Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(181,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.b (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: | \(3.11416567883\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.181 |
Dual form | 390.2.b.c.181.4 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 2.60555i | − 0.984806i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
0.870367 | − | 0.492403i | \(-0.163881\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.60555 | −0.631939 | −0.315970 | − | 0.948769i | \(-0.602330\pi\) | ||||
−0.315970 | + | 0.948769i | \(0.602330\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 2.60555i | − 0.597754i | −0.954292 | − | 0.298877i | \(-0.903388\pi\) | ||||
0.954292 | − | 0.298877i | \(-0.0966121\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 2.60555i | 0.568578i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.60555 | −1.79438 | −0.897191 | − | 0.441643i | \(-0.854396\pi\) | ||||
−0.897191 | + | 0.441643i | \(0.854396\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.60555i | 0.707107i | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.60555i | 0.492403i | ||||||||
\(29\) | −2.60555 | −0.483839 | −0.241919 | − | 0.970296i | \(-0.577777\pi\) | ||||
−0.241919 | + | 0.970296i | \(0.577777\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 6.00000i | − 1.07763i | −0.842424 | − | 0.538816i | \(-0.818872\pi\) | ||||
0.842424 | − | 0.538816i | \(-0.181128\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.60555i | 0.446848i | ||||||||
\(35\) | −2.60555 | −0.440419 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 5.21110i | − 0.856700i | −0.903613 | − | 0.428350i | \(-0.859095\pi\) | ||||
0.903613 | − | 0.428350i | \(-0.140905\pi\) | |||||||
\(38\) | −2.60555 | −0.422676 | ||||||||
\(39\) | 3.60555 | 0.577350 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 11.2111i | 1.75088i | 0.483327 | + | 0.875440i | \(0.339428\pi\) | ||||
−0.483327 | + | 0.875440i | \(0.660572\pi\) | |||||||
\(42\) | 2.60555 | 0.402045 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 8.60555i | 1.26882i | ||||||||
\(47\) | − 5.21110i | − 0.760117i | −0.924962 | − | 0.380059i | \(-0.875904\pi\) | ||||
0.924962 | − | 0.380059i | \(-0.124096\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.211103 | 0.0301575 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 2.60555 | 0.364850 | ||||||||
\(52\) | 3.60555 | 0.500000 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.60555 | 0.348181 | ||||||||
\(57\) | 2.60555i | 0.345114i | ||||||||
\(58\) | 2.60555i | 0.342126i | ||||||||
\(59\) | − 5.21110i | − 0.678428i | −0.940709 | − | 0.339214i | \(-0.889839\pi\) | ||||
0.940709 | − | 0.339214i | \(-0.110161\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | 3.21110 | 0.411140 | 0.205570 | − | 0.978642i | \(-0.434095\pi\) | ||||
0.205570 | + | 0.978642i | \(0.434095\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | − 2.60555i | − 0.328269i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.60555i | 0.447214i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.2111i | − 1.36965i | −0.728706 | − | 0.684827i | \(-0.759878\pi\) | ||||
0.728706 | − | 0.684827i | \(-0.240122\pi\) | |||||||
\(68\) | 2.60555 | 0.315970 | ||||||||
\(69\) | 8.60555 | 1.03599 | ||||||||
\(70\) | 2.60555i | 0.311423i | ||||||||
\(71\) | 5.21110i | 0.618444i | 0.950990 | + | 0.309222i | \(0.100069\pi\) | ||||
−0.950990 | + | 0.309222i | \(0.899931\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 8.60555i | 1.00720i | 0.863936 | + | 0.503602i | \(0.167992\pi\) | ||||
−0.863936 | + | 0.503602i | \(0.832008\pi\) | |||||||
\(74\) | −5.21110 | −0.605778 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 2.60555i | 0.298877i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 3.60555i | − 0.408248i | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.2111 | 1.23806 | ||||||||
\(83\) | − 17.2111i | − 1.88916i | −0.328276 | − | 0.944582i | \(-0.606467\pi\) | ||||
0.328276 | − | 0.944582i | \(-0.393533\pi\) | |||||||
\(84\) | − 2.60555i | − 0.284289i | ||||||||
\(85\) | 2.60555i | 0.282612i | ||||||||
\(86\) | − 8.00000i | − 0.862662i | ||||||||
\(87\) | 2.60555 | 0.279344 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 0.788897i | − 0.0836230i | −0.999126 | − | 0.0418115i | \(-0.986687\pi\) | ||||
0.999126 | − | 0.0418115i | \(-0.0133129\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 9.39445i | 0.984806i | ||||||||
\(92\) | 8.60555 | 0.897191 | ||||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | −5.21110 | −0.537484 | ||||||||
\(95\) | −2.60555 | −0.267324 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − 8.60555i | − 0.873761i | −0.899519 | − | 0.436881i | \(-0.856083\pi\) | ||||
0.899519 | − | 0.436881i | \(-0.143917\pi\) | |||||||
\(98\) | − 0.211103i | − 0.0213246i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.6056 | −1.45331 | −0.726653 | − | 0.687004i | \(-0.758925\pi\) | ||||
−0.726653 | + | 0.687004i | \(0.758925\pi\) | |||||||
\(102\) | − 2.60555i | − 0.257988i | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | − 3.60555i | − 0.353553i | ||||||||
\(105\) | 2.60555 | 0.254276 | ||||||||
\(106\) | − 6.00000i | − 0.582772i | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 8.60555i | − 0.824262i | −0.911125 | − | 0.412131i | \(-0.864785\pi\) | ||||
0.911125 | − | 0.412131i | \(-0.135215\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.21110i | 0.494616i | ||||||||
\(112\) | − 2.60555i | − 0.246201i | ||||||||
\(113\) | 7.81665 | 0.735329 | 0.367664 | − | 0.929959i | \(-0.380157\pi\) | ||||
0.367664 | + | 0.929959i | \(0.380157\pi\) | |||||||
\(114\) | 2.60555 | 0.244032 | ||||||||
\(115\) | 8.60555i | 0.802472i | ||||||||
\(116\) | 2.60555 | 0.241919 | ||||||||
\(117\) | −3.60555 | −0.333333 | ||||||||
\(118\) | −5.21110 | −0.479721 | ||||||||
\(119\) | 6.78890i | 0.622337i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | − 3.21110i | − 0.290720i | ||||||||
\(123\) | − 11.2111i | − 1.01087i | ||||||||
\(124\) | 6.00000i | 0.538816i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.60555 | −0.232121 | ||||||||
\(127\) | −13.2111 | −1.17230 | −0.586148 | − | 0.810204i | \(-0.699356\pi\) | ||||
−0.586148 | + | 0.810204i | \(0.699356\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 3.60555 | 0.316228 | ||||||||
\(131\) | 15.3944 | 1.34502 | 0.672510 | − | 0.740088i | \(-0.265216\pi\) | ||||
0.672510 | + | 0.740088i | \(0.265216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.78890 | −0.588672 | ||||||||
\(134\) | −11.2111 | −0.968492 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 2.60555i | − 0.223424i | ||||||||
\(137\) | 11.2111i | 0.957829i | 0.877862 | + | 0.478915i | \(0.158970\pi\) | ||||
−0.877862 | + | 0.478915i | \(0.841030\pi\) | |||||||
\(138\) | − 8.60555i | − 0.732553i | ||||||||
\(139\) | 2.78890 | 0.236551 | 0.118276 | − | 0.992981i | \(-0.462263\pi\) | ||||
0.118276 | + | 0.992981i | \(0.462263\pi\) | |||||||
\(140\) | 2.60555 | 0.220209 | ||||||||
\(141\) | 5.21110i | 0.438854i | ||||||||
\(142\) | 5.21110 | 0.437306 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.60555i | 0.216379i | ||||||||
\(146\) | 8.60555 | 0.712200 | ||||||||
\(147\) | −0.211103 | −0.0174114 | ||||||||
\(148\) | 5.21110i | 0.428350i | ||||||||
\(149\) | − 0.788897i | − 0.0646290i | −0.999478 | − | 0.0323145i | \(-0.989712\pi\) | ||||
0.999478 | − | 0.0323145i | \(-0.0102878\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 6.00000i | − 0.488273i | −0.969741 | − | 0.244137i | \(-0.921495\pi\) | ||||
0.969741 | − | 0.244137i | \(-0.0785045\pi\) | |||||||
\(152\) | 2.60555 | 0.211338 | ||||||||
\(153\) | −2.60555 | −0.210646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −3.60555 | −0.288675 | ||||||||
\(157\) | −8.42221 | −0.672165 | −0.336083 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336083 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(158\) | − 14.4222i | − 1.14737i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 22.4222i | 1.76712i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 4.42221i | 0.346374i | 0.984889 | + | 0.173187i | \(0.0554065\pi\) | ||||
−0.984889 | + | 0.173187i | \(0.944594\pi\) | |||||||
\(164\) | − 11.2111i | − 0.875440i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2111 | −1.33584 | ||||||||
\(167\) | 5.21110i | 0.403247i | 0.979463 | + | 0.201624i | \(0.0646218\pi\) | ||||
−0.979463 | + | 0.201624i | \(0.935378\pi\) | |||||||
\(168\) | −2.60555 | −0.201023 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 2.60555 | 0.199837 | ||||||||
\(171\) | − 2.60555i | − 0.199251i | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | 16.4222 | 1.24856 | 0.624279 | − | 0.781202i | \(-0.285393\pi\) | ||||
0.624279 | + | 0.781202i | \(0.285393\pi\) | |||||||
\(174\) | − 2.60555i | − 0.197526i | ||||||||
\(175\) | 2.60555i | 0.196961i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.21110i | 0.391690i | ||||||||
\(178\) | −0.788897 | −0.0591304 | ||||||||
\(179\) | 1.81665 | 0.135783 | 0.0678915 | − | 0.997693i | \(-0.478373\pi\) | ||||
0.0678915 | + | 0.997693i | \(0.478373\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −20.4222 | −1.51797 | −0.758985 | − | 0.651108i | \(-0.774305\pi\) | ||||
−0.758985 | + | 0.651108i | \(0.774305\pi\) | |||||||
\(182\) | 9.39445 | 0.696363 | ||||||||
\(183\) | −3.21110 | −0.237372 | ||||||||
\(184\) | − 8.60555i | − 0.634410i | ||||||||
\(185\) | −5.21110 | −0.383128 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.21110i | 0.380059i | ||||||||
\(189\) | 2.60555i | 0.189526i | ||||||||
\(190\) | 2.60555i | 0.189027i | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 13.8167i | 0.994545i | 0.867595 | + | 0.497272i | \(0.165665\pi\) | ||||
−0.867595 | + | 0.497272i | \(0.834335\pi\) | |||||||
\(194\) | −8.60555 | −0.617843 | ||||||||
\(195\) | − 3.60555i | − 0.258199i | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.42221 | −0.455258 | −0.227629 | − | 0.973748i | \(-0.573097\pi\) | ||||
−0.227629 | + | 0.973748i | \(0.573097\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 11.2111i | 0.790770i | ||||||||
\(202\) | 14.6056i | 1.02764i | ||||||||
\(203\) | 6.78890i | 0.476487i | ||||||||
\(204\) | −2.60555 | −0.182425 | ||||||||
\(205\) | 11.2111 | 0.783017 | ||||||||
\(206\) | 4.00000i | 0.278693i | ||||||||
\(207\) | −8.60555 | −0.598127 | ||||||||
\(208\) | −3.60555 | −0.250000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | − 2.60555i | − 0.179800i | ||||||||
\(211\) | −2.78890 | −0.191996 | −0.0959978 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959978 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | − 5.21110i | − 0.357059i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 8.00000i | − 0.545595i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | −15.6333 | −1.06126 | ||||||||
\(218\) | −8.60555 | −0.582841 | ||||||||
\(219\) | − 8.60555i | − 0.581509i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.39445 | 0.631939 | ||||||||
\(222\) | 5.21110 | 0.349746 | ||||||||
\(223\) | 19.8167i | 1.32702i | 0.748167 | + | 0.663511i | \(0.230934\pi\) | ||||
−0.748167 | + | 0.663511i | \(0.769066\pi\) | |||||||
\(224\) | −2.60555 | −0.174091 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 7.81665i | − 0.519956i | ||||||||
\(227\) | − 24.0000i | − 1.59294i | −0.604681 | − | 0.796468i | \(-0.706699\pi\) | ||||
0.604681 | − | 0.796468i | \(-0.293301\pi\) | |||||||
\(228\) | − 2.60555i | − 0.172557i | ||||||||
\(229\) | − 1.81665i | − 0.120048i | −0.998197 | − | 0.0600239i | \(-0.980882\pi\) | ||||
0.998197 | − | 0.0600239i | \(-0.0191177\pi\) | |||||||
\(230\) | 8.60555 | 0.567433 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 2.60555i | − 0.171063i | ||||||||
\(233\) | 19.8167 | 1.29823 | 0.649116 | − | 0.760689i | \(-0.275139\pi\) | ||||
0.649116 | + | 0.760689i | \(0.275139\pi\) | |||||||
\(234\) | 3.60555i | 0.235702i | ||||||||
\(235\) | −5.21110 | −0.339935 | ||||||||
\(236\) | 5.21110i | 0.339214i | ||||||||
\(237\) | −14.4222 | −0.936823 | ||||||||
\(238\) | 6.78890 | 0.440059 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | − 22.4222i | − 1.44434i | −0.691715 | − | 0.722171i | \(-0.743145\pi\) | ||||
0.691715 | − | 0.722171i | \(-0.256855\pi\) | |||||||
\(242\) | − 11.0000i | − 0.707107i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.21110 | −0.205570 | ||||||||
\(245\) | − 0.211103i | − 0.0134868i | ||||||||
\(246\) | −11.2111 | −0.714794 | ||||||||
\(247\) | 9.39445i | 0.597754i | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 17.2111i | 1.09071i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −20.6056 | −1.30061 | −0.650305 | − | 0.759673i | \(-0.725359\pi\) | ||||
−0.650305 | + | 0.759673i | \(0.725359\pi\) | |||||||
\(252\) | 2.60555i | 0.164134i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 13.2111i | 0.828938i | ||||||||
\(255\) | − 2.60555i | − 0.163166i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.3944 | −1.33455 | −0.667275 | − | 0.744812i | \(-0.732539\pi\) | ||||
−0.667275 | + | 0.744812i | \(0.732539\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | −13.5778 | −0.843683 | ||||||||
\(260\) | − 3.60555i | − 0.223607i | ||||||||
\(261\) | −2.60555 | −0.161280 | ||||||||
\(262\) | − 15.3944i | − 0.951072i | ||||||||
\(263\) | 13.8167 | 0.851971 | 0.425986 | − | 0.904730i | \(-0.359927\pi\) | ||||
0.425986 | + | 0.904730i | \(0.359927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 6.00000i | − 0.368577i | ||||||||
\(266\) | 6.78890i | 0.416254i | ||||||||
\(267\) | 0.788897i | 0.0482797i | ||||||||
\(268\) | 11.2111i | 0.684827i | ||||||||
\(269\) | 4.18335 | 0.255063 | 0.127532 | − | 0.991835i | \(-0.459295\pi\) | ||||
0.127532 | + | 0.991835i | \(0.459295\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 28.4222i | − 1.72653i | −0.504754 | − | 0.863263i | \(-0.668417\pi\) | ||||
0.504754 | − | 0.863263i | \(-0.331583\pi\) | |||||||
\(272\) | −2.60555 | −0.157985 | ||||||||
\(273\) | − 9.39445i | − 0.568578i | ||||||||
\(274\) | 11.2111 | 0.677287 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.60555 | −0.517993 | ||||||||
\(277\) | 12.4222 | 0.746378 | 0.373189 | − | 0.927755i | \(-0.378264\pi\) | ||||
0.373189 | + | 0.927755i | \(0.378264\pi\) | |||||||
\(278\) | − 2.78890i | − 0.167267i | ||||||||
\(279\) | − 6.00000i | − 0.359211i | ||||||||
\(280\) | − 2.60555i | − 0.155711i | ||||||||
\(281\) | − 12.7889i | − 0.762922i | −0.924385 | − | 0.381461i | \(-0.875421\pi\) | ||||
0.924385 | − | 0.381461i | \(-0.124579\pi\) | |||||||
\(282\) | 5.21110 | 0.310317 | ||||||||
\(283\) | −18.4222 | −1.09509 | −0.547543 | − | 0.836777i | \(-0.684437\pi\) | ||||
−0.547543 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(284\) | − 5.21110i | − 0.309222i | ||||||||
\(285\) | 2.60555 | 0.154340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.2111 | 1.72428 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −10.2111 | −0.600653 | ||||||||
\(290\) | 2.60555 | 0.153003 | ||||||||
\(291\) | 8.60555i | 0.504466i | ||||||||
\(292\) | − 8.60555i | − 0.503602i | ||||||||
\(293\) | − 18.0000i | − 1.05157i | −0.850617 | − | 0.525786i | \(-0.823771\pi\) | ||||
0.850617 | − | 0.525786i | \(-0.176229\pi\) | |||||||
\(294\) | 0.211103i | 0.0123118i | ||||||||
\(295\) | −5.21110 | −0.303402 | ||||||||
\(296\) | 5.21110 | 0.302889 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.788897 | −0.0456996 | ||||||||
\(299\) | 31.0278 | 1.79438 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − 20.8444i | − 1.20145i | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 14.6056 | 0.839067 | ||||||||
\(304\) | − 2.60555i | − 0.149439i | ||||||||
\(305\) | − 3.21110i | − 0.183867i | ||||||||
\(306\) | 2.60555i | 0.148949i | ||||||||
\(307\) | 23.2111i | 1.32473i | 0.749182 | + | 0.662364i | \(0.230447\pi\) | ||||
−0.749182 | + | 0.662364i | \(0.769553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 6.00000i | 0.340777i | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 3.60555i | 0.204124i | ||||||||
\(313\) | 32.4222 | 1.83261 | 0.916306 | − | 0.400480i | \(-0.131156\pi\) | ||||
0.916306 | + | 0.400480i | \(0.131156\pi\) | |||||||
\(314\) | 8.42221i | 0.475293i | ||||||||
\(315\) | −2.60555 | −0.146806 | ||||||||
\(316\) | −14.4222 | −0.811312 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 22.4222 | 1.24954 | ||||||||
\(323\) | 6.78890i | 0.377744i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 3.60555 | 0.200000 | ||||||||
\(326\) | 4.42221 | 0.244923 | ||||||||
\(327\) | 8.60555i | 0.475888i | ||||||||
\(328\) | −11.2111 | −0.619030 | ||||||||
\(329\) | −13.5778 | −0.748568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.39445i | 0.516366i | 0.966096 | + | 0.258183i | \(0.0831237\pi\) | ||||
−0.966096 | + | 0.258183i | \(0.916876\pi\) | |||||||
\(332\) | 17.2111i | 0.944582i | ||||||||
\(333\) | − 5.21110i | − 0.285567i | ||||||||
\(334\) | 5.21110 | 0.285139 | ||||||||
\(335\) | −11.2111 | −0.612528 | ||||||||
\(336\) | 2.60555i | 0.142144i | ||||||||
\(337\) | −29.6333 | −1.61423 | −0.807115 | − | 0.590395i | \(-0.798972\pi\) | ||||
−0.807115 | + | 0.590395i | \(0.798972\pi\) | |||||||
\(338\) | − 13.0000i | − 0.707107i | ||||||||
\(339\) | −7.81665 | −0.424542 | ||||||||
\(340\) | − 2.60555i | − 0.141306i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.60555 | −0.140892 | ||||||||
\(343\) | − 18.7889i | − 1.01451i | ||||||||
\(344\) | 8.00000i | 0.431331i | ||||||||
\(345\) | − 8.60555i | − 0.463307i | ||||||||
\(346\) | − 16.4222i | − 0.882863i | ||||||||
\(347\) | 15.6333 | 0.839240 | 0.419620 | − | 0.907700i | \(-0.362163\pi\) | ||||
0.419620 | + | 0.907700i | \(0.362163\pi\) | |||||||
\(348\) | −2.60555 | −0.139672 | ||||||||
\(349\) | − 13.8167i | − 0.739589i | −0.929114 | − | 0.369794i | \(-0.879428\pi\) | ||||
0.929114 | − | 0.369794i | \(-0.120572\pi\) | |||||||
\(350\) | 2.60555 | 0.139273 | ||||||||
\(351\) | 3.60555 | 0.192450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.2111i | 1.23540i | 0.786413 | + | 0.617701i | \(0.211936\pi\) | ||||
−0.786413 | + | 0.617701i | \(0.788064\pi\) | |||||||
\(354\) | 5.21110 | 0.276967 | ||||||||
\(355\) | 5.21110 | 0.276577 | ||||||||
\(356\) | 0.788897i | 0.0418115i | ||||||||
\(357\) | − 6.78890i | − 0.359307i | ||||||||
\(358\) | − 1.81665i | − 0.0960131i | ||||||||
\(359\) | 27.6333i | 1.45843i | 0.684285 | + | 0.729215i | \(0.260115\pi\) | ||||
−0.684285 | + | 0.729215i | \(0.739885\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 12.2111 | 0.642690 | ||||||||
\(362\) | 20.4222i | 1.07337i | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | − 9.39445i | − 0.492403i | ||||||||
\(365\) | 8.60555 | 0.450435 | ||||||||
\(366\) | 3.21110i | 0.167847i | ||||||||
\(367\) | 23.6333 | 1.23365 | 0.616824 | − | 0.787101i | \(-0.288419\pi\) | ||||
0.616824 | + | 0.787101i | \(0.288419\pi\) | |||||||
\(368\) | −8.60555 | −0.448595 | ||||||||
\(369\) | 11.2111i | 0.583627i | ||||||||
\(370\) | 5.21110i | 0.270912i | ||||||||
\(371\) | − 15.6333i | − 0.811641i | ||||||||
\(372\) | − 6.00000i | − 0.311086i | ||||||||
\(373\) | 8.42221 | 0.436085 | 0.218043 | − | 0.975939i | \(-0.430033\pi\) | ||||
0.218043 | + | 0.975939i | \(0.430033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | 5.21110 | 0.268742 | ||||||||
\(377\) | 9.39445 | 0.483839 | ||||||||
\(378\) | 2.60555 | 0.134015 | ||||||||
\(379\) | 1.02776i | 0.0527923i | 0.999652 | + | 0.0263961i | \(0.00840313\pi\) | ||||
−0.999652 | + | 0.0263961i | \(0.991597\pi\) | |||||||
\(380\) | 2.60555 | 0.133662 | ||||||||
\(381\) | 13.2111 | 0.676825 | ||||||||
\(382\) | 12.0000i | 0.613973i | ||||||||
\(383\) | − 15.6333i | − 0.798825i | −0.916771 | − | 0.399412i | \(-0.869214\pi\) | ||||
0.916771 | − | 0.399412i | \(-0.130786\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8167 | 0.703249 | ||||||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | 8.60555i | 0.436881i | ||||||||
\(389\) | −2.60555 | −0.132107 | −0.0660533 | − | 0.997816i | \(-0.521041\pi\) | ||||
−0.0660533 | + | 0.997816i | \(0.521041\pi\) | |||||||
\(390\) | −3.60555 | −0.182574 | ||||||||
\(391\) | 22.4222 | 1.13394 | ||||||||
\(392\) | 0.211103i | 0.0106623i | ||||||||
\(393\) | −15.3944 | −0.776547 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | − 14.4222i | − 0.725660i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 39.6333i | − 1.98914i | −0.104076 | − | 0.994569i | \(-0.533189\pi\) | ||||
0.104076 | − | 0.994569i | \(-0.466811\pi\) | |||||||
\(398\) | 6.42221i | 0.321916i | ||||||||
\(399\) | 6.78890 | 0.339870 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 23.2111i | − 1.15911i | −0.814934 | − | 0.579554i | \(-0.803227\pi\) | ||||
0.814934 | − | 0.579554i | \(-0.196773\pi\) | |||||||
\(402\) | 11.2111 | 0.559159 | ||||||||
\(403\) | 21.6333i | 1.07763i | ||||||||
\(404\) | 14.6056 | 0.726653 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 6.78890 | 0.336927 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.60555i | 0.128994i | ||||||||
\(409\) | 29.2111i | 1.44440i | 0.691686 | + | 0.722198i | \(0.256868\pi\) | ||||
−0.691686 | + | 0.722198i | \(0.743132\pi\) | |||||||
\(410\) | − 11.2111i | − 0.553677i | ||||||||
\(411\) | − 11.2111i | − 0.553003i | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | −13.5778 | −0.668120 | ||||||||
\(414\) | 8.60555i | 0.422940i | ||||||||
\(415\) | −17.2111 | −0.844860 | ||||||||
\(416\) | 3.60555i | 0.176777i | ||||||||
\(417\) | −2.78890 | −0.136573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.8167 | 1.26123 | 0.630613 | − | 0.776097i | \(-0.282804\pi\) | ||||
0.630613 | + | 0.776097i | \(0.282804\pi\) | |||||||
\(420\) | −2.60555 | −0.127138 | ||||||||
\(421\) | − 1.81665i | − 0.0885383i | −0.999020 | − | 0.0442691i | \(-0.985904\pi\) | ||||
0.999020 | − | 0.0442691i | \(-0.0140959\pi\) | |||||||
\(422\) | 2.78890i | 0.135761i | ||||||||
\(423\) | − 5.21110i | − 0.253372i | ||||||||
\(424\) | 6.00000i | 0.291386i | ||||||||
\(425\) | 2.60555 | 0.126388 | ||||||||
\(426\) | −5.21110 | −0.252479 | ||||||||
\(427\) | − 8.36669i | − 0.404893i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | − 12.0000i | − 0.578020i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) | ||||
0.957326 | − | 0.289010i | \(-0.0933260\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.78890 | 0.230140 | 0.115070 | − | 0.993357i | \(-0.463291\pi\) | ||||
0.115070 | + | 0.993357i | \(0.463291\pi\) | |||||||
\(434\) | 15.6333i | 0.750423i | ||||||||
\(435\) | − 2.60555i | − 0.124927i | ||||||||
\(436\) | 8.60555i | 0.412131i | ||||||||
\(437\) | 22.4222i | 1.07260i | ||||||||
\(438\) | −8.60555 | −0.411189 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.211103 | 0.0100525 | ||||||||
\(442\) | − 9.39445i | − 0.446848i | ||||||||
\(443\) | −27.6333 | −1.31290 | −0.656449 | − | 0.754370i | \(-0.727942\pi\) | ||||
−0.656449 | + | 0.754370i | \(0.727942\pi\) | |||||||
\(444\) | − 5.21110i | − 0.247308i | ||||||||
\(445\) | −0.788897 | −0.0373973 | ||||||||
\(446\) | 19.8167 | 0.938346 | ||||||||
\(447\) | 0.788897i | 0.0373136i | ||||||||
\(448\) | 2.60555i | 0.123101i | ||||||||
\(449\) | 9.63331i | 0.454624i | 0.973822 | + | 0.227312i | \(0.0729937\pi\) | ||||
−0.973822 | + | 0.227312i | \(0.927006\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.81665 | −0.367664 | ||||||||
\(453\) | 6.00000i | 0.281905i | ||||||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 9.39445 | 0.440419 | ||||||||
\(456\) | −2.60555 | −0.122016 | ||||||||
\(457\) | 12.2389i | 0.572510i | 0.958154 | + | 0.286255i | \(0.0924104\pi\) | ||||
−0.958154 | + | 0.286255i | \(0.907590\pi\) | |||||||
\(458\) | −1.81665 | −0.0848867 | ||||||||
\(459\) | 2.60555 | 0.121617 | ||||||||
\(460\) | − 8.60555i | − 0.401236i | ||||||||
\(461\) | − 9.63331i | − 0.448668i | −0.974512 | − | 0.224334i | \(-0.927979\pi\) | ||||
0.974512 | − | 0.224334i | \(-0.0720206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.6056i | 1.79415i | 0.441876 | + | 0.897076i | \(0.354313\pi\) | ||||
−0.441876 | + | 0.897076i | \(0.645687\pi\) | |||||||
\(464\) | −2.60555 | −0.120960 | ||||||||
\(465\) | 6.00000 | 0.278243 | ||||||||
\(466\) | − 19.8167i | − 0.917989i | ||||||||
\(467\) | −1.57779 | −0.0730116 | −0.0365058 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365058 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(468\) | 3.60555 | 0.166667 | ||||||||
\(469\) | −29.2111 | −1.34884 | ||||||||
\(470\) | 5.21110i | 0.240370i | ||||||||
\(471\) | 8.42221 | 0.388075 | ||||||||
\(472\) | 5.21110 | 0.239860 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.4222i | 0.662434i | ||||||||
\(475\) | 2.60555i | 0.119551i | ||||||||
\(476\) | − 6.78890i | − 0.311169i | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 34.4222i | − 1.57279i | −0.617724 | − | 0.786395i | \(-0.711945\pi\) | ||||
0.617724 | − | 0.786395i | \(-0.288055\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 18.7889i | 0.856700i | ||||||||
\(482\) | −22.4222 | −1.02130 | ||||||||
\(483\) | − 22.4222i | − 1.02025i | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −8.60555 | −0.390758 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 37.0278i | 1.67789i | 0.544218 | + | 0.838944i | \(0.316826\pi\) | ||||
−0.544218 | + | 0.838944i | \(0.683174\pi\) | |||||||
\(488\) | 3.21110i | 0.145360i | ||||||||
\(489\) | − 4.42221i | − 0.199979i | ||||||||
\(490\) | −0.211103 | −0.00953664 | ||||||||
\(491\) | −13.8167 | −0.623537 | −0.311768 | − | 0.950158i | \(-0.600921\pi\) | ||||
−0.311768 | + | 0.950158i | \(0.600921\pi\) | |||||||
\(492\) | 11.2111i | 0.505436i | ||||||||
\(493\) | 6.78890 | 0.305757 | ||||||||
\(494\) | 9.39445 | 0.422676 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 6.00000i | − 0.269408i | ||||||||
\(497\) | 13.5778 | 0.609047 | ||||||||
\(498\) | 17.2111 | 0.771248 | ||||||||
\(499\) | 13.0278i | 0.583202i | 0.956540 | + | 0.291601i | \(0.0941880\pi\) | ||||
−0.956540 | + | 0.291601i | \(0.905812\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 5.21110i | − 0.232815i | ||||||||
\(502\) | 20.6056i | 0.919671i | ||||||||
\(503\) | −41.4500 | −1.84816 | −0.924081 | − | 0.382196i | \(-0.875168\pi\) | ||||
−0.924081 | + | 0.382196i | \(0.875168\pi\) | |||||||
\(504\) | 2.60555 | 0.116060 | ||||||||
\(505\) | 14.6056i | 0.649939i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | 13.2111 | 0.586148 | ||||||||
\(509\) | − 9.63331i | − 0.426989i | −0.976944 | − | 0.213494i | \(-0.931515\pi\) | ||||
0.976944 | − | 0.213494i | \(-0.0684845\pi\) | |||||||
\(510\) | −2.60555 | −0.115376 | ||||||||
\(511\) | 22.4222 | 0.991900 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 2.60555i | 0.115038i | ||||||||
\(514\) | 21.3944i | 0.943669i | ||||||||
\(515\) | 4.00000i | 0.176261i | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.5778i | 0.596574i | ||||||||
\(519\) | −16.4222 | −0.720855 | ||||||||
\(520\) | −3.60555 | −0.158114 | ||||||||
\(521\) | −21.6333 | −0.947772 | −0.473886 | − | 0.880586i | \(-0.657149\pi\) | ||||
−0.473886 | + | 0.880586i | \(0.657149\pi\) | |||||||
\(522\) | 2.60555i | 0.114042i | ||||||||
\(523\) | −24.8444 | −1.08637 | −0.543185 | − | 0.839613i | \(-0.682782\pi\) | ||||
−0.543185 | + | 0.839613i | \(0.682782\pi\) | |||||||
\(524\) | −15.3944 | −0.672510 | ||||||||
\(525\) | − 2.60555i | − 0.113716i | ||||||||
\(526\) | − 13.8167i | − 0.602435i | ||||||||
\(527\) | 15.6333i | 0.680998i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.0555 | 2.21980 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | − 5.21110i | − 0.226143i | ||||||||
\(532\) | 6.78890 | 0.294336 | ||||||||
\(533\) | − 40.4222i | − 1.75088i | ||||||||
\(534\) | 0.788897 | 0.0341389 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.2111 | 0.484246 | ||||||||
\(537\) | −1.81665 | −0.0783944 | ||||||||
\(538\) | − 4.18335i | − 0.180357i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 43.0278i | − 1.84991i | −0.380079 | − | 0.924954i | \(-0.624103\pi\) | ||||
0.380079 | − | 0.924954i | \(-0.375897\pi\) | |||||||
\(542\) | −28.4222 | −1.22084 | ||||||||
\(543\) | 20.4222 | 0.876401 | ||||||||
\(544\) | 2.60555i | 0.111712i | ||||||||
\(545\) | −8.60555 | −0.368621 | ||||||||
\(546\) | −9.39445 | −0.402045 | ||||||||
\(547\) | −14.4222 | −0.616649 | −0.308324 | − | 0.951281i | \(-0.599768\pi\) | ||||
−0.308324 | + | 0.951281i | \(0.599768\pi\) | |||||||
\(548\) | − 11.2111i | − 0.478915i | ||||||||
\(549\) | 3.21110 | 0.137047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.78890i | 0.289217i | ||||||||
\(552\) | 8.60555i | 0.366277i | ||||||||
\(553\) | − 37.5778i | − 1.59797i | ||||||||
\(554\) | − 12.4222i | − 0.527769i | ||||||||
\(555\) | 5.21110 | 0.221199 | ||||||||
\(556\) | −2.78890 | −0.118276 | ||||||||
\(557\) | − 40.4222i | − 1.71274i | −0.516360 | − | 0.856372i | \(-0.672713\pi\) | ||||
0.516360 | − | 0.856372i | \(-0.327287\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | −28.8444 | −1.21999 | ||||||||
\(560\) | −2.60555 | −0.110105 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7889 | −0.539467 | ||||||||
\(563\) | −38.0555 | −1.60385 | −0.801924 | − | 0.597426i | \(-0.796190\pi\) | ||||
−0.801924 | + | 0.597426i | \(0.796190\pi\) | |||||||
\(564\) | − 5.21110i | − 0.219427i | ||||||||
\(565\) | − 7.81665i | − 0.328849i | ||||||||
\(566\) | 18.4222i | 0.774343i | ||||||||
\(567\) | − 2.60555i | − 0.109423i | ||||||||
\(568\) | −5.21110 | −0.218653 | ||||||||
\(569\) | −9.63331 | −0.403849 | −0.201925 | − | 0.979401i | \(-0.564720\pi\) | ||||
−0.201925 | + | 0.979401i | \(0.564720\pi\) | |||||||
\(570\) | − 2.60555i | − 0.109135i | ||||||||
\(571\) | 42.0555 | 1.75997 | 0.879984 | − | 0.475003i | \(-0.157553\pi\) | ||||
0.879984 | + | 0.475003i | \(0.157553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | − 29.2111i | − 1.21925i | ||||||||
\(575\) | 8.60555 | 0.358876 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 44.6056i | 1.85695i | 0.371391 | + | 0.928477i | \(0.378881\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(578\) | 10.2111i | 0.424726i | ||||||||
\(579\) | − 13.8167i | − 0.574201i | ||||||||
\(580\) | − 2.60555i | − 0.108190i | ||||||||
\(581\) | −44.8444 | −1.86046 | ||||||||
\(582\) | 8.60555 | 0.356712 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.60555 | −0.356100 | ||||||||
\(585\) | 3.60555i | 0.149071i | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | − 22.4222i | − 0.925463i | −0.886498 | − | 0.462732i | \(-0.846869\pi\) | ||||
0.886498 | − | 0.462732i | \(-0.153131\pi\) | |||||||
\(588\) | 0.211103 | 0.00870572 | ||||||||
\(589\) | −15.6333 | −0.644159 | ||||||||
\(590\) | 5.21110i | 0.214538i | ||||||||
\(591\) | − 6.00000i | − 0.246807i | ||||||||
\(592\) | − 5.21110i | − 0.214175i | ||||||||
\(593\) | − 4.42221i | − 0.181598i | −0.995869 | − | 0.0907991i | \(-0.971058\pi\) | ||||
0.995869 | − | 0.0907991i | \(-0.0289421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.78890 | 0.278318 | ||||||||
\(596\) | 0.788897i | 0.0323145i | ||||||||
\(597\) | 6.42221 | 0.262843 | ||||||||
\(598\) | − 31.0278i | − 1.26882i | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −41.6333 | −1.69826 | −0.849129 | − | 0.528185i | \(-0.822873\pi\) | ||||
−0.849129 | + | 0.528185i | \(0.822873\pi\) | |||||||
\(602\) | −20.8444 | −0.849555 | ||||||||
\(603\) | − 11.2111i | − 0.456551i | ||||||||
\(604\) | 6.00000i | 0.244137i | ||||||||
\(605\) | − 11.0000i | − 0.447214i | ||||||||
\(606\) | − 14.6056i | − 0.593310i | ||||||||
\(607\) | 2.78890 | 0.113198 | 0.0565989 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0565989 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(608\) | −2.60555 | −0.105669 | ||||||||
\(609\) | − 6.78890i | − 0.275100i | ||||||||
\(610\) | −3.21110 | −0.130014 | ||||||||
\(611\) | 18.7889i | 0.760117i | ||||||||
\(612\) | 2.60555 | 0.105323 | ||||||||
\(613\) | 18.7889i | 0.758876i | 0.925217 | + | 0.379438i | \(0.123883\pi\) | ||||
−0.925217 | + | 0.379438i | \(0.876117\pi\) | |||||||
\(614\) | 23.2111 | 0.936724 | ||||||||
\(615\) | −11.2111 | −0.452075 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4222i | 0.661133i | 0.943783 | + | 0.330567i | \(0.107240\pi\) | ||||
−0.943783 | + | 0.330567i | \(0.892760\pi\) | |||||||
\(618\) | − 4.00000i | − 0.160904i | ||||||||
\(619\) | − 4.18335i | − 0.168143i | −0.996460 | − | 0.0840714i | \(-0.973208\pi\) | ||||
0.996460 | − | 0.0840714i | \(-0.0267924\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 8.60555 | 0.345329 | ||||||||
\(622\) | − 12.0000i | − 0.481156i | ||||||||
\(623\) | −2.05551 | −0.0823524 | ||||||||
\(624\) | 3.60555 | 0.144338 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 32.4222i | − 1.29585i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.42221 | 0.336083 | ||||||||
\(629\) | 13.5778i | 0.541382i | ||||||||
\(630\) | 2.60555i | 0.103808i | ||||||||
\(631\) | 11.2111i | 0.446307i | 0.974783 | + | 0.223153i | \(0.0716351\pi\) | ||||
−0.974783 | + | 0.223153i | \(0.928365\pi\) | |||||||
\(632\) | 14.4222i | 0.573685i | ||||||||
\(633\) | 2.78890 | 0.110849 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 13.2111i | 0.524267i | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −0.761141 | −0.0301575 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.21110i | 0.206148i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −28.4222 | −1.12261 | −0.561305 | − | 0.827609i | \(-0.689700\pi\) | ||||
−0.561305 | + | 0.827609i | \(0.689700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6333i | 1.32637i | 0.748456 | + | 0.663184i | \(0.230795\pi\) | ||||
−0.748456 | + | 0.663184i | \(0.769205\pi\) | |||||||
\(644\) | − 22.4222i | − 0.883559i | ||||||||
\(645\) | 8.00000i | 0.315000i | ||||||||
\(646\) | 6.78890 | 0.267106 | ||||||||
\(647\) | −27.3944 | −1.07699 | −0.538493 | − | 0.842630i | \(-0.681006\pi\) | ||||
−0.538493 | + | 0.842630i | \(0.681006\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 3.60555i | − 0.141421i | ||||||||
\(651\) | 15.6333 | 0.612718 | ||||||||
\(652\) | − 4.42221i | − 0.173187i | ||||||||
\(653\) | 24.7889 | 0.970065 | 0.485032 | − | 0.874496i | \(-0.338808\pi\) | ||||
0.485032 | + | 0.874496i | \(0.338808\pi\) | |||||||
\(654\) | 8.60555 | 0.336504 | ||||||||
\(655\) | − 15.3944i | − 0.601511i | ||||||||
\(656\) | 11.2111i | 0.437720i | ||||||||
\(657\) | 8.60555i | 0.335735i | ||||||||
\(658\) | 13.5778i | 0.529318i | ||||||||
\(659\) | 24.2389 | 0.944212 | 0.472106 | − | 0.881542i | \(-0.343494\pi\) | ||||
0.472106 | + | 0.881542i | \(0.343494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.238859i | 0.00929054i | 0.999989 | + | 0.00464527i | \(0.00147864\pi\) | ||||
−0.999989 | + | 0.00464527i | \(0.998521\pi\) | |||||||
\(662\) | 9.39445 | 0.365126 | ||||||||
\(663\) | −9.39445 | −0.364850 | ||||||||
\(664\) | 17.2111 | 0.667920 | ||||||||
\(665\) | 6.78890i | 0.263262i | ||||||||
\(666\) | −5.21110 | −0.201926 | ||||||||
\(667\) | 22.4222 | 0.868191 | ||||||||
\(668\) | − 5.21110i | − 0.201624i | ||||||||
\(669\) | − 19.8167i | − 0.766156i | ||||||||
\(670\) | 11.2111i | 0.433123i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.60555 | 0.100511 | ||||||||
\(673\) | 5.63331 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465372\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465372\pi\) | |||||||
\(674\) | 29.6333i | 1.14143i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 44.0555 | 1.69319 | 0.846595 | − | 0.532237i | \(-0.178648\pi\) | ||||
0.846595 | + | 0.532237i | \(0.178648\pi\) | |||||||
\(678\) | 7.81665i | 0.300197i | ||||||||
\(679\) | −22.4222 | −0.860485 | ||||||||
\(680\) | −2.60555 | −0.0999183 | ||||||||
\(681\) | 24.0000i | 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.21110i | 0.199397i | 0.995018 | + | 0.0996986i | \(0.0317879\pi\) | ||||
−0.995018 | + | 0.0996986i | \(0.968212\pi\) | |||||||
\(684\) | 2.60555i | 0.0996257i | ||||||||
\(685\) | 11.2111 | 0.428354 | ||||||||
\(686\) | −18.7889 | −0.717363 | ||||||||
\(687\) | 1.81665i | 0.0693097i | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −21.6333 | −0.824163 | ||||||||
\(690\) | −8.60555 | −0.327608 | ||||||||
\(691\) | 30.2389i | 1.15034i | 0.818034 | + | 0.575170i | \(0.195064\pi\) | ||||
−0.818034 | + | 0.575170i | \(0.804936\pi\) | |||||||
\(692\) | −16.4222 | −0.624279 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 15.6333i | − 0.593432i | ||||||||
\(695\) | − 2.78890i | − 0.105789i | ||||||||
\(696\) | 2.60555i | 0.0987632i | ||||||||
\(697\) | − 29.2111i | − 1.10645i | ||||||||
\(698\) | −13.8167 | −0.522968 | ||||||||
\(699\) | −19.8167 | −0.749535 | ||||||||
\(700\) | − 2.60555i | − 0.0984806i | ||||||||
\(701\) | 10.9722 | 0.414416 | 0.207208 | − | 0.978297i | \(-0.433562\pi\) | ||||
0.207208 | + | 0.978297i | \(0.433562\pi\) | |||||||
\(702\) | − 3.60555i | − 0.136083i | ||||||||
\(703\) | −13.5778 | −0.512096 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.21110 | 0.196261 | ||||||||
\(706\) | 23.2111 | 0.873561 | ||||||||
\(707\) | 38.0555i | 1.43122i | ||||||||
\(708\) | − 5.21110i | − 0.195845i | ||||||||
\(709\) | 8.60555i | 0.323188i | 0.986857 | + | 0.161594i | \(0.0516635\pi\) | ||||
−0.986857 | + | 0.161594i | \(0.948336\pi\) | |||||||
\(710\) | − 5.21110i | − 0.195569i | ||||||||
\(711\) | 14.4222 | 0.540875 | ||||||||
\(712\) | 0.788897 | 0.0295652 | ||||||||
\(713\) | 51.6333i | 1.93368i | ||||||||
\(714\) | −6.78890 | −0.254068 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.81665 | −0.0678915 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.6333 | 1.03127 | ||||||||
\(719\) | −8.36669 | −0.312025 | −0.156012 | − | 0.987755i | \(-0.549864\pi\) | ||||
−0.156012 | + | 0.987755i | \(0.549864\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 10.4222i | 0.388143i | ||||||||
\(722\) | − 12.2111i | − 0.454450i | ||||||||
\(723\) | 22.4222i | 0.833891i | ||||||||
\(724\) | 20.4222 | 0.758985 | ||||||||
\(725\) | 2.60555 | 0.0967677 | ||||||||
\(726\) | 11.0000i | 0.408248i | ||||||||
\(727\) | 14.4222 | 0.534890 | 0.267445 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267445 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(728\) | −9.39445 | −0.348181 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 8.60555i | − 0.318506i | ||||||||
\(731\) | −20.8444 | −0.770958 | ||||||||
\(732\) | 3.21110 | 0.118686 | ||||||||
\(733\) | − 38.0555i | − 1.40561i | −0.711381 | − | 0.702806i | \(-0.751930\pi\) | ||||
0.711381 | − | 0.702806i | \(-0.248070\pi\) | |||||||
\(734\) | − 23.6333i | − 0.872321i | ||||||||
\(735\) | 0.211103i | 0.00778663i | ||||||||
\(736\) | 8.60555i | 0.317205i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.2111 | 0.412686 | ||||||||
\(739\) | 30.2389i | 1.11235i | 0.831064 | + | 0.556177i | \(0.187732\pi\) | ||||
−0.831064 | + | 0.556177i | \(0.812268\pi\) | |||||||
\(740\) | 5.21110 | 0.191564 | ||||||||
\(741\) | − 9.39445i | − 0.345114i | ||||||||
\(742\) | −15.6333 | −0.573917 | ||||||||
\(743\) | 20.8444i | 0.764707i | 0.924016 | + | 0.382354i | \(0.124886\pi\) | ||||
−0.924016 | + | 0.382354i | \(0.875114\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −0.788897 | −0.0289030 | ||||||||
\(746\) | − 8.42221i | − 0.308359i | ||||||||
\(747\) | − 17.2111i | − 0.629721i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 18.4222 | 0.672236 | 0.336118 | − | 0.941820i | \(-0.390886\pi\) | ||||
0.336118 | + | 0.941820i | \(0.390886\pi\) | |||||||
\(752\) | − 5.21110i | − 0.190029i | ||||||||
\(753\) | 20.6056 | 0.750908 | ||||||||
\(754\) | − 9.39445i | − 0.342126i | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | − 2.60555i | − 0.0947630i | ||||||||
\(757\) | 27.2111 | 0.989004 | 0.494502 | − | 0.869176i | \(-0.335350\pi\) | ||||
0.494502 | + | 0.869176i | \(0.335350\pi\) | |||||||
\(758\) | 1.02776 | 0.0373298 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 2.60555i | − 0.0945133i | ||||||||
\(761\) | 9.63331i | 0.349207i | 0.984639 | + | 0.174604i | \(0.0558644\pi\) | ||||
−0.984639 | + | 0.174604i | \(0.944136\pi\) | |||||||
\(762\) | − 13.2111i | − 0.478588i | ||||||||
\(763\) | −22.4222 | −0.811738 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 2.60555i | 0.0942039i | ||||||||
\(766\) | −15.6333 | −0.564854 | ||||||||
\(767\) | 18.7889i | 0.678428i | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − 44.8444i | − 1.61713i | −0.588406 | − | 0.808565i | \(-0.700244\pi\) | ||||
0.588406 | − | 0.808565i | \(-0.299756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.3944 | 0.770502 | ||||||||
\(772\) | − 13.8167i | − 0.497272i | ||||||||
\(773\) | − 30.0000i | − 1.07903i | −0.841978 | − | 0.539513i | \(-0.818609\pi\) | ||||
0.841978 | − | 0.539513i | \(-0.181391\pi\) | |||||||
\(774\) | − 8.00000i | − 0.287554i | ||||||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | 8.60555 | 0.308921 | ||||||||
\(777\) | 13.5778 | 0.487101 | ||||||||
\(778\) | 2.60555i | 0.0934135i | ||||||||
\(779\) | 29.2111 | 1.04660 | ||||||||
\(780\) | 3.60555i | 0.129099i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 22.4222i | − 0.801816i | ||||||||
\(783\) | 2.60555 | 0.0931148 | ||||||||
\(784\) | 0.211103 | 0.00753938 | ||||||||
\(785\) | 8.42221i | 0.300601i | ||||||||
\(786\) | 15.3944i | 0.549102i | ||||||||
\(787\) | 37.2666i | 1.32841i | 0.747550 | + | 0.664206i | \(0.231230\pi\) | ||||
−0.747550 | + | 0.664206i | \(0.768770\pi\) | |||||||
\(788\) | − 6.00000i | − 0.213741i | ||||||||
\(789\) | −13.8167 | −0.491886 | ||||||||
\(790\) | −14.4222 | −0.513119 | ||||||||
\(791\) | − 20.3667i | − 0.724156i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5778 | −0.411140 | ||||||||
\(794\) | −39.6333 | −1.40653 | ||||||||
\(795\) | 6.00000i | 0.212798i | ||||||||
\(796\) | 6.42221 | 0.227629 | ||||||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | − 6.78890i | − 0.240324i | ||||||||
\(799\) | 13.5778i | 0.480348i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 0.788897i | − 0.0278743i | ||||||||
\(802\) | −23.2111 | −0.819613 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − 11.2111i | − 0.395385i | ||||||||
\(805\) | 22.4222 | 0.790279 | ||||||||
\(806\) | 21.6333 | 0.762001 | ||||||||
\(807\) | −4.18335 | −0.147261 | ||||||||
\(808\) | − 14.6056i | − 0.513822i | ||||||||
\(809\) | 50.8444 | 1.78759 | 0.893797 | − | 0.448471i | \(-0.148031\pi\) | ||||
0.893797 | + | 0.448471i | \(0.148031\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 18.2389i | 0.640453i | 0.947341 | + | 0.320226i | \(0.103759\pi\) | ||||
−0.947341 | + | 0.320226i | \(0.896241\pi\) | |||||||
\(812\) | − 6.78890i | − 0.238244i | ||||||||
\(813\) | 28.4222i | 0.996810i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.42221 | 0.154903 | ||||||||
\(816\) | 2.60555 | 0.0912125 | ||||||||
\(817\) | − 20.8444i | − 0.729254i | ||||||||
\(818\) | 29.2111 | 1.02134 | ||||||||
\(819\) | 9.39445i | 0.328269i | ||||||||
\(820\) | −11.2111 | −0.391509 | ||||||||
\(821\) | − 11.2111i | − 0.391270i | −0.980677 | − | 0.195635i | \(-0.937323\pi\) | ||||
0.980677 | − | 0.195635i | \(-0.0626768\pi\) | |||||||
\(822\) | −11.2111 | −0.391032 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | − 4.00000i | − 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5778i | 0.472432i | ||||||||
\(827\) | − 15.6333i | − 0.543623i | −0.962350 | − | 0.271812i | \(-0.912377\pi\) | ||||
0.962350 | − | 0.271812i | \(-0.0876228\pi\) | |||||||
\(828\) | 8.60555 | 0.299064 | ||||||||
\(829\) | −10.8444 | −0.376642 | −0.188321 | − | 0.982108i | \(-0.560305\pi\) | ||||
−0.188321 | + | 0.982108i | \(0.560305\pi\) | |||||||
\(830\) | 17.2111i | 0.597406i | ||||||||
\(831\) | −12.4222 | −0.430922 | ||||||||
\(832\) | 3.60555 | 0.125000 | ||||||||
\(833\) | −0.550039 | −0.0190577 | ||||||||
\(834\) | 2.78890i | 0.0965716i | ||||||||
\(835\) | 5.21110 | 0.180338 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000i | 0.207390i | ||||||||
\(838\) | − 25.8167i | − 0.891822i | ||||||||
\(839\) | − 10.4222i | − 0.359814i | −0.983684 | − | 0.179907i | \(-0.942420\pi\) | ||||
0.983684 | − | 0.179907i | \(-0.0575798\pi\) | |||||||
\(840\) | 2.60555i | 0.0899001i | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | −1.81665 | −0.0626060 | ||||||||
\(843\) | 12.7889i | 0.440473i | ||||||||
\(844\) | 2.78890 | 0.0959978 | ||||||||
\(845\) | − 13.0000i | − 0.447214i | ||||||||
\(846\) | −5.21110 | −0.179161 | ||||||||
\(847\) | − 28.6611i | − 0.984806i | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 18.4222 | 0.632248 | ||||||||
\(850\) | − 2.60555i | − 0.0893697i | ||||||||
\(851\) | 44.8444i | 1.53725i | ||||||||
\(852\) | 5.21110i | 0.178529i | ||||||||
\(853\) | 29.2111i | 1.00017i | 0.865977 | + | 0.500085i | \(0.166698\pi\) | ||||
−0.865977 | + | 0.500085i | \(0.833302\pi\) | |||||||
\(854\) | −8.36669 | −0.286302 | ||||||||
\(855\) | −2.60555 | −0.0891080 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0278 | 0.445020 | 0.222510 | − | 0.974930i | \(-0.428575\pi\) | ||||
0.222510 | + | 0.974930i | \(0.428575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7889 | 0.368112 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(860\) | 8.00000i | 0.272798i | ||||||||
\(861\) | −29.2111 | −0.995512 | ||||||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | − 8.36669i | − 0.284806i | −0.989809 | − | 0.142403i | \(-0.954517\pi\) | ||||
0.989809 | − | 0.142403i | \(-0.0454828\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 16.4222i | − 0.558372i | ||||||||
\(866\) | − 4.78890i | − 0.162733i | ||||||||
\(867\) | 10.2111 | 0.346787 | ||||||||
\(868\) | 15.6333 | 0.530629 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.60555 | −0.0883365 | ||||||||
\(871\) | 40.4222i | 1.36965i | ||||||||
\(872\) | 8.60555 | 0.291421 | ||||||||
\(873\) | − 8.60555i | − 0.291254i | ||||||||
\(874\) | 22.4222 | 0.758442 | ||||||||
\(875\) | 2.60555 | 0.0880837 | ||||||||
\(876\) | 8.60555i | 0.290755i | ||||||||
\(877\) | − 32.8444i | − 1.10908i | −0.832158 | − | 0.554538i | \(-0.812895\pi\) | ||||
0.832158 | − | 0.554538i | \(-0.187105\pi\) | |||||||
\(878\) | − 8.00000i | − 0.269987i | ||||||||
\(879\) | 18.0000i | 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7889 | 0.835159 | 0.417580 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417580 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(882\) | − 0.211103i | − 0.00710819i | ||||||||
\(883\) | 38.4222 | 1.29301 | 0.646505 | − | 0.762910i | \(-0.276230\pi\) | ||||
0.646505 | + | 0.762910i | \(0.276230\pi\) | |||||||
\(884\) | −9.39445 | −0.315970 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | 27.6333i | 0.928359i | ||||||||
\(887\) | 43.0278 | 1.44473 | 0.722365 | − | 0.691512i | \(-0.243055\pi\) | ||||
0.722365 | + | 0.691512i | \(0.243055\pi\) | |||||||
\(888\) | −5.21110 | −0.174873 | ||||||||
\(889\) | 34.4222i | 1.15448i | ||||||||
\(890\) | 0.788897i | 0.0264439i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 19.8167i | − 0.663511i | ||||||||
\(893\) | −13.5778 | −0.454364 | ||||||||
\(894\) | 0.788897 | 0.0263847 | ||||||||
\(895\) | − 1.81665i | − 0.0607240i | ||||||||
\(896\) | 2.60555 | 0.0870454 | ||||||||
\(897\) | −31.0278 | −1.03599 | ||||||||
\(898\) | 9.63331 | 0.321468 | ||||||||
\(899\) | 15.6333i | 0.521400i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −15.6333 | −0.520821 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.8444i | 0.693659i | ||||||||
\(904\) | 7.81665i | 0.259978i | ||||||||
\(905\) | 20.4222i | 0.678857i | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | 50.4222 | 1.67424 | 0.837121 | − | 0.547018i | \(-0.184237\pi\) | ||||
0.837121 | + | 0.547018i | \(0.184237\pi\) | |||||||
\(908\) | 24.0000i | 0.796468i | ||||||||
\(909\) | −14.6056 | −0.484436 | ||||||||
\(910\) | − 9.39445i | − 0.311423i | ||||||||
\(911\) | 15.6333 | 0.517955 | 0.258977 | − | 0.965883i | \(-0.416615\pi\) | ||||
0.258977 | + | 0.965883i | \(0.416615\pi\) | |||||||
\(912\) | 2.60555i | 0.0862784i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 12.2389 | 0.404825 | ||||||||
\(915\) | 3.21110i | 0.106156i | ||||||||
\(916\) | 1.81665i | 0.0600239i | ||||||||
\(917\) | − 40.1110i | − 1.32458i | ||||||||
\(918\) | − 2.60555i | − 0.0859960i | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | −8.60555 | −0.283717 | ||||||||
\(921\) | − 23.2111i | − 0.764832i | ||||||||
\(922\) | −9.63331 | −0.317256 | ||||||||
\(923\) | − 18.7889i | − 0.618444i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21110i | 0.171340i | ||||||||
\(926\) | 38.6056 | 1.26866 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 2.60555i | 0.0855314i | ||||||||
\(929\) | − 24.7889i | − 0.813297i | −0.913585 | − | 0.406649i | \(-0.866697\pi\) | ||||
0.913585 | − | 0.406649i | \(-0.133303\pi\) | |||||||
\(930\) | − 6.00000i | − 0.196748i | ||||||||
\(931\) | − 0.550039i | − 0.0180268i | ||||||||
\(932\) | −19.8167 | −0.649116 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 1.57779i | 0.0516270i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − 3.60555i | − 0.117851i | ||||||||
\(937\) | −53.6333 | −1.75212 | −0.876062 | − | 0.482199i | \(-0.839838\pi\) | ||||
−0.876062 | + | 0.482199i | \(0.839838\pi\) | |||||||
\(938\) | 29.2111i | 0.953776i | ||||||||
\(939\) | −32.4222 | −1.05806 | ||||||||
\(940\) | 5.21110 | 0.169967 | ||||||||
\(941\) | 54.0000i | 1.76035i | 0.474650 | + | 0.880175i | \(0.342575\pi\) | ||||
−0.474650 | + | 0.880175i | \(0.657425\pi\) | |||||||
\(942\) | − 8.42221i | − 0.274410i | ||||||||
\(943\) | − 96.4777i | − 3.14175i | ||||||||
\(944\) | − 5.21110i | − 0.169607i | ||||||||
\(945\) | 2.60555 | 0.0847586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 27.6333i | − 0.897962i | −0.893541 | − | 0.448981i | \(-0.851787\pi\) | ||||
0.893541 | − | 0.448981i | \(-0.148213\pi\) | |||||||
\(948\) | 14.4222 | 0.468411 | ||||||||
\(949\) | − 31.0278i | − 1.00720i | ||||||||
\(950\) | 2.60555 | 0.0845352 | ||||||||
\(951\) | − 18.0000i | − 0.583690i | ||||||||
\(952\) | −6.78890 | −0.220029 | ||||||||
\(953\) | 30.2389 | 0.979533 | 0.489766 | − | 0.871854i | \(-0.337082\pi\) | ||||
0.489766 | + | 0.871854i | \(0.337082\pi\) | |||||||
\(954\) | − 6.00000i | − 0.194257i | ||||||||
\(955\) | 12.0000i | 0.388311i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.4222 | −1.11213 | ||||||||
\(959\) | 29.2111 | 0.943276 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 18.7889 | 0.605778 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.4222i | 0.722171i | ||||||||
\(965\) | 13.8167 | 0.444774 | ||||||||
\(966\) | −22.4222 | −0.721423 | ||||||||
\(967\) | − 42.2389i | − 1.35831i | −0.733995 | − | 0.679155i | \(-0.762346\pi\) | ||||
0.733995 | − | 0.679155i | \(-0.237654\pi\) | |||||||
\(968\) | 11.0000i | 0.353553i | ||||||||
\(969\) | − 6.78890i | − 0.218091i | ||||||||
\(970\) | 8.60555i | 0.276308i | ||||||||
\(971\) | −16.9722 | −0.544665 | −0.272333 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272333 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 7.26662i | − 0.232957i | ||||||||
\(974\) | 37.0278 | 1.18645 | ||||||||
\(975\) | −3.60555 | −0.115470 | ||||||||
\(976\) | 3.21110 | 0.102785 | ||||||||
\(977\) | 38.8444i | 1.24274i | 0.783516 | + | 0.621371i | \(0.213424\pi\) | ||||
−0.783516 | + | 0.621371i | \(0.786576\pi\) | |||||||
\(978\) | −4.42221 | −0.141407 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.211103i | 0.00674342i | ||||||||
\(981\) | − 8.60555i | − 0.274754i | ||||||||
\(982\) | 13.8167i | 0.440907i | ||||||||
\(983\) | 13.5778i | 0.433064i | 0.976275 | + | 0.216532i | \(0.0694746\pi\) | ||||
−0.976275 | + | 0.216532i | \(0.930525\pi\) | |||||||
\(984\) | 11.2111 | 0.357397 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | − 6.78890i | − 0.216203i | ||||||||
\(987\) | 13.5778 | 0.432186 | ||||||||
\(988\) | − 9.39445i | − 0.298877i | ||||||||
\(989\) | −68.8444 | −2.18912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.42221 | 0.204008 | 0.102004 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102004 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | − 9.39445i | − 0.298124i | ||||||||
\(994\) | − 13.5778i | − 0.430662i | ||||||||
\(995\) | 6.42221i | 0.203598i | ||||||||
\(996\) | − 17.2111i | − 0.545355i | ||||||||
\(997\) | 12.4222 | 0.393415 | 0.196708 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196708 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(998\) | 13.0278 | 0.412386 | ||||||||
\(999\) | 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 | 390.2.b.c.181.1 | ✓ | 4 | |
3.2 | odd | 2 | 1170.2.b.d.181.3 | 4 | |||
4.3 | odd | 2 | 3120.2.g.q.961.2 | 4 | |||
5.2 | odd | 4 | 1950.2.f.n.649.4 | 4 | |||
5.3 | odd | 4 | 1950.2.f.m.649.1 | 4 | |||
5.4 | even | 2 | 1950.2.b.k.1351.4 | 4 | |||
13.5 | odd | 4 | 5070.2.a.z.1.2 | 2 | |||
13.8 | odd | 4 | 5070.2.a.bf.1.1 | 2 | |||
13.12 | even | 2 | inner | 390.2.b.c.181.4 | yes | 4 | |
39.38 | odd | 2 | 1170.2.b.d.181.2 | 4 | |||
52.51 | odd | 2 | 3120.2.g.q.961.3 | 4 | |||
65.12 | odd | 4 | 1950.2.f.m.649.3 | 4 | |||
65.38 | odd | 4 | 1950.2.f.n.649.2 | 4 | |||
65.64 | even | 2 | 1950.2.b.k.1351.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
390.2.b.c.181.4 | yes | 4 | 13.12 | even | 2 | inner | |
1170.2.b.d.181.2 | 4 | 39.38 | odd | 2 | |||
1170.2.b.d.181.3 | 4 | 3.2 | odd | 2 | |||
1950.2.b.k.1351.1 | 4 | 65.64 | even | 2 | |||
1950.2.b.k.1351.4 | 4 | 5.4 | even | 2 | |||
1950.2.f.m.649.1 | 4 | 5.3 | odd | 4 | |||
1950.2.f.m.649.3 | 4 | 65.12 | odd | 4 | |||
1950.2.f.n.649.2 | 4 | 65.38 | odd | 4 | |||
1950.2.f.n.649.4 | 4 | 5.2 | odd | 4 | |||
3120.2.g.q.961.2 | 4 | 4.3 | odd | 2 | |||
3120.2.g.q.961.3 | 4 | 52.51 | odd | 2 | |||
5070.2.a.z.1.2 | 2 | 13.5 | odd | 4 | |||
5070.2.a.bf.1.1 | 2 | 13.8 | odd | 4 |