794\) | 39.6333 | 1.40653 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.42221 | 0.227629 | ||||||||
\(797\) | 6.00000i | 0.212531i | 0.994338 | + | 0.106265i | \(0.0338893\pi\) | ||||
−0.994338 | + | 0.106265i | \(0.966111\pi\) | |||||||
\(798\) | 6.78890 | 0.240324 | ||||||||
\(799\) | − 13.5778i | − 0.480348i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 0.788897i | − 0.0278743i | ||||||||
\(802\) | 23.2111i | 0.819613i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.2111i | 0.395385i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.6333 | 0.762001 | ||||||||
\(807\) | 4.18335i | 0.147261i | ||||||||
\(808\) | 14.6056 | 0.513822 | ||||||||
\(809\) | −50.8444 | −1.78759 | −0.893797 | − | 0.448471i | \(-0.851969\pi\) | ||||
−0.893797 | + | 0.448471i | \(0.851969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2389i | 0.640453i | 0.947341 | + | 0.320226i | \(0.103759\pi\) | ||||
−0.947341 | + | 0.320226i | \(0.896241\pi\) | |||||||
\(812\) | −6.78890 | −0.238244 | ||||||||
\(813\) | −28.4222 | −0.996810 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.60555 | 0.0912125 | ||||||||
\(817\) | −20.8444 | −0.729254 | ||||||||
\(818\) | 29.2111i | 1.02134i | ||||||||
\(819\) | − 9.39445i | − 0.328269i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 11.2111i | − 0.391270i | −0.980677 | − | 0.195635i | \(-0.937323\pi\) | ||||
0.980677 | − | 0.195635i | \(-0.0626768\pi\) | |||||||
\(822\) | 11.2111i | 0.391032i | ||||||||
\(823\) | − 4.00000i | − 0.139431i | −0.997567 | − | 0.0697156i | \(-0.977791\pi\) | ||||
0.997567 | − | 0.0697156i | \(-0.0222092\pi\) | |||||||
\(824\) | 4.00000i | 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5778i | 0.472432i | ||||||||
\(827\) | −15.6333 | −0.543623 | −0.271812 | − | 0.962350i | \(-0.587623\pi\) | ||||
−0.271812 | + | 0.962350i | \(0.587623\pi\) | |||||||
\(828\) | 8.60555i | 0.299064i | ||||||||
\(829\) | 10.8444 | 0.376642 | 0.188321 | − | 0.982108i | \(-0.439695\pi\) | ||||
0.188321 | + | 0.982108i | \(0.439695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4222 | −0.430922 | ||||||||
\(832\) | − 3.60555i | − 0.125000i | ||||||||
\(833\) | − 0.550039i | − 0.0190577i | ||||||||
\(834\) | − 2.78890i | − 0.0965716i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | 25.8167 | 0.891822 | ||||||||
\(839\) | 10.4222i | 0.359814i | 0.983684 | + | 0.179907i | \(0.0575798\pi\) | ||||
−0.983684 | + | 0.179907i | \(0.942420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | 1.81665i | 0.0626060i | ||||||||
\(843\) | −12.7889 | −0.440473 | ||||||||
\(844\) | −2.78890 | −0.0959978 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.21110 | −0.179161 | ||||||||
\(847\) | −28.6611 | −0.984806 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −18.4222 | −0.632248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.8444i | 1.53725i | ||||||||
\(852\) | 5.21110 | 0.178529 | ||||||||
\(853\) | −29.2111 | −1.00017 | −0.500085 | − | 0.865977i | \(-0.666698\pi\) | ||||
−0.500085 | + | 0.865977i | \(0.666698\pi\) | |||||||
\(854\) | 8.36669 | 0.286302 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 13.0278i | − 0.445020i | −0.974930 | − | 0.222510i | \(-0.928575\pi\) | ||||
0.974930 | − | 0.222510i | \(-0.0714249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7889 | −0.368112 | −0.184056 | − | 0.982916i | \(-0.558923\pi\) | ||||
−0.184056 | + | 0.982916i | \(0.558923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.2111 | −0.995512 | ||||||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | 8.36669 | 0.284806 | 0.142403 | − | 0.989809i | \(-0.454517\pi\) | ||||
0.142403 | + | 0.989809i | \(0.454517\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 4.78890i | − 0.162733i | ||||||||
\(867\) | − 10.2111i | − 0.346787i | ||||||||
\(868\) | 15.6333i | 0.530629i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.4222i | 1.36965i | ||||||||
\(872\) | − 8.60555i | − 0.291421i | ||||||||
\(873\) | 8.60555 | 0.291254 | ||||||||
\(874\) | −22.4222 | −0.758442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.60555i | 0.290755i | ||||||||
\(877\) | −32.8444 | −1.10908 | −0.554538 | − | 0.832158i | \(-0.687105\pi\) | ||||
−0.554538 | + | 0.832158i | \(0.687105\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | − 18.0000i | − 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7889 | 0.835159 | 0.417580 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417580 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(882\) | −0.211103 | −0.00710819 | ||||||||
\(883\) | 38.4222i | 1.29301i | 0.762910 | + | 0.646505i | \(0.223770\pi\) | ||||
−0.762910 | + | 0.646505i | \(0.776230\pi\) | |||||||
\(884\) | 9.39445 | 0.315970 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.6333i | 0.928359i | ||||||||
\(887\) | − 43.0278i | − 1.44473i | −0.691512 | − | 0.722365i | \(-0.743055\pi\) | ||||
0.691512 | − | 0.722365i | \(-0.256945\pi\) | |||||||
\(888\) | − 5.21110i | − 0.174873i | ||||||||
\(889\) | − 34.4222i | − 1.15448i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.8167 | −0.663511 | ||||||||
\(893\) | − 13.5778i | − 0.454364i | ||||||||
\(894\) | −0.788897 | −0.0263847 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.60555 | 0.0870454 | ||||||||
\(897\) | 31.0278i | 1.03599i | ||||||||
\(898\) | 9.63331i | 0.321468i | ||||||||
\(899\) | − 15.6333i | − 0.521400i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.6333 | −0.520821 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.8444 | −0.693659 | ||||||||
\(904\) | − 7.81665i | − 0.259978i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | − 50.4222i | − 1.67424i | −0.547018 | − | 0.837121i | \(-0.684237\pi\) | ||||
0.547018 | − | 0.837121i | \(-0.315763\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 14.6056 | 0.484436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.6333 | 0.517955 | 0.258977 | − | 0.965883i | \(-0.416615\pi\) | ||||
0.258977 | + | 0.965883i | \(0.416615\pi\) | |||||||
\(912\) | 2.60555 | 0.0862784 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −12.2389 | −0.404825 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.81665i | 0.0600239i | ||||||||
\(917\) | −40.1110 | −1.32458 | ||||||||
\(918\) | 2.60555 | 0.0859960 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − 23.2111i | − 0.764832i | ||||||||
\(922\) | 9.63331i | 0.317256i | ||||||||
\(923\) | 18.7889 | 0.618444 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.6056 | 1.26866 | ||||||||
\(927\) | 4.00000i | 0.131377i | ||||||||
\(928\) | −2.60555 | −0.0855314 | ||||||||
\(929\) | 24.7889i | 0.813297i | 0.913585 | + | 0.406649i | \(0.133303\pi\) | ||||
−0.913585 | + | 0.406649i | \(0.866697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 0.550039i | − 0.0180268i | ||||||||
\(932\) | 19.8167i | 0.649116i | ||||||||
\(933\) | − 12.0000i | − 0.392862i | ||||||||
\(934\) | − 1.57779i | − 0.0516270i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − 3.60555i | − 0.117851i | ||||||||
\(937\) | 53.6333i | 1.75212i | 0.482199 | + | 0.876062i | \(0.339838\pi\) | ||||
−0.482199 | + | 0.876062i | \(0.660162\pi\) | |||||||
\(938\) | −29.2111 | −0.953776 | ||||||||
\(939\) | 32.4222 | 1.05806 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.0000i | 1.76035i | 0.474650 | + | 0.880175i | \(0.342575\pi\) | ||||
−0.474650 | + | 0.880175i | \(0.657425\pi\) | |||||||
\(942\) | −8.42221 | −0.274410 | ||||||||
\(943\) | 96.4777 | 3.14175 | ||||||||
\(944\) | 5.21110i | 0.169607i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.6333 | −0.897962 | −0.448981 | − | 0.893541i | \(-0.648213\pi\) | ||||
−0.448981 | + | 0.893541i | \(0.648213\pi\) | |||||||
\(948\) | 14.4222i | 0.468411i | ||||||||
\(949\) | 31.0278i | 1.00720i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 18.0000i | − 0.583690i | ||||||||
\(952\) | 6.78890i | 0.220029i | ||||||||
\(953\) | 30.2389i | 0.979533i | 0.871854 | + | 0.489766i | \(0.162918\pi\) | ||||
−0.871854 | + | 0.489766i | \(0.837082\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 34.4222i | − 1.11213i | ||||||||
\(959\) | −29.2111 | −0.943276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | − 18.7889i | − 0.605778i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 22.4222i | − 0.722171i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −22.4222 | −0.721423 | ||||||||
\(967\) | −42.2389 | −1.35831 | −0.679155 | − | 0.733995i | \(-0.737654\pi\) | ||||
−0.679155 | + | 0.733995i | \(0.737654\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 6.78890i | 0.218091i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9722 | −0.544665 | −0.272333 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272333 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 7.26662 | 0.232957 | ||||||||
\(974\) | −37.0278 | −1.18645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.21110 | 0.102785 | ||||||||
\(977\) | 38.8444 | 1.24274 | 0.621371 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621371 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(978\) | − 4.42221i | − 0.141407i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 8.60555i | − 0.274754i | ||||||||
\(982\) | 13.8167 | 0.440907 | ||||||||
\(983\) | −13.5778 | −0.433064 | −0.216532 | − | 0.976275i | \(-0.569475\pi\) | ||||
−0.216532 | + | 0.976275i | \(0.569475\pi\) | |||||||
\(984\) | −11.2111 | −0.357397 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 6.78890i | − 0.216203i | ||||||||
\(987\) | − 13.5778i | − 0.432186i | ||||||||
\(988\) | 9.39445 | 0.298877 | ||||||||
\(989\) | 68.8444 | 2.18912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.42221 | 0.204008 | 0.102004 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102004 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(992\) | 6.00000i | 0.190500i | ||||||||
\(993\) | 9.39445 | 0.298124 | ||||||||
\(994\) | 13.5778i | 0.430662i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − 17.2111i | − 0.545355i | ||||||||
\(997\) | − 12.4222i | − 0.393415i | −0.980462 | − | 0.196708i | \(-0.936975\pi\) | ||||
0.980462 | − | 0.196708i | \(-0.0630250\pi\) | |||||||
\(998\) | 13.0278i | 0.412386i | ||||||||
\(999\) | − 5.21110i | − 0.164872i |
(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 | 1950.2.f.m.649.1 | 4 | ||
5.2 | odd | 4 | 390.2.b.c.181.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1950.2.b.k.1351.4 | 4 | |||
5.4 | even | 2 | 1950.2.f.n.649.4 | 4 | |||
13.12 | even | 2 | 1950.2.f.n.649.2 | 4 | |||
15.2 | even | 4 | 1170.2.b.d.181.3 | 4 | |||
20.7 | even | 4 | 3120.2.g.q.961.2 | 4 | |||
65.12 | odd | 4 | 390.2.b.c.181.4 | yes | 4 | ||
65.38 | odd | 4 | 1950.2.b.k.1351.1 | 4 | |||
65.47 | even | 4 | 5070.2.a.bf.1.1 | 2 | |||
65.57 | even | 4 | 5070.2.a.z.1.2 | 2 | |||
65.64 | even | 2 | inner | 1950.2.f.m.649.3 | 4 | ||
195.77 | even | 4 | 1170.2.b.d.181.2 | 4 | |||
260.207 | even | 4 | 3120.2.g.q.961.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.1 | ✓ | 4 | 5.2 | odd | 4 | ||
390.2.b.c.181.4 | yes | 4 | 65.12 | odd | 4 | ||
1170.2.b.d.181.2 | 4 | 195.77 | even | 4 | |||
1170.2.b.d.181.3 | 4 | 15.2 | even | 4 | |||
1950.2.b.k.1351.1 | 4 | 65.38 | odd | 4 | |||
1950.2.b.k.1351.4 | 4 | 5.3 | odd | 4 | |||
1950.2.f.m.649.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.f.m.649.3 | 4 | 65.64 | even | 2 | inner | ||
1950.2.f.n.649.2 | 4 | 13.12 | even | 2 | |||
1950.2.f.n.649.4 | 4 | 5.4 | even | 2 | |||
3120.2.g.q.961.2 | 4 | 20.7 | even | 4 | |||
3120.2.g.q.961.3 | 4 | 260.207 | even | 4 | |||
5070.2.a.z.1.2 | 2 | 65.57 | even | 4 | |||
5070.2.a.bf.1.1 | 2 | 65.47 | even | 4 |