Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.a (trivial) |
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: | yes |
Analytic conductor: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.44949 | 0.547856 | 0.273928 | − | 0.961750i | \(-0.411677\pi\) | ||||
0.273928 | + | 0.961750i | \(0.411677\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.89898 | −0.804032 | −0.402016 | − | 0.915633i | \(-0.631690\pi\) | ||||
−0.402016 | + | 0.915633i | \(0.631690\pi\) | |||||||
\(14\) | 1.44949 | 0.387392 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.44949 | −1.32170 | −0.660848 | − | 0.750520i | \(-0.729803\pi\) | ||||
−0.660848 | + | 0.750520i | \(0.729803\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.89898 | 1.58273 | 0.791367 | − | 0.611341i | \(-0.209370\pi\) | ||||
0.791367 | + | 0.611341i | \(0.209370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44949 | 0.316305 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.89898 | −0.568537 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.44949 | 0.273928 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | −5.44949 | −0.934580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.34847 | 1.37248 | 0.686240 | − | 0.727375i | \(-0.259260\pi\) | ||||
0.686240 | + | 0.727375i | \(0.259260\pi\) | |||||||
\(38\) | 6.89898 | 1.11916 | ||||||||
\(39\) | −2.89898 | −0.464208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 1.44949 | 0.223661 | ||||||||
\(43\) | 10.8990 | 1.66208 | 0.831039 | − | 0.556214i | \(-0.187746\pi\) | ||||
0.831039 | + | 0.556214i | \(0.187746\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.89898 | −0.568725 | −0.284362 | − | 0.958717i | \(-0.591782\pi\) | ||||
−0.284362 | + | 0.958717i | \(0.591782\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.44949 | −0.763081 | ||||||||
\(52\) | −2.89898 | −0.402016 | ||||||||
\(53\) | 0.898979 | 0.123484 | 0.0617422 | − | 0.998092i | \(-0.480334\pi\) | ||||
0.0617422 | + | 0.998092i | \(0.480334\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.44949 | 0.193696 | ||||||||
\(57\) | 6.89898 | 0.913792 | ||||||||
\(58\) | 5.00000 | 0.656532 | ||||||||
\(59\) | 10.0000 | 1.30189 | 0.650945 | − | 0.759125i | \(-0.274373\pi\) | ||||
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.89898 | −0.627250 | −0.313625 | − | 0.949547i | \(-0.601543\pi\) | ||||
−0.313625 | + | 0.949547i | \(0.601543\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 1.44949 | 0.182619 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | −5.44949 | −0.660848 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7980 | 1.28148 | 0.640741 | − | 0.767757i | \(-0.278627\pi\) | ||||
0.640741 | + | 0.767757i | \(0.278627\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.10102 | 0.245906 | 0.122953 | − | 0.992413i | \(-0.460764\pi\) | ||||
0.122953 | + | 0.992413i | \(0.460764\pi\) | |||||||
\(74\) | 8.34847 | 0.970490 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.89898 | 0.791367 | ||||||||
\(77\) | 2.89898 | 0.330369 | ||||||||
\(78\) | −2.89898 | −0.328245 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.89898 | −0.541002 | ||||||||
\(83\) | −2.55051 | −0.279955 | −0.139977 | − | 0.990155i | \(-0.544703\pi\) | ||||
−0.139977 | + | 0.990155i | \(0.544703\pi\) | |||||||
\(84\) | 1.44949 | 0.158152 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.8990 | 1.17527 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | −10.3485 | −1.09694 | −0.548468 | − | 0.836172i | \(-0.684789\pi\) | ||||
−0.548468 | + | 0.836172i | \(0.684789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.20204 | −0.440494 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | −3.89898 | −0.402149 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −12.6969 | −1.28918 | −0.644589 | − | 0.764529i | \(-0.722972\pi\) | ||||
−0.644589 | + | 0.764529i | \(0.722972\pi\) | |||||||
\(98\) | −4.89898 | −0.494872 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6969 | −1.36290 | −0.681448 | − | 0.731866i | \(-0.738650\pi\) | ||||
−0.681448 | + | 0.731866i | \(0.738650\pi\) | |||||||
\(102\) | −5.44949 | −0.539580 | ||||||||
\(103\) | −13.2474 | −1.30531 | −0.652655 | − | 0.757655i | \(-0.726345\pi\) | ||||
−0.652655 | + | 0.757655i | \(0.726345\pi\) | |||||||
\(104\) | −2.89898 | −0.284268 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.898979 | 0.0873166 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 3.44949 | 0.330401 | 0.165201 | − | 0.986260i | \(-0.447173\pi\) | ||||
0.165201 | + | 0.986260i | \(0.447173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.34847 | 0.792402 | ||||||||
\(112\) | 1.44949 | 0.136964 | ||||||||
\(113\) | 14.3485 | 1.34979 | 0.674895 | − | 0.737914i | \(-0.264189\pi\) | ||||
0.674895 | + | 0.737914i | \(0.264189\pi\) | |||||||
\(114\) | 6.89898 | 0.646149 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | −2.89898 | −0.268011 | ||||||||
\(118\) | 10.0000 | 0.920575 | ||||||||
\(119\) | −7.89898 | −0.724098 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −4.89898 | −0.443533 | ||||||||
\(123\) | −4.89898 | −0.441726 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.44949 | 0.129131 | ||||||||
\(127\) | 1.79796 | 0.159543 | 0.0797715 | − | 0.996813i | \(-0.474581\pi\) | ||||
0.0797715 | + | 0.996813i | \(0.474581\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.8990 | 0.959602 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.89898 | 0.777507 | 0.388754 | − | 0.921342i | \(-0.372906\pi\) | ||||
0.388754 | + | 0.921342i | \(0.372906\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 10.0000 | 0.867110 | ||||||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.44949 | −0.467290 | ||||||||
\(137\) | −22.3485 | −1.90936 | −0.954679 | − | 0.297636i | \(-0.903802\pi\) | ||||
−0.954679 | + | 0.297636i | \(0.903802\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 15.6969 | 1.33140 | 0.665698 | − | 0.746221i | \(-0.268134\pi\) | ||||
0.665698 | + | 0.746221i | \(0.268134\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.89898 | −0.328353 | ||||||||
\(142\) | 10.7980 | 0.906145 | ||||||||
\(143\) | −5.79796 | −0.484850 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.10102 | 0.173882 | ||||||||
\(147\) | −4.89898 | −0.404061 | ||||||||
\(148\) | 8.34847 | 0.686240 | ||||||||
\(149\) | 20.0000 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6969 | −1.52154 | −0.760768 | − | 0.649024i | \(-0.775177\pi\) | ||||
−0.760768 | + | 0.649024i | \(0.775177\pi\) | |||||||
\(152\) | 6.89898 | 0.559581 | ||||||||
\(153\) | −5.44949 | −0.440565 | ||||||||
\(154\) | 2.89898 | 0.233606 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.89898 | −0.232104 | ||||||||
\(157\) | −8.89898 | −0.710216 | −0.355108 | − | 0.934825i | \(-0.615556\pi\) | ||||
−0.355108 | + | 0.934825i | \(0.615556\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | 0.898979 | 0.0712937 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44949 | 0.114236 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 17.7980 | 1.39404 | 0.697022 | − | 0.717050i | \(-0.254508\pi\) | ||||
0.697022 | + | 0.717050i | \(0.254508\pi\) | |||||||
\(164\) | −4.89898 | −0.382546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.55051 | −0.197958 | ||||||||
\(167\) | −7.00000 | −0.541676 | −0.270838 | − | 0.962625i | \(-0.587301\pi\) | ||||
−0.270838 | + | 0.962625i | \(0.587301\pi\) | |||||||
\(168\) | 1.44949 | 0.111831 | ||||||||
\(169\) | −4.59592 | −0.353532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.89898 | 0.527578 | ||||||||
\(172\) | 10.8990 | 0.831039 | ||||||||
\(173\) | −19.7980 | −1.50521 | −0.752605 | − | 0.658472i | \(-0.771203\pi\) | ||||
−0.752605 | + | 0.658472i | \(0.771203\pi\) | |||||||
\(174\) | 5.00000 | 0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 10.0000 | 0.751646 | ||||||||
\(178\) | −10.3485 | −0.775651 | ||||||||
\(179\) | 3.10102 | 0.231781 | 0.115891 | − | 0.993262i | \(-0.463028\pi\) | ||||
0.115891 | + | 0.993262i | \(0.463028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.3485 | −1.36383 | −0.681915 | − | 0.731431i | \(-0.738853\pi\) | ||||
−0.681915 | + | 0.731431i | \(0.738853\pi\) | |||||||
\(182\) | −4.20204 | −0.311476 | ||||||||
\(183\) | −4.89898 | −0.362143 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | −10.8990 | −0.797012 | ||||||||
\(188\) | −3.89898 | −0.284362 | ||||||||
\(189\) | 1.44949 | 0.105435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | 0.144715 | 0.0723575 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723575 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 9.69694 | 0.698001 | 0.349000 | − | 0.937123i | \(-0.386521\pi\) | ||||
0.349000 | + | 0.937123i | \(0.386521\pi\) | |||||||
\(194\) | −12.6969 | −0.911587 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.89898 | −0.349927 | ||||||||
\(197\) | −3.89898 | −0.277791 | −0.138895 | − | 0.990307i | \(-0.544355\pi\) | ||||
−0.138895 | + | 0.990307i | \(0.544355\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | 24.1464 | 1.71169 | 0.855847 | − | 0.517228i | \(-0.173036\pi\) | ||||
0.855847 | + | 0.517228i | \(0.173036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | −13.6969 | −0.963713 | ||||||||
\(203\) | 7.24745 | 0.508671 | ||||||||
\(204\) | −5.44949 | −0.381541 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.2474 | −0.922993 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −2.89898 | −0.201008 | ||||||||
\(209\) | 13.7980 | 0.954425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7980 | 0.743362 | 0.371681 | − | 0.928360i | \(-0.378781\pi\) | ||||
0.371681 | + | 0.928360i | \(0.378781\pi\) | |||||||
\(212\) | 0.898979 | 0.0617422 | ||||||||
\(213\) | 10.7980 | 0.739864 | ||||||||
\(214\) | −2.00000 | −0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.89898 | 0.196796 | ||||||||
\(218\) | 3.44949 | 0.233629 | ||||||||
\(219\) | 2.10102 | 0.141974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.7980 | 1.06269 | ||||||||
\(222\) | 8.34847 | 0.560313 | ||||||||
\(223\) | 24.6969 | 1.65383 | 0.826915 | − | 0.562327i | \(-0.190094\pi\) | ||||
0.826915 | + | 0.562327i | \(0.190094\pi\) | |||||||
\(224\) | 1.44949 | 0.0968481 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.3485 | 0.954446 | ||||||||
\(227\) | −4.75255 | −0.315438 | −0.157719 | − | 0.987484i | \(-0.550414\pi\) | ||||
−0.157719 | + | 0.987484i | \(0.550414\pi\) | |||||||
\(228\) | 6.89898 | 0.456896 | ||||||||
\(229\) | 3.10102 | 0.204921 | 0.102461 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102461 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.89898 | 0.190739 | ||||||||
\(232\) | 5.00000 | 0.328266 | ||||||||
\(233\) | −26.6969 | −1.74897 | −0.874487 | − | 0.485048i | \(-0.838802\pi\) | ||||
−0.874487 | + | 0.485048i | \(0.838802\pi\) | |||||||
\(234\) | −2.89898 | −0.189512 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.0000 | 0.650945 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | −7.89898 | −0.512015 | ||||||||
\(239\) | −8.10102 | −0.524011 | −0.262006 | − | 0.965066i | \(-0.584384\pi\) | ||||
−0.262006 | + | 0.965066i | \(0.584384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.89898 | −0.313625 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.89898 | −0.312348 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | −2.55051 | −0.161632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.24745 | −0.331216 | −0.165608 | − | 0.986192i | \(-0.552959\pi\) | ||||
−0.165608 | + | 0.986192i | \(0.552959\pi\) | |||||||
\(252\) | 1.44949 | 0.0913093 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 1.79796 | 0.112814 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.20204 | −0.511629 | −0.255815 | − | 0.966726i | \(-0.582344\pi\) | ||||
−0.255815 | + | 0.966726i | \(0.582344\pi\) | |||||||
\(258\) | 10.8990 | 0.678541 | ||||||||
\(259\) | 12.1010 | 0.751921 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 8.89898 | 0.549781 | ||||||||
\(263\) | −19.7980 | −1.22079 | −0.610397 | − | 0.792095i | \(-0.708990\pi\) | ||||
−0.610397 | + | 0.792095i | \(0.708990\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.0000 | 0.613139 | ||||||||
\(267\) | −10.3485 | −0.633316 | ||||||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | 3.79796 | 0.231566 | 0.115783 | − | 0.993275i | \(-0.463062\pi\) | ||||
0.115783 | + | 0.993275i | \(0.463062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −5.44949 | −0.330424 | ||||||||
\(273\) | −4.20204 | −0.254319 | ||||||||
\(274\) | −22.3485 | −1.35012 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 25.5959 | 1.53791 | 0.768955 | − | 0.639303i | \(-0.220777\pi\) | ||||
0.768955 | + | 0.639303i | \(0.220777\pi\) | |||||||
\(278\) | 15.6969 | 0.941440 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.752551 | −0.0448934 | −0.0224467 | − | 0.999748i | \(-0.507146\pi\) | ||||
−0.0224467 | + | 0.999748i | \(0.507146\pi\) | |||||||
\(282\) | −3.89898 | −0.232181 | ||||||||
\(283\) | 11.5959 | 0.689306 | 0.344653 | − | 0.938730i | \(-0.387997\pi\) | ||||
0.344653 | + | 0.938730i | \(0.387997\pi\) | |||||||
\(284\) | 10.7980 | 0.640741 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.79796 | −0.342841 | ||||||||
\(287\) | −7.10102 | −0.419160 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 12.6969 | 0.746879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.6969 | −0.744308 | ||||||||
\(292\) | 2.10102 | 0.122953 | ||||||||
\(293\) | 7.79796 | 0.455562 | 0.227781 | − | 0.973712i | \(-0.426853\pi\) | ||||
0.227781 | + | 0.973712i | \(0.426853\pi\) | |||||||
\(294\) | −4.89898 | −0.285714 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.34847 | 0.485245 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 20.0000 | 1.15857 | ||||||||
\(299\) | −2.89898 | −0.167652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7980 | 0.910579 | ||||||||
\(302\) | −18.6969 | −1.07589 | ||||||||
\(303\) | −13.6969 | −0.786869 | ||||||||
\(304\) | 6.89898 | 0.395684 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.44949 | −0.311527 | ||||||||
\(307\) | −20.1010 | −1.14723 | −0.573613 | − | 0.819126i | \(-0.694459\pi\) | ||||
−0.573613 | + | 0.819126i | \(0.694459\pi\) | |||||||
\(308\) | 2.89898 | 0.165185 | ||||||||
\(309\) | −13.2474 | −0.753621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5959 | 0.827659 | 0.413829 | − | 0.910355i | \(-0.364191\pi\) | ||||
0.413829 | + | 0.910355i | \(0.364191\pi\) | |||||||
\(312\) | −2.89898 | −0.164122 | ||||||||
\(313\) | −12.8990 | −0.729093 | −0.364547 | − | 0.931185i | \(-0.618776\pi\) | ||||
−0.364547 | + | 0.931185i | \(0.618776\pi\) | |||||||
\(314\) | −8.89898 | −0.502198 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 10.5959 | 0.595126 | 0.297563 | − | 0.954702i | \(-0.403826\pi\) | ||||
0.297563 | + | 0.954702i | \(0.403826\pi\) | |||||||
\(318\) | 0.898979 | 0.0504123 | ||||||||
\(319\) | 10.0000 | 0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 1.44949 | 0.0807769 | ||||||||
\(323\) | −37.5959 | −2.09189 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.7980 | 0.985738 | ||||||||
\(327\) | 3.44949 | 0.190757 | ||||||||
\(328\) | −4.89898 | −0.270501 | ||||||||
\(329\) | −5.65153 | −0.311579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.79796 | −0.373650 | −0.186825 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186825 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(332\) | −2.55051 | −0.139977 | ||||||||
\(333\) | 8.34847 | 0.457493 | ||||||||
\(334\) | −7.00000 | −0.383023 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.44949 | 0.0790761 | ||||||||
\(337\) | −16.4949 | −0.898534 | −0.449267 | − | 0.893397i | \(-0.648315\pi\) | ||||
−0.449267 | + | 0.893397i | \(0.648315\pi\) | |||||||
\(338\) | −4.59592 | −0.249985 | ||||||||
\(339\) | 14.3485 | 0.779302 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | 6.89898 | 0.373054 | ||||||||
\(343\) | −17.2474 | −0.931275 | ||||||||
\(344\) | 10.8990 | 0.587634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7980 | −1.06434 | ||||||||
\(347\) | −32.6969 | −1.75526 | −0.877632 | − | 0.479335i | \(-0.840878\pi\) | ||||
−0.877632 | + | 0.479335i | \(0.840878\pi\) | |||||||
\(348\) | 5.00000 | 0.268028 | ||||||||
\(349\) | 13.1010 | 0.701282 | 0.350641 | − | 0.936510i | \(-0.385964\pi\) | ||||
0.350641 | + | 0.936510i | \(0.385964\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.89898 | −0.154736 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 10.0000 | 0.531494 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.3485 | −0.548468 | ||||||||
\(357\) | −7.89898 | −0.418058 | ||||||||
\(358\) | 3.10102 | 0.163894 | ||||||||
\(359\) | −6.20204 | −0.327331 | −0.163666 | − | 0.986516i | \(-0.552332\pi\) | ||||
−0.163666 | + | 0.986516i | \(0.552332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | −18.3485 | −0.964374 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | −4.20204 | −0.220247 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.89898 | −0.256074 | ||||||||
\(367\) | −8.20204 | −0.428143 | −0.214072 | − | 0.976818i | \(-0.568673\pi\) | ||||
−0.214072 | + | 0.976818i | \(0.568673\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −4.89898 | −0.255031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30306 | 0.0676516 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | −3.24745 | −0.168147 | −0.0840733 | − | 0.996460i | \(-0.526793\pi\) | ||||
−0.0840733 | + | 0.996460i | \(0.526793\pi\) | |||||||
\(374\) | −10.8990 | −0.563573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.89898 | −0.201075 | ||||||||
\(377\) | −14.4949 | −0.746525 | ||||||||
\(378\) | 1.44949 | 0.0745537 | ||||||||
\(379\) | −38.2929 | −1.96697 | −0.983486 | − | 0.180984i | \(-0.942072\pi\) | ||||
−0.983486 | + | 0.180984i | \(0.942072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79796 | 0.0921122 | ||||||||
\(382\) | 2.00000 | 0.102329 | ||||||||
\(383\) | −9.79796 | −0.500652 | −0.250326 | − | 0.968162i | \(-0.580538\pi\) | ||||
−0.250326 | + | 0.968162i | \(0.580538\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.69694 | 0.493561 | ||||||||
\(387\) | 10.8990 | 0.554026 | ||||||||
\(388\) | −12.6969 | −0.644589 | ||||||||
\(389\) | −23.7980 | −1.20660 | −0.603302 | − | 0.797513i | \(-0.706149\pi\) | ||||
−0.603302 | + | 0.797513i | \(0.706149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.44949 | −0.275593 | ||||||||
\(392\) | −4.89898 | −0.247436 | ||||||||
\(393\) | 8.89898 | 0.448894 | ||||||||
\(394\) | −3.89898 | −0.196428 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 28.0000 | 1.40528 | 0.702640 | − | 0.711546i | \(-0.252005\pi\) | ||||
0.702640 | + | 0.711546i | \(0.252005\pi\) | |||||||
\(398\) | 24.1464 | 1.21035 | ||||||||
\(399\) | 10.0000 | 0.500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6969 | −0.933681 | −0.466840 | − | 0.884342i | \(-0.654608\pi\) | ||||
−0.466840 | + | 0.884342i | \(0.654608\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | −5.79796 | −0.288817 | ||||||||
\(404\) | −13.6969 | −0.681448 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.24745 | 0.359685 | ||||||||
\(407\) | 16.6969 | 0.827637 | ||||||||
\(408\) | −5.44949 | −0.269790 | ||||||||
\(409\) | 25.6969 | 1.27063 | 0.635316 | − | 0.772252i | \(-0.280870\pi\) | ||||
0.635316 | + | 0.772252i | \(0.280870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.3485 | −1.10237 | ||||||||
\(412\) | −13.2474 | −0.652655 | ||||||||
\(413\) | 14.4949 | 0.713247 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.89898 | −0.142134 | ||||||||
\(417\) | 15.6969 | 0.768682 | ||||||||
\(418\) | 13.7980 | 0.674880 | ||||||||
\(419\) | 14.1464 | 0.691098 | 0.345549 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345549 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4949 | −0.608964 | −0.304482 | − | 0.952518i | \(-0.598483\pi\) | ||||
−0.304482 | + | 0.952518i | \(0.598483\pi\) | |||||||
\(422\) | 10.7980 | 0.525636 | ||||||||
\(423\) | −3.89898 | −0.189575 | ||||||||
\(424\) | 0.898979 | 0.0436583 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7980 | 0.523163 | ||||||||
\(427\) | −7.10102 | −0.343642 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | −5.79796 | −0.279928 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3031 | 0.544449 | 0.272225 | − | 0.962234i | \(-0.412241\pi\) | ||||
0.272225 | + | 0.962234i | \(0.412241\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −16.6969 | −0.802404 | −0.401202 | − | 0.915990i | \(-0.631407\pi\) | ||||
−0.401202 | + | 0.915990i | \(0.631407\pi\) | |||||||
\(434\) | 2.89898 | 0.139155 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.44949 | 0.165201 | ||||||||
\(437\) | 6.89898 | 0.330023 | ||||||||
\(438\) | 2.10102 | 0.100391 | ||||||||
\(439\) | −10.6969 | −0.510537 | −0.255269 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255269 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.89898 | −0.233285 | ||||||||
\(442\) | 15.7980 | 0.751432 | ||||||||
\(443\) | −5.30306 | −0.251956 | −0.125978 | − | 0.992033i | \(-0.540207\pi\) | ||||
−0.125978 | + | 0.992033i | \(0.540207\pi\) | |||||||
\(444\) | 8.34847 | 0.396201 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.6969 | 1.16943 | ||||||||
\(447\) | 20.0000 | 0.945968 | ||||||||
\(448\) | 1.44949 | 0.0684820 | ||||||||
\(449\) | 3.79796 | 0.179237 | 0.0896184 | − | 0.995976i | \(-0.471435\pi\) | ||||
0.0896184 | + | 0.995976i | \(0.471435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.79796 | −0.461368 | ||||||||
\(452\) | 14.3485 | 0.674895 | ||||||||
\(453\) | −18.6969 | −0.878459 | ||||||||
\(454\) | −4.75255 | −0.223048 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.89898 | 0.323074 | ||||||||
\(457\) | 0.404082 | 0.0189022 | 0.00945108 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00945108 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(458\) | 3.10102 | 0.144901 | ||||||||
\(459\) | −5.44949 | −0.254360 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4949 | 1.00112 | 0.500559 | − | 0.865703i | \(-0.333128\pi\) | ||||
0.500559 | + | 0.865703i | \(0.333128\pi\) | |||||||
\(462\) | 2.89898 | 0.134873 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 5.00000 | 0.232119 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.6969 | −1.23671 | ||||||||
\(467\) | −29.9444 | −1.38566 | −0.692830 | − | 0.721100i | \(-0.743637\pi\) | ||||
−0.692830 | + | 0.721100i | \(0.743637\pi\) | |||||||
\(468\) | −2.89898 | −0.134005 | ||||||||
\(469\) | −2.89898 | −0.133862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.89898 | −0.410043 | ||||||||
\(472\) | 10.0000 | 0.460287 | ||||||||
\(473\) | 21.7980 | 1.00227 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.89898 | −0.362049 | ||||||||
\(477\) | 0.898979 | 0.0411614 | ||||||||
\(478\) | −8.10102 | −0.370532 | ||||||||
\(479\) | −30.0000 | −1.37073 | −0.685367 | − | 0.728197i | \(-0.740358\pi\) | ||||
−0.685367 | + | 0.728197i | \(0.740358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.2020 | −1.10352 | ||||||||
\(482\) | −8.00000 | −0.364390 | ||||||||
\(483\) | 1.44949 | 0.0659541 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.1010 | −0.684293 | −0.342146 | − | 0.939647i | \(-0.611154\pi\) | ||||
−0.342146 | + | 0.939647i | \(0.611154\pi\) | |||||||
\(488\) | −4.89898 | −0.221766 | ||||||||
\(489\) | 17.7980 | 0.804852 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1010 | 1.13279 | 0.566397 | − | 0.824133i | \(-0.308337\pi\) | ||||
0.566397 | + | 0.824133i | \(0.308337\pi\) | |||||||
\(492\) | −4.89898 | −0.220863 | ||||||||
\(493\) | −27.2474 | −1.22716 | ||||||||
\(494\) | −20.0000 | −0.899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 15.6515 | 0.702067 | ||||||||
\(498\) | −2.55051 | −0.114291 | ||||||||
\(499\) | 21.8990 | 0.980333 | 0.490166 | − | 0.871629i | \(-0.336936\pi\) | ||||
0.490166 | + | 0.871629i | \(0.336936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00000 | −0.312737 | ||||||||
\(502\) | −5.24745 | −0.234205 | ||||||||
\(503\) | 14.6969 | 0.655304 | 0.327652 | − | 0.944798i | \(-0.393743\pi\) | ||||
0.327652 | + | 0.944798i | \(0.393743\pi\) | |||||||
\(504\) | 1.44949 | 0.0645654 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | −4.59592 | −0.204112 | ||||||||
\(508\) | 1.79796 | 0.0797715 | ||||||||
\(509\) | −15.0000 | −0.664863 | −0.332432 | − | 0.943127i | \(-0.607869\pi\) | ||||
−0.332432 | + | 0.943127i | \(0.607869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.04541 | 0.134721 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.89898 | 0.304597 | ||||||||
\(514\) | −8.20204 | −0.361777 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.8990 | 0.479801 | ||||||||
\(517\) | −7.79796 | −0.342954 | ||||||||
\(518\) | 12.1010 | 0.531688 | ||||||||
\(519\) | −19.7980 | −0.869034 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.1464 | 1.14550 | 0.572748 | − | 0.819732i | \(-0.305877\pi\) | ||||
0.572748 | + | 0.819732i | \(0.305877\pi\) | |||||||
\(522\) | 5.00000 | 0.218844 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | 8.89898 | 0.388754 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.7980 | −0.863232 | ||||||||
\(527\) | −10.8990 | −0.474767 | ||||||||
\(528\) | 2.00000 | 0.0870388 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 10.0000 | 0.433555 | ||||||||
\(533\) | 14.2020 | 0.615159 | ||||||||
\(534\) | −10.3485 | −0.447822 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | −0.0863868 | ||||||||
\(537\) | 3.10102 | 0.133819 | ||||||||
\(538\) | 3.79796 | 0.163742 | ||||||||
\(539\) | −9.79796 | −0.422028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5959 | −0.670521 | −0.335260 | − | 0.942125i | \(-0.608824\pi\) | ||||
−0.335260 | + | 0.942125i | \(0.608824\pi\) | |||||||
\(542\) | −8.00000 | −0.343629 | ||||||||
\(543\) | −18.3485 | −0.787408 | ||||||||
\(544\) | −5.44949 | −0.233645 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.20204 | −0.179831 | ||||||||
\(547\) | −10.7980 | −0.461687 | −0.230844 | − | 0.972991i | \(-0.574149\pi\) | ||||
−0.230844 | + | 0.972991i | \(0.574149\pi\) | |||||||
\(548\) | −22.3485 | −0.954679 | ||||||||
\(549\) | −4.89898 | −0.209083 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4949 | 1.46953 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 14.4949 | 0.616386 | ||||||||
\(554\) | 25.5959 | 1.08747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6969 | 0.665698 | ||||||||
\(557\) | 28.6969 | 1.21593 | 0.607964 | − | 0.793964i | \(-0.291986\pi\) | ||||
0.607964 | + | 0.793964i | \(0.291986\pi\) | |||||||
\(558\) | 2.00000 | 0.0846668 | ||||||||
\(559\) | −31.5959 | −1.33636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.8990 | −0.460155 | ||||||||
\(562\) | −0.752551 | −0.0317445 | ||||||||
\(563\) | −6.00000 | −0.252870 | −0.126435 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126435 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(564\) | −3.89898 | −0.164177 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.5959 | 0.487413 | ||||||||
\(567\) | 1.44949 | 0.0608728 | ||||||||
\(568\) | 10.7980 | 0.453072 | ||||||||
\(569\) | −44.4949 | −1.86532 | −0.932662 | − | 0.360753i | \(-0.882520\pi\) | ||||
−0.932662 | + | 0.360753i | \(0.882520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6969 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(572\) | −5.79796 | −0.242425 | ||||||||
\(573\) | 2.00000 | 0.0835512 | ||||||||
\(574\) | −7.10102 | −0.296391 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 12.6969 | 0.528123 | ||||||||
\(579\) | 9.69694 | 0.402991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69694 | −0.153375 | ||||||||
\(582\) | −12.6969 | −0.526305 | ||||||||
\(583\) | 1.79796 | 0.0744639 | ||||||||
\(584\) | 2.10102 | 0.0869408 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.79796 | 0.322131 | ||||||||
\(587\) | 4.89898 | 0.202203 | 0.101101 | − | 0.994876i | \(-0.467763\pi\) | ||||
0.101101 | + | 0.994876i | \(0.467763\pi\) | |||||||
\(588\) | −4.89898 | −0.202031 | ||||||||
\(589\) | 13.7980 | 0.568535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.89898 | −0.160383 | ||||||||
\(592\) | 8.34847 | 0.343120 | ||||||||
\(593\) | −43.5959 | −1.79027 | −0.895135 | − | 0.445795i | \(-0.852921\pi\) | ||||
−0.895135 | + | 0.445795i | \(0.852921\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 24.1464 | 0.988248 | ||||||||
\(598\) | −2.89898 | −0.118548 | ||||||||
\(599\) | −21.3939 | −0.874130 | −0.437065 | − | 0.899430i | \(-0.643982\pi\) | ||||
−0.437065 | + | 0.899430i | \(0.643982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0000 | 1.50926 | 0.754631 | − | 0.656150i | \(-0.227816\pi\) | ||||
0.754631 | + | 0.656150i | \(0.227816\pi\) | |||||||
\(602\) | 15.7980 | 0.643877 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | −18.6969 | −0.760768 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.6969 | −0.556400 | ||||||||
\(607\) | 18.0000 | 0.730597 | 0.365299 | − | 0.930890i | \(-0.380967\pi\) | ||||
0.365299 | + | 0.930890i | \(0.380967\pi\) | |||||||
\(608\) | 6.89898 | 0.279791 | ||||||||
\(609\) | 7.24745 | 0.293681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3031 | 0.457273 | ||||||||
\(612\) | −5.44949 | −0.220283 | ||||||||
\(613\) | −0.146428 | −0.00591418 | −0.00295709 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295709 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(614\) | −20.1010 | −0.811211 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.89898 | 0.116803 | ||||||||
\(617\) | 12.4949 | 0.503026 | 0.251513 | − | 0.967854i | \(-0.419072\pi\) | ||||
0.251513 | + | 0.967854i | \(0.419072\pi\) | |||||||
\(618\) | −13.2474 | −0.532891 | ||||||||
\(619\) | −44.4949 | −1.78840 | −0.894200 | − | 0.447667i | \(-0.852255\pi\) | ||||
−0.894200 | + | 0.447667i | \(0.852255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 14.5959 | 0.585243 | ||||||||
\(623\) | −15.0000 | −0.600962 | ||||||||
\(624\) | −2.89898 | −0.116052 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.8990 | −0.515547 | ||||||||
\(627\) | 13.7980 | 0.551037 | ||||||||
\(628\) | −8.89898 | −0.355108 | ||||||||
\(629\) | −45.4949 | −1.81400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4495 | 0.615034 | 0.307517 | − | 0.951543i | \(-0.400502\pi\) | ||||
0.307517 | + | 0.951543i | \(0.400502\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | 10.7980 | 0.429180 | ||||||||
\(634\) | 10.5959 | 0.420818 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.898979 | 0.0356469 | ||||||||
\(637\) | 14.2020 | 0.562705 | ||||||||
\(638\) | 10.0000 | 0.395904 | ||||||||
\(639\) | 10.7980 | 0.427161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.5505 | −0.969687 | −0.484843 | − | 0.874601i | \(-0.661123\pi\) | ||||
−0.484843 | + | 0.874601i | \(0.661123\pi\) | |||||||
\(642\) | −2.00000 | −0.0789337 | ||||||||
\(643\) | −19.7980 | −0.780755 | −0.390378 | − | 0.920655i | \(-0.627656\pi\) | ||||
−0.390378 | + | 0.920655i | \(0.627656\pi\) | |||||||
\(644\) | 1.44949 | 0.0571179 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37.5959 | −1.47919 | ||||||||
\(647\) | 20.5959 | 0.809709 | 0.404855 | − | 0.914381i | \(-0.367322\pi\) | ||||
0.404855 | + | 0.914381i | \(0.367322\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 20.0000 | 0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.89898 | 0.113620 | ||||||||
\(652\) | 17.7980 | 0.697022 | ||||||||
\(653\) | −0.303062 | −0.0118597 | −0.00592986 | − | 0.999982i | \(-0.501888\pi\) | ||||
−0.00592986 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(654\) | 3.44949 | 0.134886 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.89898 | −0.191273 | ||||||||
\(657\) | 2.10102 | 0.0819686 | ||||||||
\(658\) | −5.65153 | −0.220320 | ||||||||
\(659\) | −23.4495 | −0.913462 | −0.456731 | − | 0.889605i | \(-0.650980\pi\) | ||||
−0.456731 | + | 0.889605i | \(0.650980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.4495 | −0.834288 | −0.417144 | − | 0.908840i | \(-0.636969\pi\) | ||||
−0.417144 | + | 0.908840i | \(0.636969\pi\) | |||||||
\(662\) | −6.79796 | −0.264210 | ||||||||
\(663\) | 15.7980 | 0.613542 | ||||||||
\(664\) | −2.55051 | −0.0989790 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.34847 | 0.323497 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | −7.00000 | −0.270838 | ||||||||
\(669\) | 24.6969 | 0.954839 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.79796 | −0.378246 | ||||||||
\(672\) | 1.44949 | 0.0559153 | ||||||||
\(673\) | 26.5959 | 1.02520 | 0.512599 | − | 0.858628i | \(-0.328683\pi\) | ||||
0.512599 | + | 0.858628i | \(0.328683\pi\) | |||||||
\(674\) | −16.4949 | −0.635360 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.59592 | −0.176766 | ||||||||
\(677\) | −33.3939 | −1.28343 | −0.641715 | − | 0.766943i | \(-0.721777\pi\) | ||||
−0.641715 | + | 0.766943i | \(0.721777\pi\) | |||||||
\(678\) | 14.3485 | 0.551050 | ||||||||
\(679\) | −18.4041 | −0.706284 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.75255 | −0.182118 | ||||||||
\(682\) | 4.00000 | 0.153168 | ||||||||
\(683\) | 7.10102 | 0.271713 | 0.135856 | − | 0.990729i | \(-0.456621\pi\) | ||||
0.135856 | + | 0.990729i | \(0.456621\pi\) | |||||||
\(684\) | 6.89898 | 0.263789 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.2474 | −0.658511 | ||||||||
\(687\) | 3.10102 | 0.118311 | ||||||||
\(688\) | 10.8990 | 0.415520 | ||||||||
\(689\) | −2.60612 | −0.0992854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.20204 | −0.350062 | −0.175031 | − | 0.984563i | \(-0.556003\pi\) | ||||
−0.175031 | + | 0.984563i | \(0.556003\pi\) | |||||||
\(692\) | −19.7980 | −0.752605 | ||||||||
\(693\) | 2.89898 | 0.110123 | ||||||||
\(694\) | −32.6969 | −1.24116 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.00000 | 0.189525 | ||||||||
\(697\) | 26.6969 | 1.01122 | ||||||||
\(698\) | 13.1010 | 0.495881 | ||||||||
\(699\) | −26.6969 | −1.00977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −2.89898 | −0.109415 | ||||||||
\(703\) | 57.5959 | 2.17227 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | −19.8536 | −0.746670 | ||||||||
\(708\) | 10.0000 | 0.375823 | ||||||||
\(709\) | 27.9444 | 1.04947 | 0.524737 | − | 0.851265i | \(-0.324164\pi\) | ||||
0.524737 | + | 0.851265i | \(0.324164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | −10.3485 | −0.387825 | ||||||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | −7.89898 | −0.295612 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.10102 | 0.115891 | ||||||||
\(717\) | −8.10102 | −0.302538 | ||||||||
\(718\) | −6.20204 | −0.231458 | ||||||||
\(719\) | 28.7980 | 1.07398 | 0.536991 | − | 0.843588i | \(-0.319561\pi\) | ||||
0.536991 | + | 0.843588i | \(0.319561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.2020 | −0.715121 | ||||||||
\(722\) | 28.5959 | 1.06423 | ||||||||
\(723\) | −8.00000 | −0.297523 | ||||||||
\(724\) | −18.3485 | −0.681915 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.00000 | −0.259794 | ||||||||
\(727\) | 39.3939 | 1.46104 | 0.730519 | − | 0.682892i | \(-0.239278\pi\) | ||||
0.730519 | + | 0.682892i | \(0.239278\pi\) | |||||||
\(728\) | −4.20204 | −0.155738 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.3939 | −2.19676 | ||||||||
\(732\) | −4.89898 | −0.181071 | ||||||||
\(733\) | −40.1464 | −1.48284 | −0.741421 | − | 0.671040i | \(-0.765848\pi\) | ||||
−0.741421 | + | 0.671040i | \(0.765848\pi\) | |||||||
\(734\) | −8.20204 | −0.302743 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | −4.89898 | −0.180334 | ||||||||
\(739\) | 12.5959 | 0.463348 | 0.231674 | − | 0.972793i | \(-0.425580\pi\) | ||||
0.231674 | + | 0.972793i | \(0.425580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.0000 | −0.734718 | ||||||||
\(742\) | 1.30306 | 0.0478369 | ||||||||
\(743\) | −24.2929 | −0.891218 | −0.445609 | − | 0.895228i | \(-0.647013\pi\) | ||||
−0.445609 | + | 0.895228i | \(0.647013\pi\) | |||||||
\(744\) | 2.00000 | 0.0733236 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.24745 | −0.118898 | ||||||||
\(747\) | −2.55051 | −0.0933183 | ||||||||
\(748\) | −10.8990 | −0.398506 | ||||||||
\(749\) | −2.89898 | −0.105926 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.2474 | −0.921292 | −0.460646 | − | 0.887584i | \(-0.652382\pi\) | ||||
−0.460646 | + | 0.887584i | \(0.652382\pi\) | |||||||
\(752\) | −3.89898 | −0.142181 | ||||||||
\(753\) | −5.24745 | −0.191228 | ||||||||
\(754\) | −14.4949 | −0.527873 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.44949 | 0.0527174 | ||||||||
\(757\) | 10.7526 | 0.390808 | 0.195404 | − | 0.980723i | \(-0.437398\pi\) | ||||
0.195404 | + | 0.980723i | \(0.437398\pi\) | |||||||
\(758\) | −38.2929 | −1.39086 | ||||||||
\(759\) | 2.00000 | 0.0725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.0908 | −1.81579 | −0.907895 | − | 0.419197i | \(-0.862312\pi\) | ||||
−0.907895 | + | 0.419197i | \(0.862312\pi\) | |||||||
\(762\) | 1.79796 | 0.0651332 | ||||||||
\(763\) | 5.00000 | 0.181012 | ||||||||
\(764\) | 2.00000 | 0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.79796 | −0.354015 | ||||||||
\(767\) | −28.9898 | −1.04676 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 48.2929 | 1.74148 | 0.870742 | − | 0.491739i | \(-0.163639\pi\) | ||||
0.870742 | + | 0.491739i | \(0.163639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.20204 | −0.295389 | ||||||||
\(772\) | 9.69694 | 0.349000 | ||||||||
\(773\) | 10.8990 | 0.392009 | 0.196005 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196005 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(774\) | 10.8990 | 0.391756 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.6969 | −0.455794 | ||||||||
\(777\) | 12.1010 | 0.434122 | ||||||||
\(778\) | −23.7980 | −0.853198 | ||||||||
\(779\) | −33.7980 | −1.21094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.5959 | 0.772763 | ||||||||
\(782\) | −5.44949 | −0.194873 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | −4.89898 | −0.174964 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.89898 | 0.317416 | ||||||||
\(787\) | 28.0000 | 0.998092 | 0.499046 | − | 0.866575i | \(-0.333684\pi\) | ||||
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(788\) | −3.89898 | −0.138895 | ||||||||
\(789\) | −19.7980 | −0.704826 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7980 | 0.739490 | ||||||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 14.2020 | 0.504329 | ||||||||
\(794\) | 28.0000 | 0.993683 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.1464 | 0.855847 | ||||||||
\(797\) | 34.8990 | 1.23619 | 0.618093 | − | 0.786105i | \(-0.287906\pi\) | ||||
0.618093 | + | 0.786105i | \(0.287906\pi\) | |||||||
\(798\) | 10.0000 | 0.353996 | ||||||||
\(799\) | 21.2474 | 0.751681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.3485 | −0.365645 | ||||||||
\(802\) | −18.6969 | −0.660212 | ||||||||
\(803\) | 4.20204 | 0.148287 | ||||||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.79796 | −0.204224 | ||||||||
\(807\) | 3.79796 | 0.133694 | ||||||||
\(808\) | −13.6969 | −0.481857 | ||||||||
\(809\) | 11.3939 | 0.400587 | 0.200294 | − | 0.979736i | \(-0.435810\pi\) | ||||
0.200294 | + | 0.979736i | \(0.435810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.7980 | 1.60818 | 0.804092 | − | 0.594505i | \(-0.202652\pi\) | ||||
0.804092 | + | 0.594505i | \(0.202652\pi\) | |||||||
\(812\) | 7.24745 | 0.254336 | ||||||||
\(813\) | −8.00000 | −0.280572 | ||||||||
\(814\) | 16.6969 | 0.585227 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.44949 | −0.190770 | ||||||||
\(817\) | 75.1918 | 2.63063 | ||||||||
\(818\) | 25.6969 | 0.898472 | ||||||||
\(819\) | −4.20204 | −0.146831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.7980 | −1.80776 | −0.903881 | − | 0.427785i | \(-0.859294\pi\) | ||||
−0.903881 | + | 0.427785i | \(0.859294\pi\) | |||||||
\(822\) | −22.3485 | −0.779492 | ||||||||
\(823\) | 56.0908 | 1.95520 | 0.977601 | − | 0.210465i | \(-0.0674977\pi\) | ||||
0.977601 | + | 0.210465i | \(0.0674977\pi\) | |||||||
\(824\) | −13.2474 | −0.461497 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.4949 | 0.504342 | ||||||||
\(827\) | −14.7526 | −0.512996 | −0.256498 | − | 0.966545i | \(-0.582569\pi\) | ||||
−0.256498 | + | 0.966545i | \(0.582569\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −33.1010 | −1.14965 | −0.574823 | − | 0.818278i | \(-0.694929\pi\) | ||||
−0.574823 | + | 0.818278i | \(0.694929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5959 | 0.887913 | ||||||||
\(832\) | −2.89898 | −0.100504 | ||||||||
\(833\) | 26.6969 | 0.924994 | ||||||||
\(834\) | 15.6969 | 0.543541 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.7980 | 0.477212 | ||||||||
\(837\) | 2.00000 | 0.0691301 | ||||||||
\(838\) | 14.1464 | 0.488680 | ||||||||
\(839\) | −9.30306 | −0.321177 | −0.160589 | − | 0.987021i | \(-0.551339\pi\) | ||||
−0.160589 | + | 0.987021i | \(0.551339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −12.4949 | −0.430603 | ||||||||
\(843\) | −0.752551 | −0.0259192 | ||||||||
\(844\) | 10.7980 | 0.371681 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.89898 | −0.134050 | ||||||||
\(847\) | −10.1464 | −0.348635 | ||||||||
\(848\) | 0.898979 | 0.0308711 | ||||||||
\(849\) | 11.5959 | 0.397971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.34847 | 0.286182 | ||||||||
\(852\) | 10.7980 | 0.369932 | ||||||||
\(853\) | −44.9898 | −1.54042 | −0.770211 | − | 0.637790i | \(-0.779849\pi\) | ||||
−0.770211 | + | 0.637790i | \(0.779849\pi\) | |||||||
\(854\) | −7.10102 | −0.242992 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.00000 | −0.0683586 | ||||||||
\(857\) | 42.4949 | 1.45160 | 0.725799 | − | 0.687907i | \(-0.241470\pi\) | ||||
0.725799 | + | 0.687907i | \(0.241470\pi\) | |||||||
\(858\) | −5.79796 | −0.197939 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.10102 | −0.242002 | ||||||||
\(862\) | 11.3031 | 0.384984 | ||||||||
\(863\) | 20.3939 | 0.694216 | 0.347108 | − | 0.937825i | \(-0.387164\pi\) | ||||
0.347108 | + | 0.937825i | \(0.387164\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.6969 | −0.567385 | ||||||||
\(867\) | 12.6969 | 0.431211 | ||||||||
\(868\) | 2.89898 | 0.0983978 | ||||||||
\(869\) | 20.0000 | 0.678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79796 | 0.196456 | ||||||||
\(872\) | 3.44949 | 0.116814 | ||||||||
\(873\) | −12.6969 | −0.429726 | ||||||||
\(874\) | 6.89898 | 0.233361 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.10102 | 0.0709869 | ||||||||
\(877\) | −9.59592 | −0.324031 | −0.162016 | − | 0.986788i | \(-0.551799\pi\) | ||||
−0.162016 | + | 0.986788i | \(0.551799\pi\) | |||||||
\(878\) | −10.6969 | −0.361004 | ||||||||
\(879\) | 7.79796 | 0.263019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1010 | −1.04782 | −0.523910 | − | 0.851774i | \(-0.675527\pi\) | ||||
−0.523910 | + | 0.851774i | \(0.675527\pi\) | |||||||
\(882\) | −4.89898 | −0.164957 | ||||||||
\(883\) | −48.5959 | −1.63538 | −0.817691 | − | 0.575657i | \(-0.804746\pi\) | ||||
−0.817691 | + | 0.575657i | \(0.804746\pi\) | |||||||
\(884\) | 15.7980 | 0.531343 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.30306 | −0.178160 | ||||||||
\(887\) | −10.1010 | −0.339159 | −0.169580 | − | 0.985517i | \(-0.554241\pi\) | ||||
−0.169580 | + | 0.985517i | \(0.554241\pi\) | |||||||
\(888\) | 8.34847 | 0.280156 | ||||||||
\(889\) | 2.60612 | 0.0874066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 24.6969 | 0.826915 | ||||||||
\(893\) | −26.8990 | −0.900140 | ||||||||
\(894\) | 20.0000 | 0.668900 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.44949 | 0.0484241 | ||||||||
\(897\) | −2.89898 | −0.0967941 | ||||||||
\(898\) | 3.79796 | 0.126740 | ||||||||
\(899\) | 10.0000 | 0.333519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.89898 | −0.163209 | ||||||||
\(902\) | −9.79796 | −0.326236 | ||||||||
\(903\) | 15.7980 | 0.525723 | ||||||||
\(904\) | 14.3485 | 0.477223 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.6969 | −0.621164 | ||||||||
\(907\) | 2.49490 | 0.0828417 | 0.0414209 | − | 0.999142i | \(-0.486812\pi\) | ||||
0.0414209 | + | 0.999142i | \(0.486812\pi\) | |||||||
\(908\) | −4.75255 | −0.157719 | ||||||||
\(909\) | −13.6969 | −0.454299 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3031 | 0.705802 | 0.352901 | − | 0.935661i | \(-0.385195\pi\) | ||||
0.352901 | + | 0.935661i | \(0.385195\pi\) | |||||||
\(912\) | 6.89898 | 0.228448 | ||||||||
\(913\) | −5.10102 | −0.168819 | ||||||||
\(914\) | 0.404082 | 0.0133658 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.10102 | 0.102461 | ||||||||
\(917\) | 12.8990 | 0.425962 | ||||||||
\(918\) | −5.44949 | −0.179860 | ||||||||
\(919\) | −27.9444 | −0.921800 | −0.460900 | − | 0.887452i | \(-0.652473\pi\) | ||||
−0.460900 | + | 0.887452i | \(0.652473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.1010 | −0.662351 | ||||||||
\(922\) | 21.4949 | 0.707897 | ||||||||
\(923\) | −31.3031 | −1.03035 | ||||||||
\(924\) | 2.89898 | 0.0953694 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | −13.2474 | −0.435103 | ||||||||
\(928\) | 5.00000 | 0.164133 | ||||||||
\(929\) | −3.79796 | −0.124607 | −0.0623035 | − | 0.998057i | \(-0.519845\pi\) | ||||
−0.0623035 | + | 0.998057i | \(0.519845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.7980 | −1.10768 | ||||||||
\(932\) | −26.6969 | −0.874487 | ||||||||
\(933\) | 14.5959 | 0.477849 | ||||||||
\(934\) | −29.9444 | −0.979810 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.89898 | −0.0947561 | ||||||||
\(937\) | −15.7980 | −0.516097 | −0.258048 | − | 0.966132i | \(-0.583079\pi\) | ||||
−0.258048 | + | 0.966132i | \(0.583079\pi\) | |||||||
\(938\) | −2.89898 | −0.0946550 | ||||||||
\(939\) | −12.8990 | −0.420942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | −8.89898 | −0.289944 | ||||||||
\(943\) | −4.89898 | −0.159533 | ||||||||
\(944\) | 10.0000 | 0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7980 | 0.708713 | ||||||||
\(947\) | 0.404082 | 0.0131309 | 0.00656545 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656545 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(948\) | 10.0000 | 0.324785 | ||||||||
\(949\) | −6.09082 | −0.197716 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5959 | 0.343596 | ||||||||
\(952\) | −7.89898 | −0.256007 | ||||||||
\(953\) | −30.8434 | −0.999115 | −0.499557 | − | 0.866281i | \(-0.666504\pi\) | ||||
−0.499557 | + | 0.866281i | \(0.666504\pi\) | |||||||
\(954\) | 0.898979 | 0.0291055 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.10102 | −0.262006 | ||||||||
\(957\) | 10.0000 | 0.323254 | ||||||||
\(958\) | −30.0000 | −0.969256 | ||||||||
\(959\) | −32.3939 | −1.04605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −24.2020 | −0.780305 | ||||||||
\(963\) | −2.00000 | −0.0644491 | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.44949 | 0.0466366 | ||||||||
\(967\) | −29.5959 | −0.951741 | −0.475870 | − | 0.879515i | \(-0.657867\pi\) | ||||
−0.475870 | + | 0.879515i | \(0.657867\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | −37.5959 | −1.20775 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.1464 | 0.839079 | 0.419539 | − | 0.907737i | \(-0.362192\pi\) | ||||
0.419539 | + | 0.907737i | \(0.362192\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 22.7526 | 0.729413 | ||||||||
\(974\) | −15.1010 | −0.483868 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.89898 | −0.156813 | ||||||||
\(977\) | −24.7526 | −0.791904 | −0.395952 | − | 0.918271i | \(-0.629585\pi\) | ||||
−0.395952 | + | 0.918271i | \(0.629585\pi\) | |||||||
\(978\) | 17.7980 | 0.569116 | ||||||||
\(979\) | −20.6969 | −0.661477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.44949 | 0.110134 | ||||||||
\(982\) | 25.1010 | 0.801006 | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | −4.89898 | −0.156174 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −27.2474 | −0.867736 | ||||||||
\(987\) | −5.65153 | −0.179890 | ||||||||
\(988\) | −20.0000 | −0.636285 | ||||||||
\(989\) | 10.8990 | 0.346567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2020 | 0.578207 | 0.289103 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289103 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | −6.79796 | −0.215727 | ||||||||
\(994\) | 15.6515 | 0.496436 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.55051 | −0.0808160 | ||||||||
\(997\) | 21.1010 | 0.668276 | 0.334138 | − | 0.942524i | \(-0.391555\pi\) | ||||
0.334138 | + | 0.942524i | \(0.391555\pi\) | |||||||
\(998\) | 21.8990 | 0.693200 | ||||||||
\(999\) | 8.34847 | 0.264134 |
(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 | 3450.2.a.bl.1.2 | yes | 2 | |
5.2 | odd | 4 | 3450.2.d.y.2899.4 | 4 | |||
5.3 | odd | 4 | 3450.2.d.y.2899.1 | 4 | |||
5.4 | even | 2 | 3450.2.a.bf.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bf.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
3450.2.a.bl.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
3450.2.d.y.2899.1 | 4 | 5.3 | odd | 4 | |||
3450.2.d.y.2899.4 | 4 | 5.2 | odd | 4 |