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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) 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 | ||||||||
\(7\) | 4.47214 | 1.69031 | 0.845154 | − | 0.534522i | \(-0.179509\pi\) | ||||
0.845154 | + | 0.534522i | \(0.179509\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | −4.47214 | −1.19523 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.70820 | 1.30955 | 0.654776 | − | 0.755823i | \(-0.272763\pi\) | ||||
0.654776 | + | 0.755823i | \(0.272763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47214 | −0.975900 | ||||||||
\(22\) | 5.23607 | 1.11633 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.47214 | 0.877058 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.47214 | 0.845154 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.23607 | 0.911482 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.2361 | −1.84720 | −0.923599 | − | 0.383360i | \(-0.874767\pi\) | ||||
−0.923599 | + | 0.383360i | \(0.874767\pi\) | |||||||
\(38\) | −5.70820 | −0.925993 | ||||||||
\(39\) | 4.47214 | 0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 4.47214 | 0.690066 | ||||||||
\(43\) | 4.76393 | 0.726493 | 0.363246 | − | 0.931693i | \(-0.381668\pi\) | ||||
0.363246 | + | 0.931693i | \(0.381668\pi\) | |||||||
\(44\) | −5.23607 | −0.789367 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 13.0000 | 1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −4.47214 | −0.620174 | ||||||||
\(53\) | −5.23607 | −0.719229 | −0.359615 | − | 0.933101i | \(-0.617092\pi\) | ||||
−0.359615 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.47214 | −0.597614 | ||||||||
\(57\) | −5.70820 | −0.756070 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.763932 | 0.0978115 | 0.0489057 | − | 0.998803i | \(-0.484427\pi\) | ||||
0.0489057 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(62\) | 2.47214 | 0.313962 | ||||||||
\(63\) | 4.47214 | 0.563436 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.23607 | −0.644515 | ||||||||
\(67\) | −9.70820 | −1.18605 | −0.593023 | − | 0.805186i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805186i | \(0.702066\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.47214 | 0.523424 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(74\) | 11.2361 | 1.30617 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.70820 | 0.654776 | ||||||||
\(77\) | −23.4164 | −2.66855 | ||||||||
\(78\) | −4.47214 | −0.506370 | ||||||||
\(79\) | 4.47214 | 0.503155 | 0.251577 | − | 0.967837i | \(-0.419051\pi\) | ||||
0.251577 | + | 0.967837i | \(0.419051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | −13.2361 | −1.45285 | −0.726424 | − | 0.687247i | \(-0.758819\pi\) | ||||
−0.726424 | + | 0.687247i | \(0.758819\pi\) | |||||||
\(84\) | −4.47214 | −0.487950 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.76393 | −0.513708 | ||||||||
\(87\) | 4.47214 | 0.479463 | ||||||||
\(88\) | 5.23607 | 0.558167 | ||||||||
\(89\) | −10.4721 | −1.11004 | −0.555022 | − | 0.831836i | \(-0.687290\pi\) | ||||
−0.555022 | + | 0.831836i | \(0.687290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.0000 | −2.09657 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 2.47214 | 0.256349 | ||||||||
\(94\) | 4.00000 | 0.412568 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | −13.0000 | −1.31320 | ||||||||
\(99\) | −5.23607 | −0.526245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 4.47214 | 0.438529 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.23607 | 0.508572 | ||||||||
\(107\) | 12.6525 | 1.22316 | 0.611581 | − | 0.791182i | \(-0.290534\pi\) | ||||
0.611581 | + | 0.791182i | \(0.290534\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.76393 | 0.456302 | 0.228151 | − | 0.973626i | \(-0.426732\pi\) | ||||
0.228151 | + | 0.973626i | \(0.426732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.2361 | 1.06648 | ||||||||
\(112\) | 4.47214 | 0.422577 | ||||||||
\(113\) | 5.52786 | 0.520018 | 0.260009 | − | 0.965606i | \(-0.416275\pi\) | ||||
0.260009 | + | 0.965606i | \(0.416275\pi\) | |||||||
\(114\) | 5.70820 | 0.534622 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 8.94427 | 0.823387 | ||||||||
\(119\) | 17.8885 | 1.63984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | −0.763932 | −0.0691632 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | −2.47214 | −0.222004 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.47214 | −0.398410 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.76393 | −0.419441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.52786 | −0.832453 | −0.416227 | − | 0.909261i | \(-0.636648\pi\) | ||||
−0.416227 | + | 0.909261i | \(0.636648\pi\) | |||||||
\(132\) | 5.23607 | 0.455741 | ||||||||
\(133\) | 25.5279 | 2.21355 | ||||||||
\(134\) | 9.70820 | 0.838661 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −3.05573 | −0.261068 | −0.130534 | − | 0.991444i | \(-0.541669\pi\) | ||||
−0.130534 | + | 0.991444i | \(0.541669\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −16.9443 | −1.43719 | −0.718597 | − | 0.695427i | \(-0.755215\pi\) | ||||
−0.718597 | + | 0.695427i | \(0.755215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | −8.94427 | −0.750587 | ||||||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.47214 | −0.370117 | ||||||||
\(147\) | −13.0000 | −1.07222 | ||||||||
\(148\) | −11.2361 | −0.923599 | ||||||||
\(149\) | −11.7082 | −0.959173 | −0.479587 | − | 0.877494i | \(-0.659213\pi\) | ||||
−0.479587 | + | 0.877494i | \(0.659213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | −5.70820 | −0.462996 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 23.4164 | 1.88695 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.47214 | 0.358057 | ||||||||
\(157\) | 6.65248 | 0.530925 | 0.265463 | − | 0.964121i | \(-0.414475\pi\) | ||||
0.265463 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(158\) | −4.47214 | −0.355784 | ||||||||
\(159\) | 5.23607 | 0.415247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47214 | −0.352454 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.47214 | 0.193633 | 0.0968163 | − | 0.995302i | \(-0.469134\pi\) | ||||
0.0968163 | + | 0.995302i | \(0.469134\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2361 | 1.02732 | ||||||||
\(167\) | −16.9443 | −1.31119 | −0.655594 | − | 0.755114i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755114i | \(0.727582\pi\) | |||||||
\(168\) | 4.47214 | 0.345033 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.70820 | 0.436517 | ||||||||
\(172\) | 4.76393 | 0.363246 | ||||||||
\(173\) | 17.4164 | 1.32414 | 0.662072 | − | 0.749440i | \(-0.269677\pi\) | ||||
0.662072 | + | 0.749440i | \(0.269677\pi\) | |||||||
\(174\) | −4.47214 | −0.339032 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.23607 | −0.394683 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 10.4721 | 0.784920 | ||||||||
\(179\) | 19.4164 | 1.45125 | 0.725625 | − | 0.688090i | \(-0.241551\pi\) | ||||
0.725625 | + | 0.688090i | \(0.241551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2361 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(182\) | 20.0000 | 1.48250 | ||||||||
\(183\) | −0.763932 | −0.0564715 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.47214 | −0.181266 | ||||||||
\(187\) | −20.9443 | −1.53160 | ||||||||
\(188\) | −4.00000 | −0.291730 | ||||||||
\(189\) | −4.47214 | −0.325300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −23.8885 | −1.71954 | −0.859768 | − | 0.510686i | \(-0.829392\pi\) | ||||
−0.859768 | + | 0.510686i | \(0.829392\pi\) | |||||||
\(194\) | 0.472136 | 0.0338974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0000 | 0.928571 | ||||||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 5.23607 | 0.372111 | ||||||||
\(199\) | 17.4164 | 1.23462 | 0.617308 | − | 0.786721i | \(-0.288223\pi\) | ||||
0.617308 | + | 0.786721i | \(0.288223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.70820 | 0.684764 | ||||||||
\(202\) | −4.47214 | −0.314658 | ||||||||
\(203\) | −20.0000 | −1.40372 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | −0.418040 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −4.47214 | −0.310087 | ||||||||
\(209\) | −29.8885 | −2.06743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4164 | −1.61205 | −0.806026 | − | 0.591880i | \(-0.798386\pi\) | ||||
−0.806026 | + | 0.591880i | \(0.798386\pi\) | |||||||
\(212\) | −5.23607 | −0.359615 | ||||||||
\(213\) | −8.94427 | −0.612851 | ||||||||
\(214\) | −12.6525 | −0.864905 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −11.0557 | −0.750512 | ||||||||
\(218\) | −4.76393 | −0.322654 | ||||||||
\(219\) | −4.47214 | −0.302199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.8885 | −1.20331 | ||||||||
\(222\) | −11.2361 | −0.754116 | ||||||||
\(223\) | −19.4164 | −1.30022 | −0.650109 | − | 0.759841i | \(-0.725277\pi\) | ||||
−0.650109 | + | 0.759841i | \(0.725277\pi\) | |||||||
\(224\) | −4.47214 | −0.298807 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.52786 | −0.367708 | ||||||||
\(227\) | 9.23607 | 0.613019 | 0.306510 | − | 0.951868i | \(-0.400839\pi\) | ||||
0.306510 | + | 0.951868i | \(0.400839\pi\) | |||||||
\(228\) | −5.70820 | −0.378035 | ||||||||
\(229\) | 17.7082 | 1.17019 | 0.585096 | − | 0.810964i | \(-0.301057\pi\) | ||||
0.585096 | + | 0.810964i | \(0.301057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.4164 | 1.54069 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | −19.8885 | −1.30294 | −0.651471 | − | 0.758674i | \(-0.725848\pi\) | ||||
−0.651471 | + | 0.758674i | \(0.725848\pi\) | |||||||
\(234\) | 4.47214 | 0.292353 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.94427 | −0.582223 | ||||||||
\(237\) | −4.47214 | −0.290496 | ||||||||
\(238\) | −17.8885 | −1.15954 | ||||||||
\(239\) | −4.94427 | −0.319818 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4721 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(242\) | −16.4164 | −1.05529 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.763932 | 0.0489057 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −25.5279 | −1.62430 | ||||||||
\(248\) | 2.47214 | 0.156981 | ||||||||
\(249\) | 13.2361 | 0.838802 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7082 | −1.24397 | −0.621985 | − | 0.783029i | \(-0.713674\pi\) | ||||
−0.621985 | + | 0.783029i | \(0.713674\pi\) | |||||||
\(252\) | 4.47214 | 0.281718 | ||||||||
\(253\) | 5.23607 | 0.329189 | ||||||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.8885 | 0.741587 | 0.370793 | − | 0.928715i | \(-0.379086\pi\) | ||||
0.370793 | + | 0.928715i | \(0.379086\pi\) | |||||||
\(258\) | 4.76393 | 0.296589 | ||||||||
\(259\) | −50.2492 | −3.12233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.47214 | −0.276818 | ||||||||
\(262\) | 9.52786 | 0.588633 | ||||||||
\(263\) | −24.9443 | −1.53813 | −0.769065 | − | 0.639171i | \(-0.779278\pi\) | ||||
−0.769065 | + | 0.639171i | \(0.779278\pi\) | |||||||
\(264\) | −5.23607 | −0.322258 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −25.5279 | −1.56521 | ||||||||
\(267\) | 10.4721 | 0.640884 | ||||||||
\(268\) | −9.70820 | −0.593023 | ||||||||
\(269\) | −13.0557 | −0.796022 | −0.398011 | − | 0.917381i | \(-0.630299\pi\) | ||||
−0.398011 | + | 0.917381i | \(0.630299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9443 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672076\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672076\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 20.0000 | 1.21046 | ||||||||
\(274\) | 3.05573 | 0.184603 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 20.4721 | 1.23005 | 0.615026 | − | 0.788507i | \(-0.289146\pi\) | ||||
0.615026 | + | 0.788507i | \(0.289146\pi\) | |||||||
\(278\) | 16.9443 | 1.01625 | ||||||||
\(279\) | −2.47214 | −0.148003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5279 | −0.807005 | −0.403502 | − | 0.914979i | \(-0.632207\pi\) | ||||
−0.403502 | + | 0.914979i | \(0.632207\pi\) | |||||||
\(282\) | −4.00000 | −0.238197 | ||||||||
\(283\) | 3.81966 | 0.227055 | 0.113528 | − | 0.993535i | \(-0.463785\pi\) | ||||
0.113528 | + | 0.993535i | \(0.463785\pi\) | |||||||
\(284\) | 8.94427 | 0.530745 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.4164 | −1.38464 | ||||||||
\(287\) | −8.94427 | −0.527964 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.472136 | 0.0276771 | ||||||||
\(292\) | 4.47214 | 0.261712 | ||||||||
\(293\) | −0.291796 | −0.0170469 | −0.00852345 | − | 0.999964i | \(-0.502713\pi\) | ||||
−0.00852345 | + | 0.999964i | \(0.502713\pi\) | |||||||
\(294\) | 13.0000 | 0.758175 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.2361 | 0.653083 | ||||||||
\(297\) | 5.23607 | 0.303827 | ||||||||
\(298\) | 11.7082 | 0.678238 | ||||||||
\(299\) | 4.47214 | 0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.3050 | 1.22800 | ||||||||
\(302\) | 14.4721 | 0.832778 | ||||||||
\(303\) | −4.47214 | −0.256917 | ||||||||
\(304\) | 5.70820 | 0.327388 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | −15.4164 | −0.879861 | −0.439930 | − | 0.898032i | \(-0.644997\pi\) | ||||
−0.439930 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(308\) | −23.4164 | −1.33427 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9443 | −1.18764 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(312\) | −4.47214 | −0.253185 | ||||||||
\(313\) | −15.5279 | −0.877687 | −0.438843 | − | 0.898564i | \(-0.644612\pi\) | ||||
−0.438843 | + | 0.898564i | \(0.644612\pi\) | |||||||
\(314\) | −6.65248 | −0.375421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.47214 | 0.251577 | ||||||||
\(317\) | −19.5279 | −1.09679 | −0.548397 | − | 0.836218i | \(-0.684762\pi\) | ||||
−0.548397 | + | 0.836218i | \(0.684762\pi\) | |||||||
\(318\) | −5.23607 | −0.293624 | ||||||||
\(319\) | 23.4164 | 1.31107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6525 | −0.706192 | ||||||||
\(322\) | 4.47214 | 0.249222 | ||||||||
\(323\) | 22.8328 | 1.27045 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.47214 | −0.136919 | ||||||||
\(327\) | −4.76393 | −0.263446 | ||||||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | −17.8885 | −0.986227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4721 | −0.575601 | −0.287800 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287800 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(332\) | −13.2361 | −0.726424 | ||||||||
\(333\) | −11.2361 | −0.615733 | ||||||||
\(334\) | 16.9443 | 0.927149 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.47214 | −0.243975 | ||||||||
\(337\) | 19.8885 | 1.08340 | 0.541699 | − | 0.840573i | \(-0.317781\pi\) | ||||
0.541699 | + | 0.840573i | \(0.317781\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | −5.52786 | −0.300232 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9443 | 0.700972 | ||||||||
\(342\) | −5.70820 | −0.308664 | ||||||||
\(343\) | 26.8328 | 1.44884 | ||||||||
\(344\) | −4.76393 | −0.256854 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.4164 | −0.936312 | ||||||||
\(347\) | −30.4721 | −1.63583 | −0.817915 | − | 0.575339i | \(-0.804870\pi\) | ||||
−0.817915 | + | 0.575339i | \(0.804870\pi\) | |||||||
\(348\) | 4.47214 | 0.239732 | ||||||||
\(349\) | 3.88854 | 0.208149 | 0.104074 | − | 0.994570i | \(-0.466812\pi\) | ||||
0.104074 | + | 0.994570i | \(0.466812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 5.23607 | 0.279083 | ||||||||
\(353\) | 3.88854 | 0.206966 | 0.103483 | − | 0.994631i | \(-0.467001\pi\) | ||||
0.103483 | + | 0.994631i | \(0.467001\pi\) | |||||||
\(354\) | −8.94427 | −0.475383 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.4721 | −0.555022 | ||||||||
\(357\) | −17.8885 | −0.946762 | ||||||||
\(358\) | −19.4164 | −1.02619 | ||||||||
\(359\) | 29.3050 | 1.54666 | 0.773328 | − | 0.634006i | \(-0.218591\pi\) | ||||
0.773328 | + | 0.634006i | \(0.218591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5836 | 0.714926 | ||||||||
\(362\) | 11.2361 | 0.590555 | ||||||||
\(363\) | −16.4164 | −0.861638 | ||||||||
\(364\) | −20.0000 | −1.04828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.763932 | 0.0399314 | ||||||||
\(367\) | −9.41641 | −0.491532 | −0.245766 | − | 0.969329i | \(-0.579040\pi\) | ||||
−0.245766 | + | 0.969329i | \(0.579040\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.4164 | −1.21572 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | 35.5967 | 1.84313 | 0.921565 | − | 0.388224i | \(-0.126911\pi\) | ||||
0.921565 | + | 0.388224i | \(0.126911\pi\) | |||||||
\(374\) | 20.9443 | 1.08300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | 20.0000 | 1.03005 | ||||||||
\(378\) | 4.47214 | 0.230022 | ||||||||
\(379\) | 13.7082 | 0.704143 | 0.352072 | − | 0.935973i | \(-0.385477\pi\) | ||||
0.352072 | + | 0.935973i | \(0.385477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | −6.47214 | −0.331143 | ||||||||
\(383\) | −7.05573 | −0.360531 | −0.180265 | − | 0.983618i | \(-0.557696\pi\) | ||||
−0.180265 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8885 | 1.21589 | ||||||||
\(387\) | 4.76393 | 0.242164 | ||||||||
\(388\) | −0.472136 | −0.0239691 | ||||||||
\(389\) | 23.7082 | 1.20205 | 0.601027 | − | 0.799229i | \(-0.294758\pi\) | ||||
0.601027 | + | 0.799229i | \(0.294758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | −13.0000 | −0.656599 | ||||||||
\(393\) | 9.52786 | 0.480617 | ||||||||
\(394\) | 2.94427 | 0.148330 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.23607 | −0.263122 | ||||||||
\(397\) | −26.9443 | −1.35229 | −0.676147 | − | 0.736767i | \(-0.736352\pi\) | ||||
−0.676147 | + | 0.736767i | \(0.736352\pi\) | |||||||
\(398\) | −17.4164 | −0.873006 | ||||||||
\(399\) | −25.5279 | −1.27799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.94427 | 0.446656 | 0.223328 | − | 0.974743i | \(-0.428308\pi\) | ||||
0.223328 | + | 0.974743i | \(0.428308\pi\) | |||||||
\(402\) | −9.70820 | −0.484201 | ||||||||
\(403\) | 11.0557 | 0.550725 | ||||||||
\(404\) | 4.47214 | 0.222497 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.0000 | 0.992583 | ||||||||
\(407\) | 58.8328 | 2.91623 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | −35.8885 | −1.77457 | −0.887287 | − | 0.461217i | \(-0.847413\pi\) | ||||
−0.887287 | + | 0.461217i | \(0.847413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.05573 | 0.150728 | ||||||||
\(412\) | 6.00000 | 0.295599 | ||||||||
\(413\) | −40.0000 | −1.96827 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.47214 | 0.219265 | ||||||||
\(417\) | 16.9443 | 0.829765 | ||||||||
\(418\) | 29.8885 | 1.46190 | ||||||||
\(419\) | 28.0689 | 1.37125 | 0.685627 | − | 0.727953i | \(-0.259528\pi\) | ||||
0.685627 | + | 0.727953i | \(0.259528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.763932 | −0.0372318 | −0.0186159 | − | 0.999827i | \(-0.505926\pi\) | ||||
−0.0186159 | + | 0.999827i | \(0.505926\pi\) | |||||||
\(422\) | 23.4164 | 1.13989 | ||||||||
\(423\) | −4.00000 | −0.194487 | ||||||||
\(424\) | 5.23607 | 0.254286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.94427 | 0.433351 | ||||||||
\(427\) | 3.41641 | 0.165332 | ||||||||
\(428\) | 12.6525 | 0.611581 | ||||||||
\(429\) | −23.4164 | −1.13055 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.4164 | −1.12793 | −0.563964 | − | 0.825799i | \(-0.690724\pi\) | ||||
−0.563964 | + | 0.825799i | \(0.690724\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 21.4164 | 1.02921 | 0.514603 | − | 0.857428i | \(-0.327939\pi\) | ||||
0.514603 | + | 0.857428i | \(0.327939\pi\) | |||||||
\(434\) | 11.0557 | 0.530692 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.76393 | 0.228151 | ||||||||
\(437\) | −5.70820 | −0.273060 | ||||||||
\(438\) | 4.47214 | 0.213687 | ||||||||
\(439\) | 19.0557 | 0.909480 | 0.454740 | − | 0.890624i | \(-0.349732\pi\) | ||||
0.454740 | + | 0.890624i | \(0.349732\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | 0.619048 | ||||||||
\(442\) | 17.8885 | 0.850871 | ||||||||
\(443\) | 15.0557 | 0.715319 | 0.357660 | − | 0.933852i | \(-0.383575\pi\) | ||||
0.357660 | + | 0.933852i | \(0.383575\pi\) | |||||||
\(444\) | 11.2361 | 0.533240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.4164 | 0.919394 | ||||||||
\(447\) | 11.7082 | 0.553779 | ||||||||
\(448\) | 4.47214 | 0.211289 | ||||||||
\(449\) | 15.8885 | 0.749827 | 0.374913 | − | 0.927060i | \(-0.377672\pi\) | ||||
0.374913 | + | 0.927060i | \(0.377672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4721 | 0.493114 | ||||||||
\(452\) | 5.52786 | 0.260009 | ||||||||
\(453\) | 14.4721 | 0.679960 | ||||||||
\(454\) | −9.23607 | −0.433470 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70820 | 0.267311 | ||||||||
\(457\) | −27.5279 | −1.28770 | −0.643850 | − | 0.765152i | \(-0.722664\pi\) | ||||
−0.643850 | + | 0.765152i | \(0.722664\pi\) | |||||||
\(458\) | −17.7082 | −0.827450 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000 | 1.02464 | 0.512321 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512321 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(462\) | −23.4164 | −1.08943 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8885 | 0.921319 | ||||||||
\(467\) | 17.8197 | 0.824596 | 0.412298 | − | 0.911049i | \(-0.364726\pi\) | ||||
0.412298 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(468\) | −4.47214 | −0.206725 | ||||||||
\(469\) | −43.4164 | −2.00478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.65248 | −0.306530 | ||||||||
\(472\) | 8.94427 | 0.411693 | ||||||||
\(473\) | −24.9443 | −1.14694 | ||||||||
\(474\) | 4.47214 | 0.205412 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.8885 | 0.819920 | ||||||||
\(477\) | −5.23607 | −0.239743 | ||||||||
\(478\) | 4.94427 | 0.226146 | ||||||||
\(479\) | −28.9443 | −1.32250 | −0.661249 | − | 0.750167i | \(-0.729973\pi\) | ||||
−0.661249 | + | 0.750167i | \(0.729973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.2492 | 2.29117 | ||||||||
\(482\) | 12.4721 | 0.568090 | ||||||||
\(483\) | 4.47214 | 0.203489 | ||||||||
\(484\) | 16.4164 | 0.746200 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −9.88854 | −0.448093 | −0.224046 | − | 0.974578i | \(-0.571927\pi\) | ||||
−0.224046 | + | 0.974578i | \(0.571927\pi\) | |||||||
\(488\) | −0.763932 | −0.0345816 | ||||||||
\(489\) | −2.47214 | −0.111794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3050 | 1.32251 | 0.661257 | − | 0.750159i | \(-0.270023\pi\) | ||||
0.661257 | + | 0.750159i | \(0.270023\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | −17.8885 | −0.805659 | ||||||||
\(494\) | 25.5279 | 1.14855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.47214 | −0.111002 | ||||||||
\(497\) | 40.0000 | 1.79425 | ||||||||
\(498\) | −13.2361 | −0.593122 | ||||||||
\(499\) | 0.583592 | 0.0261252 | 0.0130626 | − | 0.999915i | \(-0.495842\pi\) | ||||
0.0130626 | + | 0.999915i | \(0.495842\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.9443 | 0.757014 | ||||||||
\(502\) | 19.7082 | 0.879620 | ||||||||
\(503\) | −10.4721 | −0.466929 | −0.233465 | − | 0.972365i | \(-0.575006\pi\) | ||||
−0.233465 | + | 0.972365i | \(0.575006\pi\) | |||||||
\(504\) | −4.47214 | −0.199205 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.23607 | −0.232772 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | −33.4164 | −1.48116 | −0.740578 | − | 0.671970i | \(-0.765448\pi\) | ||||
−0.740578 | + | 0.671970i | \(0.765448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.70820 | −0.252023 | ||||||||
\(514\) | −11.8885 | −0.524381 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.76393 | −0.209720 | ||||||||
\(517\) | 20.9443 | 0.921128 | ||||||||
\(518\) | 50.2492 | 2.20782 | ||||||||
\(519\) | −17.4164 | −0.764495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0000 | 0.700973 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(522\) | 4.47214 | 0.195740 | ||||||||
\(523\) | −25.7082 | −1.12414 | −0.562071 | − | 0.827089i | \(-0.689995\pi\) | ||||
−0.562071 | + | 0.827089i | \(0.689995\pi\) | |||||||
\(524\) | −9.52786 | −0.416227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.9443 | 1.08762 | ||||||||
\(527\) | −9.88854 | −0.430752 | ||||||||
\(528\) | 5.23607 | 0.227871 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 25.5279 | 1.10677 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | −10.4721 | −0.453174 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.70820 | 0.419331 | ||||||||
\(537\) | −19.4164 | −0.837880 | ||||||||
\(538\) | 13.0557 | 0.562872 | ||||||||
\(539\) | −68.0689 | −2.93193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.11146 | 0.348739 | 0.174369 | − | 0.984680i | \(-0.444211\pi\) | ||||
0.174369 | + | 0.984680i | \(0.444211\pi\) | |||||||
\(542\) | 16.9443 | 0.727819 | ||||||||
\(543\) | 11.2361 | 0.482186 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20.0000 | −0.855921 | ||||||||
\(547\) | −41.3050 | −1.76607 | −0.883036 | − | 0.469305i | \(-0.844504\pi\) | ||||
−0.883036 | + | 0.469305i | \(0.844504\pi\) | |||||||
\(548\) | −3.05573 | −0.130534 | ||||||||
\(549\) | 0.763932 | 0.0326038 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5279 | −1.08752 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 20.0000 | 0.850487 | ||||||||
\(554\) | −20.4721 | −0.869778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9443 | −0.718597 | ||||||||
\(557\) | 15.1246 | 0.640850 | 0.320425 | − | 0.947274i | \(-0.396174\pi\) | ||||
0.320425 | + | 0.947274i | \(0.396174\pi\) | |||||||
\(558\) | 2.47214 | 0.104654 | ||||||||
\(559\) | −21.3050 | −0.901103 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 13.5279 | 0.570639 | ||||||||
\(563\) | −24.6525 | −1.03898 | −0.519489 | − | 0.854477i | \(-0.673878\pi\) | ||||
−0.519489 | + | 0.854477i | \(0.673878\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.81966 | −0.160552 | ||||||||
\(567\) | 4.47214 | 0.187812 | ||||||||
\(568\) | −8.94427 | −0.375293 | ||||||||
\(569\) | 20.0000 | 0.838444 | 0.419222 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419222 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.2918 | −0.598093 | −0.299047 | − | 0.954239i | \(-0.596669\pi\) | ||||
−0.299047 | + | 0.954239i | \(0.596669\pi\) | |||||||
\(572\) | 23.4164 | 0.979089 | ||||||||
\(573\) | −6.47214 | −0.270377 | ||||||||
\(574\) | 8.94427 | 0.373327 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.3607 | 1.43045 | 0.715227 | − | 0.698892i | \(-0.246323\pi\) | ||||
0.715227 | + | 0.698892i | \(0.246323\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 23.8885 | 0.992774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −59.1935 | −2.45576 | ||||||||
\(582\) | −0.472136 | −0.0195707 | ||||||||
\(583\) | 27.4164 | 1.13547 | ||||||||
\(584\) | −4.47214 | −0.185058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.291796 | 0.0120540 | ||||||||
\(587\) | −6.47214 | −0.267134 | −0.133567 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133567 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(588\) | −13.0000 | −0.536111 | ||||||||
\(589\) | −14.1115 | −0.581452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.94427 | 0.121111 | ||||||||
\(592\) | −11.2361 | −0.461800 | ||||||||
\(593\) | −33.7771 | −1.38706 | −0.693529 | − | 0.720428i | \(-0.743945\pi\) | ||||
−0.693529 | + | 0.720428i | \(0.743945\pi\) | |||||||
\(594\) | −5.23607 | −0.214838 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.7082 | −0.479587 | ||||||||
\(597\) | −17.4164 | −0.712806 | ||||||||
\(598\) | −4.47214 | −0.182879 | ||||||||
\(599\) | 33.8885 | 1.38465 | 0.692324 | − | 0.721587i | \(-0.256587\pi\) | ||||
0.692324 | + | 0.721587i | \(0.256587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3607 | −0.422621 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(602\) | −21.3050 | −0.868325 | ||||||||
\(603\) | −9.70820 | −0.395349 | ||||||||
\(604\) | −14.4721 | −0.588863 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.47214 | 0.181668 | ||||||||
\(607\) | 17.5279 | 0.711434 | 0.355717 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355717 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(608\) | −5.70820 | −0.231498 | ||||||||
\(609\) | 20.0000 | 0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.8885 | 0.723693 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 25.1246 | 1.01477 | 0.507387 | − | 0.861718i | \(-0.330612\pi\) | ||||
0.507387 | + | 0.861718i | \(0.330612\pi\) | |||||||
\(614\) | 15.4164 | 0.622156 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.4164 | 0.943474 | ||||||||
\(617\) | −20.3607 | −0.819690 | −0.409845 | − | 0.912155i | \(-0.634417\pi\) | ||||
−0.409845 | + | 0.912155i | \(0.634417\pi\) | |||||||
\(618\) | 6.00000 | 0.241355 | ||||||||
\(619\) | 18.2918 | 0.735209 | 0.367605 | − | 0.929982i | \(-0.380178\pi\) | ||||
0.367605 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 20.9443 | 0.839789 | ||||||||
\(623\) | −46.8328 | −1.87632 | ||||||||
\(624\) | 4.47214 | 0.179029 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.5279 | 0.620618 | ||||||||
\(627\) | 29.8885 | 1.19363 | ||||||||
\(628\) | 6.65248 | 0.265463 | ||||||||
\(629\) | −44.9443 | −1.79205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.00000 | −0.238856 | −0.119428 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119428 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(632\) | −4.47214 | −0.177892 | ||||||||
\(633\) | 23.4164 | 0.930719 | ||||||||
\(634\) | 19.5279 | 0.775551 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.23607 | 0.207624 | ||||||||
\(637\) | −58.1378 | −2.30350 | ||||||||
\(638\) | −23.4164 | −0.927064 | ||||||||
\(639\) | 8.94427 | 0.353830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.00000 | 0.157991 | 0.0789953 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789953 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(642\) | 12.6525 | 0.499353 | ||||||||
\(643\) | 32.5410 | 1.28329 | 0.641646 | − | 0.767001i | \(-0.278252\pi\) | ||||
0.641646 | + | 0.767001i | \(0.278252\pi\) | |||||||
\(644\) | −4.47214 | −0.176227 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8328 | −0.898345 | ||||||||
\(647\) | −12.9443 | −0.508892 | −0.254446 | − | 0.967087i | \(-0.581893\pi\) | ||||
−0.254446 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 46.8328 | 1.83835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0557 | 0.433308 | ||||||||
\(652\) | 2.47214 | 0.0968163 | ||||||||
\(653\) | −9.41641 | −0.368493 | −0.184246 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184246 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(654\) | 4.76393 | 0.186284 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 4.47214 | 0.174475 | ||||||||
\(658\) | 17.8885 | 0.697368 | ||||||||
\(659\) | −32.6525 | −1.27196 | −0.635980 | − | 0.771706i | \(-0.719404\pi\) | ||||
−0.635980 | + | 0.771706i | \(0.719404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.81966 | 0.148568 | 0.0742838 | − | 0.997237i | \(-0.476333\pi\) | ||||
0.0742838 | + | 0.997237i | \(0.476333\pi\) | |||||||
\(662\) | 10.4721 | 0.407011 | ||||||||
\(663\) | 17.8885 | 0.694733 | ||||||||
\(664\) | 13.2361 | 0.513659 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.2361 | 0.435389 | ||||||||
\(667\) | 4.47214 | 0.173162 | ||||||||
\(668\) | −16.9443 | −0.655594 | ||||||||
\(669\) | 19.4164 | 0.750682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 4.47214 | 0.172516 | ||||||||
\(673\) | −4.47214 | −0.172388 | −0.0861941 | − | 0.996278i | \(-0.527471\pi\) | ||||
−0.0861941 | + | 0.996278i | \(0.527471\pi\) | |||||||
\(674\) | −19.8885 | −0.766078 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | −19.1246 | −0.735019 | −0.367509 | − | 0.930020i | \(-0.619789\pi\) | ||||
−0.367509 | + | 0.930020i | \(0.619789\pi\) | |||||||
\(678\) | 5.52786 | 0.212296 | ||||||||
\(679\) | −2.11146 | −0.0810303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.23607 | −0.353927 | ||||||||
\(682\) | −12.9443 | −0.495662 | ||||||||
\(683\) | −14.4721 | −0.553761 | −0.276880 | − | 0.960904i | \(-0.589301\pi\) | ||||
−0.276880 | + | 0.960904i | \(0.589301\pi\) | |||||||
\(684\) | 5.70820 | 0.218259 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.8328 | −1.02448 | ||||||||
\(687\) | −17.7082 | −0.675610 | ||||||||
\(688\) | 4.76393 | 0.181623 | ||||||||
\(689\) | 23.4164 | 0.892094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.5836 | 0.630870 | 0.315435 | − | 0.948947i | \(-0.397850\pi\) | ||||
0.315435 | + | 0.948947i | \(0.397850\pi\) | |||||||
\(692\) | 17.4164 | 0.662072 | ||||||||
\(693\) | −23.4164 | −0.889516 | ||||||||
\(694\) | 30.4721 | 1.15671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.47214 | −0.169516 | ||||||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | −3.88854 | −0.147184 | ||||||||
\(699\) | 19.8885 | 0.752254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.12461 | −0.118015 | −0.0590075 | − | 0.998258i | \(-0.518794\pi\) | ||||
−0.0590075 | + | 0.998258i | \(0.518794\pi\) | |||||||
\(702\) | −4.47214 | −0.168790 | ||||||||
\(703\) | −64.1378 | −2.41900 | ||||||||
\(704\) | −5.23607 | −0.197342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.88854 | −0.146347 | ||||||||
\(707\) | 20.0000 | 0.752177 | ||||||||
\(708\) | 8.94427 | 0.336146 | ||||||||
\(709\) | 35.0132 | 1.31495 | 0.657473 | − | 0.753478i | \(-0.271625\pi\) | ||||
0.657473 | + | 0.753478i | \(0.271625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.47214 | 0.167718 | ||||||||
\(712\) | 10.4721 | 0.392460 | ||||||||
\(713\) | 2.47214 | 0.0925822 | ||||||||
\(714\) | 17.8885 | 0.669462 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.4164 | 0.725625 | ||||||||
\(717\) | 4.94427 | 0.184647 | ||||||||
\(718\) | −29.3050 | −1.09365 | ||||||||
\(719\) | −3.05573 | −0.113959 | −0.0569797 | − | 0.998375i | \(-0.518147\pi\) | ||||
−0.0569797 | + | 0.998375i | \(0.518147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8328 | 0.999306 | ||||||||
\(722\) | −13.5836 | −0.505529 | ||||||||
\(723\) | 12.4721 | 0.463844 | ||||||||
\(724\) | −11.2361 | −0.417585 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.4164 | 0.609270 | ||||||||
\(727\) | 19.3050 | 0.715981 | 0.357991 | − | 0.933725i | \(-0.383462\pi\) | ||||
0.357991 | + | 0.933725i | \(0.383462\pi\) | |||||||
\(728\) | 20.0000 | 0.741249 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.0557 | 0.704802 | ||||||||
\(732\) | −0.763932 | −0.0282357 | ||||||||
\(733\) | 21.7082 | 0.801811 | 0.400905 | − | 0.916119i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916119i | \(0.368696\pi\) | |||||||
\(734\) | 9.41641 | 0.347566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 50.8328 | 1.87245 | ||||||||
\(738\) | 2.00000 | 0.0736210 | ||||||||
\(739\) | −32.9443 | −1.21187 | −0.605937 | − | 0.795512i | \(-0.707202\pi\) | ||||
−0.605937 | + | 0.795512i | \(0.707202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.5279 | 0.937790 | ||||||||
\(742\) | 23.4164 | 0.859643 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | −2.47214 | −0.0906329 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.5967 | −1.30329 | ||||||||
\(747\) | −13.2361 | −0.484282 | ||||||||
\(748\) | −20.9443 | −0.765798 | ||||||||
\(749\) | 56.5836 | 2.06752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | −0.656829 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(752\) | −4.00000 | −0.145865 | ||||||||
\(753\) | 19.7082 | 0.718207 | ||||||||
\(754\) | −20.0000 | −0.728357 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.47214 | −0.162650 | ||||||||
\(757\) | 1.34752 | 0.0489766 | 0.0244883 | − | 0.999700i | \(-0.492204\pi\) | ||||
0.0244883 | + | 0.999700i | \(0.492204\pi\) | |||||||
\(758\) | −13.7082 | −0.497904 | ||||||||
\(759\) | −5.23607 | −0.190057 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.05573 | −0.183270 | −0.0916350 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916350 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(762\) | 4.00000 | 0.144905 | ||||||||
\(763\) | 21.3050 | 0.771291 | ||||||||
\(764\) | 6.47214 | 0.234154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.05573 | 0.254934 | ||||||||
\(767\) | 40.0000 | 1.44432 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.4721 | 0.449757 | 0.224878 | − | 0.974387i | \(-0.427802\pi\) | ||||
0.224878 | + | 0.974387i | \(0.427802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8885 | −0.428155 | ||||||||
\(772\) | −23.8885 | −0.859768 | ||||||||
\(773\) | 38.1803 | 1.37325 | 0.686626 | − | 0.727011i | \(-0.259091\pi\) | ||||
0.686626 | + | 0.727011i | \(0.259091\pi\) | |||||||
\(774\) | −4.76393 | −0.171236 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.472136 | 0.0169487 | ||||||||
\(777\) | 50.2492 | 1.80268 | ||||||||
\(778\) | −23.7082 | −0.849980 | ||||||||
\(779\) | −11.4164 | −0.409035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.8328 | −1.67581 | ||||||||
\(782\) | 4.00000 | 0.143040 | ||||||||
\(783\) | 4.47214 | 0.159821 | ||||||||
\(784\) | 13.0000 | 0.464286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.52786 | −0.339848 | ||||||||
\(787\) | −35.2361 | −1.25603 | −0.628015 | − | 0.778201i | \(-0.716132\pi\) | ||||
−0.628015 | + | 0.778201i | \(0.716132\pi\) | |||||||
\(788\) | −2.94427 | −0.104885 | ||||||||
\(789\) | 24.9443 | 0.888040 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.7214 | 0.878990 | ||||||||
\(792\) | 5.23607 | 0.186056 | ||||||||
\(793\) | −3.41641 | −0.121320 | ||||||||
\(794\) | 26.9443 | 0.956216 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4164 | 0.617308 | ||||||||
\(797\) | −41.5967 | −1.47343 | −0.736716 | − | 0.676202i | \(-0.763625\pi\) | ||||
−0.736716 | + | 0.676202i | \(0.763625\pi\) | |||||||
\(798\) | 25.5279 | 0.903677 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4721 | −0.370015 | ||||||||
\(802\) | −8.94427 | −0.315833 | ||||||||
\(803\) | −23.4164 | −0.826347 | ||||||||
\(804\) | 9.70820 | 0.342382 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.0557 | −0.389421 | ||||||||
\(807\) | 13.0557 | 0.459583 | ||||||||
\(808\) | −4.47214 | −0.157329 | ||||||||
\(809\) | 42.9443 | 1.50984 | 0.754920 | − | 0.655817i | \(-0.227676\pi\) | ||||
0.754920 | + | 0.655817i | \(0.227676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.3050 | 1.45041 | 0.725207 | − | 0.688531i | \(-0.241744\pi\) | ||||
0.725207 | + | 0.688531i | \(0.241744\pi\) | |||||||
\(812\) | −20.0000 | −0.701862 | ||||||||
\(813\) | 16.9443 | 0.594262 | ||||||||
\(814\) | −58.8328 | −2.06209 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 27.1935 | 0.951380 | ||||||||
\(818\) | 35.8885 | 1.25481 | ||||||||
\(819\) | −20.0000 | −0.698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.5279 | 1.37953 | 0.689766 | − | 0.724032i | \(-0.257713\pi\) | ||||
0.689766 | + | 0.724032i | \(0.257713\pi\) | |||||||
\(822\) | −3.05573 | −0.106581 | ||||||||
\(823\) | 52.3607 | 1.82518 | 0.912589 | − | 0.408877i | \(-0.134080\pi\) | ||||
0.912589 | + | 0.408877i | \(0.134080\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.0000 | 1.39178 | ||||||||
\(827\) | 21.5967 | 0.750993 | 0.375496 | − | 0.926824i | \(-0.377472\pi\) | ||||
0.375496 | + | 0.926824i | \(0.377472\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.4721 | −0.710171 | ||||||||
\(832\) | −4.47214 | −0.155043 | ||||||||
\(833\) | 52.0000 | 1.80169 | ||||||||
\(834\) | −16.9443 | −0.586732 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −29.8885 | −1.03372 | ||||||||
\(837\) | 2.47214 | 0.0854495 | ||||||||
\(838\) | −28.0689 | −0.969623 | ||||||||
\(839\) | −45.8885 | −1.58425 | −0.792124 | − | 0.610360i | \(-0.791025\pi\) | ||||
−0.792124 | + | 0.610360i | \(0.791025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0.763932 | 0.0263268 | ||||||||
\(843\) | 13.5279 | 0.465924 | ||||||||
\(844\) | −23.4164 | −0.806026 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | 73.4164 | 2.52262 | ||||||||
\(848\) | −5.23607 | −0.179807 | ||||||||
\(849\) | −3.81966 | −0.131090 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.2361 | 0.385167 | ||||||||
\(852\) | −8.94427 | −0.306426 | ||||||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | −3.41641 | −0.116907 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.6525 | −0.432453 | ||||||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | 23.4164 | 0.799423 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.94427 | 0.304820 | ||||||||
\(862\) | 23.4164 | 0.797566 | ||||||||
\(863\) | −14.8328 | −0.504915 | −0.252457 | − | 0.967608i | \(-0.581239\pi\) | ||||
−0.252457 | + | 0.967608i | \(0.581239\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.4164 | −0.727759 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −11.0557 | −0.375256 | ||||||||
\(869\) | −23.4164 | −0.794347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.4164 | 1.47111 | ||||||||
\(872\) | −4.76393 | −0.161327 | ||||||||
\(873\) | −0.472136 | −0.0159794 | ||||||||
\(874\) | 5.70820 | 0.193083 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.47214 | −0.151099 | ||||||||
\(877\) | 48.2492 | 1.62926 | 0.814630 | − | 0.579981i | \(-0.196940\pi\) | ||||
0.814630 | + | 0.579981i | \(0.196940\pi\) | |||||||
\(878\) | −19.0557 | −0.643100 | ||||||||
\(879\) | 0.291796 | 0.00984204 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.4164 | 1.32797 | 0.663986 | − | 0.747745i | \(-0.268863\pi\) | ||||
0.663986 | + | 0.747745i | \(0.268863\pi\) | |||||||
\(882\) | −13.0000 | −0.437733 | ||||||||
\(883\) | −13.5279 | −0.455249 | −0.227624 | − | 0.973749i | \(-0.573096\pi\) | ||||
−0.227624 | + | 0.973749i | \(0.573096\pi\) | |||||||
\(884\) | −17.8885 | −0.601657 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0557 | −0.505807 | ||||||||
\(887\) | 16.9443 | 0.568933 | 0.284466 | − | 0.958686i | \(-0.408184\pi\) | ||||
0.284466 | + | 0.958686i | \(0.408184\pi\) | |||||||
\(888\) | −11.2361 | −0.377058 | ||||||||
\(889\) | 17.8885 | 0.599963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23607 | −0.175415 | ||||||||
\(892\) | −19.4164 | −0.650109 | ||||||||
\(893\) | −22.8328 | −0.764071 | ||||||||
\(894\) | −11.7082 | −0.391581 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.47214 | −0.149404 | ||||||||
\(897\) | −4.47214 | −0.149320 | ||||||||
\(898\) | −15.8885 | −0.530208 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.9443 | −0.697755 | ||||||||
\(902\) | −10.4721 | −0.348684 | ||||||||
\(903\) | −21.3050 | −0.708984 | ||||||||
\(904\) | −5.52786 | −0.183854 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.4721 | −0.480805 | ||||||||
\(907\) | −4.18034 | −0.138806 | −0.0694030 | − | 0.997589i | \(-0.522109\pi\) | ||||
−0.0694030 | + | 0.997589i | \(0.522109\pi\) | |||||||
\(908\) | 9.23607 | 0.306510 | ||||||||
\(909\) | 4.47214 | 0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.5836 | 0.549439 | 0.274719 | − | 0.961524i | \(-0.411415\pi\) | ||||
0.274719 | + | 0.961524i | \(0.411415\pi\) | |||||||
\(912\) | −5.70820 | −0.189018 | ||||||||
\(913\) | 69.3050 | 2.29366 | ||||||||
\(914\) | 27.5279 | 0.910541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.7082 | 0.585096 | ||||||||
\(917\) | −42.6099 | −1.40710 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −16.4721 | −0.543366 | −0.271683 | − | 0.962387i | \(-0.587580\pi\) | ||||
−0.271683 | + | 0.962387i | \(0.587580\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4164 | 0.507988 | ||||||||
\(922\) | −22.0000 | −0.724531 | ||||||||
\(923\) | −40.0000 | −1.31662 | ||||||||
\(924\) | 23.4164 | 0.770343 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 4.47214 | 0.146805 | ||||||||
\(929\) | −24.8328 | −0.814738 | −0.407369 | − | 0.913264i | \(-0.633554\pi\) | ||||
−0.407369 | + | 0.913264i | \(0.633554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 74.2067 | 2.43202 | ||||||||
\(932\) | −19.8885 | −0.651471 | ||||||||
\(933\) | 20.9443 | 0.685685 | ||||||||
\(934\) | −17.8197 | −0.583077 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.47214 | 0.146176 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 43.4164 | 1.41760 | ||||||||
\(939\) | 15.5279 | 0.506733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1803 | 1.24464 | 0.622322 | − | 0.782762i | \(-0.286190\pi\) | ||||
0.622322 | + | 0.782762i | \(0.286190\pi\) | |||||||
\(942\) | 6.65248 | 0.216749 | ||||||||
\(943\) | 2.00000 | 0.0651290 | ||||||||
\(944\) | −8.94427 | −0.291111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.9443 | 0.811008 | ||||||||
\(947\) | 47.1935 | 1.53358 | 0.766791 | − | 0.641897i | \(-0.221852\pi\) | ||||
0.766791 | + | 0.641897i | \(0.221852\pi\) | |||||||
\(948\) | −4.47214 | −0.145248 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5279 | 0.633234 | ||||||||
\(952\) | −17.8885 | −0.579771 | ||||||||
\(953\) | 47.7771 | 1.54765 | 0.773826 | − | 0.633398i | \(-0.218341\pi\) | ||||
0.773826 | + | 0.633398i | \(0.218341\pi\) | |||||||
\(954\) | 5.23607 | 0.169524 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.94427 | −0.159909 | ||||||||
\(957\) | −23.4164 | −0.756945 | ||||||||
\(958\) | 28.9443 | 0.935147 | ||||||||
\(959\) | −13.6656 | −0.441286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | −50.2492 | −1.62010 | ||||||||
\(963\) | 12.6525 | 0.407720 | ||||||||
\(964\) | −12.4721 | −0.401700 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.47214 | −0.143889 | ||||||||
\(967\) | −15.4164 | −0.495758 | −0.247879 | − | 0.968791i | \(-0.579734\pi\) | ||||
−0.247879 | + | 0.968791i | \(0.579734\pi\) | |||||||
\(968\) | −16.4164 | −0.527643 | ||||||||
\(969\) | −22.8328 | −0.733496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.1246 | −0.613738 | −0.306869 | − | 0.951752i | \(-0.599281\pi\) | ||||
−0.306869 | + | 0.951752i | \(0.599281\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −75.7771 | −2.42930 | ||||||||
\(974\) | 9.88854 | 0.316849 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.763932 | 0.0244529 | ||||||||
\(977\) | −1.16718 | −0.0373415 | −0.0186708 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186708 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(978\) | 2.47214 | 0.0790502 | ||||||||
\(979\) | 54.8328 | 1.75246 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.76393 | 0.152101 | ||||||||
\(982\) | −29.3050 | −0.935159 | ||||||||
\(983\) | −0.583592 | −0.0186137 | −0.00930685 | − | 0.999957i | \(-0.502963\pi\) | ||||
−0.00930685 | + | 0.999957i | \(0.502963\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.8885 | 0.569687 | ||||||||
\(987\) | 17.8885 | 0.569399 | ||||||||
\(988\) | −25.5279 | −0.812150 | ||||||||
\(989\) | −4.76393 | −0.151484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4721 | −0.332658 | −0.166329 | − | 0.986070i | \(-0.553191\pi\) | ||||
−0.166329 | + | 0.986070i | \(0.553191\pi\) | |||||||
\(992\) | 2.47214 | 0.0784904 | ||||||||
\(993\) | 10.4721 | 0.332323 | ||||||||
\(994\) | −40.0000 | −1.26872 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.2361 | 0.419401 | ||||||||
\(997\) | −5.05573 | −0.160117 | −0.0800583 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800583 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(998\) | −0.583592 | −0.0184733 | ||||||||
\(999\) | 11.2361 | 0.355493 |
(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.be.1.2 | 2 | ||
5.2 | odd | 4 | 3450.2.d.x.2899.2 | 4 | |||
5.3 | odd | 4 | 3450.2.d.x.2899.3 | 4 | |||
5.4 | even | 2 | 138.2.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 414.2.a.f.1.1 | 2 | |||
20.19 | odd | 2 | 1104.2.a.j.1.2 | 2 | |||
35.34 | odd | 2 | 6762.2.a.cb.1.1 | 2 | |||
40.19 | odd | 2 | 4416.2.a.bl.1.1 | 2 | |||
40.29 | even | 2 | 4416.2.a.bh.1.1 | 2 | |||
60.59 | even | 2 | 3312.2.a.bc.1.1 | 2 | |||
115.114 | odd | 2 | 3174.2.a.s.1.1 | 2 | |||
345.344 | even | 2 | 9522.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
414.2.a.f.1.1 | 2 | 15.14 | odd | 2 | |||
1104.2.a.j.1.2 | 2 | 20.19 | odd | 2 | |||
3174.2.a.s.1.1 | 2 | 115.114 | odd | 2 | |||
3312.2.a.bc.1.1 | 2 | 60.59 | even | 2 | |||
3450.2.a.be.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3450.2.d.x.2899.2 | 4 | 5.2 | odd | 4 | |||
3450.2.d.x.2899.3 | 4 | 5.3 | odd | 4 | |||
4416.2.a.bh.1.1 | 2 | 40.29 | even | 2 | |||
4416.2.a.bl.1.1 | 2 | 40.19 | odd | 2 | |||
6762.2.a.cb.1.1 | 2 | 35.34 | odd | 2 | |||
9522.2.a.q.1.2 | 2 | 345.344 | even | 2 |