Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.3 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.84494 | −1.71951 | −0.859755 | − | 0.510707i | \(-0.829384\pi\) | ||||
−0.859755 | + | 0.510707i | \(0.829384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.14597 | −0.811101 | −0.405551 | − | 0.914073i | \(-0.632920\pi\) | ||||
−0.405551 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.389573i | 0.117461i | 0.998274 | + | 0.0587304i | \(0.0187052\pi\) | ||||
−0.998274 | + | 0.0587304i | \(0.981295\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.51059i | 1.52836i | 0.645002 | + | 0.764181i | \(0.276857\pi\) | ||||
−0.645002 | + | 0.764181i | \(0.723143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.90150 | −1.67386 | −0.836930 | − | 0.547310i | \(-0.815652\pi\) | ||||
−0.836930 | + | 0.547310i | \(0.815652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.97103 | −1.59926 | −0.799632 | − | 0.600490i | \(-0.794972\pi\) | ||||
−0.799632 | + | 0.600490i | \(0.794972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.97768 | −1.03792 | −0.518959 | − | 0.854799i | \(-0.673680\pi\) | ||||
−0.518959 | + | 0.854799i | \(0.673680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.78356 | 1.95671 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.02613i | 1.30472i | 0.757910 | + | 0.652359i | \(0.226221\pi\) | ||||
−0.757910 | + | 0.652359i | \(0.773779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.566791 | 0.101799 | 0.0508993 | − | 0.998704i | \(-0.483791\pi\) | ||||
0.0508993 | + | 0.998704i | \(0.483791\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.25113 | 1.39470 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.77849i | − | 1.27878i | −0.768884 | − | 0.639388i | \(-0.779188\pi\) | ||
0.768884 | − | 0.639388i | \(-0.220812\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.87875 | −1.38663 | −0.693314 | − | 0.720636i | \(-0.743850\pi\) | ||||
−0.693314 | + | 0.720636i | \(0.743850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.56851i | 0.544193i | 0.962270 | + | 0.272096i | \(0.0877170\pi\) | ||||
−0.962270 | + | 0.272096i | \(0.912283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8085i | 1.86831i | 0.356865 | + | 0.934156i | \(0.383845\pi\) | ||||
−0.356865 | + | 0.934156i | \(0.616155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.39480 | −0.342115 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.41777 | −0.194746 | −0.0973728 | − | 0.995248i | \(-0.531044\pi\) | ||||
−0.0973728 | + | 0.995248i | \(0.531044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.49789i | − | 0.201975i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.04798 | −0.917569 | −0.458785 | − | 0.888548i | \(-0.651715\pi\) | ||||
−0.458785 | + | 0.888548i | \(0.651715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28271 | 0.292271 | 0.146136 | − | 0.989265i | \(-0.453316\pi\) | ||||
0.146136 | + | 0.989265i | \(0.453316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 21.1879i | − | 2.62803i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4511i | 1.52114i | 0.649257 | + | 0.760569i | \(0.275080\pi\) | ||||
−0.649257 | + | 0.760569i | \(0.724920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.35431 | −0.279405 | −0.139703 | − | 0.990193i | \(-0.544615\pi\) | ||||
−0.139703 | + | 0.990193i | \(0.544615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7908i | 1.61409i | 0.590489 | + | 0.807045i | \(0.298935\pi\) | ||||
−0.590489 | + | 0.807045i | \(0.701065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.836013i | − | 0.0952725i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.60434i | − | 0.743046i | −0.928424 | − | 0.371523i | \(-0.878836\pi\) | ||
0.928424 | − | 0.371523i | \(-0.121164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0867 | 1.10716 | 0.553578 | − | 0.832797i | \(-0.313262\pi\) | ||||
0.553578 | + | 0.832797i | \(0.313262\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.5359 | 2.87822 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.1160i | − | 1.39030i | −0.718867 | − | 0.695148i | \(-0.755339\pi\) | ||
0.718867 | − | 0.695148i | \(-0.244661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 11.8256i | − | 1.23966i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.8032 | 2.74995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0804 | −1.32812 | −0.664059 | − | 0.747680i | \(-0.731168\pi\) | ||||
−0.664059 | + | 0.747680i | \(0.731168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2424 | −1.01916 | −0.509581 | − | 0.860423i | \(-0.670199\pi\) | ||||
−0.509581 | + | 0.860423i | \(0.670199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.81035i | 0.473978i | 0.971512 | + | 0.236989i | \(0.0761605\pi\) | ||||
−0.971512 | + | 0.236989i | \(0.923840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17.4053i | − | 1.68264i | −0.540540 | − | 0.841318i | \(-0.681780\pi\) | ||
0.540540 | − | 0.841318i | \(-0.318220\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.344407i | 0.0329882i | 0.999864 | + | 0.0164941i | \(0.00525048\pi\) | ||||
−0.999864 | + | 0.0164941i | \(0.994750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.14643 | −0.295992 | −0.147996 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147996 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.1389 | 1.78471 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.8104 | 1.35767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8482 | 0.986203 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.3925 | −1.64508 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.31278 | 0.560168 | 0.280084 | − | 0.959975i | \(-0.409638\pi\) | ||||
0.280084 | + | 0.959975i | \(0.409638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3867 | −1.51909 | −0.759544 | − | 0.650456i | \(-0.774578\pi\) | ||||
−0.759544 | + | 0.650456i | \(0.774578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9596 | 1.29717 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.61256i | 0.735821i | 0.929861 | + | 0.367911i | \(0.119927\pi\) | ||||
−0.929861 | + | 0.367911i | \(0.880073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3981i | 1.13641i | 0.822887 | + | 0.568205i | \(0.192362\pi\) | ||||
−0.822887 | + | 0.568205i | \(0.807638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.14678 | −0.179523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 27.0150i | − | 2.24348i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.5320 | −1.84590 | −0.922948 | − | 0.384925i | \(-0.874227\pi\) | ||||
−0.922948 | + | 0.384925i | \(0.874227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.63828i | − | 0.458837i | −0.973328 | − | 0.229418i | \(-0.926318\pi\) | ||
0.973328 | − | 0.229418i | \(-0.0736824\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.17928 | −0.175044 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8304 | 1.74225 | 0.871126 | − | 0.491059i | \(-0.163390\pi\) | ||||
0.871126 | + | 0.491059i | \(0.163390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.6820 | 0.841857 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5361i | 1.13856i | 0.822145 | + | 0.569278i | \(0.192777\pi\) | ||||
−0.822145 | + | 0.569278i | \(0.807223\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.86706 | − | 12.3307i | 0.299242 | − | 0.954177i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.3666 | −1.33589 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.41761i | − | 0.335865i | −0.985798 | − | 0.167932i | \(-0.946291\pi\) | ||
0.985798 | − | 0.167932i | \(-0.0537091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.9953 | −1.58709 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.15992i | 0.385670i | 0.981231 | + | 0.192835i | \(0.0617683\pi\) | ||||
−0.981231 | + | 0.192835i | \(0.938232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.15190 | −0.531597 | −0.265798 | − | 0.964029i | \(-0.585636\pi\) | ||||
−0.265798 | + | 0.964029i | \(0.585636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.9078i | 2.19887i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.68864i | − | 0.196613i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.4303i | − | 0.754709i | −0.926069 | − | 0.377354i | \(-0.876834\pi\) | ||
0.926069 | − | 0.377354i | \(-0.123166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.17362i | − | 0.372405i | −0.982511 | − | 0.186203i | \(-0.940382\pi\) | ||
0.982511 | − | 0.186203i | \(-0.0596181\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6148 | 1.18375 | 0.591877 | − | 0.806028i | \(-0.298387\pi\) | ||||
0.591877 | + | 0.806028i | \(0.298387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.121544 | −0.00861603 | −0.00430802 | − | 0.999991i | \(-0.501371\pi\) | ||||
−0.00430802 | + | 0.999991i | \(0.501371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 15.0779i | − | 1.05826i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.1383 | 2.38432 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.71573i | − | 0.187851i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7050 | 1.21886 | 0.609431 | − | 0.792839i | \(-0.291398\pi\) | ||||
0.609431 | + | 0.792839i | \(0.291398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 13.7207i | − | 0.935745i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.21632 | −0.0825690 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 38.0314i | − | 2.55827i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.69361 | −0.381272 | −0.190636 | − | 0.981661i | \(-0.561055\pi\) | ||||
−0.190636 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7274 | −0.712004 | −0.356002 | − | 0.934485i | \(-0.615860\pi\) | ||||
−0.356002 | + | 0.934485i | \(0.615860\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.8467 | −0.716773 | −0.358386 | − | 0.933573i | \(-0.616673\pi\) | ||||
−0.358386 | + | 0.933573i | \(0.616673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.490036i | − | 0.0321033i | −0.999871 | − | 0.0160517i | \(-0.994890\pi\) | ||
0.999871 | − | 0.0160517i | \(-0.00510962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 49.2479i | − | 3.21258i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7501i | 1.01879i | 0.860532 | + | 0.509396i | \(0.170131\pi\) | ||||
−0.860532 | + | 0.509396i | \(0.829869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.55929i | 0.358105i | 0.983839 | + | 0.179053i | \(0.0573032\pi\) | ||||
−0.983839 | + | 0.179053i | \(0.942697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.20788 | 0.588270 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 38.4145i | − | 2.44426i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0853i | 0.952176i | 0.879398 | + | 0.476088i | \(0.157946\pi\) | ||||
−0.879398 | + | 0.476088i | \(0.842054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.93917i | − | 0.121915i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.73533 | 0.544895 | 0.272447 | − | 0.962171i | \(-0.412167\pi\) | ||||
0.272447 | + | 0.962171i | \(0.412167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.6924i | 1.03722i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.7921i | − | 1.77540i | −0.460423 | − | 0.887700i | \(-0.652302\pi\) | ||
0.460423 | − | 0.887700i | \(-0.347698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.45124 | 0.334867 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.4007 | 1.30483 | 0.652413 | − | 0.757864i | \(-0.273757\pi\) | ||||
0.652413 | + | 0.757864i | \(0.273757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.7899i | − | 1.14141i | −0.821156 | − | 0.570704i | \(-0.806670\pi\) | ||
0.821156 | − | 0.570704i | \(-0.193330\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.81141i | 0.229837i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.7280i | − | 1.00509i | −0.864551 | − | 0.502545i | \(-0.832397\pi\) | ||
0.864551 | − | 0.502545i | \(-0.167603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6978i | 1.71197i | 0.517005 | + | 0.855983i | \(0.327047\pi\) | ||||
−0.517005 | + | 0.855983i | \(0.672953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.08638 | −0.242910 | −0.121455 | − | 0.992597i | \(-0.538756\pi\) | ||||
−0.121455 | + | 0.992597i | \(0.538756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.0535 | 1.12470 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.6308 | 1.80181 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.1321i | − | 0.650341i | −0.945655 | − | 0.325171i | \(-0.894578\pi\) | ||
0.945655 | − | 0.325171i | \(-0.105422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0991 | 1.57777 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 27.4300i | − | 1.58632i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 7.65793i | − | 0.441396i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.77689 | −0.502563 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.8026i | − | 1.87214i | −0.351811 | − | 0.936071i | \(-0.614434\pi\) | ||
0.351811 | − | 0.936071i | \(-0.385566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.24173i | 0.183822i | 0.995767 | + | 0.0919109i | \(0.0292975\pi\) | ||||
−0.995767 | + | 0.0919109i | \(0.970702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.5298i | − | 1.21693i | −0.793579 | − | 0.608467i | \(-0.791785\pi\) | ||
0.793579 | − | 0.608467i | \(-0.208215\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 12.4153i | − | 0.697312i | −0.937251 | − | 0.348656i | \(-0.886638\pi\) | ||
0.937251 | − | 0.348656i | \(-0.113362\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73719 | −0.153253 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.1106 | 2.67695 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 53.9132i | 2.99057i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 27.4867i | − | 1.51539i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9.46960i | − | 0.520496i | −0.965542 | − | 0.260248i | \(-0.916196\pi\) | ||
0.965542 | − | 0.260248i | \(-0.0838043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 47.8735i | − | 2.61561i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2526 | −1.70244 | −0.851219 | − | 0.524811i | \(-0.824136\pi\) | ||||
−0.851219 | + | 0.524811i | \(0.824136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.220806i | 0.0119573i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1610 | 1.08859 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.8933 | −0.745833 | −0.372916 | − | 0.927865i | \(-0.621642\pi\) | ||||
−0.372916 | + | 0.927865i | \(0.621642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4127i | 1.09267i | 0.837568 | + | 0.546333i | \(0.183977\pi\) | ||||
−0.837568 | + | 0.546333i | \(0.816023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.97509i | − | 0.105123i | −0.998618 | − | 0.0525617i | \(-0.983261\pi\) | ||
0.998618 | − | 0.0525617i | \(-0.0167386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.05219 | 0.480440 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.84437i | 0.361232i | 0.983554 | + | 0.180616i | \(0.0578092\pi\) | ||||
−0.983554 | + | 0.180616i | \(0.942191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.5953 | 1.55765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 53.0248i | − | 2.77544i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.5647 | −1.49107 | −0.745533 | − | 0.666469i | \(-0.767805\pi\) | ||||
−0.745533 | + | 0.666469i | \(0.767805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.04249 | 0.157958 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.3680i | − | 0.847501i | −0.905779 | − | 0.423750i | \(-0.860713\pi\) | ||
0.905779 | − | 0.423750i | \(-0.139287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.7181 | −1.99408 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.4090i | − | 0.637408i | −0.947854 | − | 0.318704i | \(-0.896752\pi\) | ||
0.947854 | − | 0.318704i | \(-0.103248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7233i | 1.36550i | 0.730653 | + | 0.682749i | \(0.239216\pi\) | ||||
−0.730653 | + | 0.682749i | \(0.760784\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.21442i | 0.163822i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.794694 | 0.0402926 | 0.0201463 | − | 0.999797i | \(-0.493587\pi\) | ||||
0.0201463 | + | 0.999797i | \(0.493587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.3535 | 1.73733 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.3933i | 1.27767i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.4180 | 1.42626 | 0.713130 | − | 0.701032i | \(-0.247277\pi\) | ||||
0.713130 | + | 0.701032i | \(0.247277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.657033 | 0.0328107 | 0.0164053 | − | 0.999865i | \(-0.494778\pi\) | ||||
0.0164053 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12335i | 0.155585i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.03029 | 0.150206 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1429 | −0.550981 | −0.275491 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275491 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.1248 | 0.744241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.7827 | −1.90377 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.61669i | 0.225540i | 0.993621 | + | 0.112770i | \(0.0359724\pi\) | ||||
−0.993621 | + | 0.112770i | \(0.964028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3568 | 0.553497 | 0.276749 | − | 0.960942i | \(-0.410743\pi\) | ||||
0.276749 | + | 0.960942i | \(0.410743\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −67.5213 | −3.27526 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.89864 | −0.237062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6836i | 0.851789i | 0.904773 | + | 0.425895i | \(0.140041\pi\) | ||||
−0.904773 | + | 0.425895i | \(0.859959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.9960 | −0.720660 | −0.360330 | − | 0.932825i | \(-0.617336\pi\) | ||||
−0.360330 | + | 0.932825i | \(0.617336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.6996 | 1.65991 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.5369i | 1.17108i | 0.810642 | + | 0.585542i | \(0.199118\pi\) | ||||
−0.810642 | + | 0.585542i | \(0.800882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.39883 | 0.113972 | 0.0569858 | − | 0.998375i | \(-0.481851\pi\) | ||||
0.0569858 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.4303i | 2.39063i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2497i | 0.530906i | 0.964124 | + | 0.265453i | \(0.0855215\pi\) | ||||
−0.964124 | + | 0.265453i | \(0.914478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.45892i | − | 0.162874i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.4686i | 2.13160i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.2665i | 1.41581i | 0.706309 | + | 0.707903i | \(0.250359\pi\) | ||||
−0.706309 | + | 0.707903i | \(0.749641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.77808i | 0.175963i | 0.996122 | + | 0.0879814i | \(0.0280416\pi\) | ||||
−0.996122 | + | 0.0879814i | \(0.971958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.9705i | 1.90406i | 0.306005 | + | 0.952030i | \(0.401008\pi\) | ||||
−0.306005 | + | 0.952030i | \(0.598992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.7738i | 1.70169i | 0.525417 | + | 0.850845i | \(0.323909\pi\) | ||||
−0.525417 | + | 0.850845i | \(0.676091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 26.7196i | − | 1.23380i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.39020 | −0.0639213 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −68.2016 | −3.12930 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.4612 | −1.57457 | −0.787285 | − | 0.616589i | \(-0.788514\pi\) | ||||
−0.787285 | + | 0.616589i | \(0.788514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.8641 | 1.95443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 50.2935 | 2.28371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7395i | 0.803855i | 0.915672 | + | 0.401927i | \(0.131660\pi\) | ||||
−0.915672 | + | 0.401927i | \(0.868340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.84701i | 0.354130i | 0.984199 | + | 0.177065i | \(0.0566604\pi\) | ||||
−0.984199 | + | 0.177065i | \(0.943340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 48.4908i | − | 2.18392i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.05229 | 0.226626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5691i | 1.41323i | 0.707600 | + | 0.706613i | \(0.249778\pi\) | ||||
−0.707600 | + | 0.706613i | \(0.750222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4593i | 0.555532i | 0.960649 | + | 0.277766i | \(0.0895939\pi\) | ||||
−0.960649 | + | 0.277766i | \(0.910406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.3816 | 1.75246 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.7294i | 1.76097i | 0.474071 | + | 0.880486i | \(0.342784\pi\) | ||||
−0.474071 | + | 0.880486i | \(0.657216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 29.5947i | − | 1.30919i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 18.4955i | − | 0.815009i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.98985 | −0.219453 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.8198 | 0.561648 | 0.280824 | − | 0.959759i | \(-0.409392\pi\) | ||||
0.280824 | + | 0.959759i | \(0.409392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.6321 | 1.90790 | 0.953950 | − | 0.299965i | \(-0.0969749\pi\) | ||||
0.953950 | + | 0.299965i | \(0.0969749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.91171 | −0.170397 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.77731 | 0.0772744 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 48.9272i | − | 2.11927i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66.9224i | 2.89331i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.932952i | − | 0.0401851i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.44318i | − | 0.191027i | −0.995428 | − | 0.0955135i | \(-0.969551\pi\) | ||
0.995428 | − | 0.0955135i | \(-0.0304493\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.32423i | − | 0.0567236i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.608706i | − | 0.0260264i | −0.999915 | − | 0.0130132i | \(-0.995858\pi\) | ||
0.999915 | − | 0.0130132i | \(-0.00414234\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 48.9794i | − | 2.08659i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.1727i | 0.602685i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.0939i | − | 1.02089i | −0.859910 | − | 0.510446i | \(-0.829481\pi\) | ||
0.859910 | − | 0.510446i | \(-0.170519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.6646 | −0.831724 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.0205i | 1.56023i | 0.625638 | + | 0.780114i | \(0.284839\pi\) | ||||
−0.625638 | + | 0.780114i | \(0.715161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0979 | 0.508960 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.6770 | −0.531447 | −0.265724 | − | 0.964049i | \(-0.585611\pi\) | ||||
−0.265724 | + | 0.964049i | \(0.585611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6157i | 1.53232i | 0.642649 | + | 0.766160i | \(0.277835\pi\) | ||||
−0.642649 | + | 0.766160i | \(0.722165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.6995 | −2.03091 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.0676 | −1.45988 | −0.729942 | − | 0.683509i | \(-0.760453\pi\) | ||||
−0.729942 | + | 0.683509i | \(0.760453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6457 | −0.898016 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.552325i | − | 0.0228750i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.5617 | 1.46779 | 0.733894 | − | 0.679264i | \(-0.237701\pi\) | ||||
0.733894 | + | 0.679264i | \(0.237701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.95112 | −0.162803 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.86416 | 0.364007 | 0.182004 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182004 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56.9452 | −2.33453 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9526i | 0.937816i | 0.883247 | + | 0.468908i | \(0.155352\pi\) | ||||
−0.883247 | + | 0.468908i | \(0.844648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.5175 | −1.65275 | −0.826373 | − | 0.563124i | \(-0.809599\pi\) | ||||
−0.826373 | + | 0.563124i | \(0.809599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −41.7108 | −1.69579 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.3296i | − | 1.59634i | −0.602434 | − | 0.798169i | \(-0.705802\pi\) | ||
0.602434 | − | 0.798169i | \(-0.294198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −70.5824 | −2.85546 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.06987 | −0.0432116 | −0.0216058 | − | 0.999767i | \(-0.506878\pi\) | ||||
−0.0216058 | + | 0.999767i | \(0.506878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 44.8837i | − | 1.80695i | −0.428640 | − | 0.903476i | \(-0.641007\pi\) | ||
0.428640 | − | 0.903476i | \(-0.358993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27.7345i | − | 1.11475i | −0.830262 | − | 0.557373i | \(-0.811809\pi\) | ||
0.830262 | − | 0.557373i | \(-0.188191\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.1466i | 1.12767i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8003 | 0.872012 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.6833i | 2.14049i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3534 | −0.969495 | −0.484747 | − | 0.874654i | \(-0.661088\pi\) | ||||
−0.484747 | + | 0.874654i | \(0.661088\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.2722 | −0.963215 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 13.1968i | − | 0.522876i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.8492 | 1.02098 | 0.510492 | − | 0.859883i | \(-0.329463\pi\) | ||||
0.510492 | + | 0.859883i | \(0.329463\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.67452i | 0.302654i | 0.988484 | + | 0.151327i | \(0.0483546\pi\) | ||||
−0.988484 | + | 0.151327i | \(0.951645\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.2381 | −1.07084 | −0.535420 | − | 0.844586i | \(-0.679847\pi\) | ||||
−0.535420 | + | 0.844586i | \(0.679847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.74571i | − | 0.107778i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 11.5414i | − | 0.451650i | −0.974168 | − | 0.225825i | \(-0.927492\pi\) | ||
0.974168 | − | 0.225825i | \(-0.0725077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 66.8510 | 2.61208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.76163 | 0.380259 | 0.190130 | − | 0.981759i | \(-0.439109\pi\) | ||||
0.190130 | + | 0.981759i | \(0.439109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.42557i | − | 0.0554482i | −0.999616 | − | 0.0277241i | \(-0.991174\pi\) | ||
0.999616 | − | 0.0277241i | \(-0.00882598\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −57.5189 | −2.23049 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.9738i | − | 1.35419i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.889284i | 0.0343304i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.6409i | − | 0.602911i | −0.953480 | − | 0.301456i | \(-0.902527\pi\) | ||
0.953480 | − | 0.301456i | \(-0.0974725\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 32.2251i | − | 1.23851i | −0.785190 | − | 0.619255i | \(-0.787435\pi\) | ||
0.785190 | − | 0.619255i | \(-0.212565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.0703 | 1.07724 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.8122 | −0.758093 | −0.379047 | − | 0.925378i | \(-0.623748\pi\) | ||||
−0.379047 | + | 0.925378i | \(0.623748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 33.1148i | − | 1.26525i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.81275i | − | 0.297642i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.57096i | 0.0597621i | 0.999553 | + | 0.0298811i | \(0.00951285\pi\) | ||||
−0.999553 | + | 0.0298811i | \(0.990487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 51.5148i | − | 1.95407i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.2767 | 2.32102 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.3493i | − | 1.22182i | −0.791701 | − | 0.610909i | \(-0.790804\pi\) | ||
0.791701 | − | 0.610909i | \(-0.209196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.2241i | 2.04510i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.9800 | 0.826643 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 0.370820i | − | 0.0139264i | −0.999976 | − | 0.00696322i | \(-0.997784\pi\) | ||
0.999976 | − | 0.00696322i | \(-0.00221648\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.82130 | −0.105659 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.25423 | 0.308691 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.74411 | −0.288806 | −0.144403 | − | 0.989519i | \(-0.546126\pi\) | ||||
−0.144403 | + | 0.989519i | \(0.546126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.3229i | − | 0.384444i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 68.7406i | 2.55296i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.4401i | − | 0.387203i | −0.981080 | − | 0.193602i | \(-0.937983\pi\) | ||
0.981080 | − | 0.193602i | \(-0.0620169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 24.6281i | − | 0.910903i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6827 | −0.468445 | −0.234222 | − | 0.972183i | \(-0.575254\pi\) | ||||
−0.234222 | + | 0.972183i | \(0.575254\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.85060 | −0.178674 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8453i | 1.06109i | 0.847656 | + | 0.530547i | \(0.178013\pi\) | ||||
−0.847656 | + | 0.530547i | \(0.821987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.3349i | 0.709329i | 0.934994 | + | 0.354665i | \(0.115405\pi\) | ||||
−0.934994 | + | 0.354665i | \(0.884595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 86.6343 | 3.17403 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.3513i | 1.36479i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2753i | 0.520913i | 0.965486 | + | 0.260457i | \(0.0838731\pi\) | ||||
−0.965486 | + | 0.260457i | \(0.916127\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.6789i | 0.788974i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.35269 | 0.339929 | 0.169965 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169965 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.70767i | 0.243153i | 0.992582 | + | 0.121577i | \(0.0387950\pi\) | ||||
−0.992582 | + | 0.121577i | \(0.961205\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.739088i | − | 0.0267568i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 38.8385i | − | 1.40238i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.17188i | 0.294686i | 0.989085 | + | 0.147343i | \(0.0470721\pi\) | ||||
−0.989085 | + | 0.147343i | \(0.952928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.64691 | 0.239073 | 0.119536 | − | 0.992830i | \(-0.461859\pi\) | ||||
0.119536 | + | 0.992830i | \(0.461859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.54523 | 0.199191 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 61.8941 | 2.21759 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.917177i | − | 0.0328192i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −83.9364 | −2.99582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9964i | 0.534563i | 0.963618 | + | 0.267282i | \(0.0861254\pi\) | ||||
−0.963618 | + | 0.267282i | \(0.913875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.75216 | 0.240079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.5791i | 0.446697i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1470 | −0.465690 | −0.232845 | − | 0.972514i | \(-0.574803\pi\) | ||||
−0.232845 | + | 0.972514i | \(0.574803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 88.3979i | − | 3.12729i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.37253 | −0.189592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.0715 | −1.44758 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4313i | 0.577695i | 0.957375 | + | 0.288847i | \(0.0932720\pi\) | ||||
−0.957375 | + | 0.288847i | \(0.906728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.49533i | 0.0525083i | 0.999655 | + | 0.0262541i | \(0.00835791\pi\) | ||||
−0.999655 | + | 0.0262541i | \(0.991642\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 55.8904i | − | 1.95776i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.8762i | − | 0.870309i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.0593 | 1.18868 | 0.594339 | − | 0.804215i | \(-0.297414\pi\) | ||||
0.594339 | + | 0.804215i | \(0.297414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.5580i | 0.577177i | 0.957453 | + | 0.288589i | \(0.0931860\pi\) | ||||
−0.957453 | + | 0.288589i | \(0.906814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2447 | 0.356244 | 0.178122 | − | 0.984008i | \(-0.442998\pi\) | ||||
0.178122 | + | 0.984008i | \(0.442998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4080i | 0.708799i | 0.935094 | + | 0.354400i | \(0.115315\pi\) | ||||
−0.935094 | + | 0.354400i | \(0.884685\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5278 | 0.572653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8686 | + | 47.4107i | −0.514550 | + | 1.64072i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6286i | 0.815749i | 0.913038 | + | 0.407875i | \(0.133730\pi\) | ||||
−0.913038 | + | 0.407875i | \(0.866270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.3664 | −0.702291 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 66.7735 | 2.29708 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.2800 | −0.799910 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.7188i | 1.32726i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0584 | −0.755266 | −0.377633 | − | 0.925955i | \(-0.623262\pi\) | ||||
−0.377633 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.4917i | 0.597507i | 0.954330 | + | 0.298753i | \(0.0965708\pi\) | ||||
−0.954330 | + | 0.298753i | \(0.903429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3423 | −1.06939 | −0.534693 | − | 0.845047i | \(-0.679573\pi\) | ||||
−0.534693 | + | 0.845047i | \(0.679573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.9509i | 1.25782i | 0.777477 | + | 0.628911i | \(0.216499\pi\) | ||||
−0.777477 | + | 0.628911i | \(0.783501\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.9855i | 0.577523i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.57287 | 0.0872787 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.6126 | −2.32485 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39.4698 | 1.33432 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9347 | 1.58487 | 0.792436 | − | 0.609955i | \(-0.208812\pi\) | ||||
0.792436 | + | 0.609955i | \(0.208812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.3396 | −1.22431 | −0.612157 | − | 0.790736i | \(-0.709698\pi\) | ||||
−0.612157 | + | 0.790736i | \(0.709698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.6825 | −1.84021 | −0.920106 | − | 0.391669i | \(-0.871898\pi\) | ||||
−0.920106 | + | 0.391669i | \(0.871898\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.2189 | 0.880345 | 0.440172 | − | 0.897913i | \(-0.354917\pi\) | ||||
0.440172 | + | 0.897913i | \(0.354917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.5470 | −0.454353 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 89.2885i | − | 2.98792i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.8396i | − | 0.663164i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.98234i | 0.132819i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.78474 | 0.325977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.4986 | 0.914085 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.4105 | −0.445289 | −0.222644 | − | 0.974900i | \(-0.571469\pi\) | ||||
−0.222644 | + | 0.974900i | \(0.571469\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.2573i | 1.03560i | 0.855501 | + | 0.517800i | \(0.173249\pi\) | ||||
−0.855501 | + | 0.517800i | \(0.826751\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.92950i | 0.130047i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.3115 | 1.23213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.47586 | −0.246606 | −0.123303 | − | 0.992369i | \(-0.539349\pi\) | ||||
−0.123303 | + | 0.992369i | \(0.539349\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 12.9736i | − | 0.427033i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 76.1014i | − | 2.50220i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.5518i | 1.69136i | 0.533692 | + | 0.845679i | \(0.320804\pi\) | ||||
−0.533692 | + | 0.845679i | \(0.679196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.6943 | 0.547132 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.3377i | 0.338078i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.8861i | 1.89106i | 0.325540 | + | 0.945528i | \(0.394454\pi\) | ||||
−0.325540 | + | 0.945528i | \(0.605546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5630 | 0.735534 | 0.367767 | − | 0.929918i | \(-0.380122\pi\) | ||||
0.367767 | + | 0.929918i | \(0.380122\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.1956 | 1.43921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3205i | 0.400364i | 0.979759 | + | 0.200182i | \(0.0641533\pi\) | ||||
−0.979759 | + | 0.200182i | \(0.935847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −75.9954 | −2.46692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.5993 | 0.602490 | 0.301245 | − | 0.953547i | \(-0.402598\pi\) | ||||
0.301245 | + | 0.953547i | \(0.402598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.1038i | 1.29773i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 18.4823i | − | 0.596825i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6787 | −0.989637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.8923i | 0.640354i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.7935 | −0.700831 | −0.350415 | − | 0.936594i | \(-0.613960\pi\) | ||||
−0.350415 | + | 0.936594i | \(0.613960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.44236 | 0.0462876 | 0.0231438 | − | 0.999732i | \(-0.492632\pi\) | ||||
0.0231438 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 28.7519i | − | 0.921744i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.8828 | 0.380165 | 0.190083 | − | 0.981768i | \(-0.439124\pi\) | ||||
0.190083 | + | 0.981768i | \(0.439124\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.10965 | 0.163305 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8552 | 0.824651 | 0.412326 | − | 0.911037i | \(-0.364717\pi\) | ||||
0.412326 | + | 0.911037i | \(0.364717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.8828 | −2.03548 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 17.7629i | − | 0.564828i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 37.1094i | − | 1.17882i | −0.807835 | − | 0.589409i | \(-0.799361\pi\) | ||
0.807835 | − | 0.589409i | \(-0.200639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.467330 | 0.0148153 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.1981 | 1.39977 | 0.699884 | − | 0.714257i | \(-0.253235\pi\) | ||||
0.699884 | + | 0.714257i | \(0.253235\pi\) | |||||||
\(998\) | 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 | 6012.2.h.a.3005.3 | ✓ | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.54 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.53 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.4 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.3 | ✓ | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.4 | yes | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.53 | yes | 56 | 167.166 | odd | 2 | inner | |
6012.2.h.a.3005.54 | yes | 56 | 3.2 | odd | 2 | inner |