Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, 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("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.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: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 768) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.03528 | −0.462990 | −0.231495 | − | 0.972836i | \(-0.574362\pi\) | ||||
−0.231495 | + | 0.972836i | \(0.574362\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46410 | −1.64749 | −0.823744 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823744 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.535898 | 0.122944 | 0.0614718 | − | 0.998109i | \(-0.480421\pi\) | ||||
0.0614718 | + | 0.998109i | \(0.480421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.92820 | −0.785641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.93426 | −1.10196 | −0.550982 | − | 0.834517i | \(-0.685747\pi\) | ||||
−0.550982 | + | 0.834517i | \(0.685747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.34847 | −1.31982 | −0.659912 | − | 0.751343i | \(-0.729406\pi\) | ||||
−0.659912 | + | 0.751343i | \(0.729406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53590 | 0.428645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.14162 | 1.50287 | 0.751437 | − | 0.659805i | \(-0.229361\pi\) | ||||
0.751437 | + | 0.659805i | \(0.229361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4641 | −1.79039 | −0.895196 | − | 0.445673i | \(-0.852964\pi\) | ||||
−0.895196 | + | 0.445673i | \(0.852964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.52056 | −1.30775 | −0.653875 | − | 0.756603i | \(-0.726858\pi\) | ||||
−0.653875 | + | 0.756603i | \(0.726858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.8564 | 1.80395 | 0.901975 | − | 0.431788i | \(-0.142117\pi\) | ||||
0.901975 | + | 0.431788i | \(0.142117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.14162 | −1.17046 | −0.585232 | − | 0.810866i | \(-0.698997\pi\) | ||||
−0.585232 | + | 0.810866i | \(0.698997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.39230 | 0.544798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.07180 | 0.130941 | 0.0654704 | − | 0.997855i | \(-0.479145\pi\) | ||||
0.0654704 | + | 0.997855i | \(0.479145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.2127 | −1.92409 | −0.962046 | − | 0.272887i | \(-0.912021\pi\) | ||||
−0.962046 | + | 0.272887i | \(0.912021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.3843 | 1.52528 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44949 | 0.275589 | 0.137795 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.46410 | 0.160706 | 0.0803530 | − | 0.996766i | \(-0.474395\pi\) | ||||
0.0803530 | + | 0.996766i | \(0.474395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.58630 | 0.388989 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.92820 | −0.946388 | −0.473194 | − | 0.880958i | \(-0.656899\pi\) | ||||
−0.473194 | + | 0.880958i | \(0.656899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3923 | 1.08941 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.554803 | −0.0569216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9282 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.277401 | 0.0276025 | 0.0138012 | − | 0.999905i | \(-0.495607\pi\) | ||||
0.0138012 | + | 0.999905i | \(0.495607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.10634 | −0.798742 | −0.399371 | − | 0.916789i | \(-0.630771\pi\) | ||||
−0.399371 | + | 0.916789i | \(0.630771\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.41421 | −0.135457 | −0.0677285 | − | 0.997704i | \(-0.521575\pi\) | ||||
−0.0677285 | + | 0.997704i | \(0.521575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.92820 | 0.273056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528 | 0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.24316 | 0.826733 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.4201 | 1.72325 | 0.861625 | − | 0.507545i | \(-0.169447\pi\) | ||||
0.861625 | + | 0.507545i | \(0.169447\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.07180 | 0.0936433 | 0.0468217 | − | 0.998903i | \(-0.485091\pi\) | ||||
0.0468217 | + | 0.998903i | \(0.485091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.31268 | −0.113824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.39230 | 0.546131 | 0.273066 | − | 0.961995i | \(-0.411962\pi\) | ||||
0.273066 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.1822 | 1.93859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.14359 | 0.510198 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0764 | −1.64472 | −0.822361 | − | 0.568966i | \(-0.807344\pi\) | ||||
−0.822361 | + | 0.568966i | \(0.807344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.9043 | −1.45703 | −0.728516 | − | 0.685029i | \(-0.759789\pi\) | ||||
−0.728516 | + | 0.685029i | \(0.759789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.60770 | 0.611065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9700 | −0.955314 | −0.477657 | − | 0.878546i | \(-0.658514\pi\) | ||||
−0.477657 | + | 0.878546i | \(0.658514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4641 | 0.897938 | 0.448969 | − | 0.893547i | \(-0.351791\pi\) | ||||
0.448969 | + | 0.893547i | \(0.351791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07055 | −0.160224 | −0.0801121 | − | 0.996786i | \(-0.525528\pi\) | ||||
−0.0801121 | + | 0.996786i | \(0.525528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.55103 | −0.193951 | −0.0969754 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969754 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.62209 | 0.727362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.07180 | 0.379084 | 0.189542 | − | 0.981873i | \(-0.439300\pi\) | ||||
0.189542 | + | 0.981873i | \(0.439300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07107 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.46410 | −0.695815 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.9282 | 1.38417 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.07055 | −0.149820 | −0.0749100 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749100 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.93426 | 0.422798 | 0.211399 | − | 0.977400i | \(-0.432198\pi\) | ||||
0.211399 | + | 0.977400i | \(0.432198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.96524 | 0.281088 | 0.140544 | − | 0.990074i | \(-0.455115\pi\) | ||||
0.140544 | + | 0.990074i | \(0.455115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.5359 | 1.02022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8685 | 0.828933 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.92820 | −0.202548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92820 | −0.476957 | −0.238479 | − | 0.971148i | \(-0.576649\pi\) | ||||
−0.238479 | + | 0.971148i | \(0.576649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.58630 | −0.244584 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | 1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6969 | 0.988623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.4201 | −1.30046 | −0.650231 | − | 0.759736i | \(-0.725328\pi\) | ||||
−0.650231 | + | 0.759736i | \(0.725328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3205 | 1.54784 | 0.773918 | − | 0.633286i | \(-0.218294\pi\) | ||||
0.773918 | + | 0.633286i | \(0.218294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.72689 | −0.180198 | −0.0900990 | − | 0.995933i | \(-0.528718\pi\) | ||||
−0.0900990 | + | 0.995933i | \(0.528718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.928203 | 0.0608086 | 0.0304043 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304043 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.92820 | −0.191015 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.07055 | 0.133933 | 0.0669664 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669664 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7846 | 0.952360 | 0.476180 | − | 0.879348i | \(-0.342021\pi\) | ||||
0.476180 | + | 0.879348i | \(0.342021\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03528 | 0.0661414 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.27362 | −0.144667 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4641 | 0.849847 | 0.424923 | − | 0.905229i | \(-0.360301\pi\) | ||||
0.424923 | + | 0.905229i | \(0.360301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4548 | 0.971636 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7846 | −1.17175 | −0.585876 | − | 0.810401i | \(-0.699249\pi\) | ||||
−0.585876 | + | 0.810401i | \(0.699249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3923 | −1.39139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.6274 | −1.39527 | −0.697633 | − | 0.716455i | \(-0.745763\pi\) | ||||
−0.697633 | + | 0.716455i | \(0.745763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.85641 | 0.605474 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1774 | 0.925383 | 0.462692 | − | 0.886519i | \(-0.346884\pi\) | ||||
0.462692 | + | 0.886519i | \(0.346884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.10634 | −0.492425 | −0.246213 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246213 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.4641 | 1.29433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.6670 | 1.60226 | 0.801132 | − | 0.598488i | \(-0.204231\pi\) | ||||
0.801132 | + | 0.598488i | \(0.204231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.8564 | −1.06145 | −0.530727 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530727 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0812 | 1.65758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6617 | −0.798123 | −0.399061 | − | 0.916924i | \(-0.630664\pi\) | ||||
−0.399061 | + | 0.916924i | \(0.630664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3452 | −0.835210 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | 0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.48528 | −0.489083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.46410 | 0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07180 | 0.517755 | 0.258877 | − | 0.965910i | \(-0.416647\pi\) | ||||
0.258877 | + | 0.965910i | \(0.416647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8295 | −0.727492 | −0.363746 | − | 0.931498i | \(-0.618502\pi\) | ||||
−0.363746 | + | 0.931498i | \(0.618502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8564 | −1.34844 | −0.674222 | − | 0.738529i | \(-0.735521\pi\) | ||||
−0.674222 | + | 0.738529i | \(0.735521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.79315 | 0.100713 | 0.0503567 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503567 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.4254 | 1.81547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.85641 | −0.103293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.6660 | 0.924461 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9282 | 0.820528 | 0.410264 | − | 0.911967i | \(-0.365437\pi\) | ||||
0.410264 | + | 0.911967i | \(0.365437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10961 | −0.0606242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8564 | −0.972700 | −0.486350 | − | 0.873764i | \(-0.661672\pi\) | ||||
−0.486350 | + | 0.873764i | \(0.661672\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.1528 | 2.17440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.46410 | −0.508060 | −0.254030 | − | 0.967196i | \(-0.581756\pi\) | ||||
−0.254030 | + | 0.967196i | \(0.581756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.96902 | 0.105399 | 0.0526995 | − | 0.998610i | \(-0.483217\pi\) | ||||
0.0526995 | + | 0.998610i | \(0.483217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7846 | 0.890835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.1518 | 1.59135 | 0.795674 | − | 0.605725i | \(-0.207117\pi\) | ||||
0.795674 | + | 0.605725i | \(0.207117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7128 | −0.984885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.14110 | −0.216755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7023 | 1.44605 | 0.723023 | − | 0.690824i | \(-0.242752\pi\) | ||||
0.723023 | + | 0.690824i | \(0.242752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3205 | 1.21074 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1112 | −0.834204 | −0.417102 | − | 0.908860i | \(-0.636954\pi\) | ||||
−0.417102 | + | 0.908860i | \(0.636954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.1769 | 1.29668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.3205 | −1.09516 | −0.547580 | − | 0.836753i | \(-0.684451\pi\) | ||||
−0.547580 | + | 0.836753i | \(0.684451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.554803 | 0.0283491 | 0.0141746 | − | 0.999900i | \(-0.495488\pi\) | ||||
0.0141746 | + | 0.999900i | \(0.495488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8564 | −0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.62158 | 0.234323 | 0.117162 | − | 0.993113i | \(-0.462620\pi\) | ||||
0.117162 | + | 0.993113i | \(0.462620\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796 | 0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.53590 | −0.127595 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.9091 | −1.30034 | −0.650171 | − | 0.759788i | \(-0.725303\pi\) | ||||
−0.650171 | + | 0.759788i | \(0.725303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.39230 | −0.119466 | −0.0597330 | − | 0.998214i | \(-0.519025\pi\) | ||||
−0.0597330 | + | 0.998214i | \(0.519025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.1769 | 1.55303 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.9507 | −2.47597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.9282 | −1.13373 | −0.566863 | − | 0.823812i | \(-0.691843\pi\) | ||||
−0.566863 | + | 0.823812i | \(0.691843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.9411 | −1.67013 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.51575 | −0.0744052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.3923 | 0.996229 | 0.498115 | − | 0.867111i | \(-0.334026\pi\) | ||||
0.498115 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.101536 | −0.00494856 | −0.00247428 | − | 0.999997i | \(-0.500788\pi\) | ||||
−0.00247428 | + | 0.999997i | \(0.500788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.6077 | 0.660070 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.3923 | 1.08364 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.9401 | −1.15315 | −0.576577 | − | 0.817043i | \(-0.695612\pi\) | ||||
−0.576577 | + | 0.817043i | \(0.695612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.14359 | −0.103015 | −0.0515073 | − | 0.998673i | \(-0.516403\pi\) | ||||
−0.0515073 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.51575 | −0.0725081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.4601 | −1.35833 | −0.679164 | − | 0.733986i | \(-0.737658\pi\) | ||||
−0.679164 | + | 0.733986i | \(0.737658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.679492 | 0.0322836 | 0.0161418 | − | 0.999870i | \(-0.494862\pi\) | ||||
0.0161418 | + | 0.999870i | \(0.494862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.24316 | 0.438168 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3923 | −0.679215 | −0.339607 | − | 0.940567i | \(-0.610294\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 62.6410 | 2.94965 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7589 | −0.504385 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7846 | 0.972263 | 0.486132 | − | 0.873886i | \(-0.338408\pi\) | ||||
0.486132 | + | 0.873886i | \(0.338408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.7017 | −1.05733 | −0.528663 | − | 0.848832i | \(-0.677306\pi\) | ||||
−0.528663 | + | 0.848832i | \(0.677306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.72311 | −0.219502 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2487 | −0.844450 | −0.422225 | − | 0.906491i | \(-0.638751\pi\) | ||||
−0.422225 | + | 0.906491i | \(0.638751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.62536 | −0.121228 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.9282 | −0.870320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.10512 | −0.0965894 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.8401 | 1.77465 | 0.887325 | − | 0.461145i | \(-0.152561\pi\) | ||||
0.887325 | + | 0.461145i | \(0.152561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7846 | −1.76843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.4548 | −0.701767 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.8033 | −1.03332 | −0.516658 | − | 0.856192i | \(-0.672824\pi\) | ||||
−0.516658 | + | 0.856192i | \(0.672824\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.8564 | 0.986366 | 0.493183 | − | 0.869926i | \(-0.335833\pi\) | ||||
0.493183 | + | 0.869926i | \(0.335833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5569 | 0.925835 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.7128 | 1.78136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.1833 | −1.47957 | −0.739784 | − | 0.672844i | \(-0.765072\pi\) | ||||
−0.739784 | + | 0.672844i | \(0.765072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.287187 | −0.0127797 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.0459 | 1.19879 | 0.599395 | − | 0.800454i | \(-0.295408\pi\) | ||||
0.599395 | + | 0.800454i | \(0.295408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.39230 | 0.369809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4548 | −0.679702 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3205 | −0.583582 | −0.291791 | − | 0.956482i | \(-0.594251\pi\) | ||||
−0.291791 | + | 0.956482i | \(0.594251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.5359 | 1.07288 | 0.536440 | − | 0.843938i | \(-0.319769\pi\) | ||||
0.536440 | + | 0.843938i | \(0.319769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.6381 | 2.10675 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.14110 | −0.179036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.46410 | 0.235356 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.58682 | 0.369176 | 0.184588 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184588 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.46410 | 0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.1769 | −1.67508 | −0.837542 | − | 0.546373i | \(-0.816008\pi\) | ||||
−0.837542 | + | 0.546373i | \(0.816008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.18016 | −0.135479 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | −0.255146 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.7038 | −1.80942 | −0.904709 | − | 0.426030i | \(-0.859912\pi\) | ||||
−0.904709 | + | 0.426030i | \(0.859912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6969 | −0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.46410 | 0.230284 | 0.115142 | − | 0.993349i | \(-0.463268\pi\) | ||||
0.115142 | + | 0.993349i | \(0.463268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6350 | 0.783979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.46410 | −0.145223 | −0.0726113 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726113 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.7128 | 0.992350 | 0.496175 | − | 0.868222i | \(-0.334737\pi\) | ||||
0.496175 | + | 0.868222i | \(0.334737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1106 | 0.463346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.85641 | 0.243805 | 0.121903 | − | 0.992542i | \(-0.461100\pi\) | ||||
0.121903 | + | 0.992542i | \(0.461100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.58630 | −0.148785 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.0213 | 2.15450 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0718 | 1.19992 | 0.599961 | − | 0.800029i | \(-0.295183\pi\) | ||||
0.599961 | + | 0.800029i | \(0.295183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.93803 | −0.162264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7128 | 0.727378 | 0.363689 | − | 0.931520i | \(-0.381517\pi\) | ||||
0.363689 | + | 0.931520i | \(0.381517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.78461 | −0.360134 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6264 | 0.515900 | 0.257950 | − | 0.966158i | \(-0.416953\pi\) | ||||
0.257950 | + | 0.966158i | \(0.416953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.7128 | −1.45676 | −0.728378 | − | 0.685176i | \(-0.759725\pi\) | ||||
−0.728378 | + | 0.685176i | \(0.759725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.5216 | −0.793665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8434 | 1.29248 | 0.646241 | − | 0.763133i | \(-0.276340\pi\) | ||||
0.646241 | + | 0.763133i | \(0.276340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.8797 | −1.73189 | −0.865947 | − | 0.500136i | \(-0.833283\pi\) | ||||
−0.865947 | + | 0.500136i | \(0.833283\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1436 | 0.488883 | 0.244441 | − | 0.969664i | \(-0.421395\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8695 | 0.876185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.6675 | −1.26267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.933740 | 0.0371716 | 0.0185858 | − | 0.999827i | \(-0.494084\pi\) | ||||
0.0185858 | + | 0.999827i | \(0.494084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1051 | −0.797847 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24264 | 0.168100 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.3923 | 1.83239 | 0.916193 | − | 0.400737i | \(-0.131246\pi\) | ||||
0.916193 | + | 0.400737i | \(0.131246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.4641 | −1.39857 | −0.699284 | − | 0.714844i | \(-0.746498\pi\) | ||||
−0.699284 | + | 0.714844i | \(0.746498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.3147 | −0.837969 | −0.418984 | − | 0.907993i | \(-0.637614\pi\) | ||||
−0.418984 | + | 0.907993i | \(0.637614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −75.7128 | −2.97199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.480473 | −0.0188024 | −0.00940119 | − | 0.999956i | \(-0.502993\pi\) | ||||
−0.00940119 | + | 0.999956i | \(0.502993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10961 | −0.0433559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9101 | −1.39674 | −0.698371 | − | 0.715736i | \(-0.746092\pi\) | ||||
−0.698371 | + | 0.715736i | \(0.746092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.35898 | 0.0526991 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.7846 | 0.649903 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.9507 | 1.92833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8038 | 1.06859 | 0.534293 | − | 0.845299i | \(-0.320578\pi\) | ||||
0.534293 | + | 0.845299i | \(0.320578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.5665 | −1.40329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.1769 | 1.42254 | 0.711268 | − | 0.702921i | \(-0.248121\pi\) | ||||
0.711268 | + | 0.702921i | \(0.248121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.61780 | −0.252853 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.3923 | 1.53882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.60770 | 0.213327 | 0.106663 | − | 0.994295i | \(-0.465983\pi\) | ||||
0.106663 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.17260 | 0.272072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7128 | 1.50423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.1165 | 1.09971 | 0.549857 | − | 0.835259i | \(-0.314682\pi\) | ||||
0.549857 | + | 0.835259i | \(0.314682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | 0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.679492 | −0.0255549 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.2923 | −1.10010 | −0.550048 | − | 0.835133i | \(-0.685391\pi\) | ||||
−0.550048 | + | 0.835133i | \(0.685391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846 | 0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | −0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.6675 | 1.18100 | 0.590499 | − | 0.807038i | \(-0.298931\pi\) | ||||
0.590499 | + | 0.807038i | \(0.298931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8564 | 0.739491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.3110 | 0.865747 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.20736 | −0.118955 | −0.0594773 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594773 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.07107 | −0.261176 | −0.130588 | − | 0.991437i | \(-0.541686\pi\) | ||||
−0.130588 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.85641 | −0.215724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0000 | 1.32428 | 0.662141 | − | 0.749380i | \(-0.269648\pi\) | ||||
0.662141 | + | 0.749380i | \(0.269648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.6665 | 0.794866 | 0.397433 | − | 0.917631i | \(-0.369901\pi\) | ||||
0.397433 | + | 0.917631i | \(0.369901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7846 | 0.761489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.79796 | −0.358010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6937 | 0.791614 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.5359 | 0.674590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1512 | −0.914137 | −0.457069 | − | 0.889431i | \(-0.651101\pi\) | ||||
−0.457069 | + | 0.889431i | \(0.651101\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.75129 | 0.135984 | 0.0679921 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679921 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.46410 | 0.125409 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.7878 | −2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.82465 | 0.173531 | 0.0867653 | − | 0.996229i | \(-0.472347\pi\) | ||||
0.0867653 | + | 0.996229i | \(0.472347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.8663 | 1.03691 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.14359 | −0.220117 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 88.5878 | 3.16992 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3923 | 0.442300 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5359 | −0.589441 | −0.294721 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294721 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.0908 | 1.56769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.7846 | 1.37728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7429 | −1.47861 | −0.739304 | − | 0.673372i | \(-0.764845\pi\) | ||||
−0.739304 | + | 0.673372i | \(0.764845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | −0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.8564 | −0.771296 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.17260 | −0.252801 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3205 | 1.45275 | 0.726376 | − | 0.687298i | \(-0.241203\pi\) | ||||
0.726376 | + | 0.687298i | \(0.241203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.6077 | 1.18013 | 0.590063 | − | 0.807357i | \(-0.299103\pi\) | ||||
0.590063 | + | 0.807357i | \(0.299103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8685 | −0.415736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.85641 | 0.0649474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.8754 | −1.39166 | −0.695830 | − | 0.718206i | \(-0.744963\pi\) | ||||
−0.695830 | + | 0.718206i | \(0.744963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.9149 | −1.53078 | −0.765389 | − | 0.643567i | \(-0.777454\pi\) | ||||
−0.765389 | + | 0.643567i | \(0.777454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.21539 | −0.111810 | −0.0559050 | − | 0.998436i | \(-0.517804\pi\) | ||||
−0.0559050 | + | 0.998436i | \(0.517804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.8091 | 1.41736 | 0.708680 | − | 0.705530i | \(-0.249291\pi\) | ||||
0.708680 | + | 0.705530i | \(0.249291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.14359 | 0.0741821 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.38323 | −0.116802 | −0.0584010 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0584010 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.21539 | 0.214324 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.17638 | −0.178073 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.1886 | −1.58706 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8564 | −0.886346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5649 | 0.738369 | 0.369185 | − | 0.929356i | \(-0.379637\pi\) | ||||
0.369185 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1769 | 0.655071 | 0.327535 | − | 0.944839i | \(-0.393782\pi\) | ||||
0.327535 | + | 0.944839i | \(0.393782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2487 | 0.554399 | 0.277199 | − | 0.960812i | \(-0.410594\pi\) | ||||
0.277199 | + | 0.960812i | \(0.410594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.4644 | −1.07106 | −0.535531 | − | 0.844516i | \(-0.679888\pi\) | ||||
−0.535531 | + | 0.844516i | \(0.679888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.64102 | 0.0897972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.3843 | −0.454030 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.54725 | −0.154078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.6410 | −0.765406 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.8786 | −1.11023 | −0.555116 | − | 0.831773i | \(-0.687326\pi\) | ||||
−0.555116 | + | 0.831773i | \(0.687326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6410 | −1.09970 | −0.549852 | − | 0.835262i | \(-0.685316\pi\) | ||||
−0.549852 | + | 0.835262i | \(0.685316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.3923 | −0.888172 | −0.444086 | − | 0.895984i | \(-0.646471\pi\) | ||||
−0.444086 | + | 0.895984i | \(0.646471\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.62536 | −0.0881508 | −0.0440754 | − | 0.999028i | \(-0.514034\pi\) | ||||
−0.0440754 | + | 0.999028i | \(0.514034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.5692 | −1.59542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.51575 | 0.0507226 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.25071 | −0.175512 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.6077 | 1.45440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.9802 | 1.09873 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.32051 | 0.243342 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.6077 | −0.717472 | −0.358736 | − | 0.933439i | \(-0.616792\pi\) | ||||
−0.358736 | + | 0.933439i | \(0.616792\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4665 | −1.70516 | −0.852580 | − | 0.522596i | \(-0.824964\pi\) | ||||
−0.852580 | + | 0.522596i | \(0.824964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.62536 | −0.0866969 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6728 | 1.47362 | 0.736810 | − | 0.676100i | \(-0.236331\pi\) | ||||
0.736810 | + | 0.676100i | \(0.236331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.7846 | 2.26407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.9101 | −1.18072 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6795 | 0.350383 | 0.175191 | − | 0.984534i | \(-0.443946\pi\) | ||||
0.175191 | + | 0.984534i | \(0.443946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.535898 | −0.0175634 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.5959 | −0.640855 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7942 | −0.384479 | −0.192240 | − | 0.981348i | \(-0.561575\pi\) | ||||
−0.192240 | + | 0.981348i | \(0.561575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.4254 | 1.05592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.9282 | −1.39498 | −0.697490 | − | 0.716595i | \(-0.745700\pi\) | ||||
−0.697490 | + | 0.716595i | \(0.745700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.9706 | −0.550888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.6077 | −0.829515 | −0.414757 | − | 0.909932i | \(-0.636134\pi\) | ||||
−0.414757 | + | 0.909932i | \(0.636134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.14359 | 0.0693651 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6579 | −0.505619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.21166 | −0.199960 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.8749 | −1.12150 | −0.560750 | − | 0.827985i | \(-0.689487\pi\) | ||||
−0.560750 | + | 0.827985i | \(0.689487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.2487 | 0.842361 | 0.421181 | − | 0.906977i | \(-0.361616\pi\) | ||||
0.421181 | + | 0.906977i | \(0.361616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9706 | 0.544051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.1769 | −0.869467 | −0.434733 | − | 0.900559i | \(-0.643157\pi\) | ||||
−0.434733 | + | 0.900559i | \(0.643157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.7846 | 1.55916 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.0507 | −1.11794 | −0.558972 | − | 0.829186i | \(-0.688804\pi\) | ||||
−0.558972 | + | 0.829186i | \(0.688804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.14359 | −0.195751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.79796 | −0.311557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2474 | −0.389053 | −0.194527 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194527 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.10512 | −0.130141 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.82894 | −0.247945 | −0.123973 | − | 0.992286i | \(-0.539563\pi\) | ||||
−0.123973 | + | 0.992286i | \(0.539563\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9216.2.a.bc.1.2 | 4 | ||
3.2 | odd | 2 | 3072.2.a.r.1.3 | 4 | |||
4.3 | odd | 2 | 9216.2.a.bi.1.2 | 4 | |||
8.3 | odd | 2 | inner | 9216.2.a.bc.1.3 | 4 | ||
8.5 | even | 2 | 9216.2.a.bi.1.3 | 4 | |||
12.11 | even | 2 | 3072.2.a.l.1.3 | 4 | |||
24.5 | odd | 2 | 3072.2.a.l.1.2 | 4 | |||
24.11 | even | 2 | 3072.2.a.r.1.2 | 4 | |||
32.3 | odd | 8 | 2304.2.k.e.577.3 | 8 | |||
32.5 | even | 8 | 2304.2.k.l.1729.1 | 8 | |||
32.11 | odd | 8 | 2304.2.k.e.1729.4 | 8 | |||
32.13 | even | 8 | 2304.2.k.l.577.2 | 8 | |||
32.19 | odd | 8 | 2304.2.k.l.577.1 | 8 | |||
32.21 | even | 8 | 2304.2.k.e.1729.3 | 8 | |||
32.27 | odd | 8 | 2304.2.k.l.1729.2 | 8 | |||
32.29 | even | 8 | 2304.2.k.e.577.4 | 8 | |||
48.5 | odd | 4 | 3072.2.d.h.1537.3 | 8 | |||
48.11 | even | 4 | 3072.2.d.h.1537.7 | 8 | |||
48.29 | odd | 4 | 3072.2.d.h.1537.6 | 8 | |||
48.35 | even | 4 | 3072.2.d.h.1537.2 | 8 | |||
96.5 | odd | 8 | 768.2.j.e.193.2 | ✓ | 8 | ||
96.11 | even | 8 | 768.2.j.f.193.1 | yes | 8 | ||
96.29 | odd | 8 | 768.2.j.f.577.3 | yes | 8 | ||
96.35 | even | 8 | 768.2.j.f.577.1 | yes | 8 | ||
96.53 | odd | 8 | 768.2.j.f.193.3 | yes | 8 | ||
96.59 | even | 8 | 768.2.j.e.193.4 | yes | 8 | ||
96.77 | odd | 8 | 768.2.j.e.577.2 | yes | 8 | ||
96.83 | even | 8 | 768.2.j.e.577.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.2 | ✓ | 8 | 96.5 | odd | 8 | ||
768.2.j.e.193.4 | yes | 8 | 96.59 | even | 8 | ||
768.2.j.e.577.2 | yes | 8 | 96.77 | odd | 8 | ||
768.2.j.e.577.4 | yes | 8 | 96.83 | even | 8 | ||
768.2.j.f.193.1 | yes | 8 | 96.11 | even | 8 | ||
768.2.j.f.193.3 | yes | 8 | 96.53 | odd | 8 | ||
768.2.j.f.577.1 | yes | 8 | 96.35 | even | 8 | ||
768.2.j.f.577.3 | yes | 8 | 96.29 | odd | 8 | ||
2304.2.k.e.577.3 | 8 | 32.3 | odd | 8 | |||
2304.2.k.e.577.4 | 8 | 32.29 | even | 8 | |||
2304.2.k.e.1729.3 | 8 | 32.21 | even | 8 | |||
2304.2.k.e.1729.4 | 8 | 32.11 | odd | 8 | |||
2304.2.k.l.577.1 | 8 | 32.19 | odd | 8 | |||
2304.2.k.l.577.2 | 8 | 32.13 | even | 8 | |||
2304.2.k.l.1729.1 | 8 | 32.5 | even | 8 | |||
2304.2.k.l.1729.2 | 8 | 32.27 | odd | 8 | |||
3072.2.a.l.1.2 | 4 | 24.5 | odd | 2 | |||
3072.2.a.l.1.3 | 4 | 12.11 | even | 2 | |||
3072.2.a.r.1.2 | 4 | 24.11 | even | 2 | |||
3072.2.a.r.1.3 | 4 | 3.2 | odd | 2 | |||
3072.2.d.h.1537.2 | 8 | 48.35 | even | 4 | |||
3072.2.d.h.1537.3 | 8 | 48.5 | odd | 4 | |||
3072.2.d.h.1537.6 | 8 | 48.29 | odd | 4 | |||
3072.2.d.h.1537.7 | 8 | 48.11 | even | 4 | |||
9216.2.a.bc.1.2 | 4 | 1.1 | even | 1 | trivial | ||
9216.2.a.bc.1.3 | 4 | 8.3 | odd | 2 | inner | ||
9216.2.a.bi.1.2 | 4 | 4.3 | odd | 2 | |||
9216.2.a.bi.1.3 | 4 | 8.5 | even | 2 |